diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/-vf2iYBhTKU_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/-vf2iYBhTKU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e429342a90035a5b4b2c720f2e60fe8090a09ece
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/-vf2iYBhTKU_raw.srt
@@ -0,0 +1,2700 @@
+1
+00:00:05,040 --> 00:00:07,260
+بسم الله الرحمن الرحيم يا ربكوا العفو يا شباب
+
+2
+00:00:07,260 --> 00:00:11,260
+اليوم بنكمل ان شاء الله تعالى ال summation بعد ما
+
+3
+00:00:11,260 --> 00:00:14,960
+خلصنا ال sequence و ال string اتكلمنا عن ال
+
+4
+00:00:14,960 --> 00:00:18,000
+sequence و اتكلمنا عن ال string عشان ننتقل لان
+
+5
+00:00:18,000 --> 00:00:20,600
+لموضوع ال summation و ال summation هو الحقيقة شوية
+
+6
+00:00:20,600 --> 00:00:25,260
+مرتبط بجزئية ال sequence على اعتبار ان احنا هنعمل
+
+7
+00:00:25,260 --> 00:00:28,760
+summation ل sequence of elements مجموعة elements
+
+8
+00:00:28,760 --> 00:00:32,700
+بدنا نعملهم عملية summation و نشوفأيش بتطلع
+
+9
+00:00:32,700 --> 00:00:35,160
+المجموعة أو أيش بتطلع عملية ال summation هذه كيف
+
+10
+00:00:35,160 --> 00:00:41,380
+ممكن نتعامل معاها ففعليا أنا بتعامل مع sequence أو
+
+11
+00:00:41,380 --> 00:00:44,940
+series سلسلة من البيانات أو سلسلة من المعلومات أو
+
+12
+00:00:44,940 --> 00:00:50,520
+سلسلة من الأرقام هنا عبارة عن a m بدأ من ال index
+
+13
+00:00:50,520 --> 00:00:58,100
+موجود فإذا أنا بتكلم عن series أو sequenceالانتجار
+
+14
+00:00:58,100 --> 00:01:03,830
+تبحّى لل lower pound بمعنى من امتى ببدأأكيد لازم
+
+15
+00:01:03,830 --> 00:01:07,710
+يبدأ من قيمة ال index لازم يبدأ من قيمة عملية ال
+
+16
+00:01:07,710 --> 00:01:10,910
+summation عشان أضحكوا أكتر خلّينا نكتبها هنا و
+
+17
+00:01:10,910 --> 00:01:17,090
+نفصلها أكتر هاي a1 a2 او a in general zero لإن
+
+18
+00:01:17,090 --> 00:01:20,090
+ممكن نستخدم ال zero مش هيك كنتوا بتقولوا ده من هيك
+
+19
+00:01:20,090 --> 00:01:22,670
+كنتوا بتقدروا تستخدمه في ال array مثلا ال array
+
+20
+00:01:22,670 --> 00:01:25,910
+اللي هي برمجيا تمثل ال sequence عنا أو ال series
+
+21
+00:01:25,910 --> 00:01:30,730
+عنا فإذا ممكن نبدأ بهذا الشكل
+
+22
+00:01:35,380 --> 00:01:39,000
+وهذا الشكل اللي احنا بتعامل معاه، كويس، بالشكل هذا
+
+23
+00:01:39,000 --> 00:01:44,840
+ال summation لازم تكون بنجمع مجموعة elements من
+
+24
+00:01:44,840 --> 00:01:50,360
+داخل ال set هذه، قد يكون كلهم، قد يكون جزء منهم،
+
+25
+00:01:50,360 --> 00:01:53,720
+مش هيك؟ أكيد، طيب، فإذا لما نبدأ، نقول والله وين
+
+26
+00:01:54,480 --> 00:01:58,260
+الـ lower bound أو الـ start الـ start الطبيعي
+
+27
+00:01:58,260 --> 00:02:03,620
+يبدأ من index 0 فأكثر يعني يمكن أقولك ابدأ من
+
+28
+00:02:03,620 --> 00:02:09,580
+بدايته okay خلاص معناته الـ j 0 فإذا بدي أبدأ من j
+
+29
+00:02:09,580 --> 00:02:13,720
+بتساوي 0 كأني بدي أبدأ من أول ال string أو ال
+
+30
+00:02:13,720 --> 00:02:18,160
+sequence كامل أو أقولك لأ بديش أبدأ من الأول بدي
+
+31
+00:02:18,160 --> 00:02:24,370
+أبدأ منأي اتنين وكمل بعده خلاص صارت ال j هنا
+
+32
+00:02:24,370 --> 00:02:28,470
+بتساوي اتنين ال j أصبحت في الحالة بتساوي اتنين
+
+33
+00:02:28,470 --> 00:02:36,410
+تمام هذه معناه انه ال lower bound او ال limit j هي
+
+34
+00:02:36,410 --> 00:02:41,390
+اكبر من او يساوي zero فانا اما ببدأ من ال index
+
+35
+00:02:41,390 --> 00:02:47,360
+صفر او اكتر مافيش اذلبالظبط هنا في عندك أجل من
+
+36
+00:02:47,360 --> 00:02:52,160
+الصفر ك index فش فطبيعي بداية ال summation بدها
+
+37
+00:02:52,160 --> 00:02:56,580
+تبدأ من ال index الأول أو مابعده أو مابعده طيب ال
+
+38
+00:02:56,580 --> 00:03:01,900
+upper bound طبيعي هتكون K ال K هذه عشان يكون في
+
+39
+00:03:01,900 --> 00:03:06,600
+عندك حاجة تحسبها بدها تكون إذا ال J فعلا أكبر من
+
+40
+00:03:06,600 --> 00:03:10,480
+أو يساوي صفر فال K هذه ال K سمناها كمية أه مظبوط
+
+41
+00:03:10,480 --> 00:03:15,210
+أكبر من أو تساوي ال J ال startبحيث إن لو بتسويها
+
+42
+00:03:15,210 --> 00:03:21,570
+معناته أصلا مش أن هي أنصر واحد هي AJ بس AJ فقط لا
+
+43
+00:03:21,570 --> 00:03:24,250
+أكثر ولا أقل أما إذا كان أكبر معناته فيه عدة عناصر
+
+44
+00:03:24,250 --> 00:03:27,890
+بدنا نجمع مجموعة العناصر هذه بس لا يجوز إن K تكون
+
+45
+00:03:27,890 --> 00:03:33,590
+أقل تقولني جمالي من اتنين لصفر لأ هي المفروض
+
+46
+00:03:33,590 --> 00:03:36,550
+عكستها من صفر لاتنين مفهومة بس من اتنين لصفر لا
+
+47
+00:03:36,550 --> 00:03:41,460
+بتنظبطش تماموالشغلة التانية و المهمة أن ك لازم
+
+48
+00:03:41,460 --> 00:03:47,580
+تكون أقل من أو يساوي in مظبوط؟
+
+49
+00:03:47,580 --> 00:03:53,620
+in إذا هي limited أو finite series معناته أنا
+
+50
+00:03:53,620 --> 00:03:58,560
+مابقدر أطلع أعديها هذه لازم في النهاية برضه ك تكون
+
+51
+00:03:58,560 --> 00:04:06,610
+أقل من أو تساوي inبكون أقل من أو تسوين؟ جيد فأصبح
+
+52
+00:04:06,610 --> 00:04:11,190
+في الآخر عندي كإني بعمل summation ل ال sequence أو
+
+53
+00:04:11,190 --> 00:04:17,900
+ال series تبعتنا from Jبنعملها summation j to k و
+
+54
+00:04:17,900 --> 00:04:24,460
+بنحطها a i بحيث ان ال index تبعنا يبدأ من j ل k
+
+55
+00:04:24,460 --> 00:04:30,640
+كأن بقول هذه equivalent ل a j plus a j plus واحد a
+
+56
+00:04:30,640 --> 00:04:36,660
+j plus اتنين لعند a k بنرجف خلاص بدي أجمع مجموعة
+
+57
+00:04:36,660 --> 00:04:40,460
+العناصر هذه بحيث ان زي ما قلنا ال I هنا ال index
+
+58
+00:04:40,460 --> 00:04:45,430
+of summationفي ال continuous بعيدا عن ال C عن ال
+
+59
+00:04:45,430 --> 00:04:48,950
+discrete كنت بتسموها integration كنت بتقوله
+
+60
+00:04:48,950 --> 00:04:56,470
+integration from J to K و AI على طول هذه صارت I
+
+61
+00:04:57,660 --> 00:05:01,120
+from j to k كنتوا هيك تكتبوها بالشكل هذا لأ احنا
+
+62
+00:05:01,120 --> 00:05:05,500
+ماعناش continuous ال and function لأ انا بتكلم عنه
+
+63
+00:05:05,500 --> 00:05:09,620
+لأ انا بتكلم عن discrete completely discrete زي ما
+
+64
+00:05:09,620 --> 00:05:12,600
+احنا شايفين المصاق طبعا كله discrete اصلا ففي ال
+
+65
+00:05:12,600 --> 00:05:18,120
+discrete summation فضل ال index
+
+66
+00:05:18,120 --> 00:05:23,190
+ال index لآخر element بده اجمعهال index لآخر
+
+67
+00:05:23,190 --> 00:05:27,210
+element بده اجمعه و ال j أول element بده اجمعه من
+
+68
+00:05:27,210 --> 00:05:32,710
+ال series ال index ال index تمام اللي هو صفر واحد
+
+69
+00:05:32,710 --> 00:05:38,490
+اتنين تلاتة to n هذا ال index okay generalized
+
+70
+00:05:38,490 --> 00:05:42,030
+summations ممكن اقول انه ممكن قد يكون في بعض
+
+71
+00:05:42,030 --> 00:05:45,670
+الأحوال في عندي infinite sequence اه ممكن يكون في
+
+72
+00:05:45,670 --> 00:05:48,450
+عندي infinite sequence و بنها عليه بده اجيب ال
+
+73
+00:05:48,450 --> 00:05:51,780
+summation لل infinite sequence ممكنقد يكون تعمله
+
+74
+00:05:51,780 --> 00:05:55,360
+في الآخر limit قد يكون تعمله ان هو يقول ل infinity
+
+75
+00:05:55,360 --> 00:05:58,740
+قد تعمله انه يقول لك بس في النهاية ممكن تعمله بشكل
+
+76
+00:05:58,740 --> 00:06:05,240
+limit و يطلع للقيمة و طلع للقيمة بنكتبها بالصيغة J
+
+77
+00:06:05,240 --> 00:06:11,260
+زي ما هي J لكن ال K مدام infinite to infinity ال K
+
+78
+00:06:11,260 --> 00:06:15,900
+مالهاش limit خلاص to infinity لنفس العنصر هو هو و
+
+79
+00:06:15,900 --> 00:06:20,400
+هنا ellipses و بنوقفش في آخرهخلاص ال lips بتظل ..
+
+80
+00:06:20,400 --> 00:06:25,080
+ال lips بتظل شغالة طيب ممكن ال summation نتعامل
+
+81
+00:06:25,080 --> 00:06:28,680
+معاها و نستبدلها بحاجة اسمها summation function
+
+82
+00:06:28,680 --> 00:06:32,140
+بمعنى انه العنصر نفسه هذا اتعامل معاه انه function
+
+83
+00:06:32,140 --> 00:06:36,140
+هناخد عدة أمثلة ممكن نتعامل معها ال summation ل
+
+84
+00:06:36,140 --> 00:06:41,200
+function زي to sum a function over all members of
+
+85
+00:06:41,200 --> 00:06:46,040
+a set capital X مثلا يعني خليني اقول انه عندك set
+
+86
+00:06:47,310 --> 00:06:52,330
+وخلاص ال set هذه لها index لكن مش بضروري يكون مرتب
+
+87
+00:06:52,330 --> 00:06:57,350
+مش بضروري .. مدام حكيت set تقوى لما عرفناها في ال
+
+88
+00:06:57,350 --> 00:07:01,230
+slide اللي جابنا قولنا series وعرفنا ان ال series
+
+89
+00:07:01,230 --> 00:07:08,530
+هنا جالي set set وبدنا نجمع عناصر ال set بغض النظر
+
+90
+00:07:08,530 --> 00:07:14,470
+ترتيبهم كيف فهنا بتقول summation ل F of X و X
+
+91
+00:07:14,470 --> 00:07:19,480
+belong to capital Sوخلاص مين إتيجي ال X اللي جابله
+
+92
+00:07:19,480 --> 00:07:23,460
+التاني مابتفرجش معاه X belong to capital X خلاص
+
+93
+00:07:23,460 --> 00:07:27,780
+مين إيجيه جابل مين المهم أنه كل العناصر بتتنج مع
+
+94
+00:07:27,780 --> 00:07:32,060
+بعض وخلاص فهذه كأنه F of X واحد F of X اتنين واحد
+
+95
+00:07:32,060 --> 00:07:36,800
+يقوللي F of X اتنين زي F of X واحد okay ماشي فليكن
+
+96
+00:07:36,800 --> 00:07:42,930
+هي unordered هي مش مرتبة تمام أو ممكن نقولهاإذا
+
+97
+00:07:42,930 --> 00:07:50,590
+كان X الـ set X هي عبارة عن set of elements وكل
+
+98
+00:07:50,590 --> 00:07:56,730
+element X such that P of X بمعنى إنه هذه مجموعة
+
+99
+00:07:56,730 --> 00:08:03,490
+العناصر اللي تحقق المعادلة P of X مجموعة العناصر
+
+100
+00:08:03,490 --> 00:08:06,990
+اللي تحقق معادلة P of X أو predicate P of X مثلا
+
+101
+00:08:06,990 --> 00:08:12,380
+زي ما قعدنا هناخدبنكتبها كتالي summation of P of X
+
+102
+00:08:12,380 --> 00:08:17,620
+يعني summation للعناصر اللي تحقق ال function P of
+
+103
+00:08:17,620 --> 00:08:21,740
+X خلاص لل F of X خلصنا بنكتبها بهذا الشكل فكأني
+
+104
+00:08:21,740 --> 00:08:25,680
+برضه برجع F of X واحد X اتنين X تلاتة اللي هم اللي
+
+105
+00:08:25,680 --> 00:08:31,610
+بيحققوابيحققوا الشرط هذا اللي هو P of X فكل عنصر
+
+106
+00:08:31,610 --> 00:08:34,870
+بيحقق P of X هقول يا هذا X واحد اللي ورا حقق X
+
+107
+00:08:34,870 --> 00:08:39,230
+اتنين بغض النظر ترتيبهم كمان بغض النظر كيف ترتيبهم
+
+108
+00:08:39,230 --> 00:08:46,370
+مثال مثال واضح يك بس سريع نشط حالنا في الموضوع ال
+
+109
+00:08:46,370 --> 00:08:50,050
+summation ممكن يكون عندك summation from two to
+
+110
+00:08:50,050 --> 00:08:55,630
+four فانا بقول هنا ال index Iالاندكس I ال lower
+
+111
+00:08:55,630 --> 00:09:02,670
+bound اتنين ال upper bound اربع ال function I
+
+112
+00:09:02,670 --> 00:09:06,670
+تربيع زائد واحد ال function هنا I تربيع زائد واحد
+
+113
+00:09:06,670 --> 00:09:10,590
+بحيث انه لما بدي اجي اعوض بنعود element by element
+
+114
+00:09:10,590 --> 00:09:15,950
+فببدأ من J العنصر
+
+115
+00:09:15,950 --> 00:09:19,010
+I ببدأ من اتنين اللي هي ال J قيمة ال J فعليا فهنا
+
+116
+00:09:19,010 --> 00:09:26,540
+كأنهj تساوي اتنين و هنا كأنه k تساوي اربعة هنبتدأ
+
+117
+00:09:26,540 --> 00:09:30,760
+ب I بتساوي اتنين اللي هي تمثل قيمة ال J و هيا
+
+118
+00:09:30,760 --> 00:09:36,500
+عوضنا طيب اللي وراها تلاتة اربعة اه وصلنا ال upper
+
+119
+00:09:36,500 --> 00:09:41,200
+وقف عند الاربعة خلاص اتنين و تلاتة و اربعة بنجمع
+
+120
+00:09:41,200 --> 00:09:43,480
+طبعا لاحظ ان احنا بنجمع ال function كلها ال
+
+121
+00:09:43,480 --> 00:09:47,610
+function كلها كاملة مع بعضمش بتشتغل على ال I
+
+122
+00:09:47,610 --> 00:09:51,330
+للتربية لحالها وبعدين تضيف لمرة واحدة الواحد كل
+
+123
+00:09:51,330 --> 00:09:55,010
+على بعض function كاملة عشان هيك قلتلكوا كاملة على
+
+124
+00:09:55,010 --> 00:09:59,250
+بعضها function هي كاملة كاملة كاملة خلصنا بعدك
+
+125
+00:09:59,250 --> 00:10:04,370
+صارت عملية حسابية لا أكثر ولا أقل موضوع بسيط كتير
+
+126
+00:10:04,370 --> 00:10:10,100
+ومر عليكم أكيد من زمان تمامما زلنا في ال infinite
+
+127
+00:10:10,100 --> 00:10:12,980
+series ال infinite series هتلاقي ان بعض ال
+
+128
+00:10:12,980 --> 00:10:17,500
+summations زي مثلا summation two to the power
+
+129
+00:10:17,500 --> 00:10:22,480
+minus I to the power minus I from zero to infinity
+
+130
+00:10:24,120 --> 00:10:27,820
+لو جينا عوضنا بقى كم من term في البداية as a
+
+131
+00:10:27,820 --> 00:10:33,300
+sequence خليني افترض بده عوض بالصفر فهذا هتطلع
+
+132
+00:10:33,300 --> 00:10:35,980
+تنين to the power of zero زائد اتنين to the power
+
+133
+00:10:35,980 --> 00:10:38,420
+of minus one اتنين to the power of minus two عساس
+
+134
+00:10:38,420 --> 00:10:42,440
+اشوف شكل ال behavior لل series كيف شكلها وممكن
+
+135
+00:10:42,440 --> 00:10:46,200
+تعطينا اي حق للجمع وين بده يروح كيف بنا نعمل تجميع
+
+136
+00:10:46,200 --> 00:10:52,790
+فهذا هي ساوي واحدهذه عبارة عن ايش نص كأنك بتجلبها
+
+137
+00:10:52,790 --> 00:10:56,230
+مادان في minus هنا كأنك بتعكس بتجلب واحد على اتنين
+
+138
+00:10:56,230 --> 00:11:00,050
+واحد على اربعة واحد على تمانية واحد على ستاشت واحد
+
+139
+00:11:00,050 --> 00:11:05,730
+على اتنين وثلاثين لاحظ عندك واحد عشان تصل الاتنين
+
+140
+00:11:05,730 --> 00:11:10,730
+محتاج واحد كامل أخد نصه فصار المجموعة واحد و نص
+
+141
+00:11:10,730 --> 00:11:15,390
+جديش ضايق النص النص هاخد نصه معناته ضايق النص
+
+142
+00:11:15,390 --> 00:11:19,530
+التاني طيب النص التاني هاخد نصه واحد على تمانية
+
+143
+00:11:20,500 --> 00:11:24,240
+الواحدة على تمانية هاخد نصه واحدة على سبتاشر بس
+
+144
+00:11:24,240 --> 00:11:29,940
+for infinity هتكمل بتصل للاثنين for infinity هتكمل
+
+145
+00:11:29,940 --> 00:11:33,480
+معاك للاثنين فعشان هي كويسة انك بتعملك اكمل
+
+146
+00:11:33,480 --> 00:11:35,860
+element في البداية بتشوف behavior بتاعة ال
+
+147
+00:11:35,860 --> 00:11:40,170
+summation كيف رايح لاحظته كيف؟هذا واحد خلاص واحد
+
+148
+00:11:40,170 --> 00:11:43,850
+صحي الكامل الباقي هل بيكمل الواحد هاجد انه فيه نص
+
+149
+00:11:43,850 --> 00:11:47,090
+محتاج كمان نص لأ ماعطانيش نص اعطاني كمان ربع
+
+150
+00:11:47,090 --> 00:11:50,670
+معناته محتاج كمان ربع اللي ورا هو مش ربع نص الربع
+
+151
+00:11:50,670 --> 00:11:54,210
+واحد على تمانية سرددش لسه محتاج كمان واحد على
+
+152
+00:11:54,210 --> 00:11:57,790
+تمانية اللي ورا لأ هو نص الواحد على تمانيةعطاني
+
+153
+00:11:57,790 --> 00:12:00,150
+واحدة على ستة عشر طب جدش ال dial واحدة على ستة عشر
+
+154
+00:12:00,150 --> 00:12:04,370
+طب نصه نصه نصه بس في ال infinity اذا وصلنا و قدرنا
+
+155
+00:12:04,370 --> 00:12:07,710
+ربنا انه نصل لها infinity بنكون سكرنا ال summation
+
+156
+00:12:07,710 --> 00:12:13,590
+و limit to اتنين فبصير هنا قيمته بتنين فإذا هذه
+
+157
+00:12:13,590 --> 00:12:15,830
+واحدة من ال functions اللي اه رغم ان هي infinite
+
+158
+00:12:15,830 --> 00:12:22,650
+بس لها قيمة لها قيمة واضحة قيمتها باين تمام طب حد
+
+159
+00:12:22,650 --> 00:12:26,230
+منكوا هيكي يدعي يقولنا مثلا ليش هذه فعلا لها قيمة
+
+160
+00:12:28,880 --> 00:12:33,680
+كيف أعرف إنه لها قيمة ولا مالهاش قيمة؟ ماشي أه ال
+
+161
+00:12:33,680 --> 00:12:38,560
+limit لابد تساوي اتنين طب أكتب .. أكتبلك إياها
+
+162
+00:12:38,560 --> 00:12:45,540
+هأوضحلكوا إياها هتعامل
+
+163
+00:12:45,540 --> 00:12:51,600
+معها هيك ال function بتعمل convergence يعني معناته
+
+164
+00:12:51,600 --> 00:12:56,680
+بتطلاقة مع الصفر في ال infinityو مدام التطلاق مع
+
+165
+00:12:56,680 --> 00:13:05,640
+الصفر يعني يوجد area under the curve في
+
+166
+00:13:05,640 --> 00:13:10,680
+ال infinity هتصل للصفر هتصل zero معناه ذلك ان ال
+
+167
+00:13:10,680 --> 00:13:17,920
+area under the curve موجودة صح؟
+
+168
+00:13:17,920 --> 00:13:20,540
+و انت في النهاية بعد من من؟ بعد من عند الصفر من
+
+169
+00:13:20,540 --> 00:13:24,400
+هنا من عند ال zeroخلاص هذه كانت وقع عند ال zero
+
+170
+00:13:24,400 --> 00:13:28,740
+وكانت قيمتها واحد في ال infinity هتكون صفر فانت
+
+171
+00:13:28,740 --> 00:13:33,160
+عندك closed area closed area اه أنا ممكن اتوقع
+
+172
+00:13:33,160 --> 00:13:37,500
+Argentation للصماشن بس اذا كان open area لأ هنا
+
+173
+00:13:37,500 --> 00:13:41,640
+بتكون infinity هنا بتكون infinity فدائما ال
+
+174
+00:13:41,640 --> 00:13:45,180
+inverse في الغالب بدك تتوقع ان انا ممكن احققلك
+
+175
+00:13:45,180 --> 00:13:50,790
+الكلام هذا لأن ال inverse بجلبعمل decreasing
+
+176
+00:13:50,790 --> 00:13:57,090
+بتتوقع أنه عند لحظة معينة بيصل ويعمل تقاطع مع ال X
+
+177
+00:13:57,090 --> 00:14:01,510
+Axis طبعا هنا بيعمل تقاطع مع ال X Axis في ال
+
+178
+00:14:01,510 --> 00:14:05,790
+infinity عشان تصل لمجموع اتنين هتصلوا في ال
+
+179
+00:14:05,790 --> 00:14:08,530
+infinity نقطة التلاقي عند نقطة التلاقي هتصل
+
+180
+00:14:08,530 --> 00:14:14,490
+للاتنين لما نقول والله بدي استخدم ال predicate
+
+181
+00:14:14,490 --> 00:14:19,120
+لتعريف ال limits تعونةاو two pounds ال upper و ال
+
+182
+00:14:19,120 --> 00:14:24,560
+lower بنقول مثلا x تربيع summation x تربيع for
+
+183
+00:14:24,560 --> 00:14:31,180
+what for x is prime أقل من عشرة ل x prime أقل من
+
+184
+00:14:31,180 --> 00:14:35,520
+عشرة predicate تمام خلاص بنعوض بالمعادلة اللي
+
+185
+00:14:35,520 --> 00:14:37,820
+كتبليها اللي هي ال predicate function اللي كتبليها
+
+186
+00:14:37,820 --> 00:14:45,140
+كل ال prime أقل من عشرة اتنين تلاتة خمسة سبعة stop
+
+187
+00:14:45,140 --> 00:14:51,550
+خلصناهنا حطناهم ضمن المعادلة بنجيب رقم مافيش أي
+
+188
+00:14:51,550 --> 00:14:56,490
+مشكلة فطريقة التعريف ال upper و ال lower تتنوع
+
+189
+00:14:56,490 --> 00:14:59,810
+ممكن نستخدم function نستخدم set نستخدم predicate
+
+190
+00:14:59,810 --> 00:15:07,230
+مافيش أي مشكلة تمام بعض ال manipulations أو بعض ال
+
+191
+00:15:07,230 --> 00:15:13,450
+rules اللي ممكن نستخدمها لعملية ال summation ومهمة
+
+192
+00:15:13,450 --> 00:15:20,280
+جدا زي ان اقول summation ل cفى f of x هذا ثابت و
+
+193
+00:15:20,280 --> 00:15:23,060
+ثابت زي و زي ال integration ايش كنت تعمل فى ال
+
+194
+00:15:23,060 --> 00:15:24,900
+integration كنت تطلعها ثابت برضه فى ال summation
+
+195
+00:15:24,900 --> 00:15:28,060
+طلعه برا مافيش اي مشكلة لأن هد integration
+
+196
+00:15:28,060 --> 00:15:32,060
+لدiscrete هد ال discrete integration بالظبط
+
+197
+00:15:32,060 --> 00:15:34,460
+summation مافيش حاجة اسمها integration فى ال
+
+198
+00:15:34,460 --> 00:15:38,560
+discrete كويس فهد بتساوي كأنه C وكمل ال summation
+
+199
+00:15:38,560 --> 00:15:42,000
+لتسهيل عشان مش كل مرة تجد تضربه فى القيم بتاعة
+
+200
+00:15:42,000 --> 00:15:42,540
+التجميع
+
+201
+00:15:47,570 --> 00:15:50,810
+ممكن تفصل ال two functions بالظبط ممكن تفصل تعمل
+
+202
+00:15:50,810 --> 00:15:53,710
+summation للأولى لحال و للتانى لحال و بعدين جمع
+
+203
+00:15:53,710 --> 00:15:59,900
+المجموعين ممكن تعمل shift لل indexتعمل shift لل
+
+204
+00:15:59,900 --> 00:16:04,040
+index طبعا هذه هتقول انك انت هيك بده تعملها لمجرد
+
+205
+00:16:04,040 --> 00:16:06,600
+الترفيه لمجرد ان انا بس بده اعمل shift مالهاش كتير
+
+206
+00:16:06,600 --> 00:16:09,840
+معناه لكن بتستخدمها لما تكون في اثبات في حاجة بدك
+
+207
+00:16:09,840 --> 00:16:14,460
+تقارن قيمتين مجموعين مع بعض عملية المقارنة فبتضطر
+
+208
+00:16:14,460 --> 00:16:17,380
+تعمل ال shift لأن ساعتها بكون انت عارف ال shift
+
+209
+00:16:17,380 --> 00:16:21,180
+اللي بدك ياده اديشلما تكون بدك تقارن two
+
+210
+00:16:21,180 --> 00:16:24,080
+summations مع بعض فانت عارف ان بدك تجرب واحد
+
+211
+00:16:24,080 --> 00:16:26,880
+للتاني بيصير عندك رؤية واضحة ال shift جدش بدك ايه
+
+212
+00:16:26,880 --> 00:16:31,860
+فهنا الفكرة كانت تالي انه هتبدأ من ال J to K لل
+
+213
+00:16:31,860 --> 00:16:39,820
+index I كل اللي حمله انه اضيف N لل limits و اطرحها
+
+214
+00:16:39,820 --> 00:16:46,640
+من ال index ضفناها و طرحناها بحيث ان ال total واحد
+
+215
+00:16:48,250 --> 00:16:53,370
+Total في الأخر وحل عيد عوض هيها ب J زائد N حتى ال
+
+216
+00:16:53,370 --> 00:16:57,270
+J نفس ال element الأول هنا هو هو و نفس الكلام ال
+
+217
+00:16:57,270 --> 00:17:01,390
+element الأخر هنا عوضنا بال I N مع N حتى ال K فهو
+
+218
+00:17:01,390 --> 00:17:04,310
+نفس ال answer هو هو لكن عملنا عملية shift لأ أكثر
+
+219
+00:17:04,310 --> 00:17:10,750
+ولا أقل اللي أهم منها يمكن هي ال splitting ال
+
+220
+00:17:10,750 --> 00:17:14,690
+splitting بحيث أن أنت أحيانا بتضطر أن أنت عارف
+
+221
+00:17:14,690 --> 00:17:20,030
+submission معين أو في عندك closed formجاهز ل
+
+222
+00:17:20,030 --> 00:17:24,550
+submission معين لكن ال limits مش مظبوطة ال limits
+
+223
+00:17:24,550 --> 00:17:28,970
+أكتر منه اعمل splitting و خد ال limit اللي انت
+
+224
+00:17:28,970 --> 00:17:32,910
+محتاجه بحيث يتفق مع قانون انت بتقدر على طول تنفذ
+
+225
+00:17:32,910 --> 00:17:37,190
+او تجيب المعادلة الحل على السريع فيهفبتعمل فترتين
+
+226
+00:17:37,190 --> 00:17:43,450
+splitting فصلناها فهي من j to k ال splitting او
+
+227
+00:17:43,450 --> 00:17:47,870
+الحد اللي بتعمل عنده عملية splitting لازم يكون ما
+
+228
+00:17:47,870 --> 00:17:52,410
+بين ال j و ال k منطقي صحيح؟ انا عندي مسافة من صفر
+
+229
+00:17:52,410 --> 00:17:55,430
+لعشرة بدي اعمل splitting محدش هيجي يقول بدي اعمل
+
+230
+00:17:55,430 --> 00:17:59,100
+splitting عد 11أكيد بتكون ما بين الصفر و العشرة
+
+231
+00:17:59,100 --> 00:18:02,260
+عند الخمسة عند السبعة عند التمانية عند الأربعة عند
+
+232
+00:18:02,260 --> 00:18:05,240
+.. okay اعمل splitting و جيب هذا مجموحم لحاله و
+
+233
+00:18:05,240 --> 00:18:08,840
+جيب هدول مجموحم لحاله مافيش مشكلة فبنعملها ل M و M
+
+234
+00:18:08,840 --> 00:18:12,800
+اتفقنا ان هي بين ال I و ال K بحيث ان يصبح عندي
+
+235
+00:18:12,800 --> 00:18:19,320
+summation from J to M خلصنا لعند M اللي متبقي زائد
+
+236
+00:18:19,320 --> 00:18:24,170
+واحدأحنا بتكلم discrete .. discrete بالظبط مابعد
+
+237
+00:18:24,170 --> 00:18:28,330
+لإن إذا حطيتها من M معناته ال M انجمع مرتين من M
+
+238
+00:18:28,330 --> 00:18:31,770
+زائد واحد و أنا بتكلم عن discrete يعني مدام خلصت
+
+239
+00:18:31,770 --> 00:18:34,690
+ال M هروح ل M زائد واحد مافيش بينهم إشي هذه
+
+240
+00:18:34,690 --> 00:18:38,230
+discrete تمام it's okay فبنكون عاملنا عملية
+
+241
+00:18:38,230 --> 00:18:43,150
+splitting في الحالة اللي عندنا ال reversalorder
+
+242
+00:18:43,150 --> 00:18:48,830
+reversal انك ممكن بشوية مهارة بدل ما تجمع من
+
+243
+00:18:48,830 --> 00:18:54,510
+الأصغر للأكبر جمع من الأكبر للأصغر بس هاي كل اللي
+
+244
+00:18:54,510 --> 00:18:57,450
+بدك تعمله كتالي هتعمله أول شغلة معناته ال function
+
+245
+00:18:57,450 --> 00:19:02,670
+نفسها بدك تعملها flip تعكسها لأنه بتصير العد تبح
+
+246
+00:19:02,670 --> 00:19:07,770
+تنازلي مش تصعدي فهذه تاخد بالك منها بدل ما كانت I
+
+247
+00:19:07,770 --> 00:19:14,420
+بتصير minus Iهتصبح minus I و بعدين هتحط ال upper
+
+248
+00:19:14,420 --> 00:19:17,520
+في الأول لإنه بده يصير ال reference تبعك هو ال
+
+249
+00:19:17,520 --> 00:19:23,780
+upper بدك تبدأ منه بدك تبدأ منه و اتخليها زي ما
+
+250
+00:19:23,780 --> 00:19:29,080
+هنا ال lower تطرحه من الناحيتين طرحنا من الناحيتين
+
+251
+00:19:29,080 --> 00:19:37,180
+بحيث إن لو عوضنا صفر هي صفر جيبنا F of K آخر عنصر
+
+252
+00:19:37,180 --> 00:19:45,050
+كان هنا كان آخر عنصرطيب لو عوضنا بال upper مكان ال
+
+253
+00:19:45,050 --> 00:19:49,490
+J هتلاقي انه ال K مع ال K هيروح و هتبقى لل J أول
+
+254
+00:19:49,490 --> 00:19:54,370
+عنصر كان هنا فعكسناهم بدل ما كنا بنجمع من الأصغر
+
+255
+00:19:54,370 --> 00:19:58,030
+للأكبر او من ال lower لل upper صرنا نجمع من ال
+
+256
+00:19:58,030 --> 00:20:01,650
+upper لل lower لكن ال elements هي هي ال elements
+
+257
+00:20:01,650 --> 00:20:06,520
+هي هيكويس ايش فيه كمان ضالهنا؟ ضالهنا اه ال
+
+258
+00:20:06,520 --> 00:20:11,160
+grouping ان انا ممكن في النهاية اعمل grouping ل ال
+
+259
+00:20:11,160 --> 00:20:15,440
+summation بكل بساطة و أبسط نوع من الأنواع حد اني
+
+260
+00:20:15,440 --> 00:20:22,520
+اعمله مثلا ل ال odd و ال even اجمع كل ال odd
+
+261
+00:20:22,520 --> 00:20:27,580
+indices ال index odd اجمحهم مع بعض و ال indices
+
+262
+00:20:27,580 --> 00:20:33,400
+تبعته even اجمحهم مع بعض بكل بساطة من صفر ل اتنين
+
+263
+00:20:33,400 --> 00:20:39,090
+Kفي الحالة هذه بدي أعملها ل K واحدة هعملها ل K
+
+264
+00:20:39,090 --> 00:20:43,110
+واحدة مش هضطر أعمل summation كتير هعمل نص عملية ال
+
+265
+00:20:43,110 --> 00:20:45,950
+summation بس بدي أكون عارف في الحالة هذه إن أنا
+
+266
+00:20:45,950 --> 00:20:51,600
+مدان بعد بالشكل هذا بدي أعد زوجي اتنين اتنينبتكشف
+
+267
+00:20:51,600 --> 00:20:55,840
+تعد بسرعة زي اقولك اللي بيعده الفلوس بتشوفه اصلا
+
+268
+00:20:55,840 --> 00:20:59,540
+على اليوتيوب اللي بتجه تتعد بشكل سريح هذه بكل
+
+269
+00:20:59,540 --> 00:21:02,320
+بساطة احد المهارات ممكن اللي تستخدم في هيك حالة
+
+270
+00:21:02,320 --> 00:21:05,900
+انك بدل ما تعدها ورقة وورقة عدهم ورقتين وورقتين
+
+271
+00:21:05,900 --> 00:21:13,180
+عدهم تلاتة تلاتة grouping فكل ورقتين بتعد واحد كل
+
+272
+00:21:13,180 --> 00:21:17,360
+ورقتين بتعد واحد شوف كده هتصير أسرع إذا عندك
+
+273
+00:21:17,360 --> 00:21:20,360
+إمكانية تعد أكتر من هيك عد أكتر من هيكبدك تعدهم
+
+274
+00:21:20,360 --> 00:21:23,100
+تلاتة تلاتة عدهم تلاتة تلاتة و جدش الرقم اللي
+
+275
+00:21:23,100 --> 00:21:28,880
+بتحصل عليه اضغط في تلاتة و خلاص خلصت هاي كل الفكرة
+
+276
+00:21:28,880 --> 00:21:31,900
+كلها ان انت جدش بتقدر تعمل grouping جدش بتقدر تعمل
+
+277
+00:21:31,900 --> 00:21:36,680
+نفس الفكرة هيها بديش اعمل summation كتير مدل ما
+
+278
+00:21:36,680 --> 00:21:40,540
+اعمل summation ل 2k بدي اعملها ل k واحدة بس انا
+
+279
+00:21:40,540 --> 00:21:45,070
+عارف اني بعدي 2 2باخد اتنين اتنين ووركتين وبعدهم
+
+280
+00:21:45,070 --> 00:21:50,610
+مرة فهي من صفر ل K واحدة بس انا عارف ان مرة اتنين
+
+281
+00:21:50,610 --> 00:22:00,110
+I ال even و اتنين I زائد واحد ال odd بس فجمعنا two
+
+282
+00:22:00,110 --> 00:22:04,310
+مع بعض لاحظته الفكرة كيف تصير فهي عملية grouping
+
+283
+00:22:04,310 --> 00:22:09,780
+عملية grouping طيب نبدأ نشوف بعضال submissions
+
+284
+00:22:09,780 --> 00:22:14,920
+المهمة يمكن leonhard euler كان أول واحد جابلنا
+
+285
+00:22:14,920 --> 00:22:18,220
+إياه وكان عمره اتناشر سنة يعني نتكلم في واحد فوق
+
+286
+00:22:18,220 --> 00:22:24,040
+الأعداد مثلا يعني الفكرة كان إن هو معاقب وروح قدّل
+
+287
+00:22:24,040 --> 00:22:27,200
+الأعداد من واحد لمية ارجع ورا قد الأعداد من واحد
+
+288
+00:22:27,200 --> 00:22:31,060
+لمية عمل شغب للمعلمة ارجع لينك بعد دقيقة واحدة
+
+289
+00:22:31,060 --> 00:22:35,850
+اللي هو راجع بيقولها النتيجة كذاماصدقتش هتنشوف
+
+290
+00:22:35,850 --> 00:22:39,550
+هتمش نشوف اكد عليها لأ انا متأكد انه حل صح اخدوها
+
+291
+00:22:39,550 --> 00:22:43,150
+على المدير اه اه و الله صح طب كيف جبتها انت غششها
+
+292
+00:22:43,150 --> 00:22:46,510
+لأ و الله ماغشت و الله ماعملت اعملتها بالطريقة
+
+293
+00:22:46,510 --> 00:22:49,950
+الفلانية تك اللي هي طلعت قانون و دل باسمه مر 12
+
+294
+00:22:49,950 --> 00:22:55,210
+سنة ف Euler هذا ممكن تستخدمه انك انت زي ما بقوله
+
+295
+00:22:55,210 --> 00:22:57,770
+تبهر عزيزي العلوان اللي احنا كتبينه تبهر أصدقاءك
+
+296
+00:22:57,770 --> 00:23:02,850
+ان انت بتعرف تعد او تجمع مجموعة عناصر متلاحقة ورا
+
+297
+00:23:02,850 --> 00:23:06,850
+بعضزي تقولي والله بدي جمع اجمعلك اشراك اجمعلك من
+
+298
+00:23:06,850 --> 00:23:11,650
+واحد لعشر بسرعة هيك اصحابك بين اصحابك ولا على اخوك
+
+299
+00:23:11,650 --> 00:23:15,550
+مع اخوك الصغير اشراك اجمعلك من واحد لمية ع السريع
+
+300
+00:23:15,550 --> 00:23:19,290
+okay نفس الفكرة هذه مهارات هذه الفكرة اللي عملها
+
+301
+00:23:19,290 --> 00:23:25,410
+فكأنك انت بتقول بدك اتجمع مجموعة عناصر تبدأ من
+
+302
+00:23:25,410 --> 00:23:29,610
+واحد لأي رقم بدكيا تقولي والله اشراك اجمعلك من
+
+303
+00:23:29,610 --> 00:23:34,510
+واحد لميةبكل بساطة لجالها formula ال formula هذه
+
+304
+00:23:34,510 --> 00:23:39,350
+كالتالي هنشوف نتخيلها عشان نعرف إيش ال formula
+
+305
+00:23:39,350 --> 00:23:43,270
+اللي زهرت معاه هتقول واحد زائد اتنين زائد تلاتة
+
+306
+00:23:43,270 --> 00:23:48,490
+زائد أربعة لعند ما تصل لمين لأن منطقيا هيك المنطق
+
+307
+00:23:48,490 --> 00:23:53,610
+اللي يقول طيب لكن هو لاحظ شغلة لاحظ أنه في أزواج
+
+308
+00:23:53,610 --> 00:24:00,490
+متساويةفي أزواج متساوية كتير بين أن أنت أول عنصر و
+
+309
+00:24:00,490 --> 00:24:08,470
+آخر عنصر مجموحهم N زائد واحد طيب التاني مع ما قبل
+
+310
+00:24:08,470 --> 00:24:15,330
+الأخير طيب لما نصل لعند المنتصف هنصل عند ال N على
+
+311
+00:24:15,330 --> 00:24:20,430
+اتنين و N على اتنين زائد واحد برضه مجموحهم N زائد
+
+312
+00:24:20,430 --> 00:24:25,030
+واحدفجلّك خلاص معناته هي الفكرة كلها إن أنا عندي
+
+313
+00:24:25,030 --> 00:24:29,170
+أزواج مجمعة بتعطيني N زائد واحد N زائد واحد N زائد
+
+314
+00:24:29,170 --> 00:24:36,490
+واحد أكمرة كررت N على اتنين خلاص معناته N زائد
+
+315
+00:24:36,490 --> 00:24:42,730
+واحد في N على اتنين خلاص أنا عندي مجموحم N زائد
+
+316
+00:24:42,730 --> 00:24:46,210
+واحد أكمرة كررت N على اتنين خلاص معناته N على
+
+317
+00:24:46,210 --> 00:24:51,340
+اتنين في N زائد واحد انتهى طيب مع الترتيبن على
+
+318
+00:24:51,340 --> 00:24:57,160
+اتنين في n زائد واحد بترتيبه بسيطه حطها بتصير ن في
+
+319
+00:24:57,160 --> 00:25:02,340
+n زائد واحد على اتنين يعني بدك تجمع لمية مية في
+
+320
+00:25:02,340 --> 00:25:06,840
+مية واحد على اتنين لعند عشرة عشرة في احداش على
+
+321
+00:25:06,840 --> 00:25:13,000
+اتنين خلص انت انتهى فعشرة في احداش مية وعشرة نصها
+
+322
+00:25:13,000 --> 00:25:16,420
+خمسة وخمسين يقولوا يلا هي عندك ايه اللي حاسب اجمع
+
+323
+00:25:16,420 --> 00:25:21,950
+هاني جمعتلكيهم في لحظةتمام فهي الفكرة بكل بساطة هى
+
+324
+00:25:21,950 --> 00:25:25,410
+اول series او trick من ال tricks اللى هنتكلم عنهم
+
+325
+00:25:25,410 --> 00:25:30,610
+اليوم اول واحدة ل Euler و اللى عملها عمره اتناشر
+
+326
+00:25:30,610 --> 00:25:33,270
+سنة و خلصها طيب نقطة تانى من ال series اللى
+
+327
+00:25:33,270 --> 00:25:39,430
+محتاجين برضه انجبلها summation
+
+328
+00:25:41,060 --> 00:25:44,700
+اللي هي الـ Geometric Progression، عارفين هال
+
+329
+00:25:44,700 --> 00:25:49,940
+متسلسل الهندسية؟ متسلسل الهندسية ماتعتمدش أني بجمع
+
+330
+00:25:49,940 --> 00:25:55,380
+عنصر واحد بين كل element والتاني، لأ بنضرب في عنصر
+
+331
+00:25:56,160 --> 00:25:59,680
+كل مرة بنضرب في عنصر تمام الانصر هو اللي بنضرب فيه
+
+332
+00:25:59,680 --> 00:26:03,300
+اللي هي قيمة R قيمة R فال summation اندي فعلا كأنه
+
+333
+00:26:03,300 --> 00:26:06,760
+أول element A في عندك constant عندك constant معين
+
+334
+00:26:06,760 --> 00:26:10,740
+A تضربه في R عشان تجيب ال element اللي ورا ال
+
+335
+00:26:10,740 --> 00:26:13,340
+element كله على بعضه تضربه في R عشان تجيب ال
+
+336
+00:26:13,340 --> 00:26:16,020
+element التالت ال element التالت تضرب في R عشان
+
+337
+00:26:16,020 --> 00:26:20,900
+تجيب الرابع و هكذا ف totally بتقدر تحطه في معادلة
+
+338
+00:26:20,900 --> 00:26:26,650
+A R to the power Kحسب انت اي index وصلت لل index
+
+339
+00:26:26,650 --> 00:26:29,450
+اللي انت .. بس لاحظ هنا ان انت بدأت ال index تبعك
+
+340
+00:26:29,450 --> 00:26:34,650
+بال zero بمعنى .. وهذا مهم جدا اتركز فيها لإنه
+
+341
+00:26:34,650 --> 00:26:38,230
+هنحتاج عادنا هنا انت بدأ ب R to the power صفر وهذا
+
+342
+00:26:38,230 --> 00:26:43,350
+R to the power واحدأو تطبع صفر البوئة هتخلص مش
+
+343
+00:26:43,350 --> 00:26:47,450
+فارقة مش هتفرج كتير معانا تمام فبهذا الشكل فانت
+
+344
+00:26:47,450 --> 00:26:51,850
+بدأ ال index تبعك فعليا من الصفر عشان هيك ممكن
+
+345
+00:26:51,850 --> 00:26:54,950
+نقول ساعتها ال summation تبعنا بيبدأ من zero
+
+346
+00:27:04,490 --> 00:27:08,350
+معامل الزيادة او معامل الضرب في الآخر لان كل مرة
+
+347
+00:27:08,350 --> 00:27:12,710
+بضربه R to the power I بدنا ال summation هذه كدش
+
+348
+00:27:12,710 --> 00:27:19,530
+القيمة هذه هاتلي closed formula بد formula زي طوى
+
+349
+00:27:19,530 --> 00:27:23,250
+بدل ما تقول جمعلي من واحد لان على طول اعطيني قانون
+
+350
+00:27:24,100 --> 00:27:30,840
+closed formula حل فيه مباشرة بشكل سريع بدنا الحل
+
+351
+00:27:30,840 --> 00:27:34,080
+السريع
+
+352
+00:27:34,080 --> 00:27:34,500
+تبعها
+
+353
+00:27:38,740 --> 00:27:41,960
+انا مش مفردش معانا اثباتها لكن بدنا نتعلم نشوف
+
+354
+00:27:41,960 --> 00:27:45,820
+اثباتها حنشوف اثباتها عشان نجيب القانون النهائي
+
+355
+00:27:45,820 --> 00:27:48,420
+انا بهمن القانون النهائي لا يمنع ان احنا بدنا
+
+356
+00:27:48,420 --> 00:27:52,500
+نشوفه لكن اقولك احفظه مش مطلوب حفظ اثباته كاثبات
+
+357
+00:27:52,500 --> 00:27:55,820
+رغم ان هو بسيط و منطقي جدا و هنشوفه الآن جدش هو
+
+358
+00:27:55,820 --> 00:27:59,720
+منطقي الآن هتبدأ بال summation الأصلية هيا ده ال
+
+359
+00:27:59,720 --> 00:28:05,940
+summation أساسامعامل الزيادة واحدة وهذه واحدة من
+
+360
+00:28:05,940 --> 00:28:08,760
+ال strategies اللي هنتعلمها لقدام ان انت دائما
+
+361
+00:28:08,760 --> 00:28:15,860
+بتحاول تفترض تجيب العنصر اللي بعدها عشان تشوف قداش
+
+362
+00:28:15,860 --> 00:28:20,200
+مقدار الزيادة اللي صارت هذه ال strategy هناخدها
+
+363
+00:28:20,200 --> 00:28:25,590
+لقدام في ال induction و هنعمل عليها اثباتاتبس لسه
+
+364
+00:28:25,590 --> 00:28:28,310
+بدري عليها يمكن فى النص التانى من المصاق كويس
+
+365
+00:28:28,310 --> 00:28:31,610
+هناخد حاجة اسمها ال induction هتكون بتعتمد على هيك
+
+366
+00:28:31,610 --> 00:28:35,710
+ان انا اذا انا عارف ان ال summation عند العنصر
+
+367
+00:28:35,710 --> 00:28:40,730
+اللى انا موجود فيه ايه قيمة محددة بجيبه العنصر
+
+368
+00:28:40,730 --> 00:28:44,410
+اللى وراه بدلالته طيب انت عشان تيبقى العنصر اللى
+
+369
+00:28:44,410 --> 00:28:49,610
+بعد هذا هو عبارة عن ضرب R مش هيك احنا ايش الفرق
+
+370
+00:28:49,610 --> 00:28:52,810
+بين كل عنصر و التانى تضرب كل مرة في R بس اضرب
+
+371
+00:28:52,810 --> 00:28:57,100
+الطرفين في Rغيرنا المعادلة ماغيرناش المعادلة هي هي
+
+372
+00:28:57,100 --> 00:29:00,100
+فهذه استراتيجية هنتكلم عنها برضه لاحقا زي ما
+
+373
+00:29:00,100 --> 00:29:05,980
+قلتلكم هاي ضربنا في ال R الان بس بدنا نرتب الأمور
+
+374
+00:29:05,980 --> 00:29:09,020
+بعد ما نضربت في ال R كل اللي ضايل الان كيف نرتب
+
+375
+00:29:09,020 --> 00:29:14,720
+الأمور بحيث انه من هنا اللي زادت هذه اللي صارت N
+
+376
+00:29:14,720 --> 00:29:21,140
+زائد 1 هيك تعتبر هذه بدي أجيب منها ال S نفسها بحيث
+
+377
+00:29:21,140 --> 00:29:22,840
+أنه يكون لغية ال summation
+
+378
+00:29:25,530 --> 00:29:31,470
+لاحظوا ك strategy أنا عندي عنصر أنا موجود الآن فيه
+
+379
+00:29:31,470 --> 00:29:36,370
+وهذا العنصر summation و بديش أدحي ال summation بدي
+
+380
+00:29:36,370 --> 00:29:43,330
+أجيب العنصر اللي وراه بدلالته جيبناه بدلالته طلعت
+
+381
+00:29:43,330 --> 00:29:47,190
+شوية أرقام لأن بحاول من مجموعة ال formula اللي
+
+382
+00:29:47,190 --> 00:29:55,620
+زهرتها دي في n زائد واحد أطلع summation لحالهبحيث
+
+383
+00:29:55,620 --> 00:29:58,280
+انه يختصر مع التاني، مع اللي موجود على الطرف
+
+384
+00:29:58,280 --> 00:30:02,040
+التاني فبتكون لغية ال summation من الموضوع وضل ash
+
+385
+00:30:02,040 --> 00:30:06,540
+closed formula مجموعة عناصر تساوي قيمة ال
+
+386
+00:30:06,540 --> 00:30:09,880
+summation وخلاصتساوي قيمة ال submission فهذه اللي
+
+387
+00:30:09,880 --> 00:30:13,220
+بدنا نحاول نعمله عشان انا عارف انه الان في شوية
+
+388
+00:30:13,220 --> 00:30:16,700
+حاجات هنعملها تكون انت فاهم ليش بتنعمل ليش احنا
+
+389
+00:30:16,700 --> 00:30:21,440
+بنعمل هذا الكلام تمام هاي بدأنا دخلنا C مش تقولنا
+
+390
+00:30:21,440 --> 00:30:24,760
+C constant دخله او طلعه مش هتفرق بدنا ندخله لجوه
+
+391
+00:30:24,760 --> 00:30:31,040
+بدلنا لجوه بدلناهم مافيش اشي التبديل صار كأنه دبار
+
+392
+00:30:31,040 --> 00:30:36,560
+واحد لاحظ انا قاعد بفصل التبصيل الممل كمانبنجمعهم
+
+393
+00:30:36,560 --> 00:30:41,240
+صارت R I زائد واحد هنا فعلا صرنا نتكلم الآن في
+
+394
+00:30:41,240 --> 00:30:46,140
+العنصر الجديد العنصر ما بعد ال summation العنصر
+
+395
+00:30:46,140 --> 00:30:49,880
+اللي هو ما بعد ال summation كويس العنصر هذا ما بعد
+
+396
+00:30:49,880 --> 00:30:56,100
+ال summation بنعمله shift اجمع واحد اجمع واحد اطرح
+
+397
+00:30:56,100 --> 00:31:01,080
+واحد بده اشيله احنا الان قاعدين بنفكر في ايش انه
+
+398
+00:31:01,080 --> 00:31:04,980
+صار عندي الآنأه زائد واحد بس أنا بدي أحاول ال
+
+399
+00:31:04,980 --> 00:31:08,940
+summation هذا كله أرجع لهذه الصيغة okay في حاجات
+
+400
+00:31:08,940 --> 00:31:12,380
+هتفرز أشمال ويمين اللي هي زوائد وهي طبيعي المنطقة
+
+401
+00:31:12,380 --> 00:31:16,660
+لازم تظهر زوائد ليش؟ لأن أنا الأن بتكلم عن الأنصار
+
+402
+00:31:16,660 --> 00:31:18,940
+اللي ورا باتكلمش عن نفس الأنصار اللي موجود فيه
+
+403
+00:31:18,940 --> 00:31:22,940
+فطبيعي فيه زيادة قيمة الزيادة هذه بدي أحطها يا
+
+404
+00:31:22,940 --> 00:31:26,120
+زائد هنا يا زائد هنا المهم أنه عشان أعملها و
+
+405
+00:31:26,120 --> 00:31:28,820
+أقولها واضحة ال summation هذا بدي أرجع لهذه الصيغة
+
+406
+00:31:28,820 --> 00:31:35,730
+أول شر لزارة عندي فوقطيب فوق هذه I هنا I زائد واحد
+
+407
+00:31:35,730 --> 00:31:40,890
+طيب إيش بدى أسوي؟ shift بدى أرجحها مع أنها تقطع من
+
+408
+00:31:40,890 --> 00:31:44,470
+هنا واحد بس عشان تترح واحد من هنا ال shift rule
+
+409
+00:31:44,470 --> 00:31:49,430
+جالك بدك تزود هنا واحد على ال two limits okay فاش
+
+410
+00:31:49,430 --> 00:31:54,470
+مشكلة طرحنا واحد فوق هايهم التلاتة هدولة بنغيرهم
+
+411
+00:31:54,470 --> 00:32:01,510
+بحيث أنه أصبحت I من واحد ل N زائد واحد وهنا صارت I
+
+412
+00:32:02,620 --> 00:32:06,320
+ناقص واحد زائد واحد راحوا مع بعض عشان أصل الان
+
+413
+00:32:06,320 --> 00:32:12,580
+مبدئيين اللي جوا زبط هدول ضلوا عامليني مشكلة
+
+414
+00:32:12,580 --> 00:32:18,560
+splitting صح
+
+415
+00:32:18,560 --> 00:32:22,860
+splitting نعمل splitting خلاص عشان أعمل splitting
+
+416
+00:32:22,860 --> 00:32:25,920
+بدنا نقول أن ال term تبع n زائد واحد هذا بديش إياه
+
+417
+00:32:25,920 --> 00:32:31,100
+أنا بديها ال n بسفإذا N زائد واحد بخليها كلها ال
+
+418
+00:32:31,100 --> 00:32:36,500
+summation ل N فقط بيبقى term واحد إضافي حطه كأنصر
+
+419
+00:32:36,500 --> 00:32:41,040
+عوّد فيه تعويض يعني رسمي عوّد عوّد اللي هو آخر
+
+420
+00:32:41,040 --> 00:32:43,940
+عنصر اللي هو N زائد واحد هذه N زائد واحد بديش يها
+
+421
+00:32:43,940 --> 00:32:49,240
+N زائد واحد بديها N يعني كأنه بيبقى عندك عنصر
+
+422
+00:32:49,240 --> 00:32:54,200
+الأخير لحاله فهي ل N من واحد ل N تمام خلصنا
+
+423
+00:32:54,200 --> 00:32:59,550
+مشكلتنا زائد آخر عنصراللي هو من in زائد واحد ل in
+
+424
+00:32:59,550 --> 00:33:03,670
+زائد واحد يعني هو عنصر واحد فعليا بس هو عنصر واحد
+
+425
+00:33:03,670 --> 00:33:07,470
+فقط هو هذا عوض مافيه تعويض مباشر مدام عنصر عوضه
+
+426
+00:33:07,470 --> 00:33:11,030
+خلصنا بدأ ال I حط in زائد واحد هاي I حط in زائد
+
+427
+00:33:11,030 --> 00:33:17,170
+واحد هاي ال term انضاف خلصنا ال function خلصنا ال
+
+428
+00:33:17,170 --> 00:33:24,450
+upper دل ال lower bound اللي هي قيمة ال J لسه مش
+
+429
+00:33:24,450 --> 00:33:24,910
+متفقة
+
+430
+00:33:28,010 --> 00:33:31,950
+نفس الفكرة ما هدى عملية splitting بدك تضيف صفر
+
+431
+00:33:31,950 --> 00:33:35,470
+يعني عملية عكسية لل splitting بدك تضيف صفر و تنقص
+
+432
+00:33:35,470 --> 00:33:39,790
+صفر او تنقص عند الصفر عند ال index صفر لل function
+
+433
+00:33:39,790 --> 00:33:46,490
+هضيفها خلينا نخلص من هدول فهضيفها و تطرحها okay
+
+434
+00:33:46,490 --> 00:33:52,300
+ضفناها و طرحناهاهيدفناها و طرحناها كويس اللي
+
+435
+00:33:52,300 --> 00:33:54,800
+بالسالب هذي هناخدها على الطرف التاني خلاص يفرزوا
+
+436
+00:33:54,800 --> 00:33:59,420
+بعض هدول هنجمحهم مع بعض عشان يبقى A R to the bar 0
+
+437
+00:33:59,420 --> 00:34:03,560
+زائد ال summation فصارت العملية أكسية لهذا ال
+
+438
+00:34:03,560 --> 00:34:08,580
+splitting هنا من صفر هايها من صفر صفر لصفر يعني
+
+439
+00:34:08,580 --> 00:34:12,220
+أنا بتكلم عن answer واحد من صفر لصفر و بعدين من
+
+440
+00:34:12,220 --> 00:34:16,380
+واحد to N مجموحهم مع بعض من نفس ال function من صفر
+
+441
+00:34:16,380 --> 00:34:16,680
+to N
+
+442
+00:34:20,330 --> 00:34:23,050
+بس احنا .. لحظة طول ما احنا ماشيين انا من الاساس
+
+443
+00:34:23,050 --> 00:34:26,410
+فاهم انا اش بده اروح احنا فاهمين من الاول اش بدنا
+
+444
+00:34:26,410 --> 00:34:31,830
+نعمل جبنا العنصر N زائد واحد بدلالة N و بعدين من
+
+445
+00:34:31,830 --> 00:34:37,610
+ال N زائد واحد بدي اطلع ال summation تبع ال Nبس
+
+446
+00:34:37,610 --> 00:34:42,330
+إذا الفكرة هذي ال strategy هذي بواضحة عندك كل
+
+447
+00:34:42,330 --> 00:34:46,230
+القطوات هذي انت عارف ليش عملناها اصلا لأن وصلت انا
+
+448
+00:34:46,230 --> 00:34:50,450
+اول شغل بده واحد ال function عملنا shift بده واحد
+
+449
+00:34:50,450 --> 00:34:54,970
+ال upper عملنا عملية عكسية لل splitting تعويض لاخر
+
+450
+00:34:54,970 --> 00:34:59,690
+عنصر بدنا ال lower ضفنا عنصر و بينفعش اضيفه و اسكت
+
+451
+00:34:59,690 --> 00:35:04,870
+ضفته و طرحته هاي التلت معالجات اللي عملناهم
+
+452
+00:35:04,870 --> 00:35:10,090
+ماعملناش اش غيرهمفمايغركاش انه اللي زي ما بيقوله
+
+453
+00:35:10,090 --> 00:35:13,210
+أخد شوية وقت لأنه أنا بفسر فيزيا ده عن اللزومش
+
+454
+00:35:13,210 --> 00:35:19,550
+أكتر وانصلنا ووصلنا زي ما قلنا لها دي هايها خلاص
+
+455
+00:35:19,550 --> 00:35:22,590
+من صفر زائد واحد وخلصنا هذا ال terms فهنا زبطت
+
+456
+00:35:22,590 --> 00:35:26,030
+هايها صارت من صفر to N لنفس ال function ال
+
+457
+00:35:26,030 --> 00:35:32,360
+function واحدة هذه قيمة S هذه نفسهاS اللي بدأنا
+
+458
+00:35:32,360 --> 00:35:35,340
+فيها في الأول ال summation الأصلي ال summation
+
+459
+00:35:35,340 --> 00:35:41,300
+الأصلي تمام فانت أصبح عندك S زائد ال term اللي
+
+460
+00:35:41,300 --> 00:35:45,020
+انفرز عندك جديد اللي هم مجموعة الأثنين ال upper و
+
+461
+00:35:45,020 --> 00:35:47,340
+ال lower لما أخدناها لما فصلناها لحالها لما
+
+462
+00:35:47,340 --> 00:35:52,460
+طرحناها لحالها لما طرحناها لحالها تمام مجرد تصفية
+
+463
+00:35:52,460 --> 00:35:55,300
+للموضوع عشان يصلي عندي ال S و ال S اللي يدير بالك
+
+464
+00:35:55,300 --> 00:35:59,880
+هي كلها تساوي R في Sفمعنا ذلك كله بده ينطرح بده
+
+465
+00:35:59,880 --> 00:36:05,900
+ينقسم على
+
+466
+00:36:05,900 --> 00:36:10,580
+الطرف الآخر لازم هذا ناقصه على الطرف التاني عشان
+
+467
+00:36:10,580 --> 00:36:15,760
+تصير RS ناقص S فR ناقص واحد نقسمها على الطرف اللي
+
+468
+00:36:15,760 --> 00:36:21,240
+موجود عندك صار عندك closed loopأصبحت ال S اللي
+
+469
+00:36:21,240 --> 00:36:24,520
+احنا عارفين ان هي ال summation هي فعليا تساوي ال
+
+470
+00:36:24,520 --> 00:36:27,480
+constant اللي انت بتحكي عنه اللي بدأت فيه ال
+
+471
+00:36:27,480 --> 00:36:32,460
+constant مضروب كله في R to the power N زائد واحد
+
+472
+00:36:32,460 --> 00:36:37,740
+كله ناقص واحد على R ناقص واحد على R ناقص واحد
+
+473
+00:36:37,740 --> 00:36:42,940
+هلاحظ انه الكلام دهمظبوط دائما إلا في حالة واحدة
+
+474
+00:36:42,940 --> 00:36:49,200
+بيكون في عندك vanish ل ال determinant
+
+475
+00:36:49,200 --> 00:36:54,380
+ل المقام طيب عند R بتساوي واحد طيب فإيش بدي أسوي
+
+476
+00:36:54,380 --> 00:36:58,140
+عند R بتساوي واحد عوض مباشرة لأنه هتصير زي Euler
+
+477
+00:36:58,140 --> 00:37:04,840
+لاحظ لما هذه تصير واحد هذه مش هذه صارت واحد okay
+
+478
+00:37:04,840 --> 00:37:10,270
+صارت واحد هي و هنعوضها هنا هي واحدمعنى ذلك أنه
+
+479
+00:37:10,270 --> 00:37:12,810
+جدّاش ال power، ال power جدّاش مش هتفرج، كلها
+
+480
+00:37:12,810 --> 00:37:19,330
+شيلها ال I خمسة، ال I صفر، ال I عشرة، ال I مية، ال
+
+481
+00:37:19,330 --> 00:37:22,630
+I مليون، one million، هتفرج معاك و مش هتفرج معاك،
+
+482
+00:37:22,630 --> 00:37:26,990
+هتظل دايما واحد، فشيلها كاملة، فبتظل ايه؟ A في
+
+483
+00:37:26,990 --> 00:37:34,210
+واحد، طب ال A بالنسبالي constant، مش constant؟ A
+
+484
+00:37:34,210 --> 00:37:39,160
+بالنسبالي ال index I هي constant، طلّحها براصار
+
+485
+00:37:39,160 --> 00:37:45,020
+عملية summation للواحد بعدد مرات كأنك بتقول واحد
+
+486
+00:37:45,020 --> 00:37:49,600
+زائد واحد زائد واحد أكم مرة من صفر to n
+
+487
+00:37:53,110 --> 00:37:55,650
+من صفر to n عند صفر او عند واحد او عند اتنين او
+
+488
+00:37:55,650 --> 00:37:59,370
+عند التلاتة اربع مرات و انا بقول عند التلاتة فهنا
+
+489
+00:37:59,370 --> 00:38:02,910
+لما اقول عند ال n فبتصير n زائد واحد مضربة في ايش
+
+490
+00:38:02,910 --> 00:38:06,710
+في ال a اللي طلعناها constant فهذه الحالة الوحيدة
+
+491
+00:38:06,710 --> 00:38:10,950
+عند r بتساوي واحد لان هنا مش هيش تغيب معاك هنا مش
+
+492
+00:38:10,950 --> 00:38:16,370
+هيش هتبع undefined عند ال ايش؟بالظبط اه عند ال
+
+493
+00:38:16,370 --> 00:38:18,890
+numerator و denominator عند ال denominator zero
+
+494
+00:38:18,890 --> 00:38:24,010
+اكيد هتكون vanished ف undefined ففي الحالة هذه هي
+
+495
+00:38:24,010 --> 00:38:26,150
+الحالة الوحيدة اللي لأ بنعوض عليها بشكل مباشر
+
+496
+00:38:26,150 --> 00:38:33,590
+بنعوض عنها بصورة مباشرة تمام طيب في نستد زي ما كان
+
+497
+00:38:33,590 --> 00:38:36,470
+في نستد integration لما يكون عندك double
+
+498
+00:38:36,470 --> 00:38:39,430
+integration او اكتر برضه نفس الكلام موجود علنا هنا
+
+499
+00:38:39,430 --> 00:38:42,850
+ممكن يكون عندك اكتر من integration
+
+500
+00:38:44,230 --> 00:38:47,350
+زي مثلا ال summation اللي عندي هنا من summation ل
+
+501
+00:38:47,350 --> 00:38:51,770
+I و ل J إيش كنت تعمل في ال integration دايما ال
+
+502
+00:38:51,770 --> 00:38:54,850
+integration الداخلية بتعمله في الأول بس تاخد بالك
+
+503
+00:38:54,850 --> 00:39:00,970
+من ال constants لما أقول ال summation الداخلي هذا
+
+504
+00:39:00,970 --> 00:39:05,950
+لمين؟ ل J يعني I بالنسباله constant بتطلحها برا
+
+505
+00:39:05,950 --> 00:39:10,670
+هنابس بتطلعهاش برا نهائيا لأنه في summation لها
+
+506
+00:39:10,670 --> 00:39:13,370
+فبنطلعها بهذا الشكل اننا عملها group لحالها
+
+507
+00:39:13,370 --> 00:39:16,770
+بنطلعها برا هنا عشان نسهل على حالنا ال summation
+
+508
+00:39:16,770 --> 00:39:19,370
+هنا من واحد لتلاتة فبتكلم عن واحد زي اتنين زي
+
+509
+00:39:19,370 --> 00:39:24,290
+اتنين تلاتة هي ستة الستة constant طلعها برا
+
+510
+00:39:24,290 --> 00:39:28,090
+طلعناها برا بيضل عندك ال I من واحد لاربعة خلصت
+
+511
+00:39:28,090 --> 00:39:32,150
+انتهت الجثة بالظبط نفس فكرة إذا متذكرين ل
+
+512
+00:39:32,150 --> 00:39:35,680
+quantification ل quantifiersمتذكرين ال
+
+513
+00:39:35,680 --> 00:39:37,840
+quantifiers؟ لما يكون فيه عندك أكتر من ال
+
+514
+00:39:37,840 --> 00:39:40,780
+quantifier بدك تحدد مين ال bound و مين ال free
+
+515
+00:39:40,780 --> 00:39:43,900
+وهنا نفس الكلام حددنا مين ال bound و مين ال free
+
+516
+00:39:43,900 --> 00:39:45,940
+ال bound و ال free فهنا بالنسبالي ال summation
+
+517
+00:39:45,940 --> 00:39:57,250
+الأولى ال j bound ال I free طلحها free طلّه تمامزي
+
+518
+00:39:57,250 --> 00:40:00,750
+فكرة ال constant تماما الان ملخص الموضوع ان صار في
+
+519
+00:40:00,750 --> 00:40:06,910
+عندك مجموعة shortcut expressions او closed form
+
+520
+00:40:06,910 --> 00:40:11,230
+جاهزة ممكن نتعامل معها اول واحدة هي ال geometric
+
+521
+00:40:11,230 --> 00:40:15,790
+seriesماعنداش أي مشكلة زي ما قلتلكوا الحلو الوحيد
+
+522
+00:40:15,790 --> 00:40:20,270
+بس اللي بدك تحلها مباشر عند r بتساوي واحد عند r
+
+523
+00:40:20,270 --> 00:40:22,810
+بتساوي واحد فهد ماكنش فيه أنك مشكلة ال constant
+
+524
+00:40:22,810 --> 00:40:26,810
+مضروب في r to the power n زائد واحد كله ناقص واحد
+
+525
+00:40:26,810 --> 00:40:32,830
+على r ناقص واحد وانتهى عند الواحد لأ عند الواحد لأ
+
+526
+00:40:32,830 --> 00:40:36,470
+Euler اتفجنا معه اويلر ماكنش فيه أنه مشكلة ماكنش
+
+527
+00:40:36,470 --> 00:40:41,870
+مهندى مشكلة مع اويلر لما يكون تربيةمش عادي تربيع
+
+528
+00:40:41,870 --> 00:40:45,590
+ففي الحالة دي مشابهة تماما in في in زائد واحد
+
+529
+00:40:45,590 --> 00:40:51,970
+هنضيف بس في اتنين in ناقص زائد واحد برضه على ستة
+
+530
+00:40:51,970 --> 00:40:58,610
+على تلاتة بنقسم على ستة كويس فهدي للتربيع اذا كان
+
+531
+00:40:58,610 --> 00:41:03,830
+تكييب هدي تربيع لحظة
+
+532
+00:41:04,420 --> 00:41:08,920
+إذا كانت تتكلم عن كتر كعيب و بدك تجمع معناته نفسها
+
+533
+00:41:08,920 --> 00:41:12,060
+إذا كان في Euler كان بيقول in في in زائد واحد على
+
+534
+00:41:12,060 --> 00:41:15,940
+اتنين هنا بتصير in تربية في in زائد واحد تربية على
+
+535
+00:41:15,940 --> 00:41:22,620
+اربعة اللي هو اتنين تربية طبعا في closed forms
+
+536
+00:41:22,620 --> 00:41:26,940
+كتيرة على جد هدولة لأن هدول واضحين مش محتاجين تحفظ
+
+537
+00:41:26,940 --> 00:41:32,920
+فيهم كتيرمش محتاج حفظ فيهم كتير فمافيش تبسط من هيك
+
+538
+00:41:32,920 --> 00:41:37,460
+بكفي على جد هدولة و هنستخدمهم بس فى شوية الحيال
+
+539
+00:41:37,460 --> 00:41:43,300
+بتاعة الأسئلة اللى ممكن تيجي زى سؤال زى هذا تربية
+
+540
+00:41:43,300 --> 00:41:47,760
+حقيقة تربية عادية جدا اللى هى مجرد ايه عشان n فى n
+
+541
+00:41:47,760 --> 00:41:53,120
+زائد 1 مضروب فى 2n زائد 1 على 6 تمام لكن هنا خد
+
+542
+00:41:53,120 --> 00:41:55,980
+بالك من ال limitsهذه اللي هنركز عليها في
+
+543
+00:41:55,980 --> 00:42:01,220
+الliterics هقولك انا لأ من خمسين لمية انا مقولتش
+
+544
+00:42:01,220 --> 00:42:04,800
+من صفر ولا من واحد زي ال form نفسه طب في الحلقة دي
+
+545
+00:42:04,800 --> 00:42:07,700
+بدك تعمل splitting splitting معناته بدك تحط هذا
+
+546
+00:42:07,700 --> 00:42:12,800
+term لحاله يكون واضح فبتحطها من واحد لمية هو عبارة
+
+547
+00:42:12,800 --> 00:42:15,920
+عن من واحد لتسعة واربعين ومن خمسين لمية هاي اللي
+
+548
+00:42:15,920 --> 00:42:19,540
+بديها خده على الطرف التاني او خدها دي نقولها على
+
+549
+00:42:19,540 --> 00:42:22,360
+الطرف التاني بالسالب وهد صارت بدية من واحد وهد
+
+550
+00:42:22,360 --> 00:42:26,480
+بدية من واحد مظبوط خلاص مش مشكلةبس بتتغير ال n في
+
+551
+00:42:26,480 --> 00:42:32,000
+كل مرة من المرات عشان تتعود ما هنا بدأت ال n ب 100
+
+552
+00:42:32,000 --> 00:42:37,360
+فبتبدأ ب 100 و بتكمل ال n تبعت 100 هنا 49 فبتبدأ ب
+
+553
+00:42:37,360 --> 00:42:44,340
+49 زائد 1 و 2 في 49 زائد 1 و بتكمل جسمها على 6
+
+554
+00:42:44,340 --> 00:42:50,180
+طلعنا نتائجنا جيد الآن أخر شغل بتكلم عنها هي ال
+
+555
+00:42:50,180 --> 00:42:53,860
+cardinalityهي جزئية ال cardinality و بدنا ناخد
+
+556
+00:42:53,860 --> 00:42:57,020
+بالنا لإنه بدنا نطلع التعريفين قبل ما ننهي موضوع
+
+557
+00:42:57,020 --> 00:42:59,540
+ال summation لإنه خلاص بدنا ننهي موضوع الآن ال
+
+558
+00:42:59,540 --> 00:43:05,020
+summation بشكله الكامل و بتضل جزئية وحيدة هي ال
+
+559
+00:43:05,020 --> 00:43:08,300
+cardinality امتى انا بقدر اقول ان ال sets ال
+
+560
+00:43:08,300 --> 00:43:12,080
+cardinality بتاعتهم متشابهة طبعا إذا كان finite
+
+561
+00:43:12,080 --> 00:43:15,960
+فاش مشكلةبدي اشوف جديش عدد ال elements هنا و جديش
+
+562
+00:43:15,960 --> 00:43:18,060
+عدد ال elements هنا و اتكلمنا عنها سابقا ماكانش اي
+
+563
+00:43:18,060 --> 00:43:22,220
+في مشكلة اطلاقا بس اذا كانت to infinite او
+
+564
+00:43:22,220 --> 00:43:27,560
+infinite sets كيف هتتعامل معها infinite set ال
+
+565
+00:43:27,560 --> 00:43:30,500
+cardinality جديش و كيف بجد رجلي منه متساوي لو مش
+
+566
+00:43:30,500 --> 00:43:33,880
+متساوية فهنا هنتكلم في هذا الموضوع زي ما قلنا a و
+
+567
+00:43:33,880 --> 00:43:39,020
+b finite الجثة سهلة بشوف عددهم هنا و عددهم هنا و
+
+568
+00:43:39,020 --> 00:43:44,870
+انتهى الموضوعلكن إذا كانوا infinite أول شغلة بدك
+
+569
+00:43:44,870 --> 00:43:48,290
+تفحصها لإن بعد ال set احنا أخدنا ال function إذا
+
+570
+00:43:48,290 --> 00:43:50,710
+كانت ال two sets هدولة بقدر أقول إن ال relation
+
+571
+00:43:50,710 --> 00:43:52,370
+between them أو ال function between them هي
+
+572
+00:43:52,370 --> 00:43:59,650
+bijection فهم متساويتين bijection
+
+573
+00:43:59,650 --> 00:44:03,610
+a و b في علاقة bijection between them معناه ذلك إن
+
+574
+00:44:03,610 --> 00:44:06,170
+كل واحدة ممكن تكون domain والتانية تكون codomain
+
+575
+00:44:06,170 --> 00:44:09,270
+والعكس صحيح ممكن تكون التانية هي ال domain والأولى
+
+576
+00:44:09,270 --> 00:44:13,210
+هي ال codomain لهابمعنى one to one و on to في نفس
+
+577
+00:44:13,210 --> 00:44:18,150
+الوقت إذا فعلا ال relation أو ال function بينهم
+
+578
+00:44:18,150 --> 00:44:21,970
+بتحقق هذا الكلام بيجيكشن بقول على طول إنهم بيسووا
+
+579
+00:44:21,970 --> 00:44:27,710
+بعض حتى لو كانوا infinite حتى لو كانوا infinite
+
+580
+00:44:27,710 --> 00:44:32,830
+setتمام في الحالة هذه بدنا نفهم حاجة مهمة امتى
+
+581
+00:44:32,830 --> 00:44:35,710
+بقدر اقول ان ال function بقدر اتعامل معها بهذا
+
+582
+00:44:35,710 --> 00:44:40,370
+الشكل البسيط ال 6 هذي اني اقول والله اه تنازلا او
+
+583
+00:44:40,370 --> 00:44:43,710
+تجاوزا بقدر اعدها و اقول ان هي فيه bijection خلاص
+
+584
+00:44:43,710 --> 00:44:48,670
+معناته cardinality معروفة كلمة cardinality معناته
+
+585
+00:44:48,670 --> 00:44:52,570
+انا بتكلم عن عدد elements معنى ذلك انه في الحالة
+
+586
+00:44:52,570 --> 00:44:57,130
+هذه بدنا نحدد countable و uncountable معدود و غير
+
+587
+00:44:57,130 --> 00:45:03,490
+معدودالمعدود و غير المعدود هل بقدر اقول ان ال set
+
+588
+00:45:03,490 --> 00:45:09,170
+اللي جدامي هي countable set بمعنى انه بقدر اعد ال
+
+589
+00:45:09,170 --> 00:45:14,730
+elements حتى لو to infinity هذا الكلام يتحقق في
+
+590
+00:45:14,730 --> 00:45:20,560
+حالة واحدة إذا كان هيfinite ماعندي مشكلة فيها صحيح
+
+591
+00:45:20,560 --> 00:45:23,140
+اذا finite ماعندي اي مشكلة بقول عليها countable
+
+592
+00:45:23,140 --> 00:45:28,140
+لأنه finite محدودة يعني بتقدر تعدها هتغلبك بس ممكن
+
+593
+00:45:28,140 --> 00:45:31,620
+حتى واحدة يحدها تمسكهم و تعدهم ماعندكش اي مشكلة
+
+594
+00:45:31,620 --> 00:45:35,880
+دخلهم للكمبيوتر بيعدلك اياهم is a finite لكن
+
+595
+00:45:35,880 --> 00:45:41,160
+otherwise انت مش جادر تعدهم ك natural number ك
+
+596
+00:45:41,160 --> 00:45:46,130
+natural number لأ بتقول لأفينيت او مش فينيت هنا
+
+597
+00:45:46,130 --> 00:45:49,670
+اللي عنده فينات سهلة لكن اذا ماكنتش فينيت يكفي
+
+598
+00:45:49,670 --> 00:45:56,590
+انها تكون بتعمل بيجيكشن مع ال natural number اذا
+
+599
+00:45:56,590 --> 00:46:01,590
+بتعمل بيجيكشن مع ال natural number سميهاcountable
+
+600
+00:46:01,590 --> 00:46:09,050
+قابلة للعدل بمعنى ان بتقدر تعد عناصرها وفقا لعناصر
+
+601
+00:46:09,050 --> 00:46:12,030
+ال natural number ال natural number كيف بتعدها ك
+
+602
+00:46:12,030 --> 00:46:16,110
+integers صح؟ معناه ذلك ان هي واحد او صفر واحد
+
+603
+00:46:16,110 --> 00:46:24,250
+اتنين تلاتة اربعة اذا في المقابل نفس المقابلها ست
+
+604
+00:46:24,250 --> 00:46:30,540
+بقدرأقول إن هي bijection معها بمعنى إن الصفر هذا
+
+605
+00:46:30,540 --> 00:46:34,860
+يقابل عنصر integer و الواحد يقابل عنصر integer
+
+606
+00:46:34,860 --> 00:46:37,100
+بحيث إنه ممكن نحطه ك index
+
+607
+00:46:41,270 --> 00:46:45,030
+لحظة ك index فهنا صارت كأنك بتتكلم عن ال function
+
+608
+00:46:45,030 --> 00:46:48,010
+اللي حكينا عنها bijection بين ال natural number
+
+609
+00:46:48,010 --> 00:46:51,070
+وال set اللي بدنا نجيسها هي countable ولا
+
+610
+00:46:51,070 --> 00:46:59,290
+uncountable والله إذا قدرنا نحط ال index لها لكل
+
+611
+00:46:59,290 --> 00:47:03,470
+element فيها وضلت متوافقة bijection مع ال index
+
+612
+00:47:03,470 --> 00:47:09,590
+تبعها بقول عنها خلاص هي countable هي مقابلة موازية
+
+613
+00:47:09,590 --> 00:47:14,790
+لل natural numberبنسميها countable طبعا في أنثية
+
+614
+00:47:14,790 --> 00:47:18,590
+كتير او في أنثية كتير زي ال natural number نفسها
+
+615
+00:47:18,590 --> 00:47:24,110
+رغم ان هي to infinity بس countable معدودة ليش؟
+
+616
+00:47:24,110 --> 00:47:27,990
+لأنه بقدر اعدها بالطريقة العد التقليدية صفر واحد
+
+617
+00:47:27,990 --> 00:47:32,170
+اتنين تلاتة اي six بتقدر تعد عناصرها بهذا الشكل
+
+618
+00:47:32,170 --> 00:47:39,110
+countable طيب ال z حتى ال integers لأن انت عارف ان
+
+619
+00:47:39,110 --> 00:47:42,930
+ال integers هي اتنين من ال naturalكويس فبتقدر
+
+620
+00:47:42,930 --> 00:47:47,610
+تسميها واحد اتنين تلاتة اربعة خمسة اتعدها لأ
+
+621
+00:47:47,610 --> 00:47:53,090
+uncountable لأنه بين كل عنصر عنصر في عدد النهائي
+
+622
+00:47:53,090 --> 00:47:57,930
+من العناصر جوا مش هتعرف تعطيه indicesمش هتقدر
+
+623
+00:47:57,930 --> 00:48:01,910
+تعطيه index ففي الحلقة هذه هتكون الأمور كتير صعبة
+
+624
+00:48:01,910 --> 00:48:05,590
+عندك انك تتعامل مع ال real number لأنه فيها كسور
+
+625
+00:48:05,590 --> 00:48:10,110
+كيف ده تحطها bijection مع integers اللي هي ال
+
+626
+00:48:10,110 --> 00:48:13,850
+natural number مصبوطوش مش هيقابلوا بعض ال index بس
+
+627
+00:48:13,850 --> 00:48:18,270
+بياخد ال integer بس أكيد أكيد طبعا انت بتقدر تقول
+
+628
+00:48:18,270 --> 00:48:20,650
+العنصر الأول العنصر التاني بتقدرش تقول العنصر
+
+629
+00:48:20,650 --> 00:48:23,460
+اتنين و نصمافيش حاجة اسمها عنصر اتنين اتنين اتنين
+
+630
+00:48:23,460 --> 00:48:25,340
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+631
+00:48:25,340 --> 00:48:29,140
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+632
+00:48:29,140 --> 00:48:35,100
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+633
+00:48:35,100 --> 00:48:36,760
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+634
+00:48:36,760 --> 00:48:37,080
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+635
+00:48:37,080 --> 00:48:40,300
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+636
+00:48:40,300 --> 00:48:49,480
+اتنين اتنين
+
+637
+00:48:55,360 --> 00:48:59,180
+subset من ال natural number طب هذا عدد لانهاء من
+
+638
+00:48:59,180 --> 00:49:05,040
+ال subsets بتقدر تطلع عدد لانهاء من ال subsets ف
+
+639
+00:49:05,040 --> 00:49:09,660
+uncountable هنا بتصير تمام فإذا نقدر منهي نقول ان
+
+640
+00:49:09,660 --> 00:49:16,840
+ال countable هي كل شيء معدود بقدر أعده زي ال zوحدة
+
+641
+00:49:16,840 --> 00:49:20,040
+منهم اللي هي ال integers لإنه integers معدودة بقدر
+
+642
+00:49:20,040 --> 00:49:24,640
+أعدها هي countable بنبقى بقول إن كل ordered pairs
+
+643
+00:49:24,640 --> 00:49:29,720
+كل برضه الأزواج المرتبة إذا كانت natural number
+
+644
+00:49:29,720 --> 00:49:35,970
+فهي countable أما إذا كانت real numberuncountable
+
+645
+00:49:35,970 --> 00:49:40,170
+و لايمكن تقدر تعدها و لايمكن تقدر تعدها انت اصلا
+
+646
+00:49:40,170 --> 00:49:45,090
+بين الصفر و الواحد يعني عارف ال interval بين الصفر
+
+647
+00:49:45,090 --> 00:49:48,210
+و الواحد عدل للنهائي هذه uncountable رغم ان انا
+
+648
+00:49:48,210 --> 00:49:51,910
+بتكلم عن يدوب جزء بسيط فيها يدوب جزء بسيط داخل ال
+
+649
+00:49:51,910 --> 00:49:55,350
+interval اللى موجودة عندنا فهنا uncountable رغم ان
+
+650
+00:49:55,350 --> 00:50:00,190
+انا بتكلم real number لان عدد لنهائي هتحط فاصلة و
+
+651
+00:50:00,190 --> 00:50:03,570
+جيس وراها عدد لنهائي من ال partitions اللى ممكن
+
+652
+00:50:03,570 --> 00:50:10,030
+تحطهامن دقة للرقم العشرى عدد ال .. طب الدجوز صفر
+
+653
+00:50:10,030 --> 00:50:14,730
+تسعة تسعة تسعة لإمتى لأ
+
+654
+00:50:14,730 --> 00:50:17,230
+لسه غير صفر تسعة تسعة تسعة لإمتى لإمتى لأ لسه غير
+
+655
+00:50:17,230 --> 00:50:18,090
+صفر تسعة تسعة تسعة لإمتى لإمتى لإمتى لإمتى لإمتى
+
+656
+00:50:18,090 --> 00:50:18,430
+لإمتى لإمتى لإمتى لإمتى لإمتى لإمتى لإمتى لإمتى
+
+657
+00:50:18,430 --> 00:50:18,890
+لإمتى لإمتى لإمتى لإمتى لإمتى لإمتى لإمتى لإمتى
+
+658
+00:50:18,890 --> 00:50:19,450
+لإمتى لإمتى لإمتى لإمتى لإمتى لإمتى لإمتى لإمتى
+
+659
+00:50:19,450 --> 00:50:25,480
+لإمتى لإمتى لإمتى لإمتى لإمتى لإمتى لو عد على هيك
+
+660
+00:50:25,480 --> 00:50:30,160
+فحتى بين الصفر و الواحد عدد لنهائي من الاعداد فهذه
+
+661
+00:50:30,160 --> 00:50:33,060
+uncountable فاخدنا هنا ال countable و ال
+
+662
+00:50:33,060 --> 00:50:39,620
+uncountable و عرفنا نفس ال cardinality و لا لأ اذا
+
+663
+00:50:39,620 --> 00:50:43,780
+كان finite فاش مشكلة فيها بتعد هدول بتعد هدول
+
+664
+00:50:43,780 --> 00:50:47,730
+بتعرف اما اذا كانت infinite setزي ما قلتلك بتعملها
+
+665
+00:50:47,730 --> 00:50:50,670
+bijection أو بتقارنها بال natural number إذا بتقدر
+
+666
+00:50:50,670 --> 00:50:53,950
+تعدها زي ال natural number فهي countable otherwise
+
+667
+00:50:53,950 --> 00:50:59,550
+زي ال real numbers واضحة جدا أن هذه uncountable
+
+668
+00:50:59,550 --> 00:51:06,230
+تمام هيا نكون خلصنا الجزء تبعناه المرة القادمة لسه
+
+669
+00:51:06,230 --> 00:51:08,430
+عندنا ال matrices عندنا ال matrices لسه
+
+670
+00:51:10,970 --> 00:51:14,910
+لأ المرة القادمة هناخد مراجعة ان شاء الله تعالى
+
+671
+00:51:14,910 --> 00:51:18,790
+هشوف .. ناخد شوية matrices و هنعمل مراجعة هنعمل
+
+672
+00:51:18,790 --> 00:51:21,970
+شوية أسئلة المرة الأخيرة ماخدناش أسئلة تمام بنعمل
+
+673
+00:51:21,970 --> 00:51:25,210
+شوية أسئلة ان شاء الله تعالى و بنحدد للأسبوع اللي
+
+674
+00:51:25,210 --> 00:51:28,850
+ورا موقع لل quiz أخدنا كمية كويسة بدنا .. محتاجين
+
+675
+00:51:28,850 --> 00:51:30,790
+نعمل شوية quizzة يعطيكوا العفو يا شباب
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1DXhPKvs1dE_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1DXhPKvs1dE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..957336382f9309a4656ea8f6c54f4b6328bc47d6
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1DXhPKvs1dE_postprocess.srt
@@ -0,0 +1,2808 @@
+1
+00:00:05,110 --> 00:00:08,130
+بسم الله الرحمن الرحيم، يعطيكوا العفو يا شباب،
+
+2
+00:00:08,130 --> 00:00:11,050
+نكمل اليوم إن شاء الله تعالى الجزء اللي كان
+
+3
+00:00:11,050 --> 00:00:15,790
+متبقيناه في ال .. ال .. ال growth و ال order of
+
+4
+00:00:15,790 --> 00:00:20,490
+growth عشان نشوف كيف بنستخدم المعلومات هذه في حساب
+
+5
+00:00:20,490 --> 00:00:24,070
+ال complexity للأكواد، لل algorithm اللي أخدناها
+
+6
+00:00:24,070 --> 00:00:26,670
+من الأسبوع اللي فات، اللي كنا بنتكلم فيه عن ال
+
+7
+00:00:26,670 --> 00:00:30,120
+pseudocodeبغض نوفر طبعا إيش اللغة اللي انت
+
+8
+00:00:30,120 --> 00:00:34,440
+هتستخدمها في النهاية انت عارف ان في عندك code و
+
+9
+00:00:34,440 --> 00:00:36,980
+بدك تحسبله ال complexity طيب جابر ما نروح نخد في
+
+10
+00:00:36,980 --> 00:00:40,500
+ال complexity كان ضروري جدا نفهم انه عشان أحسب
+
+11
+00:00:40,500 --> 00:00:43,820
+complexity فانا فعليا بتعامل مع ال algorithm اللي
+
+12
+00:00:43,820 --> 00:00:48,260
+هو ال code كأنه function function في مين؟ function
+
+13
+00:00:48,260 --> 00:00:51,760
+فيفي ال inputs function في ال inputs مدام function
+
+14
+00:00:51,760 --> 00:00:55,600
+في ال inputs معناته بهمني جدا أدرس ال functions
+
+15
+00:00:55,600 --> 00:00:58,620
+نفسها وإيش أنواع ال functions وكيف أميز بين ال
+
+16
+00:00:58,620 --> 00:01:01,720
+functions وبعضها من حيث ال order of growth عشان
+
+17
+00:01:01,720 --> 00:01:07,380
+بعدين لما نحطالأكواد بصفة ال functionality بتاعتهم
+
+18
+00:01:07,380 --> 00:01:10,980
+أقدر أقارن بينهم هذه .. هذا كانت الفكرة الأساسية
+
+19
+00:01:10,980 --> 00:01:14,580
+في الموضوع خلصنا الأكواد و انتهينا من هذا الموضوع
+
+20
+00:01:14,580 --> 00:01:17,460
+انه و الله في حاجة اسمها pseudocode و طلعنا ..
+
+21
+00:01:17,460 --> 00:01:20,520
+شفنا إيش ال .. ال .. ال statement سبعته أخدنا أكم
+
+22
+00:01:20,520 --> 00:01:24,740
+من مثال بدأنا نتكلم في مين؟ في ال functions و ال
+
+23
+00:01:24,740 --> 00:01:28,480
+order و في growth لل functions ليش الكلام هذا؟
+
+24
+00:01:28,480 --> 00:01:31,200
+لأنه مش أنا معني بال functions ك functions لأ أنا
+
+25
+00:01:31,200 --> 00:01:34,770
+معني فيها لأنهاللي جاي اليوم هنتكلم عنه ان كيف
+
+26
+00:01:34,770 --> 00:01:39,310
+اخلي ال code يصبح function فمعناه ذلك بصير اقيص ال
+
+27
+00:01:39,310 --> 00:01:41,490
+functionality بتاعته ال function هت هي اللي بتصير
+
+28
+00:01:41,490 --> 00:01:45,990
+قدامي معيار المقارنة واضحة ليش احنا بنروح ل ..
+
+29
+00:01:45,990 --> 00:01:50,570
+لموضوع ال order of growth لأنه ال code هيمثل as a
+
+30
+00:01:50,570 --> 00:01:56,510
+function ك function طيب ايش ال .. ال .. ال .. ال
+
+31
+00:01:56,510 --> 00:02:00,250
+function value بتاعة ال code هذا هنتكلم فيه بس
+
+32
+00:02:00,250 --> 00:02:04,700
+احنا عارفين ان ال inputال input هي مدخلات ال
+
+33
+00:02:04,700 --> 00:02:08,840
+function هي ال arguments مجموعة ال inputs ال array
+
+34
+00:02:08,840 --> 00:02:14,780
+اللى بدنا ندخلها لل algorithm كمدخلات كويس نكمل
+
+35
+00:02:14,780 --> 00:02:17,660
+اللى كنا اتكلمنا المرة الماضية و كنا جولنا او يمكن
+
+36
+00:02:17,660 --> 00:02:21,380
+مادخلناش الا ال big O المرة الماضية فقط جولنا ان
+
+37
+00:02:21,380 --> 00:02:25,140
+at most big O ايش يعني at most big O يعني لما اقول
+
+38
+00:02:25,140 --> 00:02:32,740
+if هي تساوي او belong to او at mostأي واحدة هكتبها
+
+39
+00:02:32,740 --> 00:02:36,520
+بمش الحال Of if مثلا يعني كأني بقول ان ال function
+
+40
+00:02:36,520 --> 00:02:41,060
+هي دي في أسوأ أحوالها في أكبر order لها هي first
+
+41
+00:02:41,060 --> 00:02:46,140
+order أكبر ممكن تكون أقل أو ممكن تكون أقل ممكن
+
+42
+00:02:46,140 --> 00:02:51,180
+تكون أقل يمكن أنا مش قادر تحديدها exactly بس في
+
+43
+00:02:51,180 --> 00:02:55,040
+أسوأ أحوالها هتكون first order أو في أسوأ أحوالها
+
+44
+00:02:55,040 --> 00:02:58,380
+second orderأو third order اكتب اللي بدكيها بس في
+
+45
+00:02:58,380 --> 00:03:02,500
+النهاية نفهم الفكرة فال big O هي at most بمعنى ان
+
+46
+00:03:02,500 --> 00:03:09,420
+ال function في أسوأ أحوالها هي تربيعية مثلا for
+
+47
+00:03:09,420 --> 00:03:12,700
+example ممكن تكون أقل او ممكن تكون أقل ممكن تكون
+
+48
+00:03:12,700 --> 00:03:15,800
+أقل فاحنا دايما بنشتغل على ال worst case وهذا
+
+49
+00:03:15,800 --> 00:03:19,120
+بتهيألي معلومة أكيد موجودة عندكم احنا في الأكواد
+
+50
+00:03:19,120 --> 00:03:21,780
+بنشتغل على ال worst case في الأسوأ الأحوال لإن انت
+
+51
+00:03:21,780 --> 00:03:25,410
+مش عارف فعليا شكل ال inputs اللي داخل عندكانت
+
+52
+00:03:25,410 --> 00:03:28,310
+المفروض بتعمل generality ل ال code زي ال
+
+53
+00:03:28,310 --> 00:03:30,670
+characteristics اللي أخدناها المرة الماضية و قلنا
+
+54
+00:03:30,670 --> 00:03:32,690
+من أهم ال characteristics .. مجموعة
+
+55
+00:03:32,690 --> 00:03:35,350
+characteristics أخدناها ال generality انه يكون ال
+
+56
+00:03:35,350 --> 00:03:38,890
+code general .. general بغض النظر إيش ال inputs
+
+57
+00:03:38,890 --> 00:03:43,270
+اللي أعطتهيا .. تمام؟ فهذه ال big O .. نبدأ نشوف
+
+58
+00:03:43,270 --> 00:03:47,690
+مجموعة facts عن ال big O ممكن نحتاجها لقدام .. لو
+
+59
+00:03:47,690 --> 00:03:51,920
+قلنا ال Fهي ال function هي belong to او تساوي او
+
+60
+00:03:51,920 --> 00:03:56,380
+at most اكتب اللي بدك ياه مش هتفرج معناه او هي is
+
+61
+00:03:56,380 --> 00:04:02,020
+على طول بمشي الحال big O of G فإذا ال F في أسوأ
+
+62
+00:04:02,020 --> 00:04:10,520
+أحوالها هي من ال order G and G big O of H فحسب ال
+
+63
+00:04:10,520 --> 00:04:13,620
+relation بتاعة ال transitive معناه ذلك ان ال F
+
+64
+00:04:13,620 --> 00:04:19,900
+بالضرورة هتكون big O of Hيعني بهذا الشكل طب لما
+
+65
+00:04:19,900 --> 00:04:26,740
+اقول هذه عبارة عن جي وجي
+
+66
+00:04:26,740 --> 00:04:33,480
+هنا عبارة عن انتر بيعي وقولنا جي big O of H وH هذه
+
+67
+00:04:33,480 --> 00:04:41,640
+تكعيب تمام؟ بمشي الحال هيك صحيح؟ اف big O of G اف
+
+68
+00:04:41,640 --> 00:04:45,500
+هذه ممكن تكون first order بمشي second order اه
+
+69
+00:04:45,500 --> 00:04:51,600
+بمشي برضهماشي، مافيش مشكلة، مدام big O of G، طيب G
+
+70
+00:04:51,600 --> 00:04:55,000
+second order، طيب الـ G هذه اللي هي second order
+
+71
+00:04:55,000 --> 00:04:59,860
+أكيد هتكون big O of H، H كانت second order، بمشي
+
+72
+00:04:59,860 --> 00:05:03,640
+الحال، third order، بمشي الحال، fourth order، بمشي
+
+73
+00:05:03,640 --> 00:05:10,320
+الحال، لأ، بتنفعش big O، احنا قولنا at most، بمعنى
+
+74
+00:05:10,320 --> 00:05:15,950
+في أسوأ أحوالها G، هي هتكون هذا ال ..يا بتسويها يا
+
+75
+00:05:15,950 --> 00:05:18,490
+أقل منها ال G، يا بتسويها أقل منها، فإذا
+
+76
+00:05:18,490 --> 00:05:23,350
+automatically بقدر أستنتج أن F نفسها هي big O of
+
+77
+00:05:23,350 --> 00:05:31,430
+H، صح؟ لأن F حسب التعريف اللي لقناه هنا، هي تربيع
+
+78
+00:05:31,430 --> 00:05:32,110
+فأقل
+
+79
+00:05:35,740 --> 00:05:43,540
+بمشي الحل .. بمشي الحل .. بمشي الحل .. بمشي
+
+80
+00:05:43,540 --> 00:05:45,640
+الحل .. بمشي الحل .. بمشي الحل .. بمشي الحل ..
+
+81
+00:05:45,640 --> 00:05:46,100
+بمشي الحل .. بمشي الحل .. بمشي الحل .. بمشي الحل
+
+82
+00:05:46,100 --> 00:05:46,300
+الحل .. بمشي الحل .. بمشي الحل .. بمشي الحل ..
+
+83
+00:05:46,300 --> 00:05:46,440
+بمشي الحل .. بمشي الحل .. بمشي الحل .. بمشي الحل
+
+84
+00:05:46,440 --> 00:05:46,780
+.. بمشي الحل .. بمشي الحل .. بمشي الحل .. بمشي
+
+85
+00:05:46,780 --> 00:05:47,500
+الحل .. بمشي الحل .. بمشي الحل .. بمشي الحل ..
+
+86
+00:05:47,500 --> 00:05:52,610
+بمشي الحل .. بمشي الحل .. بمشي الحل ..الـ function
+
+87
+00:05:52,610 --> 00:05:57,350
+فبتسمي ال code بمسماه تمام حدنا هنشوفه بس احنا
+
+88
+00:05:57,350 --> 00:05:59,990
+الآن بنحدد فقط مجموعة ال facts اللي عندى هنا
+
+89
+00:05:59,990 --> 00:06:04,690
+فtransitivity اه متحققة ال transitivity relation
+
+90
+00:06:04,690 --> 00:06:10,170
+واضحة تماما كويس ال big O لما يكون فيه عندى
+
+91
+00:06:10,170 --> 00:06:16,000
+constant ل ال multiplication بيأثرشيعني تربيع مثلا
+
+92
+00:06:16,000 --> 00:06:20,660
+in تربيع طب خمسة in تربيع تغير ال order مية in
+
+93
+00:06:20,660 --> 00:06:26,060
+تربيع هي تربيعية ضالت تربيعية فحنشوف ال roots و ال
+
+94
+00:06:26,060 --> 00:06:29,420
+log حنشوف ال log ايش بتغير معانا في كل function أو
+
+95
+00:06:29,420 --> 00:06:32,780
+نوع من الأنواع هذه لو افترضنا أن ال F نفسها هي
+
+96
+00:06:32,780 --> 00:06:40,020
+small omega of واحد معناته الآن بدنا نوجف شوية
+
+97
+00:06:40,020 --> 00:06:43,180
+لأنه أصبحنا مضطرين ان نعرف أنواع تانية غير ال big
+
+98
+00:06:43,180 --> 00:06:54,870
+Oفي عنده ال big omega if تساوي big omega of g هذه
+
+99
+00:06:54,870 --> 00:07:01,470
+عكس ال big O فال big O في أسوأ أحوالها هي ال order
+
+100
+00:07:01,470 --> 00:07:09,270
+g هنا لأ في أحسن أحوالها هي g بمعنى إن هي if هنا
+
+101
+00:07:09,270 --> 00:07:11,630
+ال order تبعها g فأعلى
+
+102
+00:07:14,750 --> 00:07:20,450
+عكس ال big O تماما عكس ال big O هنا كنا بنقول if
+
+103
+00:07:20,450 --> 00:07:28,990
+هي نفس order g فأقل فلما بقول هنا in تربية يعني
+
+104
+00:07:28,990 --> 00:07:33,190
+بقول ان هاد ال function هي second order فأقل ممكن
+
+105
+00:07:33,190 --> 00:07:36,710
+تكون first inverse log بمشي ماكولهم أقل من ال
+
+106
+00:07:36,710 --> 00:07:41,810
+second بمشي الحال كويس هنا لأ بالعكس هنا كأني بقول
+
+107
+00:07:41,810 --> 00:07:47,330
+ifو هنا in نفطر التربية يعني كأني بقول إن ال F هذه
+
+108
+00:07:47,330 --> 00:07:54,650
+هي second order فأعلى second third fourth
+
+109
+00:07:54,650 --> 00:07:59,810
+exponential زي ما تطلع power of power power of
+
+110
+00:07:59,810 --> 00:08:04,420
+variable المهم إنه أكبر منال order عكس ال big O
+
+111
+00:08:04,420 --> 00:08:10,240
+هنا أقل طيب تمام او تسويها بالضبط او تسويها ليش
+
+112
+00:08:10,240 --> 00:08:13,660
+لأنه لما بدي اقول ساعتها small omega هذي big omega
+
+113
+00:08:13,660 --> 00:08:18,320
+هذي small omega if strictly أكبر منها ولا تسويها
+
+114
+00:08:18,320 --> 00:08:21,700
+فإذن
+
+115
+00:08:21,700 --> 00:08:26,300
+هذي ممكن نقول عنها أكبر من أو يساوي هذي ممكن
+
+116
+00:08:26,300 --> 00:08:33,210
+تسميها أكبر من وبسهذه ممكن تسميها أقل من أو يساوي
+
+117
+00:08:33,210 --> 00:08:44,250
+و طبعا أكيد في small o ف small o هذه
+
+118
+00:08:44,250 --> 00:08:51,790
+هتكون أقل من هاي أخدنا مجموعة عشان لما نيجي نتكلم
+
+119
+00:08:51,790 --> 00:08:56,580
+عن إيش الليالاعتراض اللي دخل عندي هذا هذا اللي هي
+
+120
+00:08:56,580 --> 00:09:00,140
+ال small omega إيش معناها small omega لو تفهمناها؟
+
+121
+00:09:00,140 --> 00:09:06,700
+إنه إذا كانت F أكبر والزمن أكبر من إيش؟ إيش يعني
+
+122
+00:09:06,700 --> 00:09:11,140
+واحد؟ constant إيش يعني constant؟ يعني هدف فعليًا
+
+123
+00:09:11,140 --> 00:09:16,910
+n to the power صفريعني Zero Order Zero Order يعني
+
+124
+00:09:16,910 --> 00:09:20,310
+ثابت Constant ف Zero Order كلنا عارفين أي شيء
+
+125
+00:09:20,310 --> 00:09:24,950
+تظبّر صفر بنحطه بواحد فعشانك انت عارف مسبقا انه
+
+126
+00:09:24,950 --> 00:09:29,110
+الواحدة دي جاية من فعليا من ال Zero Order هي فعليا
+
+127
+00:09:29,110 --> 00:09:33,870
+جاية من Zero Order بنكتبها واحد تسهيلا لكن احنا
+
+128
+00:09:33,870 --> 00:09:38,010
+كلنا عارفين هي Order Zero فال Order Zero معناته ان
+
+129
+00:09:38,010 --> 00:09:41,910
+انا بتكلم ان ال F دي أكبر من Constantأكبر من
+
+130
+00:09:41,910 --> 00:09:46,010
+constant فرست log اش ما تطلع تطلع بس هي فعليا أكبر
+
+131
+00:09:46,010 --> 00:09:51,070
+من constant تمام لكل ال F إذا كانت هي function
+
+132
+00:09:51,070 --> 00:09:55,410
+أكتر من constant ومجموعة constants A وB هي real
+
+133
+00:09:55,410 --> 00:10:00,030
+numbers بحيث أنه B تكون أكبر أو يسوء صفر بقدر أقول
+
+134
+00:10:00,030 --> 00:10:09,290
+ساعتها A اللي هي A constant مضروب في Fهيكون نفس
+
+135
+00:10:09,290 --> 00:10:15,530
+big O of F زي ما قلنا تربيعية in تربيع طب مليون في
+
+136
+00:10:15,530 --> 00:10:21,010
+in تربيع ايش ال order برضه تربيع مش هيتغير فإذا
+
+137
+00:10:21,010 --> 00:10:24,290
+ايه ايش ما تكون قيمتها هي constant في المعادلة
+
+138
+00:10:24,290 --> 00:10:27,930
+تلتة in تربيع خمسة in تربيع عشرة in تربيع مية in
+
+139
+00:10:27,930 --> 00:10:32,190
+تربيع هتظل المعادلة in general تربيعية فبسميها big
+
+140
+00:10:32,190 --> 00:10:36,500
+O of F of تربيع خلاصمش هيتغير ايش معنى طيب إذا
+
+141
+00:10:36,500 --> 00:10:42,640
+كانت F to the power 1 minus B وB زي ما قولنا أكبر
+
+142
+00:10:42,640 --> 00:10:46,340
+من أو يساوي صفر بي أكبر من أو يساوي صفر معنى ذلك
+
+143
+00:10:46,340 --> 00:10:49,900
+أنه برضه بقدر أقول أن هي big O of F طب هتنحلل
+
+144
+00:10:49,900 --> 00:10:55,280
+الموضوع بي أكبر من صفر يعني أقل قيمة إيه؟ صفر فإذا
+
+145
+00:10:55,280 --> 00:10:59,300
+كانت صفرصارت الـ function نفسها طيب الـ function
+
+146
+00:10:59,300 --> 00:11:02,340
+نفسها ما هي big O of function ماعناهاش مشكلة ما
+
+147
+00:11:02,340 --> 00:11:08,400
+اتغيرش شيء طيب إذا كانت أكبر أكبر فبمعنى إنه هنا
+
+148
+00:11:08,400 --> 00:11:14,640
+واحد مثلا إذا واحد بتصير constant مش مش هيك صارت
+
+149
+00:11:14,640 --> 00:11:17,860
+تتبار سفر constant طيب ال constant ما هو مشمول ضمن
+
+150
+00:11:17,860 --> 00:11:21,540
+ال big O of F بدليل إن احنا قلنا إنه أكبر من
+
+151
+00:11:21,540 --> 00:11:28,520
+constant لكل function أكبر من constantو فعليا او
+
+152
+00:11:28,520 --> 00:11:31,540
+تساوي constant يعني هنا الكتاب اللي ناياها big
+
+153
+00:11:31,540 --> 00:11:36,880
+برضه ماشي ال fact الحقيقة صحيحة الحقيقة الكتاب
+
+154
+00:11:36,880 --> 00:11:40,500
+اللي ناياها صحيحة تمشي مافيش مشكلة طيب log كلنا
+
+155
+00:11:40,500 --> 00:11:44,640
+عارفين أن ال log أقل من ال function نفسها لو عندك
+
+156
+00:11:44,640 --> 00:11:51,580
+linear لل in ما هي in لما تقولفبتساوي N مباشرة
+
+157
+00:11:51,580 --> 00:11:56,020
+كإني بقول إن هي خطية اللي أقل منها اللي هي ال log
+
+158
+00:11:56,020 --> 00:11:57,860
+اللي أقل منها اللي هي ال log اللي أقل منها اللي هي
+
+159
+00:11:57,860 --> 00:11:57,900
+اللي هي ال log اللي أقل منها اللي هي ال log اللي
+
+160
+00:11:57,900 --> 00:11:58,000
+أقل منها اللي هي ال log اللي أقل منها اللي هي ال
+
+161
+00:11:58,000 --> 00:11:58,080
+log اللي أقل منها اللي هي ال log اللي أقل منها
+
+162
+00:11:58,080 --> 00:12:07,660
+اللي هي ال log اللي أقل منها اللي هي ال log اللي
+
+163
+00:12:07,660 --> 00:12:09,520
+أقل منها اللي هي ال
+
+164
+00:12:15,700 --> 00:12:19,580
+عند المية هنا كانت اتنين هنا مية فعليًا linear
+
+165
+00:12:19,580 --> 00:12:23,900
+فإذا واضح أنه فعلا أقل من ال linear أقل من ال
+
+166
+00:12:23,900 --> 00:12:27,400
+linear فال log أجمالًا برضه مشمول مع ال big O of F
+
+167
+00:12:27,400 --> 00:12:34,120
+مشمول لأنه أقل منه أقل منه تمام نفس الفكرة مجموع
+
+168
+00:12:34,120 --> 00:12:37,780
+ال functions لما يكون علينا جي belong to big O of
+
+169
+00:12:37,780 --> 00:12:47,560
+F و H belong to big O of F برضهعندي G تربيعية وH
+
+170
+00:12:47,560 --> 00:12:53,660
+تربيعية مجموحهم برضه تربيعي مش هيتغيرش معاك، مش
+
+171
+00:12:53,660 --> 00:12:57,040
+هيتغير حاجة إطلاقا معاك، فهتضل برضه مجموحهم
+
+172
+00:12:57,040 --> 00:12:58,920
+تربيعي، مجموحهم هيدل تربيعي
+
+173
+00:13:01,400 --> 00:13:04,660
+إذا كان عندى c أكبر من صفر بقدر أقول زي ما قولناها
+
+174
+00:13:04,660 --> 00:13:06,660
+قبل شوية إذا كان في constant مضروب في ال function
+
+175
+00:13:06,660 --> 00:13:09,740
+بغيرش مجموعة ال function مش هيغير انتربيع زائد
+
+176
+00:13:09,740 --> 00:13:15,120
+خمسة هتضل ال order انتربيع انتربيع ناقص مية هتضل
+
+177
+00:13:15,120 --> 00:13:19,120
+انتربيع فهتضل big O of F مش عندي مشكلة طيب إذا كان
+
+178
+00:13:19,120 --> 00:13:23,460
+F1 هنا هتختلف شوية بدنا نركز فيها F1 belong to big
+
+179
+00:13:23,460 --> 00:13:29,640
+O of G1 فهي من ال order G1طيب و F2 هي ال order G2
+
+180
+00:13:29,640 --> 00:13:36,980
+مضروبهم في بعض مضروبهم في بعض حيساوي belong to O
+
+181
+00:13:36,980 --> 00:13:43,500
+of مضروب ال orders أكيد لأن انت ربيع فانت كعيب لأ
+
+182
+00:13:43,500 --> 00:13:48,140
+هي صارت into the power خمسة فعليا مش شاك صارت into
+
+183
+00:13:48,140 --> 00:13:52,590
+the power خمسة تمامإنتوا the power خمسة؟ أه مظبوط
+
+184
+00:13:52,590 --> 00:13:56,350
+خمسة نجمع ال powers ففي الحالة هذه لما أقول ال
+
+185
+00:13:56,350 --> 00:14:00,610
+order ضربهم أه بتصير ضمن ال big O مافيش مشكلة تمام
+
+186
+00:14:00,610 --> 00:14:05,690
+انت مافيش إشكال طيب لو مجموعهم بس هنا اختلفت عن
+
+187
+00:14:05,690 --> 00:14:09,710
+المجموع التعتوي المجموع التعتوي هنا الإتنين اللي
+
+188
+00:14:09,710 --> 00:14:14,610
+هو نفس ال order هنا F و هنا F فمجموعهم هيضل F بس
+
+189
+00:14:14,610 --> 00:14:18,360
+هنا ماحدش قال إن هما نفس ال orderاحنا بالعادة يعني
+
+190
+00:14:18,360 --> 00:14:22,980
+بنقول جي وان و جي تو مختلفين جي وان و جي تو هدول
+
+191
+00:14:22,980 --> 00:14:26,900
+بعض عن بعض واحد تربيع واحد تكعيب مثلا فإذا واحدة
+
+192
+00:14:26,900 --> 00:14:29,780
+تربيع واحدة تكعيب مجموعهم بقدر أقول انهم مجموع ال
+
+193
+00:14:29,780 --> 00:14:33,200
+orders واحدة تربيع واحدة تكعيب يعني تتباور خمسة
+
+194
+00:14:33,200 --> 00:14:37,500
+تتباور خمسة بس هاد هيك انت عارف زي ولد صغير اللي
+
+195
+00:14:37,500 --> 00:14:43,120
+لبسته جلبية أبوهكتير وسعتها يعني انت ماوضحتليش ال
+
+196
+00:14:43,120 --> 00:14:46,720
+code تبعك من أي order كويس يعني بكل بساطة ما انت
+
+197
+00:14:46,720 --> 00:14:51,180
+بده اقولك وصفلي ال code تبعك فانت احترط فيه والله
+
+198
+00:14:51,180 --> 00:14:53,900
+ما انا عارف هو تربيع ولا تكعيب اقولك هحطه تظبور
+
+199
+00:14:53,900 --> 00:14:58,600
+اربعة ما هو اكيد ال big O بتشبر مش هيك احنا هيك
+
+200
+00:14:58,600 --> 00:15:04,410
+عملنا وهذا مش صح ان هذا مش صح انت هيك مش مهندسبدام
+
+201
+00:15:04,410 --> 00:15:07,290
+انت بتدور على القريح واسع مش مشكلة معناته انت
+
+202
+00:15:07,290 --> 00:15:12,110
+كلفني cost لإن انت مش عارف تصبط الشغلة كلفني cost
+
+203
+00:15:12,110 --> 00:15:16,350
+زيادة كويس فالأصح من هيك انك تاخد ال maximum منهم
+
+204
+00:15:16,350 --> 00:15:21,450
+تربيع زي التكعيب خلاص المجموع هيكون تكعيب مش share
+
+205
+00:15:21,450 --> 00:15:25,730
+خلاص تكعيب انتهى فإذا ناخد ال maximum من ال two
+
+206
+00:15:25,730 --> 00:15:29,750
+orders مين الأكبر من التاني تربيعه تكعيب التكعيب
+
+207
+00:15:29,750 --> 00:15:34,800
+أكبر خلاص تكعيبوانتهى تمام طبعا هذا الكلام زي ما
+
+208
+00:15:34,800 --> 00:15:38,000
+قلنا بناخد مثلا جي إذا كانت جي هي الأكبر فمعنى ذلك
+
+209
+00:15:38,000 --> 00:15:41,840
+إذا جي الأكبر معناته جي واحد عفوا الأكبر معناته جي
+
+210
+00:15:41,840 --> 00:15:45,660
+اتنين هي big O of جي واحد تكعيب و تربيع هنقول
+
+211
+00:15:45,660 --> 00:15:49,420
+والله لأ بديها تكعيب فإذا إذا قلنا تكعيب معناته
+
+212
+00:15:49,420 --> 00:15:55,440
+التربيع هو big O من التكعيب صح مظبوط منطقية صحيح
+
+213
+00:15:55,440 --> 00:16:02,470
+كلام منطقي تمامناخد أمثلة على هذا الكلام على معظم
+
+214
+00:16:02,470 --> 00:16:05,930
+ال facts اللي أخدناها مثال مثال مثال هيك عالسريع
+
+215
+00:16:05,930 --> 00:16:07,870
+زي ما قلنا الحل الأول إذا كان بدي أقول و الله
+
+216
+00:16:07,870 --> 00:16:12,850
+تلاتة في function تكعيبية هتظل بيقوق في تكعيبية
+
+217
+00:16:12,850 --> 00:16:17,370
+عفوا تربيعية هتظل بيقوق في تربيع مش هيتغير شيء طيب
+
+218
+00:16:17,370 --> 00:16:24,250
+ال function مع أي function أقل أو تسويها بتظل نفس
+
+219
+00:16:24,250 --> 00:16:30,290
+order ال function فهي x تربيعزاد سواء X تربيع او
+
+220
+00:16:30,290 --> 00:16:35,170
+اقل حد الاكس تربيع حد الاكس تربيع مافيش مشكلة نفس
+
+221
+00:16:35,170 --> 00:16:39,810
+الكلب هي ال big omega هي big omega في الحالة هذه
+
+222
+00:16:39,810 --> 00:16:43,410
+بنقدر نقول ان ال F to the power واحد ناقص بيه هي
+
+223
+00:16:43,410 --> 00:16:48,810
+big O of F زي نقول X to the power minus one احنا
+
+224
+00:16:48,810 --> 00:16:51,910
+عارفين ان هذا واحد على X بتصير طيب واحد على X
+
+225
+00:16:51,910 --> 00:16:57,250
+دايما اقل من Xأكيد دائما أقل من X، صح؟ فمعناه دارك
+
+226
+00:16:57,250 --> 00:17:00,690
+بقدر بأريحية أقول أن هي big O of X لأن X دائما
+
+227
+00:17:00,690 --> 00:17:06,150
+أكبر من 1 على X بدليل أنك أنت قاعد تقييم X، X
+
+228
+00:17:06,150 --> 00:17:12,310
+بخمسة، طيب، 1 على X، خمس، أقل، X بمية، 1 على 100،
+
+229
+00:17:12,310 --> 00:17:17,430
+أقل، هتلاقيها دائما أقل طول ما أنت قاعد بتزود عدد
+
+230
+00:17:17,430 --> 00:17:23,020
+ال inputs، اللي هي قيم X يعنيطيب ال log ال log
+
+231
+00:17:23,020 --> 00:17:26,780
+متفقين هي دايما إذا كان log x هي دايما big O of x
+
+232
+00:17:26,780 --> 00:17:33,600
+وهيهم الدليل واضح قدامنا هي ال log وهي ال x فخالص
+
+233
+00:17:33,600 --> 00:17:41,020
+كويس إيش فيه كمان عندنا G بتساوي big O of F في G
+
+234
+00:17:41,020 --> 00:17:46,650
+بمعنى إذا كانت XX نفسها ممكن تكون هي big O of X
+
+235
+00:17:46,650 --> 00:17:56,170
+مضروب في أي function تانية فوق الواحد فإذا
+
+236
+00:17:56,170 --> 00:18:01,150
+لازم تكون هي constant فأكثر لازم تكون أصلا بتكلم
+
+237
+00:18:01,150 --> 00:18:07,360
+عن constant فأكثرليش؟ لأنه لزيادة هذا constant ما
+
+238
+00:18:07,360 --> 00:18:10,580
+هي هاي constant هي كده متحققة أصلا أكتر من
+
+239
+00:18:10,580 --> 00:18:13,580
+constant معناه ذلك أنه okay مافي مشكلة هتبقى
+
+240
+00:18:13,580 --> 00:18:22,560
+مشمولة ال G داخلها زي لما نقول والله التربيع العكس
+
+241
+00:18:22,560 --> 00:18:29,600
+N to the power تربيع هذه أكيد big O of N تربيع
+
+242
+00:18:29,600 --> 00:18:36,030
+مافيش عندنا مشكلة كويس لكن لما أقولin تربيع هي big
+
+243
+00:18:36,030 --> 00:18:41,850
+O of in تربيع في in باشي
+
+244
+00:18:41,850 --> 00:18:45,410
+هي صارت big O of in تكعيب يعني صح ال relation
+
+245
+00:18:45,410 --> 00:18:48,530
+صحيحة بس زي ما قلنا احنا وسعناها زيادة مش اكتر من
+
+246
+00:18:48,530 --> 00:18:53,390
+هيك اما كرياضيات صحيح رياضيات الان لما نيجي
+
+247
+00:18:53,390 --> 00:18:57,150
+نستخدمها في ال complexity تاعت الأكواد هناخد اللي
+
+248
+00:18:57,150 --> 00:19:01,010
+احنا بدنايا من الرياضيات بس احنا فاهمين ايش يعني
+
+249
+00:19:01,010 --> 00:19:05,100
+ال mathematicsهنا mathematics عدنا لما نروح ل ال
+
+250
+00:19:05,100 --> 00:19:07,580
+complexity ل الأكواد بنقول احنا إيش اللي بدنا ياه
+
+251
+00:19:07,580 --> 00:19:11,900
+منه؟ من كل هال اللي اتعلمنا احنا إيش بدنا منه؟
+
+252
+00:19:11,900 --> 00:19:17,490
+هقولك أنه لأ بدنا more specificبدك تعطيني تحديد لل
+
+253
+00:19:17,490 --> 00:19:22,950
+code لإنك بدك تصير تعمل تحليل بدك تعمل analysis لل
+
+254
+00:19:22,950 --> 00:19:26,550
+code طب هل يعقل إنك انت تكون تعمل analysis لل code
+
+255
+00:19:26,550 --> 00:19:31,250
+وانت مش فاهم أقرب تقريب ممكن لوصف ال code؟ لأ
+
+256
+00:19:31,250 --> 00:19:34,730
+بنفعش معناه ان انت بطلت محلل برامج انت بدك تتخرج
+
+257
+00:19:34,730 --> 00:19:38,900
+تصير محلل برامجتمسك البرنامج ال code تبعك وتحلله
+
+258
+00:19:38,900 --> 00:19:43,200
+تعرف هذا منيح ولا مش منيح مش مجرد انك مبرمج بس لأ
+
+259
+00:19:43,200 --> 00:19:47,020
+انت اكبر من مجرد مبرمج انت اكبر من مجرد مبرمج بكرا
+
+260
+00:19:47,020 --> 00:19:52,220
+طيب فإذا متفقين على هذا الموضوع ايش بسواق العكس
+
+261
+00:19:52,220 --> 00:19:56,640
+غير صحيح طبعا العكس غير صحيح يعني لما تيجي تقولي
+
+262
+00:19:56,640 --> 00:20:00,320
+هل وجد inter B في N صارت N تكعيب هل هي big O of
+
+263
+00:20:00,320 --> 00:20:05,150
+inter B أكيد لأأكيد لأ، أكيد هيكون لأ، مدام أنا
+
+264
+00:20:05,150 --> 00:20:11,090
+بقول أن ال F هي أكبر constant فأكثر، فإذا لأ بقدرش
+
+265
+00:20:11,090 --> 00:20:14,210
+أقول هذا الكلام صحيح، بقدرش نقول هذا الكلام صحيح
+
+266
+00:20:14,210 --> 00:20:20,970
+ال A هي ال constant، أكيد هي big O of F، باعتبار
+
+267
+00:20:20,970 --> 00:20:25,250
+أن ال F برضه هينا معرفينها هي constant فأكثر، فأي
+
+268
+00:20:25,250 --> 00:20:30,090
+constant هو ضمن هذا التعريف، ضمن هذا التعريف
+
+269
+00:20:31,120 --> 00:20:35,500
+طبعا، ضالت الحاجة اللي بحبوها اكتر المحللين هي
+
+270
+00:20:35,500 --> 00:20:39,660
+الـθيتا اللي بفضلوها اكتر ان هو اعطيني exactly
+
+271
+00:20:39,660 --> 00:20:43,940
+order exactly order فهي الثيتا و اللي هي بقدر من
+
+272
+00:20:43,940 --> 00:20:48,960
+خلالها اقول اذا كانت F هي big O of G و G big O of
+
+273
+00:20:48,960 --> 00:20:55,080
+F معناته انه G و F متساويتين exactly بقدر اقول ان
+
+274
+00:20:55,080 --> 00:21:00,690
+ال F belonging to ثيتا و Gهذه ال relation اللي
+
+275
+00:21:00,690 --> 00:21:05,850
+بيحبوها المهندسين اللي هو محللين البرامج اعطيني
+
+276
+00:21:05,850 --> 00:21:09,790
+theta كل ما اعطتني theta بكون بأثق بقرارك أكتر
+
+277
+00:21:09,790 --> 00:21:14,990
+بقدر أثق أكتر بقرارك تمام فهي الفكرة ببساطة طبعا
+
+278
+00:21:14,990 --> 00:21:19,350
+إيش بتختلف ال theta عن ال big O اللي أخدناهم
+
+279
+00:21:19,350 --> 00:21:26,550
+بتختلف في بعض الأمور اللي هي هتحكملي أنه ماتلبسنيش
+
+280
+00:21:26,550 --> 00:21:31,470
+top أكبر من Toby ببساطةببساطة بتحكمني انه لأ كل
+
+281
+00:21:31,470 --> 00:21:35,150
+حاجة بالظبط جايف لي على جدى لما توصفني وصفني على
+
+282
+00:21:35,150 --> 00:21:43,090
+جدى بس طيب هي شبيهة بال big O لكن مع اختلاف ان ال
+
+283
+00:21:43,090 --> 00:21:48,550
+A F هي نفسها theta of F مش مشكلة ال constant مغيرش
+
+284
+00:21:48,550 --> 00:21:53,150
+شيء مغيرش شيء لكن لما بقول F not belong to big
+
+285
+00:21:53,150 --> 00:21:59,950
+theta of F G F G هذه يعني ان انت جبتلي توب كبيرلأ
+
+286
+00:21:59,950 --> 00:22:04,010
+مش مقبول اقول ان هي θ ماشية لأ θ هيك مش ماشية لأنه
+
+287
+00:22:04,010 --> 00:22:07,470
+هنا زي ما قلنا ممكن تكون هنا in تكعيب و هنا in
+
+288
+00:22:07,470 --> 00:22:14,170
+تربيع بيجؤع بمش الحال احنا طبعا ماخدينها بس كانت
+
+289
+00:22:14,170 --> 00:22:18,590
+بيجؤع ماشية valid وقولنا مافيش مشكلة رياضيا مافيش
+
+290
+00:22:18,590 --> 00:22:21,770
+مشكلة قولنا بس احنا لبسناها top أكبر و بمش الحال
+
+291
+00:22:21,770 --> 00:22:25,890
+زي لما تقول بدك x أقل من أو يساوي خمسة هقولك طب
+
+292
+00:22:25,890 --> 00:22:30,920
+ماشي خد سالب ميةتقدر تقولي غلط؟ لأ بس أنا كتير
+
+293
+00:22:30,920 --> 00:22:39,000
+يعني رميت رقم بعيد يعني مش كتير منطقي تمام طيب نفس
+
+294
+00:22:39,000 --> 00:22:44,040
+الكلام بمين؟ لأ ال to the power minus constant
+
+295
+00:22:44,040 --> 00:22:49,240
+صارت inverse ال inverse هي لا تساوي ال function
+
+296
+00:22:49,240 --> 00:22:52,600
+نفسها ال inverse لا تساوي ال function هي تساوي أقل
+
+297
+00:22:52,600 --> 00:22:55,560
+منها أه تساوي أقل منها ف big O بمشي الحال لكن big
+
+298
+00:22:55,560 --> 00:23:01,430
+theta لأف big theta هنا بتصبتش X لا تساوي سالب
+
+299
+00:23:01,430 --> 00:23:08,090
+عفوا واحد على X لايمكن تساويها فهنا بعكس ال big O
+
+300
+00:23:08,090 --> 00:23:13,190
+هنا لا تساويها طيب ال log نفس الكلام لا يساوي لأن
+
+301
+00:23:13,190 --> 00:23:18,150
+ال log هي بينين هي أقل هي فعليا أقلتساوي لأ
+
+302
+00:23:18,150 --> 00:23:21,550
+لاتساوي فهي الفرق الوحيد بين ال big O و ال big
+
+303
+00:23:21,550 --> 00:23:26,110
+theta ال big theta exactly تساوي ال order بالظبط
+
+304
+00:23:26,110 --> 00:23:31,150
+كويس ف strictly في
+
+305
+00:23:31,150 --> 00:23:35,630
+ال order نفس ال order ناخد مثال ناخد مثال نروح ل
+
+306
+00:23:35,630 --> 00:23:37,530
+Euler ماذا ذاكرين Euler summation
+
+307
+00:23:40,820 --> 00:23:44,780
+أولى لما جلنا بتعمل summation لمجموعة الأرقام من 1
+
+308
+00:23:44,780 --> 00:23:49,820
+to N كويس خلاص أخدناها و كلنا متفقين أنه جلنا N في
+
+309
+00:23:49,820 --> 00:23:54,120
+N زائد 1 على 2 وانتهت على هيك N في N زائد 1 على 2
+
+310
+00:23:54,120 --> 00:23:59,180
+طيب لحظوا ال input تبعنا هو فعلا المدخلات ال N انت
+
+311
+00:23:59,180 --> 00:24:01,800
+اللي بتغيره هنا المتغير عندك ال variable عندك هي
+
+312
+00:24:01,800 --> 00:24:05,760
+قيمة N شك؟ طيب قيمة N هذه ممكن تاخدها خمسة عشر
+
+313
+00:24:05,760 --> 00:24:10,220
+عشرين تلاتينفمتغيرة هذه هي القيمة المتغيرة هي
+
+314
+00:24:10,220 --> 00:24:12,440
+مجموعة ال input اللي انت بدك تدخله معاها ال
+
+315
+00:24:12,440 --> 00:24:17,420
+summation تمام كلنا عارفين لما بقول in زائد واحد
+
+316
+00:24:17,420 --> 00:24:23,440
+فهي ال order in زائد constant فبتضل ال order in
+
+317
+00:24:23,440 --> 00:24:29,760
+فبتضل order in مش مشكلة big theta exactly order in
+
+318
+00:24:29,760 --> 00:24:35,960
+فهي تساوي ال order in طيب ال order in في constant
+
+319
+00:24:35,960 --> 00:24:42,710
+نصعلى 2 ما هي constant مش هيك بتظل نفس ال order in
+
+320
+00:24:42,710 --> 00:24:45,730
+طيب
+
+321
+00:24:45,730 --> 00:24:51,070
+جيد جدا ال order in في in في order in برضه في نفس
+
+322
+00:24:51,070 --> 00:24:55,730
+ال order in يعني كأنه صارت هنا θ of n وهذه برضه θ
+
+323
+00:24:55,730 --> 00:25:01,350
+of n أكيد التربيع فانت بتمسكهم تضربهم زي ما هما
+
+324
+00:25:01,350 --> 00:25:05,230
+أخدناها fact برضه لل big O و هنا مماثلة لها في ال
+
+325
+00:25:05,230 --> 00:25:11,940
+big θin في in، in تربيع، تربيع في in تكعيب، و
+
+326
+00:25:11,940 --> 00:25:14,920
+هكذا، فإذن هذه بتساوي in تربيع، فبقدر أقول إن ال
+
+327
+00:25:14,920 --> 00:25:18,500
+summation هذا هو من ال order التاني أو second
+
+328
+00:25:18,500 --> 00:25:23,500
+order ك code عشان نكتب code لهذا الموضوع هيكون
+
+329
+00:25:23,500 --> 00:25:27,400
+للمعادلة هذه عشان نطبقها بدها second order بدها
+
+330
+00:25:27,400 --> 00:25:33,280
+second order ك complexityممكن هذه احنا سبجنا فيها
+
+331
+00:25:33,280 --> 00:25:37,980
+سبجنا في حكاية ال theta ال big theta و ال small o
+
+332
+00:25:37,980 --> 00:25:45,980
+و ال small omega small omega أخدناهم كلهم هذه و
+
+333
+00:25:45,980 --> 00:25:49,880
+هذه و هذه كلهم أخدناهم الفرق كان في وين في أكبر من
+
+334
+00:25:49,880 --> 00:25:55,860
+أو أيش أو أصغر من فهنا belonged to العكس إذا كنت
+
+335
+00:25:55,860 --> 00:25:56,520
+بتكلم عن
+
+336
+00:26:00,010 --> 00:26:04,090
+G فمعنى ذلك ان هي كل ال functions F اللي أكبر من G
+
+337
+00:26:04,090 --> 00:26:09,970
+لاحظ صارت ال بالعكس بالنسبة لمن؟ لل O فهي عكس ال O
+
+338
+00:26:09,970 --> 00:26:18,230
+يعني صارت F belong to of G هي نفسها G belong big O
+
+339
+00:26:18,230 --> 00:26:25,400
+of Fعكس بعض أكبر من أو يساوي و أصغر من أو يساوي
+
+340
+00:26:25,400 --> 00:26:31,380
+نفس ال relation بس عكسية بتصير عكسية تمام ال small
+
+341
+00:26:31,380 --> 00:26:35,860
+نفس تعريف ال big بس بدون ما نحط أو يساوي هنا تعريف
+
+342
+00:26:35,860 --> 00:26:39,000
+اللي خدناه المرة الماضية شرحناه مع المعادلتين تعون
+
+343
+00:26:39,000 --> 00:26:44,200
+ال linear و التربيع فقط بس مش هنحط هنا أو يساوي
+
+344
+00:26:44,890 --> 00:26:48,670
+فبتصير أصغر من strictly أصغر من ال small ال small
+
+345
+00:26:48,670 --> 00:26:53,190
+هي نفس ال capital ولكن بدون اليساوي ليه؟ التسهيل
+
+346
+00:26:53,190 --> 00:27:01,030
+هنكتبهم بالشكل اللي احنا شايفينه if
+
+347
+00:27:01,030 --> 00:27:04,370
+تقريبا أقل من بس أنا هنا بقول أقل من as a function
+
+348
+00:27:04,370 --> 00:27:07,810
+ك order فبحطهاش الأقل من الطبيعية بنحط هيك شوية
+
+349
+00:27:07,810 --> 00:27:16,010
+مدلعة يعني شوية مدلعة العلامةدلعوها شوية عشان نعرف
+
+350
+00:27:16,010 --> 00:27:19,530
+ان انا بتكلم عن order مش عن two terms او two
+
+351
+00:27:19,530 --> 00:27:23,870
+values كويس فبنقول if ال order of f أقل من ال
+
+352
+00:27:23,870 --> 00:27:31,870
+order of g فمعنى ذلك ان هي small o لما نقول تقريبا
+
+353
+00:27:31,870 --> 00:27:36,910
+approximately معناته theta بنسميها theta فهي علامة
+
+354
+00:27:36,910 --> 00:27:43,760
+theta كويس كلنا عارفين ان لو تكون ifsmall O of G
+
+355
+00:27:43,760 --> 00:27:50,840
+معناته أن F فعليا أقل من G Strictly أقل من G، لا
+
+356
+00:27:50,840 --> 00:27:55,900
+تساوي، هي مش big O، هي small O، مدام Strictly هي
+
+357
+00:27:55,900 --> 00:28:00,700
+أقل من، أقل من، يمكن أقل من قيمة يدوب صغيرة جدا،
+
+358
+00:28:00,700 --> 00:28:03,980
+مش هيك؟ يعني الأثنين هيوم بدوا مع بعض و بعدين
+
+359
+00:28:03,980 --> 00:28:06,740
+بدأوا يبعدوا شوية شوية عن بعض، شوية شوية شوية شوية
+
+360
+00:28:06,740 --> 00:28:11,510
+أنا ضامن أنه في ال Infinityفي ال infinity هيكون
+
+361
+00:28:11,510 --> 00:28:16,410
+الفرق بينهم صار شاسع جدا لدرجة ان f بالنسبة ل g لا
+
+362
+00:28:16,410 --> 00:28:23,030
+تذكر كأنها limit at x limit to infinity بتصير
+
+363
+00:28:23,030 --> 00:28:27,770
+النسبة بينهم كأنها صفر كأن قيمة g مش شايفة قيمة f
+
+364
+00:28:28,900 --> 00:28:32,820
+عند ال infinity عند ال infinity فlimitation هنا
+
+365
+00:28:32,820 --> 00:28:36,300
+بحدد لإنه معناه ذلك إنه هذه أصبحت قيمة جدا كبيرة
+
+366
+00:28:36,300 --> 00:28:42,860
+مقابل قيمة كتير صغيرة لل F يعني F أصغر من G يعني
+
+367
+00:28:42,860 --> 00:28:47,200
+معناته F أصغر من G فعليا تمام الآن هناخد بعض ال
+
+368
+00:28:47,200 --> 00:28:50,800
+functions بعض ال functions اللي كتير كويس نتعامل
+
+369
+00:28:50,800 --> 00:28:55,560
+معها واحد ال constant هو أقل من ال log of log
+
+370
+00:28:57,060 --> 00:29:00,200
+تعرفين log of log هذه من ال functions الرائعة لو
+
+371
+00:29:00,200 --> 00:29:02,440
+قدرتوا ال .. ال quad تبعاتكم تكتبوها log of log
+
+372
+00:29:02,440 --> 00:29:06,780
+يعني معنى ذلك أن هي يعني ال complexity كتير صغيرة
+
+373
+00:29:06,780 --> 00:29:10,860
+تقريبا ما .. ما .. مافيش complexity لكن في جميع
+
+374
+00:29:10,860 --> 00:29:13,860
+الأحوال هي أكبر من الواحد في جميع الأحوال هي أكبر
+
+375
+00:29:13,860 --> 00:29:18,540
+من الواحد لو نيجي نتكلم عن عشرة مثلا العشرة عارفين
+
+376
+00:29:18,540 --> 00:29:28,600
+أن هي log عشرة بواحد log واحد بصفر مش هيكطيب زود
+
+377
+00:29:28,600 --> 00:29:35,840
+عند المية عند المية بيصير عندك هنا اتنين log
+
+378
+00:29:35,840 --> 00:29:42,860
+الاتنين بيكون زاد عن الواحد طيب زاد عن الواحد هيك؟
+
+379
+00:29:42,860 --> 00:29:47,600
+لأ لسه مازادش عن الواحد مازادش عن الواحد مازال أقل
+
+380
+00:29:47,600 --> 00:29:51,340
+من الواحد لكن احنا متذكرين تعريفنا السابق قلنا عند
+
+381
+00:29:51,340 --> 00:29:58,100
+نقطة معينة K بعدهاخلاص حيك هتصير ال term هذا أكبر
+
+382
+00:29:58,100 --> 00:30:01,920
+من الواحد و يستمر أكبر منه طب عارفين إيش هو ال
+
+383
+00:30:01,920 --> 00:30:10,240
+term هذا اللي هيتكلم عنه ال K جديش؟ عشرة قص عشرة
+
+384
+00:30:10,240 --> 00:30:16,600
+100% عشرة قص عشرة هنا لما تقول عشرة قص عشرة إيش
+
+385
+00:30:16,600 --> 00:30:21,560
+يعني؟ log هيطلع هذا ال term كله عشرة log عشرة واحد
+
+386
+00:30:21,560 --> 00:30:26,860
+بعد هيكأكيد الـ function هذه هي أكبر من الواحد،
+
+387
+00:30:26,860 --> 00:30:31,280
+أكبر من ال constant واضحة؟
+
+388
+00:30:31,280 --> 00:30:36,360
+تمام، فإذا في K، بغض النظر K قيمة صغيرة ولا قيمة
+
+389
+00:30:36,360 --> 00:30:40,340
+كبيرة، المهم إنه يوجد K بعدها ال function أكبر من
+
+390
+00:30:40,340 --> 00:30:45,540
+ال constant، يوجد، خلاص، وقدرين نصلها، عشرة طب، هو
+
+391
+00:30:45,540 --> 00:30:50,480
+عشرة، طيب، في جميع الأحوال، في جميع الأحوال، log
+
+392
+00:30:50,480 --> 00:30:57,380
+of log هي أصغر من log لحالهاأكيد أكيد أكيد تو هنا
+
+393
+00:30:57,380 --> 00:31:04,840
+كانت واحد هنا كانت عشرة هنا كانت عشرة تمام هذه
+
+394
+00:31:04,840 --> 00:31:10,720
+تساوي نفس ال log لأي أساس بغض النظر هى log decimal
+
+395
+00:31:10,720 --> 00:31:15,300
+ولا binary ولا ايش نوع الأساس تبع مش هتفرج أما ال
+
+396
+00:31:15,300 --> 00:31:18,060
+order logarithmic بظل ال order بظل logarithmic
+
+397
+00:31:18,060 --> 00:31:25,110
+فبغض النظر عن k بس تكون k أكبر من واحدانتوا عندكوا
+
+398
+00:31:25,110 --> 00:31:29,450
+حاجة اسمها log لحالها بس هادى by default هي للعشرة
+
+399
+00:31:29,450 --> 00:31:32,030
+الأساس عشرة اللى احنا بنشتغلها و احنا تاول لما
+
+400
+00:31:32,030 --> 00:31:34,550
+اشتغلنا هنا اشتغلنا للأساس عشرة عشان هيك روحنا
+
+401
+00:31:34,550 --> 00:31:38,030
+لرقم كبير بس ممكن هنا تكون للأساس اتنين فمضطرش
+
+402
+00:31:38,030 --> 00:31:42,370
+اروح لعشرة ثم بوارة عشرة هتكون ال K أقرب من العشرة
+
+403
+00:31:42,370 --> 00:31:47,170
+ثم بوارة عشرة بناء على الأساس تمام لما تكوني
+
+404
+00:31:47,170 --> 00:31:52,090
+بنشتغل في ال binary لأ بتصير هادى log للأساس اتنين
+
+405
+00:31:53,070 --> 00:31:56,590
+فبغض النظر عن إيش نوع ال base اللي مشتغل عليه لل
+
+406
+00:31:56,590 --> 00:32:02,250
+log كلهم نفس ال order كلهم نفس ال order تمام، في
+
+407
+00:32:02,250 --> 00:32:09,050
+نفس الوقت log n هو أقل من log to the power k log k
+
+408
+00:32:09,050 --> 00:32:14,170
+للأساس k هو أقل في جميع الأحوال من log k، ليش؟ أه
+
+409
+00:32:14,170 --> 00:32:17,690
+نعم، بصحيح كنت مذكرين لسه، كنت مذكرين كل ال .. لأن
+
+410
+00:32:17,690 --> 00:32:21,950
+ال k هذه كأنها بالنسبة لل log هي k في log of n
+
+411
+00:32:24,220 --> 00:32:31,520
+بالظبط يعني زادت بمقدار ال K اللي انه ضربت لأ
+
+412
+00:32:31,520 --> 00:32:35,920
+ل .. بتفرجش للتانية للتانية لل operation نفسها لل
+
+413
+00:32:35,920 --> 00:32:41,560
+function نفسها لل function نفسها to the power K ف
+
+414
+00:32:41,560 --> 00:32:44,360
+to the power K معناته بتضربها برا في ال K أه
+
+415
+00:32:44,360 --> 00:32:48,180
+بتضربها كأنها K برا كأنها K برا طيب في جميع
+
+416
+00:32:48,180 --> 00:32:56,290
+الأحوال ال log هو يعني أقل من ال rootأقل من ال
+
+417
+00:32:56,290 --> 00:33:01,470
+root هذه فعلياً root يعني لو افترض k ب 2 معناته
+
+418
+00:33:01,470 --> 00:33:06,350
+الجذر التربيعي تلاتة الجذر التكعيبي and so on هنا
+
+419
+00:33:06,350 --> 00:33:10,250
+الجذر order k الجذر order k يعني كأنك أنت هنا
+
+420
+00:33:10,250 --> 00:33:18,630
+بتقول جذر in لل order k هذه هتكون أكبر من ال
+
+421
+00:33:18,630 --> 00:33:21,250
+logarithmic function فال root أكبر من ال logarithm
+
+422
+00:33:21,950 --> 00:33:26,970
+عند الحياة كويس طيب لعندي لأن كل هدول السابقين أقل
+
+423
+00:33:26,970 --> 00:33:35,290
+من ال linear أكيد جذر n أكيد أصغر من n صح؟ أكيد
+
+424
+00:33:35,290 --> 00:33:38,770
+منطق جدا يعني فكل اللي فات هذا هو كله أصغر من
+
+425
+00:33:38,770 --> 00:33:43,670
+first order لسه ال first order في عندك بعدها n هي
+
+426
+00:33:43,670 --> 00:33:46,790
+ال first order في ال log ليش؟ لأن احنا مسبقا هنا
+
+427
+00:33:46,790 --> 00:33:51,230
+قلنا ال log أكبر من واحد فهذه كأنها مضروبة في واحد
+
+428
+00:33:53,250 --> 00:33:58,790
+فال N هي نفس ال N وعارفين أن ال 1 أقل من log ما
+
+429
+00:33:58,790 --> 00:34:05,590
+هيها؟ واحد أقل من log تمام؟ فإذا أكيد مظبوطة إيش
+
+430
+00:34:05,590 --> 00:34:09,670
+اسمها دي؟ إلها اسم، هناخده .. هناخده .. زي ما
+
+431
+00:34:09,670 --> 00:34:11,590
+قلتلكوا هناخده أنواع ال functions لأن أنت ممكن
+
+432
+00:34:11,590 --> 00:34:15,070
+تضطر توصفوا الأكواد بتاعتكوا باسم ال function
+
+433
+00:34:15,070 --> 00:34:18,510
+هناخد مجموعة كويسة عبنا بس نبدأ ناخد ال complexity
+
+434
+00:34:19,950 --> 00:34:23,110
+لوجاريثمك هذه لوجاريثمك بس هذه لها اسم تاني
+
+435
+00:34:23,110 --> 00:34:28,190
+linearithmic اسمها linearithmic هناخدها ماتجلخوش
+
+436
+00:34:28,190 --> 00:34:34,090
+طيب هذه أقل من polynomial اللي هي انت ربيع انت
+
+437
+00:34:34,090 --> 00:34:38,130
+كعيب انت ثبار أربع انت ثبار خمسة polynomial متعددة
+
+438
+00:34:38,130 --> 00:34:42,130
+الحدود متعددة الحدود طيب هذه أصغر من ال
+
+439
+00:34:42,130 --> 00:34:47,050
+exponential ثابت ثبار المتغير هذه ال exponential
+
+440
+00:34:47,050 --> 00:34:48,070
+factorial
+
+441
+00:34:50,390 --> 00:34:53,630
+الفكتوريال أكبر منها لسه طيب اللي أكبر من
+
+442
+00:34:53,630 --> 00:34:56,690
+الفكتوريال in to the power in لأن هذه عبارة عن
+
+443
+00:34:56,690 --> 00:35:00,130
+واحد في اتنين في تلاتة لعند in هذه لأ in في in في
+
+444
+00:35:00,130 --> 00:35:06,220
+in في in لعند inفأكيد أكبر أكيد أكبر تمام ممتاز
+
+445
+00:35:06,220 --> 00:35:10,040
+هذه مجموعة أنواع هذه اللي هنتعامل معها الحقيقة لما
+
+446
+00:35:10,040 --> 00:35:14,380
+نروح نبدأ نوصف ال code تبعنا و هل هو مقبول انت
+
+447
+00:35:14,380 --> 00:35:18,280
+كمحل البيانات و كمحل البرامج لعند أي حد بتقدر تقبل
+
+448
+00:35:18,280 --> 00:35:21,220
+ال code لعند أي حد بتقدر تقبل ال code هو هذا
+
+449
+00:35:21,220 --> 00:35:26,760
+الموضوع اللي احنا بدنا نتكلم في جزئية ال
+
+450
+00:35:26,760 --> 00:35:27,320
+complexity
+
+451
+00:35:35,920 --> 00:35:40,170
+في جزئية ال complexity فلما بجي أتكلم عنهالـ
+
+452
+00:35:40,170 --> 00:35:43,270
+Algorithmic Complexity خلاص افهمنا ايش يعني ال
+
+453
+00:35:43,270 --> 00:35:46,850
+order of growth الان كل الفكرة انه بدي احول ال
+
+454
+00:35:46,850 --> 00:35:51,590
+code ل function و اطبق عليها مين اكبر من مين مين
+
+455
+00:35:51,590 --> 00:35:55,530
+big O of مين بس عشان نعرف مين احسن من مين مش اكتر
+
+456
+00:35:55,530 --> 00:35:59,390
+من هيك كلنا عارفين انه في النهاية و قولناها مرارا
+
+457
+00:35:59,390 --> 00:36:03,230
+و تكرارا ان ال input تبعنا هي مجموعة ال inputs ال
+
+458
+00:36:03,230 --> 00:36:08,480
+function هي ال costال cost ايش بتهتكلفني بالنسبة
+
+459
+00:36:08,480 --> 00:36:11,200
+لعدد ال inputs لزيادة على اعتبار ان ال input هو
+
+460
+00:36:11,200 --> 00:36:17,040
+المتغير أصبحت عندك function of of in ان هذه ال
+
+461
+00:36:17,040 --> 00:36:22,020
+inputs مجموعة ال inputs اللي هنشتغلها طيب كلها على
+
+462
+00:36:22,020 --> 00:36:28,600
+بعض ال cost تكلفة ال code من أي ناحية تكلفة ال
+
+463
+00:36:28,600 --> 00:36:31,060
+code فهذه هي ال function اللي بدنا نتعامل معها هي
+
+464
+00:36:31,060 --> 00:36:35,320
+هتقيس ليه ال cost ال cost تقاس بطريقتين إما ك time
+
+465
+00:36:36,160 --> 00:36:41,520
+أو ك space ك space في الحالتين هي cost هي تكلفة
+
+466
+00:36:41,520 --> 00:36:47,660
+إما هتكلفني وقت وقت انتظار جدش بده يكلفني الوقت ك
+
+467
+00:36:47,660 --> 00:36:52,460
+function في ال input أو جدش بده يكلفني ال space
+
+468
+00:36:52,460 --> 00:36:56,100
+لأنه مساحة هذه طيب المساحة هذه ما أنا بده أضطر
+
+469
+00:36:56,100 --> 00:37:01,000
+أشتري لها وسعة عشان نفذ البرامج بتاعتنا بدك تضطر
+
+470
+00:37:01,000 --> 00:37:05,590
+تحط لها وسعةفهذه بالنسبالك cost هي ال memory bits
+
+471
+00:37:05,590 --> 00:37:10,470
+requirement required او ال bits اللي انت محتاجها
+
+472
+00:37:10,470 --> 00:37:16,150
+او مطلوبة بالنسبالك في ال memory اذا والله المحتاج
+
+473
+00:37:16,150 --> 00:37:20,530
+space اكبر يمكن ال RAM عندك تضطر تشيلها تشتريلك
+
+474
+00:37:20,530 --> 00:37:26,250
+RAM اجسع اكبر عشان تقول والله هيك ال جهاز
+
+475
+00:37:26,250 --> 00:37:30,630
+تبعي أصبح بقدر ينفذ برامج كبيرة في الأول لأ كان
+
+476
+00:37:30,630 --> 00:37:35,370
+على برامج صغيرةو هكذا هل في الآخر كمان ال compiler
+
+477
+00:37:35,370 --> 00:37:41,570
+smart enough انه يعمل إدارة مناسبة ل ال memory ولا
+
+478
+00:37:41,570 --> 00:37:44,910
+لأ تاخدوا بالكم الجزئية دي اللي في بعض ال
+
+479
+00:37:44,910 --> 00:37:48,590
+compilers هو smart enough انه يعملك إدارة كويسة ل
+
+480
+00:37:48,590 --> 00:37:53,570
+ال memory و الغالبية لأ الغالبية خصوصا لما بدك
+
+481
+00:37:53,570 --> 00:37:57,570
+تيجي تعمل مثلا ال method و ال recurrence method
+
+482
+00:37:58,580 --> 00:38:02,980
+Recurrence انك انت نفس ال code بدك تفتحه كل مرة
+
+483
+00:38:02,980 --> 00:38:06,640
+لعند ما تصل ل ال bases تبعته هناخدها برضه لجدام
+
+484
+00:38:06,640 --> 00:38:12,200
+عشان تصل ل ال bases هدى أكم مرة هتضطر تفتح برامج
+
+485
+00:38:12,200 --> 00:38:16,800
+نفس البرنامج كذا مرة ما انت معناته بدك ذاكرةال
+
+486
+00:38:16,800 --> 00:38:19,860
+recursion اللى هو ال recurrence code ال recursion
+
+487
+00:38:19,860 --> 00:38:23,900
+كنتوا بتسموها معناته بدي افتح كذا مرة نفس الملف او
+
+488
+00:38:23,900 --> 00:38:29,500
+نفس ال code كل مرة ب input جديد طب اللى جداش بتسعى
+
+489
+00:38:29,500 --> 00:38:33,540
+الذاكرة معناه ذلك هنا ناس بفضلوا انه يشتغلوا بال
+
+490
+00:38:33,540 --> 00:38:35,960
+space ناس بفضلوا يشتغلوا بال time بالنسبة لل
+
+491
+00:38:35,960 --> 00:38:40,620
+course طبعا احنا هنتعامل مع مين مع ال time مع ال
+
+492
+00:38:40,620 --> 00:38:48,500
+time كويس واتفقنا انه ال inputال input هي ال
+
+493
+00:38:48,500 --> 00:38:50,900
+different sizes اللي بتعمل معاه، يعني هي المتغير،
+
+494
+00:38:50,900 --> 00:38:54,380
+هي المتغير في شغلنا زي لما نقول والله بدي أعمل
+
+495
+00:38:54,380 --> 00:38:57,440
+عملية searching عملية ال searching ل long list
+
+496
+00:38:57,440 --> 00:39:01,470
+أكيد هتاخد time أكتر من ال short listبديهي يعني
+
+497
+00:39:01,470 --> 00:39:06,650
+هذا اشي بديهي جدا انا بدي ابحث في list من عشرة
+
+498
+00:39:06,650 --> 00:39:10,710
+elements غير لما ابحث من 100 elements أكيد ال 100
+
+499
+00:39:10,710 --> 00:39:14,170
+elements هتاخد وقت أطول .. هتاخد وقت أطول فجدش
+
+500
+00:39:14,170 --> 00:39:19,670
+بيصير تضخم في الوقت مقابل كل input زيادة هذا ال
+
+501
+00:39:19,670 --> 00:39:24,150
+complexity هذا ال order of growth معدل النمو كل ما
+
+502
+00:39:24,150 --> 00:39:27,270
+بتزيد ال input زيادة واحد جدش بتزيد مقابلها ال
+
+503
+00:39:27,270 --> 00:39:31,560
+timeهي معدل اللي اتكلمنا عنه ال order of growth
+
+504
+00:39:31,560 --> 00:39:35,980
+نمو ال function .. نمو ال function .. اي function؟
+
+505
+00:39:35,980 --> 00:39:38,540
+function ال time اما احنا خلاص اتفقنا لانه بدنا
+
+506
+00:39:38,540 --> 00:39:42,300
+نشتغل ال time معناته function ال time اللي هي
+
+507
+00:39:42,300 --> 00:39:46,280
+معتمدة على ايش؟ معتمدة على عدد ال inputs فهي ال
+
+508
+00:39:46,280 --> 00:39:49,860
+function بتاعتنا لان ال time خلاص نتكلم عن ال time
+
+509
+00:39:49,860 --> 00:39:55,020
+complexity و متفقين ان كلنا هنشتغل على ال worst
+
+510
+00:39:55,020 --> 00:40:00,930
+case inputsأسوأ حالة لعدد ال inputs؟ إيش ممكن
+
+511
+00:40:00,930 --> 00:40:03,410
+يكون؟ فهذا هو اللي بنشتغل عليه وهذا اللي من خلاله
+
+512
+00:40:03,410 --> 00:40:08,190
+بتشتغل و بتقرر بالنسباله تعمل analysis لمن؟ لل
+
+513
+00:40:08,190 --> 00:40:11,170
+code بتسترش على ال best ولا حتى على ال average
+
+514
+00:40:11,170 --> 00:40:15,950
+بتاخد إيش أسوأ حالة ممكنة لل code؟ لمن؟ إيش اللي
+
+515
+00:40:15,950 --> 00:40:18,290
+في ال code ممكن يكون أسوأ ما يمكن؟ الشيء اللي
+
+516
+00:40:18,290 --> 00:40:23,460
+بتغير اللي بتغير هو ال input كويسلو أخدنا suppose
+
+517
+00:40:23,460 --> 00:40:27,500
+that أو بدنا نفرض حالة معينة الحالة هذه بدنا نفرض
+
+518
+00:40:27,500 --> 00:40:32,220
+أن عندي algorithm A ال algorithm A هذا ال worst
+
+519
+00:40:32,220 --> 00:40:35,200
+case time complexity فبنسميها ال worst case time
+
+520
+00:40:35,200 --> 00:40:42,090
+complexity F of Nالـ function هتوطه بهذا ال order
+
+521
+00:40:42,090 --> 00:40:47,350
+بهذا الشكل بناء على ال inputs بطول N بطول N فهي
+
+522
+00:40:47,350 --> 00:40:51,990
+فعلا function في ال N بينما ال algorithm B بياخد
+
+523
+00:40:51,990 --> 00:40:55,110
+ال function بتاعة ال time أو ال time function G
+
+524
+00:40:55,110 --> 00:41:01,150
+فعندي two time functions واحدة ل system أول أو
+
+525
+00:41:01,150 --> 00:41:04,790
+algorithm أول والتاني لل algorithm التاني إذا F
+
+526
+00:41:04,790 --> 00:41:12,200
+belong to big omega of Gلأن انت هذه اللي وجدت time
+
+527
+00:41:12,200 --> 00:41:15,280
+ال time ايش المطلوب اللي انت تعمل تجيبلي ال
+
+528
+00:41:15,280 --> 00:41:18,520
+function تبعته ال order تبع ال function و بعدين
+
+529
+00:41:18,520 --> 00:41:22,420
+تيجي تقارن ال two orders في بعض اجيت لجيت والله ان
+
+530
+00:41:22,420 --> 00:41:30,920
+ال F هي small omega of G يعني G أصغر من F ايش يعني
+
+531
+00:41:30,920 --> 00:41:35,900
+ال small omega تاول لسه مكتوبة معناته هيها لاحظ F
+
+532
+00:41:35,900 --> 00:41:42,500
+أكبر من GF أكبر من G طب automatic معناته صار هنا
+
+533
+00:41:42,500 --> 00:41:48,140
+عندك ال algorithm اللي هيكون أسرع في حالة ال worst
+
+534
+00:41:48,140 --> 00:41:57,080
+case inputs مين؟ A ولا B؟
+
+535
+00:41:57,080 --> 00:42:05,800
+مين الأسرع؟ A ال order تبعه أكبرطيب، في ندفة صغيرة
+
+536
+00:42:05,800 --> 00:42:08,920
+هيك معناته، بدنا نرجع نأكد عليها هون، ها هذه صارت
+
+537
+00:42:08,920 --> 00:42:17,880
+in و function هنا سواء f أو g في الـtime مش احنا
+
+538
+00:42:17,880 --> 00:42:20,300
+خلاص اتفقنا time، مش هتكلم في ال space، نهائي
+
+539
+00:42:20,300 --> 00:42:29,160
+time، في ال time، وجدنا أن ال f بهذا الشكل، ال g
+
+540
+00:42:29,160 --> 00:42:35,850
+أصغر منهاطيب عند N معينة ال worst case أنه والله
+
+541
+00:42:35,850 --> 00:42:39,810
+ال input بزيدش عن قيمة N مثلا هنا لا يزيد عن قيمة
+
+542
+00:42:39,810 --> 00:42:45,770
+N ك input مثلا معناه ذلك أنه هذه طلعت F وهذه هيك
+
+543
+00:42:45,770 --> 00:42:54,030
+طلعت G أكيد F أقل كقيمة من G أقل في أي ناحية في ال
+
+544
+00:42:54,030 --> 00:43:02,590
+time صح أنا بتكلم عن time ف Gالـtime تبعها أقل،
+
+545
+00:43:02,590 --> 00:43:08,150
+طيب إيش علاقة الـtime بالسرعة؟ بالعكس، كل ما كنت
+
+546
+00:43:08,150 --> 00:43:11,970
+أسرع معناته بتستغرق الـtime أقل، معناه ذلك أنه مين
+
+547
+00:43:11,970 --> 00:43:16,710
+الأسرع الـmore faster من التاني الـG اللي هي تمثل
+
+548
+00:43:16,710 --> 00:43:21,570
+أنه code B فلما بتيجي بتعمل selection في حالة زي
+
+549
+00:43:21,570 --> 00:43:24,450
+هذه هروح لل algorithm B و أقول هذا اللي بتعمله
+
+550
+00:43:24,450 --> 00:43:30,360
+selection وهذا اللي بتختارهB أسرع لإيش؟ لأنه أخد
+
+551
+00:43:30,360 --> 00:43:35,060
+وقت أقل في التنفيذ في ال execution time كان أقل
+
+552
+00:43:35,060 --> 00:43:41,050
+فمعنى ذلك أكيد قراري هيروح لمين؟ ل Bقررنا لازم
+
+553
+00:43:41,050 --> 00:43:44,150
+يروح ل B في الحالة هذه واضحة نرجع نقيتها تاني و لا
+
+554
+00:43:44,150 --> 00:43:49,210
+كويسة تمام ممتاز خلاص نبدأ هالواجهة عاد خلاص نبدأ
+
+555
+00:43:49,210 --> 00:43:52,550
+مهندسين رسمي و نبدأ في الأكواد و نبدأ نتكلم في إشي
+
+556
+00:43:52,550 --> 00:43:55,810
+واضح قدامنا هي code عندك و اللي أخدناه أول ما
+
+557
+00:43:55,810 --> 00:43:58,150
+بدأنا في الأكواد اللي هو كان بدنا نحسب ال maximum
+
+558
+00:43:58,150 --> 00:44:00,810
+عشان نحسبله ال time اللي يعني ال time complexity
+
+559
+00:44:00,810 --> 00:44:06,890
+اللي بدنا نحسبها خلاص نبدأ خليهاالـ procedure بدي
+
+560
+00:44:06,890 --> 00:44:09,710
+اقرأ كمان مرة احنا كتبناه المرة المفاتة بس
+
+561
+00:44:09,710 --> 00:44:12,750
+استوردناه من هناك عملناه recalling ك method و
+
+562
+00:44:12,750 --> 00:44:15,790
+سحبناه من هناك جيبناه عندنا كويس هايه بهذا الشكل
+
+563
+00:44:15,790 --> 00:44:20,510
+كالتالي بجي بقول اول line هنا او ال statement
+
+564
+00:44:20,510 --> 00:44:24,830
+الأولى محتاجة مثلا time T1 طبعا بتعتمد على ايش في
+
+565
+00:44:24,830 --> 00:44:29,170
+الآخر مواصفات الجهاز عندك بس في النهاية الجهاز
+
+566
+00:44:29,170 --> 00:44:34,650
+هيكون ثابتالـ times تبعته لكل الأكواد مدهو نفس
+
+567
+00:44:34,650 --> 00:44:38,550
+الجهاز نفس ال machine هي هي بدأ أقول أنه عشان ينفذ
+
+568
+00:44:38,550 --> 00:44:42,530
+ال statement هذه محتاج زمن T1 طيب ال for loop عشان
+
+569
+00:44:42,530 --> 00:44:45,710
+يعمل عملية المقارنة و يشوف امتى بده يزود و امتى
+
+570
+00:44:45,710 --> 00:44:51,860
+بده يوقف عملية ال process هذه بدها T2 طيبالـ F
+
+571
+00:44:51,860 --> 00:44:55,300
+statement كلها على بعض بدها T تلاتة هقول والله ال
+
+572
+00:44:55,300 --> 00:44:58,200
+return عشان يرجع ليه بدها T أربعة يمكن تكون T أقل
+
+573
+00:44:58,200 --> 00:45:00,460
+من الباقيين على اعتبار انه مش مهتم بس في النهاية
+
+574
+00:45:00,460 --> 00:45:03,380
+بدها زمن محتاجة زمن بال nano second بال micro
+
+575
+00:45:03,380 --> 00:45:06,260
+second يطلع اللي يطلع بس لازم ناخد حسابنا معاه لإن
+
+576
+00:45:06,260 --> 00:45:10,200
+ناخد حسابه في الحسبة ليش؟ لأنه هذا إذا اتكرر اتنين
+
+577
+00:45:10,200 --> 00:45:16,660
+مليون مرة مثلا لأ بيصير محرز بيحرز حسابه كويس في
+
+578
+00:45:16,660 --> 00:45:20,840
+هاي يوم بالنسبالنا بدنا نشتغل على ال worst caseال
+
+579
+00:45:20,840 --> 00:45:23,880
+worst case ايش ال worst case الان انك انت هتعمل
+
+580
+00:45:23,880 --> 00:45:30,100
+scan على كل ال elements صح؟ و هي لازم هتعمل على
+
+581
+00:45:30,100 --> 00:45:33,300
+الكل هذه فش فيها best اصلا انت بتدور على ال
+
+582
+00:45:33,300 --> 00:45:38,280
+maximum element داخل list فلازم تعمل scan عليهم
+
+583
+00:45:38,280 --> 00:45:41,520
+كلهم لازم تعمل scan عليهم كلهم فش مجال فش مجال
+
+584
+00:45:41,520 --> 00:45:48,680
+فهنا ببساطة ال time ال total time بده يكون T1 و T2
+
+585
+00:45:49,290 --> 00:45:56,710
+و T ثلاثة و T أربعة ممتاز T واحد أكان مرة هكرره
+
+586
+00:45:56,710 --> 00:46:04,770
+أثناء ال code مرة واحدة خلاص خلّيه زائد T اتنين N
+
+587
+00:46:04,770 --> 00:46:14,670
+مرة هنا معناته نعمله summation من اتنين اتنين
+
+588
+00:46:14,670 --> 00:46:18,330
+ل two N فإذا من اتنين to N كويس
+
+589
+00:46:20,390 --> 00:46:26,510
+تلاتة T تلاتة in مرة برضه in مرة لأنه هيفحصها في
+
+590
+00:46:26,510 --> 00:46:30,350
+كل مرة عند كل loop قيمة في ال loop هنا بده يفحص ال
+
+591
+00:46:30,350 --> 00:46:33,990
+term هذا فمعناته زائد و هنعمل نفس الكلام summation
+
+592
+00:46:33,990 --> 00:46:38,870
+للكل لل total طيب T أربعة مرة واحدة هو هيعمل
+
+593
+00:46:38,870 --> 00:46:41,590
+return مرة واحدة خلاص هايلي تم return مرة واحدة
+
+594
+00:46:42,350 --> 00:46:46,370
+Okay هطلعنا شكلها معادلة جلبناها معادلة الآن بدنا
+
+595
+00:46:46,370 --> 00:46:49,850
+نشوف ال order للمعادلة هذه order المعادلة هذا
+
+596
+00:46:49,850 --> 00:46:54,050
+بالنسبالي مدام أنا دايما بشتغل على نفس الجهاز ثابت
+
+597
+00:46:55,670 --> 00:46:59,370
+صحيح دائما انت بتشغل على نفس ال laptop تبعك فمعنى
+
+598
+00:46:59,370 --> 00:47:02,670
+ذلك انه كل مرة بتنفذ هو بيكون تقريبا ثابت ال time
+
+599
+00:47:02,670 --> 00:47:06,050
+هذا التغييرات بتكون بسيطة اذا في برامج تانية
+
+600
+00:47:06,050 --> 00:47:08,290
+مفتوحة معك ولا مافيش برامج ولا انت في اول ال
+
+601
+00:47:08,290 --> 00:47:12,010
+running للبرنامج بس في النهاية مدام انت على نفس
+
+602
+00:47:12,010 --> 00:47:17,570
+الجهاز ماغيرتش فهو بالنسبالي ثابت
+
+603
+00:47:17,570 --> 00:47:24,010
+وهذا نفس الكلام لمن؟ للاخيرة فعليا نفس الكلام ل
+
+604
+00:47:25,660 --> 00:47:33,920
+للمجموع الاتنين هدول بس مع ال summation مع
+
+605
+00:47:33,920 --> 00:47:42,060
+ال summation تمام هذا ثابت مع ثابت ثابت زائد هنا
+
+606
+00:47:42,060 --> 00:47:49,060
+جدش عدد مرات التكرار هنقول n مرة او n ناقص واحد
+
+607
+00:47:49,060 --> 00:47:52,080
+على تبارك الله بدء من اتنين بس زي ما قلنا هي
+
+608
+00:47:52,080 --> 00:47:56,780
+بالنسبة لل orderin linear طب in ناقص واحد برضه
+
+609
+00:47:56,780 --> 00:48:00,600
+هتظل linear بدك more specific تكون okay نكتبها زي
+
+610
+00:48:00,600 --> 00:48:05,560
+ما هي in ناقص واحد في big theta of واحد وهدي
+
+611
+00:48:05,560 --> 00:48:09,600
+جمعناها مع هدي خلصنا تمام كلنا عارفين ان هدي إيهاش
+
+612
+00:48:09,600 --> 00:48:17,820
+of in طيب مضروبة في constant هنا هتظل زي ما هي
+
+613
+00:48:17,820 --> 00:48:20,860
+مجموعة مع constant هتظل زي ما هي فإذا ال order
+
+614
+00:48:20,860 --> 00:48:21,640
+linear
+
+615
+00:48:27,110 --> 00:48:33,210
+فيه أبسط من هيك؟ تمام فهي الشغل هتنمحاه لإنه الشغل
+
+616
+00:48:33,210 --> 00:48:36,530
+أصلا هيك هيك مكتوب بس بيكون أحسن إنك ماتقرأش
+
+617
+00:48:36,530 --> 00:48:39,490
+تتفاعل معايا فيه بيكون أفضل إن احنا نكتبه بس في
+
+618
+00:48:39,490 --> 00:48:41,090
+النهاية هو كله مكتوب الكلام هذا
+
+619
+00:48:45,450 --> 00:48:49,750
+لأن أنا بتتكلم عن time، نتكلم عن مين؟ عن time، ال
+
+620
+00:48:49,750 --> 00:48:53,010
+function بتاعتنا time، خدوا بالكوا، time كمان مرة،
+
+621
+00:48:53,010 --> 00:48:54,610
+بعرفش في ال data structure بتش تقولوا time ولا
+
+622
+00:48:54,610 --> 00:48:57,870
+space؟ time، تمام، ممتاز، معناته إحنا هم اتفقين و
+
+623
+00:48:57,870 --> 00:49:00,390
+الآن شغالين مع بعضنا، هاي كل ال analysis اللي طوى
+
+624
+00:49:00,390 --> 00:49:04,110
+عملناها، هاي كل شغلنا اللي احنا طوى عملناها، وهيه
+
+625
+00:49:04,110 --> 00:49:08,180
+عملنا كيام more specific كمان هيهمن N ناقص واحد
+
+626
+00:49:08,180 --> 00:49:12,840
+عدد مرات التكرار عدد مرات التكرار لاحظوا اللي
+
+627
+00:49:12,840 --> 00:49:18,420
+بيعملك ال orders عادة ال for loops لأن
+
+628
+00:49:18,420 --> 00:49:21,400
+otherwise هي constants مدام ان انت بتشتر على نفس
+
+629
+00:49:21,400 --> 00:49:27,070
+الجهازجهازك ثابت لما بتيجي بتقارن algorithms مع
+
+630
+00:49:27,070 --> 00:49:30,210
+بعض فانت بتشتغلهم عشان تكون fair حتى بتشتغلهم على
+
+631
+00:49:30,210 --> 00:49:33,450
+نفس الجهاز فال constants هذه مافيش فيها مشكلة مين
+
+632
+00:49:33,450 --> 00:49:38,250
+اللي بيعطيك ال orders هي ال loops فدائما ال loop
+
+633
+00:49:38,250 --> 00:49:41,330
+هي اللي بتاخد بالك منها اه هذه ممكن تعملي order
+
+634
+00:49:41,330 --> 00:49:44,890
+تمام خلصنا وصلنا لنفس النتيجة بتاعتنا ان انا بتكلم
+
+635
+00:49:44,890 --> 00:49:52,510
+عن يلا ناشيOkay هاي كمان code اللي هو إيش اللي
+
+636
+00:49:52,510 --> 00:49:55,370
+أخدناها ده سابقا هنعمل recalling بس لإيش هذا لل
+
+637
+00:49:55,370 --> 00:49:59,690
+linear لل linear search هتنمسك ال linear ساشة
+
+638
+00:49:59,690 --> 00:50:03,910
+أخدناها مش هنقعد نقرأ و نكمل مرة مش هيك خلاص
+
+639
+00:50:03,910 --> 00:50:07,310
+عارفين أنه أول I بتكون واحد و بعدين بعمل while طول
+
+640
+00:50:07,310 --> 00:50:12,110
+ما أنا أقل من N بفحصكويس و بدور X وجدتها ولا
+
+641
+00:50:12,110 --> 00:50:16,970
+ماوجدتهاش و بعدين بنوقف بعدين بنوقف تلاحظ أنه هنا
+
+642
+00:50:16,970 --> 00:50:20,850
+بعكس اللي أولى مش دايما أنت بتروح لل worst case
+
+643
+00:50:20,850 --> 00:50:27,350
+أنت بتدور عن X على X يمكن تكون أول واحدة هذا ال
+
+644
+00:50:27,350 --> 00:50:31,870
+best case أو ممكن تكون في النص average case أو
+
+645
+00:50:31,870 --> 00:50:37,000
+ممكن تكون آخر أقول لك مش موجودةهد ال worst case لأ
+
+646
+00:50:37,000 --> 00:50:40,240
+هتمر عليهم كلهم و هتعمل كل process اللي بعدك عشان
+
+647
+00:50:40,240 --> 00:50:46,540
+تعمل ال check ان انت صرت برا ال list كمان هد أسوأ
+
+648
+00:50:46,540 --> 00:50:51,200
+حالة ممكنة طب على إيش هنشتغل؟ على الأسوأ لما تيجي
+
+649
+00:50:51,200 --> 00:50:54,440
+تقارن تشتغل على الأسوأ على أسوأ شيء هفترض ان كل
+
+650
+00:50:54,440 --> 00:50:58,630
+فعل كل line من هدولة إلهال time تبعه كل واحد اللي
+
+651
+00:50:58,630 --> 00:51:02,050
+ال time تبعه مبدأيا خليني نشتغل على ال worst case
+
+652
+00:51:02,050 --> 00:51:05,810
+على ال worst case والباقين هنشوفهم مع الشرح
+
+653
+00:51:05,810 --> 00:51:09,150
+هنشرحهم بس خليني افترض انه انا هشتغل اسوأ اشي لان
+
+654
+00:51:09,150 --> 00:51:14,430
+هو ده الصح هو ده الصح لان بدأنا T واحد فاذا ال T
+
+655
+00:51:14,430 --> 00:51:25,410
+of N هتساوي T واحد و T اتنين و T تلاتة و T اربعةو
+
+656
+00:51:25,410 --> 00:51:30,630
+T5 ماعطيني لعين 6 هيو كمان و هاي T6 نبدأ نشوف
+
+657
+00:51:30,630 --> 00:51:37,030
+تكراراتهم خلاص واحد هي جاعدة لحالها خلصنا منها طيب
+
+658
+00:51:37,030 --> 00:51:43,270
+اتنين اه بالظبط هتلاحظ انه في أسوأ حالة ان انت
+
+659
+00:51:43,270 --> 00:51:52,380
+تعمل scan على كل شغلك فهنا هتعملمن I بدأنا ب إيش؟
+
+660
+00:51:52,380 --> 00:51:56,500
+بواحد هتبدأ من واحد و هتكمل ل N فإذا من واحد ل N
+
+661
+00:51:56,500 --> 00:52:03,660
+لمين؟ ل T اتنين نبعدها شوية عشان نتبين T اتنين
+
+662
+00:52:03,660 --> 00:52:11,880
+تمام هاي خلصنا من T اتنين ال I N مرة زائد نشملها
+
+663
+00:52:11,880 --> 00:52:17,800
+معاها مدام نفس الاشي هاي شملناها معاها تمام T
+
+664
+00:52:17,800 --> 00:52:23,420
+أربعةمرة واحدة فعليا مرة واحدة لأن ال loop سكر
+
+665
+00:52:23,420 --> 00:52:27,920
+خلاص هي ال loop تبعك هي
+
+666
+00:52:27,920 --> 00:52:35,220
+ال loop بهذا الشكل فعليا هيخلص ال loop انا مش عمله
+
+667
+00:52:35,220 --> 00:52:39,500
+لا begin ولا end ال loop فعليا هو السطرين هدول بس
+
+668
+00:52:39,500 --> 00:52:46,440
+خلصت و false تطلع بتشوف ال if then ال if then
+
+669
+00:52:46,440 --> 00:52:55,860
+هتعملها مرةو مش هتتحقق صح؟ يعني انت فحصتها انت
+
+670
+00:52:55,860 --> 00:53:01,380
+فعلا فحصتها okay وين روحنا؟ اه فحصناها فصار زائد T
+
+671
+00:53:01,380 --> 00:53:08,720
+أربعة و إن جبرت تروح تنفذ ال else كمان صح؟ لأن انت
+
+672
+00:53:08,720 --> 00:53:12,900
+فعلا في أسوأ الحوار انك مالجتش فاطلعت و ال then
+
+673
+00:53:12,900 --> 00:53:18,530
+ماتحققتشthen مش هتتحقق، لإن انت فحصت، انت فحصت
+
+674
+00:53:18,530 --> 00:53:23,270
+فانت استنفذت الوقت تبع تي أربعة و روحت التي خمسة
+
+675
+00:53:23,270 --> 00:53:27,930
+نفذتها كمان عشان ترجعلي بصفر تقولي انك انت ماوجدتش
+
+676
+00:53:27,930 --> 00:53:36,370
+x فزائد خمسة كمان ثم return جاء زائد ستة تمام؟
+
+677
+00:53:36,370 --> 00:53:39,150
+اتوقع ابتيش بتقدر هيك تطلع تقولي ال order total
+
+678
+00:53:39,150 --> 00:53:45,760
+يقداش inصح زي ما توعملنا فهتلاقي ان هي فعليا θ of
+
+679
+00:53:45,760 --> 00:53:53,540
+n أصبحت بايسنز ممتاز تمام فأصبحت بهذا الشكل هي
+
+680
+00:53:53,540 --> 00:53:57,820
+الحالة الأولى اللي هي ال worst case program في
+
+681
+00:53:57,820 --> 00:54:02,080
+حالة ال worst case طب the best case ايش ده best
+
+682
+00:54:02,080 --> 00:54:05,780
+case انه من أول مرة لجيته من أول مرة هتجد انه
+
+683
+00:54:05,780 --> 00:54:09,840
+وجدته طيب من أول مرة معناته حاجة اطبق
+
+684
+00:54:12,300 --> 00:54:18,620
+واحد و هطبق اتنين لانه لازم اعمل فحص هروح لتلاته
+
+685
+00:54:18,620 --> 00:54:23,500
+مش مضطر لانه من اتنين صار false فمش هاخد تلاته
+
+686
+00:54:23,500 --> 00:54:27,800
+هروح لاربعة اه هروح اعمل اربعة و اربعة هنا هتكون
+
+687
+00:54:27,800 --> 00:54:34,200
+trueفهنفذها مش هروح لخمسة ليش لأنه نفذت ال
+
+688
+00:54:34,200 --> 00:54:37,800
+condition و ال condition true مش false true فإذا
+
+689
+00:54:37,800 --> 00:54:42,740
+تلاتة و خمسة مش محتاجهم طيب totally إيش طلع
+
+690
+00:54:42,740 --> 00:54:47,020
+constant بس هذه أفضل الحالات اللي بضمانش أشتغل
+
+691
+00:54:47,020 --> 00:54:50,200
+دايما عليها بضمانش عملنا دايما عليها في ال average
+
+692
+00:54:50,200 --> 00:54:54,960
+في المتوسط أني أقول في نص البحث
+
+693
+00:54:55,630 --> 00:54:59,550
+في نص ال list وجدت X المطلوبة هضلت زيها زي ال
+
+694
+00:54:59,550 --> 00:55:07,750
+worst بالاستثناء T5 ليش T5؟ لأنه فعليا انا هطبق و
+
+695
+00:55:07,750 --> 00:55:12,570
+هلاجأ ان then it true ال condition هنا true فمش
+
+696
+00:55:12,570 --> 00:55:19,950
+هروح ل else مش هنروح لل else فخمسة مش مشمولة T5 بس
+
+697
+00:55:19,950 --> 00:55:22,170
+ك order ضال نفس ال order لل worst case
+
+698
+00:55:25,660 --> 00:55:30,980
+لأن ال order in أو ال order نُص in دلت first order
+
+699
+00:55:30,980 --> 00:55:34,200
+ربطه في نُص النُص بالنسبالك كأنه constant و
+
+700
+00:55:34,200 --> 00:55:37,480
+constant في ال function بتضل زي ما هي لعندي كخلصنا
+
+701
+00:55:37,480 --> 00:55:40,280
+المرة القادمة ان شاء الله بنكمل باجي أكواد نعمل
+
+702
+00:55:40,280 --> 00:55:42,300
+لهم تحليل ان شاء الله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1DXhPKvs1dE_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1DXhPKvs1dE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ecd8a8dcb50a0208fd0c1acde119035e3cbd4451
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1DXhPKvs1dE_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2719, "start": 5.11, "end": 27.19, "text": "بسم الله الرحمن الرحيم، يعطيكوا العفو يا شباب، نكمل اليوم إن شاء الله تعالى الجزء اللي كان متبقيناه في ال .. ال .. ال growth و ال order of growth عشان نشوف كيف بنستخدم المعلومات هذه في حساب ال complexity للأكواد، لل algorithm اللي أخدناها من الأسبوع اللي فات، اللي كنا بنتكلم فيه عن ال pseudocode", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 12399, 37495, 9566, 1829, 4117, 14407, 18863, 5172, 2407, 35186, 13412, 3555, 16758, 12399, 8717, 24793, 1211, 45595, 20498, 36145, 13412, 16606, 21984, 37279, 6027, 7578, 25724, 11622, 38207, 13672, 1829, 25961, 44650, 3555, 38436, 8315, 3224, 8978, 2423, 4386, 2423, 4386, 2423, 4599, 4032, 2423, 1668, 295, 4599, 6225, 8592, 7649, 8717, 8592, 38688, 9122, 33911, 44945, 14851, 9778, 40448, 9673, 30241, 20498, 9307, 29538, 8978, 11331, 3794, 16758, 2423, 14024, 24976, 10721, 4117, 14407, 3215, 12399, 24976, 9284, 13672, 1829, 5551, 9778, 3215, 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عندي هذا هذا اللي هي ال small omega إيش معناها small omega لو تفهمناها؟ إنه إذا كانت F أكبر والزمن أكبر من إيش؟ إيش يعني واحد؟ constant إيش يعني constant؟ يعني هدف فعليًا n to the power صفر", "tokens": [6027, 995, 34268, 2288, 46958, 13672, 1829, 11778, 9778, 1211, 18871, 16254, 23758, 23758, 13672, 1829, 39896, 2423, 1359, 10498, 11933, 1829, 8592, 20449, 8315, 11296, 1359, 10498, 45164, 6055, 5172, 16095, 8315, 11296, 22807, 36145, 3224, 11933, 15730, 25961, 2655, 479, 5551, 4117, 26890, 4032, 6027, 11622, 27842, 5551, 4117, 26890, 9154, 11933, 1829, 8592, 22807, 11933, 1829, 8592, 37495, 22653, 36764, 24401, 22807, 5754, 11933, 1829, 8592, 37495, 22653, 5754, 22807, 37495, 22653, 8032, 3215, 5172, 6156, 3615, 20292, 14111, 995, 297, 281, 264, 1347, 20328, 5172, 2288], "avg_logprob": -0.2081043887269366, "compression_ratio": 1.689119170984456, "no_speech_prob": 1.1324882507324219e-06, "words": [{"start": 534.3, "end": 534.9, "word": "الاعتراض", "probability": 0.87080078125}, 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{"start": 670.84, "end": 671.34, "word": " واحد", "probability": 0.987548828125}, {"start": 671.34, "end": 672.24, "word": " بتصير", "probability": 0.9308268229166666}, {"start": 672.24, "end": 672.82, "word": " constant", "probability": 0.95263671875}, {"start": 672.82, "end": 673.84, "word": " مش", "probability": 0.93896484375}, {"start": 673.84, "end": 674.04, "word": " مش", "probability": 0.458251953125}, {"start": 674.04, "end": 674.28, "word": " هيك", "probability": 0.6630859375}, {"start": 674.28, "end": 674.64, "word": " صارت", "probability": 0.9345703125}, {"start": 674.64, "end": 674.9, "word": " تتبار", "probability": 0.58447265625}, {"start": 674.9, "end": 675.28, "word": " سفر", "probability": 0.8065592447916666}, {"start": 675.28, "end": 676.14, "word": " constant", "probability": 0.8115234375}, {"start": 676.14, "end": 676.38, "word": " طيب", "probability": 0.9567057291666666}, {"start": 676.38, "end": 676.5, "word": " ال", "probability": 0.98046875}, {"start": 676.5, 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الحقيقة صحيحة الحقيقة الكتاب اللي ناياها صحيحة تمشي مافيش مشكلة طيب log كلنا عارفين أن ال log أقل من ال function نفسها لو عندك linear لل in ما هي in لما تقول", "tokens": [2407, 6156, 3615, 20292, 995, 1975, 2407, 6055, 3794, 995, 45865, 5754, 37495, 22653, 34105, 33251, 2655, 16758, 13672, 1829, 8717, 995, 25528, 11296, 955, 4724, 43042, 3224, 3714, 33599, 1829, 2423, 1186, 21542, 38436, 28671, 20328, 5016, 1829, 5016, 3660, 21542, 38436, 28671, 33251, 2655, 16758, 13672, 1829, 8717, 995, 25528, 11296, 20328, 5016, 1829, 5016, 3660, 46811, 8592, 1829, 19446, 41185, 8592, 37893, 28820, 3660, 23032, 1829, 3555, 3565, 28242, 8315, 6225, 9640, 5172, 9957, 14739, 2423, 3565, 5551, 4587, 1211, 9154, 2423, 2445, 8717, 36178, 11296, 45164, 43242, 4117, 8213, 24976, 294, 19446, 39896, 294, 5296, 15042, 6055, 39648], "avg_logprob": -0.16823422387965675, "compression_ratio": 1.7887323943661972, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 687.84, "end": 688.02, "word": "و", 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"seek": 170777, "start": 1689.91, "end": 1707.77, "text": "في ال infinity هيكون الفرق بينهم صار شاسع جدا لدرجة ان f بالنسبة ل g لا تذكر كأنها limit at x limit to infinity بتصير النسبة بينهم كأنها صفر كأن قيمة g مش شايفة قيمة f", "tokens": [41185, 2423, 13202, 39896, 30544, 27188, 2288, 4587, 49374, 16095, 20328, 9640, 13412, 32277, 3615, 10874, 28259, 5296, 3215, 47341, 3660, 16472, 283, 20666, 1863, 35457, 3660, 5296, 290, 20193, 6055, 8848, 37983, 9122, 33456, 11296, 4948, 412, 2031, 4948, 281, 13202, 39894, 9381, 13546, 28239, 35457, 3660, 49374, 16095, 9122, 33456, 11296, 20328, 5172, 2288, 9122, 33456, 12174, 32640, 3660, 290, 37893, 13412, 995, 33911, 3660, 12174, 32640, 3660, 283], "avg_logprob": -0.1591796891556846, "compression_ratio": 1.6196319018404908, "no_speech_prob": 1.6391277313232422e-05, "words": [{"start": 1689.91, "end": 1690.09, "word": "في", "probability": 0.525390625}, {"start": 1690.09, "end": 1690.21, "word": " ال", "probability": 0.8310546875}, {"start": 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قيمة جدا كبيرة مقابل قيمة كتير صغيرة لل F يعني F أصغر من G يعني معناته F أصغر من G فعليا تمام الآن هناخد بعض ال functions بعض ال functions اللي كتير كويس نتعامل معها واحد ال constant هو أقل من ال log of log", "tokens": [3615, 41260, 2423, 13202, 43242, 2423, 13202, 6156, 4197, 4614, 34105, 4724, 24401, 3215, 5296, 28814, 1863, 3224, 20449, 8315, 3224, 29910, 23275, 36145, 3224, 29538, 5551, 9381, 3555, 33753, 12174, 32640, 3660, 10874, 28259, 9122, 3555, 48923, 3714, 4587, 16758, 1211, 12174, 32640, 3660, 9122, 2655, 13546, 20328, 17082, 48923, 24976, 479, 37495, 22653, 479, 5551, 9381, 17082, 2288, 9154, 460, 37495, 22653, 20449, 8315, 47395, 479, 5551, 9381, 17082, 2288, 9154, 460, 6156, 3615, 20292, 995, 46811, 10943, 6024, 48506, 8032, 1863, 47283, 3215, 45030, 11242, 2423, 6828, 45030, 11242, 2423, 6828, 13672, 1829, 9122, 2655, 13546, 9122, 45865, 3794, 8717, 2655, 3615, 10943, 1211, 20449, 11296, 36764, 24401, 2423, 5754, 31439, 5551, 4587, 1211, 9154, 2423, 3565, 295, 3565], 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بدنا نفرض أن عندي algorithm A ال algorithm A هذا ال worst case time complexity فبنسميها ال worst case time complexity F of N", "tokens": [1211, 2407, 5551, 9778, 3215, 8315, 7297, 300, 34051, 47525, 8315, 8717, 5172, 43042, 11331, 6027, 3660, 20449, 9957, 3660, 21542, 6027, 3660, 29538, 47525, 8315, 8717, 5172, 43042, 14739, 18871, 16254, 9284, 316, 2423, 9284, 316, 23758, 2423, 5855, 1389, 565, 14024, 6156, 3555, 1863, 38251, 1829, 11296, 2423, 5855, 1389, 565, 14024, 479, 295, 426], "avg_logprob": -0.25107759494206, "compression_ratio": 1.5833333333333333, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 2422.24, "end": 2422.54, "word": "لو", "probability": 0.81787109375}, {"start": 2422.54, "end": 2423.02, "word": " أخدنا", "probability": 0.869384765625}, {"start": 2423.02, "end": 2423.46, "word": " suppose", "probability": 0.65625}, {"start": 2423.46, "end": 2423.74, "word": " that", "probability": 0.92626953125}, {"start": 2423.74, "end": 2423.98, "word": " أو", 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0.4453125}, {"start": 3297.51, "end": 3298.23, "word": " المطلوبة", "probability": 0.9775390625}, {"start": 3298.23, "end": 3299.05, "word": " هضلت", "probability": 0.64453125}, {"start": 3299.05, "end": 3299.29, "word": " زيها", "probability": 0.9469401041666666}, {"start": 3299.29, "end": 3299.45, "word": " زي", "probability": 0.971435546875}, {"start": 3299.45, "end": 3299.55, "word": " ال", "probability": 0.94384765625}, {"start": 3299.55, "end": 3299.77, "word": " worst", "probability": 0.96630859375}, {"start": 3299.77, "end": 3300.57, "word": " بالاستثناء", "probability": 0.7822672526041666}, {"start": 3300.57, "end": 3302.31, "word": " T5", "probability": 0.724365234375}, {"start": 3302.31, "end": 3303.65, "word": " ليش", "probability": 0.867431640625}, {"start": 3303.65, "end": 3304.75, "word": " T5؟", "probability": 0.8079427083333334}, {"start": 3304.75, "end": 3305.69, "word": " لأنه", "probability": 0.8751627604166666}, {"start": 3305.69, "end": 3306.27, "word": " فعليا", "probability": 0.9322509765625}, {"start": 3306.27, "end": 3306.41, "word": " انا", "probability": 0.755615234375}, {"start": 3306.41, "end": 3307.15, "word": " هطبق", "probability": 0.9705810546875}, {"start": 3307.15, "end": 3307.75, "word": " و", "probability": 0.9375}, {"start": 3307.75, "end": 3308.13, "word": " هلاجأ", "probability": 0.732177734375}, {"start": 3308.13, "end": 3308.25, "word": " ان", "probability": 0.7744140625}, {"start": 3308.25, "end": 3308.63, "word": " then", "probability": 0.306640625}, {"start": 3308.63, "end": 3309.21, "word": " it", "probability": 0.2200927734375}, {"start": 3309.21, "end": 3309.51, "word": " true", "probability": 0.849609375}, {"start": 3309.51, "end": 3309.99, "word": " ال", "probability": 0.859375}, {"start": 3309.99, "end": 3310.39, "word": " condition", "probability": 0.96337890625}, {"start": 3310.39, "end": 3310.69, "word": " هنا", "probability": 0.9677734375}, {"start": 3310.69, "end": 3311.35, "word": " true", "probability": 0.505859375}, {"start": 3311.35, "end": 3312.57, "word": " فمش", "probability": 0.8408203125}, {"start": 3312.57, "end": 3312.87, "word": " هروح", "probability": 0.91015625}, {"start": 3312.87, "end": 3312.97, "word": " ل", "probability": 0.77392578125}, {"start": 3312.97, "end": 3313.27, "word": " else", "probability": 0.869140625}, {"start": 3313.27, "end": 3314.89, "word": " مش", "probability": 0.488525390625}, {"start": 3314.89, "end": 3315.15, "word": " هنروح", "probability": 0.9193115234375}, {"start": 3315.15, "end": 3315.29, "word": " لل", "probability": 0.6796875}, {"start": 3315.29, "end": 3315.55, "word": " else", "probability": 0.9619140625}, {"start": 3315.55, "end": 3317.37, "word": " فخمسة", "probability": 0.82275390625}, {"start": 3317.37, "end": 3317.63, "word": " مش", "probability": 0.97802734375}, {"start": 3317.63, "end": 3318.41, "word": " مشمولة", "probability": 0.9595947265625}, {"start": 3318.41, "end": 3319.19, "word": " T5", "probability": 0.826904296875}, {"start": 3319.19, "end": 3319.95, "word": " بس", "probability": 0.9765625}, {"start": 3319.95, "end": 3320.09, "word": " ك", "probability": 0.98583984375}, {"start": 3320.09, "end": 3320.47, "word": " order", "probability": 0.970703125}, {"start": 3320.47, "end": 3320.81, "word": " ضال", "probability": 0.5751953125}, {"start": 3320.81, "end": 3321.01, "word": " نفس", "probability": 0.994140625}, {"start": 3321.01, "end": 3321.13, "word": " ال", "probability": 0.96728515625}, {"start": 3321.13, "end": 3321.35, "word": " order", "probability": 0.9775390625}, {"start": 3321.35, "end": 3321.55, "word": " لل", "probability": 0.6201171875}, {"start": 3321.55, "end": 3321.79, "word": " worst", "probability": 0.98046875}, {"start": 3321.79, "end": 3322.17, "word": " case", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 131, "seek": 334230, "start": 3325.66, "end": 3342.3, "text": "لأن ال order in أو ال order نُص in دلت first order ربطه في نُص النُص بالنسبالك كأنه constant و constant في ال function بتضل زي ما هي لعندي كخلصنا المرة القادمة ان شاء الله بنكمل باجي أكواد نعمل لهم تحليل ان شاء الله يعطيكوا العافية", "tokens": [1211, 33456, 2423, 1668, 294, 34051, 2423, 1668, 8717, 10859, 9381, 294, 11778, 1211, 2655, 700, 1668, 12602, 3555, 9566, 3224, 8978, 8717, 10859, 9381, 28239, 10859, 9381, 20666, 1863, 35457, 6027, 4117, 9122, 33456, 3224, 5754, 4032, 5754, 8978, 2423, 2445, 39894, 11242, 1211, 30767, 1829, 19446, 39896, 5296, 3615, 1863, 16254, 9122, 9778, 1211, 9381, 8315, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 44945, 24793, 1211, 4724, 995, 7435, 1829, 5551, 4117, 14407, 3215, 8717, 25957, 1211, 5296, 16095, 6055, 5016, 20292, 1211, 16472, 13412, 16606, 21984, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.2884375101327896, "compression_ratio": 1.7571428571428571, "no_speech_prob": 2.3603439331054688e-05, "words": [{"start": 3325.6600000000003, "end": 3326.2200000000003, "word": "لأن", "probability": 0.2003173828125}, {"start": 3326.2200000000003, "end": 3326.78, "word": " ال", "probability": 0.306396484375}, {"start": 3326.78, "end": 3327.06, "word": " order", "probability": 0.7392578125}, {"start": 3327.06, "end": 3327.42, "word": " in", "probability": 0.51416015625}, {"start": 3327.42, "end": 3328.08, "word": " أو", "probability": 0.69580078125}, {"start": 3328.08, "end": 3328.2, "word": " ال", "probability": 0.73486328125}, {"start": 3328.2, "end": 3328.44, "word": " order", "probability": 0.96533203125}, {"start": 3328.44, "end": 3328.76, "word": " نُص", "probability": 0.8026529947916666}, {"start": 3328.76, "end": 3329.0, "word": " in", "probability": 0.91064453125}, {"start": 3329.0, "end": 3330.4, "word": " دلت", "probability": 0.6890869140625}, {"start": 3330.4, "end": 3330.6, "word": " first", "probability": 0.61181640625}, {"start": 3330.6, "end": 3330.98, "word": " order", "probability": 0.97119140625}, {"start": 3330.98, "end": 3332.36, "word": " ربطه", "probability": 0.761810302734375}, {"start": 3332.36, "end": 3332.42, "word": " في", "probability": 0.66455078125}, {"start": 3332.42, "end": 3332.66, "word": " نُص", "probability": 0.9461263020833334}, {"start": 3332.66, "end": 3332.94, "word": " النُص", "probability": 0.7562662760416666}, {"start": 3332.94, "end": 3333.44, "word": " بالنسبالك", "probability": 0.85078125}, {"start": 3333.44, "end": 3333.7, "word": " كأنه", "probability": 0.8680013020833334}, {"start": 3333.7, "end": 3334.04, "word": " constant", "probability": 0.94970703125}, {"start": 3334.04, "end": 3334.2, "word": " و", "probability": 0.671875}, {"start": 3334.2, "end": 3334.48, "word": " constant", "probability": 0.69580078125}, {"start": 3334.48, "end": 3334.62, "word": " في", "probability": 0.81103515625}, {"start": 3334.62, "end": 3334.66, "word": " ال", "probability": 0.54736328125}, {"start": 3334.66, "end": 3334.86, "word": " function", "probability": 0.826171875}, {"start": 3334.86, "end": 3335.22, "word": " بتضل", "probability": 0.5249837239583334}, {"start": 3335.22, "end": 3335.38, "word": " زي", "probability": 0.904052734375}, {"start": 3335.38, "end": 3335.46, "word": " ما", "probability": 0.947265625}, {"start": 3335.46, "end": 3335.66, "word": " هي", "probability": 0.8974609375}, {"start": 3335.66, "end": 3336.92, "word": " لعندي", "probability": 0.579010009765625}, {"start": 3336.92, "end": 3337.48, "word": " كخلصنا", "probability": 0.800732421875}, {"start": 3337.48, "end": 3337.82, "word": " المرة", "probability": 0.927734375}, {"start": 3337.82, "end": 3338.2, "word": " القادمة", "probability": 0.9873046875}, {"start": 3338.2, "end": 3338.32, "word": " ان", "probability": 0.454345703125}, {"start": 3338.32, "end": 3338.44, "word": " شاء", "probability": 0.961669921875}, {"start": 3338.44, "end": 3338.48, "word": " الله", "probability": 0.92529296875}, {"start": 3338.48, "end": 3339.2, "word": " بنكمل", "probability": 0.9451497395833334}, {"start": 3339.2, "end": 3339.6, "word": " باجي", "probability": 0.7691650390625}, {"start": 3339.6, "end": 3339.98, "word": " أكواد", "probability": 0.9146728515625}, {"start": 3339.98, "end": 3340.28, "word": " نعمل", "probability": 0.94384765625}, {"start": 3340.28, "end": 3340.46, "word": " لهم", "probability": 0.7396240234375}, {"start": 3340.46, "end": 3340.88, "word": " تحليل", "probability": 0.968017578125}, {"start": 3340.88, "end": 3341.0, "word": " ان", "probability": 0.7490234375}, {"start": 3341.0, "end": 3341.2, "word": " شاء", "probability": 0.993896484375}, {"start": 3341.2, "end": 3341.34, "word": " الله", "probability": 0.951171875}, {"start": 3341.34, "end": 3342.04, "word": " يعطيكوا", "probability": 0.894140625}, {"start": 3342.04, "end": 3342.3, "word": " العافية", "probability": 0.92138671875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3342.3499375, "duration_after_vad": 3227.6006249999873}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1DXhPKvs1dE_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1DXhPKvs1dE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..dc15a76618ebc0bab7867bf16472adaf462860de
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1DXhPKvs1dE_raw.srt
@@ -0,0 +1,2828 @@
+1
+00:00:05,110 --> 00:00:08,130
+بسم الله الرحمن الرحيم، يعطيكوا العفو يا شباب،
+
+2
+00:00:08,130 --> 00:00:11,050
+نكمل اليوم إن شاء الله تعالى الجزء اللي كان
+
+3
+00:00:11,050 --> 00:00:15,790
+متبقيناه في ال .. ال .. ال growth و ال order of
+
+4
+00:00:15,790 --> 00:00:20,490
+growth عشان نشوف كيف بنستخدم المعلومات هذه في حساب
+
+5
+00:00:20,490 --> 00:00:24,070
+ال complexity للأكواد، لل algorithm اللي أخدناها
+
+6
+00:00:24,070 --> 00:00:26,670
+من الأسبوع اللي فات، اللي كنا بنتكلم فيه عن ال
+
+7
+00:00:26,670 --> 00:00:30,120
+pseudocodeبغض نوفر طبعا إيش اللغة اللي انت
+
+8
+00:00:30,120 --> 00:00:34,440
+هتستخدمها في النهاية انت عارف ان في عندك code و
+
+9
+00:00:34,440 --> 00:00:36,980
+بدك تحسبله ال complexity طيب جابر ما نروح نخد في
+
+10
+00:00:36,980 --> 00:00:40,500
+ال complexity كان ضروري جدا نفهم انه عشان أحسب
+
+11
+00:00:40,500 --> 00:00:43,820
+complexity فانا فعليا بتعامل مع ال algorithm اللي
+
+12
+00:00:43,820 --> 00:00:48,260
+هو ال code كأنه function function في مين؟ function
+
+13
+00:00:48,260 --> 00:00:51,760
+فيفي ال inputs function في ال inputs مدام function
+
+14
+00:00:51,760 --> 00:00:55,600
+في ال inputs معناته بهمني جدا أدرس ال functions
+
+15
+00:00:55,600 --> 00:00:58,620
+نفسها وإيش أنواع ال functions وكيف أميز بين ال
+
+16
+00:00:58,620 --> 00:01:01,720
+functions وبعضها من حيث ال order of growth عشان
+
+17
+00:01:01,720 --> 00:01:07,380
+بعدين لما نحطالأكواد بصفة ال functionality بتاعتهم
+
+18
+00:01:07,380 --> 00:01:10,980
+أقدر أقارن بينهم هذه .. هذا كانت الفكرة الأساسية
+
+19
+00:01:10,980 --> 00:01:14,580
+في الموضوع خلصنا الأكواد و انتهينا من هذا الموضوع
+
+20
+00:01:14,580 --> 00:01:17,460
+انه و الله في حاجة اسمها pseudocode و طلعنا ..
+
+21
+00:01:17,460 --> 00:01:20,520
+شفنا إيش ال .. ال .. ال statement سبعته أخدنا أكم
+
+22
+00:01:20,520 --> 00:01:24,740
+من مثال بدأنا نتكلم في مين؟ في ال functions و ال
+
+23
+00:01:24,740 --> 00:01:28,480
+order و في growth لل functions ليش الكلام هذا؟
+
+24
+00:01:28,480 --> 00:01:31,200
+لأنه مش أنا معني بال functions ك functions لأ أنا
+
+25
+00:01:31,200 --> 00:01:34,770
+معني فيها لأنهاللي جاي اليوم هنتكلم عنه ان كيف
+
+26
+00:01:34,770 --> 00:01:39,310
+اخلي ال code يصبح function فمعناه ذلك بصير اقيص ال
+
+27
+00:01:39,310 --> 00:01:41,490
+functionality بتاعته ال function هت هي اللي بتصير
+
+28
+00:01:41,490 --> 00:01:45,990
+قدامي معيار المقارنة واضحة ليش احنا بنروح ل ..
+
+29
+00:01:45,990 --> 00:01:50,570
+لموضوع ال order of growth لأنه ال code هيمثل as a
+
+30
+00:01:50,570 --> 00:01:56,510
+function ك function طيب ايش ال .. ال .. ال .. ال
+
+31
+00:01:56,510 --> 00:02:00,250
+function value بتاعة ال code هذا هنتكلم فيه بس
+
+32
+00:02:00,250 --> 00:02:04,700
+احنا عارفين ان ال inputال input هي مدخلات ال
+
+33
+00:02:04,700 --> 00:02:08,840
+function هي ال arguments مجموعة ال inputs ال array
+
+34
+00:02:08,840 --> 00:02:14,780
+اللى بدنا ندخلها لل algorithm كمدخلات كويس نكمل
+
+35
+00:02:14,780 --> 00:02:17,660
+اللى كنا اتكلمنا المرة الماضية و كنا جولنا او يمكن
+
+36
+00:02:17,660 --> 00:02:21,380
+مادخلناش الا ال big O المرة الماضية فقط جولنا ان
+
+37
+00:02:21,380 --> 00:02:25,140
+at most big O ايش يعني at most big O يعني لما اقول
+
+38
+00:02:25,140 --> 00:02:32,740
+if هي تساوي او belong to او at mostأي واحدة هكتبها
+
+39
+00:02:32,740 --> 00:02:36,520
+بمش الحال Of if مثلا يعني كأني بقول ان ال function
+
+40
+00:02:36,520 --> 00:02:41,060
+هي دي في أسوأ أحوالها في أكبر order لها هي first
+
+41
+00:02:41,060 --> 00:02:46,140
+order أكبر ممكن تكون أقل أو ممكن تكون أقل ممكن
+
+42
+00:02:46,140 --> 00:02:51,180
+تكون أقل يمكن أنا مش قادر تحديدها exactly بس في
+
+43
+00:02:51,180 --> 00:02:55,040
+أسوأ أحوالها هتكون first order أو في أسوأ أحوالها
+
+44
+00:02:55,040 --> 00:02:58,380
+second orderأو third order اكتب اللي بدكيها بس في
+
+45
+00:02:58,380 --> 00:03:02,500
+النهاية نفهم الفكرة فال big O هي at most بمعنى ان
+
+46
+00:03:02,500 --> 00:03:09,420
+ال function في أسوأ أحوالها هي تربيعية مثلا for
+
+47
+00:03:09,420 --> 00:03:12,700
+example ممكن تكون أقل او ممكن تكون أقل ممكن تكون
+
+48
+00:03:12,700 --> 00:03:15,800
+أقل فاحنا دايما بنشتغل على ال worst case وهذا
+
+49
+00:03:15,800 --> 00:03:19,120
+بتهيألي معلومة أكيد موجودة عندكم احنا في الأكواد
+
+50
+00:03:19,120 --> 00:03:21,780
+بنشتغل على ال worst case في الأسوأ الأحوال لإن انت
+
+51
+00:03:21,780 --> 00:03:25,410
+مش عارف فعليا شكل ال inputs اللي داخل عندكانت
+
+52
+00:03:25,410 --> 00:03:28,310
+المفروض بتعمل generality ل ال code زي ال
+
+53
+00:03:28,310 --> 00:03:30,670
+characteristics اللي أخدناها المرة الماضية و قلنا
+
+54
+00:03:30,670 --> 00:03:32,690
+من أهم ال characteristics .. مجموعة
+
+55
+00:03:32,690 --> 00:03:35,350
+characteristics أخدناها ال generality انه يكون ال
+
+56
+00:03:35,350 --> 00:03:38,890
+code general .. general بغض النظر إيش ال inputs
+
+57
+00:03:38,890 --> 00:03:43,270
+اللي أعطتهيا .. تمام؟ فهذه ال big O .. نبدأ نشوف
+
+58
+00:03:43,270 --> 00:03:47,690
+مجموعة facts عن ال big O ممكن نحتاجها لقدام .. لو
+
+59
+00:03:47,690 --> 00:03:51,920
+قلنا ال Fهي ال function هي belong to او تساوي او
+
+60
+00:03:51,920 --> 00:03:56,380
+at most اكتب اللي بدك ياه مش هتفرج معناه او هي is
+
+61
+00:03:56,380 --> 00:04:02,020
+على طول بمشي الحال big O of G فإذا ال F في أسوأ
+
+62
+00:04:02,020 --> 00:04:10,520
+أحوالها هي من ال order G and G big O of H فحسب ال
+
+63
+00:04:10,520 --> 00:04:13,620
+relation بتاعة ال transitive معناه ذلك ان ال F
+
+64
+00:04:13,620 --> 00:04:19,900
+بالضرورة هتكون big O of Hيعني بهذا الشكل طب لما
+
+65
+00:04:19,900 --> 00:04:26,740
+اقول هذه عبارة عن جي وجي
+
+66
+00:04:26,740 --> 00:04:33,480
+هنا عبارة عن انتر بيعي وقولنا جي big O of H وH هذه
+
+67
+00:04:33,480 --> 00:04:41,640
+تكعيب تمام؟ بمشي الحال هيك صحيح؟ اف big O of G اف
+
+68
+00:04:41,640 --> 00:04:45,500
+هذه ممكن تكون first order بمشي second order اه
+
+69
+00:04:45,500 --> 00:04:51,600
+بمشي برضهماشي، مافيش مشكلة، مدام big O of G، طيب G
+
+70
+00:04:51,600 --> 00:04:55,000
+second order، طيب الـ G هذه اللي هي second order
+
+71
+00:04:55,000 --> 00:04:59,860
+أكيد هتكون big O of H، H كانت second order، بمشي
+
+72
+00:04:59,860 --> 00:05:03,640
+الحال، third order، بمشي الحال، fourth order، بمشي
+
+73
+00:05:03,640 --> 00:05:10,320
+الحال، لأ، بتنفعش big O، احنا قولنا at most، بمعنى
+
+74
+00:05:10,320 --> 00:05:15,950
+في أسوأ أحوالها G، هي هتكون هذا ال ..يا بتسويها يا
+
+75
+00:05:15,950 --> 00:05:18,490
+أقل منها ال G، يا بتسويها أقل منها، فإذا
+
+76
+00:05:18,490 --> 00:05:23,350
+automatically بقدر أستنتج أن F نفسها هي big O of
+
+77
+00:05:23,350 --> 00:05:31,430
+H، صح؟ لأن F حسب التعريف اللي لقناه هنا، هي تربيع
+
+78
+00:05:31,430 --> 00:05:32,110
+فأقل
+
+79
+00:05:35,740 --> 00:05:43,540
+بمشي الحل .. بمشي الحل .. بمشي الحل .. بمشي
+
+80
+00:05:43,540 --> 00:05:45,640
+الحل .. بمشي الحل .. بمشي الحل .. بمشي الحل ..
+
+81
+00:05:45,640 --> 00:05:46,100
+بمشي الحل .. بمشي الحل .. بمشي الحل .. بمشي الحل
+
+82
+00:05:46,100 --> 00:05:46,100
+.. بمشي الحل .. بمشي الحل .. بمشي الحل .. بمشي
+
+83
+00:05:46,100 --> 00:05:46,300
+الحل .. بمشي الحل .. بمشي الحل .. بمشي الحل ..
+
+84
+00:05:46,300 --> 00:05:46,440
+بمشي الحل .. بمشي الحل .. بمشي الحل .. بمشي الحل
+
+85
+00:05:46,440 --> 00:05:46,780
+.. بمشي الحل .. بمشي الحل .. بمشي الحل .. بمشي
+
+86
+00:05:46,780 --> 00:05:47,500
+الحل .. بمشي الحل .. بمشي الحل .. بمشي الحل ..
+
+87
+00:05:47,500 --> 00:05:52,610
+بمشي الحل .. بمشي الحل .. بمشي الحل ..الـ function
+
+88
+00:05:52,610 --> 00:05:57,350
+فبتسمي ال code بمسماه تمام حدنا هنشوفه بس احنا
+
+89
+00:05:57,350 --> 00:05:59,990
+الآن بنحدد فقط مجموعة ال facts اللي عندى هنا
+
+90
+00:05:59,990 --> 00:06:04,690
+فtransitivity اه متحققة ال transitivity relation
+
+91
+00:06:04,690 --> 00:06:10,170
+واضحة تماما كويس ال big O لما يكون فيه عندى
+
+92
+00:06:10,170 --> 00:06:16,000
+constant ل ال multiplication بيأثرشيعني تربيع مثلا
+
+93
+00:06:16,000 --> 00:06:20,660
+in تربيع طب خمسة in تربيع تغير ال order مية in
+
+94
+00:06:20,660 --> 00:06:26,060
+تربيع هي تربيعية ضالت تربيعية فحنشوف ال roots و ال
+
+95
+00:06:26,060 --> 00:06:29,420
+log حنشوف ال log ايش بتغير معانا في كل function أو
+
+96
+00:06:29,420 --> 00:06:32,780
+نوع من الأنواع هذه لو افترضنا أن ال F نفسها هي
+
+97
+00:06:32,780 --> 00:06:40,020
+small omega of واحد معناته الآن بدنا نوجف شوية
+
+98
+00:06:40,020 --> 00:06:43,180
+لأنه أصبحنا مضطرين ان نعرف أنواع تانية غير ال big
+
+99
+00:06:43,180 --> 00:06:54,870
+Oفي عنده ال big omega if تساوي big omega of g هذه
+
+100
+00:06:54,870 --> 00:07:01,470
+عكس ال big O فال big O في أسوأ أحوالها هي ال order
+
+101
+00:07:01,470 --> 00:07:09,270
+g هنا لأ في أحسن أحوالها هي g بمعنى إن هي if هنا
+
+102
+00:07:09,270 --> 00:07:11,630
+ال order تبعها g فأعلى
+
+103
+00:07:14,750 --> 00:07:20,450
+عكس ال big O تماما عكس ال big O هنا كنا بنقول if
+
+104
+00:07:20,450 --> 00:07:28,990
+هي نفس order g فأقل فلما بقول هنا in تربية يعني
+
+105
+00:07:28,990 --> 00:07:33,190
+بقول ان هاد ال function هي second order فأقل ممكن
+
+106
+00:07:33,190 --> 00:07:36,710
+تكون first inverse log بمشي ماكولهم أقل من ال
+
+107
+00:07:36,710 --> 00:07:41,810
+second بمشي الحال كويس هنا لأ بالعكس هنا كأني بقول
+
+108
+00:07:41,810 --> 00:07:47,330
+ifو هنا in نفطر التربية يعني كأني بقول إن ال F هذه
+
+109
+00:07:47,330 --> 00:07:54,650
+هي second order فأعلى second third fourth
+
+110
+00:07:54,650 --> 00:07:59,810
+exponential زي ما تطلع power of power power of
+
+111
+00:07:59,810 --> 00:08:04,420
+variable المهم إنه أكبر منال order عكس ال big O
+
+112
+00:08:04,420 --> 00:08:10,240
+هنا أقل طيب تمام او تسويها بالضبط او تسويها ليش
+
+113
+00:08:10,240 --> 00:08:13,660
+لأنه لما بدي اقول ساعتها small omega هذي big omega
+
+114
+00:08:13,660 --> 00:08:18,320
+هذي small omega if strictly أكبر منها ولا تسويها
+
+115
+00:08:18,320 --> 00:08:21,700
+فإذن
+
+116
+00:08:21,700 --> 00:08:26,300
+هذي ممكن نقول عنها أكبر من أو يساوي هذي ممكن
+
+117
+00:08:26,300 --> 00:08:33,210
+تسميها أكبر من وبسهذه ممكن تسميها أقل من أو يساوي
+
+118
+00:08:33,210 --> 00:08:44,250
+و طبعا أكيد في small o ف small o هذه
+
+119
+00:08:44,250 --> 00:08:51,790
+هتكون أقل من هاي أخدنا مجموعة عشان لما نيجي نتكلم
+
+120
+00:08:51,790 --> 00:08:56,580
+عن إيش الليالاعتراض اللي دخل عندي هذا هذا اللي هي
+
+121
+00:08:56,580 --> 00:09:00,140
+ال small omega إيش معناها small omega لو تفهمناها؟
+
+122
+00:09:00,140 --> 00:09:06,700
+إنه إذا كانت F أكبر والزمن أكبر من إيش؟ إيش يعني
+
+123
+00:09:06,700 --> 00:09:11,140
+واحد؟ constant إيش يعني constant؟ يعني هدف فعليًا
+
+124
+00:09:11,140 --> 00:09:16,910
+n to the power صفريعني Zero Order Zero Order يعني
+
+125
+00:09:16,910 --> 00:09:20,310
+ثابت Constant ف Zero Order كلنا عارفين أي شيء
+
+126
+00:09:20,310 --> 00:09:24,950
+تظبّر صفر بنحطه بواحد فعشانك انت عارف مسبقا انه
+
+127
+00:09:24,950 --> 00:09:29,110
+الواحدة دي جاية من فعليا من ال Zero Order هي فعليا
+
+128
+00:09:29,110 --> 00:09:33,870
+جاية من Zero Order بنكتبها واحد تسهيلا لكن احنا
+
+129
+00:09:33,870 --> 00:09:38,010
+كلنا عارفين هي Order Zero فال Order Zero معناته ان
+
+130
+00:09:38,010 --> 00:09:41,910
+انا بتكلم ان ال F دي أكبر من Constantأكبر من
+
+131
+00:09:41,910 --> 00:09:46,010
+constant فرست log اش ما تطلع تطلع بس هي فعليا أكبر
+
+132
+00:09:46,010 --> 00:09:51,070
+من constant تمام لكل ال F إذا كانت هي function
+
+133
+00:09:51,070 --> 00:09:55,410
+أكتر من constant ومجموعة constants A وB هي real
+
+134
+00:09:55,410 --> 00:10:00,030
+numbers بحيث أنه B تكون أكبر أو يسوء صفر بقدر أقول
+
+135
+00:10:00,030 --> 00:10:09,290
+ساعتها A اللي هي A constant مضروب في Fهيكون نفس
+
+136
+00:10:09,290 --> 00:10:15,530
+big O of F زي ما قلنا تربيعية in تربيع طب مليون في
+
+137
+00:10:15,530 --> 00:10:21,010
+in تربيع ايش ال order برضه تربيع مش هيتغير فإذا
+
+138
+00:10:21,010 --> 00:10:24,290
+ايه ايش ما تكون قيمتها هي constant في المعادلة
+
+139
+00:10:24,290 --> 00:10:27,930
+تلتة in تربيع خمسة in تربيع عشرة in تربيع مية in
+
+140
+00:10:27,930 --> 00:10:32,190
+تربيع هتظل المعادلة in general تربيعية فبسميها big
+
+141
+00:10:32,190 --> 00:10:36,500
+O of F of تربيع خلاصمش هيتغير ايش معنى طيب إذا
+
+142
+00:10:36,500 --> 00:10:42,640
+كانت F to the power 1 minus B وB زي ما قولنا أكبر
+
+143
+00:10:42,640 --> 00:10:46,340
+من أو يساوي صفر بي أكبر من أو يساوي صفر معنى ذلك
+
+144
+00:10:46,340 --> 00:10:49,900
+أنه برضه بقدر أقول أن هي big O of F طب هتنحلل
+
+145
+00:10:49,900 --> 00:10:55,280
+الموضوع بي أكبر من صفر يعني أقل قيمة إيه؟ صفر فإذا
+
+146
+00:10:55,280 --> 00:10:59,300
+كانت صفرصارت الـ function نفسها طيب الـ function
+
+147
+00:10:59,300 --> 00:11:02,340
+نفسها ما هي big O of function ماعناهاش مشكلة ما
+
+148
+00:11:02,340 --> 00:11:08,400
+اتغيرش شيء طيب إذا كانت أكبر أكبر فبمعنى إنه هنا
+
+149
+00:11:08,400 --> 00:11:14,640
+واحد مثلا إذا واحد بتصير constant مش مش هيك صارت
+
+150
+00:11:14,640 --> 00:11:17,860
+تتبار سفر constant طيب ال constant ما هو مشمول ضمن
+
+151
+00:11:17,860 --> 00:11:21,540
+ال big O of F بدليل إن احنا قلنا إنه أكبر من
+
+152
+00:11:21,540 --> 00:11:28,520
+constant لكل function أكبر من constantو فعليا او
+
+153
+00:11:28,520 --> 00:11:31,540
+تساوي constant يعني هنا الكتاب اللي ناياها big
+
+154
+00:11:31,540 --> 00:11:36,880
+برضه ماشي ال fact الحقيقة صحيحة الحقيقة الكتاب
+
+155
+00:11:36,880 --> 00:11:40,500
+اللي ناياها صحيحة تمشي مافيش مشكلة طيب log كلنا
+
+156
+00:11:40,500 --> 00:11:44,640
+عارفين أن ال log أقل من ال function نفسها لو عندك
+
+157
+00:11:44,640 --> 00:11:51,580
+linear لل in ما هي in لما تقولفبتساوي N مباشرة
+
+158
+00:11:51,580 --> 00:11:56,020
+كإني بقول إن هي خطية اللي أقل منها اللي هي ال log
+
+159
+00:11:56,020 --> 00:11:57,860
+اللي أقل منها اللي هي ال log اللي أقل منها اللي هي
+
+160
+00:11:57,860 --> 00:11:57,860
+ال log اللي أقل منها اللي هي ال log اللي أقل منها
+
+161
+00:11:57,860 --> 00:11:57,860
+اللي هي ال log اللي أقل منها اللي هي ال log اللي
+
+162
+00:11:57,860 --> 00:11:57,860
+أقل منها اللي هي ال log اللي أقل منها اللي هي ال
+
+163
+00:11:57,860 --> 00:11:57,860
+log اللي أقل منها اللي هي ال log اللي أقل منها
+
+164
+00:11:57,860 --> 00:11:57,900
+اللي هي ال log اللي أقل منها اللي هي ال log اللي
+
+165
+00:11:57,900 --> 00:11:58,000
+أقل منها اللي هي ال log اللي أقل منها اللي هي ال
+
+166
+00:11:58,000 --> 00:11:58,080
+log اللي أقل منها اللي هي ال log اللي أقل منها
+
+167
+00:11:58,080 --> 00:12:07,660
+اللي هي ال log اللي أقل منها اللي هي ال log اللي
+
+168
+00:12:07,660 --> 00:12:09,520
+أقل منها اللي هي ال
+
+169
+00:12:15,700 --> 00:12:19,580
+عند المية هنا كانت اتنين هنا مية فعليًا linear
+
+170
+00:12:19,580 --> 00:12:23,900
+فإذا واضح أنه فعلا أقل من ال linear أقل من ال
+
+171
+00:12:23,900 --> 00:12:27,400
+linear فال log أجمالًا برضه مشمول مع ال big O of F
+
+172
+00:12:27,400 --> 00:12:34,120
+مشمول لأنه أقل منه أقل منه تمام نفس الفكرة مجموع
+
+173
+00:12:34,120 --> 00:12:37,780
+ال functions لما يكون علينا جي belong to big O of
+
+174
+00:12:37,780 --> 00:12:47,560
+F و H belong to big O of F برضهعندي G تربيعية وH
+
+175
+00:12:47,560 --> 00:12:53,660
+تربيعية مجموحهم برضه تربيعي مش هيتغيرش معاك، مش
+
+176
+00:12:53,660 --> 00:12:57,040
+هيتغير حاجة إطلاقا معاك، فهتضل برضه مجموحهم
+
+177
+00:12:57,040 --> 00:12:58,920
+تربيعي، مجموحهم هيدل تربيعي
+
+178
+00:13:01,400 --> 00:13:04,660
+إذا كان عندى c أكبر من صفر بقدر أقول زي ما قولناها
+
+179
+00:13:04,660 --> 00:13:06,660
+قبل شوية إذا كان في constant مضروب في ال function
+
+180
+00:13:06,660 --> 00:13:09,740
+بغيرش مجموعة ال function مش هيغير انتربيع زائد
+
+181
+00:13:09,740 --> 00:13:15,120
+خمسة هتضل ال order انتربيع انتربيع ناقص مية هتضل
+
+182
+00:13:15,120 --> 00:13:19,120
+انتربيع فهتضل big O of F مش عندي مشكلة طيب إذا كان
+
+183
+00:13:19,120 --> 00:13:23,460
+F1 هنا هتختلف شوية بدنا نركز فيها F1 belong to big
+
+184
+00:13:23,460 --> 00:13:29,640
+O of G1 فهي من ال order G1طيب و F2 هي ال order G2
+
+185
+00:13:29,640 --> 00:13:36,980
+مضروبهم في بعض مضروبهم في بعض حيساوي belong to O
+
+186
+00:13:36,980 --> 00:13:43,500
+of مضروب ال orders أكيد لأن انت ربيع فانت كعيب لأ
+
+187
+00:13:43,500 --> 00:13:48,140
+هي صارت into the power خمسة فعليا مش شاك صارت into
+
+188
+00:13:48,140 --> 00:13:52,590
+the power خمسة تمامإنتوا the power خمسة؟ أه مظبوط
+
+189
+00:13:52,590 --> 00:13:56,350
+خمسة نجمع ال powers ففي الحالة هذه لما أقول ال
+
+190
+00:13:56,350 --> 00:14:00,610
+order ضربهم أه بتصير ضمن ال big O مافيش مشكلة تمام
+
+191
+00:14:00,610 --> 00:14:05,690
+انت مافيش إشكال طيب لو مجموعهم بس هنا اختلفت عن
+
+192
+00:14:05,690 --> 00:14:09,710
+المجموع التعتوي المجموع التعتوي هنا الإتنين اللي
+
+193
+00:14:09,710 --> 00:14:14,610
+هو نفس ال order هنا F و هنا F فمجموعهم هيضل F بس
+
+194
+00:14:14,610 --> 00:14:18,360
+هنا ماحدش قال إن هما نفس ال orderاحنا بالعادة يعني
+
+195
+00:14:18,360 --> 00:14:22,980
+بنقول جي وان و جي تو مختلفين جي وان و جي تو هدول
+
+196
+00:14:22,980 --> 00:14:26,900
+بعض عن بعض واحد تربيع واحد تكعيب مثلا فإذا واحدة
+
+197
+00:14:26,900 --> 00:14:29,780
+تربيع واحدة تكعيب مجموعهم بقدر أقول انهم مجموع ال
+
+198
+00:14:29,780 --> 00:14:33,200
+orders واحدة تربيع واحدة تكعيب يعني تتباور خمسة
+
+199
+00:14:33,200 --> 00:14:37,500
+تتباور خمسة بس هاد هيك انت عارف زي ولد صغير اللي
+
+200
+00:14:37,500 --> 00:14:43,120
+لبسته جلبية أبوهكتير وسعتها يعني انت ماوضحتليش ال
+
+201
+00:14:43,120 --> 00:14:46,720
+code تبعك من أي order كويس يعني بكل بساطة ما انت
+
+202
+00:14:46,720 --> 00:14:51,180
+بده اقولك وصفلي ال code تبعك فانت احترط فيه والله
+
+203
+00:14:51,180 --> 00:14:53,900
+ما انا عارف هو تربيع ولا تكعيب اقولك هحطه تظبور
+
+204
+00:14:53,900 --> 00:14:58,600
+اربعة ما هو اكيد ال big O بتشبر مش هيك احنا هيك
+
+205
+00:14:58,600 --> 00:15:04,410
+عملنا وهذا مش صح ان هذا مش صح انت هيك مش مهندسبدام
+
+206
+00:15:04,410 --> 00:15:07,290
+انت بتدور على القريح واسع مش مشكلة معناته انت
+
+207
+00:15:07,290 --> 00:15:12,110
+كلفني cost لإن انت مش عارف تصبط الشغلة كلفني cost
+
+208
+00:15:12,110 --> 00:15:16,350
+زيادة كويس فالأصح من هيك انك تاخد ال maximum منهم
+
+209
+00:15:16,350 --> 00:15:21,450
+تربيع زي التكعيب خلاص المجموع هيكون تكعيب مش share
+
+210
+00:15:21,450 --> 00:15:25,730
+خلاص تكعيب انتهى فإذا ناخد ال maximum من ال two
+
+211
+00:15:25,730 --> 00:15:29,750
+orders مين الأكبر من التاني تربيعه تكعيب التكعيب
+
+212
+00:15:29,750 --> 00:15:34,800
+أكبر خلاص تكعيبوانتهى تمام طبعا هذا الكلام زي ما
+
+213
+00:15:34,800 --> 00:15:38,000
+قلنا بناخد مثلا جي إذا كانت جي هي الأكبر فمعنى ذلك
+
+214
+00:15:38,000 --> 00:15:41,840
+إذا جي الأكبر معناته جي واحد عفوا الأكبر معناته جي
+
+215
+00:15:41,840 --> 00:15:45,660
+اتنين هي big O of جي واحد تكعيب و تربيع هنقول
+
+216
+00:15:45,660 --> 00:15:49,420
+والله لأ بديها تكعيب فإذا إذا قلنا تكعيب معناته
+
+217
+00:15:49,420 --> 00:15:55,440
+التربيع هو big O من التكعيب صح مظبوط منطقية صحيح
+
+218
+00:15:55,440 --> 00:16:02,470
+كلام منطقي تمامناخد أمثلة على هذا الكلام على معظم
+
+219
+00:16:02,470 --> 00:16:05,930
+ال facts اللي أخدناها مثال مثال مثال هيك عالسريع
+
+220
+00:16:05,930 --> 00:16:07,870
+زي ما قلنا الحل الأول إذا كان بدي أقول و الله
+
+221
+00:16:07,870 --> 00:16:12,850
+تلاتة في function تكعيبية هتظل بيقوق في تكعيبية
+
+222
+00:16:12,850 --> 00:16:17,370
+عفوا تربيعية هتظل بيقوق في تربيع مش هيتغير شيء طيب
+
+223
+00:16:17,370 --> 00:16:24,250
+ال function مع أي function أقل أو تسويها بتظل نفس
+
+224
+00:16:24,250 --> 00:16:30,290
+order ال function فهي x تربيعزاد سواء X تربيع او
+
+225
+00:16:30,290 --> 00:16:35,170
+اقل حد الاكس تربيع حد الاكس تربيع مافيش مشكلة نفس
+
+226
+00:16:35,170 --> 00:16:39,810
+الكلب هي ال big omega هي big omega في الحالة هذه
+
+227
+00:16:39,810 --> 00:16:43,410
+بنقدر نقول ان ال F to the power واحد ناقص بيه هي
+
+228
+00:16:43,410 --> 00:16:48,810
+big O of F زي نقول X to the power minus one احنا
+
+229
+00:16:48,810 --> 00:16:51,910
+عارفين ان هذا واحد على X بتصير طيب واحد على X
+
+230
+00:16:51,910 --> 00:16:57,250
+دايما اقل من Xأكيد دائما أقل من X، صح؟ فمعناه دارك
+
+231
+00:16:57,250 --> 00:17:00,690
+بقدر بأريحية أقول أن هي big O of X لأن X دائما
+
+232
+00:17:00,690 --> 00:17:06,150
+أكبر من 1 على X بدليل أنك أنت قاعد تقييم X، X
+
+233
+00:17:06,150 --> 00:17:12,310
+بخمسة، طيب، 1 على X، خمس، أقل، X بمية، 1 على 100،
+
+234
+00:17:12,310 --> 00:17:17,430
+أقل، هتلاقيها دائما أقل طول ما أنت قاعد بتزود عدد
+
+235
+00:17:17,430 --> 00:17:23,020
+ال inputs، اللي هي قيم X يعنيطيب ال log ال log
+
+236
+00:17:23,020 --> 00:17:26,780
+متفقين هي دايما إذا كان log x هي دايما big O of x
+
+237
+00:17:26,780 --> 00:17:33,600
+وهيهم الدليل واضح قدامنا هي ال log وهي ال x فخالص
+
+238
+00:17:33,600 --> 00:17:41,020
+كويس إيش فيه كمان عندنا G بتساوي big O of F في G
+
+239
+00:17:41,020 --> 00:17:46,650
+بمعنى إذا كانت XX نفسها ممكن تكون هي big O of X
+
+240
+00:17:46,650 --> 00:17:56,170
+مضروب في أي function تانية فوق الواحد فإذا
+
+241
+00:17:56,170 --> 00:18:01,150
+لازم تكون هي constant فأكثر لازم تكون أصلا بتكلم
+
+242
+00:18:01,150 --> 00:18:07,360
+عن constant فأكثرليش؟ لأنه لزيادة هذا constant ما
+
+243
+00:18:07,360 --> 00:18:10,580
+هي هاي constant هي كده متحققة أصلا أكتر من
+
+244
+00:18:10,580 --> 00:18:13,580
+constant معناه ذلك أنه okay مافي مشكلة هتبقى
+
+245
+00:18:13,580 --> 00:18:22,560
+مشمولة ال G داخلها زي لما نقول والله التربيع العكس
+
+246
+00:18:22,560 --> 00:18:29,600
+N to the power تربيع هذه أكيد big O of N تربيع
+
+247
+00:18:29,600 --> 00:18:36,030
+مافيش عندنا مشكلة كويس لكن لما أقولin تربيع هي big
+
+248
+00:18:36,030 --> 00:18:41,850
+O of in تربيع في in باشي
+
+249
+00:18:41,850 --> 00:18:45,410
+هي صارت big O of in تكعيب يعني صح ال relation
+
+250
+00:18:45,410 --> 00:18:48,530
+صحيحة بس زي ما قلنا احنا وسعناها زيادة مش اكتر من
+
+251
+00:18:48,530 --> 00:18:53,390
+هيك اما كرياضيات صحيح رياضيات الان لما نيجي
+
+252
+00:18:53,390 --> 00:18:57,150
+نستخدمها في ال complexity تاعت الأكواد هناخد اللي
+
+253
+00:18:57,150 --> 00:19:01,010
+احنا بدنايا من الرياضيات بس احنا فاهمين ايش يعني
+
+254
+00:19:01,010 --> 00:19:05,100
+ال mathematicsهنا mathematics عدنا لما نروح ل ال
+
+255
+00:19:05,100 --> 00:19:07,580
+complexity ل الأكواد بنقول احنا إيش اللي بدنا ياه
+
+256
+00:19:07,580 --> 00:19:11,900
+منه؟ من كل هال اللي اتعلمنا احنا إيش بدنا منه؟
+
+257
+00:19:11,900 --> 00:19:17,490
+هقولك أنه لأ بدنا more specificبدك تعطيني تحديد لل
+
+258
+00:19:17,490 --> 00:19:22,950
+code لإنك بدك تصير تعمل تحليل بدك تعمل analysis لل
+
+259
+00:19:22,950 --> 00:19:26,550
+code طب هل يعقل إنك انت تكون تعمل analysis لل code
+
+260
+00:19:26,550 --> 00:19:31,250
+وانت مش فاهم أقرب تقريب ممكن لوصف ال code؟ لأ
+
+261
+00:19:31,250 --> 00:19:34,730
+بنفعش معناه ان انت بطلت محلل برامج انت بدك تتخرج
+
+262
+00:19:34,730 --> 00:19:38,900
+تصير محلل برامجتمسك البرنامج ال code تبعك وتحلله
+
+263
+00:19:38,900 --> 00:19:43,200
+تعرف هذا منيح ولا مش منيح مش مجرد انك مبرمج بس لأ
+
+264
+00:19:43,200 --> 00:19:47,020
+انت اكبر من مجرد مبرمج انت اكبر من مجرد مبرمج بكرا
+
+265
+00:19:47,020 --> 00:19:52,220
+طيب فإذا متفقين على هذا الموضوع ايش بسواق العكس
+
+266
+00:19:52,220 --> 00:19:56,640
+غير صحيح طبعا العكس غير صحيح يعني لما تيجي تقولي
+
+267
+00:19:56,640 --> 00:20:00,320
+هل وجد inter B في N صارت N تكعيب هل هي big O of
+
+268
+00:20:00,320 --> 00:20:05,150
+inter B أكيد لأأكيد لأ، أكيد هيكون لأ، مدام أنا
+
+269
+00:20:05,150 --> 00:20:11,090
+بقول أن ال F هي أكبر constant فأكثر، فإذا لأ بقدرش
+
+270
+00:20:11,090 --> 00:20:14,210
+أقول هذا الكلام صحيح، بقدرش نقول هذا الكلام صحيح
+
+271
+00:20:14,210 --> 00:20:20,970
+ال A هي ال constant، أكيد هي big O of F، باعتبار
+
+272
+00:20:20,970 --> 00:20:25,250
+أن ال F برضه هينا معرفينها هي constant فأكثر، فأي
+
+273
+00:20:25,250 --> 00:20:30,090
+constant هو ضمن هذا التعريف، ضمن هذا التعريف
+
+274
+00:20:31,120 --> 00:20:35,500
+طبعا، ضالت الحاجة اللي بحبوها اكتر المحللين هي
+
+275
+00:20:35,500 --> 00:20:39,660
+الـθيتا اللي بفضلوها اكتر ان هو اعطيني exactly
+
+276
+00:20:39,660 --> 00:20:43,940
+order exactly order فهي الثيتا و اللي هي بقدر من
+
+277
+00:20:43,940 --> 00:20:48,960
+خلالها اقول اذا كانت F هي big O of G و G big O of
+
+278
+00:20:48,960 --> 00:20:55,080
+F معناته انه G و F متساويتين exactly بقدر اقول ان
+
+279
+00:20:55,080 --> 00:21:00,690
+ال F belonging to ثيتا و Gهذه ال relation اللي
+
+280
+00:21:00,690 --> 00:21:05,850
+بيحبوها المهندسين اللي هو محللين البرامج اعطيني
+
+281
+00:21:05,850 --> 00:21:09,790
+theta كل ما اعطتني theta بكون بأثق بقرارك أكتر
+
+282
+00:21:09,790 --> 00:21:14,990
+بقدر أثق أكتر بقرارك تمام فهي الفكرة ببساطة طبعا
+
+283
+00:21:14,990 --> 00:21:19,350
+إيش بتختلف ال theta عن ال big O اللي أخدناهم
+
+284
+00:21:19,350 --> 00:21:26,550
+بتختلف في بعض الأمور اللي هي هتحكملي أنه ماتلبسنيش
+
+285
+00:21:26,550 --> 00:21:31,470
+top أكبر من Toby ببساطةببساطة بتحكمني انه لأ كل
+
+286
+00:21:31,470 --> 00:21:35,150
+حاجة بالظبط جايف لي على جدى لما توصفني وصفني على
+
+287
+00:21:35,150 --> 00:21:43,090
+جدى بس طيب هي شبيهة بال big O لكن مع اختلاف ان ال
+
+288
+00:21:43,090 --> 00:21:48,550
+A F هي نفسها theta of F مش مشكلة ال constant مغيرش
+
+289
+00:21:48,550 --> 00:21:53,150
+شيء مغيرش شيء لكن لما بقول F not belong to big
+
+290
+00:21:53,150 --> 00:21:59,950
+theta of F G F G هذه يعني ان انت جبتلي توب كبيرلأ
+
+291
+00:21:59,950 --> 00:22:04,010
+مش مقبول اقول ان هي θ ماشية لأ θ هيك مش ماشية لأنه
+
+292
+00:22:04,010 --> 00:22:07,470
+هنا زي ما قلنا ممكن تكون هنا in تكعيب و هنا in
+
+293
+00:22:07,470 --> 00:22:14,170
+تربيع بيجؤع بمش الحال احنا طبعا ماخدينها بس كانت
+
+294
+00:22:14,170 --> 00:22:18,590
+بيجؤع ماشية valid وقولنا مافيش مشكلة رياضيا مافيش
+
+295
+00:22:18,590 --> 00:22:21,770
+مشكلة قولنا بس احنا لبسناها top أكبر و بمش الحال
+
+296
+00:22:21,770 --> 00:22:25,890
+زي لما تقول بدك x أقل من أو يساوي خمسة هقولك طب
+
+297
+00:22:25,890 --> 00:22:30,920
+ماشي خد سالب ميةتقدر تقولي غلط؟ لأ بس أنا كتير
+
+298
+00:22:30,920 --> 00:22:39,000
+يعني رميت رقم بعيد يعني مش كتير منطقي تمام طيب نفس
+
+299
+00:22:39,000 --> 00:22:44,040
+الكلام بمين؟ لأ ال to the power minus constant
+
+300
+00:22:44,040 --> 00:22:49,240
+صارت inverse ال inverse هي لا تساوي ال function
+
+301
+00:22:49,240 --> 00:22:52,600
+نفسها ال inverse لا تساوي ال function هي تساوي أقل
+
+302
+00:22:52,600 --> 00:22:55,560
+منها أه تساوي أقل منها ف big O بمشي الحال لكن big
+
+303
+00:22:55,560 --> 00:23:01,430
+theta لأف big theta هنا بتصبتش X لا تساوي سالب
+
+304
+00:23:01,430 --> 00:23:08,090
+عفوا واحد على X لايمكن تساويها فهنا بعكس ال big O
+
+305
+00:23:08,090 --> 00:23:13,190
+هنا لا تساويها طيب ال log نفس الكلام لا يساوي لأن
+
+306
+00:23:13,190 --> 00:23:18,150
+ال log هي بينين هي أقل هي فعليا أقلتساوي لأ
+
+307
+00:23:18,150 --> 00:23:21,550
+لاتساوي فهي الفرق الوحيد بين ال big O و ال big
+
+308
+00:23:21,550 --> 00:23:26,110
+theta ال big theta exactly تساوي ال order بالظبط
+
+309
+00:23:26,110 --> 00:23:31,150
+كويس ف strictly في
+
+310
+00:23:31,150 --> 00:23:35,630
+ال order نفس ال order ناخد مثال ناخد مثال نروح ل
+
+311
+00:23:35,630 --> 00:23:37,530
+Euler ماذا ذاكرين Euler summation
+
+312
+00:23:40,820 --> 00:23:44,780
+أولى لما جلنا بتعمل summation لمجموعة الأرقام من 1
+
+313
+00:23:44,780 --> 00:23:49,820
+to N كويس خلاص أخدناها و كلنا متفقين أنه جلنا N في
+
+314
+00:23:49,820 --> 00:23:54,120
+N زائد 1 على 2 وانتهت على هيك N في N زائد 1 على 2
+
+315
+00:23:54,120 --> 00:23:59,180
+طيب لحظوا ال input تبعنا هو فعلا المدخلات ال N انت
+
+316
+00:23:59,180 --> 00:24:01,800
+اللي بتغيره هنا المتغير عندك ال variable عندك هي
+
+317
+00:24:01,800 --> 00:24:05,760
+قيمة N شك؟ طيب قيمة N هذه ممكن تاخدها خمسة عشر
+
+318
+00:24:05,760 --> 00:24:10,220
+عشرين تلاتينفمتغيرة هذه هي القيمة المتغيرة هي
+
+319
+00:24:10,220 --> 00:24:12,440
+مجموعة ال input اللي انت بدك تدخله معاها ال
+
+320
+00:24:12,440 --> 00:24:17,420
+summation تمام كلنا عارفين لما بقول in زائد واحد
+
+321
+00:24:17,420 --> 00:24:23,440
+فهي ال order in زائد constant فبتضل ال order in
+
+322
+00:24:23,440 --> 00:24:29,760
+فبتضل order in مش مشكلة big theta exactly order in
+
+323
+00:24:29,760 --> 00:24:35,960
+فهي تساوي ال order in طيب ال order in في constant
+
+324
+00:24:35,960 --> 00:24:42,710
+نصعلى 2 ما هي constant مش هيك بتظل نفس ال order in
+
+325
+00:24:42,710 --> 00:24:45,730
+طيب
+
+326
+00:24:45,730 --> 00:24:51,070
+جيد جدا ال order in في in في order in برضه في نفس
+
+327
+00:24:51,070 --> 00:24:55,730
+ال order in يعني كأنه صارت هنا θ of n وهذه برضه θ
+
+328
+00:24:55,730 --> 00:25:01,350
+of n أكيد التربيع فانت بتمسكهم تضربهم زي ما هما
+
+329
+00:25:01,350 --> 00:25:05,230
+أخدناها fact برضه لل big O و هنا مماثلة لها في ال
+
+330
+00:25:05,230 --> 00:25:11,940
+big θin في in، in تربيع، تربيع في in تكعيب، و
+
+331
+00:25:11,940 --> 00:25:14,920
+هكذا، فإذن هذه بتساوي in تربيع، فبقدر أقول إن ال
+
+332
+00:25:14,920 --> 00:25:18,500
+summation هذا هو من ال order التاني أو second
+
+333
+00:25:18,500 --> 00:25:23,500
+order ك code عشان نكتب code لهذا الموضوع هيكون
+
+334
+00:25:23,500 --> 00:25:27,400
+للمعادلة هذه عشان نطبقها بدها second order بدها
+
+335
+00:25:27,400 --> 00:25:33,280
+second order ك complexityممكن هذه احنا سبجنا فيها
+
+336
+00:25:33,280 --> 00:25:37,980
+سبجنا في حكاية ال theta ال big theta و ال small o
+
+337
+00:25:37,980 --> 00:25:45,980
+و ال small omega small omega أخدناهم كلهم هذه و
+
+338
+00:25:45,980 --> 00:25:49,880
+هذه و هذه كلهم أخدناهم الفرق كان في وين في أكبر من
+
+339
+00:25:49,880 --> 00:25:55,860
+أو أيش أو أصغر من فهنا belonged to العكس إذا كنت
+
+340
+00:25:55,860 --> 00:25:56,520
+بتكلم عن
+
+341
+00:26:00,010 --> 00:26:04,090
+G فمعنى ذلك ان هي كل ال functions F اللي أكبر من G
+
+342
+00:26:04,090 --> 00:26:09,970
+لاحظ صارت ال بالعكس بالنسبة لمن؟ لل O فهي عكس ال O
+
+343
+00:26:09,970 --> 00:26:18,230
+يعني صارت F belong to of G هي نفسها G belong big O
+
+344
+00:26:18,230 --> 00:26:25,400
+of Fعكس بعض أكبر من أو يساوي و أصغر من أو يساوي
+
+345
+00:26:25,400 --> 00:26:31,380
+نفس ال relation بس عكسية بتصير عكسية تمام ال small
+
+346
+00:26:31,380 --> 00:26:35,860
+نفس تعريف ال big بس بدون ما نحط أو يساوي هنا تعريف
+
+347
+00:26:35,860 --> 00:26:39,000
+اللي خدناه المرة الماضية شرحناه مع المعادلتين تعون
+
+348
+00:26:39,000 --> 00:26:44,200
+ال linear و التربيع فقط بس مش هنحط هنا أو يساوي
+
+349
+00:26:44,890 --> 00:26:48,670
+فبتصير أصغر من strictly أصغر من ال small ال small
+
+350
+00:26:48,670 --> 00:26:53,190
+هي نفس ال capital ولكن بدون اليساوي ليه؟ التسهيل
+
+351
+00:26:53,190 --> 00:27:01,030
+هنكتبهم بالشكل اللي احنا شايفينه if
+
+352
+00:27:01,030 --> 00:27:04,370
+تقريبا أقل من بس أنا هنا بقول أقل من as a function
+
+353
+00:27:04,370 --> 00:27:07,810
+ك order فبحطهاش الأقل من الطبيعية بنحط هيك شوية
+
+354
+00:27:07,810 --> 00:27:16,010
+مدلعة يعني شوية مدلعة العلامةدلعوها شوية عشان نعرف
+
+355
+00:27:16,010 --> 00:27:19,530
+ان انا بتكلم عن order مش عن two terms او two
+
+356
+00:27:19,530 --> 00:27:23,870
+values كويس فبنقول if ال order of f أقل من ال
+
+357
+00:27:23,870 --> 00:27:31,870
+order of g فمعنى ذلك ان هي small o لما نقول تقريبا
+
+358
+00:27:31,870 --> 00:27:36,910
+approximately معناته theta بنسميها theta فهي علامة
+
+359
+00:27:36,910 --> 00:27:43,760
+theta كويس كلنا عارفين ان لو تكون ifsmall O of G
+
+360
+00:27:43,760 --> 00:27:50,840
+معناته أن F فعليا أقل من G Strictly أقل من G، لا
+
+361
+00:27:50,840 --> 00:27:55,900
+تساوي، هي مش big O، هي small O، مدام Strictly هي
+
+362
+00:27:55,900 --> 00:28:00,700
+أقل من، أقل من، يمكن أقل من قيمة يدوب صغيرة جدا،
+
+363
+00:28:00,700 --> 00:28:03,980
+مش هيك؟ يعني الأثنين هيوم بدوا مع بعض و بعدين
+
+364
+00:28:03,980 --> 00:28:06,740
+بدأوا يبعدوا شوية شوية عن بعض، شوية شوية شوية شوية
+
+365
+00:28:06,740 --> 00:28:11,510
+أنا ضامن أنه في ال Infinityفي ال infinity هيكون
+
+366
+00:28:11,510 --> 00:28:16,410
+الفرق بينهم صار شاسع جدا لدرجة ان f بالنسبة ل g لا
+
+367
+00:28:16,410 --> 00:28:23,030
+تذكر كأنها limit at x limit to infinity بتصير
+
+368
+00:28:23,030 --> 00:28:27,770
+النسبة بينهم كأنها صفر كأن قيمة g مش شايفة قيمة f
+
+369
+00:28:28,900 --> 00:28:32,820
+عند ال infinity عند ال infinity فlimitation هنا
+
+370
+00:28:32,820 --> 00:28:36,300
+بحدد لإنه معناه ذلك إنه هذه أصبحت قيمة جدا كبيرة
+
+371
+00:28:36,300 --> 00:28:42,860
+مقابل قيمة كتير صغيرة لل F يعني F أصغر من G يعني
+
+372
+00:28:42,860 --> 00:28:47,200
+معناته F أصغر من G فعليا تمام الآن هناخد بعض ال
+
+373
+00:28:47,200 --> 00:28:50,800
+functions بعض ال functions اللي كتير كويس نتعامل
+
+374
+00:28:50,800 --> 00:28:55,560
+معها واحد ال constant هو أقل من ال log of log
+
+375
+00:28:57,060 --> 00:29:00,200
+تعرفين log of log هذه من ال functions الرائعة لو
+
+376
+00:29:00,200 --> 00:29:02,440
+قدرتوا ال .. ال quad تبعاتكم تكتبوها log of log
+
+377
+00:29:02,440 --> 00:29:06,780
+يعني معنى ذلك أن هي يعني ال complexity كتير صغيرة
+
+378
+00:29:06,780 --> 00:29:10,860
+تقريبا ما .. ما .. مافيش complexity لكن في جميع
+
+379
+00:29:10,860 --> 00:29:13,860
+الأحوال هي أكبر من الواحد في جميع الأحوال هي أكبر
+
+380
+00:29:13,860 --> 00:29:18,540
+من الواحد لو نيجي نتكلم عن عشرة مثلا العشرة عارفين
+
+381
+00:29:18,540 --> 00:29:28,600
+أن هي log عشرة بواحد log واحد بصفر مش هيكطيب زود
+
+382
+00:29:28,600 --> 00:29:35,840
+عند المية عند المية بيصير عندك هنا اتنين log
+
+383
+00:29:35,840 --> 00:29:42,860
+الاتنين بيكون زاد عن الواحد طيب زاد عن الواحد هيك؟
+
+384
+00:29:42,860 --> 00:29:47,600
+لأ لسه مازادش عن الواحد مازادش عن الواحد مازال أقل
+
+385
+00:29:47,600 --> 00:29:51,340
+من الواحد لكن احنا متذكرين تعريفنا السابق قلنا عند
+
+386
+00:29:51,340 --> 00:29:58,100
+نقطة معينة K بعدهاخلاص حيك هتصير ال term هذا أكبر
+
+387
+00:29:58,100 --> 00:30:01,920
+من الواحد و يستمر أكبر منه طب عارفين إيش هو ال
+
+388
+00:30:01,920 --> 00:30:10,240
+term هذا اللي هيتكلم عنه ال K جديش؟ عشرة قص عشرة
+
+389
+00:30:10,240 --> 00:30:16,600
+100% عشرة قص عشرة هنا لما تقول عشرة قص عشرة إيش
+
+390
+00:30:16,600 --> 00:30:21,560
+يعني؟ log هيطلع هذا ال term كله عشرة log عشرة واحد
+
+391
+00:30:21,560 --> 00:30:26,860
+بعد هيكأكيد الـ function هذه هي أكبر من الواحد،
+
+392
+00:30:26,860 --> 00:30:31,280
+أكبر من ال constant واضحة؟
+
+393
+00:30:31,280 --> 00:30:36,360
+تمام، فإذا في K، بغض النظر K قيمة صغيرة ولا قيمة
+
+394
+00:30:36,360 --> 00:30:40,340
+كبيرة، المهم إنه يوجد K بعدها ال function أكبر من
+
+395
+00:30:40,340 --> 00:30:45,540
+ال constant، يوجد، خلاص، وقدرين نصلها، عشرة طب، هو
+
+396
+00:30:45,540 --> 00:30:50,480
+عشرة، طيب، في جميع الأحوال، في جميع الأحوال، log
+
+397
+00:30:50,480 --> 00:30:57,380
+of log هي أصغر من log لحالهاأكيد أكيد أكيد تو هنا
+
+398
+00:30:57,380 --> 00:31:04,840
+كانت واحد هنا كانت عشرة هنا كانت عشرة تمام هذه
+
+399
+00:31:04,840 --> 00:31:10,720
+تساوي نفس ال log لأي أساس بغض النظر هى log decimal
+
+400
+00:31:10,720 --> 00:31:15,300
+ولا binary ولا ايش نوع الأساس تبع مش هتفرج أما ال
+
+401
+00:31:15,300 --> 00:31:18,060
+order logarithmic بظل ال order بظل logarithmic
+
+402
+00:31:18,060 --> 00:31:25,110
+فبغض النظر عن k بس تكون k أكبر من واحدانتوا عندكوا
+
+403
+00:31:25,110 --> 00:31:29,450
+حاجة اسمها log لحالها بس هادى by default هي للعشرة
+
+404
+00:31:29,450 --> 00:31:32,030
+الأساس عشرة اللى احنا بنشتغلها و احنا تاول لما
+
+405
+00:31:32,030 --> 00:31:34,550
+اشتغلنا هنا اشتغلنا للأساس عشرة عشان هيك روحنا
+
+406
+00:31:34,550 --> 00:31:38,030
+لرقم كبير بس ممكن هنا تكون للأساس اتنين فمضطرش
+
+407
+00:31:38,030 --> 00:31:42,370
+اروح لعشرة ثم بوارة عشرة هتكون ال K أقرب من العشرة
+
+408
+00:31:42,370 --> 00:31:47,170
+ثم بوارة عشرة بناء على الأساس تمام لما تكوني
+
+409
+00:31:47,170 --> 00:31:52,090
+بنشتغل في ال binary لأ بتصير هادى log للأساس اتنين
+
+410
+00:31:53,070 --> 00:31:56,590
+فبغض النظر عن إيش نوع ال base اللي مشتغل عليه لل
+
+411
+00:31:56,590 --> 00:32:02,250
+log كلهم نفس ال order كلهم نفس ال order تمام، في
+
+412
+00:32:02,250 --> 00:32:09,050
+نفس الوقت log n هو أقل من log to the power k log k
+
+413
+00:32:09,050 --> 00:32:14,170
+للأساس k هو أقل في جميع الأحوال من log k، ليش؟ أه
+
+414
+00:32:14,170 --> 00:32:17,690
+نعم، بصحيح كنت مذكرين لسه، كنت مذكرين كل ال .. لأن
+
+415
+00:32:17,690 --> 00:32:21,950
+ال k هذه كأنها بالنسبة لل log هي k في log of n
+
+416
+00:32:24,220 --> 00:32:31,520
+بالظبط يعني زادت بمقدار ال K اللي انه ضربت لأ
+
+417
+00:32:31,520 --> 00:32:35,920
+ل .. بتفرجش للتانية للتانية لل operation نفسها لل
+
+418
+00:32:35,920 --> 00:32:41,560
+function نفسها لل function نفسها to the power K ف
+
+419
+00:32:41,560 --> 00:32:44,360
+to the power K معناته بتضربها برا في ال K أه
+
+420
+00:32:44,360 --> 00:32:48,180
+بتضربها كأنها K برا كأنها K برا طيب في جميع
+
+421
+00:32:48,180 --> 00:32:56,290
+الأحوال ال log هو يعني أقل من ال rootأقل من ال
+
+422
+00:32:56,290 --> 00:33:01,470
+root هذه فعلياً root يعني لو افترض k ب 2 معناته
+
+423
+00:33:01,470 --> 00:33:06,350
+الجذر التربيعي تلاتة الجذر التكعيبي and so on هنا
+
+424
+00:33:06,350 --> 00:33:10,250
+الجذر order k الجذر order k يعني كأنك أنت هنا
+
+425
+00:33:10,250 --> 00:33:18,630
+بتقول جذر in لل order k هذه هتكون أكبر من ال
+
+426
+00:33:18,630 --> 00:33:21,250
+logarithmic function فال root أكبر من ال logarithm
+
+427
+00:33:21,950 --> 00:33:26,970
+عند الحياة كويس طيب لعندي لأن كل هدول السابقين أقل
+
+428
+00:33:26,970 --> 00:33:35,290
+من ال linear أكيد جذر n أكيد أصغر من n صح؟ أكيد
+
+429
+00:33:35,290 --> 00:33:38,770
+منطق جدا يعني فكل اللي فات هذا هو كله أصغر من
+
+430
+00:33:38,770 --> 00:33:43,670
+first order لسه ال first order في عندك بعدها n هي
+
+431
+00:33:43,670 --> 00:33:46,790
+ال first order في ال log ليش؟ لأن احنا مسبقا هنا
+
+432
+00:33:46,790 --> 00:33:51,230
+قلنا ال log أكبر من واحد فهذه كأنها مضروبة في واحد
+
+433
+00:33:53,250 --> 00:33:58,790
+فال N هي نفس ال N وعارفين أن ال 1 أقل من log ما
+
+434
+00:33:58,790 --> 00:34:05,590
+هيها؟ واحد أقل من log تمام؟ فإذا أكيد مظبوطة إيش
+
+435
+00:34:05,590 --> 00:34:09,670
+اسمها دي؟ إلها اسم، هناخده .. هناخده .. زي ما
+
+436
+00:34:09,670 --> 00:34:11,590
+قلتلكوا هناخده أنواع ال functions لأن أنت ممكن
+
+437
+00:34:11,590 --> 00:34:15,070
+تضطر توصفوا الأكواد بتاعتكوا باسم ال function
+
+438
+00:34:15,070 --> 00:34:18,510
+هناخد مجموعة كويسة عبنا بس نبدأ ناخد ال complexity
+
+439
+00:34:19,950 --> 00:34:23,110
+لوجاريثمك هذه لوجاريثمك بس هذه لها اسم تاني
+
+440
+00:34:23,110 --> 00:34:28,190
+linearithmic اسمها linearithmic هناخدها ماتجلخوش
+
+441
+00:34:28,190 --> 00:34:34,090
+طيب هذه أقل من polynomial اللي هي انت ربيع انت
+
+442
+00:34:34,090 --> 00:34:38,130
+كعيب انت ثبار أربع انت ثبار خمسة polynomial متعددة
+
+443
+00:34:38,130 --> 00:34:42,130
+الحدود متعددة الحدود طيب هذه أصغر من ال
+
+444
+00:34:42,130 --> 00:34:47,050
+exponential ثابت ثبار المتغير هذه ال exponential
+
+445
+00:34:47,050 --> 00:34:48,070
+factorial
+
+446
+00:34:50,390 --> 00:34:53,630
+الفكتوريال أكبر منها لسه طيب اللي أكبر من
+
+447
+00:34:53,630 --> 00:34:56,690
+الفكتوريال in to the power in لأن هذه عبارة عن
+
+448
+00:34:56,690 --> 00:35:00,130
+واحد في اتنين في تلاتة لعند in هذه لأ in في in في
+
+449
+00:35:00,130 --> 00:35:06,220
+in في in لعند inفأكيد أكبر أكيد أكبر تمام ممتاز
+
+450
+00:35:06,220 --> 00:35:10,040
+هذه مجموعة أنواع هذه اللي هنتعامل معها الحقيقة لما
+
+451
+00:35:10,040 --> 00:35:14,380
+نروح نبدأ نوصف ال code تبعنا و هل هو مقبول انت
+
+452
+00:35:14,380 --> 00:35:18,280
+كمحل البيانات و كمحل البرامج لعند أي حد بتقدر تقبل
+
+453
+00:35:18,280 --> 00:35:21,220
+ال code لعند أي حد بتقدر تقبل ال code هو هذا
+
+454
+00:35:21,220 --> 00:35:26,760
+الموضوع اللي احنا بدنا نتكلم في جزئية ال
+
+455
+00:35:26,760 --> 00:35:27,320
+complexity
+
+456
+00:35:35,920 --> 00:35:40,170
+في جزئية ال complexity فلما بجي أتكلم عنهالـ
+
+457
+00:35:40,170 --> 00:35:43,270
+Algorithmic Complexity خلاص افهمنا ايش يعني ال
+
+458
+00:35:43,270 --> 00:35:46,850
+order of growth الان كل الفكرة انه بدي احول ال
+
+459
+00:35:46,850 --> 00:35:51,590
+code ل function و اطبق عليها مين اكبر من مين مين
+
+460
+00:35:51,590 --> 00:35:55,530
+big O of مين بس عشان نعرف مين احسن من مين مش اكتر
+
+461
+00:35:55,530 --> 00:35:59,390
+من هيك كلنا عارفين انه في النهاية و قولناها مرارا
+
+462
+00:35:59,390 --> 00:36:03,230
+و تكرارا ان ال input تبعنا هي مجموعة ال inputs ال
+
+463
+00:36:03,230 --> 00:36:08,480
+function هي ال costال cost ايش بتهتكلفني بالنسبة
+
+464
+00:36:08,480 --> 00:36:11,200
+لعدد ال inputs لزيادة على اعتبار ان ال input هو
+
+465
+00:36:11,200 --> 00:36:17,040
+المتغير أصبحت عندك function of of in ان هذه ال
+
+466
+00:36:17,040 --> 00:36:22,020
+inputs مجموعة ال inputs اللي هنشتغلها طيب كلها على
+
+467
+00:36:22,020 --> 00:36:28,600
+بعض ال cost تكلفة ال code من أي ناحية تكلفة ال
+
+468
+00:36:28,600 --> 00:36:31,060
+code فهذه هي ال function اللي بدنا نتعامل معها هي
+
+469
+00:36:31,060 --> 00:36:35,320
+هتقيس ليه ال cost ال cost تقاس بطريقتين إما ك time
+
+470
+00:36:36,160 --> 00:36:41,520
+أو ك space ك space في الحالتين هي cost هي تكلفة
+
+471
+00:36:41,520 --> 00:36:47,660
+إما هتكلفني وقت وقت انتظار جدش بده يكلفني الوقت ك
+
+472
+00:36:47,660 --> 00:36:52,460
+function في ال input أو جدش بده يكلفني ال space
+
+473
+00:36:52,460 --> 00:36:56,100
+لأنه مساحة هذه طيب المساحة هذه ما أنا بده أضطر
+
+474
+00:36:56,100 --> 00:37:01,000
+أشتري لها وسعة عشان نفذ البرامج بتاعتنا بدك تضطر
+
+475
+00:37:01,000 --> 00:37:05,590
+تحط لها وسعةفهذه بالنسبالك cost هي ال memory bits
+
+476
+00:37:05,590 --> 00:37:10,470
+requirement required او ال bits اللي انت محتاجها
+
+477
+00:37:10,470 --> 00:37:16,150
+او مطلوبة بالنسبالك في ال memory اذا والله المحتاج
+
+478
+00:37:16,150 --> 00:37:20,530
+space اكبر يمكن ال RAM عندك تضطر تشيلها تشتريلك
+
+479
+00:37:20,530 --> 00:37:26,250
+RAM اجسع اكبر عشان تقول والله هيك ال جهاز
+
+480
+00:37:26,250 --> 00:37:30,630
+تبعي أصبح بقدر ينفذ برامج كبيرة في الأول لأ كان
+
+481
+00:37:30,630 --> 00:37:35,370
+على برامج صغيرةو هكذا هل في الآخر كمان ال compiler
+
+482
+00:37:35,370 --> 00:37:41,570
+smart enough انه يعمل إدارة مناسبة ل ال memory ولا
+
+483
+00:37:41,570 --> 00:37:44,910
+لأ تاخدوا بالكم الجزئية دي اللي في بعض ال
+
+484
+00:37:44,910 --> 00:37:48,590
+compilers هو smart enough انه يعملك إدارة كويسة ل
+
+485
+00:37:48,590 --> 00:37:53,570
+ال memory و الغالبية لأ الغالبية خصوصا لما بدك
+
+486
+00:37:53,570 --> 00:37:57,570
+تيجي تعمل مثلا ال method و ال recurrence method
+
+487
+00:37:58,580 --> 00:38:02,980
+Recurrence انك انت نفس ال code بدك تفتحه كل مرة
+
+488
+00:38:02,980 --> 00:38:06,640
+لعند ما تصل ل ال bases تبعته هناخدها برضه لجدام
+
+489
+00:38:06,640 --> 00:38:12,200
+عشان تصل ل ال bases هدى أكم مرة هتضطر تفتح برامج
+
+490
+00:38:12,200 --> 00:38:16,800
+نفس البرنامج كذا مرة ما انت معناته بدك ذاكرةال
+
+491
+00:38:16,800 --> 00:38:19,860
+recursion اللى هو ال recurrence code ال recursion
+
+492
+00:38:19,860 --> 00:38:23,900
+كنتوا بتسموها معناته بدي افتح كذا مرة نفس الملف او
+
+493
+00:38:23,900 --> 00:38:29,500
+نفس ال code كل مرة ب input جديد طب اللى جداش بتسعى
+
+494
+00:38:29,500 --> 00:38:33,540
+الذاكرة معناه ذلك هنا ناس بفضلوا انه يشتغلوا بال
+
+495
+00:38:33,540 --> 00:38:35,960
+space ناس بفضلوا يشتغلوا بال time بالنسبة لل
+
+496
+00:38:35,960 --> 00:38:40,620
+course طبعا احنا هنتعامل مع مين مع ال time مع ال
+
+497
+00:38:40,620 --> 00:38:48,500
+time كويس واتفقنا انه ال inputال input هي ال
+
+498
+00:38:48,500 --> 00:38:50,900
+different sizes اللي بتعمل معاه، يعني هي المتغير،
+
+499
+00:38:50,900 --> 00:38:54,380
+هي المتغير في شغلنا زي لما نقول والله بدي أعمل
+
+500
+00:38:54,380 --> 00:38:57,440
+عملية searching عملية ال searching ل long list
+
+501
+00:38:57,440 --> 00:39:01,470
+أكيد هتاخد time أكتر من ال short listبديهي يعني
+
+502
+00:39:01,470 --> 00:39:06,650
+هذا اشي بديهي جدا انا بدي ابحث في list من عشرة
+
+503
+00:39:06,650 --> 00:39:10,710
+elements غير لما ابحث من 100 elements أكيد ال 100
+
+504
+00:39:10,710 --> 00:39:14,170
+elements هتاخد وقت أطول .. هتاخد وقت أطول فجدش
+
+505
+00:39:14,170 --> 00:39:19,670
+بيصير تضخم في الوقت مقابل كل input زيادة هذا ال
+
+506
+00:39:19,670 --> 00:39:24,150
+complexity هذا ال order of growth معدل النمو كل ما
+
+507
+00:39:24,150 --> 00:39:27,270
+بتزيد ال input زيادة واحد جدش بتزيد مقابلها ال
+
+508
+00:39:27,270 --> 00:39:31,560
+timeهي معدل اللي اتكلمنا عنه ال order of growth
+
+509
+00:39:31,560 --> 00:39:35,980
+نمو ال function .. نمو ال function .. اي function؟
+
+510
+00:39:35,980 --> 00:39:38,540
+function ال time اما احنا خلاص اتفقنا لانه بدنا
+
+511
+00:39:38,540 --> 00:39:42,300
+نشتغل ال time معناته function ال time اللي هي
+
+512
+00:39:42,300 --> 00:39:46,280
+معتمدة على ايش؟ معتمدة على عدد ال inputs فهي ال
+
+513
+00:39:46,280 --> 00:39:49,860
+function بتاعتنا لان ال time خلاص نتكلم عن ال time
+
+514
+00:39:49,860 --> 00:39:55,020
+complexity و متفقين ان كلنا هنشتغل على ال worst
+
+515
+00:39:55,020 --> 00:40:00,930
+case inputsأسوأ حالة لعدد ال inputs؟ إيش ممكن
+
+516
+00:40:00,930 --> 00:40:03,410
+يكون؟ فهذا هو اللي بنشتغل عليه وهذا اللي من خلاله
+
+517
+00:40:03,410 --> 00:40:08,190
+بتشتغل و بتقرر بالنسباله تعمل analysis لمن؟ لل
+
+518
+00:40:08,190 --> 00:40:11,170
+code بتسترش على ال best ولا حتى على ال average
+
+519
+00:40:11,170 --> 00:40:15,950
+بتاخد إيش أسوأ حالة ممكنة لل code؟ لمن؟ إيش اللي
+
+520
+00:40:15,950 --> 00:40:18,290
+في ال code ممكن يكون أسوأ ما يمكن؟ الشيء اللي
+
+521
+00:40:18,290 --> 00:40:23,460
+بتغير اللي بتغير هو ال input كويسلو أخدنا suppose
+
+522
+00:40:23,460 --> 00:40:27,500
+that أو بدنا نفرض حالة معينة الحالة هذه بدنا نفرض
+
+523
+00:40:27,500 --> 00:40:32,220
+أن عندي algorithm A ال algorithm A هذا ال worst
+
+524
+00:40:32,220 --> 00:40:35,200
+case time complexity فبنسميها ال worst case time
+
+525
+00:40:35,200 --> 00:40:42,090
+complexity F of Nالـ function هتوطه بهذا ال order
+
+526
+00:40:42,090 --> 00:40:47,350
+بهذا الشكل بناء على ال inputs بطول N بطول N فهي
+
+527
+00:40:47,350 --> 00:40:51,990
+فعلا function في ال N بينما ال algorithm B بياخد
+
+528
+00:40:51,990 --> 00:40:55,110
+ال function بتاعة ال time أو ال time function G
+
+529
+00:40:55,110 --> 00:41:01,150
+فعندي two time functions واحدة ل system أول أو
+
+530
+00:41:01,150 --> 00:41:04,790
+algorithm أول والتاني لل algorithm التاني إذا F
+
+531
+00:41:04,790 --> 00:41:12,200
+belong to big omega of Gلأن انت هذه اللي وجدت time
+
+532
+00:41:12,200 --> 00:41:15,280
+ال time ايش المطلوب اللي انت تعمل تجيبلي ال
+
+533
+00:41:15,280 --> 00:41:18,520
+function تبعته ال order تبع ال function و بعدين
+
+534
+00:41:18,520 --> 00:41:22,420
+تيجي تقارن ال two orders في بعض اجيت لجيت والله ان
+
+535
+00:41:22,420 --> 00:41:30,920
+ال F هي small omega of G يعني G أصغر من F ايش يعني
+
+536
+00:41:30,920 --> 00:41:35,900
+ال small omega تاول لسه مكتوبة معناته هيها لاحظ F
+
+537
+00:41:35,900 --> 00:41:42,500
+أكبر من GF أكبر من G طب automatic معناته صار هنا
+
+538
+00:41:42,500 --> 00:41:48,140
+عندك ال algorithm اللي هيكون أسرع في حالة ال worst
+
+539
+00:41:48,140 --> 00:41:57,080
+case inputs مين؟ A ولا B؟
+
+540
+00:41:57,080 --> 00:42:05,800
+مين الأسرع؟ A ال order تبعه أكبرطيب، في ندفة صغيرة
+
+541
+00:42:05,800 --> 00:42:08,920
+هيك معناته، بدنا نرجع نأكد عليها هون، ها هذه صارت
+
+542
+00:42:08,920 --> 00:42:17,880
+in و function هنا سواء f أو g في الـtime مش احنا
+
+543
+00:42:17,880 --> 00:42:20,300
+خلاص اتفقنا time، مش هتكلم في ال space، نهائي
+
+544
+00:42:20,300 --> 00:42:29,160
+time، في ال time، وجدنا أن ال f بهذا الشكل، ال g
+
+545
+00:42:29,160 --> 00:42:35,850
+أصغر منهاطيب عند N معينة ال worst case أنه والله
+
+546
+00:42:35,850 --> 00:42:39,810
+ال input بزيدش عن قيمة N مثلا هنا لا يزيد عن قيمة
+
+547
+00:42:39,810 --> 00:42:45,770
+N ك input مثلا معناه ذلك أنه هذه طلعت F وهذه هيك
+
+548
+00:42:45,770 --> 00:42:54,030
+طلعت G أكيد F أقل كقيمة من G أقل في أي ناحية في ال
+
+549
+00:42:54,030 --> 00:43:02,590
+time صح أنا بتكلم عن time ف Gالـtime تبعها أقل،
+
+550
+00:43:02,590 --> 00:43:08,150
+طيب إيش علاقة الـtime بالسرعة؟ بالعكس، كل ما كنت
+
+551
+00:43:08,150 --> 00:43:11,970
+أسرع معناته بتستغرق الـtime أقل، معناه ذلك أنه مين
+
+552
+00:43:11,970 --> 00:43:16,710
+الأسرع الـmore faster من التاني الـG اللي هي تمثل
+
+553
+00:43:16,710 --> 00:43:21,570
+أنه code B فلما بتيجي بتعمل selection في حالة زي
+
+554
+00:43:21,570 --> 00:43:24,450
+هذه هروح لل algorithm B و أقول هذا اللي بتعمله
+
+555
+00:43:24,450 --> 00:43:30,360
+selection وهذا اللي بتختارهB أسرع لإيش؟ لأنه أخد
+
+556
+00:43:30,360 --> 00:43:35,060
+وقت أقل في التنفيذ في ال execution time كان أقل
+
+557
+00:43:35,060 --> 00:43:41,050
+فمعنى ذلك أكيد قراري هيروح لمين؟ ل Bقررنا لازم
+
+558
+00:43:41,050 --> 00:43:44,150
+يروح ل B في الحالة هذه واضحة نرجع نقيتها تاني و لا
+
+559
+00:43:44,150 --> 00:43:49,210
+كويسة تمام ممتاز خلاص نبدأ هالواجهة عاد خلاص نبدأ
+
+560
+00:43:49,210 --> 00:43:52,550
+مهندسين رسمي و نبدأ في الأكواد و نبدأ نتكلم في إشي
+
+561
+00:43:52,550 --> 00:43:55,810
+واضح قدامنا هي code عندك و اللي أخدناه أول ما
+
+562
+00:43:55,810 --> 00:43:58,150
+بدأنا في الأكواد اللي هو كان بدنا نحسب ال maximum
+
+563
+00:43:58,150 --> 00:44:00,810
+عشان نحسبله ال time اللي يعني ال time complexity
+
+564
+00:44:00,810 --> 00:44:06,890
+اللي بدنا نحسبها خلاص نبدأ خليهاالـ procedure بدي
+
+565
+00:44:06,890 --> 00:44:09,710
+اقرأ كمان مرة احنا كتبناه المرة المفاتة بس
+
+566
+00:44:09,710 --> 00:44:12,750
+استوردناه من هناك عملناه recalling ك method و
+
+567
+00:44:12,750 --> 00:44:15,790
+سحبناه من هناك جيبناه عندنا كويس هايه بهذا الشكل
+
+568
+00:44:15,790 --> 00:44:20,510
+كالتالي بجي بقول اول line هنا او ال statement
+
+569
+00:44:20,510 --> 00:44:24,830
+الأولى محتاجة مثلا time T1 طبعا بتعتمد على ايش في
+
+570
+00:44:24,830 --> 00:44:29,170
+الآخر مواصفات الجهاز عندك بس في النهاية الجهاز
+
+571
+00:44:29,170 --> 00:44:34,650
+هيكون ثابتالـ times تبعته لكل الأكواد مدهو نفس
+
+572
+00:44:34,650 --> 00:44:38,550
+الجهاز نفس ال machine هي هي بدأ أقول أنه عشان ينفذ
+
+573
+00:44:38,550 --> 00:44:42,530
+ال statement هذه محتاج زمن T1 طيب ال for loop عشان
+
+574
+00:44:42,530 --> 00:44:45,710
+يعمل عملية المقارنة و يشوف امتى بده يزود و امتى
+
+575
+00:44:45,710 --> 00:44:51,860
+بده يوقف عملية ال process هذه بدها T2 طيبالـ F
+
+576
+00:44:51,860 --> 00:44:55,300
+statement كلها على بعض بدها T تلاتة هقول والله ال
+
+577
+00:44:55,300 --> 00:44:58,200
+return عشان يرجع ليه بدها T أربعة يمكن تكون T أقل
+
+578
+00:44:58,200 --> 00:45:00,460
+من الباقيين على اعتبار انه مش مهتم بس في النهاية
+
+579
+00:45:00,460 --> 00:45:03,380
+بدها زمن محتاجة زمن بال nano second بال micro
+
+580
+00:45:03,380 --> 00:45:06,260
+second يطلع اللي يطلع بس لازم ناخد حسابنا معاه لإن
+
+581
+00:45:06,260 --> 00:45:10,200
+ناخد حسابه في الحسبة ليش؟ لأنه هذا إذا اتكرر اتنين
+
+582
+00:45:10,200 --> 00:45:16,660
+مليون مرة مثلا لأ بيصير محرز بيحرز حسابه كويس في
+
+583
+00:45:16,660 --> 00:45:20,840
+هاي يوم بالنسبالنا بدنا نشتغل على ال worst caseال
+
+584
+00:45:20,840 --> 00:45:23,880
+worst case ايش ال worst case الان انك انت هتعمل
+
+585
+00:45:23,880 --> 00:45:30,100
+scan على كل ال elements صح؟ و هي لازم هتعمل على
+
+586
+00:45:30,100 --> 00:45:33,300
+الكل هذه فش فيها best اصلا انت بتدور على ال
+
+587
+00:45:33,300 --> 00:45:38,280
+maximum element داخل list فلازم تعمل scan عليهم
+
+588
+00:45:38,280 --> 00:45:41,520
+كلهم لازم تعمل scan عليهم كلهم فش مجال فش مجال
+
+589
+00:45:41,520 --> 00:45:48,680
+فهنا ببساطة ال time ال total time بده يكون T1 و T2
+
+590
+00:45:49,290 --> 00:45:56,710
+و T ثلاثة و T أربعة ممتاز T واحد أكان مرة هكرره
+
+591
+00:45:56,710 --> 00:46:04,770
+أثناء ال code مرة واحدة خلاص خلّيه زائد T اتنين N
+
+592
+00:46:04,770 --> 00:46:14,670
+مرة هنا معناته نعمله summation من اتنين اتنين
+
+593
+00:46:14,670 --> 00:46:18,330
+ل two N فإذا من اتنين to N كويس
+
+594
+00:46:20,390 --> 00:46:26,510
+تلاتة T تلاتة in مرة برضه in مرة لأنه هيفحصها في
+
+595
+00:46:26,510 --> 00:46:30,350
+كل مرة عند كل loop قيمة في ال loop هنا بده يفحص ال
+
+596
+00:46:30,350 --> 00:46:33,990
+term هذا فمعناته زائد و هنعمل نفس الكلام summation
+
+597
+00:46:33,990 --> 00:46:38,870
+للكل لل total طيب T أربعة مرة واحدة هو هيعمل
+
+598
+00:46:38,870 --> 00:46:41,590
+return مرة واحدة خلاص هايلي تم return مرة واحدة
+
+599
+00:46:42,350 --> 00:46:46,370
+Okay هطلعنا شكلها معادلة جلبناها معادلة الآن بدنا
+
+600
+00:46:46,370 --> 00:46:49,850
+نشوف ال order للمعادلة هذه order المعادلة هذا
+
+601
+00:46:49,850 --> 00:46:54,050
+بالنسبالي مدام أنا دايما بشتغل على نفس الجهاز ثابت
+
+602
+00:46:55,670 --> 00:46:59,370
+صحيح دائما انت بتشغل على نفس ال laptop تبعك فمعنى
+
+603
+00:46:59,370 --> 00:47:02,670
+ذلك انه كل مرة بتنفذ هو بيكون تقريبا ثابت ال time
+
+604
+00:47:02,670 --> 00:47:06,050
+هذا التغييرات بتكون بسيطة اذا في برامج تانية
+
+605
+00:47:06,050 --> 00:47:08,290
+مفتوحة معك ولا مافيش برامج ولا انت في اول ال
+
+606
+00:47:08,290 --> 00:47:12,010
+running للبرنامج بس في النهاية مدام انت على نفس
+
+607
+00:47:12,010 --> 00:47:17,570
+الجهاز ماغيرتش فهو بالنسبالي ثابت
+
+608
+00:47:17,570 --> 00:47:24,010
+وهذا نفس الكلام لمن؟ للاخيرة فعليا نفس الكلام ل
+
+609
+00:47:25,660 --> 00:47:33,920
+للمجموع الاتنين هدول بس مع ال summation مع
+
+610
+00:47:33,920 --> 00:47:42,060
+ال summation تمام هذا ثابت مع ثابت ثابت زائد هنا
+
+611
+00:47:42,060 --> 00:47:49,060
+جدش عدد مرات التكرار هنقول n مرة او n ناقص واحد
+
+612
+00:47:49,060 --> 00:47:52,080
+على تبارك الله بدء من اتنين بس زي ما قلنا هي
+
+613
+00:47:52,080 --> 00:47:56,780
+بالنسبة لل orderin linear طب in ناقص واحد برضه
+
+614
+00:47:56,780 --> 00:48:00,600
+هتظل linear بدك more specific تكون okay نكتبها زي
+
+615
+00:48:00,600 --> 00:48:05,560
+ما هي in ناقص واحد في big theta of واحد وهدي
+
+616
+00:48:05,560 --> 00:48:09,600
+جمعناها مع هدي خلصنا تمام كلنا عارفين ان هدي إيهاش
+
+617
+00:48:09,600 --> 00:48:17,820
+of in طيب مضروبة في constant هنا هتظل زي ما هي
+
+618
+00:48:17,820 --> 00:48:20,860
+مجموعة مع constant هتظل زي ما هي فإذا ال order
+
+619
+00:48:20,860 --> 00:48:21,640
+linear
+
+620
+00:48:27,110 --> 00:48:33,210
+فيه أبسط من هيك؟ تمام فهي الشغل هتنمحاه لإنه الشغل
+
+621
+00:48:33,210 --> 00:48:36,530
+أصلا هيك هيك مكتوب بس بيكون أحسن إنك ماتقرأش
+
+622
+00:48:36,530 --> 00:48:39,490
+تتفاعل معايا فيه بيكون أفضل إن احنا نكتبه بس في
+
+623
+00:48:39,490 --> 00:48:41,090
+النهاية هو كله مكتوب الكلام هذا
+
+624
+00:48:45,450 --> 00:48:49,750
+لأن أنا بتتكلم عن time، نتكلم عن مين؟ عن time، ال
+
+625
+00:48:49,750 --> 00:48:53,010
+function بتاعتنا time، خدوا بالكوا، time كمان مرة،
+
+626
+00:48:53,010 --> 00:48:54,610
+بعرفش في ال data structure بتش تقولوا time ولا
+
+627
+00:48:54,610 --> 00:48:57,870
+space؟ time، تمام، ممتاز، معناته إحنا هم اتفقين و
+
+628
+00:48:57,870 --> 00:49:00,390
+الآن شغالين مع بعضنا، هاي كل ال analysis اللي طوى
+
+629
+00:49:00,390 --> 00:49:04,110
+عملناها، هاي كل شغلنا اللي احنا طوى عملناها، وهيه
+
+630
+00:49:04,110 --> 00:49:08,180
+عملنا كيام more specific كمان هيهمن N ناقص واحد
+
+631
+00:49:08,180 --> 00:49:12,840
+عدد مرات التكرار عدد مرات التكرار لاحظوا اللي
+
+632
+00:49:12,840 --> 00:49:18,420
+بيعملك ال orders عادة ال for loops لأن
+
+633
+00:49:18,420 --> 00:49:21,400
+otherwise هي constants مدام ان انت بتشتر على نفس
+
+634
+00:49:21,400 --> 00:49:27,070
+الجهازجهازك ثابت لما بتيجي بتقارن algorithms مع
+
+635
+00:49:27,070 --> 00:49:30,210
+بعض فانت بتشتغلهم عشان تكون fair حتى بتشتغلهم على
+
+636
+00:49:30,210 --> 00:49:33,450
+نفس الجهاز فال constants هذه مافيش فيها مشكلة مين
+
+637
+00:49:33,450 --> 00:49:38,250
+اللي بيعطيك ال orders هي ال loops فدائما ال loop
+
+638
+00:49:38,250 --> 00:49:41,330
+هي اللي بتاخد بالك منها اه هذه ممكن تعملي order
+
+639
+00:49:41,330 --> 00:49:44,890
+تمام خلصنا وصلنا لنفس النتيجة بتاعتنا ان انا بتكلم
+
+640
+00:49:44,890 --> 00:49:52,510
+عن يلا ناشيOkay هاي كمان code اللي هو إيش اللي
+
+641
+00:49:52,510 --> 00:49:55,370
+أخدناها ده سابقا هنعمل recalling بس لإيش هذا لل
+
+642
+00:49:55,370 --> 00:49:59,690
+linear لل linear search هتنمسك ال linear ساشة
+
+643
+00:49:59,690 --> 00:50:03,910
+أخدناها مش هنقعد نقرأ و نكمل مرة مش هيك خلاص
+
+644
+00:50:03,910 --> 00:50:07,310
+عارفين أنه أول I بتكون واحد و بعدين بعمل while طول
+
+645
+00:50:07,310 --> 00:50:12,110
+ما أنا أقل من N بفحصكويس و بدور X وجدتها ولا
+
+646
+00:50:12,110 --> 00:50:16,970
+ماوجدتهاش و بعدين بنوقف بعدين بنوقف تلاحظ أنه هنا
+
+647
+00:50:16,970 --> 00:50:20,850
+بعكس اللي أولى مش دايما أنت بتروح لل worst case
+
+648
+00:50:20,850 --> 00:50:27,350
+أنت بتدور عن X على X يمكن تكون أول واحدة هذا ال
+
+649
+00:50:27,350 --> 00:50:31,870
+best case أو ممكن تكون في النص average case أو
+
+650
+00:50:31,870 --> 00:50:37,000
+ممكن تكون آخر أقول لك مش موجودةهد ال worst case لأ
+
+651
+00:50:37,000 --> 00:50:40,240
+هتمر عليهم كلهم و هتعمل كل process اللي بعدك عشان
+
+652
+00:50:40,240 --> 00:50:46,540
+تعمل ال check ان انت صرت برا ال list كمان هد أسوأ
+
+653
+00:50:46,540 --> 00:50:51,200
+حالة ممكنة طب على إيش هنشتغل؟ على الأسوأ لما تيجي
+
+654
+00:50:51,200 --> 00:50:54,440
+تقارن تشتغل على الأسوأ على أسوأ شيء هفترض ان كل
+
+655
+00:50:54,440 --> 00:50:58,630
+فعل كل line من هدولة إلهال time تبعه كل واحد اللي
+
+656
+00:50:58,630 --> 00:51:02,050
+ال time تبعه مبدأيا خليني نشتغل على ال worst case
+
+657
+00:51:02,050 --> 00:51:05,810
+على ال worst case والباقين هنشوفهم مع الشرح
+
+658
+00:51:05,810 --> 00:51:09,150
+هنشرحهم بس خليني افترض انه انا هشتغل اسوأ اشي لان
+
+659
+00:51:09,150 --> 00:51:14,430
+هو ده الصح هو ده الصح لان بدأنا T واحد فاذا ال T
+
+660
+00:51:14,430 --> 00:51:25,410
+of N هتساوي T واحد و T اتنين و T تلاتة و T اربعةو
+
+661
+00:51:25,410 --> 00:51:30,630
+T5 ماعطيني لعين 6 هيو كمان و هاي T6 نبدأ نشوف
+
+662
+00:51:30,630 --> 00:51:37,030
+تكراراتهم خلاص واحد هي جاعدة لحالها خلصنا منها طيب
+
+663
+00:51:37,030 --> 00:51:43,270
+اتنين اه بالظبط هتلاحظ انه في أسوأ حالة ان انت
+
+664
+00:51:43,270 --> 00:51:52,380
+تعمل scan على كل شغلك فهنا هتعملمن I بدأنا ب إيش؟
+
+665
+00:51:52,380 --> 00:51:56,500
+بواحد هتبدأ من واحد و هتكمل ل N فإذا من واحد ل N
+
+666
+00:51:56,500 --> 00:52:03,660
+لمين؟ ل T اتنين نبعدها شوية عشان نتبين T اتنين
+
+667
+00:52:03,660 --> 00:52:11,880
+تمام هاي خلصنا من T اتنين ال I N مرة زائد نشملها
+
+668
+00:52:11,880 --> 00:52:17,800
+معاها مدام نفس الاشي هاي شملناها معاها تمام T
+
+669
+00:52:17,800 --> 00:52:23,420
+أربعةمرة واحدة فعليا مرة واحدة لأن ال loop سكر
+
+670
+00:52:23,420 --> 00:52:27,920
+خلاص هي ال loop تبعك هي
+
+671
+00:52:27,920 --> 00:52:35,220
+ال loop بهذا الشكل فعليا هيخلص ال loop انا مش عمله
+
+672
+00:52:35,220 --> 00:52:39,500
+لا begin ولا end ال loop فعليا هو السطرين هدول بس
+
+673
+00:52:39,500 --> 00:52:46,440
+خلصت و false تطلع بتشوف ال if then ال if then
+
+674
+00:52:46,440 --> 00:52:55,860
+هتعملها مرةو مش هتتحقق صح؟ يعني انت فحصتها انت
+
+675
+00:52:55,860 --> 00:53:01,380
+فعلا فحصتها okay وين روحنا؟ اه فحصناها فصار زائد T
+
+676
+00:53:01,380 --> 00:53:08,720
+أربعة و إن جبرت تروح تنفذ ال else كمان صح؟ لأن انت
+
+677
+00:53:08,720 --> 00:53:12,900
+فعلا في أسوأ الحوار انك مالجتش فاطلعت و ال then
+
+678
+00:53:12,900 --> 00:53:18,530
+ماتحققتشthen مش هتتحقق، لإن انت فحصت، انت فحصت
+
+679
+00:53:18,530 --> 00:53:23,270
+فانت استنفذت الوقت تبع تي أربعة و روحت التي خمسة
+
+680
+00:53:23,270 --> 00:53:27,930
+نفذتها كمان عشان ترجعلي بصفر تقولي انك انت ماوجدتش
+
+681
+00:53:27,930 --> 00:53:36,370
+x فزائد خمسة كمان ثم return جاء زائد ستة تمام؟
+
+682
+00:53:36,370 --> 00:53:39,150
+اتوقع ابتيش بتقدر هيك تطلع تقولي ال order total
+
+683
+00:53:39,150 --> 00:53:45,760
+يقداش inصح زي ما توعملنا فهتلاقي ان هي فعليا θ of
+
+684
+00:53:45,760 --> 00:53:53,540
+n أصبحت بايسنز ممتاز تمام فأصبحت بهذا الشكل هي
+
+685
+00:53:53,540 --> 00:53:57,820
+الحالة الأولى اللي هي ال worst case program في
+
+686
+00:53:57,820 --> 00:54:02,080
+حالة ال worst case طب the best case ايش ده best
+
+687
+00:54:02,080 --> 00:54:05,780
+case انه من أول مرة لجيته من أول مرة هتجد انه
+
+688
+00:54:05,780 --> 00:54:09,840
+وجدته طيب من أول مرة معناته حاجة اطبق
+
+689
+00:54:12,300 --> 00:54:18,620
+واحد و هطبق اتنين لانه لازم اعمل فحص هروح لتلاته
+
+690
+00:54:18,620 --> 00:54:23,500
+مش مضطر لانه من اتنين صار false فمش هاخد تلاته
+
+691
+00:54:23,500 --> 00:54:27,800
+هروح لاربعة اه هروح اعمل اربعة و اربعة هنا هتكون
+
+692
+00:54:27,800 --> 00:54:34,200
+trueفهنفذها مش هروح لخمسة ليش لأنه نفذت ال
+
+693
+00:54:34,200 --> 00:54:37,800
+condition و ال condition true مش false true فإذا
+
+694
+00:54:37,800 --> 00:54:42,740
+تلاتة و خمسة مش محتاجهم طيب totally إيش طلع
+
+695
+00:54:42,740 --> 00:54:47,020
+constant بس هذه أفضل الحالات اللي بضمانش أشتغل
+
+696
+00:54:47,020 --> 00:54:50,200
+دايما عليها بضمانش عملنا دايما عليها في ال average
+
+697
+00:54:50,200 --> 00:54:54,960
+في المتوسط أني أقول في نص البحث
+
+698
+00:54:55,630 --> 00:54:59,550
+في نص ال list وجدت X المطلوبة هضلت زيها زي ال
+
+699
+00:54:59,550 --> 00:55:07,750
+worst بالاستثناء T5 ليش T5؟ لأنه فعليا انا هطبق و
+
+700
+00:55:07,750 --> 00:55:12,570
+هلاجأ ان then it true ال condition هنا true فمش
+
+701
+00:55:12,570 --> 00:55:19,950
+هروح ل else مش هنروح لل else فخمسة مش مشمولة T5 بس
+
+702
+00:55:19,950 --> 00:55:22,170
+ك order ضال نفس ال order لل worst case
+
+703
+00:55:25,660 --> 00:55:30,980
+لأن ال order in أو ال order نُص in دلت first order
+
+704
+00:55:30,980 --> 00:55:34,200
+ربطه في نُص النُص بالنسبالك كأنه constant و
+
+705
+00:55:34,200 --> 00:55:37,480
+constant في ال function بتضل زي ما هي لعندي كخلصنا
+
+706
+00:55:37,480 --> 00:55:40,280
+المرة القادمة ان شاء الله بنكمل باجي أكواد نعمل
+
+707
+00:55:40,280 --> 00:55:42,300
+لهم تحليل ان شاء الله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1yMI1kNL2Xs.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1yMI1kNL2Xs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..47d1a29a6c7465c35dac37038c7738988d051d62
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1yMI1kNL2Xs.srt
@@ -0,0 +1,2233 @@
+1
+00:00:05,230 --> 00:00:08,930
+طب السلام عليكم وعليكم السلام يا شباب، نكمل اليوم إن
+
+2
+00:00:08,930 --> 00:00:12,090
+شاء الله تعالى موضوع الـ functions اللي حكينا فيه
+
+3
+00:00:12,090 --> 00:00:17,410
+من المرة الماضية. كنا بدأنا فيه، اتكلمنا عن معظم الـ
+
+4
+00:00:17,410 --> 00:00:21,130
+applications أو الصور السابقة اللي أخذناها في
+
+5
+00:00:21,130 --> 00:00:25,450
+المصاد، وشوفنا كيف ممكن كلها نعبر عنها بشكل
+
+6
+00:00:25,450 --> 00:00:31,050
+functions. ثم اتكلمنا في نهاية المحاضرة على أنواع
+
+7
+00:00:31,050 --> 00:00:35,580
+الـ functions، واللي بدأنا فيها بالـ one to one وكان
+
+8
+00:00:35,580 --> 00:00:40,640
+في جزئية في الـ one to one اتكلمنا عنها، هي الـ
+
+9
+00:00:40,640 --> 00:00:46,140
+monotonic increasing أو decreasing، كويس؟ واتكلمنا
+
+10
+00:00:46,140 --> 00:00:50,600
+إذا كانت monotonic increasing أو decreasing فهي
+
+11
+00:00:50,600 --> 00:00:55,040
+على طول بتصير one to one. وأخذنا بشكل سريع مثال
+
+12
+00:00:55,040 --> 00:01:00,440
+عليها في جزئية الـ X تكعيب.
+
+13
+00:01:03,380 --> 00:01:10,200
+صحيح؟ X تكعيب. واتكلمنا عن نوع ثاني من الـ functions
+
+14
+00:01:10,200 --> 00:01:15,640
+ثانية، اللي هي ليس بالضروري العكس يكون صحيح، بمعنى
+
+15
+00:01:15,640 --> 00:01:19,420
+أنه ممكن تكون one to one لكن هي ليست increasing
+
+16
+00:01:19,420 --> 00:01:24,060
+باستمرار، أو decreasing باستمرار. وأخذنا مثال عليها
+
+17
+00:01:24,060 --> 00:01:32,490
+الواحد على X، اللي هي الـ function اللي بهذا الشكل:
+
+18
+00:01:32,490 --> 00:01:38,730
+واحد على X. فقد يكون صار في خلط المرة اللي
+
+19
+00:01:38,730 --> 00:01:44,350
+فاتت، فيها فكويس إن احنا نرجع لها. هذه مثلاً، بالعكس one
+
+20
+00:01:44,350 --> 00:01:51,720
+to one، لكن مش إيش؟ مش decreasing، لأن هذا الشكل
+
+21
+00:01:51,720 --> 00:01:54,620
+العام، يبين أن المفروض تكون decreasing، مش هيك؟ إيه
+
+22
+00:01:54,620 --> 00:02:00,240
+نازلة، بس فاليه عند الـ zero بيصير فيه سقوط، فمعناه
+
+23
+00:02:00,240 --> 00:02:03,580
+ذلك أنه في الجزء عند zero صار increasing، و
+
+24
+00:02:03,580 --> 00:02:07,560
+increasing حاد جداً، increasing حاد جداً، يعني لو بدنا
+
+25
+00:02:07,560 --> 00:02:10,840
+نجيء عند الزاوية هذه، عند النقطة هذه، ونعمل zoom
+
+26
+00:02:10,840 --> 00:02:16,420
+كبير على طول الـ y-axis، هنجد أن هي فعلياً نازلة هيك، و
+
+27
+00:02:16,420 --> 00:02:22,340
+بعدين طالعة ورجعت ورجعت مكملة تنزل، رغم أن فعلياً هي
+
+28
+00:02:22,340 --> 00:02:28,000
+one to one، ليش؟ لأن مش هناخد قيمة الـ zero، فعلياً هي
+
+29
+00:02:28,000 --> 00:02:30,460
+undefined، هي مش معروفة، undefined، negative or
+
+30
+00:02:30,460 --> 00:02:35,180
+positive، or positive، فكان ضروري نرجع للنقطة هذه
+
+31
+00:02:35,180 --> 00:02:42,720
+عشان نوضحها، ونزيل الخربطة اللي صارت المرة الماضية.
+
+32
+00:02:42,720 --> 00:02:48,180
+تمام. النوع الثاني من أنواع الـ functions بعد الـ one
+
+33
+00:02:48,180 --> 00:02:53,670
+to one اللي وجدنا عندها حقيقة، هي الـ onto، الـ onto، الـ
+
+34
+00:02:53,670 --> 00:02:56,990
+بقدر أقول عليها onto أو surjective، surjective، بقدر
+
+35
+00:02:56,990 --> 00:02:59,990
+أقول عليها للـ function، طبعاً كل كلامنا للـ function
+
+36
+00:02:59,990 --> 00:03:05,170
+اللي هي الـ F from A أو from set A to set B، يعني من
+
+37
+00:03:05,170 --> 00:03:10,050
+الـ domain للـ codomain، domain للـ codomain، if and
+
+38
+00:03:10,050 --> 00:03:14,190
+only if بقول عليها onto، if and only if الـ range
+
+39
+00:03:14,190 --> 00:03:18,000
+بيساوي الـ codomain، إذا الـ range يساوي الـ codomain،
+
+40
+00:03:18,000 --> 00:03:22,620
+بمعنى إنه الـ codomain كله مغطى، إيش يعني كله
+
+41
+00:03:22,620 --> 00:03:29,160
+مغطى؟ بمعنى إنه for all B، كل element في الـ codomain
+
+42
+00:03:29,160 --> 00:03:35,260
+يوجد له preimage، يوجد له preimage، فاحنا
+
+43
+00:03:35,260 --> 00:03:40,400
+عارفين إنه B في النهاية هي تساوي F of A، وA هذه الـ
+
+44
+00:03:40,400 --> 00:03:46,500
+preimage لـ... لـ B، الـ preimage لـ B، بمعنى أن كل B
+
+45
+00:03:46,500 --> 00:03:54,340
+موجودة في الـ codomain يمكن إنتاجها من خلال تطبيق
+
+46
+00:03:54,340 --> 00:03:58,880
+الـ function على preimage corresponding لها، أو خاصة
+
+47
+00:03:58,880 --> 00:04:04,320
+فيها، واللي تنتمي لمين؟ لإيه؟ تنتمي لإيه؟ فهذه
+
+48
+00:04:04,320 --> 00:04:10,520
+معناها for all B، لكل عناصر الـ codomain، يوجد
+
+49
+00:04:10,520 --> 00:04:14,600
+preimage، preimage، لازم أكيد هتكون جاية من الـ domain
+
+50
+00:04:14,600 --> 00:04:18,580
+بحيث
+
+51
+00:04:18,580 --> 00:04:23,980
+أن الـ F of الـ preimage تساوي الـ B، وهذا الكلام لكل
+
+52
+00:04:23,980 --> 00:04:30,620
+الـ B، بمعنى كل عناصر الـ codomain ممكن أو مرشحين
+
+53
+00:04:30,620 --> 00:04:35,460
+يكونوا ناتج للـ function. طيب، واحنا عارفين إنه مدام
+
+54
+00:04:35,460 --> 00:04:38,040
+مرشح هيكون ناتج للـ function، فعلياً هتكون ناتج للـ
+
+55
+00:04:38,040 --> 00:04:41,930
+function، فهي range، فهي range، المعنى ذلك أن الـ range
+
+56
+00:04:41,930 --> 00:04:49,650
+يساوي الـ codomain. الـ onto هي معناها إنه كامل
+
+57
+00:04:49,650 --> 00:04:54,710
+عناصر الـ B كاملة
+
+58
+00:04:54,710 --> 00:04:59,230
+هي موجودة كنتاج للـ function، أو هي موجودة في الـ
+
+59
+00:04:59,230 --> 00:05:03,970
+range، لأن احنا عارفين مدام هتطلع للـ function كنتاج
+
+60
+00:05:03,970 --> 00:05:06,170
+أو result للـ function، فهي range.
+
+61
+00:05:08,830 --> 00:05:11,730
+for example، وليس جزء منها، وليس جزء من الـ codomain،
+
+62
+00:05:11,730 --> 00:05:14,150
+بمعنى أن الـ range مش هو جزء من الـ codomain،
+
+63
+00:05:14,150 --> 00:05:16,890
+اللي هو كل الـ codomain. هناخد أمثلة عليها
+
+64
+00:05:16,890 --> 00:05:23,190
+زي الـ X تكعيب، زي الـ X to the power 3، cube، واللي
+
+65
+00:05:23,190 --> 00:05:26,890
+رسمناها، لسه كنا ورسمناها كمثال على الـ one to one،
+
+66
+00:05:26,890 --> 00:05:33,610
+وهي نفسها كمثال على الـ one to
+
+67
+00:05:39,460 --> 00:05:49,400
+هي دي، اللي هي f of x تساوي x تكعيب، وهنا x وهي الـ y،
+
+68
+00:05:49,400 --> 00:05:54,880
+أو الـ f of x، هنجد أن الـ codomain هو ظاهر في الـ
+
+69
+00:05:54,880 --> 00:05:58,980
+function، كان ناتج للـ function كاملاً، من minus
+
+70
+00:05:58,980 --> 00:06:04,950
+infinity to infinity، كامل موجود بشكل كامل، هو موجود
+
+71
+00:06:04,950 --> 00:06:08,870
+فإذا الـ function هذه، بقدر بسهولة أقول أن هي onto،
+
+72
+00:06:08,870 --> 00:06:12,710
+onto، بمعنى أن الـ domain هو الـ codomain، هو نفسه
+
+73
+00:06:12,710 --> 00:06:15,790
+الـ range، بشكل كامل هيظهر في الـ range، لكن في
+
+74
+00:06:15,790 --> 00:06:20,290
+المقابل عندك
+
+75
+00:06:20,290 --> 00:06:29,570
+الـ X تربيع، أو square، الـ F of X مقابل الـ X، هنجد
+
+76
+00:06:29,570 --> 00:06:34,770
+أنه اسمياً الـ codomain من negative infinity إلى
+
+77
+00:06:34,770 --> 00:06:38,830
+infinity، زي الـ domain اللي هي الـ R، لكن actually
+
+78
+00:06:38,830 --> 00:06:44,000
+الـ range هو من صفر بالضبط، من صفر لـ positive
+
+79
+00:06:44,000 --> 00:06:48,520
+infinity، الـ negative كله ما ظهرش، ولا يمكن يطلع كنتاج
+
+80
+00:06:48,520 --> 00:06:53,100
+فإذا الـ range هنا فعلياً أقل من الـ codomain،
+
+81
+00:06:53,100 --> 00:06:56,840
+فعلياً تقريباً نصف الـ codomain، مش شير، نصف الـ codomain،
+
+82
+00:06:56,840 --> 00:07:01,200
+فإذا هذه ما أقدرش أقول عنها onto، هذه لا ينطبق
+
+83
+00:07:01,200 --> 00:07:05,180
+عليها الـ function onto، فهي ليست onto بالأساس، تمام.
+
+84
+00:07:06,260 --> 00:07:10,280
+النوع الثالث، طبعاً هنوضح زي ما وضحنا اللي فاتوا من
+
+85
+00:07:10,280 --> 00:07:15,460
+خلال الـ... الـ bipartite figures، function بهذا
+
+86
+00:07:15,460 --> 00:07:21,880
+الشكل، بقدر أقول عليها onto؟ على طول لما بدنا نسأل عن
+
+87
+00:07:21,880 --> 00:07:25,720
+عن الـ onto، اتطلع على مين؟ على الـ codomain، هل كله
+
+88
+00:07:25,720 --> 00:07:28,880
+ظاهر في نتيجة الـ relations هذه ولا لأ؟ فكلهم
+
+89
+00:07:28,880 --> 00:07:35,980
+ظاهرين، بغض النظر هي اثنين لواحد ولا واحد لواحد؟ أنا
+
+90
+00:07:35,980 --> 00:07:38,600
+ما سألتش عن one to one، هذه one to one؟ لأ، مش one to
+
+91
+00:07:38,600 --> 00:07:44,160
+one، صح؟ لأن هي في two inputs لنفس الـ output، فهي one
+
+92
+00:07:44,160 --> 00:07:46,580
+to one؟ لأ، ليست متوفرة one to one، لكن onto، آه onto،
+
+93
+00:07:46,580 --> 00:07:52,640
+to، كل الـ codomain ظاهر في الـ relation، فهذه onto،
+
+94
+00:07:52,640 --> 00:07:57,440
+ما فيش مشكلة، تمام. الثانية
+
+95
+00:07:59,330 --> 00:08:01,990
+هي أولاً one to one؟ لأ، مش one to one، فهي في عندي
+
+96
+00:08:01,990 --> 00:08:05,470
+عنصرين، أو preimage، اللي هما نفس الـ image، preimage
+
+97
+00:08:05,470 --> 00:08:08,310
+اللي هما نفس الـ image، فهي مش one to one، طيب onto،
+
+98
+00:08:08,310 --> 00:08:12,550
+ليست onto، في عنصر برضه هنا موجود في الـ codomain،
+
+99
+00:08:12,550 --> 00:08:15,510
+بس مش موجود في الـ range، مش موجود في الـ
+
+100
+00:08:15,510 --> 00:08:21,970
+range، فهذه لا هيك ولا هيك، حتى الآن. الثالثة حقيقة
+
+101
+00:08:21,970 --> 00:08:26,490
+الاثنين، هي one to one، وفي نفس الوقت onto، لأن كل
+
+102
+00:08:26,490 --> 00:08:32,350
+الـ codomain مغطى في الـ range، تمام. هذه one to one،
+
+103
+00:08:32,350 --> 00:08:35,330
+وليس onto، أكيد واضح تماماً، لأن لسه في عنصر
+
+104
+00:08:35,330 --> 00:08:38,950
+constant هنا موجود كـ first element، هو موجود في الـ
+
+105
+00:08:38,950 --> 00:08:44,890
+codomain، وغير موجود في الـ range. طيب، كمان
+
+106
+00:08:44,890 --> 00:08:48,450
+function ثانية أو ثالثة هيك صارت، اللي هي الـ
+
+107
+00:08:48,450 --> 00:08:53,050
+bijection، الـ bijection بكل بساطة هي كل function
+
+108
+00:08:53,050 --> 00:08:56,550
+بقدر أقول عنها one to one و onto في نفس الوقت.
+
+109
+00:08:59,580 --> 00:09:02,380
+بمعنى ممكن نسميها one-to-one correspondence،
+
+110
+00:09:02,380 --> 00:09:06,580
+correspondence، هي correlation one-to-one في
+
+111
+00:09:06,580 --> 00:09:12,540
+الاتجاهين. هي معناها، عشان هي اسمها bijection، فإذن هي
+
+112
+00:09:12,540 --> 00:09:17,460
+فإذا من الـ domain للـ codomain هي one-to-one، ومن
+
+113
+00:09:17,460 --> 00:09:19,720
+الـ domain للـ codomain هي برضه one، أو من الـ codomain
+
+114
+00:09:19,720 --> 00:09:22,600
+للـ domain برضه one-to-one، فنسميها
+
+115
+00:09:22,600 --> 00:09:28,340
+bijection، أو reversible، أو invertible، فإذا قابلة
+
+116
+00:09:28,340 --> 00:09:32,530
+للعكس، قابلة للعكس، بمعنى أن هي في الاتجاهين ممكن تكون
+
+117
+00:09:32,530 --> 00:09:36,090
+function في الاتجاهين، ممكن تكون function، فهي قابلة
+
+118
+00:09:36,090 --> 00:09:41,450
+للعكس. بمعنى، هنا لما بنتكلم قلنا عن هذه، قلنا أن هي
+
+119
+00:09:41,450 --> 00:09:50,150
+في الآخر one to one، هذه لو عكسناها أكيد هتبطل هي
+
+120
+00:09:50,150 --> 00:09:55,490
+هتبطل function، هي هنا هتبطل function، صح؟ لاحظ
+
+121
+00:09:55,490 --> 00:10:00,320
+لأن answer لها two outputs، تصير لو بدنا نعكسها على
+
+122
+00:10:00,320 --> 00:10:04,240
+الـ function، فبتصبح أكيد هي one to one، ماشي، لكن مش
+
+123
+00:10:04,240 --> 00:10:07,940
+one to one correspondence، بمعنى bijection، اللي هي
+
+124
+00:10:07,940 --> 00:10:13,760
+ممكن تكون بالعكس، على النقيض من الـ y للـ x، فعشان هيك
+
+125
+00:10:13,760 --> 00:10:18,480
+ما نقدرش نسميها reversible، قابلة للعكس، أنه أجيب
+
+126
+00:10:18,480 --> 00:10:22,400
+المعكوس تبعها، invertible، معناته بقدر أجيب المعكوس
+
+127
+00:10:22,400 --> 00:10:25,520
+تبعها؟ لأ، هذه مش invertible، لأنه أصلاً تصبح ليست
+
+128
+00:10:25,520 --> 00:10:29,160
+function، أصلاً، زي الـ X تربيع.
+
+129
+00:10:31,640 --> 00:10:36,400
+لأ، الـ X تربيع أنت بتقدر تعكسها؟ الـ X تربيع أنا
+
+130
+00:10:36,400 --> 00:10:39,420
+بتقدرش تعكسها، لإنه بتجيبش، بتجيبش الـ inverse، بتقدرش
+
+131
+00:10:39,420 --> 00:10:42,380
+تجيب لها inverse، لإنه بيصير عندك نفس الـ output، نفس
+
+132
+00:10:42,380 --> 00:10:45,620
+الـ input، إله two outputs، اللي هما، واحد
+
+133
+00:10:45,620 --> 00:10:47,840
+positive، واحد negative، واحد positive، واحد negative،
+
+134
+00:10:47,840 --> 00:10:51,300
+صارت جاية زي مكان الجذر، والجذر بيصير إله two
+
+135
+00:10:51,300 --> 00:10:55,560
+outputs، تمام. طيب، الـ bijection هذه، مدام أنا بقول هي
+
+136
+00:10:55,560 --> 00:10:59,790
+one to one، وهي onto في نفس الوقت، بقدر أقول، أعرفكم
+
+137
+00:10:59,790 --> 00:11:03,710
+التالي، الـ bijection هي F from set A to set B،
+
+138
+00:11:03,710 --> 00:11:09,690
+معناته يوجد لها inverse of F، معناته يوجد إليها
+
+139
+00:11:09,690 --> 00:11:13,950
+inverse، إذا قدرت أقول إن الـ F فعلاً هي bijection، لأ
+
+140
+00:11:13,950 --> 00:11:16,370
+أنا بفهم على طول إن هي one to one، وهي onto، يعني
+
+141
+00:11:16,370 --> 00:11:21,330
+ببساطة جداً، بقدر أوجد لها الـ inverse، أو يوجد إليها
+
+142
+00:11:21,330 --> 00:11:24,170
+inverse، والـ inverse هذا هيكون F to the power
+
+143
+00:11:24,170 --> 00:11:27,790
+minus one، اللي هو الـ inverse of F، هيكون من مين؟ من
+
+144
+00:11:27,790 --> 00:11:34,130
+B، من الـ codomain للـ domain، أصبحت من الـ B للـ A،
+
+145
+00:11:34,130 --> 00:11:38,070
+وفي الحالة هذه أكيد هيكون لكل function unique
+
+146
+00:11:38,070 --> 00:11:43,170
+inverse function، صحيح؟ أكيد، ليش؟ لأنه إذا ضربناها
+
+147
+00:11:43,170 --> 00:11:46,450
+في الـ inverse تبعها، المفروض أنه يعطيني الـ identity،
+
+148
+00:11:46,450 --> 00:11:50,890
+بالضبط، الواحد، الـ identity، فـ الـ identity function
+
+149
+00:11:50,890 --> 00:11:59,830
+هي فعلياً، هي هذي، composition، مش حاصل ضرب، حاصل
+
+150
+00:11:59,830 --> 00:12:05,030
+compose، الـ inverse بالـ function تبعها، فخذوا بالكم،
+
+151
+00:12:05,030 --> 00:12:09,090
+وأنا ما ضربتها، مش ضرب، هدول مش ضرب، هي حاصل الـ
+
+152
+00:12:09,090 --> 00:12:12,430
+identity function هي حاصل الـ composition للـ
+
+153
+00:12:12,430 --> 00:12:15,110
+function مع الـ inverse تبعها، عشان يعطيني الـ
+
+154
+00:12:15,110 --> 00:12:19,650
+identity function، عشان يعطي identity function، طيب،
+
+155
+00:12:19,650 --> 00:12:21,690
+الـ identity function من الـ functions اللي مشهورة
+
+156
+00:12:21,690 --> 00:12:26,430
+جداً، ومعروفة جداً، وكتير بتستخدم في شغلنا، وعندي
+
+157
+00:12:26,430 --> 00:12:29,830
+استخدمناها كذا مرة، فعلياً، فعلياً احنا استخدمناها كذا
+
+158
+00:12:29,830 --> 00:12:33,310
+مرة، لما بقول identity function، هي من الـ domain
+
+159
+00:12:33,310 --> 00:12:37,550
+لنفس، ليش من الـ domain لنفسه؟ لأن هي فعلياً زي ما بيقولوا،
+
+160
+00:12:37,550 --> 00:12:43,750
+يقول لنا F from A to B، ثم قلنا الـ F minus one from
+
+161
+00:12:43,750 --> 00:12:49,390
+B to A، فلما أعمل composition للاتنين مع بعضهم، F
+
+162
+00:12:49,390 --> 00:12:56,820
+العكس، طبعاً، لما بقول compose if هذه، هيساوي الـ
+
+163
+00:12:56,820 --> 00:13:01,420
+identity، معناته هيكون عبارة عن function identity،
+
+164
+00:13:01,420 --> 00:13:07,540
+اللي هي الحصيلة الاتنين من A، برجع ثاني لـ A، نرجع ثاني
+
+165
+00:13:07,540 --> 00:13:13,940
+لنفسه A، هي هي، تمام. من A لـ B، ثم من B لـ A، فرجعنا من A
+
+166
+00:13:13,940 --> 00:13:21,500
+لـ A، تمام. فنكتبها بهذا الشكل، الـ identity function،
+
+167
+00:13:21,500 --> 00:13:25,760
+from domain A to codomain A، والـ domain والـ
+
+168
+00:13:25,760 --> 00:13:30,980
+codomain نفس الشيء، نفس الشيء، نكتبها إما I A، فمعناه
+
+169
+00:13:30,980 --> 00:13:33,900
+ذلك أنا بتكلم عن identity function في الـ domain A،
+
+170
+00:13:33,900 --> 00:13:38,720
+أو الواحد، أو واحد للـ domain A، على اعتبار أن الواحد
+
+171
+00:13:38,720 --> 0
+
+223
+00:17:36,990 --> 00:17:42,790
+بحيث أنه هي مجموعة من أزواج مرتبة، طب كل زوج لحاله
+
+224
+00:17:42,790 --> 00:17:47,160
+عبارة عن A والـ functional value بتاعة الـ A بشرط أن
+
+225
+00:17:47,160 --> 00:17:52,680
+الـ A تنتمي للـ domain بس فكل عنصر ينتمي للـ domain
+
+226
+00:17:52,680 --> 00:17:56,140
+بدك تشوف قديش الـ functional value تبعته، هو الـ
+
+227
+00:17:56,140 --> 00:18:00,260
+functional value نقطة مع بعض بحيث أنك ترسمها x مع
+
+228
+00:18:00,260 --> 00:18:06,540
+y و بترسمها على الـ plane تبعتك، فبتلاحظ أن لكل عناصر
+
+229
+00:18:06,540 --> 00:18:12,240
+A يوجد فقط one pair أو زوج مرتب واحد اللي هو A مع
+
+230
+00:18:12,240 --> 00:18:16,800
+الـ functional value، طبعاً مستحيل يطلع له أكثر من
+
+231
+00:18:16,800 --> 00:18:22,400
+functional value صحيح. فإذا لكل قيمة A مش هتلاقي f
+
+232
+00:18:22,400 --> 00:18:29,340
+of A مختلفتين، إنتَ واحدة فقط. فمعنى ذلك أن حتى
+
+233
+00:18:29,340 --> 00:18:34,240
+الزوج المرتب هو واحد فقط فقط للـ A. ففي الحالة
+
+234
+00:18:34,240 --> 00:18:38,430
+هذه بنقدر نرسمها بالنسبة للأرقام، عادة تمثل أزواج
+
+235
+00:18:38,430 --> 00:18:42,110
+مرتبة x و y، زمان إنتوا عارفين أخذتوها زمان، بنكتبها
+
+236
+00:18:42,110 --> 00:18:46,870
+عبارة عن مجموعة points، فهذه تمثل point واحدة. فكل
+
+237
+00:18:46,870 --> 00:18:51,210
+ما عددنا قيم x واللي هي الـ elements بتاعت الـ
+
+238
+00:18:51,210 --> 00:18:55,110
+domain، بيصير عندي مجموعة أكبر من الـ points. قديش إنتَ
+
+239
+00:18:55,110 --> 00:18:58,990
+بتفترض قيم لـ x، قديش إنتَ بتطلع نقاط إضافية، قديش إنتَ
+
+240
+00:18:58,990 --> 00:19:02,150
+بتحطهم، كل النقاط هذه مع بعض، الـ points هذه مع بعض
+
+241
+00:19:02,150 --> 00:19:06,650
+as a set، element of set، وبتحطهم، بتوقعهم على الـ
+
+242
+00:19:06,650 --> 00:19:11,170
+plane تبعك عشان ترسم curve ما بين نقاطهم، فبتظهر
+
+243
+00:19:11,170 --> 00:19:15,610
+معاك كنقاط على الـ plane أو على المستوى، على الصبورة
+
+244
+00:19:15,610 --> 00:19:19,850
+بحيث أنها تبين الـ function كمرسومة، كـ curve مرسوم، و
+
+245
+00:19:19,850 --> 00:19:24,370
+هو في النهاية عبارة عن set of points، وعبارة عن
+
+246
+00:19:24,370 --> 00:19:29,190
+مجموعة نقاط، set of points، تمام، دي بحيث أن دائماً
+
+247
+00:19:29,190 --> 00:19:37,590
+يكون في y لكل x، في دائماً y لكل x، طيب، واحدة أو
+
+248
+00:19:37,590 --> 00:19:41,110
+خلينا نقول قبل من الـ functions، two functions من الـ
+
+249
+00:19:41,110 --> 00:19:44,090
+functions المهمة جداً والجوهرية جداً واللي هنتكلم
+
+250
+00:19:44,090 --> 00:19:46,350
+عنها بشكل سريع، طبعاً أكيد الـ functions لو بدنا
+
+251
+00:19:46,350 --> 00:19:49,110
+نتكلم عن الـ functions، مش هنخلص هذه لحالها، مصعب
+
+252
+00:19:49,110 --> 00:19:53,150
+تصير، لكن إحنا هنتكلم عن two functions، بسميهم قبل of
+
+253
+00:19:53,150 --> 00:19:57,770
+key functions... functions أساسية، الإثنين هدول هم
+
+254
+00:19:57,770 --> 00:20:01,510
+الـ floor والـ ceiling، floor و ceiling اللي هو
+
+255
+00:20:01,510 --> 00:20:06,030
+بتقرب للأقل وللأعلى، بس يعني كل اللي بدك تعمله، الـ
+
+256
+00:20:06,030 --> 00:20:10,150
+input تبعك هو عبارة عن real number، والـ output
+
+257
+00:20:10,150 --> 00:20:15,690
+integer، مش هيك integer، بتقربه لأقرب عدد صحيح. ففي الـ
+
+258
+00:20:15,690 --> 00:20:19,210
+discrete، طبيعي، frequently بنستخدم هدول النوعين
+
+259
+00:20:19,210 --> 00:20:23,410
+بشكل كتير، مستمر منهم، أولهم الـ floor، الـ floor
+
+260
+00:20:23,410 --> 00:20:28,510
+ببساطة جداً بنعمله floor، ولاحظوا الشرطات اللي تحت
+
+261
+00:20:28,510 --> 00:20:31,970
+معناه ذلك أن الـ x بيتقربها للأرض تبعها، لأرضها،
+
+262
+00:20:31,970 --> 00:20:36,190
+floor، للأرض، للأرضية، هذه عبارة عن إيش هي؟ the
+
+263
+00:20:36,190 --> 00:20:44,080
+largest هي أكبر integer أقل من x، فبتقريبها لأي
+
+264
+00:20:44,080 --> 00:20:48,620
+integer أقل منها وخلاص، لأكبر integer أقل منها، فـ
+
+265
+00:20:48,620 --> 00:20:52,740
+greatest integer function، بيسموها greatest integer
+
+266
+00:20:52,740 --> 00:20:57,180
+function، فهذه أكبر قيمة أقل من الـ x. في المقابل الـ
+
+267
+00:20:57,180 --> 00:21:00,920
+ceiling أو السقف، ceiling أو السقف، هتلاقي أنه
+
+268
+00:21:00,920 --> 00:21:05,640
+الشرطات هتكون لفوق، بمعنى أن الـ x بتقريبها لفوق، هذه
+
+269
+00:21:05,640 --> 00:21:16,320
+the smallest integer أكبر أو يساوي x، فهد أقل قيمة
+
+270
+00:21:16,320 --> 00:21:23,280
+صحيحة أكبر من x، مش والله يالا أي أكبر وفوق وخلاص،
+
+271
+00:21:23,280 --> 00:21:29,700
+لأ، أقل قيمة أكبر من x. ففي الحالة هذه بتكون integer
+
+272
+00:21:29,700 --> 00:21:32,840
+بس طبعاً لازم يكون integer في الآخر، أو يساوي، لأنه
+
+273
+00:21:32,840 --> 00:21:36,080
+ممكن أصلاً نفسها الـ x تكون هي نفسها integer، ممكن هي
+
+274
+00:21:36,080 --> 00:21:38,740
+نفسها تكون integer، فبتسيبها زي ما هي، في الحالة هذه
+
+275
+00:21:38,740 --> 00:21:45,950
+طيب، بعض الخصائص المهمة للـ floor وللـ ceiling هي
+
+276
+00:21:45,950 --> 00:21:50,730
+توضيح لهم، أول حالة من الحالات اللي بنتكلم عنها، إذا
+
+277
+00:21:50,730 --> 00:21:55,950
+كانت x لا تنتمي للـ integers، بمعنى إنها fraction،
+
+278
+00:21:55,950 --> 00:22:00,690
+هي فيها كسر، فيها كسور، ففي الحالة هذه، in general، أو
+
+279
+00:22:00,690 --> 00:22:07,950
+حقيقة مدام هي ليست integer، فبالضرورة floor minus x
+
+280
+00:22:07,950 --> 00:22:14,660
+لا تساوي minus floor x. هيهم هي عندك الحالات اللي
+
+281
+00:22:14,660 --> 00:22:18,380
+عندك، خلينا ناخد مثلاً، for example، floor، بنتكلم هي
+
+282
+00:22:18,380 --> 00:22:22,200
+واحدة هي floor، وين السالب تبعها، وهي السالب تبعها
+
+283
+00:22:25,610 --> 00:22:29,750
+هذا السالب، تبقى حقه هاي سالب ها، لاحظ، فهتلاقي أنه
+
+284
+00:22:29,750 --> 00:22:33,690
+هنا هاي سالب جوا سالب واحد فاصلة ستة، الـ floor
+
+285
+00:22:33,690 --> 00:22:38,990
+بتصير سالب اتنين، طيب أما سالب الـ floor واحد فاصلة
+
+286
+00:22:38,990 --> 00:22:42,270
+ستة بتصير سالب واحد، أكيد لا تساوي بعض. ونفس الكلام
+
+287
+00:22:42,270 --> 00:22:46,550
+لمين؟ للـ ceiling، لو بدنا ناخد هاي ceiling، وهاي
+
+288
+00:22:46,550 --> 00:22:55,040
+ceiling، نفس الفكرة، ceiling نيجاتيف x هي ceiling
+
+289
+00:22:55,040 --> 00:22:59,920
+نيجاتيف x هيساوي سالب واحد بالنسبة للمثال، طبعاً
+
+290
+00:22:59,920 --> 00:23:06,460
+فاصلة one point six، طيب بينما سالب ceiling x هي
+
+291
+00:23:06,460 --> 00:23:10,800
+ceiling x، واحد فاصلة ستة بتطلع اتنين، سالب اتنين،
+
+292
+00:23:10,800 --> 00:23:14,480
+بتطلع سالب اتنين، طب هنا سالب واحد، فإذا لا تساويها
+
+293
+00:23:14,480 --> 00:23:21,290
+بشكل، بشكل مطلق. طيب بينما إذا كانت x هي belong to
+
+294
+00:23:21,290 --> 00:23:24,850
+integer، يعني هي أصلاً integer، فهي نفس الـ ceiling
+
+295
+00:23:24,850 --> 00:23:28,330
+وهي نفس الـ floor، هي نفس الـ element، منطق جداً لما
+
+296
+00:23:28,330 --> 00:23:31,150
+تقولي والله جرب لي الخمسة، لأقرأ بعضها صحيح، طب ما هي
+
+297
+00:23:31,150 --> 00:23:35,310
+خمسة، مش هتفرق ساعتها بدك تعمل floor ولا ceiling،
+
+298
+00:23:35,310 --> 00:23:39,610
+يعني معنها تيجي تسألني تقولي دكتور floor ولا
+
+299
+00:23:39,610 --> 00:23:43,290
+ceiling، أنا بقول لك خمسة يعني مش هتفرق، floor ceiling
+
+300
+00:23:43,290 --> 00:23:52,000
+هي هي، حاضر، تمام، كـ plot ترسم بالشكل اللي إحنا هنشوفه،
+
+301
+00:23:52,000 --> 00:23:55,360
+لأن، لأن في مفهومين أكيد مرو عليكوا بس مش غلط نرجع
+
+302
+00:23:55,360 --> 00:24:01,460
+أننا نكررهم من خلال المثال، f of x تساوي floor x
+
+303
+00:24:01,460 --> 00:24:06,440
+over 3، floor x over 3، هتيجي تقول بكل بساطة، تعوض
+
+304
+00:24:06,440 --> 00:24:11,040
+قيم في الـ domain تبعك، في الـ x domain، عشان تشوف الـ
+
+305
+00:24:11,040 --> 00:24:15,200
+co-domain اللي هو الـ f of x، بعد ما تطبق هذه الـ
+
+306
+00:24:15,200 --> 00:24:19,480
+function اللي هي floor أو ceiling، نفس الشيء، مع
+
+307
+00:24:19,480 --> 00:24:23,880
+اختلاف بس، الواقعين كيف حتصير. طيب عند الصفر صفر،
+
+308
+00:24:23,880 --> 00:24:27,980
+فالصفر مشمول، يعني عند الصفر الناتج صفر، عشان هيك
+
+309
+00:24:27,980 --> 00:24:33,740
+بنجيب، نكتبها solid، مسكرة بالظبط، مسكرة، معناته أن
+
+310
+00:24:33,740 --> 00:24:39,260
+العنصر صفر هو مشمول معهم، بحيث أن الناتج تبعه بيطلع
+
+311
+00:24:39,260 --> 00:24:48,600
+صفر، طيب عند الواحد برضه صفر، طيب عند الاتنين صفر، عند
+
+312
+00:24:48,600 --> 00:24:54,580
+التلاتة واحد، عند التلاتة واحد، طيب لكن عند الاتنين
+
+313
+00:24:54,580 --> 00:24:56,920
+فاصلة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+314
+00:24:56,920 --> 00:24:58,620
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+315
+00:24:58,620 --> 00:24:58,820
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+316
+00:24:58,820 --> 00:24:58,880
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+317
+00:24:58,880 --> 00:24:59,240
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+318
+00:24:59,240 --> 00:25:03,460
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+319
+00:25:03,460 --> 00:25:09,790
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة، هنا open cycle،
+
+320
+00:25:09,790 --> 00:25:14,090
+بعرف منها أنها مستمرة للتلاتة، لكن التلاتة فقط غير
+
+321
+00:25:14,090 --> 00:25:19,450
+مشمولة، لأن التلاتة موجودة مع الواحد. طبعاً المفاهيم
+
+322
+00:25:19,450 --> 00:25:23,050
+أكيد مرت عليكم سابقاً وعارفين هذا الكلام، تمام.
+
+323
+00:25:23,050 --> 00:25:25,870
+فتاخدوا بالكوا في الرسومات اللي زي هذه، في الواجبات
+
+324
+00:25:25,870 --> 00:25:29,190
+ممكن تكون موجودة معاكم، بالمناسبة نزلنا أول واجب
+
+325
+00:25:29,190 --> 00:25:32,990
+لسه اليوم، هيبدأ استحقاقه، فتقدرّوا تبدأوا تشتغلوا
+
+326
+00:25:32,990 --> 00:25:35,730
+عليه اليوم للأسبوع القادم إن شاء الله تعالى، على الـ
+
+327
+00:25:35,730 --> 00:25:40,930
+mood اللي بتـ بتحلوه، بتنزلوه، تمام، فممكن تيجي أسئلة
+
+328
+00:25:40,930 --> 00:25:43,810
+بهذا الشكل، بدك تكون ماخد بالك مين الـ open cycle،
+
+329
+00:25:43,810 --> 00:25:51,060
+ومين الـ solid أو الـ closed cycle، تمام. في الحالة هذه،
+
+330
+00:25:51,060 --> 00:25:55,460
+إحنا خلصنا الجزئية اللي كانت متبقية عندنا في الـ
+
+331
+00:25:55,460 --> 00:26:00,200
+functions، عشان نبدأ برضه نكمل بنفس مواضيعنا فعلياً.
+
+332
+00:26:01,390 --> 00:26:04,550
+كنا بنتكلم عن الـ set، ومن الـ set إجت الـ functions،
+
+333
+00:26:04,550 --> 00:26:08,810
+نوع مهم من أنواع الـ sets هي الـ sequence أو الـ
+
+334
+00:26:08,810 --> 00:26:12,410
+strings، ثم لاحقاً المرة القادمة ناخد الـ summation
+
+335
+00:26:12,410 --> 00:26:18,030
+لمجموعة الـ sequence هذه، فنبدأ في جزئية الـ sequence
+
+336
+00:26:20,680 --> 00:26:24,740
+لما بتكلم عن الـ sequence أو الـ strings، وفيه فرق
+
+337
+00:26:24,740 --> 00:26:28,220
+خفيف كتير بينهم، وقد يختلفوا فيه أحياناً، بعض الكتب
+
+338
+00:26:28,220 --> 00:26:30,940
+هتلاقيهم يختلفوا فيه، لكن خلينا ناخدها شوية شوية،
+
+339
+00:26:30,940 --> 00:26:33,420
+لما بتكلم عن sequence هي عبارة عن discrete
+
+340
+00:26:33,420 --> 00:26:39,500
+structure، هو مجموعة عناصر متتالية ورا بعض، مدام
+
+341
+00:26:39,500 --> 00:26:42,140
+مجموعة عناصر فهي منفصلة، هي مش continuous، عشان
+
+342
+00:26:42,140 --> 00:26:45,000
+تكون فعلاً discrete، وتكون sequence، هذه لحالها، هذه
+
+343
+00:26:45,000 --> 00:26:49,030
+لحالها، هذه لحالها، هذه لحالها، discrete منفصلين عن بعض
+
+344
+00:26:49,030 --> 00:26:54,350
+فيمثلوا بشكل ordered list، ordered list، فهي أول
+
+345
+00:26:54,350 --> 00:26:58,450
+اختلاف بينها وبين الـ set، check، الـ set كانت إيه؟
+
+346
+00:26:58,450 --> 00:27:03,010
+عشان ordered، ماكنتش مرتبة، هنا لأ، بتكلم عن ordered
+
+347
+00:27:03,010 --> 00:27:07,570
+set، فإذا القائمة أو الـ list اللي موجودة عندنا،
+
+348
+00:27:07,570 --> 00:27:10,790
+القائمة اللي موجودة عندنا هي لازم تكون مرتبة، طيب
+
+349
+00:27:10,790 --> 00:27:18,220
+مرتبة، إيش اللي بيفرق بينها وبين الـ set؟ الـ location،
+
+350
+00:27:18,220 --> 00:27:24,160
+الـ location، العنصر هو اللي هيفرق، مدام ordered، فإذا
+
+351
+00:27:24,160 --> 00:27:28,720
+كل عنصر إله location، إله المكان داخل الـ set اللي
+
+352
+00:27:28,720 --> 00:27:32,600
+ماينفعش يتغير، ماينفعش يتغير، وإلا بتصير unordered،
+
+353
+00:27:32,600 --> 00:27:36,860
+تصبح غير مرتبة زيها زي الـ set، طيب الـ set ماكنتش
+
+354
+00:27:36,860 --> 00:27:42,870
+هتفرق، ماكنتش بتفرق، في حال من الحلول، واحد حط العنصر
+
+355
+00:27:42,870 --> 00:27:46,330
+الأول ثم الثاني، واحد هو بحل حط الثاني قبل الأول،
+
+356
+00:27:46,330 --> 00:27:50,230
+هقوله صح، مش هتفرق معانا، لكن لما بتكلم عن sequence،
+
+357
+00:27:50,230 --> 00:27:54,530
+لأ، الأول بيجي قبل الثاني حتماً، بيجي قبل الثاني، فإذا
+
+358
+00:27:54,530 --> 00:27:59,510
+مين اللي بيحدد لنا هذا الكلام؟ أنه هي معتمدة على الـ
+
+359
+00:27:59,510 --> 00:28:04,510
+location أو الـ position داخل الـ what، الـ set،
+
+360
+00:28:04,510 --> 00:28:08,110
+location داخل الـ set مهم جداً هنا، فبيصير اسمها مش
+
+361
+00:28:08,110 --> 00:28:13,310
+set، sequence، في الحالة هذه لازم يكون العنصر
+
+362
+00:28:13,310 --> 00:28:17,950
+function في الـ location عشان نضمن فعلاً أن الـ
+
+363
+00:28:17,950 --> 00:28:20,790
+location مهم، فبتصبح function في main في الـ
+
+364
+00:28:20,790 --> 00:28:22,890
+location، وإحنا لسه يدوبن وماخدين الـ function،
+
+365
+00:28:22,890 --> 00:28:29,410
+فإذا كأن الـ domain تبعها هي أرقام الـ locations أو
+
+366
+00:28:29,410 --> 00:28:33,390
+الـ positions داخل الـ set، إذا الـ set تبعتنا فيها
+
+367
+00:28:33,390 --> 00:28:37,710
+end position، فإذا من واحد أو من صفر زي الـ array،
+
+368
+00:28:37,710 --> 00:28:40,330
+لما كنتوا بتشتغلوا على الـ array في البرمجة كنتوا
+
+369
+00:28:40,330 --> 00:28:43,850
+بتبدأ أحياناً من صفر، مش هيك، فإذا من صفر إذا كان
+
+370
+00:28:43,850 --> 00:28:46,570
+بتكلم عن natural number، أو من الواحد في بعضهم
+
+371
+00:28:46,570 --> 00:28:50,810
+بيبدأ واحد، مش مشكلة، فكأنها الـ natural number minus
+
+372
+00:28:50,810 --> 00:28:56,320
+zero، minus zero، بيمشي الحل، في الحالة هذه 2n، فهيكون
+
+373
+00:28:56,320 --> 00:29:00,620
+عندك عدد العناصر، in elements أو in positions داخل
+
+374
+00:29:00,620 --> 00:29:04,320
+الـ set، طيب مثال على ذلك لما تقول واحد اتنين تلاتة
+
+375
+00:29:04,320 --> 00:29:09,000
+خمسة تمانية، هي sequence with five elements، طبعاً
+
+376
+00:29:09,000 --> 00:29:11,680
+ممكن تزود، أو ممكن تزود واحدة من الـ sequences
+
+377
+00:29:11,680 --> 00:29:15,220
+المهمة جداً أو الـ strings المهمة جداً، هذه اللي
+
+378
+00:29:15,220 --> 00:29:19,830
+هناخدها لاحقاً، أعتقد مرت عليكم يمكن، هذا الـ sequence،
+
+379
+00:29:19,830 --> 00:29:23,250
+هذا بتقدروا الآن يعني زي ما بيقولوا تتوقعوا
+
+380
+00:29:23,250 --> 00:29:26,630
+العناصر اللي وراه، فيكفي أن إحنا نكتب مجموعة أول
+
+381
+00:29:26,630 --> 00:29:31,610
+مجموعة عناصر بحيث أنه عرفنا نسبياً أو جزئياً الـ
+
+382
+00:29:31,610 --> 00:29:35,850
+sequence، فالـ sequence أحد طرق تعريفه أنه نعرفه بـ
+
+383
+00:29:35,850 --> 00:29:40,840
+few first elements أو last elements، حتى، حتى في الـ
+
+384
+00:29:40,840 --> 00:29:44,440
+last elements تبعته، تلاتة أربعة elements، خلاص إنتَ
+
+385
+00:29:44,440 --> 00:29:47,480
+حاول تطلع زي ما بيقوله، لما في المدارس كنا بيقول
+
+386
+00:29:47,480 --> 00:29:54,420
+النمط، شكله، اكتب النمط واعمل creation أو generation
+
+387
+00:29:54,420 --> 00:29:58,400
+لكمان two elements مثلاً أو one element بعدهم، okay،
+
+388
+00:29:58,400 --> 00:30
+
+445
+00:34:13,250 --> 00:34:16,870
+هذه السلسلة هذه من العناصر زي ما قلنا
+
+446
+00:34:16,870 --> 00:34:23,350
+يشار إليها بـ first elements أو last
+
+447
+00:34:23,350 --> 00:34:27,810
+elements مش بالضروري أول تلت أربع عناصر، يمكن آخر
+
+448
+00:34:27,810 --> 00:34:32,670
+تلت أربع عناصر أو أكثر، عنصر في النص المهم أنك أنت
+
+449
+00:34:32,670 --> 00:34:35,690
+تحصل من مجموعة العناصر على النمط زي ما كنا نأخذه
+
+450
+00:34:35,690 --> 00:34:39,090
+في المدرسة زمان، اللي هو الـ formula، بدك تجيب الـ
+
+451
+00:34:39,090 --> 00:34:45,090
+formula نفسها، ومجموعة ellipses، بفهم منها أن الـ
+
+452
+00:34:45,090 --> 00:34:48,860
+sequence مستمرة، مجموعة ellipses اللي هي مجموعة ثلاثة
+
+453
+00:34:48,860 --> 00:34:53,740
+نقاط على الأقل، بفهم منها أن الـ series أو الـ
+
+454
+00:34:53,740 --> 00:35:02,680
+sequence مستمر، هذا مثال، set of a n، تمام، n في index
+
+455
+00:35:02,680 --> 00:35:07,360
+هنا رغم أن هي set، فأفهم أن هذه sequence الـ
+
+456
+00:35:07,360 --> 00:35:11,420
+sequence هذه، قال لي صفر، واحد، أربعة، تسعة، ستة عشر، خمسة و
+
+457
+00:35:11,420 --> 00:35:16,090
+عشرين، ellipses، يعني مستمرة، يعني مستمرة كتير
+
+458
+00:35:16,090 --> 00:35:19,730
+واضحة، هي دي كإني بقول أنا بتكلم عن natural number
+
+459
+00:35:19,730 --> 00:35:24,850
+و n تربيع، الـ formula هي n تربيع في natural number
+
+460
+00:35:24,850 --> 00:35:29,090
+ببدأ من الصفر، okay، صفر تربيع، واحد تربيع، اثنين
+
+461
+00:35:29,090 --> 00:35:31,730
+تربيع، ثلاثة تربيع، أربعة تربيع، خمسة تربيع، and so on
+
+462
+00:35:31,730 --> 00:35:35,590
+لو قلت لك هات العنصر رقم مئة، مش هتبقى ماشي فيها لما
+
+463
+00:35:35,590 --> 00:35:39,050
+تصل للمئة، على طول بتعود بالـ formula مباشرة، بتعود
+
+464
+00:35:39,050 --> 00:35:39,990
+بالـ formula، وتجيبها
+
+465
+00:35:43,190 --> 00:35:48,350
+كمان sequences، ممكن نتكلم عن الـ sequence، نستعيض
+
+466
+00:35:48,350 --> 00:35:52,970
+عنه، بدل ما أحطه داخل الـ set، أقول خلاص هي a1،2
+
+467
+00:35:52,970 --> 00:35:57,390
+مجموعة ellipses، بعرف أن هي مستمرة وخلاص، بدل ما
+
+468
+00:35:57,390 --> 00:36:01,950
+أضطر أحطها داخل set، فهذه مقبولة برضه، ما فيش أي
+
+469
+00:36:01,950 --> 00:36:05,870
+مشكلة في sequence بهذا الشكل، بحيث أنها تكون موجودة
+
+470
+00:36:05,870 --> 00:36:10,590
+لكن المهم التأكيد، حتى لو حطيتها داخل الـ curly
+
+471
+00:36:10,590 --> 00:36:14,970
+braces، أتأكد على الـ index، لأن هو هذا المؤشر الوحيد
+
+472
+00:36:14,970 --> 00:36:18,430
+اللي بفهم منه أنت بتتكلم عن set ولا بتتكلم عن
+
+473
+00:36:18,430 --> 00:36:23,610
+sequence، فالـ index أو الـ indices لازم تكون واضحة
+
+474
+00:36:23,610 --> 00:36:29,070
+لازم تكون واضحة، اللي هي مجموعة الـ index اللي
+
+475
+00:36:29,070 --> 00:36:33,280
+موجودة عندك، لازم تكون واضحة، مثال، ممكن تكتبها بهذا
+
+476
+00:36:33,280 --> 00:36:39,260
+الشكل، set a n، ما فيه index، هي واضحة، معناه ذلك أن
+
+477
+00:36:39,260 --> 00:36:44,060
+هذه عبارة عن a1، a2، ellipses، مستمرة، وأقول لك مثلاً
+
+478
+00:36:44,060 --> 00:36:49,400
+أعرفها بهذا الشكل، for all n أكبر من أو يساوي واحد، a
+
+479
+00:36:49,400 --> 00:36:54,700
+n تساوي f of n، واحد على n، طيب هذه، مدام قال لي for
+
+480
+00:36:54,700 --> 00:37:02,120
+all أكبر من واحد، طب لأ، لامتى؟ فإذا infinite sequence
+
+481
+00:37:02,120 --> 00:37:07,520
+هنا بنتكلم عن infinite sequence، غير نهائي، هذه series
+
+482
+00:37:07,520 --> 00:37:11,720
+أو سلسلة غير نهائية من مجموعة من العناصر، مستمرة طول
+
+483
+00:37:11,720 --> 00:37:17,820
+ما هتكبر في N، هتعطيك قيمة، هتعطيك locations، لأن N
+
+484
+00:37:17,820 --> 00:37:21,120
+هنا أصبحت تعبر عن location، كل ما تكبر في قيمة N
+
+485
+00:37:21,120 --> 00:37:25,780
+هتعطيك locations إضافية، طبعاً خصوصاً عندما نتكلم عن
+
+486
+00:37:25,780 --> 00:37:27,800
+الـ natural number، فالـ natural number to infinity
+
+487
+00:37:27,800 --> 00:37:34,680
+فحضرتها infinity، إذا هذه كأنها تمثل واحد على واحد، 1
+
+488
+00:37:34,680 --> 00:37:38,920
+على 2، 1 على 3، 1 على 4، 1 على 5، 1 على 6، وضل ماشي
+
+489
+00:37:38,920 --> 00:37:42,300
+فيها، ضل ماشي فيها، هنا احنا عبارة عن مجموعة
+
+490
+00:37:42,300 --> 00:37:47,580
+sequence أو مجموعة elements تمثل sequence، طيب هذه
+
+491
+00:37:47,580 --> 00:37:50,680
+في إيش بتفيدنا؟ لأن عارف أنه لعند الآن السؤال
+
+492
+00:37:50,680 --> 00:37:53,720
+الأهم، احنا ليش بناخذ هذا الكلام؟ أنت بتاخذه لأنه
+
+493
+00:37:53,720 --> 00:37:57,000
+هنضطر قدامنا نعمله summation، فبدنا نكون عارفين
+
+494
+00:37:57,000 --> 00:38:00,080
+على الأقل عناصر، إيش هم العناصر؟ هتقول لي ليش بدي الـ
+
+495
+00:38:00,080 --> 00:38:04,690
+summation؟ سؤال منطقي جداً، أنا وجدت، والمفروض أنه
+
+496
+00:38:04,690 --> 00:38:07,790
+ما بيش من درسنا، بس شايفكم شوية مستغربين احنا إيش
+
+497
+00:38:07,790 --> 00:38:10,690
+دخلنا في هذا الموضوع، لأ، الموضوع هذا كتير مهم،
+
+498
+00:38:10,690 --> 00:38:16,310
+ليش؟ تبديل وتوفيق؟ يعني بس ما له علاقة بـ sequence
+
+499
+00:38:16,310 --> 00:38:19,090
+تبديل وتوفيق، تبديل وتوفيق، أنت بتتكلم عن group،
+
+500
+00:38:19,090 --> 00:38:23,590
+عن set، set واضحة، أنا ما بروحش لـ sequence، هي set زي
+
+501
+00:38:23,590 --> 00:38:26,110
+الـ set اللي احنا موجودين الآن فيها، اللي هي مجموعة
+
+502
+00:38:26,960 --> 00:38:30,180
+طلبة في discrete، جا علينا لجنة ثقافية أو لجنة
+
+503
+00:38:30,180 --> 00:38:33,800
+علمية، وجالنا والله يبدوا من عندك ثلاثة، فكم
+
+504
+00:38:33,800 --> 00:38:37,580
+possibility أن أختار الثلاثة؟ هذه تبديل وتوافق
+
+505
+00:38:37,580 --> 00:38:40,640
+اللي بتتكلم فيها، ما فيش مشكلة، لكن أنا بتكلم عن الـ
+
+506
+00:38:40,640 --> 00:38:44,400
+sequence، الـ sequence هنا عشان نحدد العنصر...
+
+507
+00:38:44,400 --> 00:38:46,680
+العناصر بتاعتنا، الـ formula، أول شغلة هي الـ
+
+508
+00:38:46,680 --> 00:38:49,980
+function، فلما أنت تقول لي بكل بساطة اعمل لي
+
+509
+00:38:49,980 --> 00:38:54,260
+integration، إيش يعني integration؟ area under the
+
+510
+00:38:54,260 --> 00:38:57,280
+curve، صح؟ يعني لازم أكون عارف الـ curve اللي هي الـ
+
+511
+00:38:57,280 --> 00:39:01,640
+function، طيب، ولازم أكون عارف عناصر الـ curve حسب
+
+512
+00:39:01,640 --> 00:39:04,780
+الـ limits بتاعة الـ integration، والله بده إني أن
+
+513
+00:39:04,780 --> 00:39:08,580
+أعمل integration من واحد لمئة، طيب، معناته بده أعرف
+
+514
+00:39:08,580 --> 00:39:12,720
+العناصر من واحد لمئة، وأعملهم accumulation، صح؟
+
+515
+00:39:12,720 --> 00:39:19,060
+تمام، فإذا هذه عبارة عن sequence of elements، صح؟ هي
+
+516
+00:39:19,060 --> 00:39:25,570
+sequence of elements، عناصر عادية، هي curve، وقلت لك
+
+517
+00:39:25,570 --> 00:39:30,570
+من واحد ل... خلّيني أقول لعشرة، الـ area under the
+
+518
+00:39:30,570 --> 00:39:32,850
+curve، وأنا بشتغل discrete... discrete يعني معناه
+
+519
+00:39:32,850 --> 00:39:35,870
+ذلك، بدي آخذ samples عند الواحد، وعند الاثنين، وعند
+
+520
+00:39:35,870 --> 00:39:38,790
+الثلاثة، وعند الأربعة، خمسة، ستة، سبعة، وهكذا، okay، بس
+
+521
+00:39:38,790 --> 00:39:44,750
+بدي عناصرهم، جد قيمهم، هي discrete، طب كويس، بدنا نعمل
+
+522
+00:39:44,750 --> 00:39:48,010
+summation، summation لإيش؟ لـ sequence of elements
+
+523
+00:39:48,010 --> 00:39:50,870
+كل ما في الموضوع أني هحدد لك بدايته ونهايته، ومش
+
+524
+00:39:50,870 --> 00:39:53,530
+أكثر من هي، عشان هيك لازم تكونوا من الأساس عارفين إيش
+
+525
+00:39:53,530 --> 00:39:58,250
+يعني sequence of elements، واضحة، لأن عشان ما بديش
+
+526
+00:39:58,250 --> 00:40:01,870
+أشوف نظرة الحيرة أن احنا ليش اللي أودانا هنا، أنا
+
+527
+00:40:01,870 --> 00:40:04,030
+هيك، شوفت هيك في عينكم، كم من واحد، احنا إيش اللي
+
+528
+00:40:04,030 --> 00:40:10,870
+جابنا هنا، فواضحة تماماً، ليش احنا هنا، تمام، okay، with
+
+529
+00:40:10,870 --> 00:40:14,750
+repetitions، repetition بسيطة جداً، هذه repetition
+
+530
+00:40:14,750 --> 00:40:23,110
+بلا الـ... الـ... الـ... بهذا الشكل، قلنا لك بهذا
+
+531
+00:40:23,110 --> 00:40:27,630
+الشكل، ونفس الشيء، بدنا نجيب الـ free transform، مثلاً
+
+532
+00:40:27,630 --> 00:40:30,550
+الـ free transform، أنت بتعمل integration لمين؟ للـ
+
+533
+00:40:30,550 --> 00:40:33,930
+signs، الصنعات، مش هيك بتعمله؟ okay، نفس الفكرة، هذه
+
+534
+00:40:33,930 --> 00:40:37,450
+هتجد أنه بعد فترة، هترجع تتكرر
+
+535
+00:40:39,880 --> 00:40:44,480
+هترجع تتكرر، فإذا هل اتكرر، أجمع ولا ما أجمعوش؟ طب ما
+
+536
+00:40:44,480 --> 00:40:48,020
+هي فعلاً area، زيادة صارت عندك، sequence الـ location
+
+537
+00:40:48,020 --> 00:40:50,700
+بتاع القيمة، هذا القيمة اللي هنا، غير الـ location
+
+538
+00:40:50,700 --> 00:40:54,020
+بتاع القيمة اللي هنا، ليش تقول لي بدي أجمعهم أو بدي
+
+539
+00:40:54,020 --> 00:40:57,360
+لأ، لو ما لهم علاقة، ده sequence، أنا راجع طول على set
+
+540
+00:40:57,360 --> 00:41:01,540
+لأ، ده مش set، هذا sequence، و sequence معناته بيقبل
+
+541
+00:41:01,540 --> 00:41:06,910
+repetition، بيقبل الـ repetition، فهنا unlike sets، هنا
+
+542
+00:41:06,910 --> 00:41:12,070
+الـ sequence ممكن يأخذ repeated elements، عناصر
+
+543
+00:41:12,070 --> 00:41:19,970
+مكررة، آه ما فيش أي مشكلة، لما أقول set of b of n، ب
+
+544
+00:41:19,970 --> 00:41:24,710
+node بواحد، ellipses، يعني مستمرة، خلاص، طيب وبعدين
+
+545
+00:41:24,710 --> 00:41:31,190
+عرفنا الـ bn على أساس أن هي minus one all to the
+
+546
+00:41:31,190 --> 00:41:38,010
+power، هذه على طول بفهم منها أن هي set أو sequence لـ
+
+547
+00:41:38,010 --> 00:41:43,370
+واحد، minus واحد، واحد، minus واحد، واحد، minus واحد،
+
+548
+00:41:43,370 --> 00:41:47,970
+الـ ellipses، وبتسيبها هيك، ما تقوليش لأن بتعامل معاها
+
+549
+00:41:47,970 --> 00:41:52,430
+set، فتروح تعاملها بهذا الشكل، واحد، سالب واحد، وخلاص، لأ
+
+550
+00:41:52,430 --> 00:41:55,510
+واضح أن هذه مختلفة تماماً عن ذلك، وعشان هيك يا دوب
+
+551
+00:41:55,510 --> 00:42:01,240
+احنا هنخلص موضوع الـ set، عفواً، الـ sequence والـ
+
+552
+00:42:01,240 --> 00:42:05,260
+string، على طول هندخل في مين؟ في الـ summation، لأنه
+
+553
+00:42:05,260 --> 00:42:08,560
+هدف التمهيد أن أنا بدي أكمل للـ summation، الهدف
+
+554
+00:42:08,560 --> 00:42:11,980
+الأساسي أن أنا أروح لـ summation، تمام؟ فلأ، مدام الـ
+
+555
+00:42:11,980 --> 00:42:16,340
+summation، لازم العناصر كلها تكون موجودة، الـ set شيء
+
+556
+00:42:16,340 --> 00:42:18,900
+والـ sequence شيء ثاني
+
+557
+00:42:22,270 --> 00:42:27,050
+Type recognizing sequences، كتير مهم أن احنا نميز
+
+558
+00:42:27,050 --> 00:42:30,170
+الـ sequence بشكل كتير كويس، احنا اتفقنا وقلنا أن
+
+559
+00:42:30,170 --> 00:42:35,150
+أنا بعرف أول مجموعة عناصر أو آخر مجموعة عناصر
+
+560
+00:42:35,150 --> 00:42:40,610
+بيفرق، يعني مين هنا أو هنا، بحيث أنه لو أنطلب مني
+
+561
+00:42:40,610 --> 00:42:45,350
+أعمل prediction أو تنبؤ، توقع، لأعرف العنصر اللي وراه
+
+562
+00:42:45,350 --> 00:42:50,130
+نكون قادرين نتوقع، نكون قادرين نتوقع، وهذا للأمانة
+
+563
+00:42:50,130 --> 00:42:53,910
+واحد من العلوم اللي كتير بتستخدم، أن لو عندك signal
+
+564
+00:42:53,910 --> 00:42:57,150
+وجّدت انقطعت... انقطعت الكهربا... انقطعت الـ... كيف ممكن
+
+565
+00:42:57,150 --> 00:43:01,690
+تفكر تعمل generation لباقي الـ signal؟ واحدة من
+
+566
+00:43:01,690 --> 00:43:06,410
+الفروع اللي ممكن تتعامل معها ضمن فرق الـ AI، مثلًا، بدك
+
+567
+00:43:06,410 --> 00:43:12,350
+تعمل توقع للقادم، expectation، تعمل expectation، إيش
+
+568
+00:43:12,350 --> 00:43:16,730
+النقطة اللي جاية؟ ده نفس الفكرة، أنت عندك sequence، و
+
+569
+00:43:16,730 --> 00:43:21,610
+من الـ sequence ده، بدك تحاول تجيب النمط، صحيح؟ عشان
+
+570
+00:43:21,610 --> 00:43:27,350
+تتوقع إيش القيمة القادمة، تتوقع القيمة القادمة، فهي
+
+571
+00:43:27,350 --> 00:43:31,190
+بكل بساطة، فكرة الـ recognizing الـ sequence، أن أنت
+
+572
+00:43:31,190 --> 00:43:35,210
+تكون عارف، حددت الـ sequence تبعك هو إيش بالضبط
+
+573
+00:43:35,210 --> 00:43:39,550
+حددت الـ formula تبعته، وبناء عليه تقدر تعمل
+
+574
+00:43:39,550 --> 00:43:44,270
+expectation أو توقع للرقم القادم، لما نقول مثلاً
+
+575
+00:43:44,270 --> 00:43:49,540
+for example، واحد، اثنين، ثلاثة، أربعة، أنا بتكلم واضح
+
+576
+00:43:49,540 --> 00:43:55,200
+أنه f of n بتساوي n زائد واحد، بس، فإذا the next
+
+577
+00:43:55,200 --> 00:44:00,980
+element، خمسة، the next element خمسة، طيب، واحد، ثلاثة،
+
+578
+00:44:00,980 --> 00:44:07,660
+خمسة، سبعة، تسعة، اللي هي اثنين n زائد واحد، مش هيك الـ
+
+579
+00:44:07,660 --> 00:44:14,560
+odd، الـ odd numbers، الـ odd numbers، طيب، ليش ثلاثة، عشر
+
+580
+00:44:15,790 --> 00:44:19,810
+primes؟ لأننا بنتكلم عن الـ primes، نتكلم عن الـ
+
+581
+00:44:19,810 --> 00:44:24,030
+primes، تمام، فإذا مجرد أن أنت مجموعة الـ elements
+
+582
+00:44:24,030 --> 00:44:26,990
+اللي موجودة، الـ few elements اللي موجودة قدامك
+
+583
+00:44:26,990 --> 00:44:32,330
+أعطتك النمط، خلصت، يعني انتهت المشكلة، عملت
+
+584
+00:44:32,330 --> 00:44:37,450
+recognizing، صح، أو recognition، صح، تمييز، صح، للـ
+
+585
+00:44:37,450 --> 00:44:41,390
+sequence، أنت عملت تمييز صحيح للـ sequence، لكن
+
+586
+00:44:41,390 --> 00:44:46,230
+الحقيقة مش دائماً الكلام هذا بيكون متوفر معنا
+
+587
+00:44:46,230 --> 00:44:49,390
+بيكون متحقق معنا، ممكن كتير تكون في عندك مجموعة
+
+588
+00:44:49,390 --> 00:44:54,410
+sequences، لكن مش معرفة بشكل جيد، مجموعة الـ elements
+
+589
+00:44:54,410 --> 00:44:58,630
+اللي في الأول not well defined، وهذه تعمل لك مشكلة أن
+
+590
+00:44:58,630 --> 00:45:03,550
+أنت هتجد أنه ممكن يكون أكثر من sequence لهام، ممكن
+
+591
+00:45:03,550 --> 00:45:16,830
+تعرف بأكثر من طريقة، بأكثر من طريقة، لو أخذنا
+
+592
+00:45:16,830 --> 00:45:27,490
+مثلاً، واحد قال لك ثلاثة، خمسة، وسكت، وكملها سبعة، و
+
+593
+00:45:27,490 --> 00:45:30,830
+قال لك the next element
+
+594
+00:45:33,800 --> 00:45:37,860
+ممكن تسعة، وممكن أحد عشر، صحيح؟ واحد هيفهمها لأ، هذه
+
+595
+00:45:37,860 --> 00:45:42,620
+مجموعة العناصر بتاعة الـ... الـ odd numbers، آه
+
+596
+00:45:42,620 --> 00:45:45,980
+معناته تسعة، واحد يقلك لأ لأ لأ، أنت مش اللي
+
+597
+00:45:45,980 --> 00:45:49,640
+عرفك، لأ لأ لأ، هقول له الدكتور جدي الابراهيم، أنت
+
+598
+00:45:49,640 --> 00:45:54,650
+حياتك غلط، هذه هي أحد عشر، واحد ثالث يجيه طريقة
+
+599
+00:45:54,650 --> 00:46:00,590
+ثانية، يتوقع شيء مختلف، حسب المعادلة أو الـ formula أو
+
+600
+00:46:00,590 --> 00:46:05,410
+النمط، يطلع له النمط، formula معينة، فعلاً عند الواحد
+
+601
+00:46:05,410 --> 00:46:08,150
+أو الصفر، والواحد، والاثنين بيطلعوا نفس الأرقام
+
+602
+00:46:08,150 --> 00:46:12,310
+هدول بس بيطلع رقم مختلف تماماً، في sequences هيك، آه
+
+603
+00:46:12,310 --> 00:46:15,530
+في sequences هيك، طيب، وإيش مشكلتها هذه؟ مشكلتها
+
+604
+00:46:15,530 --> 00:46:20,180
+أنها ما عرفتش، مشكلة، صحيح، من البداية، العناصر اللي تم
+
+605
+00:46:20,180 --> 00:46:24,540
+تعريفهم، هم مشتركون لمجموعة sequences كثيرة، مشتركون
+
+606
+00:46:24,540 --> 00:46:30,920
+في مجموعة sequences كثيرة، زي واحد، اثنين، ثلاثة، في
+
+607
+00:46:30,920 --> 00:46:37,860
+أسهل من هيك، the next element، المنطقي يقول، طب أنا
+
+608
+00:46:37,860 --> 00:46:43,980
+ممكن أقول لك خمسة، أنا هقول لك خمسة، من وين جبنا الخمسة؟
+
+609
+00:46:48,810 --> 00:46:52,070
+ما هي كان في sequence فعلاً هات، مش هي الـ sequence
+
+610
+00:46:52,070 --> 00:46:54,290
+هات، وقلت لكم هناخذ الـ sequence هات، وهتطلع
+
+611
+00:46:54,290 --> 00:46:58,250
+sequence مشهورة جداً، ومعروفة جداً، هي واحد، اثنين،
+
+612
+00:46:58,250 --> 00:47:04,290
+ث
+
+667
+00:51:15,250 --> 00:51:19,210
+اللي عندنا على أساس إن هي Big Sigma، الـ Big Sigma
+
+668
+00:51:19,210 --> 00:51:24,710
+هذه على طول هي finite set of symbols، تعرف على أساس
+
+669
+00:51:24,710 --> 00:51:27,770
+إن هي finite set of symbols، وتحديدًا alphabet
+
+670
+00:51:27,770 --> 00:51:35,190
+وممكن نقول إنه الـ string s، string s، أي اسم a, b, c, s
+
+671
+00:51:35,190 --> 00:51:39,730
+هنا الـ String على من خلال الـ over الـ ... الـ
+
+672
+00:51:39,730 --> 00:51:45,690
+alphabet، بيج سيجما هو عبارة عن sequence، إلها أقول لك
+
+673
+00:51:45,690 --> 00:51:50,270
+ببساطة الكلام اللي إحنا بندحكيه مكون من إيش؟
+
+674
+00:51:50,270 --> 00:51:54,130
+مجموعة العناصر هي alphabet، صح؟ حروف لكن الكلمة
+
+675
+00:51:54,130 --> 00:51:57,250
+ممكن يكون في حرف متكرر في نفس الكلمة، خلّيني أنا
+
+676
+00:51:57,250 --> 00:52:02,090
+أفترض إن الكلمة هذه هي الـ sequence S، الـ sequence S
+
+677
+00:52:02,090 --> 00:52:03,070
+مثلا computer
+
+678
+00:52:05,900 --> 00:52:14,070
+كويس، هذه S، هذه واضحة إن الـ location لكل
+
+679
+00:52:14,070 --> 00:52:18,410
+alphabet مهم جدًا، لأن إذا غيرتهم، هتصير كلمة ثانية
+
+680
+00:52:18,410 --> 00:52:21,250
+هيصير string مختلف تمامًا، مالوش علاقة باللي إحنا
+
+681
+00:52:21,250 --> 00:52:26,670
+بنحكيه، لكن في النهاية هو من الـ big sigma، فهو من الـ
+
+682
+00:52:26,670 --> 00:52:29,670
+big sigma، موجود هنا، الـ index ما عنديش، ما عندناش أي
+
+683
+00:52:29,670 --> 00:52:33,290
+مشكلة فيه، natural number أو natural minus one
+
+684
+00:52:33,290 --> 00:52:36,590
+minus zero، اللي هو يعني يبدأ من صفر، natural أو من
+
+685
+00:52:36,590 --> 00:52:41,930
+واحد ناقص الـ zero، ممكن نكتبه ABC مباشرة بدون
+
+686
+00:52:41,930 --> 00:52:44,910
+الأقواس، زي ما قلنا، وممكن نكتبها بهذا الشكل على
+
+687
+00:52:44,910 --> 00:52:48,690
+طول S هي عبارة عن ABC، وممكن تكتبها بدون الكومات
+
+688
+00:52:48,690 --> 00:52:52,830
+كمان بدون الكومات على طول بهذا الشكل، without كومة
+
+689
+00:52:52,830 --> 00:52:58,490
+الآن، حاجة مهمة، إذا كان عندك S هي عبارة عن finite
+
+690
+00:52:58,490 --> 00:53:02,270
+string، و T كمان finite string، ممكن تعمل
+
+691
+00:53:02,270 --> 00:53:08,480
+concatenation، تجميع، concatenation S with T، فبتنكتب
+
+692
+00:53:08,480 --> 00:53:14,740
+just S و T جانب بعض، زي لما تقول مثلًا الـ string T هي
+
+693
+00:53:14,740 --> 00:53:20,740
+عبارة عن ing compute
+
+694
+00:53:20,740 --> 00:53:28,080
+بيحسب، طيب، بده أحط الـ S بتاعة compute مع الـ T، فتصبح
+
+695
+00:53:28,080 --> 00:53:32,540
+S و T computing، concatenated
+
+696
+00:53:33,640 --> 00:53:37,260
+string، أصبحت concatenating string، اللي هي تحطهم
+
+697
+00:53:37,260 --> 00:53:40,000
+ورا بعض، جملة واحدة أو كلمة واحدة، فبيسموها
+
+698
+00:53:40,000 --> 00:53:42,880
+concatenation، العملية هذه، هذه العملية بيسموها
+
+699
+00:53:42,880 --> 00:53:48,660
+concatenation، في الحالة لأن طبعًا الـ length هي الـ
+
+700
+00:53:48,660 --> 00:53:52,100
+cardinality، أنت بتشوف قد إيش عدد الـ elements عشان أقول
+
+701
+00:53:52,100 --> 00:53:57,220
+عنهم، هدول الـ length بتاعتك، فهم العدد الـ positions
+
+702
+00:53:57,220 --> 00:54:00,820
+اللي موجودين فعليًا، بس تاخد بالك من الـ index عشان
+
+703
+00:54:00,820 --> 00:54:04,060
+إذا كان بدأ من صفر، بتزود واحد، N زائد واحد
+
+704
+00:54:04,060 --> 00:54:07,780
+تاخدوا بالكم منها، طبعًا إذا كانت S هي finite، فمعنى
+
+705
+00:54:07,780 --> 00:54:10,980
+ذلك إن هي لازم تكون ممتدة إلى الـ natural number
+
+706
+00:54:10,980 --> 00:54:15,160
+أكيد، إذا كان S to the power N، فأنا بعمل
+
+707
+00:54:15,160 --> 00:54:20,860
+concatenation N مرة للـ S، يعني بكررها N مرة، لما يجيك
+
+708
+00:54:20,860 --> 00:54:24,140
+بهذا الشكل، وأنت عارف إنه هادي string، معناته أنا
+
+709
+00:54:24,140 --> 00:54:29,240
+بعمل concatenation بـ N مرة للـ S، يعني بكررها كذا N
+
+710
+00:54:29,240 --> 00:54:35,480
+مرة، ابسلون صغيرة هناك كانت Big Sigma، أنا بتكلم عن
+
+711
+00:54:35,480 --> 00:54:39,340
+الـ set لكل الـ alphabet، الـ Big Sigma، لما بكتب
+
+712
+00:54:39,340 --> 00:54:42,980
+ابسلون صغيرة، هادي، هادي تعبر بالنسبة للـ string عن
+
+713
+00:54:43,620 --> 00:54:49,300
+الـ Empty Set، معناته هذا بيصير Empty String، String
+
+714
+00:54:49,300 --> 00:54:53,120
+فاضي، أو Sequence فاضي، String فاضية، هنا فبنكتبها
+
+715
+00:54:53,120 --> 00:54:56,140
+بهذا الشكل، أو Double Quotation فاضيين، Double
+
+716
+00:54:56,140 --> 00:54:59,180
+Quotation فاضيين، فهدا Empty String، فالـ String هنا
+
+717
+00:54:59,180 --> 00:55:04,660
+الـ length بتاعتها Zero، Zero، تمام؟ هي خلصنا المقدمة
+
+718
+00:55:04,660 --> 00:55:07,020
+بتاعة هذا الموضوع، عشان المرة القادمة نتكلم عن
+
+719
+00:55:07,020 --> 00:55:09,540
+summation إن شاء الله تعالى، ونشوف كيف نستخدم هذا
+
+720
+00:55:09,540 --> 00:55:10,620
+الكلام، يعطيكم العفو يا شباب
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1yMI1kNL2Xs_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1yMI1kNL2Xs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..94a3ed919537492dc1d215ab457d43f36f660744
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1yMI1kNL2Xs_postprocess.srt
@@ -0,0 +1,2880 @@
+1
+00:00:05,230 --> 00:00:08,930
+طب السلام عليكم وعليكم العفو يا شباب نكمل اليوم ان
+
+2
+00:00:08,930 --> 00:00:12,090
+شاء الله تعالى موضوع ال functions اللي حكينا فيه
+
+3
+00:00:12,090 --> 00:00:17,410
+من المرة الماضية كنا بدأنا فيه اتكلمنا عن معظم ال
+
+4
+00:00:17,410 --> 00:00:21,130
+applications او الصور السابقة اللي أخدناها في
+
+5
+00:00:21,130 --> 00:00:25,450
+المصاد وشوفنا كيف ممكن كلها نعبر عنها بشكل
+
+6
+00:00:25,450 --> 00:00:31,050
+functions ثم اتكلمنا في نهاية المحاضرة على أنواع
+
+7
+00:00:31,050 --> 00:00:35,580
+ال functions واللي بدأنا فيها بال one to oneوكان
+
+8
+00:00:35,580 --> 00:00:40,640
+في جزئية في ال one to one اتكلمنا عنها هي ال
+
+9
+00:00:40,640 --> 00:00:46,140
+monotonic increasing او decreasing كويس واتكلمنا
+
+10
+00:00:46,140 --> 00:00:50,600
+اذا كانت monotonic increasing او decreasing فهي
+
+11
+00:00:50,600 --> 00:00:55,040
+على طول بتصير one to one واخدنا بشكل سريع مثال
+
+12
+00:00:55,040 --> 00:01:00,440
+عليها في جزئية ال X تكيب
+
+13
+00:01:03,380 --> 00:01:10,200
+صحيح؟ X كايب واتكلمنا عن نوع تاني او functions
+
+14
+00:01:10,200 --> 00:01:15,640
+تانية اللي هي ليس بالضروري العكس يكون صحيح بمعنى
+
+15
+00:01:15,640 --> 00:01:19,420
+انه ممكن تكون one to one لكن هي ليست increasing
+
+16
+00:01:19,420 --> 00:01:24,060
+باستمرار او decreasing باستمرار واخدنا مثال عليها
+
+17
+00:01:24,060 --> 00:01:32,490
+الواحد على Xاللي هي ال function اللي بهذا الشكل
+
+18
+00:01:32,490 --> 00:01:38,730
+واحد على على X فهد يمكن صار في خربط المرة اللي
+
+19
+00:01:38,730 --> 00:01:44,350
+فاتت فيها فكويس ان احنا نرجعلها هد مثلا بالعكس one
+
+20
+00:01:44,350 --> 00:01:51,720
+to one لكن مش ايش؟مش decreasing لأن هذه الشكل
+
+21
+00:01:51,720 --> 00:01:54,620
+العام تباحة انه المفروض تكون decreasing مش هيك ايه
+
+22
+00:01:54,620 --> 00:02:00,240
+نازلة بس فاليه عند ال zero بصير فيه سقوط فمعناه
+
+23
+00:02:00,240 --> 00:02:03,580
+ذلك انه في الجزء عند zero صار increasing و
+
+24
+00:02:03,580 --> 00:02:07,560
+increasing حاد جدا increasing حاد جدا يعني لو بدنا
+
+25
+00:02:07,560 --> 00:02:10,840
+نيجي عند الزاوية هذه عند النقطة هذه و نعمل zoom
+
+26
+00:02:10,840 --> 00:02:16,420
+كبيرعلى طول ال y-axis هنجد ان هي فعليا نزلهيك و
+
+27
+00:02:16,420 --> 00:02:22,340
+بعدين طالع و رجع و رجع مكملة تنزل رغم ان فعليا هي
+
+28
+00:02:22,340 --> 00:02:28,000
+one to one ليش لان مش هناخد قيمة ال zero فعلياف
+
+29
+00:02:28,000 --> 00:02:30,460
+undefined هي مش معروفة undefined negative or
+
+30
+00:02:30,460 --> 00:02:35,180
+positive or positive فكان ضروري نرجع للنقطة هذه
+
+31
+00:02:35,180 --> 00:02:42,720
+عشان نوضحها و نزيل الخربطة اللي سارت المرة الماضية
+
+32
+00:02:42,720 --> 00:02:48,180
+تمام النوع التاني من أنواع ال functions بعد ال one
+
+33
+00:02:48,180 --> 00:02:53,670
+to oneاللي وجفنا عندها حقيقة هي الانتو الانتو انت
+
+34
+00:02:53,670 --> 00:02:56,990
+بقدر اقول عليها انتو او surjective surjective بقدر
+
+35
+00:02:56,990 --> 00:02:59,990
+اقول عليها لل function طبعا كل كلامنا لل function
+
+36
+00:02:59,990 --> 00:03:05,170
+اللي هي ال F from a او from set A to set B يعني من
+
+37
+00:03:05,170 --> 00:03:10,050
+ال domain لل codomain domain لل codomain if and
+
+38
+00:03:10,050 --> 00:03:14,190
+only if بقول عليها انتو if and only if ال range
+
+39
+00:03:14,190 --> 00:03:18,000
+بساوي ال codomainإذا ال range يسوي ال code domain
+
+40
+00:03:18,000 --> 00:03:22,620
+بمعنى إنه ال code domain كله مغطى إيش يعني كله
+
+41
+00:03:22,620 --> 00:03:29,160
+مغطى؟ بمعنى إنه for all B كل element في ال code
+
+42
+00:03:29,160 --> 00:03:35,260
+domain يوجد إله preimage يوجد إله preimage فاحنا
+
+43
+00:03:35,260 --> 00:03:40,400
+عارفين إنه B في النهاية هي تسوي F of A و A هدي ال
+
+44
+00:03:40,400 --> 00:03:46,500
+preimage ل .. ل Bالـ Preimage لـ B بمعنى ان كل بي
+
+45
+00:03:46,500 --> 00:03:54,340
+موجودة في ال code main يمكن انتاجها من خلال تطبيق
+
+46
+00:03:54,340 --> 00:03:58,880
+ال function على preimage corresponding لها أو خاصة
+
+47
+00:03:58,880 --> 00:04:04,320
+فيها و اللي تنتمي لمين؟ لإيه؟ تنتمي لإيه؟ فهذه
+
+48
+00:04:04,320 --> 00:04:10,520
+معناها for all بي لكل عناصر ال code main يوجد
+
+49
+00:04:10,520 --> 00:04:14,600
+preimageبري إمش لازم أكيد هتكون جاية من ال domain
+
+50
+00:04:14,600 --> 00:04:18,580
+بحيث
+
+51
+00:04:18,580 --> 00:04:23,980
+ان ال F of ال preimage تساوي ال B وهذا الكلام لكل
+
+52
+00:04:23,980 --> 00:04:30,620
+ال B بمعنى كل عناصر ال code domain ممكن أو مرشحين
+
+53
+00:04:30,620 --> 00:04:35,460
+يكونوا ناتج لل function طيب و احنا عارفين انه مدام
+
+54
+00:04:35,460 --> 00:04:38,040
+مرشح هنتكون ناتج لل function فعليا هتكون ناتج لل
+
+55
+00:04:38,040 --> 00:04:41,930
+function فهي rangeفهي range المعنى ذلك ان ال range
+
+56
+00:04:41,930 --> 00:04:49,650
+يساوي ال codomain ال on to هي معناها انه كامل
+
+57
+00:04:49,650 --> 00:04:54,710
+عناصر ال B كاملة
+
+58
+00:04:54,710 --> 00:04:59,230
+هي موجودة كنتج لل function او هي موجودة في ال
+
+59
+00:04:59,230 --> 00:05:03,970
+range لان احنا عارفين مدام هتمتش لل function كنتج
+
+60
+00:05:03,970 --> 00:05:06,170
+او result لل function فهي range
+
+61
+00:05:08,830 --> 00:05:11,730
+for example وليس جزء منها وليس جزء من ال code
+
+62
+00:05:11,730 --> 00:05:14,150
+domain بمعنى ان ال range مش هو جزء من ال code
+
+63
+00:05:14,150 --> 00:05:16,890
+domain اللي هو كل ال code domain هناخد أنفلة عليها
+
+64
+00:05:16,890 --> 00:05:23,190
+زي ال X تكعيب زي ال X to the power 3 cube و اللي
+
+65
+00:05:23,190 --> 00:05:26,890
+كتبناها لسه كنا تورسمينها كمثال على ال one to one
+
+66
+00:05:26,890 --> 00:05:33,610
+وهي نفسها كمثال على ال one to
+
+67
+00:05:39,460 --> 00:05:49,400
+هي دي اللي هي f of x تساوي x cube وهنا x وهي ال y
+
+68
+00:05:49,400 --> 00:05:54,880
+او ال f of x هنجد انه ال code main هو ظاهر في ال
+
+69
+00:05:54,880 --> 00:05:58,980
+function كان ناتج له ال function كاملا من minus
+
+70
+00:05:58,980 --> 00:06:04,950
+infinityto infinity كامل موجود بشكل كامل هو موجود
+
+71
+00:06:04,950 --> 00:06:08,870
+فإذا ال function هذه بقدر بسهولة اقول ان هي onto
+
+72
+00:06:08,870 --> 00:06:12,710
+onto بمعنى ان ال domain هو ال key domain هو نفسه
+
+73
+00:06:12,710 --> 00:06:15,790
+ال range بشكل كامل هيظهر في ال range لكن في
+
+74
+00:06:15,790 --> 00:06:20,290
+المقابل عندك
+
+75
+00:06:20,290 --> 00:06:29,570
+ال x تربيع او squareالـ F of X مقابل الـ X هنجد
+
+76
+00:06:29,570 --> 00:06:34,770
+إنه اسميا الـ Codomain من negative infinity إلى
+
+77
+00:06:34,770 --> 00:06:38,830
+infinity زي الـ domain اللي هي الـ R لكن actually
+
+78
+00:06:38,830 --> 00:06:44,000
+ال range هو من صفر بالظبطمن صفر ل positive
+
+79
+00:06:44,000 --> 00:06:48,520
+infinity ال negative كله مظهرش و لا يمكن يطلع كنتج
+
+80
+00:06:48,520 --> 00:06:53,100
+فإذا ال range هنا فعليا أقل من ال code domain
+
+81
+00:06:53,100 --> 00:06:56,840
+فعليا تقريبا نص ال code domain مش شير نص ال code
+
+82
+00:06:56,840 --> 00:07:01,200
+domain فإذا هذه مقدرش أقول عنها onto هذه لا ينطبق
+
+83
+00:07:01,200 --> 00:07:05,180
+عليها ال function onto فهي ليست onto بالأساس تمام
+
+84
+00:07:06,260 --> 00:07:10,280
+النوع التالت طبعا هنوضح زي ما وضحنا اللي فاتوا من
+
+85
+00:07:10,280 --> 00:07:15,460
+خلال ال .. ال bipartate figures function بهذا
+
+86
+00:07:15,460 --> 00:07:21,880
+الشكل بقدر أقول عليها onto؟ على طول لما بدنا نسألك
+
+87
+00:07:21,880 --> 00:07:25,720
+عن ال onto اتطلع على مين؟ على ال Q domain هل كله
+
+88
+00:07:25,720 --> 00:07:28,880
+ظاهر في نتيجة ال relations هذه ولا لأ؟ فكلهم
+
+89
+00:07:28,880 --> 00:07:35,980
+ظاهرين بغض النظر هي اتنين لواحد ولا واحد لواحد؟أنا
+
+90
+00:07:35,980 --> 00:07:38,600
+ماسألتش عن one to one هذي one to one لأ مش one to
+
+91
+00:07:38,600 --> 00:07:44,160
+one صح لإن هي في two inputs لنفس ال output فهي one
+
+92
+00:07:44,160 --> 00:07:46,580
+to one لأ ليست متوفرة one to one لكن on to اه on
+
+93
+00:07:46,580 --> 00:07:52,640
+to كل ال code main ظاهر في ال relation فهذي on to
+
+94
+00:07:52,640 --> 00:07:57,440
+مافيش مشكلة تمام التانية
+
+95
+00:07:59,330 --> 00:08:01,990
+هى اولا one to one لأ مش one to one فهى فى عندي
+
+96
+00:08:01,990 --> 00:08:05,470
+عنصرين او pre image اللى هم نفس ال image pre image
+
+97
+00:08:05,470 --> 00:08:08,310
+اللى هم نفس ال image فهى مش one to one طيب on to
+
+98
+00:08:08,310 --> 00:08:12,550
+ليست on to فى عنصر برضه هنا موجود فى ال code
+
+99
+00:08:12,550 --> 00:08:15,510
+domain بس مش موجود فى ال range مش موجود فى ال
+
+100
+00:08:15,510 --> 00:08:21,970
+range فهد لا هيك ولا هيك حتى الآن التالتة حقيقة
+
+101
+00:08:21,970 --> 00:08:26,490
+الاتنين هى one to one و في نفس الوجهة on to لإن كل
+
+102
+00:08:26,490 --> 00:08:32,350
+ال code domain مغطى فى ال rangeتمام هذه one to one
+
+103
+00:08:32,350 --> 00:08:35,330
+وليست on two أكيد واضح تماما لأن لسه في under
+
+104
+00:08:35,330 --> 00:08:38,950
+constant هنا موجود ك first element هو موجود في ال
+
+105
+00:08:38,950 --> 00:08:44,890
+code main وغير موجود في main في ال range طيب كمان
+
+106
+00:08:44,890 --> 00:08:48,450
+function تانية أو تالتة هيك سارت اللي هي ال
+
+107
+00:08:48,450 --> 00:08:53,050
+bijection ال bijection بكل بساطة هي كل function
+
+108
+00:08:53,050 --> 00:08:56,550
+بقدر أقول عنها one to one و on two في نفس الوقت
+
+109
+00:08:59,580 --> 00:09:02,380
+بمعنى ممكن نسميها one-to-one correspondence
+
+110
+00:09:02,380 --> 00:09:06,580
+correspondence هي correlation one-to-one في
+
+111
+00:09:06,580 --> 00:09:12,540
+الاتجاهين هي معناها عشان هي اسمها bijection فنائي
+
+112
+00:09:12,540 --> 00:09:17,460
+فإذا من ال domain لل co-domain هي one-to-one ومن
+
+113
+00:09:17,460 --> 00:09:19,720
+ال domain لل co-domain هي برضه one او من ال co
+
+114
+00:09:19,720 --> 00:09:22,600
+-domain لل domain برضه one-to-one فنسميها
+
+115
+00:09:22,600 --> 00:09:28,340
+bijection او reversible او invertible فإذا قابلة
+
+116
+00:09:28,340 --> 00:09:32,530
+للعكسقابلة للعكس مده ان هي في الاتجاهين ممكن تكون
+
+117
+00:09:32,530 --> 00:09:36,090
+function في الاتجاهين ممكن تكون function فهي قابلة
+
+118
+00:09:36,090 --> 00:09:41,450
+للعكس بمعنى هنا لما بنتكلم قلنا عن هذه قولنا ان هي
+
+119
+00:09:41,450 --> 00:09:50,150
+في الآخر one to one هذه لو عكسناها أكيد هتبطل هي
+
+120
+00:09:50,150 --> 00:09:55,490
+هتبطل function هي في هنا هتبطل function صح لاحظ
+
+121
+00:09:55,490 --> 00:10:00,320
+لأن answer له two outputs تصير لو بدنا نعكسهاعلى
+
+122
+00:10:00,320 --> 00:10:04,240
+ال function فبتصبح اكيد هي one to one ماشي لكن مش
+
+123
+00:10:04,240 --> 00:10:07,940
+one to one correspondence بمعنى bijection اللي هي
+
+124
+00:10:07,940 --> 00:10:13,760
+ممكن تكون بالعكس على النقيد من ال y لل x فعشان هيك
+
+125
+00:10:13,760 --> 00:10:18,480
+نقدرش نسميها reversible قابلة للعكس انه اجيب
+
+126
+00:10:18,480 --> 00:10:22,400
+المعكوز تبعها invertable معناته بقدر اجيب المعكوز
+
+127
+00:10:22,400 --> 00:10:25,520
+تبعها لأ هذه مش invertable لأنه أصلا تصبح ليست
+
+128
+00:10:25,520 --> 00:10:29,160
+function أصلا زي ال x تربية
+
+129
+00:10:31,640 --> 00:10:36,400
+لأ ال X تربية انت بتقدر تعكسها ال X تربية انا
+
+130
+00:10:36,400 --> 00:10:39,420
+بتقدرش تعكسها لإنه بتجيبش بتجيبش ال inverse بتقدرش
+
+131
+00:10:39,420 --> 00:10:42,380
+تجيبلها inverse لإنه بيصير عندك نفس ال output نفس
+
+132
+00:10:42,380 --> 00:10:45,620
+ال input فيه إلو two outputs اللي هم بين واحد
+
+133
+00:10:45,620 --> 00:10:47,840
+positive واحد negative واحد positive واحد negative
+
+134
+00:10:47,840 --> 00:10:51,300
+صارت جاي زي مكان الجذر والجذر بيصير إلو two
+
+135
+00:10:51,300 --> 00:10:55,560
+outputs تمام طيب ال bijection هذه مدام أنا بقول هي
+
+136
+00:10:55,560 --> 00:10:59,790
+one to one و هي one to في نفس الوقتبقدر اقول اعرفك
+
+137
+00:10:59,790 --> 00:11:03,710
+التالي ال bijection هي F from set A to set B
+
+138
+00:11:03,710 --> 00:11:09,690
+معناته يوجد لها inverse of Fمعناته يوجد إليها
+
+139
+00:11:09,690 --> 00:11:13,950
+inverse إذا قدرت أقول إن ال F فعلا هي bijection لأ
+
+140
+00:11:13,950 --> 00:11:16,370
+أنا بفهم على طول إن هي one to one و هي one to يعني
+
+141
+00:11:16,370 --> 00:11:21,330
+ببساطة جدا بقدر أوجد لها ال inverse أو يوجد إليها
+
+142
+00:11:21,330 --> 00:11:24,170
+inverse و ال inverse هذا هيكون F to the power
+
+143
+00:11:24,170 --> 00:11:27,790
+minus one اللي هو ال inverse of F هيكون من مين؟ من
+
+144
+00:11:27,790 --> 00:11:34,130
+P من ال code main ل ال domain أصبحتمن ال B ل ال A
+
+145
+00:11:34,130 --> 00:11:38,070
+و في الحالة هذه أكيد هيكون لكل function unique
+
+146
+00:11:38,070 --> 00:11:43,170
+inverse function صحيح؟ أكيد ليش؟ لأنه إذا ضربناها
+
+147
+00:11:43,170 --> 00:11:46,450
+في ال inverse تبعها المفروض أنه يعطيني ال identity
+
+148
+00:11:46,450 --> 00:11:50,890
+بالظبط الواحد ال identity ف ال identity function
+
+149
+00:11:50,890 --> 00:11:59,830
+هي فعليا حاصر الشي هذهcomposition مش حاصل ضرب حاصل
+
+150
+00:11:59,830 --> 00:12:05,030
+compose ال inverse بال function تبعتها فاخدوا بالك
+
+151
+00:12:05,030 --> 00:12:09,090
+و انا ما ضربتها مش ضرب هدول مش ضرب هي حاصل ال
+
+152
+00:12:09,090 --> 00:12:12,430
+identity function هي حاصل ال composition لل
+
+153
+00:12:12,430 --> 00:12:15,110
+function مع ال inverse تبعها عشان يعطيني ال
+
+154
+00:12:15,110 --> 00:12:19,650
+identity function عشان يعطي identity function طيب
+
+155
+00:12:19,650 --> 00:12:21,690
+ال identity function من ال functions اللي مشهورة
+
+156
+00:12:21,690 --> 00:12:26,430
+جدا و معروفة جدا و كتير بتستخدمفي شغلنا و لعندي
+
+157
+00:12:26,430 --> 00:12:29,830
+استخدمناها كذا مرة فعليا فعليا احنا استخدمناها كذا
+
+158
+00:12:29,830 --> 00:12:33,310
+مرة لما بقول identity function هي من ال domain
+
+159
+00:12:33,310 --> 00:12:37,550
+لنفسه ليش من ال domain لنفسه لإن هي فعليا زيته و
+
+160
+00:12:37,550 --> 00:12:43,750
+يقولنا F from A to B ثم جولنا ال F minus one from
+
+161
+00:12:43,750 --> 00:12:49,390
+B to A فلما أعمل composition للاتنين مع بعضهم F
+
+162
+00:12:49,390 --> 00:12:56,820
+العكس طبعا لما بقولcompose if هد هيساوي ال
+
+163
+00:12:56,820 --> 00:13:01,420
+identity معناته هيكون عبارة عن function identity
+
+164
+00:13:01,420 --> 00:13:07,540
+اللي هي الحص الاتنين من a برجع تاني ل aنرجع تاني
+
+165
+00:13:07,540 --> 00:13:13,940
+لنفس A هي هي تمام من A ل B ثم من B ل A فرجعنا من A
+
+166
+00:13:13,940 --> 00:13:21,500
+ل A تمام فنكتبها بهذا الشكل ال identity function
+
+167
+00:13:21,500 --> 00:13:25,760
+from domain A to codomain A و ال domain و ال
+
+168
+00:13:25,760 --> 00:13:30,980
+codomain نفس الشي نفس الشي نكتبها إما I A فمعناه
+
+169
+00:13:30,980 --> 00:13:33,900
+ذلك أنا بتكلم عن identity function في ال domain A
+
+170
+00:13:33,900 --> 00:13:38,720
+أو الواحدأو واحد لل domain A على اعتبار ان الواحد
+
+171
+00:13:38,720 --> 00:13:44,240
+هو ال identity element فممكن تكتبه identity
+
+172
+00:13:44,240 --> 00:13:47,020
+function كاملة او identity element فالنهاية هي
+
+173
+00:13:47,020 --> 00:13:51,820
+unique function بحيث انه لكل عناصرها لكل عناصر ال
+
+174
+00:13:51,820 --> 00:13:58,080
+domain فيها ال I of A تساوي Aالـ I of A تساوي A
+
+175
+00:13:58,080 --> 00:14:03,240
+بمعنى ما غيرتش على حالة ال element ال element بدخل
+
+176
+00:14:03,240 --> 00:14:07,560
+لل function بطلع زي ما هو طبعا بعض ال identity
+
+177
+00:14:07,560 --> 00:14:11,500
+functions المشهورة جدا و اللي كلكم بتعرفوها زي في
+
+178
+00:14:11,500 --> 00:14:16,620
+ال plusing ال zeroplacing zero أي حاجة أعملها plus
+
+179
+00:14:16,620 --> 00:14:23,780
+مع zero هتظل زي ما هي أو doting with one اضرب أي
+
+180
+00:14:23,780 --> 00:14:26,420
+حاجة في الواحد هتظل زي ما هي فإذا الواحد هنا
+
+181
+00:14:26,420 --> 00:14:31,460
+identity مأثرش هيه مأثرش عليها identity دخله
+
+182
+00:14:31,460 --> 00:14:35,680
+العنصر بطلع زي نفس العنصر هو هو في ال ending مع ال
+
+183
+00:14:35,680 --> 00:14:39,160
+true ending true إذا false هتظل false إذا true
+
+184
+00:14:39,160 --> 00:14:44,700
+هتظل true أو الoring مع ال falseالأورينج مع الفالس
+
+185
+00:14:44,700 --> 00:14:47,940
+نفس الأشياء، إيش هتعطي الأور مع الفالس، هترجع ..
+
+186
+00:14:47,940 --> 00:14:51,220
+هتطلع نفس ال function في ال union أو في ال union
+
+187
+00:14:51,220 --> 00:14:56,660
+.. في ال union with فاى، لما بتعمل union مع فاى،
+
+188
+00:14:56,660 --> 00:15:00,520
+بغض النظر إيش هي ال .. ال set اللي بتعملها ال
+
+189
+00:15:00,520 --> 00:15:03,840
+union مع الفاى، هتضل نفس ال union، هي .. هي نفس ال
+
+190
+00:15:03,840 --> 00:15:08,680
+set أو ال intersectionwith you ال universe of
+
+191
+00:15:08,680 --> 00:15:13,760
+discourse برضه هيبقى نفس ال 6 هي فكل هدولة أنواع
+
+192
+00:15:14,660 --> 00:15:19,220
+identity functions ال zero identity element ال
+
+193
+00:15:19,220 --> 00:15:22,580
+واحد identity element لعملية تانية ال true
+
+194
+00:15:22,580 --> 00:15:26,680
+identity element برضه ال F identity الفي identity
+
+195
+00:15:26,680 --> 00:15:29,920
+و ال universe of discourse identity بس كل واحد ل
+
+196
+00:15:29,920 --> 00:15:34,060
+function خاصة فيه لكل ل function خاصة فيه هلاحظ ان
+
+197
+00:15:34,060 --> 00:15:38,360
+ال identity function بالضرورة مدامهى identity
+
+198
+00:15:38,360 --> 00:15:43,960
+بتضرورة هتكون one to one وunto بتضرورة هتكون one
+
+199
+00:15:43,960 --> 00:15:47,940
+to one وunto ليش لأنه لازم تكون bijection بيجيكشن
+
+200
+00:15:47,940 --> 00:15:51,820
+بحيث انه يكون لها ال inverse تبعها ونقدر نجيب ال
+
+201
+00:15:51,820 --> 00:15:56,380
+inverse او هى نفسها اصلا هتصبح حاصل function مع ال
+
+202
+00:15:56,380 --> 00:15:59,340
+inverse او بالظبط مش حاصل حاصل ضربى حاصل
+
+203
+00:15:59,340 --> 00:16:05,380
+composition حاصل composition okay طبعابالـ graph
+
+204
+00:16:05,380 --> 00:16:09,580
+بالـ wind diagram هتلاحظوا انه داخل ال domain من
+
+205
+00:16:09,580 --> 00:16:12,240
+العنصر لنفسه من العنصر لنفسه من العنصر لنفسه هي
+
+206
+00:16:12,240 --> 00:16:16,420
+identity function هنا انت بتتكلم عن ايش identity
+
+207
+00:16:16,420 --> 00:16:21,160
+function مابتغيرش في العناصر طيب بالنسبة للبروتو
+
+208
+00:16:21,160 --> 00:16:27,960
+اللي بتعرفه زي x و y x بتساوي y كيف ترسمها خط بميل
+
+209
+00:16:27,960 --> 00:16:33,880
+45 و خلاص positive 45 فإذا اي عنصر x هيظهر مقابله
+
+210
+00:16:33,880 --> 00:16:39,960
+بالظبطexactly نفس القيمة ل y نفس القيمة ل y فممكن
+
+211
+00:16:39,960 --> 00:16:43,160
+تنثيلها بهذا الشكل او تنثيلها بالشكل ال by parted
+
+212
+00:16:43,160 --> 00:16:45,740
+بس هنا طبعا مش by parted لأنه ماعندكاش two parts
+
+213
+00:16:45,740 --> 00:16:50,660
+هي one part فمن العنصر لمين لنفسه من العنصر لنفسه
+
+214
+00:16:50,660 --> 00:16:54,580
+عملية ال graph ل ال functions ال graph ل ال
+
+215
+00:16:54,580 --> 00:16:57,680
+functions كلكم عارفينها لكن فلسفة ببساطة جدا لان
+
+216
+00:16:57,680 --> 00:17:03,900
+انا بشتغل على أزواج مرتبة كل عنصر في ال domainكـ
+
+217
+00:17:03,900 --> 00:17:08,360
+pre image مع ال image تبعته زوج مرتب كل pre image
+
+218
+00:17:08,360 --> 00:17:13,680
+مع ال image هدولة لحالهم زوج مرتب كنقطة على ال
+
+219
+00:17:13,680 --> 00:17:22,820
+plane لما بدنا نرسم ال plot بشكل كامل ففعليا نقدر
+
+220
+00:17:22,820 --> 00:17:27,180
+نمثل ال function اللي هي from a to b ك set of
+
+221
+00:17:27,180 --> 00:17:33,410
+ordered pairsأزواج مرتبة، ست أو مجموعة من الأزواج
+
+222
+00:17:33,410 --> 00:17:36,990
+المرتبة، المجموعة هذه هنفتحها الأقواص، هي الأقواص
+
+223
+00:17:36,990 --> 00:17:42,790
+بحيث انه هي مجموعة من أزواج مرتبة، طب كل زوج لحاله
+
+224
+00:17:42,790 --> 00:17:47,160
+عبارة عن A و ال functional value بتاعة ال Aبشرط ان
+
+225
+00:17:47,160 --> 00:17:52,680
+ال a تنتمي لل domain بس فكل عنصر ينتمي لل domain
+
+226
+00:17:52,680 --> 00:17:56,140
+بدك تشوف جداش ال functional value تبعته هو ال
+
+227
+00:17:56,140 --> 00:18:00,260
+functional value نقطة مع بعض بحيث انك ترسمها x مع
+
+228
+00:18:00,260 --> 00:18:06,540
+y و بترسمها على ال plane تبعتك فبتلاحظ ان لكلعناصر
+
+229
+00:18:06,540 --> 00:18:12,240
+a يوجد فقط one pair او زوج مرتب واحد اللي هو a مع
+
+230
+00:18:12,240 --> 00:18:16,800
+ال functional value طبعا مستحيل يطلعله اكتر من
+
+231
+00:18:16,800 --> 00:18:22,400
+functional value صحيح فإذا لكل قيمة a مش هتلاقي f
+
+232
+00:18:22,400 --> 00:18:29,340
+of a مختلفتين فانت واحدة فقط فمعنى ذلك ان حتى
+
+233
+00:18:29,340 --> 00:18:34,240
+الزوج المرتب هو واحد فقط فقط لمن لل a ففي الحالة
+
+234
+00:18:34,240 --> 00:18:38,430
+هذه بنقدرنرسمها بالنسبة للأرقام عادة تمثل أزواج
+
+235
+00:18:38,430 --> 00:18:42,110
+مرتبة x و y زمان انتوا عارفين أخدتوها زمان بنكتبها
+
+236
+00:18:42,110 --> 00:18:46,870
+عبارة عن مجموعة points فهذه تمثل point واحدة فكل
+
+237
+00:18:46,870 --> 00:18:51,210
+ما عددنا قيم x واللي هي ال elements بتاعت ال
+
+238
+00:18:51,210 --> 00:18:55,110
+domain بصير عندي مجموعة أكبر من ال points جديش أنت
+
+239
+00:18:55,110 --> 00:18:58,990
+بتفترض قيم ل x جديش أنت بتطلع نقاط إضافية جديش أنت
+
+240
+00:18:58,990 --> 00:19:02,150
+بتحطهم كل النقاط هذه مع بعض ال points هذه مع بعض
+
+241
+00:19:02,150 --> 00:19:06,650
+as a setElement of set و بتحطهم بتوقحهم على ال
+
+242
+00:19:06,650 --> 00:19:11,170
+plane تبعك عشان ترسم curve ما بين نقاطهم فبتظهر
+
+243
+00:19:11,170 --> 00:19:15,610
+معاك كنقاط على ال plane او على المستوى على الصبورة
+
+244
+00:19:15,610 --> 00:19:19,850
+بحيث انها تبين ال function كمرسومة ك curve مرسوم و
+
+245
+00:19:19,850 --> 00:19:24,370
+هو في النهاية عبارة عن set of points و عبارة عن
+
+246
+00:19:24,370 --> 00:19:29,190
+مجموعة نقاط set of pointsتمام دي بحيث ان دايما
+
+247
+00:19:29,190 --> 00:19:37,590
+يكون في y لكل لكل x في دايما y لكل x طيب واحدة او
+
+248
+00:19:37,590 --> 00:19:41,110
+خلينا نقول قبل من ال functions two functions من ال
+
+249
+00:19:41,110 --> 00:19:44,090
+functions المهمة جدا و الجوهرية جدا و اللي هنتكلم
+
+250
+00:19:44,090 --> 00:19:46,350
+عنها بشكل سريع طبعا اكيد ال functions لو بدنا
+
+251
+00:19:46,350 --> 00:19:49,110
+نتكلم عن ال functions مش هنخلص هذه لحالها مصاقب
+
+252
+00:19:49,110 --> 00:19:53,150
+تصير لكن احنا هنتكلم عن twofunctions بسميهم قبل of
+
+253
+00:19:53,150 --> 00:19:57,770
+K functions .. functions أساسية التانتين هدول هم
+
+254
+00:19:57,770 --> 00:20:01,510
+ال floor و ال ceiling floor و ceiling اللي هو
+
+255
+00:20:01,510 --> 00:20:06,030
+بتقرب للأقل و للأعلى بس يعني كل اللي بدك تعمله ال
+
+256
+00:20:06,030 --> 00:20:10,150
+input تبعك هو عبارة عن real number و ال output
+
+257
+00:20:10,150 --> 00:20:15,690
+integerمش هيك انتجر بتقربه لأقرب عدد صحيح ففي ال
+
+258
+00:20:15,690 --> 00:20:19,210
+discrete طبيعي frequently بنستخدم هدول النوعين
+
+259
+00:20:19,210 --> 00:20:23,410
+بشكل كتير مستمر منهم أولهم ال floor ال floor
+
+260
+00:20:23,410 --> 00:20:28,510
+ببساطة جدا بنعمله floor و لاحظوا الشرطات اللي تحت
+
+261
+00:20:28,510 --> 00:20:31,970
+معناه ذلك ان ال x بيتقربها للأرض تبعها لأرضها
+
+262
+00:20:31,970 --> 00:20:36,190
+floor للأرض للأرضية هذه عبارة عن إيش هي the
+
+263
+00:20:36,190 --> 00:20:44,080
+largest هي أكبر انتجرأقل من X فبتقريبهاش لأي
+
+264
+00:20:44,080 --> 00:20:48,620
+integer أقل منها و خلاص لأكبر integer أقل منها ف
+
+265
+00:20:48,620 --> 00:20:52,740
+greatest integer function بيسموها greatest integer
+
+266
+00:20:52,740 --> 00:20:57,180
+function فهذه أكبر قيمة أقل من ال X في المقابل ال
+
+267
+00:20:57,180 --> 00:21:00,920
+ceiling أو السقف ceiling أو السقف هتلاقي انه
+
+268
+00:21:00,920 --> 00:21:05,640
+الشرطات هتكون لفوق بمعنى ان ال X بتقريبها لفوق هذه
+
+269
+00:21:05,640 --> 00:21:16,320
+the smallest integer أكبر أو يساوي Xفهد أقل قيمة
+
+270
+00:21:16,320 --> 00:21:23,280
+صحيحة أكبر من Xمش والله يالا أي أكبر و فوق و خلاص
+
+271
+00:21:23,280 --> 00:21:29,700
+لأ أقل قيمة أكبر من X ففي الحالة هذه بتكون انتجار
+
+272
+00:21:29,700 --> 00:21:32,840
+بس طبعا لازم يكون انتجار في الآخر أو يساوي لأنه
+
+273
+00:21:32,840 --> 00:21:36,080
+ممكن أصلا نفسها ال X تكون هي نفسها انتجار ممكن هي
+
+274
+00:21:36,080 --> 00:21:38,740
+نفسها تكون انتجار فبتسيبها زي ما هي في الحالة هذه
+
+275
+00:21:38,740 --> 00:21:45,950
+طيب بعض الخصائص المهمة ل ال floor و ال ceilingهي
+
+276
+00:21:45,950 --> 00:21:50,730
+توضيح لهم أول حالة من الحلات اللي بنتكلم عنها إذا
+
+277
+00:21:50,730 --> 00:21:55,950
+كانت x لا تنتمي لل integers بمعنى إن هي fraction
+
+278
+00:21:55,950 --> 00:22:00,690
+هي فيها كسر فيها كسور ففي الحالة هذه in general أو
+
+279
+00:22:00,690 --> 00:22:07,950
+حقيقة مدام هي ليست integer فبالضرورة floor minus x
+
+280
+00:22:07,950 --> 00:22:14,660
+لا تساوي minus floor xهيهم هى عندك الحالات اللى
+
+281
+00:22:14,660 --> 00:22:18,380
+عندك خلينا ناخد مثلا for example floor بنتكلم هى
+
+282
+00:22:18,380 --> 00:22:22,200
+واحدة هى floor وين السلب تبعها و هى السلب تبعها
+
+283
+00:22:25,610 --> 00:22:29,750
+هذا السالب تبقى حقه هاي سالب ها لاحظ فهتلاقي انه
+
+284
+00:22:29,750 --> 00:22:33,690
+هنا هاي سالب جوا سالب واحد فاصلة ستة ال floor
+
+285
+00:22:33,690 --> 00:22:38,990
+بتصير سالب اتنين طيب اما سالب ال floor واحد فاصلة
+
+286
+00:22:38,990 --> 00:22:42,270
+ستة بتصير سالب واحد اكيد لا تساوي بعض و نفس الكلام
+
+287
+00:22:42,270 --> 00:22:46,550
+لمين لأ ال ceiling لو بدنا ناخد هاي ceiling و هاي
+
+288
+00:22:46,550 --> 00:22:55,040
+ceiling نفس الفكرة ceilingنيجاتيف X هي ceiling
+
+289
+00:22:55,040 --> 00:22:59,920
+نيجاتيف X هيساوي سالب واحد بالنسبة للمثال طبعا
+
+290
+00:22:59,920 --> 00:23:06,460
+فاصلة one point six طيب بينما سالب ceiling X هي
+
+291
+00:23:06,460 --> 00:23:10,800
+ceiling X واحد فاصلة ستة بتلع اتنين سالب اتنين
+
+292
+00:23:10,800 --> 00:23:14,480
+بتلع سالب اتنين طب هنا سالب واحد فإذا لا تسويها
+
+293
+00:23:14,480 --> 00:23:21,290
+بشكل بشكل مطلق طيببينما إذا كانت X هي belong to
+
+294
+00:23:21,290 --> 00:23:24,850
+integer يعني هي أصلا integer فهي نفس ال ceiling
+
+295
+00:23:24,850 --> 00:23:28,330
+وهي نفس ال floor هي نفس ال element منطق جدا لما
+
+296
+00:23:28,330 --> 00:23:31,150
+تقولي والله يجربلي الخمسة لأقرأ بعضة صحيح طب ما هي
+
+297
+00:23:31,150 --> 00:23:35,310
+خمسة مش هتفرج ساعتها بدك تعمل floor ولا ceiling
+
+298
+00:23:35,310 --> 00:23:39,610
+يعني ماعنى تيجي تسألني تقولي دكتور floor ولا
+
+299
+00:23:39,610 --> 00:23:43,290
+ceiling أنا بقولك خمسة يعني مش هتفرج floor ceiling
+
+300
+00:23:43,290 --> 00:23:52,000
+هي هي حضر تمام ك plot ترسمبالشكل اللي احنا هنشوفه
+
+301
+00:23:52,000 --> 00:23:55,360
+لان لإن في مفهومين اكيد مرعت عليكوا بس مش غلط نرجع
+
+302
+00:23:55,360 --> 00:24:01,460
+اننا نكررهم من خلال المثال f of x تساوي floor x
+
+303
+00:24:01,460 --> 00:24:06,440
+over 3 floor x over 3 هتيجي تقول بكل بساطة تعوض
+
+304
+00:24:06,440 --> 00:24:11,040
+قيم في ال domain تبعك في ال x domain عشان تشوف ال
+
+305
+00:24:11,040 --> 00:24:15,200
+code domain اللي هو ال f of x بعد ما تطبق هذه ال
+
+306
+00:24:15,200 --> 00:24:19,480
+function اللي هي floor او ceiling نفس الاشيمع
+
+307
+00:24:19,480 --> 00:24:23,880
+اختلاف بس الواقعين كيف حتصير طيب عند الصفر صفر
+
+308
+00:24:23,880 --> 00:24:27,980
+فالصفر مشمول يعني عند الصفر الناتج صفر عشان هيك
+
+309
+00:24:27,980 --> 00:24:33,740
+بنجيب نكتبها solid مسكرة بالظبط مسكرة معناته ان
+
+310
+00:24:33,740 --> 00:24:39,260
+العنصر صفر هو مشمول معهم بحيث ان الناتج تبعه بطلع
+
+311
+00:24:39,260 --> 00:24:48,600
+صفر طيب عند الواحد برضه صفر طيب عند الاتنين صفرعند
+
+312
+00:24:48,600 --> 00:24:54,580
+التلاتة واحد عند التلاتة واحد طيب لكن عند الاتنين
+
+313
+00:24:54,580 --> 00:24:56,920
+فاصلة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+314
+00:24:56,920 --> 00:24:58,620
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+315
+00:24:58,620 --> 00:24:58,820
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+316
+00:24:58,820 --> 00:24:58,880
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+317
+00:24:58,880 --> 00:24:59,240
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+318
+00:24:59,240 --> 00:25:03,460
+تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة تسعة
+
+319
+00:25:03,460 --> 00:25:09,790
+تسعة تسعة تسعة تسعة تسعة تسعة تسو هنا open cycle
+
+320
+00:25:09,790 --> 00:25:14,090
+بعرف منها أن هي مستمرة للتلاتة لكن التلاتة فقط غير
+
+321
+00:25:14,090 --> 00:25:19,450
+مشمولة لأن التلاتة موجودة مع الواحد طبعا المفاهيم
+
+322
+00:25:19,450 --> 00:25:23,050
+أكيد مرت عليكم سابقا و عارفين هذا الكلامتمام
+
+323
+00:25:23,050 --> 00:25:25,870
+فتاخدوا بالكوا في الرسومات اللي زي هذه في الواجبات
+
+324
+00:25:25,870 --> 00:25:29,190
+ممكن تكون موجودة معاكم بالمناسبة نزلنا أول واجب
+
+325
+00:25:29,190 --> 00:25:32,990
+لسه اليوم هيبدأ استحقاقه فتقدروا تبدأوا تشتغلوا
+
+326
+00:25:32,990 --> 00:25:35,730
+عليه اليوم للأسبوع القادم ان شاء الله تعالى على ال
+
+327
+00:25:35,730 --> 00:25:40,930
+mood اللي بت بتحلوه بتنزلوه تمام فممكن تيجي أسئلة
+
+328
+00:25:40,930 --> 00:25:43,810
+بهذا الشكل بدك تكون ماخد بالك مين ال open cycle
+
+329
+00:25:43,810 --> 00:25:51,060
+ومين ال solid او الclosed cycle تمام في الحالة هذه
+
+330
+00:25:51,060 --> 00:25:55,460
+احنا خلصنا الجزئية اللى كانت متبقية عندنا في ال
+
+331
+00:25:55,460 --> 00:26:00,200
+functions عشان نبدأ برضه نكمل بنفس مواضيعنا فعليا
+
+332
+00:26:01,390 --> 00:26:04,550
+كنا بنتكلم عن ال set و من ال set إجت ال functions
+
+333
+00:26:04,550 --> 00:26:08,810
+نوع مهم من أنواع ال sets هي ال sequence أو ال
+
+334
+00:26:08,810 --> 00:26:12,410
+strings ثم لاحقا المرة القادمة ناخد ال summation
+
+335
+00:26:12,410 --> 00:26:18,030
+لمجموعة ال sequence هذه فنبدأ في جزئية ال sequence
+
+336
+00:26:20,680 --> 00:26:24,740
+لما بتكلم عن ال sequence أو ال strings وفيه فرق
+
+337
+00:26:24,740 --> 00:26:28,220
+خفيف كتير بينهم وقد يختلفوا فيه أحيانا، بعض الكتب
+
+338
+00:26:28,220 --> 00:26:30,940
+هتلاقيهم يختلفوا فيه، لكن خلينا ناخدها شوية شوية،
+
+339
+00:26:30,940 --> 00:26:33,420
+لما بتكلم عن sequence هي عبارة عن discrete
+
+340
+00:26:33,420 --> 00:26:39,500
+structure، هو مجموعة عناصر متتالية ورا بعض، مدام
+
+341
+00:26:39,500 --> 00:26:42,140
+مجموعة عناصر فهي منفصلة، هي مش continuous، عشان
+
+342
+00:26:42,140 --> 00:26:45,000
+تكون فعلا discrete و تكون sequence، هذه لحاله، هذه
+
+343
+00:26:45,000 --> 00:26:49,030
+لحاله، هذه لحاله، هذه لحالهdiscrete منفصلين عن بعض
+
+344
+00:26:49,030 --> 00:26:54,350
+فيمثلوا بشكل ordered list ordered list فهي أول
+
+345
+00:26:54,350 --> 00:26:58,450
+اختلاف بينها وبين ال set check ال set كانت ايه
+
+346
+00:26:58,450 --> 00:27:03,010
+عشان ordered ماكنتش مرتبة هنا لأ بتكلم عن ordered
+
+347
+00:27:03,010 --> 00:27:07,570
+set فإذا القائمة أو ال list اللي موجودة عندنا
+
+348
+00:27:07,570 --> 00:27:10,790
+القائمة اللي موجودة عندنا هي لازم تكون مرتبة طيب
+
+349
+00:27:10,790 --> 00:27:18,220
+مرتبة ايش اللي بفرج بينها وبين ال setال location
+
+350
+00:27:18,220 --> 00:27:24,160
+ال location العنصر هو اللي هيفرج مدام ordered فإذا
+
+351
+00:27:24,160 --> 00:27:28,720
+كل عنصر إله location إله المكان داخل ال set اللي
+
+352
+00:27:28,720 --> 00:27:32,600
+ماينفعش يتغير ماينفعش يتغير و إلا بتصير unordered
+
+353
+00:27:32,600 --> 00:27:36,860
+تصبح غير مرتبة زيها زي ال set طيب ال set ماكنتش
+
+354
+00:27:36,860 --> 00:27:42,870
+هيفرج ماكنتش بتفرجفي حال من الحلول واحد حط العنصر
+
+355
+00:27:42,870 --> 00:27:46,330
+الأول ثم التاني واحد هو بحل حط التاني قبل الأول
+
+356
+00:27:46,330 --> 00:27:50,230
+هقوله صح مش هتفرج معانا لكن لما بتكلم عن sequence
+
+357
+00:27:50,230 --> 00:27:54,530
+لأ الأول بيجي قبل التاني حتما بيجي قبل التاني فإذا
+
+358
+00:27:54,530 --> 00:27:59,510
+مين اللي بيحددنا هذا الكلام أنه هي معتمدة على ال
+
+359
+00:27:59,510 --> 00:28:04,510
+location أو ال position داخل ال what ال set
+
+360
+00:28:04,510 --> 00:28:08,110
+location داخل ال set مهم جدا هنا فبصير اسمها مش
+
+361
+00:28:08,110 --> 00:28:13,310
+set sequenceفي الحالة هذه لازم يكون العمصر
+
+362
+00:28:13,310 --> 00:28:17,950
+function في ال location عشان نضمن فعلا ان ال
+
+363
+00:28:17,950 --> 00:28:20,790
+location مهم فبتصبح function في main في ال
+
+364
+00:28:20,790 --> 00:28:22,890
+location و احنا لسه يدوبن و ماخدين ال function
+
+365
+00:28:22,890 --> 00:28:29,410
+فإذا كأن ال domain تبعناهي أرقام ال locations أو
+
+366
+00:28:29,410 --> 00:28:33,390
+ال positions داخل ال set إذا ال set تبعتنا فيها
+
+367
+00:28:33,390 --> 00:28:37,710
+end position فإذا من واحد أو من صفر زي ال array
+
+368
+00:28:37,710 --> 00:28:40,330
+لما كنتوا بتشتغلوا على ال array في البرمجة كنتوا
+
+369
+00:28:40,330 --> 00:28:43,850
+بتبدو أحيانا من صفر مش هيك فإذا من صفر إذا كان
+
+370
+00:28:43,850 --> 00:28:46,570
+بتكلم عن natural number أو من الواحد في بعضهم
+
+371
+00:28:46,570 --> 00:28:50,810
+بيبدو واحد مش مشكلة فكأنها ال natural number minus
+
+372
+00:28:50,810 --> 00:28:56,320
+zero minus zero بيمشي الحلفي الحالة هذه 2n فهيكون
+
+373
+00:28:56,320 --> 00:29:00,620
+عندك عدد العناصر in elements او in positions داخل
+
+374
+00:29:00,620 --> 00:29:04,320
+ال set طيب مثال على ذلك لما تقول واحد اتنين تلاتة
+
+375
+00:29:04,320 --> 00:29:09,000
+خمسة تمانية هي sequence with five elements طبعا
+
+376
+00:29:09,000 --> 00:29:11,680
+ممكن تزود او ممكن تزود واحدة من ال sequences
+
+377
+00:29:11,680 --> 00:29:15,220
+المهمة جدا او ال strings المهمة جدا هذه اللي
+
+378
+00:29:15,220 --> 00:29:19,830
+هناخدها لاحقا اتوقع مرت عليكم يمكنهذا ال sequence
+
+379
+00:29:19,830 --> 00:29:23,250
+هذا بتقدروا الآن يعني زي ما بيقولوا تتوقعوا
+
+380
+00:29:23,250 --> 00:29:26,630
+العناصر اللي وراه فيكفي ان احنا نكتب مجموعة اول
+
+381
+00:29:26,630 --> 00:29:31,610
+مجموعة عناصر بحيث انه عرفنا نسبيا او جزئيا ال
+
+382
+00:29:31,610 --> 00:29:35,850
+sequence فال sequence احد طرق تعريفه انه نعرفه ب
+
+383
+00:29:35,850 --> 00:29:40,840
+few first elements او last elements حتىحتى في ال
+
+384
+00:29:40,840 --> 00:29:44,440
+last elements تبعته تلاتة اربعة elements خلاص انت
+
+385
+00:29:44,440 --> 00:29:47,480
+حاول تطلع زي ما بيقوله لما في المدارس كنا بيقول
+
+386
+00:29:47,480 --> 00:29:54,420
+النمط شك اكتب النمط و اعمل creation او generation
+
+387
+00:29:54,420 --> 00:29:58,400
+لكمان two elements مثلا او one element بعدهم okay
+
+388
+00:29:58,400 --> 00:30:03,660
+نفس الكلام فبدك اهم شغل تعرف النمطللـ sequence
+
+389
+00:30:03,660 --> 00:30:07,380
+another example ممكن نكتب برضه واحد تلاتة تسعة
+
+390
+00:30:07,380 --> 00:30:11,320
+سبعة عشرين اذا انت عرفت النمط بتريح راسك و بتكتب
+
+391
+00:30:11,320 --> 00:30:16,840
+صيغة النمط ال formula و خلاص هنا مش عارفين و خلاص
+
+392
+00:30:16,840 --> 00:30:20,860
+بنسيبها هيك sequence اه sequence بمش الحال تعريف ل
+
+393
+00:30:20,860 --> 00:30:25,200
+sequence اه كويس طيب ممكن انت تيجي تتطلع بكل بساطة
+
+394
+00:30:25,200 --> 00:30:31,890
+و تقول طب ما هدا تكيد طب لأ هاهاليبسيز و تلاتة to
+
+395
+00:30:31,890 --> 00:30:37,890
+the power n three to the power n وخلاص واجف هذه
+
+396
+00:30:37,890 --> 00:30:43,590
+عرفتنا الآن حسب ال location عرفتك ال element حسب
+
+397
+00:30:43,590 --> 00:30:47,970
+ال location بس انت لاحظ ان النمط لازم تشمل فيه انت
+
+398
+00:30:47,970 --> 00:30:50,910
+بتتكلم عن location ببدأ من الصفر ولا ببدأ من
+
+399
+00:30:50,910 --> 00:30:58,110
+الواحد فانت هنا بدأ .. هنا انت بدئي كيف؟ بدئي صفر
+
+400
+00:30:58,950 --> 00:31:02,030
+متبادى هنا صفر ف natural number متبادى بال natural
+
+401
+00:31:02,030 --> 00:31:07,450
+number العادية فإذا تقدر تقول هنا n belong to
+
+402
+00:31:07,450 --> 00:31:14,030
+capital N to natural number اه ليفش فيها مجال
+
+403
+00:31:14,030 --> 00:31:17,730
+تكرار أبدا لأ هنا بالعكس بتقبل تكرار الست بتقبلش
+
+404
+00:31:17,730 --> 00:31:25,490
+هنا بتقبل تكرار هنا لأنه كل عنصر function بال
+
+405
+00:31:25,490 --> 00:31:30,380
+locationبال position لاحظ هنا ال element هذا هو
+
+406
+00:31:30,380 --> 00:31:34,320
+مربوط بال position لكن قد تصدف أنه ال form اللي
+
+407
+00:31:34,320 --> 00:31:39,460
+تبعتك فيها تكرار بس ال answer الأول غير الأخر ليش؟
+
+408
+00:31:39,460 --> 00:31:41,720
+لأنه هدف ال position كذا وهو هدف ال position آخر
+
+409
+00:31:41,720 --> 00:31:48,140
+تماما، هنشوف بالظبط ف ال index مختلف تماما زي
+
+410
+00:31:48,140 --> 00:31:51,900
+الأمثلة اللي هناخدها لقدام فهي فعليا احنا سببنا و
+
+411
+00:31:51,900 --> 00:31:55,770
+عرفنا أنه فعليا هي functionعرفنا في النهاية أن هي
+
+412
+00:31:55,770 --> 00:32:00,730
+function ل subset of integersمش هيك ال integers
+
+413
+00:32:00,730 --> 00:32:03,870
+هذه اما تبدأ من zero فبسميها natural number او
+
+414
+00:32:03,870 --> 00:32:07,110
+تبدأ من الواحد برضه مقبولة مش اي مشكلة نبدأ من
+
+415
+00:32:07,110 --> 00:32:11,370
+الواحد فغالبا هيها بهذا الشكل natural number ببدأ
+
+416
+00:32:11,370 --> 00:32:15,390
+من zero او ببدأ من الواحد كلا هما صح و بمشي الحال
+
+417
+00:32:15,390 --> 00:32:19,370
+مين اللي بحكمك انك تعمل ال formula صح لل elements
+
+418
+00:32:19,370 --> 00:32:23,270
+انا ممكن اعطيك مجموعة elements وماتلاقيش اي معادلة
+
+419
+00:32:23,270 --> 00:32:26,750
+تبدأها من الصفر فتنجبر تبدأ من الواحد okay مقبولة
+
+420
+00:32:26,750 --> 00:32:28,150
+مش مشكلة ابدأ من الواحد
+
+421
+00:32:31,470 --> 00:32:36,310
+الان الانصر نفسه او ال element نفسه يشارله ب A N
+
+422
+00:32:36,310 --> 00:32:40,470
+فال N هى ال location او ال position او ال position
+
+423
+00:32:40,470 --> 00:32:44,950
+تبعنا بحيث ان هى عبارة عن integers فاصبحت بقدر
+
+424
+00:32:44,950 --> 00:32:49,350
+اقول عنها domain و codomain وفيه function الان ال
+
+425
+00:32:49,350 --> 00:32:52,860
+function هى ال form اللى بتكتبهاو اللي أحيانا بدك
+
+426
+00:32:52,860 --> 00:32:56,720
+تطلعها و اللي ممكن جدا ماتلاقيهاش فخلاص تسيبهم
+
+427
+00:32:56,720 --> 00:33:01,620
+مجموعة elements و مجموعة ellipses نقاط يعني ان هي
+
+428
+00:33:01,620 --> 00:33:06,420
+مستمرة كويس اما الطبيعي هي انك انت بدك تجيب ال F
+
+429
+00:33:06,420 --> 00:33:09,160
+of X هذه اللي هي ال formula نفسها ال formula نفسها
+
+430
+00:33:09,160 --> 00:33:12,780
+هتكون function في مين؟ في ال location فكأنه ال
+
+431
+00:33:12,780 --> 00:33:17,800
+domain تبعك هو ال N ال location تبعك M يبدأ من صفر
+
+432
+00:33:17,800 --> 00:33:23,760
+او يبدأ من واحدفال location هو ال domain بحيث انه
+
+433
+00:33:23,760 --> 00:33:28,100
+تطبق عليه ال formula و ال formula دي هتكون هي ال
+
+434
+00:33:28,100 --> 00:33:31,420
+sequence formula فانت عارفت معناته ايش معادلة ال
+
+435
+00:33:31,420 --> 00:33:36,280
+sequence بناء عليه تطلع العناصر كل واحد في ال
+
+436
+00:33:36,280 --> 00:33:38,760
+location تبعه بالظبط كل واحد في ال location تبعه
+
+437
+00:33:38,760 --> 00:33:42,940
+ماتقلفش فيها مشكلة فهنا ال location بنحط لكل عنصر
+
+438
+00:33:42,940 --> 00:33:50,350
+ك index as an index فال index an هذا هيكونالاندكس
+
+439
+00:33:50,350 --> 00:33:53,270
+تبعت الأنصر هذا هو ال N نفسها و اللي بتكون
+
+440
+00:33:53,270 --> 00:33:56,930
+مشارقلها هنا في الكتب الكتيرة هتلاقوها I في الكتب
+
+441
+00:33:56,930 --> 00:33:58,910
+الكتيرة و كنتوا لما اتكلمتوا في البرمجة في ال
+
+442
+00:33:58,910 --> 00:34:03,790
+array كنتوا بتكتبوها يمكن I I فمش غريبة جدا كوه
+
+443
+00:34:03,790 --> 00:34:08,410
+اتلاقوها مكتوبة I بدل N كلا هما جائز كلا هما جائز
+
+444
+00:34:08,410 --> 00:34:13,250
+مجرد رموز بدل بعضها طيب عادة ال sequence او ال
+
+445
+00:34:13,250 --> 00:34:16,870
+series هذه السلسلة هذه من العناصر زي ما قلنا
+
+446
+00:34:16,870 --> 00:34:23,350
+يشارقلها بال firstElements first elements او last
+
+447
+00:34:23,350 --> 00:34:27,810
+elements مش بالضروري اول تلت اربع عناصر يمكن اخر
+
+448
+00:34:27,810 --> 00:34:32,670
+تلت اربع عناصر او اكمل عنصر في النص المهم انك انت
+
+449
+00:34:32,670 --> 00:34:35,690
+تحول من مجموعة العناصر تجيب النمط زي ما كنا بناخد
+
+450
+00:34:35,690 --> 00:34:39,090
+في المدرسة زمان اللي هو ال formula بدك تجيب ال
+
+451
+00:34:39,090 --> 00:34:45,090
+formula نفسها و مجموعة ellipses بفهم منها انه ال
+
+452
+00:34:45,090 --> 00:34:48,860
+sequence مستمرةمجموعة ellipses اللي هي مجموعة تلتة
+
+453
+00:34:48,860 --> 00:34:53,740
+نقاط على الأقل بتفهم منها انه ال series أو ال
+
+454
+00:34:53,740 --> 00:35:02,680
+sequence مستمر هاي مثال set of a n تمام n في index
+
+455
+00:35:02,680 --> 00:35:07,360
+هنا رغم ان هي set فبفهم انه هذه sequence ال
+
+456
+00:35:07,360 --> 00:35:11,420
+sequence هذه قاللي صفر واحد اربع تسعة ستاشر خمسة و
+
+457
+00:35:11,420 --> 00:35:16,090
+عشرين ellipses يعني مستمرةيعني مستمرة بتاعي كتير
+
+458
+00:35:16,090 --> 00:35:19,730
+واضحة هي دي كإني بقوله أنا بتكلم عن natural number
+
+459
+00:35:19,730 --> 00:35:24,850
+و n تربيع ال formula in تربيع ف natural number
+
+460
+00:35:24,850 --> 00:35:29,090
+ببدأ من الصفر okay صفر تربيع واحد تربيع اتنين
+
+461
+00:35:29,090 --> 00:35:31,730
+تربيع تلاتة تربيع اربعة تربيع خمسة تربيع and so on
+
+462
+00:35:31,730 --> 00:35:35,590
+لو قلتلك هتلعنصر رقم مية مش هتبقى ماشي فيها لما
+
+463
+00:35:35,590 --> 00:35:39,050
+تصل المية على طول بتعود بال formula مباشرة بتعود
+
+464
+00:35:39,050 --> 00:35:39,990
+بال formula و تجيبها
+
+465
+00:35:43,190 --> 00:35:48,350
+كمان sequences ممكن نتكلم عن ال sequence نستعيد
+
+466
+00:35:48,350 --> 00:35:52,970
+عنه بدل ما احطه داخل ال set اقول خلاص هي a12
+
+467
+00:35:52,970 --> 00:35:57,390
+مجموعة ellipses بعرف ان هي مستمرة و خلاص بدل ما
+
+468
+00:35:57,390 --> 00:36:01,950
+اضطر احطها داخل set فهذه مقبولة برضه مافيش اي
+
+469
+00:36:01,950 --> 00:36:05,870
+مشكلة في sequence بهذا الشكلبحيث انها تكون موجودة
+
+470
+00:36:05,870 --> 00:36:10,590
+لكن المهم التأكيد حتى لو حطيتها داخل ال curly
+
+471
+00:36:10,590 --> 00:36:14,970
+braces اتأكد على ال index لان هو هذا المؤشر الوحيد
+
+472
+00:36:14,970 --> 00:36:18,430
+اللي بفهم منه انت بتتكلم عن set ولا بتتكلم عن
+
+473
+00:36:18,430 --> 00:36:23,610
+sequence فال index او ال indices لازم تكون واضحة
+
+474
+00:36:23,610 --> 00:36:29,070
+لازم تكون واضحة اللي هي مجموعة ال index اللي
+
+475
+00:36:29,070 --> 00:36:33,280
+موجودة عندك لازم تكون واضحة مثالممكن تكتبها بهذا
+
+476
+00:36:33,280 --> 00:36:39,260
+الشكل set a n مافيه index هي واضحة معناه ذلك ان
+
+477
+00:36:39,260 --> 00:36:44,060
+هذه عبارة عن a1 a2 ellipses مستمرة و اقولك مثلا
+
+478
+00:36:44,060 --> 00:36:49,400
+اعرفها بهذا الشكل for all n اكبر من او يسوى واحد a
+
+479
+00:36:49,400 --> 00:36:54,700
+n تسوى f of n واحد على n طيب هذه مدام قال لي for
+
+480
+00:36:54,700 --> 00:37:02,120
+all اكبر من واحد طب لأ امتى؟فإذا infinite sequence
+
+481
+00:37:02,120 --> 00:37:07,520
+هنا بنتكلم عن infinite sequence لنهائي هذه series
+
+482
+00:37:07,520 --> 00:37:11,720
+أو سلسلة لنهائية من مجموعة main العناصر مستمرة طول
+
+483
+00:37:11,720 --> 00:37:17,820
+ما هتكبر في N هتعطيك قيمة هتعطيك locations لأن N
+
+484
+00:37:17,820 --> 00:37:21,120
+هنا أصبحت تعبر عن location جد ما تكبر في قيمة N
+
+485
+00:37:21,120 --> 00:37:25,780
+هتعطيك locations إضافيةطبعا خصوصا عندما اتكلم عن
+
+486
+00:37:25,780 --> 00:37:27,800
+ال natural number فال natural number to infinity
+
+487
+00:37:27,800 --> 00:37:34,680
+فحضرته infinity اذا هذه كأنها تمثل واحد على واحد1
+
+488
+00:37:34,680 --> 00:37:38,920
+على 2 1 على 3 1 على 4 1 على 5 1 على 6 وضلك ماشي
+
+489
+00:37:38,920 --> 00:37:42,300
+فيها .. ضلك ماشي فيها هنا احنا عبارنا عن مجموعة
+
+490
+00:37:42,300 --> 00:37:47,580
+sequence او مجموعة elements تمثل sequence طيب هذه
+
+491
+00:37:47,580 --> 00:37:50,680
+في ايش بتفيدنا لان عارف انه لعندي الآن السؤال
+
+492
+00:37:50,680 --> 00:37:53,720
+الأهم احنا ليش بناخد هذا الكلام انت بتاخده لأنه
+
+493
+00:37:53,720 --> 00:37:57,000
+هنضطر لجدامنا نعمله summation فبدنا نكون عارفين
+
+494
+00:37:57,000 --> 00:38:00,080
+على الأقل عناصر ايش هم العناصر هتقولي ليش بدي ال
+
+495
+00:38:00,080 --> 00:38:04,690
+summationسؤال منطقي جدا، أنا وجفت والمفروض أنه
+
+496
+00:38:04,690 --> 00:38:07,790
+مابش من درسنا، بس شايفكوا شوية مستغربين إحنا إيش
+
+497
+00:38:07,790 --> 00:38:10,690
+دخلنا في هذا الموضوع، لأ الموضوع هذا كتير مهم،
+
+498
+00:38:10,690 --> 00:38:16,310
+ليش؟ تبديل و توفيق؟ يعني بس مالوش علاقة ب sequence
+
+499
+00:38:16,310 --> 00:38:19,090
+تبديل و توفيق، تبديل و توفيق أنت بتتكلم عن group،
+
+500
+00:38:19,090 --> 00:38:23,590
+عن set، set واضحة، أنا بروحش ل sequence، هي set زي
+
+501
+00:38:23,590 --> 00:38:26,110
+ال set اللي إحنا موجودين الآن فيها، اللي هي مجموعة
+
+502
+00:38:26,960 --> 00:38:30,180
+طلبة فيه discrete دج علينا لجنة ثقافية أو لجنة
+
+503
+00:38:30,180 --> 00:38:33,800
+علمية و جالنا والله يبدوا من عندك تلاتة فأكم
+
+504
+00:38:33,800 --> 00:38:37,580
+possibility ان اختار التلاتة هدى تبديل و توافق
+
+505
+00:38:37,580 --> 00:38:40,640
+اللى بتتكلم فيها مافيش مشكلة لكن انا بتتكلم عن ال
+
+506
+00:38:40,640 --> 00:38:44,400
+sequence ال sequence هنا عشان نحدد العنصر ..
+
+507
+00:38:44,400 --> 00:38:46,680
+العناصر بتاعتنا ال formula أول شغلة هدى هى ال
+
+508
+00:38:46,680 --> 00:38:49,980
+function فلما انت تقول ليه بكل بساطة اعمللي
+
+509
+00:38:49,980 --> 00:38:54,260
+integrationإيش يعني integration؟ area under the
+
+510
+00:38:54,260 --> 00:38:57,280
+curve صح؟ يعني لازم أكون عارف ال curve اللي هي ال
+
+511
+00:38:57,280 --> 00:39:01,640
+function طيب و لازم أكون عارف عناصر ال curve حسب
+
+512
+00:39:01,640 --> 00:39:04,780
+ال limits بتاعة ال integration والله بده ينقيا أن
+
+513
+00:39:04,780 --> 00:39:08,580
+أعمل integration من واحد لمية طيب معناته بده أعرف
+
+514
+00:39:08,580 --> 00:39:12,720
+العناصر من واحد لمية و أعملهم accumulation صح؟
+
+515
+00:39:12,720 --> 00:39:19,060
+تمام فإذا هذه عبارة عن sequence of elements صح؟ هي
+
+516
+00:39:19,060 --> 00:39:25,570
+sequence of elements عناصر عاديةهي curve و قلت لك
+
+517
+00:39:25,570 --> 00:39:30,570
+من واحد ل .. خلّيني أقول لعشرة ال area under the
+
+518
+00:39:30,570 --> 00:39:32,850
+curve و أنا بشتغل discrete .. discrete يعني معنا
+
+519
+00:39:32,850 --> 00:39:35,870
+ذلك بدي أخد samples عند الواحد و عند الاتنين و عند
+
+520
+00:39:35,870 --> 00:39:38,790
+التلاتة و عند الأربع خمسة ستة سبعة و هكذا okay بس
+
+521
+00:39:38,790 --> 00:39:44,750
+بدي عناصرهم جدش قيمهمهي discrete طب كويس بدنا نعمل
+
+522
+00:39:44,750 --> 00:39:48,010
+summation, summation لإيش؟ ل sequence of elements
+
+523
+00:39:48,010 --> 00:39:50,870
+كل ما في الموضوع أني هحددلك بدايته و نهايته و مش
+
+524
+00:39:50,870 --> 00:39:53,530
+أكتر من هي عشان هيك لازم تكون من الأساس عارفين إيش
+
+525
+00:39:53,530 --> 00:39:58,250
+يعني sequence of elements واضحة تلان عشان مابديش
+
+526
+00:39:58,250 --> 00:40:01,870
+أشوف نظرة الحيرة أن احنا ليش اللي ودانا هنا انا
+
+527
+00:40:01,870 --> 00:40:04,030
+هيك شوفت هيك في عيننا كم من واحد احنا إيش اللي
+
+528
+00:40:04,030 --> 00:40:10,870
+جابنا هنا فواضحة تلان ليش احنا هنا تمام okay with
+
+529
+00:40:10,870 --> 00:40:14,750
+repetationsrepetation بسيطة جدا هاي repetition
+
+530
+00:40:14,750 --> 00:40:23,110
+بلاش ال .. ال .. ال .. بهذا الشكل قولنالك بهذا
+
+531
+00:40:23,110 --> 00:40:27,630
+الشكل و نفس الجثة بدنا نجيب ال free transform مثلا
+
+532
+00:40:27,630 --> 00:40:30,550
+ال free transform انت بتعمل integration لمين؟ لل
+
+533
+00:40:30,550 --> 00:40:33,930
+signs الصوايدر مش هيك بتعمله؟ okay نفس الفكرة هاي
+
+534
+00:40:33,930 --> 00:40:37,450
+هتجد انه بعد فترة هترجع تتكرر
+
+535
+00:40:39,880 --> 00:40:44,480
+هترجح تتكرر فإذا هل اتكرر اجمع ولا ماجمعوش طب ما
+
+536
+00:40:44,480 --> 00:40:48,020
+هي فعلا area زيادة صارت عندك sequence ال location
+
+537
+00:40:48,020 --> 00:40:50,700
+بتاع القيمة هذا القيمة اللي هنا غير ال location
+
+538
+00:40:50,700 --> 00:40:54,020
+بتاع القيمة اللي هنا ليش تقولي بديش اجمعهم او بدي
+
+539
+00:40:54,020 --> 00:40:57,360
+لأ لو مانوش علاقة ده sequence انا راشد طول على set
+
+540
+00:40:57,360 --> 00:41:01,540
+لأ ده مش set هذا sequence و sequence معناته بيقبل
+
+541
+00:41:01,540 --> 00:41:06,910
+repetition بيقبل ال repetition فهنا unlike setsهنا
+
+542
+00:41:06,910 --> 00:41:12,070
+ال sequence ممكن ياخد repeated elements عناصر
+
+543
+00:41:12,070 --> 00:41:19,970
+مكررة اه مافيش اي مشكلة لما اقول set of b of n ب
+
+544
+00:41:19,970 --> 00:41:24,710
+node بواحد ellipses يعني مستمرة خلاص طيب و بعدين
+
+545
+00:41:24,710 --> 00:41:31,190
+عرفنا ال bn على اساس ان هي minus one all to the
+
+546
+00:41:31,190 --> 00:41:38,010
+powerهذه على طول بفهم منها ان هي set او sequence ل
+
+547
+00:41:38,010 --> 00:41:43,370
+واحد minus واحد واحد minus واحد واحد minus واحد
+
+548
+00:41:43,370 --> 00:41:47,970
+الapses و بتسيبها هيك ماتقوليش لان بتتعامل معاها
+
+549
+00:41:47,970 --> 00:41:52,430
+set فتروح تمالها بهذا الشكل واحد سلب واحد وخلاص لأ
+
+550
+00:41:52,430 --> 00:41:55,510
+واضح ان هذه مختلفة تماما عن ذلك وعشان هيك يا دور
+
+551
+00:41:55,510 --> 00:42:01,240
+احنا هنخلص موضوع ال set عفواالـ sequence والـ
+
+552
+00:42:01,240 --> 00:42:05,260
+string على طول هندخل في مين؟ في ال summation لأنه
+
+553
+00:42:05,260 --> 00:42:08,560
+هدف التمهيد أن أنا بدي أكمل لل summation الهدف
+
+554
+00:42:08,560 --> 00:42:11,980
+الأساسي أن انا أروح ل summation تمام؟ فلأ مدام ال
+
+555
+00:42:11,980 --> 00:42:16,340
+summation لازم العناصر كلها تكون موجودة ال set شئ
+
+556
+00:42:16,340 --> 00:42:18,900
+و ال sequence شئ تاني
+
+557
+00:42:22,270 --> 00:42:27,050
+Type recognizing sequences كتير مهم ان احنا نميز
+
+558
+00:42:27,050 --> 00:42:30,170
+ال sequence بشكل كتير كويس احنا اتفقنا و قولنا ان
+
+559
+00:42:30,170 --> 00:42:35,150
+انا بعرف اول مجموعة عناصر او اخر مجموعة عناصر
+
+560
+00:42:35,150 --> 00:42:40,610
+بيفرجش يعني مين هنا او هنا بحيث انه لو انطلب مني
+
+561
+00:42:40,610 --> 00:42:45,350
+اعمل prediction او تنبؤ توقع لاقيش العنصر اللي ورا
+
+562
+00:42:45,350 --> 00:42:50,130
+نكون قادرين نتوقعنكون قادرين نتوقع و هذا للأمانة
+
+563
+00:42:50,130 --> 00:42:53,910
+واحد من العلوم اللي كتير تستخدم ان لو عندك signal
+
+564
+00:42:53,910 --> 00:42:57,150
+وجفة تنجطعت .. جطعت الكهربا .. جطعت ال .. كيف ممكن
+
+565
+00:42:57,150 --> 00:43:01,690
+تفكر تعمل generation ل باقي ال signal؟ واحدة من
+
+566
+00:43:01,690 --> 00:43:06,410
+الفروع اللي ممكن تتعامل معها ضمن فرق ال AI مثلابدك
+
+567
+00:43:06,410 --> 00:43:12,350
+تعمل توقع للقادم expectation لتعمل expectation ايش
+
+568
+00:43:12,350 --> 00:43:16,730
+النقطة اللى جاية ده نفس الفكرة انت عندك sequence و
+
+569
+00:43:16,730 --> 00:43:21,610
+من ال sequence ده بدك تحاول تجيب النمطصحيح؟ عشان
+
+570
+00:43:21,610 --> 00:43:27,350
+تتوقع ايش القيمة القادمة تتوقع القيمة القادمة فهي
+
+571
+00:43:27,350 --> 00:43:31,190
+لكل بساطة فكرة ال recognizing ال sequence ان انت
+
+572
+00:43:31,190 --> 00:43:35,210
+تكون عارفة حددت ال sequence تبعك هو ايش بالظبط
+
+573
+00:43:35,210 --> 00:43:39,550
+حددت ال formula تبعته وبناء عليه تقدر تعمل
+
+574
+00:43:39,550 --> 00:43:44,270
+expectation او توقع له الرقم القادم لما نقول مثلا
+
+575
+00:43:44,270 --> 00:43:49,540
+for example واحد اتنين تلاتةأربعة أنا بتكلم واضح
+
+576
+00:43:49,540 --> 00:43:55,200
+أنه f of n بتساوي n زائد واحد بس فإذا the next
+
+577
+00:43:55,200 --> 00:44:00,980
+element خمس the next element خمس طيب واحد تلاتة
+
+578
+00:44:00,980 --> 00:44:07,660
+خمسة سبعة تسعة اللي هي اتنين n زائد واحد مش هيك ال
+
+579
+00:44:07,660 --> 00:44:14,560
+odd ال odd numbers ال odd numbers طيب ليش تلات عشر
+
+580
+00:44:15,790 --> 00:44:19,810
+primes لأننا بنتكلم عن الprimes نتكلم عن ايه
+
+581
+00:44:19,810 --> 00:44:24,030
+الprimes تمام فإذا مجرد أن انت مجموعة ال elements
+
+582
+00:44:24,030 --> 00:44:26,990
+اللي موجودة ال few elements اللي موجودة قدامك
+
+583
+00:44:26,990 --> 00:44:32,330
+اعتطك النمط خلصت يعني انتهت المشكلة عملت
+
+584
+00:44:32,330 --> 00:44:37,450
+recognizing صحأو recognition صح تمييز صح لل
+
+585
+00:44:37,450 --> 00:44:41,390
+sequence انت عملتيك تمييز صحيح لل sequence لكن
+
+586
+00:44:41,390 --> 00:44:46,230
+الحقيقة مش دايما الكلام هذا بيكون متوفر معانا
+
+587
+00:44:46,230 --> 00:44:49,390
+بيكون متحقق معانا ممكن كتير تكون في عندك مجموعة
+
+588
+00:44:49,390 --> 00:44:54,410
+sequences لكن مش معرفة بشكل جيد مجموعة ال elements
+
+589
+00:44:54,410 --> 00:44:58,630
+اللي في الأول not well defined وهذه تعملك مشكلة ان
+
+590
+00:44:58,630 --> 00:45:03,550
+انت هتجد انه ممكن يكون اكتر من sequence لهاممكن
+
+591
+00:45:03,550 --> 00:45:16,830
+تعرف بأكتر من طريقة بأكتر من طريقة لو أخدنا
+
+592
+00:45:16,830 --> 00:45:27,490
+مثلا واحد قالك تلاتة خمسة و سكت و كملها سبعة و
+
+593
+00:45:27,490 --> 00:45:30,830
+قالك the next element
+
+594
+00:45:33,800 --> 00:45:37,860
+ممكن تسعة و ممكن احداشر صحيح؟ واحد هيفهمها لأ هذه
+
+595
+00:45:37,860 --> 00:45:42,620
+مجموعة العناصر بتاعة ال .. ال odd numbers اه
+
+596
+00:45:42,620 --> 00:45:45,980
+معناته تسعة واحد تقوله لأ لأ لأ لأ انت مش اللي
+
+597
+00:45:45,980 --> 00:45:49,640
+عرفك، لأ لأ لأ هدوله الدكتور جزده ال إبراهيم، انت
+
+598
+00:45:49,640 --> 00:45:54,650
+.. حياتك غلط، هذه ه، احداشرواحد تالت يجيله طريقة
+
+599
+00:45:54,650 --> 00:46:00,590
+تانية يتوقع اشي مختلف حسب المعادل او ال formula او
+
+600
+00:46:00,590 --> 00:46:05,410
+النمط يطلعله النمط formula معينة فعلا عند الواحد
+
+601
+00:46:05,410 --> 00:46:08,150
+او الصفر والواحد والاتنين بيطلعوا نفس الارقام
+
+602
+00:46:08,150 --> 00:46:12,310
+هدولة بس بيطلع رقم مختلف تماما في sequences هيك اه
+
+603
+00:46:12,310 --> 00:46:15,530
+في sequences هيك طيب و ايه مشكلتها هذه؟ مشكلتها
+
+604
+00:46:15,530 --> 00:46:20,180
+انه ماتعرفتش مشكلة صحيح من البدايةالعناصر اللي تم
+
+605
+00:46:20,180 --> 00:46:24,540
+تعريفهم هم مشتركين لمجموعة sequences كتير مشتركين
+
+606
+00:46:24,540 --> 00:46:30,920
+في مجموعة sequences كتير زي واحد اتنين تلاتة في
+
+607
+00:46:30,920 --> 00:46:37,860
+أسهل من هيك the next element المنطقي يقول طب انا
+
+608
+00:46:37,860 --> 00:46:43,980
+ممكن اقولك خمسة انا هقولك خمسة من وين جبنا الخمسة
+
+609
+00:46:48,810 --> 00:46:52,070
+ما هي كان في sequence فعلا هات مش هي ال sequence
+
+610
+00:46:52,070 --> 00:46:54,290
+هات و قلتلكوا هناخد ال sequence هات و هتطلع
+
+611
+00:46:54,290 --> 00:46:58,250
+sequence مشهورة جدا و معروفة جدا هي واحد اتنين
+
+612
+00:46:58,250 --> 00:47:04,290
+تلاتة لأ مش اربعة خمسة لاحظت كده هذه ال sequence
+
+613
+00:47:04,290 --> 00:47:06,870
+كل element هو مجموع ال two elements اللي جابله
+
+614
+00:47:06,870 --> 00:47:10,850
+عشان تكون واضحة عندكم مابديش اخليكم ضامن محترين
+
+615
+00:47:10,850 --> 00:47:18,270
+كتير هي خمسة لأنه بعد التمانية ال next one
+
+616
+00:47:22,960 --> 00:47:26,040
+هناخدها ما بقولكوا هناخدها هذه اسمها في Bonacci في
+
+617
+00:47:26,040 --> 00:47:29,080
+Bonacci series هناخدها لقدام و هتزهجوا منها كمان
+
+618
+00:47:29,080 --> 00:47:35,200
+تجلجوش بس انا بده اوضحلك فكرة ان لأ مجموعة ال
+
+619
+00:47:35,200 --> 00:47:38,740
+elements اللي في البداية او في النهاية ممكن يكونوا
+
+620
+00:47:38,740 --> 00:47:46,250
+جدا مش معرفين بشكل جيد فيعملك مشكلة في التعريفwith
+
+621
+00:47:46,250 --> 00:47:52,170
+recognition بمعنى مشكلة او لغط في التعريف طيب
+
+622
+00:47:52,170 --> 00:47:56,130
+بالعادة ايش بيسووا؟ بالعادة بيروحوا بيعملوا the
+
+623
+00:47:56,130 --> 00:47:59,350
+simplest style او the simplest formula بياخدوها
+
+624
+00:47:59,350 --> 00:48:05,150
+ايش الأبسط؟ بس وجعتنا في مشكلة تانية انت بتفهم
+
+625
+00:48:05,150 --> 00:48:10,030
+الأبسط غير ما انا بفهم الأبسط صح؟ المشكلة قائمة
+
+626
+00:48:10,030 --> 00:48:15,140
+فالمشكلة قائمة و ال question ما زال حتى الآنno
+
+627
+00:48:15,140 --> 00:48:19,840
+objective right answer okay انت قلتيله انه والله
+
+628
+00:48:19,840 --> 00:48:23,100
+بكل بساطة the simplest one او the simplest
+
+629
+00:48:23,100 --> 00:48:26,760
+function بس مين قال ان ال simplest function هنا ان
+
+630
+00:48:26,760 --> 00:48:30,520
+اروح احط اربعة انا هقولك لا انا انا عارف بناتش هو
+
+631
+00:48:30,520 --> 00:48:33,780
+شايفها بسيطة او سهلة ايه مافيش حساب من انه كل عنصر
+
+632
+00:48:33,780 --> 00:48:37,360
+مجموعة الاتنين اللي جابله انت تقولي لأ الابسط اني
+
+633
+00:48:37,360 --> 00:48:42,380
+اجمع واحد وخلاصفبرضه المشكلة ما زالت قائمة في هذا
+
+634
+00:48:42,380 --> 00:48:45,300
+النوع من أنواع المشاكل لأنه أصلا من الأساس لم تعرف
+
+635
+00:48:45,300 --> 00:48:50,200
+صح مافيش إلى حل كل واحد هيفهمها زي ما بده لأن
+
+636
+00:48:50,200 --> 00:48:55,580
+مفهومنا ل ال simplest برضه مختلف من واحد للتاني
+
+637
+00:48:55,580 --> 00:48:59,860
+انت بتفهم البسيط غير ان انا بفهم البسيط وعشانك طرق
+
+638
+00:48:59,860 --> 00:49:04,860
+تفكيرنا مختلفة كويسالـ string الان ايش الفرق بين
+
+639
+00:49:04,860 --> 00:49:08,680
+ال sequence و ال string؟ ال string برضه اختلفوا
+
+640
+00:49:08,680 --> 00:49:11,920
+فيها بالمناسبة اختلفوا فيها خليني احنا نتكلم حسب
+
+641
+00:49:11,920 --> 00:49:17,360
+الكتاب اللي احنا بنشتغل عليه عشان نحاول نفهم منه
+
+642
+00:49:17,360 --> 00:49:20,000
+ال string حسب الكتاب بيقول انه هي ال finite
+
+643
+00:49:20,000 --> 00:49:26,470
+sequencefinite sequence و بعدين جالك بنقولها من a1
+
+644
+00:49:26,470 --> 00:49:30,390
+a2 to an خلاص انا عارف ان في لها نهاية في لها
+
+645
+00:49:30,390 --> 00:49:36,310
+نهاية فبسموها string كتب تانية بتقولك لأ ممكن يكون
+
+646
+00:49:36,310 --> 00:49:40,630
+في عندك finite string او ممكن نتعامل معاها as a
+
+647
+00:49:40,630 --> 00:49:45,730
+finite string ال string الأشهر هي ال DNA string ال
+
+648
+00:49:45,730 --> 00:49:49,370
+DNA string هو okay معروف انه limited بس limited
+
+649
+00:49:49,370 --> 00:49:53,550
+كتير كبيرفيمكن التعامل معاه على اساس انه finite ..
+
+650
+00:49:53,550 --> 00:49:56,950
+infinite على اساس انه infinite لأن انت في النهاية
+
+651
+00:49:56,950 --> 00:50:02,430
+حتى لما بدهم يحاولوا يحللوه بيحللهوش كله بيتحللش
+
+652
+00:50:02,430 --> 00:50:08,370
+كله فبياخدوا منه أجزاء من ال DNA عشان هيك يعمل
+
+653
+00:50:08,370 --> 00:50:13,810
+معاملة ال infinite sequence فهو finite .. بطل
+
+654
+00:50:13,810 --> 00:50:18,300
+finite stringزي ما قلنا infinite strings اه موجودة
+
+655
+00:50:18,300 --> 00:50:22,920
+ومزالت تستخدم في كتير من الأحوال بهذا الشكل طيب
+
+656
+00:50:22,920 --> 00:50:26,700
+هقش كيف انحل الموضوع جالك لأ معناه تخلينا انعرف ال
+
+657
+00:50:26,700 --> 00:50:31,220
+string ل الحالات اللي بتكون ال elements نفسها مش
+
+658
+00:50:31,220 --> 00:50:34,760
+أعداد ال elements هي alphabet ال elements alphabet
+
+659
+00:50:34,760 --> 00:50:40,870
+زي ال DNAمش ال DNA AT CG هي الأربع رموز فقط اللي
+
+660
+00:50:40,870 --> 00:50:44,790
+بيستخدموها فقط ترتيبهم هو اللي بيختلف لما بدي
+
+661
+00:50:44,790 --> 00:50:51,470
+أتكلم عنها as a set هقول إن هي فقط AT CG وبس وسكر
+
+662
+00:50:52,160 --> 00:50:55,220
+بينما هذا مش هيفيدني في إيش لما بدي أحلل شخصيت
+
+663
+00:50:55,220 --> 00:50:59,180
+شخصين مش share و أعرف إنهم علاقة ببعض و لا إنهم مش
+
+664
+00:50:59,180 --> 00:51:05,020
+علاقة ببعض فلأ لازم يكون واضح الترتيب ال T هذه غير
+
+665
+00:51:05,020 --> 00:51:08,730
+ال T هذه وال A هذه غير ال A هذهصحيح؟ فبصير اسمها
+
+666
+00:51:08,730 --> 00:51:15,250
+string ا ممكن تكون كبيرة مع بعض فبنعرفها في الحالة
+
+667
+00:51:15,250 --> 00:51:19,210
+اللي عندنا على أساس إن هي big sigma ال big sigma
+
+668
+00:51:19,210 --> 00:51:24,710
+هذه على طول هي finite set of symbols تعرف على أساس
+
+669
+00:51:24,710 --> 00:51:27,770
+إن هي finite set of symbols وتحديدًا alphabet
+
+670
+00:51:27,770 --> 00:51:35,190
+وممكن نقول إنه ال string s string s أي اسم a,b,c,s
+
+671
+00:51:35,190 --> 00:51:39,730
+هناالـ String على من خلال الـ over ال .. ال
+
+672
+00:51:39,730 --> 00:51:45,690
+alphabet بيج سيجما هو عبارة عن sequence إلها أقولك
+
+673
+00:51:45,690 --> 00:51:50,270
+ببساطة الكلام اللي إحنا بندحكيه مكون من إيش؟
+
+674
+00:51:50,270 --> 00:51:54,130
+مجموعة العناصر هي alphabet صح؟ حروف لكن الكلمة
+
+675
+00:51:54,130 --> 00:51:57,250
+ممكن يكون في حرف متكرر في نفس الكلمة خلّيني أنا
+
+676
+00:51:57,250 --> 00:52:02,090
+أفترض إن الكلمة هذه هي ال sequence S ال sequence S
+
+677
+00:52:02,090 --> 00:52:03,070
+مثلا computer
+
+678
+00:52:05,900 --> 00:52:14,070
+تور كويس هذي Sهذه واضحة ان ال location لكل
+
+679
+00:52:14,070 --> 00:52:18,410
+alphabet مهم جدا لان اذا غيرتهم هتصير كلمة تانية
+
+680
+00:52:18,410 --> 00:52:21,250
+هيصير string مختلف تماما مالوش علاقة باللي احنا
+
+681
+00:52:21,250 --> 00:52:26,670
+بنحكيه لكن في النهاية هو من ال big sigma فهو من ال
+
+682
+00:52:26,670 --> 00:52:29,670
+big sigma موجود هنا ال index ماعنديهاش ماعناش اي
+
+683
+00:52:29,670 --> 00:52:33,290
+مشكلة فيه natural number او natural minus one
+
+684
+00:52:33,290 --> 00:52:36,590
+minus zero اللي هو يعني يبدأ من صفر natural او من
+
+685
+00:52:36,590 --> 00:52:41,930
+واحد ناقص ال zeroممكن نكتبه ABC مباشرة بدون
+
+686
+00:52:41,930 --> 00:52:44,910
+الأقوات زي ما قلنا و ممكن نكتبها بهذا الشكل على
+
+687
+00:52:44,910 --> 00:52:48,690
+طول S هي عبارة عن ABC و ممكن تكتبها بدون الكوماز
+
+688
+00:52:48,690 --> 00:52:52,830
+كمان بدون الكوماز على طول بهذا الشكل without كومة
+
+689
+00:52:52,830 --> 00:52:58,490
+الان حاجة المهم إذا كان عندك S هي عبارة عن finite
+
+690
+00:52:58,490 --> 00:53:02,270
+string و T كمان finite string ممكن تعمل
+
+691
+00:53:02,270 --> 00:53:08,480
+concatenationتجميع concatenation S with T فبتنكتب
+
+692
+00:53:08,480 --> 00:53:14,740
+just S وT جانب بعض زي لما تقول مثلا ال string T هي
+
+693
+00:53:14,740 --> 00:53:20,740
+عبارة عن ing compute
+
+694
+00:53:20,740 --> 00:53:28,080
+بيحسب طيب بده احط ال S بتاعة compute مع ال T فتصبح
+
+695
+00:53:28,080 --> 00:53:32,540
+S وT computing concatenated
+
+696
+00:53:33,640 --> 00:53:37,260
+string أصبحت concatenating string اللي هي تحطهم
+
+697
+00:53:37,260 --> 00:53:40,000
+ورا بعض جملة واحدة أو كلمة واحدة فبيسموها
+
+698
+00:53:40,000 --> 00:53:42,880
+concatenation العملية هذه هذه العملية بيسموها
+
+699
+00:53:42,880 --> 00:53:48,660
+concatenation في الحالة لأن طبعا ال lengthهي ال
+
+700
+00:53:48,660 --> 00:53:52,100
+cardinality انت بتشوف قدش عدد ال elements عشان قول
+
+701
+00:53:52,100 --> 00:53:57,220
+عنهم هدول ال length تبعتك فهم العدد ال positions
+
+702
+00:53:57,220 --> 00:54:00,820
+اللي موجودين فعليا بس تاخد بالك من ال index عشان
+
+703
+00:54:00,820 --> 00:54:04,060
+إذا كان بدء من صفر بتاكي زيد واحد N زائد واحد
+
+704
+00:54:04,060 --> 00:54:07,780
+تاخدوا بالك منها طبعا إذا كانت S هي finite فمعنى
+
+705
+00:54:07,780 --> 00:54:10,980
+ذلك إن هي لازم تكون تمتم إلى ال natural number
+
+706
+00:54:10,980 --> 00:54:15,160
+أكيد إذا كان S to the power N فانا بعمل
+
+707
+00:54:15,160 --> 00:54:20,860
+concatenation N مرةلل S يعني بكررها N مرة لما يجيك
+
+708
+00:54:20,860 --> 00:54:24,140
+بهذا الشكل و انت عارف انه هادي string معناته انا
+
+709
+00:54:24,140 --> 00:54:29,240
+بعمل concatenation ب N مرة لل S يعني بكررها كذا N
+
+710
+00:54:29,240 --> 00:54:35,480
+مرة ابسلون صغيرة هناك كانت big sigma انا بتكلم عن
+
+711
+00:54:35,480 --> 00:54:39,340
+ال set لكل ال alphabet ال big sigma لما بكتب
+
+712
+00:54:39,340 --> 00:54:42,980
+ابسلون صغيرة هادي هادي تعبر بالنسبة لل string عن
+
+713
+00:54:43,620 --> 00:54:49,300
+الـ Empty Set معناته هدا بيصير Empty String String
+
+714
+00:54:49,300 --> 00:54:53,120
+فاضي او Sequence فاضي String فاضية هنا فبنكتبها
+
+715
+00:54:53,120 --> 00:54:56,140
+بهذا الشكل او Double Quotation فاضين Double
+
+716
+00:54:56,140 --> 00:54:59,180
+Quotation فاضين فهدا Empty String فال String هنا
+
+717
+00:54:59,180 --> 00:55:04,660
+ال link ثبعه Zero Zero تمام؟ هي خلصنا المقدمة
+
+718
+00:55:04,660 --> 00:55:07,020
+بتاعة هذا الموضوع عشان المرة القادمة نتكلم عن
+
+719
+00:55:07,020 --> 00:55:09,540
+summation ان شاء الله تعالى و نشوف كيف نستخدم هذا
+
+720
+00:55:09,540 --> 00:55:10,620
+الكلام يعطيكوا العفو يا شباب
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1yMI1kNL2Xs_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1yMI1kNL2Xs_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..2e91e27f83b0337a14140741093ee804d8a0cf36
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/1yMI1kNL2Xs_raw.json
@@ -0,0 +1 @@
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بمعنى ان كل بي موجودة في ال code main يمكن انتاجها من خلال تطبيق ال function على preimage corresponding لها أو خاصة فيها و اللي تنتمي لمين؟ لإيه؟ تنتمي لإيه؟ فهذه معناها for all بي لكل عناصر ال code main يوجد preimage", "tokens": [6027, 39184, 6001, 26624, 5296, 39184, 363, 4724, 2304, 3615, 1863, 7578, 16472, 28242, 4724, 1829, 3714, 29245, 23328, 3660, 8978, 2423, 3089, 2135, 7251, 43020, 16472, 2655, 26108, 11296, 9154, 16490, 1211, 6027, 6055, 9566, 21292, 4587, 2423, 2445, 15844, 659, 26624, 11760, 5296, 11296, 34051, 16490, 33546, 3660, 8978, 11296, 4032, 13672, 1829, 6055, 29399, 2304, 1829, 32767, 9957, 22807, 5296, 28814, 1829, 3224, 22807, 6055, 29399, 2304, 1829, 5296, 28814, 1829, 3224, 22807, 6156, 3224, 24192, 20449, 8315, 11296, 337, 439, 4724, 1829, 5296, 28820, 18871, 33546, 2288, 2423, 3089, 2135, 7251, 29245, 3215, 659, 26624], "avg_logprob": -0.23281249433755874, "compression_ratio": 1.6376146788990826, "no_speech_prob": 2.205371856689453e-06, "words": [{"start": 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to set B معناته يوجد لها inverse of F", "tokens": [3555, 28543, 2288, 1975, 39648, 1975, 3615, 28480, 4117, 16712, 6027, 1829, 2423, 3228, 1020, 313, 39896, 479, 490, 992, 316, 281, 992, 363, 20449, 8315, 47395, 7251, 29245, 3215, 5296, 11296, 17340, 295, 479], "avg_logprob": -0.2521701446837849, "compression_ratio": 1.1160714285714286, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 658.33, "end": 658.81, "word": "بقدر", "probability": 0.9065755208333334}, {"start": 658.81, "end": 659.13, "word": " اقول", "probability": 0.748291015625}, {"start": 659.13, "end": 659.79, "word": " اعرفك", "probability": 0.8516845703125}, {"start": 659.79, "end": 660.15, "word": " التالي", "probability": 0.9637044270833334}, {"start": 660.15, "end": 660.23, "word": " ال", "probability": 0.92333984375}, {"start": 660.23, "end": 660.73, "word": " bijection", "probability": 0.68438720703125}, {"start": 660.73, "end": 660.91, "word": " هي", "probability": 0.75439453125}, {"start": 660.91, "end": 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مختلف", "probability": 0.9786783854166666}, {"start": 1906.8, "end": 1907.72, "word": " تماما", "probability": 0.9977213541666666}, {"start": 1907.72, "end": 1908.14, "word": " زي", "probability": 0.772216796875}, {"start": 1908.14, "end": 1908.46, "word": " الأمثلة", "probability": 0.8951416015625}, {"start": 1908.46, "end": 1908.58, "word": " اللي", "probability": 0.958251953125}, {"start": 1908.58, "end": 1908.94, "word": " هناخدها", "probability": 0.9107421875}, {"start": 1908.94, "end": 1909.36, "word": " لقدام", "probability": 0.6066080729166666}, {"start": 1909.36, "end": 1909.98, "word": " فهي", "probability": 0.87646484375}, {"start": 1909.98, "end": 1910.48, "word": " فعليا", "probability": 0.835205078125}, {"start": 1910.48, "end": 1911.14, "word": " احنا", "probability": 0.88134765625}, {"start": 1911.14, "end": 1911.78, "word": " سببنا", "probability": 0.888916015625}, {"start": 1911.78, "end": 1911.9, "word": " و", "probability": 0.9921875}, {"start": 1911.9, "end": 1912.2, "word": " عرفنا", "probability": 0.9060872395833334}, {"start": 1912.2, "end": 1912.46, "word": " أنه", "probability": 0.593017578125}, {"start": 1912.46, "end": 1912.9, "word": " فعليا", "probability": 0.9158935546875}, {"start": 1912.9, "end": 1913.06, "word": " هي", "probability": 0.9453125}, {"start": 1913.06, "end": 1913.48, "word": " function", "probability": 0.9697265625}], "temperature": 1.0}, {"id": 79, "seek": 191887, "start": 1914.47, "end": 1918.87, "text": "عرفنا في النهاية أن هي function ل subset of integers", "tokens": [3615, 28480, 8315, 8978, 28239, 11296, 10632, 14739, 39896, 2445, 5296, 25993, 295, 41674], "avg_logprob": -0.24596354564030964, "compression_ratio": 0.922077922077922, "no_speech_prob": 0.0, "words": [{"start": 1914.47, "end": 1914.99, "word": "عرفنا", "probability": 0.78515625}, {"start": 1914.99, "end": 1915.15, "word": " في", "probability": 0.77099609375}, {"start": 1915.15, "end": 1915.49, "word": " النهاية", "probability": 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معادلة تبدأها من الصفر فتنجبر تبدأ من الواحد okay مقبولة مش مشكلة ابدأ من الواحد", "tokens": [2304, 8592, 39896, 4117, 2423, 41674, 29538, 1975, 15042, 6055, 44510, 10721, 9154, 4018, 6156, 3555, 38251, 1829, 11296, 3303, 1230, 1975, 2407, 6055, 44510, 10721, 9154, 2423, 14407, 24401, 4724, 43042, 3224, 3714, 4587, 3555, 12610, 3660, 37893, 1975, 1829, 37893, 28820, 3660, 8717, 44510, 10721, 9154, 2423, 14407, 24401, 6156, 17082, 6027, 3555, 995, 39896, 11296, 39627, 15730, 25124, 28820, 3303, 1230, 4724, 44510, 10721, 9154, 4018, 1975, 2407, 4724, 44510, 10721, 9154, 2423, 14407, 24401, 9122, 15040, 8032, 15042, 20328, 5016, 4032, 4724, 2304, 8592, 1829, 21542, 6027, 3714, 9957, 13672, 1829, 4724, 5016, 24793, 4117, 16472, 4117, 6055, 25957, 1211, 2423, 8513, 20328, 5016, 24976, 4959, 1975, 8315, 3714, 43020, 1975, 3615, 9566, 1829, 4117, 3714, 7435, 2304, 2407, 27884, 4959, 4032, 15042, 2655, 15040, 38436, 8592, 1975, 1829, 20449, 18513, 37977, 6055, 44510, 10721, 11296, 9154, 31767, 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1963.55, "word": " integers", "probability": 0.90185546875}, {"start": 1963.55, "end": 1964.49, "word": " فاصبحت", "probability": 0.8065185546875}, {"start": 1964.49, "end": 1964.95, "word": " بقدر", "probability": 0.9469401041666666}, {"start": 1964.95, "end": 1965.17, "word": " اقول", "probability": 0.9013671875}, {"start": 1965.17, "end": 1965.49, "word": " عنها", "probability": 0.87255859375}, {"start": 1965.49, "end": 1966.05, "word": " domain", "probability": 0.94921875}, {"start": 1966.05, "end": 1966.83, "word": " و", "probability": 0.381591796875}, {"start": 1966.83, "end": 1967.35, "word": " codomain", "probability": 0.7484537760416666}, {"start": 1967.35, "end": 1967.77, "word": " وفيه", "probability": 0.734130859375}, {"start": 1967.77, "end": 1968.13, "word": " function", "probability": 0.9501953125}, {"start": 1968.13, "end": 1969.23, "word": " الان", "probability": 0.6553955078125}, {"start": 1969.23, "end": 1969.35, "word": " ال", "probability": 0.97119140625}, 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2189.43, "end": 2189.69, "word": " عندك", "probability": 0.993408203125}, {"start": 2189.69, "end": 2189.89, "word": " لازم", "probability": 0.97216796875}, {"start": 2189.89, "end": 2190.15, "word": " تكون", "probability": 0.990966796875}, {"start": 2190.15, "end": 2190.81, "word": " واضحة", "probability": 0.98583984375}, {"start": 2190.81, "end": 2191.31, "word": " مثال", "probability": 0.84619140625}], "temperature": 1.0}, {"id": 90, "seek": 221842, "start": 2191.94, "end": 2218.42, "text": "ممكن تكتبها بهذا الشكل set a n مافيه index هي واضحة معناه ذلك ان هذه عبارة عن a1 a2 ellipses مستمرة و اقولك مثلا اعرفها بهذا الشكل for all n اكبر من او يسوى واحد a n تسوى f of n واحد على n طيب هذه مدام قال لي for all اكبر من واحد طب لأ امتى؟", "tokens": [2304, 43020, 6055, 4117, 2655, 3555, 11296, 39627, 15730, 25124, 28820, 992, 257, 297, 19446, 41185, 3224, 8186, 39896, 4032, 46958, 5016, 3660, 20449, 8315, 3224, 29910, 23275, 16472, 29538, 6225, 3555, 9640, 3660, 18871, 257, 16, 257, 17, 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0.40087890625}, {"start": 2194.66, "end": 2195.46, "word": " a", "probability": 0.271728515625}, {"start": 2195.46, "end": 2196.5, "word": " n", "probability": 0.3193359375}, {"start": 2196.5, "end": 2197.38, "word": " مافيه", "probability": 0.6745198567708334}, {"start": 2197.38, "end": 2197.68, "word": " index", "probability": 0.80224609375}, {"start": 2197.68, "end": 2197.84, "word": " هي", "probability": 0.62255859375}, {"start": 2197.84, "end": 2198.42, "word": " واضحة", "probability": 0.8504638671875}, {"start": 2198.42, "end": 2198.94, "word": " معناه", "probability": 0.8465169270833334}, {"start": 2198.94, "end": 2199.14, "word": " ذلك", "probability": 0.949951171875}, {"start": 2199.14, "end": 2199.26, "word": " ان", "probability": 0.62353515625}, {"start": 2199.26, "end": 2199.46, "word": " هذه", "probability": 0.342041015625}, {"start": 2199.46, "end": 2199.82, "word": " عبارة", "probability": 0.80670166015625}, {"start": 2199.82, "end": 2200.08, "word": " عن", 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all", "probability": 0.94384765625}, {"start": 2206.92, "end": 2207.26, "word": " n", "probability": 0.89404296875}, {"start": 2207.26, "end": 2207.7, "word": " اكبر", "probability": 0.8279622395833334}, {"start": 2207.7, "end": 2207.86, "word": " من", "probability": 0.95654296875}, {"start": 2207.86, "end": 2208.02, "word": " او", "probability": 0.889892578125}, {"start": 2208.02, "end": 2208.38, "word": " يسوى", "probability": 0.840576171875}, {"start": 2208.38, "end": 2208.84, "word": " واحد", "probability": 0.887451171875}, {"start": 2208.84, "end": 2209.4, "word": " a", "probability": 0.6474609375}, {"start": 2209.4, "end": 2209.68, "word": " n", "probability": 0.87353515625}, {"start": 2209.68, "end": 2210.36, "word": " تسوى", "probability": 0.77685546875}, {"start": 2210.36, "end": 2210.68, "word": " f", "probability": 0.71630859375}, {"start": 2210.68, "end": 2210.9, "word": " of", "probability": 0.76904296875}, {"start": 2210.9, "end": 2211.24, "word": " n", "probability": 0.97119140625}, {"start": 2211.24, "end": 2212.08, "word": " واحد", "probability": 0.88916015625}, {"start": 2212.08, "end": 2212.24, "word": " على", "probability": 0.6396484375}, {"start": 2212.24, "end": 2212.48, "word": " n", "probability": 0.54345703125}, {"start": 2212.48, "end": 2213.52, "word": " طيب", "probability": 0.85302734375}, {"start": 2213.52, "end": 2214.0, "word": " هذه", "probability": 0.6474609375}, {"start": 2214.0, "end": 2214.26, "word": " مدام", "probability": 0.6930338541666666}, {"start": 2214.26, "end": 2214.44, "word": " قال", "probability": 0.62548828125}, {"start": 2214.44, "end": 2214.54, "word": " لي", "probability": 0.439208984375}, {"start": 2214.54, "end": 2214.7, "word": " for", "probability": 0.962890625}, {"start": 2214.7, "end": 2215.02, "word": " all", "probability": 0.95703125}, {"start": 2215.02, "end": 2216.34, "word": " اكبر", "probability": 0.9052734375}, {"start": 2216.34, "end": 2216.54, "word": " من", "probability": 0.99658203125}, {"start": 2216.54, "end": 2217.02, "word": " واحد", "probability": 0.98828125}, {"start": 2217.02, "end": 2217.52, "word": " طب", "probability": 0.834716796875}, {"start": 2217.52, "end": 2217.66, "word": " لأ", "probability": 0.707763671875}, {"start": 2217.66, "end": 2218.42, "word": " امتى؟", "probability": 0.761962890625}], "temperature": 1.0}, {"id": 91, "seek": 224271, "start": 2220.12, "end": 2242.72, "text": "فإذا infinite sequence هنا بنتكلم عن infinite sequence لنهائي هذه series أو سلسلة لنهائية من مجموعة main العناصر مستمرة طول ما هتكبر في N هتعطيك قيمة هتعطيك locations لأن N هنا أصبحت تعبر عن location جد ما تكبر في قيمة N هتعطيك locations إضافية", "tokens": [5172, 28814, 15730, 13785, 8310, 34105, 4724, 29399, 4117, 19528, 18871, 13785, 8310, 5296, 1863, 3224, 16373, 1829, 29538, 2638, 34051, 8608, 1211, 3794, 37977, 5296, 1863, 3224, 16373, 10632, 9154, 3714, 7435, 2304, 2407, 27884, 2135, 18863, 1863, 33546, 2288, 3714, 14851, 29973, 3660, 23032, 12610, 19446, 8032, 2655, 4117, 26890, 8978, 426, 8032, 2655, 3615, 9566, 1829, 4117, 12174, 32640, 3660, 8032, 2655, 3615, 9566, 1829, 4117, 9253, 5296, 33456, 426, 34105, 5551, 9381, 49628, 2655, 37279, 26890, 18871, 4914, 10874, 3215, 19446, 6055, 4117, 26890, 8978, 12174, 32640, 3660, 426, 8032, 2655, 3615, 9566, 1829, 4117, 9253, 11933, 11242, 31845, 10632], "avg_logprob": -0.17991071428571428, "compression_ratio": 1.7235023041474655, "no_speech_prob": 0.0, "words": [{"start": 2220.12, "end": 2220.52, "word": "فإذا", "probability": 0.7180989583333334}, {"start": 2220.52, "end": 2221.08, "word": " infinite", "probability": 0.60888671875}, {"start": 2221.08, "end": 2222.12, "word": " sequence", "probability": 0.9736328125}, {"start": 2222.12, "end": 2222.6, "word": " هنا", "probability": 0.6689453125}, {"start": 2222.6, "end": 2222.96, "word": " بنتكلم", "probability": 0.7725830078125}, {"start": 2222.96, "end": 2223.08, "word": " عن", "probability": 0.97412109375}, {"start": 2223.08, "end": 2223.36, "word": " infinite", "probability": 0.90966796875}, {"start": 2223.36, "end": 2224.0, "word": " sequence", "probability": 0.95166015625}, {"start": 2224.0, "end": 2225.1, "word": " لنهائي", "probability": 0.82626953125}, {"start": 2225.1, "end": 2226.16, "word": " هذه", "probability": 0.55029296875}, {"start": 2226.16, "end": 2227.52, "word": " series", "probability": 0.744140625}, {"start": 2227.52, "end": 2227.82, "word": " أو", "probability": 0.6162109375}, {"start": 2227.82, "end": 2228.34, "word": " سلسلة", "probability": 0.9873046875}, {"start": 2228.34, "end": 2228.94, "word": " لنهائية", "probability": 0.9140625}, {"start": 2228.94, "end": 2229.14, "word": " من", "probability": 0.98583984375}, {"start": 2229.14, "end": 2229.62, "word": " مجموعة", "probability": 0.92392578125}, {"start": 2229.62, "end": 2229.86, "word": " main", "probability": 0.3583984375}, {"start": 2229.86, "end": 2230.62, "word": " العناصر", "probability": 0.8631591796875}, {"start": 2230.62, "end": 2231.48, "word": " مستمرة", "probability": 0.8310546875}, {"start": 2231.48, "end": 2231.72, "word": " طول", "probability": 0.96875}, {"start": 2231.72, "end": 2231.82, "word": " ما", "probability": 0.947265625}, {"start": 2231.82, "end": 2232.64, "word": " هتكبر", "probability": 0.8358154296875}, {"start": 2232.64, "end": 2233.36, "word": " في", "probability": 0.6611328125}, {"start": 2233.36, "end": 2233.6, "word": " N", "probability": 0.260498046875}, {"start": 2233.6, "end": 2234.56, "word": " هتعطيك", "probability": 0.93994140625}, {"start": 2234.56, "end": 2235.04, "word": " قيمة", "probability": 0.9093424479166666}, {"start": 2235.04, "end": 2236.32, "word": " هتعطيك", "probability": 0.94189453125}, {"start": 2236.32, "end": 2236.7, "word": " locations", "probability": 0.7529296875}, {"start": 2236.7, "end": 2237.6, "word": " لأن", "probability": 0.816162109375}, {"start": 2237.6, "end": 2237.82, "word": " N", "probability": 0.53857421875}, {"start": 2237.82, "end": 2238.0, "word": " هنا", "probability": 0.84423828125}, {"start": 2238.0, "end": 2238.36, "word": " أصبحت", "probability": 0.727783203125}, {"start": 2238.36, "end": 2238.6, "word": " تعبر", "probability": 0.671142578125}, {"start": 2238.6, "end": 2238.72, "word": " عن", "probability": 0.943359375}, {"start": 2238.72, "end": 2239.14, "word": " location", "probability": 0.9599609375}, {"start": 2239.14, "end": 2240.04, "word": " جد", "probability": 0.819580078125}, {"start": 2240.04, "end": 2240.12, "word": " ما", "probability": 0.70703125}, {"start": 2240.12, "end": 2240.5, "word": " تكبر", "probability": 0.96826171875}, {"start": 2240.5, "end": 2240.62, "word": " في", "probability": 0.95361328125}, {"start": 2240.62, "end": 2240.92, "word": " قيمة", "probability": 0.9905598958333334}, {"start": 2240.92, "end": 2241.12, "word": " N", "probability": 0.93310546875}, {"start": 2241.12, "end": 2241.86, "word": " هتعطيك", "probability": 0.983642578125}, {"start": 2241.86, "end": 2242.24, "word": " locations", "probability": 0.9150390625}, {"start": 2242.24, "end": 2242.72, "word": " إضافية", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 92, "seek": 225302, "start": 2244.12, "end": 2253.02, "text": "طبعا خصوصا عندما اتكلم عن ال natural number فال natural number to infinity فحضرته infinity اذا هذه كأنها تمثل واحد على واحد", "tokens": [9566, 3555, 3615, 995, 16490, 9381, 2407, 9381, 995, 43242, 15042, 1975, 2655, 4117, 19528, 18871, 2423, 3303, 1230, 6156, 6027, 3303, 1230, 281, 13202, 6156, 5016, 11242, 43500, 3224, 13202, 1975, 15730, 29538, 9122, 33456, 11296, 46811, 12984, 1211, 36764, 24401, 15844, 36764, 24401], "avg_logprob": -0.35835598150025244, "compression_ratio": 1.3609022556390977, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 2244.12, "end": 2244.46, "word": "طبعا", "probability": 0.7062225341796875}, {"start": 2244.46, "end": 2244.92, "word": " خصوصا", "probability": 0.92529296875}, {"start": 2244.92, "end": 2245.18, "word": " عندما", "probability": 0.4588623046875}, {"start": 2245.18, "end": 2245.5, "word": " اتكلم", "probability": 0.80010986328125}, {"start": 2245.5, "end": 2245.78, "word": " عن", "probability": 0.68212890625}, {"start": 2245.78, "end": 2245.94, "word": " ال", "probability": 0.763671875}, {"start": 2245.94, "end": 2246.1, "word": " natural", "probability": 0.18310546875}, {"start": 2246.1, "end": 2246.46, "word": " number", "probability": 0.9677734375}, {"start": 2246.46, "end": 2246.74, "word": " فال", "probability": 0.5985107421875}, {"start": 2246.74, "end": 2246.94, "word": " natural", "probability": 0.52685546875}, {"start": 2246.94, "end": 2247.22, "word": " number", "probability": 0.97412109375}, {"start": 2247.22, "end": 2247.36, "word": " to", "probability": 0.26123046875}, {"start": 2247.36, "end": 2247.8, "word": " infinity", "probability": 0.896484375}, {"start": 2247.8, "end": 2248.4, "word": " فحضرته", "probability": 0.8328125}, {"start": 2248.4, "end": 2248.76, "word": " infinity", "probability": 0.65380859375}, {"start": 2248.76, "end": 2249.04, "word": " اذا", "probability": 0.6298828125}, {"start": 2249.04, "end": 2249.6, "word": " هذه", "probability": 0.52734375}, {"start": 2249.6, "end": 2250.04, "word": " كأنها", "probability": 0.966796875}, {"start": 2250.04, "end": 2250.76, "word": " تمثل", "probability": 0.9365234375}, {"start": 2250.76, "end": 2251.46, "word": " واحد", "probability": 0.8720703125}, {"start": 2251.46, "end": 2252.5, "word": " على", "probability": 0.83154296875}, {"start": 2252.5, "end": 2253.02, "word": " واحد", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 93, "seek": 228046, "start": 2254.26, "end": 2280.46, "text": "1 على 2 1 على 3 1 على 4 1 على 5 1 على 6 وضلك ماشي فيها .. ضلك ماشي فيها هنا احنا عبارنا عن مجموعة sequence او مجموعة elements تمثل sequence طيب هذه في ايش بتفيدنا لان عارف انه لعندي الآن السؤال الأهم احنا ليش بناخد هذا الكلام انت بتاخده لأنه هنضطر لجدامنا نعمله summation فبدنا نكون عارفين على الأقل عناصر ايش هم العناصر 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" expectation", "probability": 0.96923828125}, {"start": 2620.97, "end": 2621.65, "word": " او", "probability": 0.905517578125}, {"start": 2621.65, "end": 2622.11, "word": " توقع", "probability": 0.947265625}, {"start": 2622.11, "end": 2622.33, "word": " له", "probability": 0.6240234375}, {"start": 2622.33, "end": 2622.87, "word": " الرقم", "probability": 0.9781901041666666}, {"start": 2622.87, "end": 2623.33, "word": " القادم", "probability": 0.99560546875}, {"start": 2623.33, "end": 2623.75, "word": " لما", "probability": 0.873779296875}, {"start": 2623.75, "end": 2623.93, "word": " نقول", "probability": 0.97412109375}, {"start": 2623.93, "end": 2624.27, "word": " مثلا", "probability": 0.959716796875}, {"start": 2624.27, "end": 2624.63, "word": " for", "probability": 0.84326171875}, {"start": 2624.63, "end": 2624.99, "word": " example", "probability": 0.9755859375}, {"start": 2624.99, "end": 2625.33, "word": " واحد", "probability": 0.937744140625}, {"start": 2625.33, "end": 2625.65, 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"probability": 0.9833984375}, {"start": 2646.1, "end": 2646.28, "word": " مش", "probability": 0.90576171875}, {"start": 2646.28, "end": 2646.68, "word": " هيك", "probability": 0.892578125}, {"start": 2646.68, "end": 2647.66, "word": " ال", "probability": 0.8818359375}, {"start": 2647.66, "end": 2647.84, "word": " odd", "probability": 0.845703125}, {"start": 2647.84, "end": 2648.46, "word": " ال", "probability": 0.81494140625}, {"start": 2648.46, "end": 2648.62, "word": " odd", "probability": 0.97900390625}, {"start": 2648.62, "end": 2649.04, "word": " numbers", "probability": 0.53955078125}, {"start": 2649.04, "end": 2650.22, "word": " ال", "probability": 0.86572265625}, {"start": 2650.22, "end": 2650.34, "word": " odd", "probability": 0.98828125}, {"start": 2650.34, "end": 2650.78, "word": " numbers", "probability": 0.892578125}, {"start": 2650.78, "end": 2651.7, "word": " طيب", "probability": 0.9803059895833334}, {"start": 2651.7, "end": 2654.0, "word": " ليش", "probability": 0.5946044921875}, {"start": 2654.0, "end": 2654.26, "word": " تلات", "probability": 0.8147786458333334}, {"start": 2654.26, "end": 2654.56, "word": " عشر", "probability": 0.7412109375}], "temperature": 1.0}, {"id": 109, "seek": 267457, "start": 2655.79, "end": 2674.57, "text": "primes لأننا بنتكلم عن الprimes نتكلم عن ايه الprimes تمام فإذا مجرد أن انت مجموعة ال elements اللي موجودة ال few elements اللي موجودة قدامك اعتطك النمط خلصت يعني انتهت المشكلة عملت recognizing صح", "tokens": [1424, 1532, 5296, 33456, 8315, 4724, 29399, 4117, 19528, 18871, 2423, 1424, 1532, 8717, 2655, 4117, 19528, 18871, 1975, 1829, 3224, 2423, 1424, 1532, 46811, 10943, 6156, 28814, 15730, 3714, 7435, 2288, 3215, 14739, 16472, 2655, 3714, 7435, 2304, 2407, 27884, 2423, 4959, 13672, 1829, 3714, 29245, 23328, 3660, 2423, 1326, 4959, 13672, 1829, 3714, 29245, 23328, 3660, 12174, 3215, 10943, 4117, 1975, 34268, 9566, 4117, 28239, 2304, 9566, 16490, 1211, 9381, 2655, 37495, 22653, 16472, 47395, 2655, 9673, 8592, 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اتنين تلاتة لأ مش اربعة خمسة لاحظت كده هذه ال sequence كل element هو مجموع ال two elements اللي جابله عشان تكون واضحة عندكم مابديش اخليكم ضامن محترين كتير هي خمسة لأنه بعد التمانية ال next one", "tokens": [15042, 39896, 25961, 8978, 8310, 6156, 3615, 15040, 8032, 9307, 37893, 39896, 2423, 8310, 8032, 9307, 4032, 12174, 1211, 2655, 23275, 14407, 8032, 1863, 47283, 3215, 2423, 8310, 8032, 9307, 4032, 8032, 2655, 9566, 1211, 3615, 8310, 37893, 3224, 13063, 3660, 10874, 28259, 4032, 20449, 32887, 5172, 3660, 10874, 28259, 39896, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 5296, 10721, 37893, 1975, 25513, 27884, 16490, 2304, 3794, 3660, 20193, 5016, 19913, 2655, 9122, 3215, 3224, 29538, 2423, 8310, 28242, 4478, 31439, 3714, 7435, 2304, 45367, 2423, 732, 4959, 13672, 1829, 10874, 16758, 43761, 6225, 8592, 7649, 6055, 30544, 4032, 46958, 5016, 3660, 43242, 24793, 3714, 16758, 16254, 8592, 1975, 9778, 20292, 24793, 48812, 10943, 1863, 3714, 33753, 2288, 9957, 9122, 2655, 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"probability": 0.857421875}, {"start": 3279.84, "end": 3280.22, "word": " صغيرة", "probability": 0.9908854166666666}, {"start": 3280.22, "end": 3280.54, "word": " هادي", "probability": 0.76416015625}, {"start": 3280.54, "end": 3280.96, "word": " هادي", "probability": 0.7284342447916666}, {"start": 3280.96, "end": 3281.44, "word": " تعبر", "probability": 0.8701171875}, {"start": 3281.44, "end": 3281.86, "word": " بالنسبة", "probability": 0.98583984375}, {"start": 3281.86, "end": 3282.0, "word": " لل", "probability": 0.7421875}, {"start": 3282.0, "end": 3282.46, "word": " string", "probability": 0.88134765625}, {"start": 3282.46, "end": 3282.98, "word": " عن", "probability": 0.9404296875}], "temperature": 1.0}, {"id": 135, "seek": 331062, "start": 3283.62, "end": 3310.62, "text": "الـ Empty Set معناته هدا بيصير Empty String String فاضي او Sequence فاضي String فاضية هنا فبنكتبها بهذا الشكل او Double Quotation فاضين Double Quotation فاضين فهدا Empty String فال String هنا ال link ثبعه Zero Zero تمام؟ هي خلصنا المقدمة بتاعة هذا الموضوع عشان المرة القادمة نتكلم عن summation ان شاء الله تعالى و نشوف كيف نستخدم هذا الكلام يعطيكوا العفو يا شباب", "tokens": [6027, 39184, 3968, 39420, 8928, 20449, 8315, 47395, 8032, 28259, 4724, 1829, 9381, 13546, 3968, 39420, 745, 2937, 745, 2937, 6156, 46958, 1829, 1975, 2407, 46859, 655, 6156, 46958, 1829, 745, 2937, 6156, 46958, 10632, 34105, 6156, 3555, 1863, 4117, 2655, 3555, 11296, 39627, 15730, 25124, 28820, 1975, 2407, 16633, 2326, 310, 399, 6156, 46958, 9957, 16633, 2326, 310, 399, 6156, 46958, 9957, 6156, 3224, 28259, 3968, 39420, 745, 2937, 6156, 6027, 745, 2937, 34105, 2423, 2113, 38637, 3555, 3615, 3224, 17182, 17182, 46811, 10943, 22807, 39896, 16490, 1211, 9381, 8315, 9673, 28543, 46007, 39894, 995, 27884, 23758, 9673, 2407, 11242, 45367, 6225, 8592, 7649, 9673, 25720, 25062, 18513, 46007, 8717, 2655, 4117, 19528, 18871, 28811, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 4032, 8717, 8592, 38688, 9122, 33911, 8717, 14851, 9778, 40448, 23758, 2423, 28820, 10943, 37495, 9566, 1829, 4117, 14407, 18863, 5172, 2407, 35186, 13412, 3555, 16758], "avg_logprob": -0.2117708393931389, "compression_ratio": 1.8344370860927153, "no_speech_prob": 5.4836273193359375e-06, "words": [{"start": 3283.62, "end": 3284.0, "word": "الـ", "probability": 0.38983154296875}, {"start": 3284.0, "end": 3284.32, "word": " Empty", "probability": 0.664794921875}, {"start": 3284.32, "end": 3285.02, "word": " Set", "probability": 0.4111328125}, {"start": 3285.02, "end": 3285.9, "word": " معناته", "probability": 0.7248128255208334}, {"start": 3285.9, "end": 3286.16, "word": " هدا", "probability": 0.4771728515625}, {"start": 3286.16, "end": 3286.66, "word": " بيصير", "probability": 0.83038330078125}, {"start": 3286.66, "end": 3287.14, "word": " Empty", "probability": 0.83544921875}, {"start": 3287.14, "end": 3288.1, "word": " String", "probability": 0.921875}, {"start": 3288.1, "end": 3289.3, "word": " String", "probability": 0.62249755859375}, {"start": 3289.3, "end": 3289.76, "word": " فاضي", "probability": 0.9300130208333334}, {"start": 3289.76, "end": 3290.42, "word": " او", "probability": 0.696044921875}, {"start": 3290.42, "end": 3290.82, "word": " Sequence", "probability": 0.926025390625}, {"start": 3290.82, "end": 3291.14, "word": " فاضي", "probability": 0.8421223958333334}, {"start": 3291.14, "end": 3291.62, "word": " String", "probability": 0.76708984375}, {"start": 3291.62, "end": 3292.02, "word": " فاضية", "probability": 0.9827473958333334}, {"start": 3292.02, "end": 3292.18, "word": " هنا", "probability": 0.9638671875}, {"start": 3292.18, "end": 3293.12, "word": " فبنكتبها", "probability": 0.9658900669642857}, {"start": 3293.12, "end": 3293.38, "word": " بهذا", "probability": 0.93359375}, {"start": 3293.38, "end": 3293.7, "word": " الشكل", "probability": 0.993896484375}, {"start": 3293.7, "end": 3293.98, "word": " او", "probability": 0.83544921875}, {"start": 3293.98, "end": 3294.52, "word": " Double", "probability": 0.70263671875}, {"start": 3294.52, "end": 3295.08, "word": " Quotation", "probability": 0.8995768229166666}, {"start": 3295.08, "end": 3295.72, "word": " فاضين", "probability": 0.9239908854166666}, {"start": 3295.72, "end": 3296.14, "word": " Double", "probability": 0.5556640625}, {"start": 3296.14, "end": 3296.56, "word": " Quotation", "probability": 0.9856770833333334}, {"start": 3296.56, "end": 3296.96, "word": " فاضين", "probability": 0.9864908854166666}, {"start": 3296.96, "end": 3297.26, "word": " فهدا", "probability": 0.681884765625}, {"start": 3297.26, "end": 3297.6, "word": " Empty", "probability": 0.862548828125}, {"start": 3297.6, "end": 3298.04, "word": " String", "probability": 0.977783203125}, {"start": 3298.04, "end": 3298.64, "word": " فال", "probability": 0.733154296875}, {"start": 3298.64, "end": 3298.94, "word": " String", "probability": 0.857421875}, {"start": 3298.94, "end": 3299.18, "word": " هنا", "probability": 0.97216796875}, {"start": 3299.18, "end": 3299.42, "word": " ال", "probability": 0.87744140625}, {"start": 3299.42, "end": 3299.6, "word": " link", "probability": 0.39599609375}, {"start": 3299.6, "end": 3300.1, "word": " ثبعه", "probability": 0.729248046875}, {"start": 3300.1, "end": 3300.98, "word": " Zero", "probability": 0.724609375}, {"start": 3300.98, "end": 3301.7, "word": " Zero", "probability": 0.464111328125}, {"start": 3301.7, "end": 3302.68, "word": " تمام؟", "probability": 0.748779296875}, {"start": 3302.68, "end": 3302.8, "word": " هي", "probability": 0.70068359375}, {"start": 3302.8, "end": 3303.38, "word": " خلصنا", "probability": 0.8446044921875}, {"start": 3303.38, "end": 3304.66, "word": " المقدمة", "probability": 0.9801432291666666}, {"start": 3304.66, "end": 3304.9, "word": " بتاعة", "probability": 0.7919921875}, {"start": 3304.9, "end": 3305.08, "word": " هذا", "probability": 0.857421875}, {"start": 3305.08, "end": 3305.38, "word": " الموضوع", "probability": 0.99853515625}, {"start": 3305.38, "end": 3305.68, "word": " عشان", "probability": 0.9853515625}, {"start": 3305.68, "end": 3305.96, "word": " المرة", "probability": 0.961181640625}, {"start": 3305.96, "end": 3306.34, "word": " القادمة", "probability": 0.9890950520833334}, {"start": 3306.34, "end": 3306.76, "word": " نتكلم", "probability": 0.98291015625}, {"start": 3306.76, "end": 3307.02, "word": " عن", "probability": 0.9921875}, {"start": 3307.02, "end": 3307.54, "word": " summation", "probability": 0.181640625}, {"start": 3307.54, "end": 3307.8, "word": " ان", "probability": 0.7490234375}, {"start": 3307.8, "end": 3307.98, "word": " شاء", "probability": 0.961181640625}, {"start": 3307.98, "end": 3308.04, "word": " الله", "probability": 0.95556640625}, {"start": 3308.04, "end": 3308.38, "word": " تعالى", "probability": 0.9462890625}, {"start": 3308.38, "end": 3308.48, "word": " و", "probability": 0.98583984375}, {"start": 3308.48, "end": 3308.68, "word": " نشوف", "probability": 0.85302734375}, {"start": 3308.68, "end": 3308.84, "word": " كيف", "probability": 0.984619140625}, {"start": 3308.84, "end": 3309.36, "word": " نستخدم", "probability": 0.9169921875}, {"start": 3309.36, "end": 3309.54, "word": " هذا", "probability": 0.93408203125}, {"start": 3309.54, "end": 3309.82, "word": " الكلام", "probability": 0.9602864583333334}, {"start": 3309.82, "end": 3310.12, "word": " يعطيكوا", "probability": 0.780224609375}, {"start": 3310.12, "end": 3310.34, "word": " العفو", "probability": 0.8173828125}, {"start": 3310.34, "end": 3310.5, "word": " يا", "probability": 0.490234375}, {"start": 3310.5, "end": 3310.62, "word": " شباب", "probability": 0.9710286458333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3311.281625, "duration_after_vad": 3213.9681249999862}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/3aNkUT5m_as.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/3aNkUT5m_as.srt
new file mode 100644
index 0000000000000000000000000000000000000000..526481d63e593d836ac063676bd7e82f0809bc7b
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/3aNkUT5m_as.srt
@@ -0,0 +1,2030 @@
+1
+00:00:05,150 --> 00:00:08,730
+يعطيكم العفو يا شباب، نكمل اليوم إن شاء الله تعالى
+
+2
+00:00:08,730 --> 00:00:11,410
+فيه موضوع الـ predicate اللي اتكلمنا فيه المرة
+
+3
+00:00:11,410 --> 00:00:15,910
+السابقة بإذن الله، اتكلمنا ووصلنا لفكرة الـ
+
+4
+00:00:15,910 --> 00:00:19,150
+predicate على أساس أنه propositional function، مش
+
+5
+00:00:19,150 --> 00:00:21,730
+هيك اتكلمنا عنها، أنها propositional function، فـ
+
+6
+00:00:21,730 --> 00:00:24,830
+propositional function بقدر اسميها capital P، هذه
+
+7
+00:00:24,830 --> 00:00:29,030
+الـ predicate سميناها of X، و X هذا هو الـ variable
+
+8
+00:00:29,030 --> 00:00:32,950
+تبعنا أو الـ object أو ممكن يكون الـ subject حسب الـ
+
+9
+00:00:32,950 --> 00:00:37,770
+expression اللي موجود عندك، زي لو افترضنا P of X هي
+
+10
+00:00:37,770 --> 00:00:42,990
+equal to إيش؟ X greater than 7، أكبر من سبعة، ففي
+
+11
+00:00:42,990 --> 00:00:48,390
+الحالة هذه لو قلنا P of 3، P of 3 هيك بهذا الشكل
+
+12
+00:00:48,390 --> 00:00:53,370
+اللي هي أصبحت فيه كاملة، أصبحت proposition، ليش؟
+
+13
+00:00:53,370 --> 00:00:56,750
+ببساطة لأنه اتفقنا قبل هيك قلنا إنه إذا كان بقدر
+
+14
+00:00:56,750 --> 00:01:01,850
+أعطيها value، صحيح؟ logic value أو truth value، أما
+
+15
+00:01:01,850 --> 00:01:04,890
+false أو true، واتفقنا على هذه النقطة برضه مش
+
+16
+00:01:04,890 --> 00:01:08,110
+بالضروري truth value معناته هي لازم تكون true يا
+
+17
+00:01:08,110 --> 00:01:11,710
+true يا false، أنا بقدر أقول إن هذه هي false، ليش؟
+
+18
+00:01:11,710 --> 00:01:15,010
+لأنه بعوض الـ X بالقيمة بتاعتها اللي هي الثلاثة
+
+19
+00:01:15,010 --> 00:01:19,150
+فعاجز أن ثلاثة greater than seven، أكيد false، مجرد
+
+20
+00:01:19,150 --> 00:01:22,310
+كلمة false معناته هي صارت الـ proposition، يعني
+
+21
+00:01:22,310 --> 00:01:27,250
+expression واضح كامل، complete thought، طيب P of
+
+22
+00:01:27,250 --> 00:01:32,910
+eight برضه، بنعوض، ثمانية أكبر من سبعة، آه أكبر من
+
+23
+00:01:32,910 --> 00:01:35,890
+سبعة، فإذا true، مادام قلت true فهي proposition
+
+24
+00:01:35,890 --> 00:01:39,250
+أصبحت، خلاص بطلت predicate، predicate معناته ما زال
+
+25
+00:01:39,250 --> 00:01:45,430
+فيه بنسميه free variable، ما زال فيها متغير حر، مش
+
+26
+00:01:45,430 --> 00:01:51,380
+معطى قيمة، تمام؟ لكن لما نقول مثال زي هالمثال اللي
+
+27
+00:01:51,380 --> 00:02:00,400
+لعنها، أقول P of 3، P of X، 3 و 5، لـ X plus Y greater
+
+28
+00:02:00,400 --> 00:02:06,420
+than 7، في الحالة هذه برضه ماقدرش أقول بعد ما أعوض
+
+29
+00:02:06,420 --> 00:02:13,040
+منه صح ولا غلط، ليش؟ لأنه هتصبح كالتالي: X زائد 3 أكبر
+
+30
+00:02:13,040 --> 00:02:19,020
+من 5، فهذه معناته X أكبر من 2،
+
+31
+00:02:21,330 --> 00:02:24,250
+لكن أنا مش عارف X، فأنا مش عارف أقول صح ولا غلط،
+
+32
+00:02:24,250 --> 00:02:29,290
+لإحنا عارفين X واحد عشان أقول عليها غلط، ولا عارفين
+
+33
+00:02:29,290 --> 00:02:34,010
+X هي خمسة عشان أقول عليها مثلا true، فإذا حتى الآن
+
+34
+00:02:34,010 --> 00:02:38,770
+هذه مادام بدون values نقدر نقول عنها إنها not
+
+35
+00:02:38,770 --> 00:02:42,390
+proposition، يعني predicate، إيش predicate؟
+
+36
+00:02:42,390 --> 00:02:45,210
+propositional function، معناته propositional
+
+37
+00:02:45,210 --> 00:02:50,990
+function، طيب لما أقول P three two four، بنعوض، هأجد
+
+38
+00:02:50,990 --> 00:02:54,870
+أنها والله منطقية، مع المعادلة، حققت المعادلة، فبقول
+
+39
+00:02:54,870 --> 00:02:59,570
+true، مجرد كلمة true معناته هي proposition، نفس
+
+40
+00:02:59,570 --> 00:03:04,350
+الفكرة، اتنين أربعة ثمانية is false، لو عوضنا هنجد
+
+41
+00:03:04,350 --> 00:03:09,230
+أنه ماحققتش المعادلة، فإذن هي false، مجرد كلمة false
+
+42
+00:03:09,230 --> 00:03:13,510
+معناته أنها proposition، لأن أنا قدرت أحكم عليها،
+
+43
+00:03:13,510 --> 00:03:17,450
+مادام حكمت عليها، فإذن هي بالنسبالي أعطتني فكرة،
+
+44
+00:03:17,450 --> 00:03:24,050
+الفكرة هي إما صح أو خطأ، Okay، و برضه ختمنا المحاضرة
+
+45
+00:03:24,050 --> 00:03:26,390
+الماضية بالـ example هذا، لما قلنا ممكن يكون عندي
+
+46
+00:03:26,390 --> 00:03:32,790
+أكثر من متغير، وأخذنا P of X Y and Z، وقلنا X gave
+
+47
+00:03:32,790 --> 00:03:39,920
+Y the grade Z، صار في عندي three databases، 3
+
+48
+00:03:39,920 --> 00:03:43,740
+databases أو قواعد بيانات، في عندي قاعدة بيانات لـ X،
+
+49
+00:03:43,740 --> 00:03:48,500
+وهذا هو المدرس، مجموعة المدرسين اللي بيعطوا العلامات
+
+50
+00:03:48,500 --> 00:03:54,160
+صحيح، ومجموعة في عندي database خاصة بالطلاب، هيها،
+
+51
+00:03:54,160 --> 00:03:58,960
+وهذه خاصة بالطلاب نفسهم، معناته قاعدة البيانات تحت
+
+52
+00:03:58,960 --> 00:04:02,480
+مجموعة الطلاب المسجلين في المساق، المسجلين في المساق،
+
+53
+00:04:02,480 --> 00:04:06,100
+مجموعهم جديش؟ خمسين، ستين، سبعين، في النهاية كلهم
+
+54
+00:04:06,100 --> 00:04:09,610
+بيكونوا عبارة عن database، موجودين هنا، كل عنصر
+
+55
+00:04:09,610 --> 00:04:13,210
+لحاله، كل اسم لحاله، كل رقم جامعي لحاله، ممتاز،
+
+56
+00:04:13,210 --> 00:04:18,490
+that the grade... اللي هو gave Y the grade Z، Z،
+
+57
+00:04:18,490 --> 00:04:23,550
+هذه هتكون هي هالـ أربعة، خمس... خمس grades اللي متفق
+
+58
+00:04:23,550 --> 00:04:27,850
+عليهم، ممتاز، جيد جداً، اللي هو A و B و C و D و F،
+
+59
+00:04:27,850 --> 00:04:32,930
+مش هيك؟ من الراسب للمقبول للجيد، جيد جداً، ثم
+
+60
+00:04:32,930 --> 00:04:37,490
+الممتاز، هدول محققين، ومش فيهم مشكلة، بنحطهم داخل
+
+61
+00:04:37,490 --> 00:04:40,110
+الـ array، بس بدي أعرف إن الـ array ده هو database
+
+62
+00:04:40,110 --> 00:04:45,730
+أصلًا هي database، وبعد ذلك بنعرفهم، بناخدهم، وممكن
+
+63
+00:04:45,730 --> 00:04:49,370
+نعمل combination كامل، بمعنى إن كل المدرسين مادام هم
+
+64
+00:04:49,370 --> 00:04:54,420
+بيدرسوا، والطلاب موجودين داخل قاعدة البيانات، معناته
+
+65
+00:04:54,420 --> 00:04:59,540
+كل مدرس لازم يعطي لكل طلابه علامات، لازم يعبي لهم
+
+66
+00:04:59,540 --> 00:05:05,740
+علامة Z هذه، لازم يتعب علامة Z، ففي الحالة هذه بنقدر
+
+67
+00:05:05,740 --> 00:05:12,300
+نقول إذا given عندي X Mike، و Y Mary، و Z A grade A،
+
+68
+00:05:12,300 --> 00:05:20,210
+فتصبح الجملة كأنه بقول Mike gave Mary the grade A،
+
+69
+00:05:20,210 --> 00:05:23,290
+أنا مجرد دخلت بس البيانات، وهذا اللي بيصير معنى
+
+70
+00:05:23,290 --> 00:05:28,370
+كمدرسين، أنا باجي وبلقى قدامي أرقام جامعية، الأرقام
+
+71
+00:05:28,370 --> 00:05:33,030
+الجامعية هي هذه، من وين اجت؟ من قاعدة بيانات Y،
+
+72
+00:05:33,030 --> 00:05:39,050
+فكل طالب مسجل هو element داخل قاعدة البيانات هذه، واللي
+
+73
+00:05:39,050 --> 00:05:43,830
+هنسميها لاحقًا فضاء العينة، في عينات Y هذه،
+
+74
+00:05:43,830 --> 00:05:47,270
+بديكون فضاء العينة اللي هم مين؟ الـ Y اللي مسموح له
+
+75
+00:05:47,270 --> 00:05:52,590
+أعطيه درجة، اللي مسجل فقط، اللي مش مسجل هيجيني يا
+
+76
+00:05:52,590 --> 00:05:55,850
+دكتور، بدي درجة، طب اسمك مش نازل عندي، كيف أعطيك درجة؟
+
+77
+00:05:55,850 --> 00:05:58,530
+هي مش فكرة إني بدي... يعني من عندي، أنا ما بديش
+
+78
+00:05:58,530 --> 00:06:01,690
+أعطيك درجة، بس هي الفكرة إني عندي قاعدة بيانات،
+
+79
+00:06:01,690 --> 00:06:08,420
+أنا مُضمّن في البرنامج كأستاذ X، وأنا لازم أصلًا أكون
+
+80
+00:06:08,420 --> 00:06:11,320
+موجود ضمن X، وإلا معناته مش أنا اللي بقدر أعطيك
+
+81
+00:06:11,320 --> 00:06:14,600
+العلامة، في غير بيعطيك علامة، لكن لازم أكون أنا ضمن
+
+82
+00:06:14,600 --> 00:06:20,000
+X، وأنت تكون ضمن Y، عشان أعطيك أحد علامات Z اللي هي
+
+83
+00:06:20,000 --> 00:06:26,420
+A، B، C، D، و F، تمام؟ كويس، هذا اللي خلاني أرجع للمثال
+
+84
+00:06:26,420 --> 00:06:28,780
+هذا، أنه في حاجة اسمها قاعدة بيانات، في حاجة اسمها
+
+85
+00:06:28,780 --> 00:06:34,270
+universe of discourse، فضاء العينة، فضاء العينة،
+
+86
+00:06:34,270 --> 00:06:37,470
+اللي بدنا نختار منه المتغيرات، فعندي مجموعة
+
+87
+00:06:37,470 --> 00:06:41,170
+variables اللي هما X و Y و Z، وكانوا من وين اختارهم؟ X
+
+88
+00:06:41,170 --> 00:06:44,630
+و Y و Z، فهدول هتكون موجودين في حاجة اسمها universes
+
+89
+00:06:44,630 --> 00:06:48,570
+of discourse، فضاءات العينة، بصفة عامة، هنسميها UD
+
+90
+00:06:48,570 --> 00:06:53,910
+على طول مباشرة، الـ universe of discourse، كلنا عارفين
+
+91
+00:06:53,910 --> 00:06:58,910
+إن هذه حاجة مميزة جدًا، أن أكون من الأول عارف ومين
+
+92
+00:06:58,910 --> 00:07:02,130
+الـ elements اللي مسموح لي أتعامل معاهم، فطبيعة جدًا
+
+93
+00:07:02,130 --> 00:07:05,270
+مهمة جدًا في الـ predicate، مادام أنا بتعامل مع
+
+94
+00:07:05,270 --> 00:07:10,250
+predicate، و predicate propositional function، نحط
+
+95
+00:07:10,250 --> 00:07:15,650
+كذا خط تحتها، معناته أنا بدي أعرف من وين أختار أو
+
+96
+00:07:15,650 --> 00:07:21,470
+أعمل بـ X، اختيار لقيمة X هذه من أين نختارها؟ فالجيد
+
+97
+00:07:21,470 --> 00:07:24,550
+يكون معرف لي على الأقل فضاء العينة اللي بدي أشتغل
+
+98
+00:07:24,550 --> 00:07:28,910
+فيه، هي مش مفتوحة، هيك اختار X من أي مكان في الدنيا،
+
+99
+00:07:28,910 --> 00:07:33,330
+لازم أكون عارف من قاعدة البيانات اللي بدي آخذ منها
+
+100
+00:07:33,330 --> 00:07:39,290
+قيمة X، for example، لو أخذنا مثلًا P of X هي عبارة
+
+101
+00:07:39,290 --> 00:07:44,030
+عن X زائد واحد أكبر من X، معادلة بسيطة جدًا وسهلة، ومش
+
+102
+00:07:44,030 --> 00:07:49,930
+مشكلة، هذه بكل وضوح باينة إني بدي أتعامل مع
+
+103
+00:07:49,930 --> 00:07:53,270
+قاعدة بيانات، قاعدة بيانات بصفة عامة، هقول الـ
+
+104
+00:07:53,270 --> 00:08:01,470
+natural number، الأرقام من صفر to infinity، الـ real
+
+105
+00:08:01,470 --> 00:08:05,730
+number من minus infinity to infinity، من minus
+
+106
+00:08:05,730 --> 00:08:07,770
+infinity to infinity، فإذا الفرق بينهم هو جزء الـ
+
+107
+00:08:07,770 --> 00:08:10,650
+negative، بس الـ natural number، الأرقام الطبيعية
+
+108
+00:08:10,650 --> 00:08:14,710
+بتبدأ من الصفر to infinity، إلى ما لا نهاية، كويس، في
+
+109
+00:08:14,710 --> 00:08:20,290
+الحالة دي بقدر أقول إن هذه اختزلت لي عدة معادلات، هي
+
+110
+00:08:20,290 --> 00:08:24,110
+عبارة عن صفر، يعني بدأت بالـ natural number، صفر، صفر
+
+111
+00:08:24,110 --> 00:08:28,050
+زائد واحد أكبر من واحد، and واحد زائد واحد أكبر من
+
+112
+00:08:28,050 --> 00:08:31,610
+واحد، and اتنين زائد واحد أكبر من اتنين، and ثلاثة
+
+113
+00:08:31,610 --> 00:08:34,790
+زائد واحد أكبر من ثلاثة، and، طب لقى امتى؟ to
+
+114
+00:08:34,790 --> 00:08:39,030
+infinity، هل منطقي إني أكتب هيك to infinity؟ فعشان كده
+
+115
+00:08:39,030 --> 00:08:44,550
+بنختصرها في معادلة بهذا... بهذا الشكل، وخلصناه،
+
+116
+00:08:44,550 --> 00:08:48,830
+الآن، بدل المهم جدًا، بعد ما نحط المعادلة، أن أعرف الـ
+
+117
+00:08:48,830 --> 00:08:52,930
+universe of discourse، أكون عارف بالضبط الـ universe
+
+118
+00:08:52,930 --> 00:08:57,470
+of discourse، من إلى، من جديش لجديش، من جديش لجديش، في
+
+119
+00:08:57,470 --> 00:09:02,310
+هذه أهمية أن يكون في عندك فضاء عينة، فضاء العينة،
+
+120
+00:09:02,310 --> 00:09:06,090
+الآن، فضاء العينة هذا اللي دعيناه كأنه فضاء عينة،
+
+121
+00:09:06,090 --> 00:09:12,650
+واللي هو كل قيم X الممكنة في المعادلة، أو الممكن
+
+122
+00:09:12,650 --> 00:09:17,130
+تطبيقها للمعادلة، المعادلة مين؟ الـ P of X اللي هي الـ
+
+123
+00:09:17,130 --> 00:09:23,110
+predicate، الـ predicate، okay، الآن داخل universe of
+
+124
+00:09:23,110 --> 00:09:26,090
+discourse ده، وعشان نحدد الـ universe of discourse
+
+125
+00:09:26,090 --> 00:09:30,450
+بصفة عامة، احنا بنتعامل مع أكبر مجموعة ممكنة من
+
+126
+00:09:30,450 --> 00:09:33,490
+الأعداد اللي هي الـ real number، هذه أكبر مجموعة
+
+127
+00:09:33,490 --> 00:09:37,430
+ممكنة من الأرقام أو من الأعداد، من الأرقام الممكنة،
+
+128
+00:09:37,430 --> 00:09:40,790
+فالـ real number من minus infinity to infinity، بالـ
+
+129
+00:09:40,790 --> 00:09:44,950
+fractions اللي فيهم، هذه أكبر مجموعة من المجموعات
+
+130
+00:09:44,950 --> 00:09:48,750
+الرقمية اللي بنتعامل معها، أحيانًا محتاجين داخل الـ
+
+131
+00:09:48,750 --> 00:09:54,170
+universe of discourse نعمل محددات، كيف أعمل محددات؟
+
+132
+00:09:54,170 --> 00:09:57,470
+يعني أقول والله في عندي لجنة ثقافية، بدنا نختار
+
+133
+00:09:57,470 --> 00:10:01,430
+مجموعة من الـ class تبعنا يشارك فيها، طب مين هدول
+
+134
+00:10:01,430 --> 00:10:04,850
+اللي بدأ أختارهم؟ هنقول والله كل طالب معدل، ونفترض
+
+135
+00:10:04,850 --> 00:10:10,550
+فوج التسعين، كلمة فوج التسعين هذه أنا عملت
+
+136
+00:10:10,550 --> 00:10:14,880
+quantification، فأنا صار في عندي quantifier، الـ
+
+137
+00:10:14,880 --> 00:10:18,560
+quantification هذه اللي هو التحديد من الـ universe
+
+138
+00:10:18,560 --> 00:10:21,300
+of discourse، متفقين فيه universe of discourse، فيه
+
+139
+00:10:21,300 --> 00:10:24,840
+فضاء عينة، بس أنا بدي أطبق المعادلة على جزء منهم
+
+140
+00:10:24,840 --> 00:10:30,320
+أو على كله، على كلهم، أقول بدي أدخل علاماتي آخر
+
+141
+00:10:30,320 --> 00:10:35,180
+الفصل، لمين؟ هذه للكل، ما فيش مجال، للكل، فهنعرف
+
+142
+00:10:35,180 --> 00:10:39,560
+two quantifiers، محددين للـ expression، للـ
+
+143
+00:10:39,560 --> 00:10:43,880
+expression تبعنا، الأتنين هدول هما for all و there
+
+144
+00:10:43,880 --> 00:10:50,020
+exist، ففي عندي الأولى for all بهذا الشكل، كلمة all
+
+145
+00:10:50,020 --> 00:10:56,640
+بس قلبين، حرف الـ A، there exist من exist بس عكسين
+
+146
+00:10:56,640 --> 00:11:00,920
+حرف الـ E، فبنفهم
+
+147
+00:11:00,920 --> 00:11:06,560
+منها إن الأولى هذه بنسميها for all، فبنسميها universal
+
+148
+00:11:06,560 --> 00:11:11,360
+quantifier، المحدد الشمولي أو الشامل، اللي هو بيشمل
+
+149
+00:11:11,360 --> 00:11:19,200
+كل فضاء العينة، أنا هدخل درجاتي آخر الفصل لمين؟ لكل
+
+150
+00:11:19,200 --> 00:11:25,120
+الطلاب، فلما بدي أجي أعبر عنها هكتب for all x، for
+
+151
+00:11:25,120 --> 00:11:29,400
+all x، آخر الفصل بدي أكون لهم درجات في المساق،بدأ
+
+152
+00:11:29,400 --> 00:11:33,460
+مازالوا موجودين ضمن فضاء العينة اللي هو database Y،
+
+153
+00:11:33,460 --> 00:11:37,200
+قاعدة البيانات أو university of discourse Y، تمام،
+
+154
+00:11:37,200 --> 00:11:43,740
+فبنكتبها for all X، P of X is true أو holds، فإذن
+
+155
+00:11:43,740 --> 00:11:51,340
+مطبقة لكل قيم X، P of X true، لاحظتوا كيف؟ طيب، فهذه
+
+156
+00:11:51,340 --> 00:11:54,240
+معناها إن for all X in the university of discourse،
+
+157
+00:11:54,240 --> 00:12:00,750
+P holds أو applied، هي applied، خلاص، مطبقة...
+
+158
+00:12:00,750 --> 00:12:05,110
+مطبقناها على كل العناصر اللي موجودين داخل الـ
+
+159
+00:12:05,110 --> 00:12:08,670
+universe... الـ universe of discourse، طيب الـ E اللي
+
+160
+00:12:08,670 --> 00:12:13,610
+هي there exist، هذه عبارة عن exists، موجود، وعكسنا
+
+161
+00:12:13,610 --> 00:12:17,090
+... وقلبنا... عكسنا هنا، قلبنا وهنا عكسنا حرف الـ E،
+
+162
+00:12:17,090 --> 00:12:20,690
+فصارت هي الـ notation اللي تعبر عن there exist،
+
+163
+00:12:20,690 --> 00:12:27,970
+فبنقول existential quantifier، المحدد الوجودي، المحدد
+
+164
+00:12:27,970 --> 00:12:32,110
+الوجودي، إيش معناه المحدد الوجودي؟ معناته يوجد
+
+165
+00:12:32,110 --> 00:12:39,330
+عنصر على الأقل يحقق المعادلة من داخل الـ universe
+
+166
+00:12:39,330 --> 00:12:43,590
+of discourse، على الأقل يوجد واحد يحقق المعادلة، على
+
+167
+00:12:43,590 --> 00:12:51,770
+الأقل، خليني أقول there exist x... خليني أقول n's
+
+168
+00:12:51,770 --> 00:12:57,540
+of grade A in this course، صح؟ صح، هو مش كلكوا
+
+169
+00:12:57,540 --> 00:13:02,060
+هتحصلوا، لو أخذ، يعني مش كلكوا هتحصل على A، وفي
+
+170
+00:13:02,060 --> 00:13:05,980
+نفس الوقت على الأقل في واحد بده يحصل على A، فإذا
+
+171
+00:13:05,9
+
+223
+00:17:22,380 --> 00:17:25,640
+لأنه هتعطي معنى برضه هتعطيني معنى، المعنى كيف بده
+
+224
+00:17:25,640 --> 00:17:30,940
+يصير؟ هيصير كالتالي: some بعض some parking spaces at
+
+225
+00:17:30,940 --> 00:17:36,280
+iogaza is full. بعض الـ parking spaces full في الجامعة
+
+226
+00:17:36,280 --> 00:17:40,120
+الإسلامية، وبعض الآخر free، بعض الآخر فيه معناته
+
+227
+00:17:40,120 --> 00:17:44,180
+أنه لأ أدخل، دور على الـ free، هتلاقي free دور أنت
+
+228
+00:17:44,180 --> 00:17:47,660
+نصيح، وممكن تلاقي free. طيب، there is a parking
+
+229
+00:17:47,660 --> 00:17:52,920
+space at iogaza that is full. أو ممكن نقول إن يوجد
+
+230
+00:17:52,920 --> 00:17:56,860
+من الـ parking spaces في الجامعة الإسلامية full، يوجد
+
+231
+00:17:56,860 --> 00:18:03,730
+ما قُلتش some، قُلت يوجد. بعضهم محجوز، ماشي، والبعض
+
+232
+00:18:03,730 --> 00:18:10,810
+الثاني معرفش أدخل بالسيارة، ودور لف، أعملك لفة، تمام.
+
+233
+00:18:10,810 --> 00:18:15,810
+أو at least one parking space at iogaza is full.
+
+234
+00:18:15,810 --> 00:18:19,990
+على الأقل واحد.  فالقصد أن الـ exhibitions كتيرة، و
+
+235
+00:18:19,990 --> 00:18:24,870
+كلها معناها أن على الأقل يوجد واحد أو بعض الـ spaces
+
+236
+00:18:24,870 --> 00:18:30,630
+الـ parking spaces مليانة، وبعضها الآخر معرفش خدوا
+
+237
+00:18:30,630 --> 00:18:33,390
+بالك، ومعرفش ليش، لأن there exist ممكن تشمل for all.
+
+238
+00:18:33,390 --> 00:18:38,990
+احنا قلنا at least one، طب يمكن كله؟ مش ممكن كله.
+
+239
+00:18:38,990 --> 00:18:45,330
+ممكن كله، تمام. الآن الـ there exist والـ for all
+
+240
+00:18:45,330 --> 00:18:49,890
+دول عملوا ليه bound variables، بمعنى المتغير
+
+241
+00:18:49,890 --> 00:18:58,770
+قيدناه، قيدناه إما بشمولية أو بمين؟ بـ there exist، بالـ
+
+242
+00:18:58,770 --> 00:19:03,750
+sum. في الحالة هذه بدنا نعرف شغلتين: هل الـ variable
+
+243
+00:19:03,750 --> 00:19:10,150
+free ولا bound variable؟ في الحالة هذه P of X، احنا
+
+244
+00:19:10,150 --> 00:19:14,570
+بيقول عنها هي لحالها هيك، P of X هي free، لأنه أنا
+
+245
+00:19:14,570 --> 00:19:19,550
+قولت P of X، وX متغير وما حددتش أي شيء يربط للمتغير
+
+246
+00:19:19,550 --> 00:19:24,140
+هذا، مافيش أي شيء يربط المتغير هو X وبس. طب مين X؟
+
+247
+00:19:24,140 --> 00:19:26,660
+هذا ما قُلتلكش. طب إيش الـ universe of discourse؟
+
+248
+00:19:26,660 --> 00:19:31,550
+تبعه؟ ما قُلتلكش.. ما قُلتلكش حاجة، هي X وبس X. فإذا
+
+249
+00:19:31,550 --> 00:19:36,910
+هي free variable، X. هذا معناه إن X undefined، غير
+
+250
+00:19:36,910 --> 00:19:40,330
+معرف، ومجرد غير معرف فبضل نسميها predicate.
+
+251
+00:19:40,330 --> 00:19:43,410
+predicate كمان مرة، هي معناها prepositional
+
+252
+00:19:43,410 --> 00:19:48,010
+function. فهي دالة ما أخدت صفة الـ function، إن هي دالة
+
+253
+00:19:48,010 --> 00:19:53,540
+فيها متغير، تمام. الـ quantifiers either for all or
+
+254
+00:19:53,540 --> 00:19:59,100
+there exist operates كاش للـ expression بحيث إنه
+
+255
+00:19:59,100 --> 00:20:08,800
+one or more free variables، binding بتعمل له تقييد، في
+
+256
+00:20:08,800 --> 00:20:11,940
+الحالة هذه بيصير في عندي تقييد من خلال الـ there
+
+257
+00:20:11,940 --> 00:20:16,380
+exist أو الـ for all، وهذه وظيفتها أصلاً إنه تحولها
+
+258
+00:20:16,380 --> 00:20:23,280
+من free لـ bound variable، لمتغير مقيد، مقيد بجزء
+
+259
+00:20:23,280 --> 00:20:27,440
+معين. فالجزء هذا بقدر أعبر عنه بـ language
+
+260
+00:20:27,440 --> 00:20:31,540
+expression، والـ language expression بنقدر نفهمه، و
+
+261
+00:20:31,540 --> 00:20:34,720
+مدام فهمته بقدر أقول true or false، ومدام إنك ذي
+
+262
+00:20:34,720 --> 00:20:38,300
+قولت true or false، أصبحت proposition، ومدام
+
+263
+00:20:38,300 --> 00:20:43,150
+proposition، فهي أصبحت bound variable، لأنه بطل free،
+
+264
+00:20:43,150 --> 00:20:49,210
+بطل undefined، مش هيك؟ لأ، هو صار له defined، أصبح
+
+265
+00:20:49,210 --> 00:20:55,090
+defined، أصبح defined. طيب فـ.. أين وصلنا؟ okay، to
+
+266
+00:20:55,090 --> 00:20:58,530
+produce expression have one or more bound variables.
+
+267
+00:20:58,530 --> 00:21:03,290
+فلإنتاج one أو أكثر من الـ variables تصبح bound
+
+268
+00:21:03,290 --> 00:21:05,370
+variables، بنستخدم الـ quantifiers.
+
+269
+00:21:08,390 --> 00:21:11,470
+for example، ناخد مثالًا على هذا الموضوع، لو قلنا P
+
+270
+00:21:11,470 --> 00:21:18,990
+of X and Y، هيك لحالها فيها اتنين free variables،
+
+271
+00:21:18,990 --> 00:21:22,790
+share X وY، هو أنا ما حددتلِكُم، مش لاقش هو X ولا
+
+272
+00:21:22,790 --> 00:21:27,150
+عندكوا أي quantifier لها، ونفس الكلام Y، ما حددتش
+
+273
+00:21:27,150 --> 00:21:32,030
+عندها أي quantifiers ليقولها، فبتضل free، ممكن تاخد أي
+
+274
+00:21:32,030 --> 00:21:36,900
+شيء. أنا عارف هي all ولا هي there exist ولا هي ضمن
+
+275
+00:21:36,900 --> 00:21:40,460
+boundary محددة، ولا عاملة limitation، ولا عاملة أي
+
+276
+00:21:40,460 --> 00:21:45,580
+حاجة، فهي free، والاتنين هنا هيكونوا free. طيب، for
+
+277
+00:21:45,580 --> 00:21:52,740
+all x, p of x and y، آه في عندي two variables، واحد
+
+278
+00:21:52,740 --> 00:21:58,860
+منهم free، مين هو؟ Y، ضلت free، وواحد أصبح one
+
+279
+00:21:58,860 --> 00:22:04,440
+bound variable اللي هو X، X ربطناها، فضلت الـ free Y،
+
+280
+00:22:04,440 --> 00:22:12,060
+والـ bound X. المثال الثالث P of X where X equal to
+
+281
+00:22:12,060 --> 00:22:20,160
+3، هنا أصبح إيش؟ طريقة ثانية، أو another way to bind
+
+282
+00:22:20,160 --> 00:22:24,620
+X، لتقييد X بطريقة ثانية، أن أحط له قيمة محددة من
+
+283
+00:22:24,620 --> 00:22:29,220
+الأول، رأيي حرصه، أحط له نفس القيمة وخلاص. فإذا P of
+
+284
+00:22:29,220 --> 00:22:33,940
+X ودي يبقى لـ X بيساوي ثلاثة، يعني كأني قُلت P
+
+285
+00:22:33,940 --> 00:22:39,120
+of ثلاثة، P of three وخلاص وانتهى. فإذا هنا أصبحت
+
+286
+00:22:39,120 --> 00:22:43,100
+واضحة تماماً، أنا بتكلم عن proposition، فالـ
+
+287
+00:22:43,100 --> 00:22:46,660
+expression تبعنا هنا أصبح من zero free variables.
+
+288
+00:22:46,660 --> 00:22:51,920
+ومدام أصبح فيه zero free variables، معناته
+
+289
+00:22:51,920 --> 00:22:57,800
+proposition، مافيش أي متغير مجهول، undefined، اللي
+
+290
+00:22:57,800 --> 00:23:04,300
+فوق هذه ما زالت predicate، not proposition. ليش؟
+
+291
+00:23:05,490 --> 00:23:10,790
+لأنه عندي الآن why undefined، هو مش معرف، فما زالت
+
+292
+00:23:10,790 --> 00:23:16,190
+not proposition. طيب، هي اتكلمنا عنها، فإذا كان الـ
+
+293
+00:23:16,190 --> 00:23:19,450
+expression تبعنا هو zero free variables، فبقول عليه
+
+294
+00:23:19,450 --> 00:23:23,290
+bonified proposition أو actual proposition.
+
+295
+00:23:23,290 --> 00:23:26,950
+bonified بمعنى أصلي أو غير زائف، معناته أصلي فعلاً.
+
+296
+00:23:26,950 --> 00:23:32,150
+هو free variables، free variables معناته كله
+
+297
+00:23:32,150 --> 00:23:37,250
+defined، مدام defined يعني بقدر أفهمه، ومدام بقدر
+
+298
+00:23:37,250 --> 00:23:41,090
+أفهمه بقدر أقول true or false، يعني proposition، تمام.
+
+299
+00:23:41,090 --> 00:23:45,510
+فكل expressions بـ one or more free variables هي
+
+300
+00:23:45,510 --> 00:23:51,450
+still predicate، يعني كأنه propositional function.
+
+301
+00:23:51,450 --> 00:23:56,830
+فهي ما زالت دالة معتمدة على متغير، ما زالت حتى الآن
+
+302
+00:23:56,830 --> 00:24:01,250
+هي function معتمدة على متغير. فـ for all x, p, x and
+
+303
+00:24:01,250 --> 00:24:06,450
+y، فهذه مثال اللي لها ما زال فيه y free، y ما زال
+
+304
+00:24:06,450 --> 00:24:09,130
+free، فضل.
+
+305
+00:24:14,190 --> 00:24:21,310
+بالضبط، لأ، هيك هي مش الـ proposition، إيه بتصير الـ
+
+306
+00:24:21,310 --> 00:24:26,810
+proposition؟ هي، هالاحظ for all x،
+
+307
+00:24:26,810 --> 00:24:34,510
+أصبحت الـ proposition. طيب، there exist x لـ P of X،
+
+308
+00:24:34,510 --> 00:24:39,390
+أصبحت الـ proposition. ليش؟ في المثال اللي احنا خدناه،
+
+309
+00:24:39,390 --> 00:24:46,810
+كنت بقول P of X، والـ P هي عبارة عن الـ space is full،
+
+310
+00:24:46,810 --> 00:24:50,290
+مش هي الـ parking space is full؟ في الحالة هذه أنا
+
+311
+00:24:50,290 --> 00:24:55,190
+ماعنديش وصف لـ X بدون الـ for all، فبقدر أقول إيش X
+
+312
+00:24:55,190 --> 00:25:04,230
+is full؟ أنا مقدرتش أحدد، جداش كله ولا نصه ولا ربعه،
+
+313
+00:25:04,230 --> 00:25:10,000
+لكن لما بقول for all،  زفت لها الجملة هذه، الـ for all
+
+314
+00:25:10,000 --> 00:25:15,420
+مطبق على مين؟ على x اللي هو المتغير، المتغير حددته،
+
+315
+00:25:15,420 --> 00:25:21,320
+فأصبح not free، هو bound، أصبح ليش؟ لأني حددته، وقلت
+
+316
+00:25:21,320 --> 00:25:29,150
+for all spaces are free.. are full، فهنا حددت أن كل
+
+317
+00:25:29,150 --> 00:25:33,850
+الـ parking spaces مليانة، خلاص، صار لها معنى، غير لما
+
+318
+00:25:33,850 --> 00:25:37,070
+أقول X is full، X is full، أنت حتى أنت ما فهمتش مني
+
+319
+00:25:37,070 --> 00:25:40,050
+إيش هي مليانة ولا مش مليانة، ومين X هذه؟ لكن لما
+
+320
+00:25:40,050 --> 00:25:46,870
+أقول لك for all X، يعني كل الـ parking spaces are full،
+
+321
+00:25:46,870 --> 00:25:50,050
+هتفهم أن معناته كلها مليانة. مدام أنت وصلتك
+
+322
+00:25:50,050 --> 00:25:56,150
+المعلومة، فهمتها على طول، صارت proposition، بالضبط.
+
+323
+00:25:56,150 --> 00:25:59,470
+بالضبط، الـ complete، الـ complete thought للجملة.
+
+324
+00:25:59,470 --> 00:26:02,750
+إذا الـ expression عندك، وأنت بتطلع عليه، لقيت واضح
+
+325
+00:26:02,750 --> 00:26:05,950
+بالنسبالك، بتقدر تقول true or false، فهي proposition.
+
+326
+00:26:05,950 --> 00:26:10,450
+انتهى، فيه متغير، ومش عارف أتعرف عليه، undefined،
+
+327
+00:26:10,450 --> 00:26:14,630
+بالنسبالك، لأ، not proposition. فهي نفس الفكرة تاني،
+
+328
+00:26:14,630 --> 00:26:17,610
+لما كنا نتكلم بدون الـ quantifiers، آه، هادي
+
+329
+00:26:17,610 --> 00:26:21,810
+undefined. لكن بمجرد ما حطيت لها quantifiers، لأ، أصبحت
+
+330
+00:26:21,810 --> 00:26:27,810
+معرفة. هنا بقول there exist أو some، some parking
+
+331
+00:26:27,810 --> 00:26:33,230
+spaces is full، بعضهم مليانة. طب، هاي عطتني معنى، و
+
+332
+00:26:33,230 --> 00:26:36,170
+بتنكتب في الـ language عادي، مافيش مشكلة يعني.
+
+333
+00:26:36,170 --> 00:26:42,280
+بنتقبلها. طيب، لما يكون في عندي nesting الـ
+
+334
+00:26:42,280 --> 00:26:44,700
+quantifiers، زي مثلًا في الـ universe of discourse،
+
+335
+00:26:44,700 --> 00:26:47,900
+افترضنا أن الـ universe of discourse هو الـ people، و
+
+336
+00:26:47,900 --> 00:26:54,980
+افترضنا أن الـ.. الـ predicate بتاعتنا، اللي هي like، هي
+
+337
+00:26:54,980 --> 00:26:58,160
+الـ function like، وهذه واحدة من الـ functions اللي
+
+338
+00:26:58,160 --> 00:27:02,860
+كتير هنتعامل معها، لأن شوية.. بنسميها irregular،
+
+339
+00:27:02,860 --> 00:27:08,120
+هي مالهاش قانون محدد، مالهاش حالة محددة، بقدر أحطها
+
+340
+00:27:08,120 --> 00:27:11,820
+ضمنه. فعشان هي كتير بنستشهد.. هنستشهد فيها، هي و
+
+341
+00:27:11,820 --> 00:27:14,620
+بعض الـ functions اللي ممكن نستعملها قدام في الـ
+
+342
+00:27:14,620 --> 00:27:20,850
+relations. فخلينا ناخد الـ relation like، بحيث إنه الـ
+
+343
+00:27:20,850 --> 00:27:27,990
+predicate L from X to Y، هي عبارة عن أن X likes Y، X
+
+344
+00:27:27,990 --> 00:27:33,390
+likes Y. طب في الحالة هذه، هيك بهذا الشكل هي
+
+345
+00:27:33,390 --> 00:27:39,450
+predicate ولا proposition؟ predicate، predicate. أنا
+
+346
+00:27:39,450 --> 00:27:43,980
+مش معرف، قُلت هيها، شوف الجملة كيف طلعت: X likes Y.
+
+347
+00:27:43,980 --> 00:27:48,380
+طب هو مين X ومين Y؟ هل هما كل X؟ هل هما some of X؟
+
+348
+00:27:48,380 --> 00:27:52,160
+هل الـ Y، طيب، اللي وقع عليها الفعل اللي هي الـ object،
+
+349
+00:27:52,160 --> 00:27:59,040
+بالنسبالي هل for all كل Y ولا جزء من Y؟ مافيش شيء،
+
+350
+00:27:59,040 --> 00:28:01,520
+فإذن هي ما زالت predicate with two free
+
+351
+00:28:01,520 --> 00:28:06,580
+variables. فإذن predicate. طيب، لما أقول there exists
+
+352
+00:28:06,580 --> 00:28:13,130
+Y، L of X and Y، هذا معناه إيش؟ لما آجي أترجمه: there
+
+353
+00:28:13,130 --> 00:28:21,890
+is someone، hi someone. كويس، هم x likes، يوجد بعض
+
+354
+00:28:21,890 --> 00:28:28,670
+الـ Ys، اللي هي بعض الناس، x بيفضلهم. بس ضلت الجملة
+
+355
+00:28:28,670 --> 00:28:33,610
+غامضة، لأن x معرفتش، at least one، كويس، at least one،
+
+356
+00:28:33,610 --> 00:28:38,610
+بس أنا x معرفتش، يعني كأني بقول في بعض الناس x،
+
+357
+00:28:38,610 --> 00:28:44,140
+بيفضلهم. طب استنى، هو مين x؟ معرفلِيش إياه، فأنا معناته
+
+358
+00:28:44,140 --> 00:28:48,340
+ما فهمتش لسه هو مين اللي بيفضل مين، هو مين اللي بفضل
+
+359
+00:28:48,340 --> 00:28:54,300
+مين؟ معرفتش. فإذا مازالت حتى الآن free للـ X، bound
+
+360
+00:28:54,300 --> 00:28:58,760
+للـ Y، وفي الحالة هذه مازالت predicate. لاحظ تعريفنا
+
+361
+00:28:58,760 --> 00:29:01,580
+حتى، لأن هنا عرفت predicate، هنا عرفت predicate. طيب،
+
+362
+00:29:01,580 --> 00:29:09,710
+لما نقول for all X، there exist y، l of x and y، فهنا
+
+363
+00:29:09,710 --> 00:29:13,890
+على طول for all، معناته everyone، everyone has
+
+364
+00:29:13,890 --> 00:29:20,270
+someone whom they like، okay، جملة كاملة، ومافيش
+
+365
+00:29:20,270 --> 00:29:25,690
+فيها أي متغير، مافيش أي متغير موجود فيها، وقد تكتب
+
+366
+00:29:25,690 --> 00:29:31,340
+في أي كتاب وأنت ماشي، قد تكتب كحكمة حتى، هتلاقيها
+
+367
+00:29:31,340 --> 00:29:35,660
+بوست تنزل على الـ facebook هتلاقيها متقبلة كجملة هيك
+
+368
+00:29:35,660 --> 00:29:39,840
+مكتوبة، آه بتتقبلها، وبتتعامل معاها بشكل عادي جداً، و
+
+369
+00:29:39,840 --> 00:29:44,200
+ما ضلش فيها free. فهل ما زال إيش بدي أكتب هنا؟ أكتب
+
+370
+00:29:44,200 --> 00:29:47,060
+predicate.. predicate زي دول؟ لأ، هكتب
+
+371
+00:29:47,060 --> 00:29:51,880
+proposition with zero free variables، طبعاً لازم
+
+372
+00:29:51,880 --> 00:29:55,800
+يطلع zero هنا. فالآن اختلف تعريفنا، قُلت brigade،
+
+373
+00:29:55,800 --> 00:29:57,800
+brigade زي ما كنا كاتبينه في الحالتين الأولانية،
+
+374
+00:29:57,800 --> 00:30:03,040
+with zero. طيب، مثال، ناخد مثال ونشوف وين بدنا نروح
+
+375
+00:30:03,040 --> 00:30:08,020
+فيه، مثال طبعنا، هاي في عندها realize برضه من الأفعال،
+
+376
+00:30:08,020 --> 00:30:11,600
+أو من اللي ما بديش أقول أفعال، أفعالها دي لما أتكلم
+
+377
+00:30:11,600 --> 00:30:14,340
+في الـ language اللي بنتكلم رياضيات، بدي أقول
+
+378
+00:30:14,340 --> 00:30:17,480
+relation، بدنا نسميها الآن relation، واحدة من الـ
+
+379
+00:30:17,480 --> 00:30:20,840
+relations اللي هنستخدمها في الـ math واحنا ماشيين.
+
+380
+00:30:21,230 --> 00:30:28,250
+إذا قُلت R of X and Y، هي عبارة عن X relies upon Y،
+
+381
+00:30:28,250 --> 00:30:33,130
+بمعنى إن X يعتمد على Y، الاعتمادية أو الاتكالية،
+
+382
+00:30:33,130 --> 00:30:37,150
+خليني أسميها بشكلها السلبي مثلًا، فهذه express،
+
+383
+00:30:37,150 --> 00:30:42,010
+المطلوب أن نعمل express the following of a N عن
+
+384
+00:30:42,010 --> 00:30:47,720
+بيجيبوا English. فإذا بدنا نعرفهم، مجموعة الجملة اللي
+
+385
+00:30:47,720 --> 00:30:54,120
+جاتنا، هذه الـ following، الـ following formula in
+
+386
+00:30:54,120 --> 00:30:56,840
+ambiguous، بمعنى ambiguous لحالها غامض، فـ in
+
+387
+00:30:56,840 --> 00:31:02,240
+ambiguous بشكل واضح، فبشكل واضح كلغة إنجليزية الآن.
+
+388
+00:31:02,240 --> 00:31:10,260
+for all x there exist y لـ r x and y. في البداية for
+
+389
+00:31:10,260 --> 00:31:14,850
+all، دائماً بنعبر عنها everyone، everyone، فإذا
+
+390
+00:31:14,850 --> 00:31:21,070
+everyone relies upon someone، شوف ها there exist،
+
+391
+00:31:21,070 --> 00:31:31,150
+ل
+
+445
+00:35:48,210 --> 00:35:52,330
+باعتبارهم أصلا كأنفسهم هم جزء من الـ universe of
+
+446
+00:35:52,330 --> 00:35:56,170
+discourse هم جزء من الـ universe of discourse تمام
+
+447
+00:35:57,100 --> 00:36:03,720
+Okay مازال في بعض الـ conventions أو التوحيدات اللى
+
+448
+00:36:03,720 --> 00:36:07,920
+بدنا نتفق عليها في الرياضيات نتعامل معها فيما يخص
+
+449
+00:36:07,920 --> 00:36:13,620
+الـ quantifiers نبدأ بالـ universe of discourse اللى
+
+450
+00:36:13,620 --> 00:36:19,540
+ممكن نعمله restriction زيادة أو قيود زيادة نعمله
+
+451
+00:36:19,540 --> 00:36:25,700
+قيود زيادة زي أن أقول for all x greater than zero
+
+452
+00:36:26,440 --> 00:36:29,860
+فعزيزي أنا مش استخدمت الـ quantifier بس، لأ، و
+
+453
+00:36:29,860 --> 00:36:37,160
+استخدمت كمان معادلة تربطه أكثر اللي هي أكبر من صفر
+
+454
+00:36:37,160 --> 00:36:43,280
+فعزيزي أنا أتكلم الآن مش عن بالمطلق كل X، الـ X، لأ
+
+455
+00:36:43,280 --> 00:36:47,120
+عن الـ X اللي أكبر من صفر، اللي أقل من صفر غير
+
+456
+00:36:47,120 --> 00:36:50,360
+مشمولة، مع أن أنا عامل for all، بما أن احنا عاملين
+
+457
+00:36:50,360 --> 00:36:54,980
+for all، فإذا اه في مجال أن أستخدم، أعمل restriction
+
+458
+00:36:54,980 --> 00:37:00,140
+أكثر، تقييد أكثر للـ quantification أو للـ
+
+459
+00:37:00,140 --> 00:37:03,180
+quantifiers اللي بنستخدمها زي for all x أكبر من
+
+460
+00:37:03,180 --> 00:37:08,460
+صفر، فـ P of X is true، فكتعريف بنقول for all x that
+
+461
+00:37:08,460 --> 00:37:14,900
+are greater than zero، فقط اللي أكبر من صفر، كل من هو
+
+462
+00:37:14,900 --> 00:37:19,340
+أكبر من صفر بيحقق ليه P of X، تمام، ونفس الكلام في
+
+463
+00:37:19,340 --> 00:37:23,220
+there exist، عفواً في there exist، هنا هذه لما بدنا
+
+464
+00:37:23,220 --> 00:37:26,080
+نيجي نفكفكها، لو بدأ أحطهم هدول الـ two quantifiers
+
+465
+00:37:26,080 --> 00:37:31,620
+بشكل واضح نفسهم مع بعض، كأني بقول for all of X
+
+466
+00:37:31,620 --> 00:37:41,130
+greater than 0 implies P of X، فإذن لكل قيم X، إذا X
+
+467
+00:37:41,130 --> 00:37:47,210
+أكبر من صفر، إذا P of X is true، صح، لاحظ كمان مرة
+
+468
+00:37:47,210 --> 00:37:54,590
+لكل قيم X، إذا أنت دخلت في الـ F then، إذا X أكبر من
+
+469
+00:37:54,590 --> 00:38:00,450
+صفر، فـ P of X is true، عشان هيك في الـ for all
+
+470
+00:38:00,450 --> 00:38:06,780
+بنستخدم implication، بنستخدم الـ implication في there
+
+471
+00:38:06,780 --> 00:38:13,060
+exist x greater than zero, p of x is true، ففي
+
+472
+00:38:13,060 --> 00:38:15,940
+الحالة اللي كانت there is an x greater than zero
+
+473
+00:38:15,940 --> 00:38:20,040
+such that p of x is true، نكتبها كالتالي there exist
+
+474
+00:38:20,040 --> 00:38:29,880
+يوجد x، لاحظ يوجد X هو أكبر من الصفر، ويحقق P of X
+
+475
+00:38:29,880 --> 00:38:33,840
+لازم يكون في end هنا، ليش؟ لأننا نتكلم عن there
+
+476
+00:38:33,840 --> 00:38:37,480
+exist يعني واحد، طب ما هو ممكن يكون واحد أكبر من
+
+477
+00:38:37,480 --> 00:38:43,960
+صفر وواحد ثاني تماماً بحقق الـ P of X، صح؟ احنا
+
+478
+00:38:43,960 --> 00:38:47,340
+ما قلناش for all، احنا بنقول there exist، يكفي at
+
+479
+00:38:47,340 --> 00:38:50,820
+least one، الـ one هذا ممكن يكون في أكثر فعلاً، أنصر
+
+480
+00:38:50,820 --> 00:38:54,300
+واحد هو أكبر من صفر، وفي أكثر من واحد بيحقق P of X بس
+
+481
+00:38:54,300 --> 00:38:57,800
+ما… مازبطوش مع بعض، طب عشان أضمن أن هم يظبطوا مع
+
+482
+00:38:57,800 --> 00:39:01,920
+بعض، وجملة تكون صحيحة، معناته اللي أكبر من صفر لازم
+
+483
+00:39:01,920 --> 00:39:05,380
+يكون هو نفسه اللي حقق P of X، عشان أقول there exist
+
+484
+00:39:05,380 --> 00:39:10,900
+unique أنصر أكبر من صفر حقق P of X، فمعناه لازم…
+
+485
+00:39:10,900 --> 00:39:14,940
+معناه ذلك لازم الاثنين مع بعض، الشرطين مع بعض، عشان
+
+486
+00:39:14,940 --> 00:39:22,240
+هيك هنربطهم بـ and، واضحة، لازم يرتبطوا هنا بـ and، لابد
+
+487
+00:39:22,240 --> 00:39:27,060
+فإذا ممكن يكون أنصر واحد فعلاً يحقق لي أن هي أكبر
+
+488
+00:39:27,060 --> 00:39:31,460
+من صفر، وأنصر واحد يحقق لي P of X، بس مش نفس
+
+489
+00:39:31,460 --> 00:39:35,200
+الأنصرين، واحد في بداية الـ universe of discourse و
+
+490
+00:39:35,200 --> 00:39:37,680
+واحد في نص الـ universe of discourse، مش مختلفين عن
+
+491
+00:39:37,680 --> 00:39:41,460
+بعض، لأ، أنا بدي اياهم عشان أقول أن هو فعلاً there exist
+
+492
+00:39:41,460 --> 00:39:46,080
+وأكبر برضه من صفر، وأكبر من صفر فعلاً، أحقق كلمة و
+
+493
+00:39:46,080 --> 00:39:50,940
+أكبر من صفر، فالـ and بنحطها and، لازم تكون واضحة كـ and
+
+494
+00:39:52,910 --> 00:39:56,470
+لقدام تكونوا فاهمين الخطوتين هدول، بحيث أنه لما
+
+495
+00:39:56,470 --> 00:39:59,430
+تجيكم for all على طول، أنت بتعود مكانها إيش؟ there
+
+496
+00:39:59,430 --> 00:40:02,650
+exist، عفواً implication، لما تجيك there exist بتعود
+
+497
+00:40:02,650 --> 00:40:07,920
+مكانها and، خدوا بالكم، هتيجينا أمثلة كثير لقدام، by
+
+498
+00:40:07,920 --> 00:40:12,920
+logic، بدك تفكر فيها، وتختصر أو عفواً، تحط الـ
+
+499
+00:40:12,920 --> 00:40:16,780
+equivalent لإلها، عشان تكمل باقي سؤالك، فهنا فهمناها
+
+500
+00:40:16,780 --> 00:40:21,600
+من الآن هي واضحة ومنطقية، هذه لازم يكون and، there
+
+501
+00:40:21,600 --> 00:40:25,540
+exist، ولازم تكون implication للـ for all، تبقى
+
+502
+00:40:25,540 --> 00:40:29,840
+مركزين فيها، هنحتاجها لقدام، مش ضروري اليوم في
+
+503
+00:40:29,840 --> 00:40:33,520
+محاضرتنا، بس لقدام في المحاضرة القادمة، طيب برضه
+
+504
+00:40:33,520 --> 00:40:38,260
+بدنا نتعلم أكثر عن الـ binding أو عملية التقييد، لما
+
+505
+00:40:38,260 --> 00:40:44,140
+أقول for all x there exist x of p of x، لاحظ أنه
+
+506
+00:40:44,140 --> 00:40:49,240
+two quantifier لنفس الـ variable، لنفس الـ variable
+
+507
+00:40:49,240 --> 00:40:52,620
+أكيد طبعاً، منهم، مش معنى أكيد مش هتكون أنهم كثير،
+
+508
+00:40:52,620 --> 00:40:55,340
+معنى واحد، لازم يختصر الثاني، أنا هنا أعمل there
+
+509
+00:40:55,340 --> 00:41:00,280
+exist p of x، خلاص الـ for all بقي ليها معنى، مالهاش
+
+510
+00:41:00,280 --> 00:41:03,880
+معنى، ليش كمان مالهاش معنى؟ لأن there exist هي بتشمل
+
+511
+00:41:03,880 --> 00:41:10,160
+الـ all، صح، أكيد there exist احنا قلنا at least one
+
+512
+00:41:10,160 --> 00:41:18,060
+أو كل، فإذا أكثر شمولية، فمعنى ذلك أن هذا المعنى هيك
+
+513
+00:41:18,060 --> 00:41:21,000
+بهذا الشكل هو معناه كإني بقول there exist suffices
+
+514
+00:41:21,000 --> 00:41:28,550
+بس فقط، مالهاش معنى أن أنا كنت أقول كله وبعضه يحقق P
+
+515
+00:41:28,550 --> 00:41:32,630
+of X، طب لأ، احنا بدنا جملة شاملة، الاثنين ما ينفعش، بعضه
+
+516
+00:41:32,630 --> 00:41:37,510
+أكثر واقعية، لأن بعضه ممكن تشمل for all، ممكن تشمل
+
+517
+00:41:37,510 --> 00:41:42,810
+for all، تمام، فخلاص هذه معرفة الـ X للـ P of X تبع
+
+518
+00:41:42,810 --> 00:41:47,830
+there exist وبس، فأصبحت الـ for all مالهاش معنى، طيب
+
+519
+00:41:47,830 --> 00:41:53,970
+الثانية، الثانية هنا الـ Q of X، هذه اللي جاية بعد الـ
+
+520
+00:41:53,970 --> 00:41:58,370
+and أو الـ conjunction، conjunction Q of X، لاحظوا الـ
+
+521
+00:41:58,370 --> 00:42:03,350
+priorities للأقواس، أولويات الأقواس، فمعنى ذلك أن
+
+522
+00:42:03,350 --> 00:42:10,490
+for all هنا للـ P للـ X بتاعة P فقط، هذه outside الـ
+
+523
+00:42:10,490 --> 00:42:15,310
+quantifier، خارج الـ quantifier، فإذا بالنسبة لي الآن
+
+524
+00:42:15,310 --> 00:42:22,370
+هنا هذه not proposition، ليش not proposition؟ لأن الـ
+
+525
+00:42:22,370 --> 00:42:29,270
+X هذه okay، مافيش فيها مشكلة، bound، variable،
+
+526
+00:42:29,270 --> 00:42:36,710
+مربوطة، لكن الـ X تاعة الـ Q هي free، هذه ما زالت
+
+527
+00:42:36,710 --> 00:42:36,990
+free
+
+528
+00:42:41,840 --> 00:42:47,040
+Madame Free، مستحيل… مستحيل، واضحة برضه، ما زلنا
+
+529
+00:42:47,040 --> 00:42:51,560
+بنتعامل ضمن أولويات الأقواس، ما زلنا بنتعامل ضمن الـ
+
+530
+00:42:51,560 --> 00:42:58,640
+priorities بتاعة الأقواس، فإذا الـ X الثانية طبعاً هي
+
+531
+00:42:58,640 --> 00:43:01,820
+المقصود بالـ variable X اللي بتكلم عنها هي الـ X
+
+532
+00:43:01,820 --> 00:43:05,920
+الثانية بتاعة الـ Q اللي هي is outside of scope of
+
+533
+00:43:05,920 --> 00:43:10,000
+the for all quantifier، فإذا اتفقنا أن هي not
+
+534
+00:43:10,000 --> 00:43:13,020
+proposition، طيب في الحالة هذه أكثر واقعية بتصير
+
+535
+00:43:13,020 --> 00:43:17,560
+أني أقول for all X P of X and there exist Q of X
+
+536
+00:43:17,560 --> 00:43:24,970
+هذا quantifier وهذا quantifier، وهذه X غير هذه الـ X
+
+537
+00:43:24,970 --> 00:43:29,030
+اللي هنا غير الـ X اللي هنا، تماماً غير بعض، يعني لو
+
+538
+00:43:29,030 --> 00:43:32,010
+في سؤال، في حاجة، بدك تعمل حسابك أنه ممكن يكونوا
+
+539
+00:43:32,010 --> 00:43:35,830
+مختلفين تماماً عن بعض، هذا تعريف وهذا تعريف، الـ two X
+
+540
+00:43:35,830 --> 00:43:41,270
+هدول مختلفين عن بعض، فإذا في الحالة هنا هذا legal
+
+541
+00:43:41,270 --> 00:43:44,090
+ومنطقي جداً، مافيش فيها مشكلة، بس بدنا نأخذ بالنا أن
+
+542
+00:43:44,090 --> 00:43:48,430
+في عندي two different X's، عندي two different X's
+
+543
+00:43:48,430 --> 00:43:53,090
+أو two variables، تمام
+
+544
+00:43:54,930 --> 00:43:58,310
+كويس، الـ quantifiers نفس الشيء، بنقدر نتعامل معها
+
+545
+00:43:58,310 --> 00:44:01,570
+كتعريفات
+
+546
+00:44:01,570 --> 00:44:06,590
+ونفكها ونستخدمها لاحقاً في الـ proving اللي هيكون
+
+547
+00:44:06,590 --> 00:44:09,050
+لِمحاضراتنا القادمة إن شاء الله تعالى، لأن ممكن
+
+548
+00:44:09,050 --> 00:44:12,590
+تصلني، تجيني بهذا الشكل، وبده أعملها proving، بده
+
+549
+00:44:12,590 --> 00:44:16,310
+أفكها، لما نفكها كل ما عارفين أن for all معناته أن P
+
+550
+00:44:16,310 --> 00:44:23,190
+of X هي P of واحد and P of اثنين and P of ثلاثة and
+
+551
+00:44:23,190 --> 00:44:26,130
+P of أربعة and P of خمسة، لما أخلص الـ universe of
+
+552
+00:44:26,130 --> 00:44:29,630
+discourse كامل، بدنا نكون عارفينها، and and and and
+
+553
+00:44:29,630 --> 00:44:36,030
+لأن for all معناته كله، الأول والثاني والثالث، و…و…و
+
+554
+00:44:36,030 --> 00:44:43,050
+و…و، كله، وطيب، أما لما أقول there exist، يكفي واحد، الـ
+
+555
+00:44:43,050 --> 00:44:48,390
+conjunction كافية، الـ or كافي، فإذا P of A أو واحد
+
+556
+00:44:48,390 --> 00:44:57,350
+أو P of B أو P of C، أو لما نخلص كل universe of
+
+557
+00:44:57,350 --> 00:45:02,430
+discourse، فإذا for all نربطهم بـ and، there exist
+
+558
+00:45:02,430 --> 00:45:07,450
+نربطهم بـ or، هذا الكلام منطقي جداً وبسيط جداً
+
+559
+00:45:07,450 --> 00:45:11,610
+بتقدر تستنتج أن فرق الـ X P of X هو equivalent لـ
+
+560
+00:45:11,610 --> 00:45:15,130
+negation there exist X negation P of X، مين اللي
+
+561
+00:45:15,130 --> 00:45:19,630
+قال الكلام هذا؟ دي مورغان، دي مورغان بيقول أن هذا
+
+562
+00:45:19,630 --> 00:45:23,270
+الكلام بكل أريحية وبكل بساطة، ومافيش فيها أي
+
+563
+00:45:23,270 --> 00:45:26,760
+مشكلة إطلاقاً، لأنه بتعمل هنا double negation، في
+
+564
+00:45:26,760 --> 00:45:30,460
+مشكلة بتعمل double negation، هي هي ضلت، طيب double
+
+565
+00:45:30,460 --> 00:45:33,240
+negation هذه لما تيجي تفكها دي وتقول أن هي عبارة
+
+566
+00:45:33,240 --> 00:45:42,980
+عن P of A and P of B and and so on، بهذا الشكل هي
+
+567
+00:45:42,980 --> 00:45:49,620
+دخل negation من التنتين هدول عليهم، صارت negation P
+
+568
+00:45:49,620 --> 00:46:00,740
+of A or negation P of B or، مكمل، صح، هيدي مورغان، فإذا
+
+569
+00:46:00,740 --> 00:46:08,620
+الصيغة هذه الآن أصبحت there exist، لأنه or بس، there
+
+570
+00:46:08,620 --> 00:46:14,360
+exist لمين؟ لـ negation الـ bees هدول، معناته صارت
+
+571
+00:46:14,360 --> 00:46:20,800
+negation bees للـ X، الـ X شملت لنا الـ A والـ B والـ C
+
+572
+00:46:20,800 --> 00:46:24,870
+والـ D، كله، رجعنا شملناها، والـ negation الأولى دلت زي
+
+573
+00:46:24,870 --> 00:46:28,790
+ما هي برا، ما بسكنهاش
+
+574
+00:46:28,790 --> 00:46:32,270
+هي دلت برا، احنا واحدة منهم اللي دخلناها على الخوص
+
+575
+00:46:32,270 --> 00:46:36,450
+وغيرنا الـ conjunction للـ disjunction وبس، فضلت
+
+576
+00:46:36,450 --> 00:46:39,910
+اللي برا برا، okay، ونفس الكلام، طب عمل لمين؟ لـ
+
+577
+00:46:39,910 --> 00:46:44,430
+there exist، الـ or بتتحول لـ and، فإذا if bad، مافيش
+
+578
+00:46:44,430 --> 00:46:50,550
+فيه كثير مشكلة، وواضح ووضوح كامل، okay
+
+579
+00:46:53,860 --> 00:46:57,540
+بعض القوانين السريعة البسيطة، لما بيقول for all x
+
+580
+00:46:57,540 --> 00:47:01,680
+for all y، مش هتفرق مين قبل الثاني، مين قبل الثاني
+
+581
+00:47:01,680 --> 00:47:04,640
+مش هتفرق، زي بالظبط في الجملة، أنت عاملها direct ولا
+
+582
+00:47:04,640 --> 00:47:10,920
+indirect، الجملة بس مبنية بشكل direct، الـ subject، الـ
+
+583
+00:47:10,920 --> 00:47:15,410
+verb، الـ object، ولا عكسهم، الـ object مقدمة على الـ
+
+584
+00:47:15,410 --> 00:47:18,750
+subject، هاي الفرق الوحيد، تمام، there exist، there
+
+585
+00:47:18,750 --> 00:47:22,050
+exist برضه نفس الشيء، مين قبل مين، الـ subject والـ
+
+586
+00:47:22,050 --> 00:47:25,450
+object، مين قبل الثاني، ما تفرقش، مادام الـ quantifier
+
+587
+00:47:25,450 --> 00:47:30,030
+ثابت واحد، الـ quantifier ثابت واحد، for all، وناخذ
+
+588
+00:47:30,030 --> 00:47:33,430
+بالنا الآن من الـ priorities للأقواس، الـ for all
+
+589
+00:47:33,430 --> 00:47:37,270
+شاملة القوة كلها، معناته كأني بقول for all x P of
+
+590
+00:47:37,270 --> 00:47:43,980
+X and for all x Q of X، غير المثال تبع التو…كويس؟
+
+591
+00:47:43,980 --> 00:47:47,500
+نفس الكلام، الـ there exist، نفس الفكرة، بقدر أجسم الـ
+
+592
+00:47:47,500 --> 00:47:52,340
+there exist بسهولة، مادام الـ there exist هي مشمولة
+
+593
+00:47:52,340 --> 00:47:56,820
+شاملة القوس كله، فهي نأخذ بالنا من الأقواس،
+
+594
+00:47:56,820 --> 00:48:00,400
+الأقواس هي اللي هتعطيك رؤية أو الـ scope للـ
+
+595
+00:48:00,400 --> 00:48:04,480
+quantifier تبعها، أني exactly
+
+596
+00:48:12,590 --> 00:48:15,530
+أنت بتتكلم هنا، خلّيني عشان أراك…هنا؟ اه، هنا…
+
+597
+00:48:15,530 --> 00:48:29,010
+مالها؟ for all x…هنا…الطرف هنا…تمام…لأ
+
+598
+00:48:29,010 --> 00:48:34,790
+هنا ثابتة، لأنه أنت أصلاً بإيدك فككها، أنت
+
+599
+00:48:34,790 --> 00:48:39,030
+فككها، فأنت الآن عرفت أن هما ثابتين، لكن إذا إجدك من
+
+600
+00:48:39,030 --> 00:48:45,680
+الأساس بهذا الشكل، بتكون عندك معلومة مسبقة، هما نفس الـ
+
+601
+00:48:45,680 --> 00:48:50,060
+X ولا مش نفس الـ X، لتكون معروفة عندك مسبقاً، هم هل هم
+
+602
+00:48:50,060 --> 00:48:54,880
+نفس الـ X ولا مش نفس الـ X؟ في الآخر بتبين أن هم مش
+
+603
+00:48:54,880 --> 00:48:58,220
+نفسهم، إذا كان فرضنا مثلاً هنا there exist وهنا for
+
+604
+00:48:58,220 --> 00:49:03,220
+all، معناته التعامل هنا مختلف عن التعامل هنا، بس هنا
+
+605
+00:49:03,220 --> 00:49:06,380
+for all، for all، كل اللي بهمك أن X هي universe of
+
+606
+00:49:06,380 --> 00:49:10,900
+discourse، اللي هيفرّقهم عن بعض، طبيعة الـ predicate
+
+607
+00:49:10,900 --> 00:49:16,880
+نفسيهما، هو الـ predicate بالظبط؟ like ولا rely on
+
+608
+00:49:16,880 --> 00:49:20,520
+ولا إيش بالظبط؟ طبيعة الـ Q هنا مختلفة عن الـ P
+
+609
+00:49:20,520 --> 00:49:27,520
+لكن توزيع الـ quantifier للكل بنفس الآلية، for all
+
+610
+00:49:27,520 --> 00:49:35,490
+للـ P وللـ Q، الأقواس هي الـ priority، هي اللي بتعطيك
+
+611
+00:49:35,490 --> 00:49:38,790
+الـ priority بالظبط، وبتعطيك مفهوم الفكرة تبعتك
+
+612
+00:49:38,790 --> 00:49:43,510
+بالظبط، تمام
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/3aNkUT5m_as_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/3aNkUT5m_as_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1f44fdec9aa24316dc2c985eda0ef91b2a59796c
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/3aNkUT5m_as_raw.json
@@ -0,0 +1 @@
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"text": "Okay و برضه ختمنا المحاضرة الماضية بال example هذا لما قلنا ممكن يكون عندي أكتر من متغير و أخدنا P of X Y and Z و قلنا X gave Y the grade Z صار في عندي three databases", "tokens": [8297, 4032, 4724, 43042, 3224, 16490, 39237, 8315, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 20666, 1365, 23758, 5296, 15042, 12174, 1211, 8315, 3714, 43020, 7251, 30544, 18871, 16254, 5551, 4117, 2655, 2288, 9154, 44650, 17082, 13546, 4032, 5551, 9778, 3215, 8315, 430, 295, 1783, 398, 293, 1176, 4032, 12174, 1211, 8315, 1783, 2729, 398, 264, 7204, 1176, 20328, 9640, 8978, 18871, 16254, 1045, 22380], "avg_logprob": -0.209398680564129, "compression_ratio": 1.3701657458563536, "no_speech_prob": 1.5497207641601562e-06, "words": [{"start": 199.51, "end": 199.87, "word": "Okay", "probability": 0.1292724609375}, {"start": 199.87, "end": 201.97, "word": " و", "probability": 0.78173828125}, {"start": 201.97, "end": 202.55, "word": " برضه", "probability": 0.7329915364583334}, {"start": 202.55, "end": 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Y طب في الحالة هذه هيك بهذا الشكل هي predicate ولا preposition predicate predicate انا مش معرف، قولت هيها، شوف الجملة كيف طلعت", "tokens": [6027, 9721, 411, 4724, 5016, 1829, 12984, 16472, 3224, 2423, 3852, 8700, 441, 490, 1783, 281, 398, 39896, 6225, 3555, 9640, 3660, 18871, 16472, 1783, 5902, 398, 1783, 5902, 398, 23032, 3555, 8978, 21542, 6027, 3660, 29538, 39896, 4117, 39627, 15730, 25124, 28820, 39896, 3852, 8700, 49429, 2666, 5830, 3852, 8700, 3852, 8700, 1975, 8315, 37893, 20449, 28480, 12399, 12174, 12610, 2655, 39896, 11296, 12399, 13412, 38688, 25724, 2304, 37977, 9122, 33911, 23032, 1211, 34268], "avg_logprob": -0.21217105616080134, "compression_ratio": 1.5989304812834224, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 1637.43, "end": 1637.81, "word": "ال", "probability": 0.6875}, {"start": 1637.81, "end": 1638.37, "word": " relation", "probability": 0.962890625}, {"start": 1638.37, "end": 1639.17, "word": " like", "probability": 0.8994140625}, {"start": 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1745.57, "end": 1769.79, "text": "there exist y, l of x and y فهنا على طول for all معناته everyone everyone has someone whom they like okay جملة كاملة و مافيش فيها أي متغير مافيش أي متغير موجود فيها و قد تكتب في أي كتاب و انت ماشي قد تكتب كحكمة حتى", "tokens": [15456, 2514, 288, 11, 287, 295, 2031, 293, 288, 6156, 3224, 8315, 15844, 23032, 12610, 337, 439, 20449, 8315, 47395, 1518, 1518, 575, 1580, 7101, 436, 411, 1392, 10874, 2304, 37977, 9122, 10943, 37977, 4032, 19446, 41185, 8592, 8978, 11296, 36632, 44650, 17082, 13546, 19446, 41185, 8592, 36632, 44650, 17082, 13546, 3714, 29245, 23328, 8978, 11296, 4032, 12174, 3215, 6055, 4117, 2655, 3555, 8978, 36632, 9122, 2655, 16758, 4032, 16472, 2655, 3714, 33599, 1829, 12174, 3215, 6055, 4117, 2655, 3555, 9122, 5016, 24793, 3660, 11331, 49975], "avg_logprob": -0.16190732929898405, "compression_ratio": 1.6020408163265305, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1745.57, "end": 1745.83, "word": "there", "probability": 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"word": " أمثلة", "probability": 0.9368896484375}, {"start": 2406.6, "end": 2406.84, "word": " كتير", "probability": 0.9651692708333334}, {"start": 2406.84, "end": 2407.34, "word": " لقدام", "probability": 0.8458658854166666}, {"start": 2407.34, "end": 2407.92, "word": " by", "probability": 0.5126953125}, {"start": 2407.92, "end": 2408.34, "word": " logic", "probability": 0.947265625}, {"start": 2408.34, "end": 2408.6, "word": " بدك", "probability": 0.741455078125}, {"start": 2408.6, "end": 2408.98, "word": " تفكر", "probability": 0.97216796875}, {"start": 2408.98, "end": 2409.4, "word": " فيها", "probability": 0.9921875}, {"start": 2409.4, "end": 2409.94, "word": " و", "probability": 0.417236328125}, {"start": 2409.94, "end": 2410.94, "word": " تختصر", "probability": 0.963623046875}, {"start": 2410.94, "end": 2411.34, "word": " او", "probability": 0.8486328125}, {"start": 2411.34, "end": 2411.6, "word": " عفوا", "probability": 0.7289225260416666}, {"start": 2411.6, "end": 2412.48, 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"end": 2417.76, "word": " هي", "probability": 0.38623046875}, {"start": 2417.76, "end": 2418.4, "word": " واضحة", "probability": 0.8299560546875}, {"start": 2418.4, "end": 2419.4, "word": " ومنطقية", "probability": 0.91533203125}, {"start": 2419.4, "end": 2420.18, "word": " هذه", "probability": 0.478515625}, {"start": 2420.18, "end": 2420.42, "word": " لازم", "probability": 0.98828125}, {"start": 2420.42, "end": 2420.62, "word": " يكون", "probability": 0.93115234375}, {"start": 2420.62, "end": 2421.04, "word": " and", "probability": 0.896484375}, {"start": 2421.04, "end": 2421.6, "word": " there", "probability": 0.367431640625}, {"start": 2421.6, "end": 2422.78, "word": " exist", "probability": 0.7099609375}, {"start": 2422.78, "end": 2423.2, "word": " و", "probability": 0.91064453125}, {"start": 2423.2, "end": 2423.38, "word": " لازم", "probability": 0.9695638020833334}, {"start": 2423.38, "end": 2423.54, "word": " تكون", "probability": 0.78271484375}, {"start": 2423.54, "end": 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"word": " في", "probability": 0.7197265625}, {"start": 2429.84, "end": 2430.24, "word": " محاضرتنا", "probability": 0.9150390625}, {"start": 2430.24, "end": 2430.4, "word": " بس", "probability": 0.899658203125}, {"start": 2430.4, "end": 2430.72, "word": " لقدام", "probability": 0.9840494791666666}, {"start": 2430.72, "end": 2430.82, "word": " في", "probability": 0.79833984375}, {"start": 2430.82, "end": 2431.18, "word": " المحاضرة", "probability": 0.906494140625}, {"start": 2431.18, "end": 2431.62, "word": " القادمة", "probability": 0.9881184895833334}, {"start": 2431.62, "end": 2432.34, "word": " طيب", "probability": 0.8346354166666666}, {"start": 2432.34, "end": 2433.52, "word": " برضه", "probability": 0.9371744791666666}, {"start": 2433.52, "end": 2433.86, "word": " بدنا", "probability": 0.6983642578125}, {"start": 2433.86, "end": 2434.16, "word": " نتعلم", "probability": 0.9910888671875}, {"start": 2434.16, "end": 2434.54, "word": " اكتر", "probability": 0.92626953125}, {"start": 2434.54, "end": 2434.8, "word": " عن", "probability": 0.9814453125}, {"start": 2434.8, "end": 2435.22, "word": " ال", "probability": 0.919921875}, {"start": 2435.22, "end": 2435.6, "word": " bending", "probability": 0.8583984375}, {"start": 2435.6, "end": 2436.18, "word": " او", "probability": 0.901123046875}, {"start": 2436.18, "end": 2436.84, "word": " عملية", "probability": 0.9713541666666666}, {"start": 2436.84, "end": 2437.76, "word": " التقييد", "probability": 0.9306640625}, {"start": 2437.76, "end": 2438.26, "word": " لما", "probability": 0.92236328125}, {"start": 2438.26, "end": 2438.44, "word": " اقول", "probability": 0.734130859375}, {"start": 2438.44, "end": 2438.66, "word": " for", "probability": 0.94921875}, {"start": 2438.66, "end": 2438.94, "word": " all", "probability": 0.95556640625}, {"start": 2438.94, "end": 2439.5, "word": " x", "probability": 0.6513671875}, {"start": 2439.5, "end": 2440.12, "word": " there", "probability": 0.8564453125}, {"start": 2440.12, "end": 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أكيد طبعا منهم مش معنى أكيد مش هتكون انهم كتير معنى واحد لازم يختصر التاني انا هنا اعمل there exist p of x خلاص ال for all بقى ليها معنى مالهاش معنى ليش كمان مالهاش معنى لأن there exist هي بتشمل ال all صح أكيد there exist احنا قلنا at least one او كل فإذا أكثر شمولية", "tokens": [6027, 7006, 5296, 1863, 36178, 2423, 7006, 5551, 4117, 25708, 23032, 3555, 3615, 995, 9154, 16095, 37893, 20449, 1863, 7578, 5551, 4117, 25708, 37893, 8032, 2655, 30544, 16472, 16095, 9122, 2655, 13546, 20449, 1863, 7578, 36764, 24401, 5296, 31377, 2304, 7251, 46456, 9381, 2288, 16712, 7649, 1829, 1975, 8315, 34105, 1975, 25957, 1211, 456, 2514, 280, 295, 2031, 16490, 1211, 33546, 2423, 337, 439, 4724, 4587, 7578, 32239, 11296, 20449, 1863, 7578, 3714, 6027, 3224, 33599, 20449, 1863, 7578, 32239, 8592, 9122, 2304, 7649, 3714, 6027, 3224, 33599, 20449, 1863, 7578, 5296, 33456, 456, 2514, 39896, 39894, 8592, 42213, 2423, 439, 20328, 5016, 5551, 4117, 25708, 456, 2514, 1975, 5016, 8315, 12174, 1211, 8315, 412, 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"word": " ليها", "probability": 0.8564453125}, {"start": 2458.28, "end": 2459.3, "word": " معنى", "probability": 0.9931640625}, {"start": 2459.3, "end": 2460.28, "word": " مالهاش", "probability": 0.84893798828125}, {"start": 2460.28, "end": 2460.68, "word": " معنى", "probability": 0.9807942708333334}, {"start": 2460.68, "end": 2461.5, "word": " ليش", "probability": 0.961181640625}, {"start": 2461.5, "end": 2461.72, "word": " كمان", "probability": 0.9763997395833334}, {"start": 2461.72, "end": 2462.06, "word": " مالهاش", "probability": 0.9542236328125}, {"start": 2462.06, "end": 2462.38, "word": " معنى", "probability": 0.98486328125}, {"start": 2462.38, "end": 2462.78, "word": " لأن", "probability": 0.734619140625}, {"start": 2462.78, "end": 2462.96, "word": " there", "probability": 0.76708984375}, {"start": 2462.96, "end": 2463.34, "word": " exist", "probability": 0.892578125}, {"start": 2463.34, "end": 2463.46, "word": " هي", "probability": 0.888671875}, {"start": 2463.46, "end": 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2471.84, "word": " او", "probability": 0.773681640625}, {"start": 2471.84, "end": 2472.12, "word": " كل", "probability": 0.98681640625}, {"start": 2472.12, "end": 2473.18, "word": " فإذا", "probability": 0.8121744791666666}, {"start": 2473.18, "end": 2474.08, "word": " أكثر", "probability": 0.93017578125}, {"start": 2474.08, "end": 2475.16, "word": " شمولية", "probability": 0.9813232421875}], "temperature": 1.0}, {"id": 103, "seek": 248710, "start": 2476.2, "end": 2487.1, "text": "فمعنى ذلك إن هذا المعنى هيكي بهذا الشكل هو معناه كإن بقول there exist buffets بس فقط مالهاش معنى إن أنا كنت أقول كله وبعضه", "tokens": [5172, 2304, 3615, 1863, 7578, 29910, 23275, 36145, 23758, 9673, 3615, 1863, 7578, 39896, 4117, 1829, 39627, 15730, 25124, 28820, 31439, 20449, 8315, 3224, 9122, 28814, 1863, 4724, 39648, 456, 2514, 9204, 1385, 4724, 3794, 6156, 47432, 3714, 6027, 3224, 33599, 20449, 1863, 7578, 36145, 41850, 9122, 29399, 5551, 39648, 28242, 3224, 46599, 3615, 11242, 3224], "avg_logprob": 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لل", "probability": 0.57080078125}, {"start": 2502.21, "end": 2502.35, "word": " P", "probability": 0.91552734375}, {"start": 2502.35, "end": 2502.45, "word": " of", "probability": 0.97119140625}, {"start": 2502.45, "end": 2502.61, "word": " X", "probability": 0.99609375}, {"start": 2502.61, "end": 2502.81, "word": " تبع", "probability": 0.770263671875}, {"start": 2502.81, "end": 2503.01, "word": " there", "probability": 0.60888671875}, {"start": 2503.01, "end": 2503.45, "word": " exist", "probability": 0.7626953125}, {"start": 2503.45, "end": 2503.65, "word": " و", "probability": 0.67333984375}, {"start": 2503.65, "end": 2503.97, "word": " بس", "probability": 0.962646484375}, {"start": 2503.97, "end": 2504.85, "word": " فأصبحت", "probability": 0.85419921875}, {"start": 2504.85, "end": 2505.39, "word": " ال", "probability": 0.94921875}, {"start": 2505.39, "end": 2505.57, "word": " for", "probability": 0.94189453125}, {"start": 2505.57, "end": 2505.75, "word": " all", "probability": 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X لاحظوا ال priorities للأقواس أولويات الأقواس فمعنى ذلك ان for all هنا لل P لل X بتاعة P فقط هذه outside ال quantifier خارج ال quantifier فإذا بالنسبالي الآن هنا هذه not proposition", "tokens": [3224, 24192, 13672, 1829, 10874, 995, 10632, 39182, 2423, 293, 34051, 2423, 27482, 27482, 1249, 295, 1783, 20193, 5016, 19913, 14407, 2423, 15503, 24976, 10721, 4587, 14407, 3794, 5551, 12610, 45865, 9307, 16247, 4587, 14407, 3794, 6156, 2304, 3615, 1863, 7578, 29910, 23275, 16472, 337, 439, 34105, 24976, 430, 24976, 1783, 39894, 995, 27884, 430, 6156, 47432, 29538, 2380, 2423, 4426, 9902, 16490, 9640, 7435, 2423, 4426, 9902, 6156, 28814, 15730, 20666, 1863, 35457, 6027, 1829, 6024, 48506, 34105, 29538, 406, 24830], "avg_logprob": -0.19917168818324446, "compression_ratio": 1.5555555555555556, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2511.87, "end": 2512.15, "word": "هذه", "probability": 0.71337890625}, {"start": 2512.15, "end": 2512.31, "word": " اللي", "probability": 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{"start": 2518.05, "end": 2518.37, "word": " ال", "probability": 0.953125}, {"start": 2518.37, "end": 2518.85, "word": " priorities", "probability": 0.7158203125}, {"start": 2518.85, "end": 2519.91, "word": " للأقواس", "probability": 0.814404296875}, {"start": 2519.91, "end": 2521.67, "word": " أولويات", "probability": 0.898681640625}, {"start": 2521.67, "end": 2522.27, "word": " الأقواس", "probability": 0.9522705078125}, {"start": 2522.27, "end": 2523.01, "word": " فمعنى", "probability": 0.94228515625}, {"start": 2523.01, "end": 2523.21, "word": " ذلك", "probability": 0.98876953125}, {"start": 2523.21, "end": 2523.35, "word": " ان", "probability": 0.43212890625}, {"start": 2523.35, "end": 2523.59, "word": " for", "probability": 0.86474609375}, {"start": 2523.59, "end": 2523.85, "word": " all", "probability": 0.9375}, {"start": 2523.85, "end": 2524.11, "word": " هنا", "probability": 0.9384765625}, {"start": 2524.11, "end": 2524.51, "word": " لل", "probability": 0.73291015625}, {"start": 2524.51, "end": 2524.83, "word": " P", "probability": 0.4931640625}, {"start": 2524.83, "end": 2525.09, "word": " لل", "probability": 0.70458984375}, {"start": 2525.09, "end": 2525.35, "word": " X", "probability": 0.91455078125}, {"start": 2525.35, "end": 2525.53, "word": " بتاعة", "probability": 0.7427571614583334}, {"start": 2525.53, "end": 2525.83, "word": " P", "probability": 0.63818359375}, {"start": 2525.83, "end": 2526.29, "word": " فقط", "probability": 0.99169921875}, {"start": 2526.29, "end": 2527.69, "word": " هذه", "probability": 0.82763671875}, {"start": 2527.69, "end": 2528.43, "word": " outside", "probability": 0.654296875}, {"start": 2528.43, "end": 2530.49, "word": " ال", "probability": 0.822265625}, {"start": 2530.49, "end": 2531.25, "word": " quantifier", "probability": 0.959716796875}, {"start": 2531.25, "end": 2532.17, "word": " خارج", "probability": 0.9694010416666666}, {"start": 2532.17, "end": 2532.27, "word": " ال", "probability": 0.95068359375}, 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8592, 8978, 11296, 37893, 28820, 3660, 12399, 5472, 12399, 7006, 12399, 3714, 25513, 2407, 9566, 3660, 12399, 44381, 2423, 1783, 6055, 995, 27884, 2423, 1249, 39896, 1737, 12399, 29538, 19446, 30767, 6027, 2655, 1737], "avg_logprob": -0.22688802114377418, "compression_ratio": 1.2847222222222223, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2539.57, "end": 2539.95, "word": "ليش", "probability": 0.876953125}, {"start": 2539.95, "end": 2540.11, "word": " not", "probability": 0.7001953125}, {"start": 2540.11, "end": 2541.29, "word": " proposition؟", "probability": 0.73486328125}, {"start": 2541.29, "end": 2541.65, "word": " لأن", "probability": 0.88427734375}, {"start": 2541.65, "end": 2542.37, "word": " ال", "probability": 0.71728515625}, {"start": 2542.37, "end": 2542.69, "word": " X", "probability": 0.6162109375}, {"start": 2542.69, "end": 2543.19, "word": " هذه", "probability": 0.62646484375}, {"start": 2543.19, "end": 2545.31, "word": " okay", "probability": 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القادمة ان شاء الله تعالى لان ممكن تصلني تجيني بهذا الشكل و بده اعملها proving بده فكها لما نفكها كل ما عارفين ان for all معناته ان P of X هي P of واحد", "tokens": [4117, 45865, 3794, 2423, 4426, 23463, 8717, 36178, 25724, 12984, 3660, 44945, 28543, 2288, 8717, 2655, 3615, 10943, 1211, 20449, 11296, 9122, 2655, 3615, 16572, 5172, 9307, 4032, 8717, 5172, 4117, 11296, 4032, 8717, 14851, 9778, 40448, 11296, 20193, 5016, 4587, 995, 8978, 2423, 27221, 13672, 1829, 39896, 30544, 32767, 5016, 46958, 2288, 9307, 8315, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 5296, 7649, 3714, 43020, 6055, 36520, 22653, 6055, 7435, 9957, 1829, 39627, 15730, 25124, 28820, 4032, 47525, 3224, 1975, 25957, 1211, 11296, 27221, 47525, 3224, 6156, 4117, 11296, 5296, 15042, 8717, 5172, 4117, 11296, 28242, 19446, 6225, 9640, 5172, 9957, 16472, 337, 439, 20449, 8315, 47395, 16472, 430, 295, 1783, 39896, 430, 295, 36764, 24401], "avg_logprob": -0.1810433894149528, "compression_ratio": 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"temperature": 1.0}, {"id": 115, "seek": 278172, "start": 2755.72, "end": 2781.72, "text": "or مكمل صح هيدي مورجان فإذا الصيغة هذه الأن أصبح there exist لأنه or بس there exist لمين ل negation ال bees هدولة معناته صارت negation bees لل X ال X شملت لنا ال A والB والC والD كله", "tokens": [284, 3714, 24793, 1211, 20328, 5016, 39896, 16254, 3714, 13063, 7435, 7649, 6156, 28814, 15730, 31767, 1829, 17082, 3660, 29538, 16247, 1863, 5551, 9381, 49628, 456, 2514, 5296, 33456, 3224, 420, 4724, 3794, 456, 2514, 32767, 9957, 5296, 2485, 399, 2423, 17511, 8032, 3215, 12610, 3660, 20449, 8315, 47395, 20328, 9640, 2655, 2485, 399, 17511, 24976, 1783, 2423, 1783, 13412, 42213, 2655, 5296, 8315, 2423, 316, 16070, 33, 16070, 34, 16070, 35, 28242, 3224], "avg_logprob": -0.26416667461395266, "compression_ratio": 1.4863387978142077, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 2755.72, "end": 2756.18, "word": "or", "probability": 0.521484375}, {"start": 2756.18, "end": 2757.72, "word": " 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"word": " or", "probability": 0.9189453125}, {"start": 2766.64, "end": 2768.4, "word": " بس", "probability": 0.93994140625}, {"start": 2768.4, "end": 2768.62, "word": " there", "probability": 0.88916015625}, {"start": 2768.62, "end": 2769.0, "word": " exist", "probability": 0.955078125}, {"start": 2769.0, "end": 2769.48, "word": " لمين", "probability": 0.738525390625}, {"start": 2769.48, "end": 2769.94, "word": " ل", "probability": 0.7978515625}, {"start": 2769.94, "end": 2770.74, "word": " negation", "probability": 0.75732421875}, {"start": 2770.74, "end": 2772.28, "word": " ال", "probability": 0.90185546875}, {"start": 2772.28, "end": 2772.52, "word": " bees", "probability": 0.580078125}, {"start": 2772.52, "end": 2773.42, "word": " هدولة", "probability": 0.847900390625}, {"start": 2773.42, "end": 2774.04, "word": " معناته", "probability": 0.9443359375}, {"start": 2774.04, "end": 2774.36, "word": " صارت", "probability": 0.9500325520833334}, {"start": 2774.36, "end": 2775.06, "word": 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"end": 2944.88, "word": " كل", "probability": 0.90185546875}, {"start": 2944.88, "end": 2944.98, "word": " اللي", "probability": 0.990478515625}, {"start": 2944.98, "end": 2945.34, "word": " بهمك", "probability": 0.9695638020833334}, {"start": 2945.34, "end": 2945.46, "word": " إن", "probability": 0.6865234375}, {"start": 2945.46, "end": 2945.74, "word": " X", "probability": 0.8779296875}, {"start": 2945.74, "end": 2945.9, "word": " هي", "probability": 0.9462890625}, {"start": 2945.9, "end": 2946.22, "word": " universe", "probability": 0.55859375}, {"start": 2946.22, "end": 2946.38, "word": " of", "probability": 0.96728515625}, {"start": 2946.38, "end": 2946.84, "word": " discourse", "probability": 0.83203125}, {"start": 2946.84, "end": 2947.48, "word": " اللي", "probability": 0.97998046875}, {"start": 2947.48, "end": 2948.0, "word": " هيفرجهم", "probability": 0.9228515625}, {"start": 2948.0, "end": 2948.18, "word": " عن", "probability": 0.98095703125}, {"start": 2948.18, "end": 2948.78, "word": " بعض", "probability": 0.996337890625}, {"start": 2948.78, "end": 2950.18, "word": " طبيعة", "probability": 0.962890625}, {"start": 2950.18, "end": 2950.42, "word": " ال", "probability": 0.8662109375}, {"start": 2950.42, "end": 2950.9, "word": " predicate", "probability": 0.84765625}, {"start": 2950.9, "end": 2951.38, "word": " نفسه", "probability": 0.9973958333333334}], "temperature": 1.0}, {"id": 122, "seek": 297024, "start": 2953.22, "end": 2970.24, "text": "ما هو الـ predicate بالظبط؟ Like و لا rely on و لا ايش بالظبط طبيعته الـ Q هنا مختلفة عن ال P لكن توزيع ال quantifier للكل بنفس الألية for all لل P و لل Q", "tokens": [15042, 31439, 2423, 39184, 3852, 8700, 20666, 19913, 3555, 9566, 22807, 1743, 4032, 20193, 10687, 322, 4032, 20193, 1975, 1829, 8592, 20666, 19913, 3555, 9566, 23032, 21292, 34268, 3224, 2423, 39184, 1249, 34105, 3714, 46456, 46538, 3660, 18871, 2423, 430, 44381, 33427, 11622, 40228, 2423, 4426, 9902, 24976, 28820, 44945, 36178, 16247, 1211, 10632, 337, 439, 24976, 430, 4032, 24976, 1249], "avg_logprob": -0.3336693529159792, "compression_ratio": 1.401197604790419, "no_speech_prob": 0.0, "words": [{"start": 2953.22, "end": 2953.5, "word": "ما", "probability": 0.326904296875}, {"start": 2953.5, "end": 2953.58, "word": " هو", "probability": 0.5263671875}, {"start": 2953.58, "end": 2953.72, "word": " الـ", "probability": 0.47998046875}, {"start": 2953.72, "end": 2954.04, "word": " predicate", "probability": 0.5751953125}, {"start": 2954.04, "end": 2954.98, "word": " بالظبط؟", "probability": 0.84521484375}, {"start": 2954.98, "end": 2955.4, "word": " Like", "probability": 0.1641845703125}, {"start": 2955.4, "end": 2955.64, "word": " و", "probability": 0.28369140625}, {"start": 2955.64, "end": 2955.84, "word": " لا", "probability": 0.97705078125}, {"start": 2955.84, "end": 2956.44, "word": " rely", "probability": 0.7958984375}, {"start": 2956.44, "end": 2956.88, "word": " on", "probability": 0.953125}, {"start": 2956.88, "end": 2957.32, "word": " و", "probability": 0.21435546875}, {"start": 2957.32, "end": 2957.44, "word": " لا", "probability": 0.98681640625}, {"start": 2957.44, "end": 2957.62, "word": " ايش", "probability": 0.6941731770833334}, {"start": 2957.62, "end": 2958.0, "word": " بالظبط", "probability": 0.974853515625}, {"start": 2958.0, "end": 2958.72, "word": " طبيعته", "probability": 0.9775390625}, {"start": 2958.72, "end": 2959.1, "word": " الـ", "probability": 0.480712890625}, {"start": 2959.1, "end": 2959.28, "word": " Q", "probability": 0.53662109375}, {"start": 2959.28, "end": 2959.44, "word": " هنا", "probability": 0.8408203125}, {"start": 2959.44, "end": 2959.94, "word": " مختلفة", "probability": 0.9822998046875}, {"start": 2959.94, "end": 2960.08, "word": " عن", "probability": 0.90673828125}, {"start": 2960.08, "end": 2960.32, "word": " ال", "probability": 0.90625}, {"start": 2960.32, "end": 2960.52, "word": " P", "probability": 0.70068359375}, {"start": 2960.52, "end": 2961.32, "word": " لكن", "probability": 0.82275390625}, {"start": 2961.32, "end": 2963.12, "word": " توزيع", "probability": 0.84326171875}, {"start": 2963.12, "end": 2963.5, "word": " ال", "probability": 0.91552734375}, {"start": 2963.5, "end": 2964.26, "word": " quantifier", "probability": 0.891845703125}, {"start": 2964.26, "end": 2965.92, "word": " للكل", "probability": 0.6943359375}, {"start": 2965.92, "end": 2966.66, "word": " بنفس", "probability": 0.96240234375}, {"start": 2966.66, "end": 2967.0, "word": " الألية", "probability": 0.73046875}, {"start": 2967.0, "end": 2967.22, "word": " for", "probability": 0.82763671875}, {"start": 2967.22, "end": 2967.52, "word": " all", "probability": 0.9384765625}, {"start": 2967.52, "end": 2968.0, "word": " لل", "probability": 0.78173828125}, {"start": 2968.0, "end": 2969.6, "word": " P", "probability": 0.88720703125}, {"start": 2969.6, "end": 2969.8, "word": " و", "probability": 0.62060546875}, {"start": 2969.8, "end": 2969.94, "word": " لل", "probability": 0.6845703125}, {"start": 2969.94, "end": 2970.24, "word": " Q", "probability": 0.9189453125}], "temperature": 1.0}, {"id": 123, "seek": 299125, "start": 2972.11, "end": 2991.25, "text": "الأقواس هي ال priority هي اللى بتعطيك ال priority بالظبط و بتعطيك مفهوم الفكرة تبعتك بالظبط تمام فهنا هي عملية التوزيع اللى بنتكلم عنها بنكمل المرة القادمة ان شاء الله تعالى عشان نعرف quantifier جديد و ننهي في محاضرتنا المرة الجاية ان شاء الله يعطيكوا العافية", "tokens": [6027, 10721, 4587, 14407, 3794, 39896, 2423, 9365, 39896, 13672, 7578, 39894, 3615, 9566, 1829, 4117, 2423, 9365, 20666, 19913, 3555, 9566, 4032, 39894, 3615, 9566, 1829, 4117, 3714, 5172, 3224, 20498, 27188, 4117, 25720, 6055, 3555, 34268, 4117, 20666, 19913, 3555, 9566, 46811, 10943, 6156, 3224, 8315, 39896, 6225, 42213, 10632, 16712, 2407, 11622, 40228, 13672, 7578, 44945, 2655, 4117, 19528, 18871, 11296, 44945, 24793, 1211, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 6225, 8592, 7649, 8717, 3615, 28480, 4426, 9902, 10874, 16254, 3215, 4032, 8717, 1863, 3224, 1829, 8978, 3714, 5016, 46958, 43500, 8315, 9673, 25720, 25724, 995, 10632, 16472, 13412, 16606, 21984, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.09046743710000976, "compression_ratio": 1.9267241379310345, "no_speech_prob": 1.049041748046875e-05, "words": [{"start": 2972.1099999999997, "end": 2972.87, "word": "الأقواس", "probability": 0.763427734375}, {"start": 2972.87, "end": 2973.49, "word": " هي", "probability": 0.9599609375}, {"start": 2973.49, "end": 2973.61, "word": " ال", "probability": 0.92529296875}, {"start": 2973.61, "end": 2974.03, "word": " priority", "probability": 0.9814453125}, {"start": 2974.03, "end": 2974.91, "word": " هي", "probability": 0.6337890625}, {"start": 2974.91, "end": 2975.05, "word": " اللى", "probability": 0.7025146484375}, {"start": 2975.05, "end": 2975.49, "word": " بتعطيك", "probability": 0.986328125}, {"start": 2975.49, "end": 2975.59, "word": " ال", "probability": 0.94482421875}, {"start": 2975.59, "end": 2975.91, "word": " priority", "probability": 0.994140625}, {"start": 2975.91, "end": 2976.29, "word": " بالظبط", "probability": 0.9931640625}, {"start": 2976.29, "end": 2976.37, "word": " و", "probability": 0.681640625}, {"start": 2976.37, "end": 2976.75, "word": " بتعطيك", "probability": 0.9599609375}, {"start": 2976.75, "end": 2977.23, "word": " مفهوم", "probability": 0.940673828125}, {"start": 2977.23, "end": 2977.81, "word": " الفكرة", "probability": 0.9869791666666666}, {"start": 2977.81, "end": 2978.79, "word": " تبعتك", "probability": 0.94091796875}, {"start": 2978.79, "end": 2979.55, "word": " بالظبط", "probability": 0.9947509765625}, {"start": 2979.55, "end": 2979.93, "word": " تمام", "probability": 0.79833984375}, {"start": 2979.93, "end": 2980.45, "word": " فهنا", "probability": 0.8728841145833334}, {"start": 2980.45, "end": 2980.59, "word": " هي", "probability": 0.5625}, {"start": 2980.59, "end": 2980.89, "word": " عملية", "probability": 0.9835611979166666}, {"start": 2980.89, "end": 2981.45, "word": " التوزيع", "probability": 0.96826171875}, {"start": 2981.45, "end": 2982.01, "word": " اللى", "probability": 0.989013671875}, {"start": 2982.01, "end": 2982.69, "word": " بنتكلم", "probability": 0.923828125}, {"start": 2982.69, "end": 2983.51, "word": " عنها", "probability": 0.994873046875}, {"start": 2983.51, "end": 2984.17, "word": " بنكمل", "probability": 0.86328125}, {"start": 2984.17, "end": 2984.47, "word": " المرة", "probability": 0.87255859375}, {"start": 2984.47, "end": 2984.83, "word": " القادمة", "probability": 0.9864908854166666}, {"start": 2984.83, "end": 2984.97, "word": " ان", "probability": 0.6337890625}, {"start": 2984.97, "end": 2985.05, "word": " شاء", "probability": 0.9423828125}, {"start": 2985.05, "end": 2985.13, "word": " الله", "probability": 0.95361328125}, {"start": 2985.13, "end": 2985.51, "word": " تعالى", "probability": 0.96484375}, {"start": 2985.51, "end": 2985.79, "word": " عشان", "probability": 0.984375}, {"start": 2985.79, "end": 2986.29, "word": " نعرف", "probability": 0.9606119791666666}, {"start": 2986.29, "end": 2987.35, "word": " quantifier", "probability": 0.946533203125}, {"start": 2987.35, "end": 2987.83, "word": " جديد", "probability": 0.9814453125}, {"start": 2987.83, "end": 2987.95, "word": " و", "probability": 0.9853515625}, {"start": 2987.95, "end": 2988.25, "word": " ننهي", "probability": 0.94970703125}, {"start": 2988.25, "end": 2988.45, "word": " في", "probability": 0.9462890625}, {"start": 2988.45, "end": 2989.27, "word": " محاضرتنا", "probability": 0.93125}, {"start": 2989.27, "end": 2989.55, "word": " المرة", "probability": 0.986083984375}, {"start": 2989.55, "end": 2989.91, "word": " الجاية", "probability": 0.8380533854166666}, {"start": 2989.91, "end": 2990.07, "word": " ان", "probability": 0.8876953125}, {"start": 2990.07, "end": 2990.21, "word": " شاء", "probability": 0.994140625}, {"start": 2990.21, "end": 2990.41, "word": " الله", "probability": 0.95849609375}, {"start": 2990.41, "end": 2990.91, "word": " يعطيكوا", "probability": 0.88359375}, {"start": 2990.91, "end": 2991.25, "word": " العافية", "probability": 0.87890625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2991.5893125, "duration_after_vad": 2910.359999999984}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/50_HPAABoYI.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/50_HPAABoYI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7052662becff8747cfc50c09da8a1ce01030c7eb
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/50_HPAABoYI.srt
@@ -0,0 +1,2040 @@
+1
+00:00:04,960 --> 00:00:07,780
+السلام عليكم و رحمة الله، أقول عفوا يا شباب اليوم إن شاء
+
+2
+00:00:07,780 --> 00:00:11,500
+الله، نكمل في الـ graphs. كنا أخذنا الـ undirected
+
+3
+00:00:11,500 --> 00:00:15,820
+graph، فاليوم نكمل في الـ directed graph، و التي هي
+
+4
+00:00:15,820 --> 00:00:20,280
+مُناظرةٌ  لأي binary
+
+5
+00:00:20,280 --> 00:00:24,840
+relation، التي هي need not be symmetric،  إنها ليست
+
+6
+00:00:24,840 --> 00:00:27,880
+بالضرورة أن تكون symmetric،  مثل الـ undirected الـ
+
+7
+00:00:27,880 --> 00:00:31,780
+undirected. قلنا إن هو خط بين نقطتين، و الخط الذي بين
+
+8
+00:00:31,780 --> 00:00:35,390
+النقطتين، أو edge بين نقطتين، و الـ edge هذه في الاتجاهين
+
+9
+00:00:35,390 --> 00:00:39,930
+ماشي في الاتجاهين من الـ vertex الأولى للـ vertex
+
+10
+00:00:39,930 --> 00:00:42,370
+الثانية، أو من الـ vertex الثانية للـ vertex الأولى.
+
+11
+00:00:42,370 --> 00:00:48,200
+في الآخر هي قطعة و خلاص، بهذا الشكل. هذه كانت
+
+12
+00:00:48,200 --> 00:00:51,620
+undirected، لكن لما نقول directed، فهي مُحددة من
+
+13
+00:00:51,620 --> 00:00:56,780
+إلى. فعادة نسميها من U إلى V، الـ vertices تبعتنا U و
+
+14
+00:00:56,780 --> 00:01:02,280
+V، بتكون موجهة من إلى، فهذه نسميها directed. فطبيعي
+
+15
+00:01:02,280 --> 00:01:05,180
+لن تكون symmetric، لن تكون symmetric. لماذا؟ لأنه
+
+16
+00:01:05,180 --> 00:01:07,620
+بهذا الاتجاه، هو ليس symmetric. هي كأن صار عندي زوج
+
+17
+00:01:07,620 --> 00:01:13,730
+مرتب U و V. هل يوجد V و U؟ لا، لأن ما فيش relation
+
+18
+00:01:13,730 --> 00:01:19,210
+from V to U. هي الـ relation فعلياً from U to V. هي
+
+19
+00:01:19,210 --> 00:01:22,970
+from U to V. هذا الكلام ما كان موجود أين؟ في الـ
+
+20
+00:01:22,970 --> 00:01:25,130
+undirected. في الـ undirected أنا كنت أضعه بهذا
+
+21
+00:01:25,130 --> 00:01:29,710
+الشكل، خلاص هي الـ U و الـ V. فهذه فعلياً أقدر أقرأها U
+
+22
+00:01:29,710 --> 00:01:37,370
+to V، و أقدر أقرأها V to U.  بمشي الحال. لماذا؟ لأن ما فيش
+
+23
+00:01:37,370 --> 00:01:43,240
+اتجاه. تمام. هنا لا، صار في عندي اتجاه، و هنا الـ
+
+24
+00:01:43,240 --> 00:01:46,640
+directed graph. أقدر أسميه هو مجموعة vertices و
+
+25
+00:01:46,640 --> 00:01:51,320
+edges. و في الحالة هذه، بتحتوي على set of vertices V
+
+26
+00:01:51,320 --> 00:01:56,180
+و مجموعة edges. كل edge تمثل relation، كل edge تمثل
+
+27
+00:01:56,180 --> 00:01:59,390
+أو مجموعة الـ edges هذه هي تمثل الـ relation فعلاً.  زي
+
+28
+00:01:59,390 --> 00:02:03,050
+مثال الذي نراه بهذا الشكل. فأنت تقول عبارة
+
+29
+00:02:03,050 --> 00:02:06,850
+عن مجموعة nodes عندك، و relation بينهم، بس
+
+30
+00:02:06,850 --> 00:02:11,110
+موجهة، معروفة من إلى. و أمثلة كثيرة الحقيقة على هذا
+
+31
+00:02:11,110 --> 00:02:13,570
+الكلام، زي لو قلنا مثلاً الـ vertices بتاعتنا هي الـ
+
+32
+00:02:13,570 --> 00:02:17,770
+set of people، بكل بساطة. الـ relation loves أو likes
+
+33
+00:02:17,770 --> 00:02:22,870
+تمام؟ هي ليست symmetric. فمعنى ذلك، هذه لابد أن تكون مُحدد
+
+34
+00:02:22,870 --> 00:02:27,850
+اتجاهها: x loves y.
+
+35
+00:02:28,600 --> 00:02:36,400
+أو likes، x likes y. ليس بالضرورة أن y love أو loves
+
+36
+00:02:36,400 --> 00:02:41,680
+x. ما أحد قال ذلك. اتجاهها واضح بهذا الشكل. هل في
+
+37
+00:02:41,680 --> 00:02:46,400
+اتجاه عكسي؟ لا، ما يوجد. لابد أن يكون صراحةً موجوداً، لأن هذه
+
+38
+00:02:46,400 --> 00:02:50,740
+directed graph. فلما آتي لأُمثلها هنا، سأقول مثلاً هي x
+
+39
+00:02:50,740 --> 00:03:00,870
+و هي y، و relation love. معنى ذلك أن x loves y. طيب
+
+40
+00:03:00,870 --> 00:03:11,790
+العكس؟ لا، ما يوجد العكس. لكن لما أقول مثلاً z، y loves
+
+41
+00:03:11,790 --> 00:03:17,610
+z، و z loves y. فمعنى ذلك أن الاتجاه هنا يكون واضح
+
+42
+00:03:17,610 --> 00:03:23,590
+الاتجاه هنا واضح. فهذه الـ graph مختلفة بعض الشيء عن
+
+43
+00:03:25,450 --> 00:03:28,830
+الـ undirected graph. طيب، directed multigraph، نفس
+
+44
+00:03:28,830 --> 00:03:31,510
+الفكرة، و زي ما أخذنا سابقاً، بيكون عندي أكثر من
+
+45
+00:03:31,510 --> 00:03:36,170
+path، حتى لو في نفس الاتجاه، حتى لو في نفس الاتجاه.
+
+46
+00:03:36,170 --> 00:03:39,770
+فهنا نتكلم عن هي نقطتين، نقطة من هنا لنقطة من هنا،
+
+47
+00:03:39,770 --> 00:03:42,990
+نفس الاتجاه، هو هو. ليس بالضروري أن هو يعني واحد رايح
+
+48
+00:03:42,990 --> 00:03:45,790
+واحد جاي. فأقول والله هي symmetric؟ لا، هي ليست
+
+49
+00:03:45,790 --> 00:03:51,840
+symmetric. هي multigraph. هي multigraph و بس. طيب، زي
+
+50
+00:03:51,840 --> 00:03:54,000
+الـ directed graph، زي ما قلنا، لكن ممكن يكون عندي
+
+51
+00:03:54,000 --> 00:03:59,580
+أكثر من one arc بين two points، أو from U to V، from
+
+52
+00:03:59,580 --> 00:04:05,800
+X to Y، أكثر من one arc، أو أكثر من one edge. فمع
+
+53
+00:04:05,800 --> 00:04:10,780
+ذلك، الرسم يُعبّر عنه بمجموعة، أو set of vertices و
+
+54
+00:04:10,780 --> 00:04:17,520
+مجموعة edges، و function لِجديش عدد كل edge، جديش
+
+55
+00:04:17,520 --> 00:04:22,040
+عددهم: اثنين، ثلاثة، خمسة، عشرة، وهنا الـ...الـ...
+
+56
+00:04:22,040 --> 00:04:33,280
+الـ...الـ in غير الـ out، ماشي.
+
+57
+00:04:33,280 --> 00:04:36,740
+بس احنا، ليس معنى ذلك أن هذا هيك بطلت directed.
+
+58
+00:04:36,740 --> 00:04:41,280
+احنا بنتكلم in general، ككل. لما تكون undirected،
+
+59
+00:04:41,280 --> 00:04:45,960
+معنى ذلك أنه حتى الخط هذا المفروض أنه بدون سهم، صح؟
+
+60
+00:04:45,960 --> 00:04:49,420
+و الخط هذا بدون سهم؟ لا، أنت تتكلم عن total الـ
+
+61
+00:04:49,420 --> 00:04:52,700
+graph كله على بعضه. أنا ما أبطلش لمجرد أنه في
+
+62
+00:04:52,700 --> 00:04:57,940
+self loop، أو ما فيش self loop. لا، تقدر تصنفها إيش
+
+63
+00:04:57,940 --> 00:05:03,600
+direct ولا indirect؟ لا، لا، لا. هي direct، هذه
+
+64
+00:05:03,600 --> 00:05:06,480
+directed graph. لماذا directed graph؟ لأنها فيها
+
+65
+00:05:06,480 --> 00:05:13,020
+أجزاء واضح اتجاهها، اتجاهها واضح. طب مثال، خلاص
+
+66
+00:05:13,020 --> 00:05:16,300
+اتفقنا أن الـ F هذه في النهاية هي تُعبّر عن الـ edges
+
+67
+00:05:16,300 --> 00:05:20,620
+هذه، كويس؟ جديش عددها بين الـ vertices؟ طيب، لو أخذنا
+
+68
+00:05:20,620 --> 00:05:23,380
+مثلاً الـ web pages، الـ web pages، و هي أنت عامل
+
+69
+00:05:23,380 --> 00:05:26,840
+hyperlinks. أنت ممكن تعمل من نفس الصفحة اثنين
+
+70
+00:05:26,840 --> 00:05:29,890
+hyperlink لصفحة ثانية. بس هل بالضرورة الصفحة الثانية
+
+71
+00:05:29,890 --> 00:05:33,630
+ترجعك على الصفحة الأولى؟ ما أحد قال...أنت عملت لك
+
+72
+00:05:33,630 --> 00:05:38,770
+web page، الـ web page هذه، عامل فيها شوية معلومات
+
+73
+00:05:38,770 --> 00:05:43,150
+جيدة و حلوة، و عامل hyperlink لحاجة، التي هي علاقة
+
+74
+00:05:43,150 --> 00:05:46,410
+بالويكيبيديا. ما هي المَرجّح الأساسي الذي كل الطلاب
+
+75
+00:05:46,410 --> 00:05:51,450
+صاروا يستخدمونه هذه الأيام؟ صحيح، بطلوا...لا يريدون كتب، لا يريدون مذ...
+
+76
+00:05:51,450 --> 00:05:54,390
+...مذكرة، ولا يريدون أي شيء...هي الويكيبيديا. أيش ما
+
+77
+00:05:54,390 --> 00:05:58,360
+بتقول، معناته صح، تمام. فأنت عملت لك link على الـ
+
+78
+00:05:58,360 --> 00:06:02,560
+wikipedia لكلمة مثلاً computer. بدك تعرفي الـ
+
+79
+00:06:02,560 --> 00:06:05,700
+computer، فعملت لها link. بعد شوية لتحت كمان كلمة
+
+80
+00:06:05,700 --> 00:06:08,560
+computer، و ذهبت عملت لها كمان link. هذه صارت إيش؟ هذه
+
+81
+00:06:08,560 --> 00:06:13,060
+multi. بس هل من الضروري أن الـ wikipedia ترجع لك، تعمل لك
+
+82
+00:06:13,060 --> 00:06:16,540
+بالعكس، آخذة منك أو تعمل لك hyperlink لصفحتك؟ ليس
+
+83
+00:06:16,540 --> 00:06:20,240
+بالضرورة. فهنا directed، okay. أنت ممكن تعمل من صفحتك
+
+84
+00:06:20,240 --> 00:06:24,900
+لصفحتك. زي لما...زي لما تصل لآخر الصفحة تحت، و تعمل
+
+85
+00:06:24,900 --> 00:06:27,680
+لك up. مش هيك بتلاقي السهم بيعمل لك up، إذا كانت
+
+86
+00:06:27,680 --> 00:06:30,280
+الصفحة طويلة، اعمل عليها. أنت ظليت في نفس مكانك،
+
+87
+00:06:30,280 --> 00:06:38,420
+أنت ظليت في نفس الصفحة. أنت
+
+88
+00:06:38,420 --> 00:06:41,080
+تتكلم هيك عن الحالة الخاصة، لا، الـ self loop لحاله،
+
+89
+00:06:41,080 --> 00:06:45,920
+الـ self loop لحاله. in general، أنت لما تتكلم بشكل
+
+90
+00:06:45,920 --> 00:06:48,820
+مُخصص كثير، أنت الذي تتحدث، لكن in general لا أقدر
+
+91
+00:06:48,820 --> 00:06:53,080
+أقول كلامك. لماذا؟ لأنه ببساطة جداً، دعني أفترض أنه
+
+92
+00:06:53,080 --> 00:06:56,700
+أنا بدي أطلع من...من أين نريد أن نخرج؟ دعني أقول
+
+93
+00:06:56,700 --> 00:07:01,160
+نريد أن نخرج من...إيش اسم هذه المنطقة هناك؟ من
+
+94
+00:07:01,160 --> 00:07:06,280
+معسكر الشاطئ على البحر، كويس؟ أنا ما زلت في غزة، و مشيت
+
+95
+00:07:06,280 --> 00:07:09,820
+البحر هذا، و البحر هذا مسدود باتجاه العكس تبعه، فأنا
+
+96
+00:07:09,820 --> 00:07:14,120
+ماشي في اتجاه واحد، صح؟ هي اتجاه واحد ماشي فيه، و ظليت
+
+97
+00:07:14,120 --> 00:07:17,660
+ماشي فيه، وعند تل الهوى، رجعت دخلت على غزة. أنت خرجت
+
+98
+00:07:17,660 --> 00:07:21,740
+من المدينة؟ ما خرجت. طيب، الـ self-loop هذا الذي أنت
+
+99
+00:07:21,740 --> 00:07:24,340
+...الذي يُعتبر self-loop هكذا، صح؟ هذا self-loop
+
+100
+00:07:24,340 --> 00:07:30,860
+واضح. هل هو undirected؟ أكيد، لا، أكيد directed. لماذا؟
+
+101
+00:07:30,860 --> 00:07:33,500
+خصوصاً زي ما قلت لك، يُعملون أعمال صيانة أو شيء، فهم
+
+102
+00:07:33,500 --> 00:07:38,060
+سدوا الرجعة. أنت رايح بس في اتجاه واحد. طب هي،
+
+103
+00:07:38,060 --> 00:07:42,610
+رغم أنه self-loop، وعلى مثال واقعي، على مثل
+
+104
+00:07:42,610 --> 00:07:45,770
+واقعي على مدن، الذي هو عادة يُسمى خارج الطريق
+
+105
+00:07:45,770 --> 00:07:48,810
+الدائري، الذي هو من نفس البلد لنفس البلد، إذا كانت
+
+106
+00:07:48,810 --> 00:07:52,410
+المدينة كبيرة، عادةً برا يُعملون لهم جسور، التي هي
+
+107
+00:07:52,410 --> 00:07:57,110
+المحور، المحوري، الذي هو من أول، من شرق المدينة لغرب
+
+108
+00:07:57,110 --> 00:07:59,770
+المدينة مثلاً، يُعمل لك طريق خارجي، بدل ما تدخل في نفس
+
+109
+00:07:59,770 --> 00:08:01,990
+البلد. إذا أنت فيه، ده بيطلع من الطرف للطرف. هذا
+
+110
+00:08:01,990 --> 00:08:05,310
+ممكن جداً يكون عامل لك طريقين، واحد رايح، واحد جاي، بس
+
+111
+00:08:05,310 --> 00:08:10,170
+فمعنى ذلك، كل طريق هو directed graph. أنت الذي تتحدث
+
+112
+00:08:10,170 --> 00:08:13,070
+عنه هي حالة خاصة، أنه والله هما الاثنين نفس الطريق،
+
+113
+00:08:13,070 --> 00:08:17,290
+okay. أقول لك صح، لن يفرق، بس أنا ما أقدر.  نحن
+
+114
+00:08:17,290 --> 00:08:20,230
+الآن نتكلم بالعموميات، العموميات، أن في شيء اسمه
+
+115
+00:08:20,230 --> 00:08:25,630
+directed multigraph، okay. فيه، هل وجد...إيش الأمثلة
+
+116
+00:08:25,630 --> 00:08:28,190
+التي خطر على بالك؟ لا، هي...نحن نتكلم in
+
+117
+00:08:28,190 --> 00:08:31,990
+general. هي مثلاً الـ web، تختلف عن الـ cities التي توي
+
+118
+00:08:31,990 --> 00:08:34,710
+شرحت لك إياها. مثلاً أنت هكذا خرجت من غزة، و رجعت إلى
+
+119
+00:08:34,710 --> 00:08:40,140
+غزة. لكن في الطريق في أعمال، ف الطريق هو رايح، ليس
+
+120
+00:08:40,140 --> 00:08:45,340
+جاي. معنى ذلك صار directed. وعندنا طرق كثيرة تُعتبر
+
+121
+00:08:45,340 --> 00:08:49,300
+directed في غزة. ليس هكذا؟ عادة بين الوحدة و عمرو
+
+122
+00:08:49,300 --> 00:08:52,500
+المختار، تجد الشارع يا رايح يا جاي. واحد رايح، و
+
+123
+00:08:52,500 --> 00:08:54,320
+الذي بجانبه جاي. واحد رايح، و الذي بجانبه، بجانبه ليس
+
+124
+00:08:54,320 --> 00:08:55,280
+هكذا directed.
+
+125
+00:08:58,380 --> 00:09:10,800
+طيب، فهي مثال على الـ multi-directed، okay.  فضل أقول لك
+
+126
+00:09:10,800 --> 00:09:13,900
+ببساطة جداً، نحن توّ نتكلمنا مثلاً عن المدن، هل الوقت.
+
+127
+00:09:13,900 --> 00:09:18,490
+لو تكلمت عن الجوال، و أنت تريد أن تعمل الـ... تريد أن تعمل الـ
+
+128
+00:09:18,490 --> 00:09:26,050
+و أنت ماشي، هل أنت ضامن أنه ليس سيحدث عندك hangover،
+
+129
+00:09:26,050 --> 00:09:31,270
+بمعنى أنك أنت تتبدل من شبكة لشبكة، تصير و أنت
+
+130
+00:09:31,270 --> 00:09:34,890
+تتكلم عادي جداً. طيب، الحاجة الأوضح منها، لما تريد
+
+131
+00:09:34,890 --> 00:09:37,910
+أن تُرسل message، و الـ message تبعك طالت شوية، يعني
+
+132
+00:09:37,910 --> 00:09:42,270
+كبرت حجمها أكثر من الـ 64 character باللغة العربية،
+
+133
+00:09:42,270 --> 00:09:45,990
+أو 128 باللغة الإنجليزية، زادت عن هيك، ليس يُجزّئها
+
+134
+00:09:45,990 --> 00:09:50,050
+إليها two SMS. طيب، الـ two SMS هذول لما تُرسلهم، هل هما
+
+135
+00:09:50,050 --> 00:09:54,410
+الاثنين يذهبان بنفس الـ path؟ ليس بالضرورة...ليس
+
+136
+00:09:54,410 --> 00:09:58,350
+بالضرورة. ممكن واحدة تجد path، و الـ traffic تبعها
+
+137
+00:09:58,350 --> 00:10:02,070
+عالي...كبير، و الثانية، خلاص مادام عرفت أنه في
+
+138
+00:10:02,070 --> 00:10:05,830
+traffic مُسْحُوم في هذا الاتجاه، تأخذ طريق ثاني...
+
+139
+00:10:05,830 --> 00:10:10,490
+تأخذ طريق ثاني من...يُسميها business station
+
+140
+00:10:10,490 --> 00:10:12,650
+ثانية، في عندك business station هنا، و business
+
+141
+00:10:12,650 --> 00:10:15,380
+station هنا. واحدة خرجت هنا، واحدة خرجت هنا، و الاثنين
+
+142
+00:10:15,380 --> 00:10:18,160
+ذهبا على نفس الجهاز. الآن لو وصلت الثانية، جلبت لي
+
+143
+00:10:18,160 --> 00:10:20,440
+الأولى، تستني. فأنت يأتيك message، بالـ system ليس
+
+144
+00:10:20,440 --> 00:10:24,740
+عارف يفتحها، يصير معك...لما تصل الأولى، و يعمل
+
+145
+00:10:24,740 --> 00:10:28,300
+reconstruction إليها، تُفتح معك الـ message. هذا
+
+146
+00:10:28,300 --> 00:10:32,100
+يصير واقعي فعلياً. هي multi، هي واحدة من الحالات
+
+147
+00:10:32,100 --> 00:10:35,700
+التي بت...واضحة فيها جثة الـ multi...جثة الـ multi
+
+148
+00:10:39,770 --> 00:10:44,310
+تمام. فجدول يُعمل summarization. دعنا نسميها، نقول
+
+149
+00:10:44,310 --> 00:10:48,190
+في عندي الـ symbol، نتكلم، هي undirected multi؟ لا،
+
+150
+00:10:48,190 --> 00:10:50,770
+هي ليست multi، self-loop؟ لا، هي ليست self-loop. الـ
+
+151
+00:10:50,770 --> 00:10:54,860
+multigraph تبعها، هي undirected. كويس؟ هذا طبعاً في
+
+152
+00:10:54,860 --> 00:10:58,180
+أين الـ multigraph، ل...الـ symbol multigraph. ه بس
+
+153
+00:10:58,180 --> 00:11:00,820
+بدون ما أقول directed، بدون ما أحكي أنها directed.
+
+154
+00:11:00,820 --> 00:11:04,900
+هذه معنى ذلك automatically أعرف أنها undirected.
+
+155
+00:11:04,900 --> 00:11:09,020
+فيها multi؟ اه، هي أصلاً اسمها multi. self-loop؟ لا.
+
+156
+00:11:09,020 --> 00:11:13,760
+تمام. الـ pseudo graph، هي undirected، لكن فيها multi،
+
+157
+00:11:13,760 --> 00:11:18,460
+و فيها self-loop. الـ directed graph، لا، لابد أن أميز
+
+158
+00:11:18,460 --> 00:11:22,130
+كلمة directed، لأقول أنها فعلاً directed. إذا ما
+
+159
+00:11:22,130 --> 00:11:25,250
+كتبتها، معناته أنا أتحدث عن undirected. نتكلم
+
+160
+00:11:25,250 --> 00:11:28,710
+undirected. أوي، كويسة. هل multi؟ لا، هل self؟ اه.
+
+161
+00:11:28,710 --> 00:11:31,690
+ممكن تكون self. فـ directed تأخذ self، directed
+
+162
+00:11:31,690 --> 00:11:34,570
+تأخذ self loop. طيب، directed multigraph، okay،
+
+163
+00:11:34,570 --> 00:11:38,450
+تأخذ الاثنين. هي ممكن يكون فيها multi، و ممكن
+
+164
+00:11:38,450 --> 00:11:44,600
+يكون فيها self loop. تمام. هذه كانت الجزئية التي باقية
+
+165
+00:11:44,600 --> 00:11:47,600
+من المرة الماضية، لأ نكون حددنا مجموعة أنواع من
+
+166
+00:11:47,600 --> 00:11:51,420
+أنواع الشبكات. الآن لأ نكمل شغلنا، نحتاج شوية
+
+167
+00:11:51,420 --> 00:11:57,180
+terminology نتكلم عنها للـ graphs، خاصة بالـ graphs
+
+168
+00:11:57,180 --> 00:12:01,080
+نفسها. فحنا نتكلم عن مجموعة الـ terms، نحتاجها: الـ
+
+169
+00:12:01,080 --> 00:12:05,400
+adjacent، الـ connect، الـ connects، الـ end points، إيش
+
+170
+00
+
+223
+00:16:09,390 --> 00:16:13,250
+degree ل .. لـ الـ V احنا عملناها لـ الـ V بدل الـ U مش
+
+224
+00:16:13,250 --> 00:16:17,370
+مشكلة لـ V أو لـ .. لـ U طيب إذا كان في عندك self
+
+225
+00:16:17,370 --> 00:16:22,170
+loop هيها نحسبها
+
+226
+00:16:22,170 --> 00:16:27,800
+اتنين هي واحدة اتنين تلاتة undirected معناه ذلك أن
+
+227
+00:16:27,800 --> 00:16:30,860
+هذه طريقة وهذه طريقة وهذه طريقة في عندي تلاتة فهنا
+
+228
+00:16:30,860 --> 00:16:34,200
+بتصير الـ degree بتاعتها تلاتة طيب الـ vertex with
+
+229
+00:16:34,200 --> 00:16:41,400
+degree zero بنسميها isolated صح منفصلة هايمعلجة طب
+
+230
+00:16:41,400 --> 00:16:46,480
+جداش الـ degree بتاع الـ zero فهي isolated منفصلة
+
+231
+00:16:46,480 --> 00:16:52,780
+مفصولة عن الباقي أما إذا كانت كيف اه طبعا هي تنتمل
+
+232
+00:16:52,780 --> 00:16:57,990
+الـ graph اه تنتمل الـ graph صار عندك انهيار معين في
+
+233
+00:16:57,990 --> 00:17:02,550
+بلد وقرية أو مدينة انقطع الخط طبعا وصار لسه
+
+234
+00:17:02,550 --> 00:17:04,970
+بدهم يعملوا إصلاحات وبدهم ست شهور هم بيصلحوا هل
+
+235
+00:17:04,970 --> 00:17:07,930
+معنى ذلك أُبيحها من البلد؟ لأ ما هي منتمية ما زالت
+
+236
+00:17:07,930 --> 00:17:12,050
+للبلد هي ما زالت جزء منكم جزء من الـ .. الـ .. الـ
+
+237
+00:17:12,050 --> 00:17:15,510
+graph أو من الـ map هي ما زالت جزء من الـ map ما
+
+238
+00:17:15,510 --> 00:17:18,590
+بقدر أقول لأ لأ لأ هذه برة نائية معناته بديش ياها
+
+239
+00:17:18,590 --> 00:17:23,150
+معناته كان كل قرية نائية في دول العربية كان
+
+240
+00:17:23,150 --> 00:17:27,790
+بيقنها يعني لأ تبقى موجودة مع الـ graph طيب الـ
+
+241
+00:17:27,790 --> 00:17:33,350
+vertex of degree one بنسميها pendent معلقة زي ..
+
+242
+00:17:33,350 --> 00:17:35,630
+زي .. زي .. زي .. زي .. زي .. زي .. زي .. زي .. زي
+
+243
+00:17:35,630 --> 00:17:35,830
+.. زي .. زي .. زي .. زي .. زي .. زي .. زي .. زي ..
+
+244
+00:17:35,830 --> 00:17:38,850
+زي .. زي .. زي .. زي .. زي .. زي .. زي .. زي .. زي
+
+245
+00:17:38,850 --> 00:17:42,290
+.. زي .. زي .. زي .. زي .. زي .. زي .. زي .. زي ..
+
+246
+00:17:42,290 --> 00:17:42,930
+زي .. زي .. زي .. زي .. زي .. زي .. زي .. زي .. زي
+
+247
+00:17:42,930 --> 00:17:52,590
+.. زي .. زي .. زي .. زي .. ز تمام طيب الـ hand
+
+248
+00:17:52,590 --> 00:17:57,650
+shaking theorem اللي هي علاقة جداش مجموع الـ
+
+249
+00:17:57,650 --> 00:18:02,130
+degrees كلها على بعض كل الـ degrees كاملة لكل الـ
+
+250
+00:18:02,130 --> 00:18:06,290
+vertices بتاعتنا هنجد أن هي اتنين من عدد الـ edges
+
+251
+00:18:07,220 --> 00:18:10,800
+بكل بساطة اتنين من عدد الـ edges تبعتنا فهذه بقدر
+
+252
+00:18:10,800 --> 00:18:14,320
+أقول إذا بتكلم عن undirected بالأنواع كلها اللي
+
+253
+00:18:14,320 --> 00:18:17,580
+أخدناها للـ undirected بكل بساطة الـ summation لـ
+
+254
+00:18:17,580 --> 00:18:22,820
+degree V و V هذه تنتمي أو كل small V تنتمي للـ
+
+255
+00:18:22,820 --> 00:18:26,320
+capital V للست الـ vertices فكل vertex لحالها جداش الـ
+
+256
+00:18:26,320 --> 00:18:28,620
+degree اجمعها مع الـ vertex الثانية مع الـ vertex
+
+257
+00:18:28,620 --> 00:18:33,460
+الثالثة مجموعهم كلهم على بعض هيساوي اتنين من الـ
+
+258
+00:18:33,460 --> 00:18:40,540
+cardinality of 6E capital E لأنه هذه معناته أنا
+
+259
+00:18:40,540 --> 00:18:45,500
+بتكلم عن عدد الـ small e جداش عددهم داخل الـ capital
+
+260
+00:18:45,500 --> 00:18:49,640
+E فإذا عندي E1 عندي E2 عندي E3 جداش العدد في
+
+261
+00:18:49,640 --> 00:18:52,240
+النهاية معناه ذلك أني بتكلم عن الـ cardinality
+
+262
+00:18:52,240 --> 00:18:56,280
+للمصفوفة لعددهم لمجموعتهم فهي الـ cardinality
+
+263
+00:18:56,280 --> 00:18:59,040
+للمجموع فهذا هذا مش absolute هذا هنا بنتكلم عن الـ
+
+264
+00:18:59,040 --> 00:19:00,080
+cardinality لـ 6
+
+265
+00:19:04,490 --> 00:19:09,510
+طيب كاستنتاج من .. منها بقدر أقول أن معناته لأي
+
+266
+00:19:09,510 --> 00:19:14,570
+undirected graph has an even number of vertices of
+
+267
+00:19:14,570 --> 00:19:20,330
+odd degree بمعنى لما أجي أتطلع لأي graph جداش عدد
+
+268
+00:19:20,330 --> 00:19:26,810
+الـ vertices اللي الـ degree بتاعتهم odd هلاجي عددهم
+
+269
+00:19:26,810 --> 00:19:30,350
+even منطقية
+
+270
+00:19:30,350 --> 00:19:35,020
+كتير كتير لو ركزنا فيه ليش؟ أنا قاعد بتكلم إنه
+
+271
+00:19:35,020 --> 00:19:40,000
+مجموع الـ degrees اتنين يعني لازم يكون زوجي صح؟
+
+272
+00:19:40,000 --> 00:19:44,040
+مجموعهم لازم يكون زوجي يعني إذا في حالات الـ degree
+
+273
+00:19:44,040 --> 00:19:49,060
+بتاعتها فردي لازم يكون في كمان vertex ثانية برضه
+
+274
+00:19:49,060 --> 00:19:54,500
+فردي عشان يكون المجموع زوجي فمجموع الـ degree
+
+275
+00:19:54,500 --> 00:20:00,930
+بتاعتهم odd degree لازم يكون كعدد زوجي صح؟ عشان لما
+
+276
+00:20:00,930 --> 00:20:06,030
+أجي أجمع فعلا ينطبق مع أنه 2 في كذا أنا ما أتكلمش
+
+277
+00:20:06,030 --> 00:20:08,490
+عن عدد الـ edges الـ edges يمكن يطلع فردي وهو حر بس
+
+278
+00:20:08,490 --> 00:20:11,130
+أنا ايه العلاقة بالـ total الـ total مضروب في 2 يعني
+
+279
+00:20:11,130 --> 00:20:16,850
+معناه ذلك أنه دائما هذا زوجي صح؟ هل معناه ذلك أنه
+
+280
+00:20:16,850 --> 00:20:19,190
+بدي أجي أقول هذه degree بتاعتها واحد لأ ما ينفعش
+
+281
+00:20:19,190 --> 00:20:22,250
+طب ما أخليها odd ايش المشكلة بس أنت ضامن أن الـ odd
+
+282
+00:20:22,250 --> 00:20:25,690
+هذه في odd ثانية هتشبرها عشان يصيروا زوجي مع بعض
+
+283
+00:20:25,690 --> 00:20:31,580
+واضحة؟ هي معنى الاشتقاق .. أو اللي هو النظرية
+
+284
+00:20:31,580 --> 00:20:35,400
+الإضافية هذه اللي طلعت من وراء القانون هلو أنا
+
+285
+00:20:35,400 --> 00:20:39,880
+تعالى نشوف هنا عندك واحد وهذول اتنين خليني أكتبهم
+
+286
+00:20:39,880 --> 00:20:43,340
+ايش الألوان اللي ضايلة هنا واحد هنا اتنين هنا
+
+287
+00:20:43,340 --> 00:20:46,640
+اتنين هنا عندك واحد اتنين تلاتة أربعة هاي أربعة
+
+288
+00:20:46,640 --> 00:20:54,260
+وهي هذه واحد شوفي كم واحدة فردية نتين فردية زوجي
+
+289
+00:20:54,260 --> 00:20:58,500
+يعني عددهم معادتهم زوجي عشان أضمن لما أجمع يطلع في
+
+290
+00:20:58,500 --> 00:21:07,680
+النهاية الـ total عشان أضمن
+
+291
+00:21:07,680 --> 00:21:09,020
+لما أجمع يطلع في النهاية الـ total عشان أضمن لما
+
+292
+00:21:09,020 --> 00:21:10,160
+أجمع يطلع في النهاية الـ total عشان أضمن لما أجمع
+
+293
+00:21:10,160 --> 00:21:12,240
+يطلع في النهاية الـ total عشان أضمن لما أجمع يطلع
+
+294
+00:21:12,240 --> 00:21:12,820
+في النهاية الـ total عشان أضمن لما أجمع يطلع في
+
+295
+00:21:12,820 --> 00:21:13,420
+النهاية الـ total عشان أضمن لما أجمع يطلع في
+
+296
+00:21:13,420 --> 00:21:14,180
+النهاية الـ total عشان أضمن لما أجمع يطلع في
+
+297
+00:21:14,180 --> 00:21:17,300
+النهاية الـ total عشان أضمن لما أجمع يطلع في النها
+
+298
+00:21:21,650 --> 00:21:25,130
+هي واحدة هي اتنين هي تلاتة هي أربعة هي خمسة خمسة في
+
+299
+00:21:25,130 --> 00:21:31,530
+اتنين عشر هي خمسة في اتنين عشر ففعليا الـ edges
+
+300
+00:21:31,530 --> 00:21:35,130
+مضروبة في اتنين بيطلع مجموع الـ total لكل الـ
+
+301
+00:21:35,130 --> 00:21:38,840
+degrees لـ الـ vertices بتاعتنا طيب الـ directed
+
+302
+00:21:38,840 --> 00:21:42,900
+graph أو الـ directed adjacency فالـ adjacent لـ الـ
+
+303
+00:21:42,900 --> 00:21:45,280
+directed graph ما كنا قولناه adjacent ولـ directed
+
+304
+00:21:45,280 --> 00:21:50,200
+graph وخلاص لازم نجيب الـ adjective تبعتها طيب G
+
+305
+00:21:50,200 --> 00:21:54,780
+إذا كانت فعلا directed وممكن تكون حتى multi multi
+
+306
+00:21:54,780 --> 00:21:58,340
+طبعا احنا عارفين معناته أن فيها self loop multi
+
+307
+00:21:58,340 --> 00:22:01,340
+معناته فيها self loop كويس بقدر أقول إن إذا كان من
+
+308
+00:22:01,340 --> 00:22:04,880
+U to V U
+
+309
+00:22:06,490 --> 00:22:17,930
+to V في الحلقة دي ايش نقدر نقول U is adjacent to V
+
+310
+00:22:17,930 --> 00:22:26,090
+to V طيب أو V is adjacent from U فـ from معناته أنا
+
+311
+00:22:26,090 --> 00:22:30,670
+بتكلم عن هذه البداية to هتكون النهاية هتكون
+
+312
+00:22:30,670 --> 00:22:39,400
+النهاية طيب E comes from U صحيح؟ E هي جاية من U
+
+313
+00:22:39,400 --> 00:22:46,700
+فعليا طيب وهي goes to V هي رايحة لـ V طيب E
+
+314
+00:22:46,700 --> 00:22:52,680
+connects U to V واضحة يعني حتى كل المصطلحات واضحة
+
+315
+00:22:52,680 --> 00:22:57,440
+فيها الاتجاه واضح فيها الاتجاه E goes from U to V
+
+316
+00:22:57,440 --> 00:23:05,520
+from U to V طيب الـ the initial vertex of E is U
+
+317
+00:23:06,380 --> 00:23:09,680
+صحيح؟ الـ vertex الـ initial تبعتنا البداية بتاعتها
+
+318
+00:23:09,680 --> 00:23:16,320
+هي الـ U طيب الـ terminal vertex of E terminal
+
+319
+00:23:16,320 --> 00:23:22,560
+النهاية الـ V هي نهاية الـ line تبعتنا أو الخط اللي
+
+320
+00:23:22,560 --> 00:23:26,480
+هو الـ edge التبعتنا اللي موجودة فهي الـ V يمكن
+
+321
+00:23:26,480 --> 00:23:32,800
+واضحة في كل المصطلحات الـ direct واضحة فيها كتير طيب
+
+322
+00:23:32,800 --> 00:23:36,560
+نجي لـ degree لكل vertex من الـ vertices اللي
+
+323
+00:23:36,560 --> 00:23:39,320
+موجودة كل vertex من الـ vertices اللي موجودة عندنا
+
+324
+00:23:39,320 --> 00:23:45,520
+هنا هيكون في إلها in و out لأن اللي داخل غير اللي
+
+325
+00:23:45,520 --> 00:23:49,160
+طالع اللي هتكون طالعة غير اللي داخلة فإذن هنا
+
+326
+00:23:49,160 --> 00:23:52,180
+بالنسبة لنا هنا هذه الطالعة هتكون positive هذه
+
+327
+00:23:52,180 --> 00:23:55,980
+الداخلة هتكون negative فهنا بنتكلم عن الـ in degree
+
+328
+00:23:55,980 --> 00:24:01,880
+of V فهي عدد الـ edges going to V يعني داخلة V
+
+329
+00:24:01,880 --> 00:24:06,240
+هتكون كلها داخلة V فبنسميها بالـ negative أما الـ
+
+330
+00:24:06,240 --> 00:24:13,620
+out degree لأي vertex V كويس هي عدد الـ .. الـ edges
+
+331
+00:24:13,620 --> 00:24:19,280
+اللي coming from V فهي الطالعة جاية من V طالعة من
+
+332
+00:24:19,280 --> 00:24:23,880
+V و رايحة لـ .. لـ vertices ثانية تمام الـ degree
+
+333
+00:24:23,880 --> 00:24:28,960
+totally هي مجموع الاتنين هي مجموع الاتنين اللي
+
+334
+00:24:28,960 --> 00:24:31,000
+طالعة واللي داخلة تمام
+
+335
+00:24:35,620 --> 00:24:39,060
+السالب والموجب يكون العكس ليش؟ اللي طالعة منا كان
+
+336
+00:24:39,060 --> 00:24:44,280
+يكون سالب بس داخلة الموجب لأ أنت بالعكس أنت موجب
+
+337
+00:24:44,280 --> 00:24:51,600
+معناته طالعة من عندك موجب طالعة كل ايش موجب هي هنا
+
+338
+00:24:51,600 --> 00:24:57,420
+فلأ طالعة يعني معناته أنت بالنسبة له موجب أنت موجب
+
+339
+00:24:57,420 --> 00:25:05,340
+أنت مشعّ أنت موجب معناته أنت مشعّ صح؟ اه fine
+
+340
+00:25:06,890 --> 00:25:12,670
+معناته مشعّ فإذا هذه كل شيء طالع هيها coming from
+
+341
+00:25:12,670 --> 00:25:18,190
+V جاي من V طالع من V هو إيجابي مو إيجابي أما سلبي
+
+342
+00:25:18,190 --> 00:25:24,250
+بياخد بياخد طيب مجموع زي ما قلنا الاتنين على بعض
+
+343
+00:25:24,250 --> 00:25:29,810
+اللي هو الـ degree V كـ total طيب الآن بنقدر نقول
+
+344
+00:25:29,810 --> 00:25:36,650
+أن مجموع كل اللي طالع أكيد فيه في المقابل vertex
+
+345
+00:25:36,650 --> 00:25:40,710
+أخذته معناه ذلك مجموع اللي طالع هو نفسه مجموع اللي
+
+346
+00:25:40,710 --> 00:25:46,210
+داخل يعني الـ degree أو الـ in degree بيساوي الـ out
+
+347
+00:25:46,210 --> 00:25:51,130
+degree هذول مجموعهم مع بعض طلعوا من vertex معينة
+
+348
+00:25:51,130 --> 00:25:55,190
+بس هم أكيد راحوا لـ vertex ثانية صحيح؟ فجداش الـ total
+
+349
+00:25:55,190 --> 00:26:00,010
+كمجموع الـ in بيساوي الـ out بيساوي نص الـ degree كلها
+
+350
+00:26:00,010 --> 00:26:04,510
+على بعض ويساوي absolute E لحالها الـ degree كاملة
+
+351
+00:26:04,510 --> 00:26:10,240
+على بعض كانت بتساوي 2E لو بتعامل undirected اه
+
+352
+00:26:10,240 --> 00:26:12,480
+اللي هي الـ cardinality هذه لو بتعامل ايش
+
+353
+00:26:12,480 --> 00:26:16,020
+undirected لكن أنا بتعامل directed فمعنى ذلك أنه
+
+354
+00:26:16,020 --> 00:26:18,820
+الاتنين اللي كانت هنا لو قسمت على اتنين فهي صارت
+
+355
+00:26:18,820 --> 00:26:22,360
+هذه نص الـ degree total طيب الـ degree أنا عارف أن
+
+356
+00:26:22,360 --> 00:26:27,720
+هي عبارة عن نصين فعليا الـ in يساوي الـ out معناته
+
+357
+00:26:27,720 --> 00:26:32,320
+يساوي الـ cardinality للـ edges الـ cardinality لمن؟
+
+358
+00:26:32,320 --> 00:26:37,140
+للـ edges طبعا خلاص يعني نفس الـ directed والـ
+
+359
+00:26:37,140 --> 00:26:41,300
+undirected بنفس الفكرة وما تغيرش نفس الأفكار هي هي
+
+360
+00:26:41,300 --> 00:26:46,420
+تقريبا كأفكار الآن نروح لمجموعة special graph
+
+361
+00:26:46,420 --> 00:26:50,640
+structures أو مجموعة التراكيب لأنواع من أنواع الـ
+
+362
+00:26:50,640 --> 00:26:55,040
+graphs اللي ممكن تستخدم في حالات كتير يعني في حاجات
+
+363
+00:26:55,040 --> 00:26:57,460
+كتير منها الـ complete هنتكلم عن الـ complete هنتكلم
+
+364
+00:26:57,460 --> 00:27:01,160
+عن الـ cycles هنتكلم عن الـ wheels هنتكلم عن الـ n
+
+365
+00:27:01,160 --> 00:27:04,720
+cubes والـ bipartite graphs ثم الـ complete
+
+366
+00:27:04,720 --> 00:27:09,400
+bipartite graph نمسكهم واحدة واحدة بالنسبة لـ الـ
+
+367
+00:27:09,400 --> 00:27:13,180
+complete graph complete graph هي أن يكون عندك n
+
+368
+00:27:13,180 --> 00:27:21,310
+vertices والـ N هذه أي رقم natural number بحيث
+
+369
+00:27:21,310 --> 00:27:27,130
+أني أعرف منه K complete of N فمعنى ذلك أنه عندك
+
+370
+00:27:27,130 --> 00:27:33,010
+عدد vertices N و full connected together بمعنى كل
+
+371
+00:27:33,010 --> 00:27:36,990
+node هي متصلة بالـ others كل node متصلة بالـ others
+
+372
+00:27:36,990 --> 00:27:40,530
+كاملا تمام ففي الحالة هذه الـ simple graph في
+
+373
+00:27:40,530 --> 00:27:44,790
+الحالة هذه للـ in nodes نقدر نقول عليه كل node هي
+
+374
+00:27:44,790 --> 00:27:50,930
+adjacent for other nodes لإيش to every other nodes
+
+375
+00:27:50,930 --> 00:27:57,610
+بحيث أن لكل u و v تنتمي للـ vertices set بشرط أن
+
+376
+00:27:57,610 --> 00:28:02,070
+هما لا يساويا بعض يعني ايش ما فيش self-loop .. ما فيش
+
+377
+00:28:02,070 --> 00:28:06,470
+self-loop يوجد connection between U and V يوجد
+
+378
+00:28:06,470 --> 00:28:08,350
+connection .. كيف عرفت أنه يوجد connection؟ لأنه
+
+379
+00:28:08,350 --> 00:28:12,450
+ينتمي لمين؟ لـ .. الـ capital E .. لـ capital E و
+
+380
+00:28:12,450 --> 00:28:15,530
+ما فيش isolated .. لأ ممكن يكون في isolated إذا كان
+
+381
+00:28:15,530 --> 00:28:19,290
+الـ degree zero أو .. degree one .. degree one الـ
+
+382
+00:28:19,290 --> 00:28:22,250
+degree one معناته أنا بقول K1 يعني معناته عدد الـ
+
+383
+00:28:22,250 --> 00:28:26,710
+nodes واحد فهي عدد الـ node واحد فهي node واحدة ..
+
+384
+00:28:26,710 --> 00:28:32,820
+بس مع مين؟ ما هي واحدة ..  بسهي واحدة فقط فإذا
+
+385
+00:28:32,820 --> 00:28:37,260
+لحالها بهذا الشكل K2 هي عند اتنين وكل واحدة
+
+386
+00:28:37,260 --> 00:28:39,700
+connected مع كل اللي حواليها طيب ما فيش اللي
+
+387
+00:28:39,700 --> 00:28:42,480
+حواليها واحدة ثانية فهنا bonded هنا صاروا اتنين
+
+388
+00:28:42,480 --> 00:28:47,960
+معلقتين طيب K3 هي في عند three nodes كل واحدة
+
+389
+00:28:47,960 --> 00:28:51,120
+متصلة باتنين تانيات كل واحدة متصلة بالباقين كل
+
+390
+00:28:51,120 --> 00:28:56,260
+واحدة متصلة بالباقي كويس K4 بهذا الشكل خمسة ب ..
+
+391
+00:28:56,260 --> 00:29:00,120
+ستة and so on and so on طيب قداش عدد الـ nodes في
+
+392
+00:29:00,120 --> 00:29:04,800
+الحالة .. عدد الـ .. الـ edges في الحالة هذه لما
+
+393
+00:29:04,800 --> 00:29:09,040
+كانت صفر كنا بنتكلم عن .. لما كانت واحد عفوا، كنا
+
+394
+00:29:09,040 --> 00:29:13,580
+بنتكلم عن صفر ثم واحد، تلاتة، صار عندي ستة and so
+
+395
+00:29:13,580 --> 00:29:21,020
+
+445
+00:33:02,160 --> 00:33:07,040
+سميناها مش شايرة circuit أو cycle بمعنى أنّه ال degree
+
+446
+00:33:07,040 --> 00:33:10,920
+رجعت إلى أو الـ .. الـ .. الـ transitive رجعت إلى نفسها
+
+447
+00:33:10,920 --> 00:33:16,910
+النقطة الثانية من V1 إلى V1 فسميناها Loop أو سميناها
+
+448
+00:33:16,910 --> 00:33:22,010
+Cycle وسميناها Circuit سميناهما بالحالتين تمام الآن
+
+449
+00:33:22,010 --> 00:33:26,130
+كم عدد الـ edges في الحالة هذه لو أنا أتكلم عن C
+
+450
+00:33:26,130 --> 00:33:32,690
+من الـ degree N هي مباشرة، إذا والله عندي أربعة
+
+451
+00:33:32,690 --> 00:33:35,910
+فعندي أربعة edges، عندي خمسة، فعندي خمسة edges، عندي
+
+452
+00:33:35,910 --> 00:33:42,890
+ستة، فعندي ستة edges، بسيطة جدا، لسه تمام، Okay
+
+453
+00:33:42,890 --> 00:33:51,170
+الـ wheels هي cycle لكن بيكون لها محور، عجلة، محور، عجلة
+
+454
+00:33:51,170 --> 00:33:54,410
+طيب، محور عجلة عبارة عن إيش؟ عبارة عن كمان نقطة
+
+455
+00:33:54,410 --> 00:34:00,210
+زيادة، كأنها المحور، و connected مع الـ others، تمام؟
+
+456
+00:34:00,210 --> 00:34:07,850
+أخذناها، هي cycle وعملنا لها محور أو spindle في النص
+
+457
+00:34:07,850 --> 00:34:11,790
+مش أكثر من هيك، هي مش أكثر من هذا الشكل، فأنت
+
+458
+00:34:11,790 --> 00:34:17,370
+بهذا الشكل صار كلّه totally إيش؟ Wheels أو عجلة، طيب
+
+459
+00:34:17,370 --> 00:34:24,630
+كلّنا عارفين أنّه بالنسبة للـ C N كانت N واحدة، طيب
+
+460
+00:34:24,630 --> 00:34:29,090
+الإضافية هذه كم جابت معها عدد edges، عدد الـ N
+
+461
+00:34:29,090 --> 00:34:34,590
+نفسها في 2N، في 2N، فعندك عدد هنا لو خمسة، يعني الخمسة
+
+462
+00:34:34,590 --> 00:34:38,170
+الأساسيين تبع الـ cycle زائد خمسة أجوا مع الـ node
+
+463
+00:34:38,170 --> 00:34:41,310
+هذه، لأنّه لازم تعمل connection مع الكل، فصار عندك 2
+
+464
+00:34:41,310 --> 00:34:42,550
+2N
+
+465
+00:34:44,500 --> 00:34:50,100
+تمام، طيب الـ N cubes، الـ N cube أو الـ hyper cubes، الـ
+
+466
+00:34:50,100 --> 00:34:54,640
+hyper cubes ببساطة، إذا كان أنا أتكلم عن N أي رقم
+
+467
+00:34:54,640 --> 00:34:59,480
+ينتمي إلى natural number، فـ hyper cube Q N .. Q N دي
+
+468
+00:34:59,480 --> 00:35:03,280
+ببساطة جدا هي الـ graph اللي قبلها في الدرجة مكرر
+
+469
+00:35:03,280 --> 00:35:10,500
+منها، أو هي ماخدة نسخة منه، يعني إذا كان عندك Q N نقص
+
+470
+00:35:10,500 --> 00:35:15,920
+واحد، الـ cube N نقص واحد، معناه ذلك أن cube N أو Q N
+
+471
+00:35:15,920 --> 00:35:21,300
+هي عبارة عن Q N نقص واحد، ومنسوخ منه برضه أخوه زيّه
+
+472
+00:35:21,300 --> 00:35:26,680
+بالضبط، Q N نقص واحد، وكل نقطة نسخة من نقطة في
+
+473
+00:35:26,680 --> 00:35:33,160
+بينهم connection، بدنا نوضح، هنرجع نوضحها بالـ
+
+474
+00:35:33,160 --> 00:35:39,920
+animation اللي احنا عملناه، عندك Q0 نقطة بس، نقطة، و
+
+475
+00:35:39,920 --> 00:35:43,460
+بس، كويس، لما جينا للنقطة، و بس هذه النقطة، وبس أخذت
+
+476
+00:35:43,460 --> 00:35:49,700
+منها نسخة، وكل corresponding node بوصلها مع
+
+477
+00:35:49,700 --> 00:35:54,520
+المنسوخ، الناسخ مع المنسوخ، كل نقطة أنْسخت مع النقطة
+
+478
+00:35:54,520 --> 00:35:58,340
+اللي أنْسخت منها، نعمل فيه node connection، طيب هذا
+
+479
+00:35:58,340 --> 00:36:04,700
+الـ graph صار Q1 نفسه، وهو .. بدي أعمل منه نسخة، أيوة
+
+480
+00:36:04,700 --> 00:36:08,860
+بس النقطة هذه هي منسوخة من النقطة هذه، والنقطة هذه
+
+481
+00:36:08,860 --> 00:36:10,840
+منسوخة من النقطة هذه، خلاص، اعمل connection بينهم
+
+482
+00:36:10,840 --> 00:36:15,900
+طيب Q2
+
+483
+00:36:15,900 --> 00:36:21,940
+هيه نسخة منه، النقطة هذه منسوخة من هذه، وهذه من هذه
+
+484
+00:36:21,940 --> 00:36:24,840
+وهذه من هذه، وهذه من هذه، وصلهم، كل واحدة ناسخة
+
+485
+00:36:24,840 --> 00:36:25,360
+منسوخة
+
+486
+00:36:29,260 --> 00:36:35,160
+هي cube، هي cube اللي هي هذه، Q تلاتة، طيب كمان Q
+
+487
+00:36:35,160 --> 00:36:43,100
+تلاتة، وكل نقطة بالـ correspondence لإلها، كل نقطة
+
+488
+00:36:43,100 --> 00:36:45,900
+بالـ correspondence لإلها، النقطة هذه هي منسوخة من
+
+489
+00:36:45,900 --> 00:36:48,280
+هذه النقطة، فبينهم في connection، النقطة هذه منسوخة
+
+490
+00:36:48,280 --> 00:36:52,060
+من هذه، في connection، وهكذا، بدك تجيب خمسة معناته
+
+491
+00:36:52,060 --> 00:36:55,220
+هو نفس القالب هذا زي ما هو برضه بتنسخ منه كمان مرة
+
+492
+00:36:55,220 --> 00:37:01,540
+وبتوصل كل نقطة ناسخ مع منسوخة، كبس مجموعة، كبس، فأنت
+
+493
+00:37:01,540 --> 00:37:06,480
+بتعمل فعلا two كبس من الـ order اللي جاب لها، وكل
+
+494
+00:37:06,480 --> 00:37:11,880
+نقطة متصلة بالمنسوخ منها، الآن، كم عدد الـ vertices
+
+495
+00:37:13,810 --> 00:37:16,770
+الـ vertices، أنا أتكلم لسه عن الـ vertices، هترکّز
+
+496
+00:37:16,770 --> 00:37:19,890
+فيهم، عند الـ zero كانوا واحد، عند الـ واحد كانوا
+
+497
+00:37:19,890 --> 00:37:24,610
+اثنين، اثنين كانوا أربعة، ثمانية، ستة عشر،
+
+498
+00:37:24,610 --> 00:37:26,850
+اثنين وثلاثين، تلاقي اثنين تظبر، يعني ما فيش فيهم
+
+499
+00:37:26,850 --> 00:37:36,000
+مشكلة إطلاقا، اه؟ ليش فيها مشكلة؟ كثير، بأي عددهم
+
+500
+00:37:36,000 --> 00:37:39,280
+بيطلع n to the power n ناقص واحد، اثنين to the power
+
+501
+00:37:39,280 --> 00:37:48,360
+n ناقص واحد في n في مين؟ في n، كيف؟ مع العلم أنّه
+
+502
+00:37:48,360 --> 00:37:50,960
+يعني خليني أقول واحد من الطلاب اللي جابها قبل تلت
+
+503
+00:37:50,960 --> 00:37:56,880
+سنين، يعني ما كنتش خاطرة عبالي أصلا نجيبها، ركزت
+
+504
+00:37:56,880 --> 00:38:00,360
+فيها، اه شباب، طب حقّ نقدر نجيب الـ edges، ركزت فيها، طب
+
+505
+00:38:00,360 --> 00:38:04,100
+اه، يلا، أجيب لكم الـ edges، اعتبروا quiz extra، هيك
+
+506
+00:38:04,100 --> 00:38:08,720
+لَقيت واحد واحد بس اللي جابها، واحد اللي جابها، أخد
+
+507
+00:38:08,720 --> 00:38:13,400
+الـ extra تبعه على
+
+508
+00:38:13,400 --> 00:38:20,560
+إيش؟ طيب الـ by parts، الـ by parts من اسمها عندك two
+
+509
+00:38:20,560 --> 00:38:26,380
+parts، مش هيك، part أول، part ثاني، الـ two parts هدول
+
+510
+00:38:26,380 --> 00:38:29,920
+داخل الـ graph، معناه ذلك أنّه أنا بدي أمسك كل جزء من
+
+511
+00:38:29,920 --> 00:38:34,930
+أجزاء الـ graph وأعملهم two parts، الجزء الأساسي هو الـ
+
+512
+00:38:34,930 --> 00:38:40,750
+vertices، فالـ vertices بتجسمهم لمجموعتين، vertices 1
+
+513
+00:38:40,750 --> 00:38:45,170
+أو vertices set 1 و vertices set 2، بتفترض فريقين
+
+514
+00:38:45,170 --> 00:38:49,770
+كرة قدم، جسمناهم، هل هينفع؟ طبعا بتصير أحيانا
+
+515
+00:38:49,770 --> 00:38:53,320
+واحد بيلعب مرة مع هدول ومرة مع هدول، هذا إذا كان
+
+516
+00:38:53,320 --> 00:38:56,420
+بتبقى الفائز وخلاص، بس الطبيعي أنّه لأ، هدول
+
+517
+00:38:56,420 --> 00:38:58,720
+منفصلين عن هدول، يعني معناه ذلك أن الـ intersection
+
+518
+00:38:58,720 --> 00:39:02,560
+between them المفروض في، فعندك فريق أول، فريق ثاني
+
+519
+00:39:02,560 --> 00:39:06,800
+تمام، هاي الفريق الأول وهي الفريق الثاني، ولأنّ بتعمل
+
+520
+00:39:06,800 --> 00:39:12,140
+relation بين كل عنصر من الفريق الأول مع كل عنصر من
+
+521
+00:39:12,140 --> 00:39:16,780
+الفريق الثاني، طيب عناصر الفريق نفسه مع بعضه لأ
+
+522
+00:39:16,780 --> 00:39:20,240
+ما فيش relation، ليش؟ لأنّ هدول، خليني أفترض أنّه العلاقة
+
+523
+00:39:20,240 --> 00:39:25,380
+هنا هي تنافسية، فأنت ما بتنافسش اللي زميلك، لأنّ أنتم
+
+524
+00:39:25,380 --> 00:39:30,120
+بالعكس، أنتم فريق واحد، حتى لو وصلت إلى الـ .. الـ .. الـ
+
+525
+00:39:30,120 --> 00:39:35,240
+.. الـ .. الـ goal keeper، إيش بدك تعمل؟ بتمرر له عشان
+
+526
+00:39:35,240 --> 00:39:39,100
+يجيبه، لأنّه في النهاية كلّكم مستفيدين من الـ goal، هذا
+
+527
+00:39:39,100 --> 00:39:43,980
+الصحيح، المفروض يعني، طيب، في الحالة هذه بنقدر نقول لك كلّ
+
+528
+00:39:43,980 --> 00:39:52,140
+E ينتمي إلى E، فهو فعليا يوجد V1 من المجموعة
+
+529
+00:39:52,140 --> 00:39:57,690
+الأولى، كويس؟ و V2 من المجموعة الثانية، بينهم الـ
+
+530
+00:39:57,690 --> 00:40:00,450
+relation هذه اللي هي e، بينهم الـ relation
+
+531
+00:40:00,450 --> 00:40:08,290
+e، يوجد .. يوجد لكل E يوجد V من هنا و V من
+
+532
+00:40:08,290 --> 00:40:13,310
+هنا، طيب، ممكن ما يوجدش، يعني بمعنى أنّه نلاقي الفريق
+
+533
+00:40:13,310 --> 00:40:16,530
+هنا والفريق هنا، كل واحد relation مع الثاني، زي
+
+534
+00:40:16,530 --> 00:40:20,030
+المدرب لما يقول لكل واحد من الفريق هدول أنت بتمسك
+
+535
+00:40:20,030 --> 00:40:24,690
+اللاعب فلان، ممكن الدفاع هيكون له نصيب ويمسك اثنين
+
+536
+00:40:24,690 --> 00:40:27,590
+مثلا، ليش؟ لأنّ الاثنين مهاجمين، فأنت لأ، أنت بدك
+
+537
+00:40:27,590 --> 00:40:31,490
+تمسك الاثنين، إذا قلب الدفاع، تمام، فهنا كأنّك بتعمل
+
+538
+00:40:31,490 --> 00:40:38,110
+relation على الورق، لعيب يمسكوا بعض، طيب هذه الفكرة
+
+539
+00:40:38,110 --> 00:40:44,290
+vertices أو vertex set one و vertex set two، فهذه
+
+540
+00:40:44,290 --> 00:40:48,870
+بتسميها by parts لأنّ أنت بتفصلهم إلى two parts
+
+541
+00:40:51,820 --> 00:40:56,600
+طيب لما أقول complete bipartate، معناته المنافسة
+
+542
+00:40:56,600 --> 00:41:03,840
+مفتوحة، المنافسة هنا مفتوحة، كل عنصر من الـ
+
+543
+00:41:03,840 --> 00:41:08,680
+vertex الأولى هو متصل أو يوجد relation مع كل عنصر
+
+544
+00:41:08,680 --> 00:41:13,520
+أو مع أي عنصر موجود في الثانية، فإذا كل عنصر له
+
+545
+00:41:13,520 --> 00:41:16,680
+علاقة مع أي عنصر من المجموعة الثانية، والعكس صحيح
+
+546
+00:41:16,680 --> 00:41:21,260
+من المجموعة الثانية برضه كل عنصر له علاقة مع أي
+
+547
+00:41:21,260 --> 00:41:25,500
+عنصر من المجموعة الأولى، تمام، فما فيها كتير مشكلة
+
+548
+00:41:25,500 --> 00:41:30,640
+معناته أن نتكلم عن الكل، Okay، هو شريحة هنا باللون
+
+549
+00:41:30,640 --> 00:41:34,880
+الأزرق اللي هو in the left part n nodes أو كل m
+
+550
+00:41:34,880 --> 00:41:38,640
+nodes من الـ left part والـ n nodes في الـ right
+
+551
+00:41:38,640 --> 00:41:42,460
+part، every node in the left part is connected to
+
+552
+00:41:42,460 --> 00:41:47,600
+every node in the right part، طيب ما فيش كتير مشكلة
+
+553
+00:41:47,600 --> 00:41:50,340
+لما بتقول كم عدد الـ vertices هنا، فهي مجموعة
+
+554
+00:41:50,340 --> 00:41:54,440
+الاثنين، كم عدد الـ connection اللي هي الـ edges
+
+555
+00:41:54,440 --> 00:41:58,620
+ضرب الاثنين في بعض، يعني مش كتير مشكلة في الحلقة دي
+
+556
+00:41:58,620 --> 00:42:03,180
+طيب لما بقول sub graph، لما بنحكي عن sub graph، sub
+
+557
+00:42:03,180 --> 00:42:08,020
+graph ببساطة هو G، graph يحتوي على مجموعة vertices
+
+558
+00:42:08,020 --> 00:42:13,760
+و edges، وبنقدر نسمي أن في عندك H كـ sub graph من
+
+559
+00:42:13,760 --> 00:42:20,000
+الـ G، معناه ذلك أن الـ sub graph عدد الـ vertices
+
+560
+00:42:20,000 --> 00:42:26,110
+تبعته هي subset من عدد الـ vertices للـ graph الأصلي
+
+561
+00:42:26,110 --> 00:42:30,530
+طيب عدد الـ edges برضه هي subset من عدد الـ edges
+
+562
+00:42:30,530 --> 00:42:35,690
+للـ graph الأصلي، يعني ببساطة الـ graph اللي قدامك هنا
+
+563
+00:42:35,690 --> 00:42:43,650
+هذا، طلع منه أي nodes مع أي edges، بيساوي جزء إيه
+
+564
+00:42:43,650 --> 00:42:47,370
+طلعهم على جنب، بيطلعوا كأنّه sub graph، كأنّه sub
+
+565
+00:42:47,370 --> 00:42:51,720
+graph، هو graph، جزء إيه منه، لما تقول جزء مثلا بهذا
+
+566
+00:42:51,720 --> 00:42:56,460
+الشكل، بتطلعه هو فعليا كل شيء موجود هنا هو موجود في
+
+567
+00:42:56,460 --> 00:43:00,800
+الأصل، والعكس غير صحيح، فهي sub set، فصار اسمها sub
+
+568
+00:43:00,800 --> 00:43:04,280
+graph، لأنّ أنا بأتعامل فيه مع set صحيح، أنا بعرفها
+
+569
+00:43:04,280 --> 00:43:09,720
+بالـ set، بس هنا رياضيا صار اسمه graph، فـ sub graph في
+
+570
+00:43:09,720 --> 00:43:14,430
+الحالة اللي بنتكلم عنها، طيب Graph Unions، الـ Graph
+
+571
+00:43:14,430 --> 00:43:17,170
+Unions بكل بساطة برضه عندك two graphs وبتحطهم
+
+572
+00:43:17,170 --> 00:43:20,670
+بتشوفهم على بعض، يعني هيك ترسم الاثنين مع بعضهم مع
+
+573
+00:43:20,670 --> 00:43:26,150
+بعضهم، قد يكون في أجزاء مشتركة في الآخر، لما يكون
+
+574
+00:43:26,150 --> 00:43:32,470
+عندك ABCDE، ABCDE، EF، كمان هنا بتقدر تعملهم مع بعض
+
+575
+00:43:32,470 --> 00:43:35,690
+فبتقدر تقول أن الـ G1 أو الجراف الأول Union الجراف
+
+576
+00:43:35,690 --> 00:43:41,240
+الثاني هي عبارة عن الـ vertices للأول اتحاد الـ
+
+577
+00:43:41,240 --> 00:43:46,560
+vertices للثاني، واتحاد الـ edges للأول مع الـ edges
+
+578
+00:43:46,560 --> 00:43:51,520
+للثاني، بتحط كل هدول مع كل هدول فوق بعض، وبتصير عندك
+
+579
+00:43:51,520 --> 00:43:58,870
+اتحاد الـ two graphs مع بعضهم، بهذا الشكل، فبيصير عندك
+
+580
+00:43:58,870 --> 00:44:03,290
+graph totally هو اتحاد الاثنين مع بعض، هو اتحاد
+
+581
+00:44:03,290 --> 00:44:10,770
+الاثنين مع بعضهم، طيب الـ complementary graph، الـ
+
+582
+00:44:10,770 --> 00:44:16,990
+complementary graph ببساطة جدا هي كل graph بتخصمه
+
+583
+00:44:16,990 --> 00:44:22,710
+من الـ complete graph تبع عدد الـ nodes، كل graph هو
+
+584
+00:44:22,710 --> 00:44:28,340
+عبارة عن، لما بقول الـ complementary لأي graph يعني
+
+585
+00:44:28,340 --> 00:44:33,820
+كأنّي بدي أمسك الـ graph نفسه وأطرحه من الـ complete
+
+586
+00:44:33,820 --> 00:44:40,000
+graph للـ vertices تبعته، بمعنى لو افترضنا مثلا ..
+
+587
+00:44:40,000 --> 00:44:43,340
+خلينا نشوف هنا اللي هو بنسميه كمان G bar بهذا
+
+588
+00:44:43,340 --> 00:44:47,060
+الشكل، فهو الـ complementary لإله، هو المكمل تبعه للـ
+
+589
+00:44:47,060 --> 00:44:54,140
+G، okay، بمعنى أنّه هنا لو في مثلا عندي النقطة هذه، الـ
+
+590
+00:44:54,140 --> 00:44:58,100
+adjacency تبعتها مع الأربع نقاط اللي حواليها، إذا
+
+591
+00:44:58,100 --> 00:45:01,040
+موجودين كلّهم في G، المفروض لا يكونوا موجودين في
+
+592
+00:45:01,040 --> 00:45:05,460
+مين؟ في الـ complementary، اللي أقلها، فالـ adjacency
+
+593
+00:45:05,460 --> 00:45:08,940
+هنا هي اللي بتفرج معانا، في كل نقطة من النقاط .. في
+
+594
+00:45:08,940 --> 00:45:11,820
+كل نقطة من .. من النقاط، بمعنى لما نيجي نشوف الـ ..
+
+595
+00:45:11,820 --> 00:45:16,600
+الـ .. الـ .. الأول، هو دي اللي هي K5، الـ K5 هذه بدي
+
+596
+00:45:16,600 --> 00:45:20,630
+أجيب الـ complementary تبعها، بدي أحط النقاط زي ما هم
+
+597
+00:45:20,630 --> 00:45:25,730
+صحيح؟ بدي أفترض أن هاي النقاط زي ما هم ضالوا، ونشوف
+
+598
+00:45:25,730 --> 00:45:35,270
+كل edge موجودة كانت في K5، ما بديش أحطها، إيش بضل عند
+
+599
+00:45:35,270 --> 00:45:41,070
+edges مش موجودة هنا؟ مين ضال في edges؟ في ضال أي
+
+600
+00:45:41,070 --> 00:45:46,020
+edge موجودة هنا، غير موجودة هنا؟ لو في أي H غير
+
+601
+00:45:46,020 --> 00:45:48,980
+موجودة هنا، لازم نحطّه هنا في الـ complementary، عشان
+
+602
+00:45:48,980 --> 00:45:54,920
+نصبح مكملين لبعض، بحيث أنّه لما أعمل اتحاد الاثنين
+
+603
+00:45:54,920 --> 00:46:00,200
+مع بعض يعطيني الـ complement K، طبعا واضح أن هنا ∅
+
+604
+00:46:00,200 --> 00:46:05,780
+ليش؟ لأنّ هذه أصلا complete خمسة، complete خمسة هي
+
+605
+00:46:05,780 --> 00:46:07,160
+أساسا complete خمسة
+
+606
+00:46:09,760 --> 00:46:14,900
+هي .. إيش هذه؟ لأ، خلينا نفترض .. نفترض النوع، هذا
+
+607
+00:46:14,900 --> 00:46:16,860
+هذه، الوجه اللي احنا قلنا عليها اللي هي الـ wheels
+
+608
+00:46:16,860 --> 00:46:23,000
+أربعة، مش هيك؟ هذه wheel أربعة، الأربعة هذه بدنا نجيب
+
+609
+00:46:23,000 --> 00:46:26,480
+الـ complementary تبعها، complementary تبعها، فبدي
+
+610
+00:46:26,480 --> 00:46:29,560
+برضه آخذهم الـ nodes لحالهم ونشوف إيش اللي ضال
+
+611
+00:46:29,560 --> 00:46:37,820
+متبقي كـ edges مش موجود هنا، وين
+
+612
+00:46
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/C8MOQNis1HI.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/C8MOQNis1HI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c77654f02dcb2f67a3b820690cda3b0f46c05314
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/C8MOQNis1HI.srt
@@ -0,0 +1,2061 @@
+1
+00:00:05,090 --> 00:00:08,950
+يعطيكم العفو يا شباب، طبعًا احنا خلصنا المنهج لكن
+
+2
+00:00:08,950 --> 00:00:13,190
+مكملين مع بعض إن شاء الله تعالى في حل الأسئلة كنوع
+
+3
+00:00:13,190 --> 00:00:17,530
+من أنواع المراجعة للمادة، وبناءً على طلبكم اليوم
+
+4
+00:00:17,530 --> 00:00:19,490
+ما بدنا نشتغل في الـ inductive، مش هيك؟ في الـ
+
+5
+00:00:19,490 --> 00:00:24,030
+inductive proof.  فمجهز لكم شوية أسئلة اللي هي علاقة
+
+6
+00:00:24,030 --> 00:00:27,430
+برضه بهذا الموضوع، اللي هو عملية الـ proving بس
+
+7
+00:00:27,430 --> 00:00:31,470
+باستخدام الـ mathematical induction أو من موضوع الـ
+
+8
+00:00:31,470 --> 00:00:36,390
+induction اللي أخذناه واتكلمنا فيه. فنبدأ على طول و
+
+9
+00:00:36,390 --> 00:00:40,010
+نشوف واحدة من أهم الأسئلة اللي كانت جاية في امتحان
+
+10
+00:00:40,010 --> 00:00:43,690
+سابق، معظمها امتحانات سابقة، يعني الأسئلة كلها
+
+11
+00:00:43,690 --> 00:00:47,670
+اجتهدنا أن ندور على كل امتحاناتنا السابقة اللي
+
+12
+00:00:47,670 --> 00:00:50,950
+كنا بنعملها في السنوات الماضية، وأشوف إيش الأسئلة
+
+13
+00:00:50,950 --> 00:00:53,430
+اللي كانت لها علاقة بالـ mathematical induction،
+
+14
+00:00:53,430 --> 00:00:57,830
+بحيث أن نجيبها، وطبعًا أجود حلها، وأصور لكم إياها
+
+15
+00:00:57,830 --> 00:01:00,170
+عشان نعمل لكم إياها powerpoint ونزلكم إياها إن شاء
+
+16
+00:01:00,170 --> 00:01:03,520
+الله، على الـ model، الموديل هتكون كلها منازلة وفي
+
+17
+00:01:03,520 --> 00:01:07,400
+نفس الوقت هي كمحاضرة مصورة موجودة، هتكون مع باقي
+
+18
+00:01:07,400 --> 00:01:11,760
+سلسلة المحاضرات. نشوف السؤال إيش كان بيتكلم؟ بيتكلم
+
+19
+00:01:11,760 --> 00:01:14,720
+عن الـ mathematical induction to prove that 21
+
+20
+00:01:14,720 --> 00:01:20,940
+divides 4 to the power n plus 1، كله plus 5 to the
+
+21
+00:01:20,940 --> 00:01:26,520
+power 2n minus 1، whenever n is a positive integer.
+
+22
+00:01:26,520 --> 00:01:31,620
+فلو كانت الـ n هذه positive integer، بمعنى in
+
+23
+00:01:31,620 --> 00:01:37,460
+النهاية in أكبر من zero، a positive integer، كويس.
+
+24
+00:01:37,460 --> 00:01:43,640
+فبدنا نوضح أن واحد وعشرين هي divides لأربعة to the
+
+25
+00:01:43,640 --> 00:01:48,440
+power n زائد واحد plus خمسة to the power اتنين n
+
+26
+00:01:48,440 --> 00:01:55,140
+ناقص واحد، باستخدام الـ inductive step. طيب، الخطوة
+
+27
+00:01:55,140 --> 00:01:59,960
+الأولى، الـ basis step، فيها مشكلة؟ هنبدأ بمين؟
+
+28
+00:02:00,500 --> 00:02:05,240
+بالواحد، اللي هو أول positive integer، فهنبدأ
+
+29
+00:02:05,240 --> 00:02:10,160
+بالأولى، اللي هو الـ basis، تبقى the first number
+
+30
+00:02:10,160 --> 00:02:15,780
+for n، اللي هو عند الواحد. فبكل بساطة، عند الواحد عوض
+
+31
+00:02:15,780 --> 00:02:19,060
+هنا بالواحد، وعوض هنا بالواحد، وانتهت الجثة، شوفها
+
+32
+00:02:19,060 --> 00:02:23,020
+فعلا حققت أول خطوة ولا ما حققتش أول خطوة؟ فهنحصل
+
+33
+00:02:23,020 --> 00:02:27,440
+أربعة to the power اتنين plus خمسة to the power
+
+34
+00:02:27,440 --> 00:02:31,640
+واحد، كويس، اللي هو اتنين ناقص واحد، فبتضل واحد، بيساوي
+
+35
+00:02:31,640 --> 00:02:34,180
+واحد وعشرين، فواحد وعشرين divided واحد وعشرين
+
+36
+00:02:34,180 --> 00:02:38,480
+أكيد، أكيد divided واحد وعشرين، والناتج واحد، كويس.
+
+37
+00:02:38,480 --> 00:02:45,280
+فهي أول، أول جزئية واضحة جدًا هتكون عندنا، فهنا خلصنا
+
+38
+00:02:45,280 --> 00:02:50,700
+الـ basis step، لأن الـ inductive step rule واضح و
+
+39
+00:02:50,700 --> 00:02:56,800
+ما فيهوش كتير مشاكل. بدنا assume أن at n
+
+40
+00:02:56,800 --> 00:03:02,770
+is true، ومنها نحاول نجيب at n plus واحد، ببساطة جدًا.
+
+41
+00:03:02,770 --> 00:03:06,030
+يعني الخطوة السهلة والبسيطة. فالـ inductive step بكل
+
+42
+00:03:06,030 --> 00:03:10,550
+بساطة، بدنا نثبت k زائد واحد is true إذا كانت at k
+
+43
+00:03:10,550 --> 00:03:14,430
+is true. فبكل بساطة خلاص، بنعوض عند k زائد واحد.
+
+44
+00:03:16,660 --> 00:03:19,960
+وبنحاول، يعني هذه الاستراتيجية اللي أنتم هتشتغلوا عليها
+
+45
+00:03:19,960 --> 00:03:23,420
+طول الوقت، بحط k زائد واحد في المعادلة اللي بدي أعملها
+
+46
+00:03:23,420 --> 00:03:27,020
+إثبات هذه، وبعدين بحاول ألعب في الموضوع، أعمل شوية
+
+47
+00:03:27,020 --> 00:03:31,920
+الـ manipulation الضرورية رياضيًا، بحيث أني أطلع منها
+
+48
+00:03:31,920 --> 00:03:38,680
+at n تمام. فنشوف هل وجدت هذه، هي الـ total، هي هتساوي
+
+49
+00:03:38,680 --> 00:03:43,600
+k زائد اتنين، وهنا اتنين k زائد واحد، طبعًا بعد ما
+
+50
+00:03:43,600 --> 00:03:49,620
+نعوض بدل k تصبح مين؟ طيب، لاحظوا أن احنا يعني
+
+51
+00:03:49,620 --> 00:03:51,780
+برضه من الحاجات اللي بيتلخبطوا فيها كتير في الكتب
+
+52
+00:03:51,780 --> 00:03:56,140
+أحيانًا بيتكلم هنا عن الـ n، الـ general equation،
+
+53
+00:03:56,140 --> 00:04:00,560
+نفسها، وبعدين هنا بيتكلم عن k على أساس أن k متغير من
+
+54
+00:04:00,560 --> 00:04:07,200
+واحد لعند الـ n، كويس. فبكل بساطة بدنا نطلع الـ two
+
+55
+00:04:07,200 --> 00:04:11,260
+terms هدول. فبكل بساطة، عشان هدي أرجعها لـ k بدل k
+
+56
+00:04:11,260 --> 00:04:16,940
+زائد واحد، بدي أطلع أربعة منها. بدنا نطلع الأربعة
+
+57
+00:04:16,940 --> 00:04:22,940
+منها عشان أن تصبح هذه k زائد واحد n زائد واحد،
+
+58
+00:04:22,940 --> 00:04:26,520
+كويس، يعني كل اللي محتاجه زائد واحد زائد واحد، هذه
+
+59
+00:04:26,520 --> 00:04:30,120
+هطلع على حالها برا، هي طلعناها برا، فهذا صار جزء من
+
+60
+00:04:30,120 --> 00:04:35,560
+مين؟ من at k، هي طلعنا جزء مبدئيًا الناحية التانية
+
+61
+00:04:35,560 --> 00:04:41,660
+عشان أعمل نفس الكلام للخمسة، بدنا نطلع اتنين، ليش؟
+
+62
+00:04:41,660 --> 00:04:45,820
+لأن مضروبة كانت في اتنين، فخمسة في خمسة أو خمسة to
+
+63
+00:04:45,820 --> 00:04:49,880
+the power اتنين، فهي الخمسة وعشرين اللي دخلّت فالـ
+
+64
+00:04:49,880 --> 00:04:52,640
+term هذا وterm هذا هم متناسبين مع هذا الموضوع بس
+
+65
+00:04:52,640 --> 00:04:57,360
+كيف آخدهم، أجمعهم مع بعض؟ بتفكير بسيطة، عشان أقدر
+
+66
+00:04:57,360 --> 00:05:01,720
+آخذ common، معناته الخمسة والعشرين هذه بقدر أقول أن
+
+67
+00:05:01,720 --> 00:05:07,380
+هي بتساوي أربعة زائد واحد
+
+68
+00:05:07,380 --> 00:05:14,100
+وعشرين، مش هيك؟ أربعة زائد واحد وعشرين، فهي أربعة زائد
+
+69
+00:05:14,100 --> 00:05:17,380
+الواحد والعشرين، بتهيأ لي بالـ، بكل بساطة بنقدر نأخذ
+
+70
+00:05:17,380 --> 00:05:22,920
+الأربعة، ونطلع الأربعة مع العوامل المشتركة بتاعتها
+
+71
+00:05:22,920 --> 00:05:27,600
+بكل بساطة، على اعتبار أن الأربعة مضروبة في الأربعة
+
+72
+00:05:27,600 --> 00:05:31,240
+هي to the power of k زائد واحد، وفي نفس لغة الأربعة
+
+73
+00:05:31,240 --> 00:05:35,020
+برضه مضروبة في الخمسة to the power of 2k ناقص
+
+74
+00:05:35,020 --> 00:05:39,520
+واحد، مظبوط؟ هي فالـ term هذا مع الـ term هذا
+
+75
+00:05:39,520 --> 00:05:42,480
+أخذناهم مع بعض، بيضل عندي term الواحد والعشرين في
+
+76
+00:05:42,480 --> 00:05:46,520
+خمسة، وهذا من واضح جدًا أنه بيكسب على واحد وعشرين،
+
+77
+00:05:46,520 --> 00:05:50,880
+أنت عندك term مضروب في واحد وعشرين، فإذاً الواحد
+
+78
+00:05:50,880 --> 00:05:56,290
+وعشرين divides this term، تمام؟ ونفس القصة، أيوة.
+
+79
+00:05:56,290 --> 00:06:02,730
+قُطعت، مش شايف؟ هذه الآن بدلالة at k، فهنا جبناها
+
+80
+00:06:02,730 --> 00:06:07,340
+k زائد واحد بدلالة الـ k، فهي طريقة تفكير منطقية،
+
+81
+00:06:07,340 --> 00:06:13,260
+المنطقية واحدة، الاستراتيجية واحدة، الباقي بيظل شطارة
+
+82
+00:06:13,260 --> 00:06:15,760
+كيف الأرقام تستطيع التعامل معها، بس الاستراتيجية
+
+83
+00:06:15,760 --> 00:06:18,540
+واحدة، بدنا عشان ما نخربط الاستراتيجيات مع بعض، هاي
+
+84
+00:06:18,540 --> 00:06:21,980
+استراتيجية الـ inductive بس لا أكثر ولا أقل، فهذا الـ
+
+85
+00:06:21,980 --> 00:06:24,760
+term كلنا عارفين أن هو نفس الـ term هذا اللي هو
+
+86
+00:06:24,760 --> 00:06:31,440
+فعلاً بيقسم على 21، أو 21 divides it، فهذا ما دام بيقسم
+
+87
+00:06:31,440 --> 00:06:34,360
+على 21، معناته بكل بساطة، بدرجة أنه هو 21 في integer،
+
+88
+00:06:35,400 --> 00:06:40,180
+في أي sum integer، في أي sum integer، عشان نقدر نقول
+
+89
+00:06:40,180 --> 00:06:44,560
+في الحالة هذه، نعكسهم مع بعض، ندخل الـ 21 مكان
+
+90
+00:06:44,560 --> 00:06:47,940
+الأربعة، والأربعة مكان الـ 21، يعني مين ضرب مين، مش
+
+91
+00:06:47,940 --> 00:06:51,500
+هتفرق مين صحيح؟ أنت عندك term اتنين تلاتة مضروبين
+
+92
+00:06:51,500 --> 00:06:56,080
+في بعض، مين جاب المين، مش هيفرق معاك، فطلّعهم عشان تظل
+
+93
+00:06:56,080 --> 00:07:00,720
+21 مع 21، صار 21 مضروبة في مين؟ في الـ integer هذا، الـ sum integer plus... طيب، كل هذا الـ
+
+94
+00:07:00,720 --> 00:07:04,180
+term بيكسب أكيد، لأنه أصلًا واحد وعشرين واحدة من
+
+95
+00:07:04,180 --> 00:07:08,730
+مضاعفاته، واحدة من مضاربه، فإذاً أكيد هيطلع بيكسب على
+
+96
+00:07:08,730 --> 00:07:15,230
+واحد وعشرين، sure. فإذاً أكيد النظرية صحيحة. لاحظوا إنه
+
+97
+00:07:15,230 --> 00:07:22,140
+إذا كانت اشتغلت من الأساس على فكرة الـ two
+
+98
+00:07:22,140 --> 00:07:25,060
+strategies، هدول الأساسيات، بنعوض الخطوة الأولى، بنعوض
+
+99
+00:07:25,060 --> 00:07:28,400
+الخطوة التانية، وانتهى الموضوع... انتهى الموضوع، جيد.
+
+100
+00:07:28,400 --> 00:07:32,140
+فإذاً 21 فعلاً divides this term at k plus واحد، وهذا
+
+101
+00:07:32,140 --> 00:07:39,500
+معناه إن عمومًا النظرية دائمًا صحيحة، أو الـ rule...
+
+102
+00:07:39,500 --> 00:07:42,940
+بدنا عشان نقول theorem، الـ rule دائمًا صحيحة، طيب.
+
+103
+00:07:42,940 --> 00:07:47,560
+واحدة من الـ rules اللي أخذناها في الـ summation،
+
+104
+00:07:47,560 --> 00:07:50,480
+متذكرين في الـ summation؟ أخذنا Euler وأخذنا الـ
+
+105
+00:07:51,870 --> 00:07:54,990
+geometric، وهنتكلم عندنا على الـ geometric كمان،
+
+106
+00:07:54,990 --> 00:07:57,590
+نثبتها برضه بالـ inductive. الآن كان في عندي التربيعي،
+
+107
+00:07:57,590 --> 00:08:01,410
+التكعيبي، التكعيبي، وكانت اللي هي زي Euler لكن كله
+
+108
+00:08:01,410 --> 00:08:07,090
+تربيع، هي الـ Euler term بس كله مربع، إذا متذكرين،
+
+109
+00:08:07,090 --> 00:08:11,810
+قلناها، نفس Euler لكن مربع، اللي هو الـ summation تبع
+
+110
+00:08:11,810 --> 00:08:15,350
+مين؟ الـ cube للـ terms. Okay، بكل بساطة inductive
+
+111
+00:08:20,930 --> 00:08:27,830
+step على طول at واحد، check. من هذه عبارة عن واحد to
+
+112
+00:08:27,830 --> 00:08:31,070
+the power تلاتة زائد اتنين to the power تلاتة زائد
+
+113
+00:08:31,070 --> 00:08:35,410
+تلاتة to the power تلاتة and so on لعند n to the
+
+114
+00:08:35,410 --> 00:08:40,210
+power تلاتة، okay. خلاص، هنعوض فالواحد، الـ term الأول
+
+115
+00:08:40,210 --> 00:08:43,250
+هو واحد، term التكعيب، خلاص زي ما هو، طب نعوض هنا
+
+116
+00:08:43,250 --> 00:08:48,870
+بواحد، واحد في اتنين على اتنين، واحد تربيع، يعني، يعني
+
+117
+00:08:48,870 --> 00:08:53,290
+كلاهما بيساوي واحد، بيساوي واحد، فكلاهما هتلاقوا
+
+118
+00:08:53,290 --> 00:08:58,630
+بيساوي الواحد، يعني كلهم هذا أو هذا، كلهم واحد، طيب.
+
+119
+00:08:58,630 --> 00:09:03,870
+الـ inductive step برضه بكل أريحية، بنعامل مع أن at k
+
+120
+00:09:03,870 --> 00:09:09,310
+هي true، وبنحاول نجيب at k plus واحد، at k plus واحد،
+
+121
+00:09:09,310 --> 00:09:17,040
+تمام. فهي at n زائد واحد، الـ term اللي وراه، يعني كأنه
+
+122
+00:09:17,040 --> 00:09:21,900
+بتدج مع هذا term، افترضنا أن كل هذا term هو صح،
+
+123
+00:09:21,900 --> 00:09:28,400
+بدليل أنه عوضناها هنا بنفس paint، وضفنا فقط الـ term
+
+124
+00:09:28,400 --> 00:09:34,780
+اللي ضفناه جديد. فبدنا نشوف هل هذا term يتفق مع نفس
+
+125
+00:09:34,780 --> 00:09:40,260
+النظرية، بس هنا هتكون المفروض n زائد واحد وهنا
+
+126
+00:09:40,260 --> 00:09:45,990
+هتصبح n زائد اتنين، عشان نتفق أن أنا مش في الـ term
+
+127
+00:09:45,990 --> 00:09:49,170
+n لأ، أنا في الـ term n زائد واحد، هل الكلام ده
+
+128
+00:09:49,170 --> 00:09:54,270
+حقيقة؟ بقدر أطلع من هذا الكلام، من الـ summation اللي
+
+129
+00:09:54,270 --> 00:09:59,950
+هنا ولا لأ؟ فالاستراتيجية حتى الآن ما اتغيرتش، أنا بفهم
+
+130
+00:09:59,950 --> 00:10:05,410
+يعني ماشي في نفس القالب وبنفس الطريقة. هات نشتغل
+
+131
+00:10:05,410 --> 00:10:09,480
+عليها تربيع، هندخلها على الـ numerator والـ
+
+132
+00:10:09,480 --> 00:10:14,520
+denominator، فهنا هتصبح n زائد n في n زائد 1 كلها
+
+133
+00:10:14,520 --> 00:10:18,580
+تربيع على 4، اللي هي 2 تربيع، وهذا الـ term بقدر أقول
+
+134
+00:10:18,580 --> 00:10:23,260
+أن هو تربيع في نفسه، تكعيب، تربيع في نفسه تكعيب، فإيش
+
+135
+00:10:23,260 --> 00:10:27,380
+كتير إشكالية، وهذه بتهيأ لي استراتيجيًا، أنت بمجرد
+
+136
+00:10:27,380 --> 00:10:31,380
+تطلع فيها أكيد هتفكر فيها، ليش؟ لأن أنت عندك term
+
+137
+00:10:31,380 --> 00:10:36,160
+تربيع وبدك تجمع ولا تكعيب، خلاص بدك التكعيب هذا
+
+138
+00:10:36,160 --> 00:10:39,040
+تخففه للتربيع عشان تقدر تجمع، إذا بتقدر تجمع إشي،
+
+139
+00:10:39,040 --> 00:10:43,920
+بكل بساطة معناته تربيع مضروب في نفسه، فمنطقية يعني
+
+140
+00:10:43,920 --> 00:10:46,800
+ما فيهاش كتير زي ما بيقولوا، اتفكر فيها كتير في
+
+141
+00:10:46,800 --> 00:10:49,940
+الامتحان وتقول طب من وين بدي أجيبها؟ هي أنت
+
+142
+00:10:49,940 --> 00:10:53,860
+بتحاول تجمع terms، معناته أهم حاجة أنك توحد الـ
+
+143
+00:10:53,860 --> 00:10:57,840
+terms، الـ order، طبعًا هيكمل واحد، إذا مجمعين على إيش،
+
+144
+00:10:57,840 --> 00:11:00,420
+يكونوا مجمعين على إيش، واحد، تقدر تاخد common هذا
+
+145
+00:11:00,420 --> 00:11:04,620
+اللي دائمًا نفكر فيه، كيف أقدر أجمع الـ terms أو الـ
+
+146
+00:11:04,620 --> 00:11:07,820
+term تبع الـ rule مع الـ term اللي ضفناه تبع n زائد
+
+147
+00:11:07,820 --> 00:11:11,640
+واحد أو k زائد واحد، هذه كيف بدي أجمعهم مع بعض؟ طبعًا
+
+148
+00:11:11,640 --> 00:11:16,200
+هذا تكعيب، طبعًا هذا تربيع، بسيط جدًا، هذا حولناه تربيع،
+
+149
+00:11:16,200 --> 00:11:22,020
+وخلصنا. فهذه أول جزئية خلصناها، صار واضح عندي أن
+
+150
+00:11:22,020 --> 00:11:25,000
+التربيع هذه كمان بتدخل على الـ two terms، ليش؟ لأنه
+
+151
+00:11:25,000 --> 00:11:28,900
+صار n زائد واحد، وهنا في n زائد واحد، هنا n زائد
+
+152
+00:11:28,900 --> 00:11:32,100
+واحد تربيع، هنا برضه n زائد واحد تربيع، بتوحّيك،
+
+153
+00:11:32,100 --> 00:11:35,120
+بتخلي، زي ما بيقولوا، أفكارك تروح في اتجاه أن هذا
+
+154
+00:11:35,120 --> 00:11:39,600
+common، بقدر أعمل common للـ two terms على طول،
+
+155
+00:11:39,600 --> 00:11:46,380
+بيوحّد لك المنظر، بيوحدّ لك وين رايح، جيد. فهي بكل بساطة
+
+156
+00:11:46,380 --> 00:11:51,460
+بنقدر نتعامل معها بهذا الشكل عشان نتوحد هذا term
+
+157
+00:11:51,460 --> 00:11:55,680
+مع الأربعة، وتقدر تقول والله أن في حاجات مشتركة،
+
+158
+00:11:55,680 --> 00:11:58,920
+بدك توحد المقام، معناته أضرب في أربعة وأقسم على
+
+159
+00:11:58,920 --> 00:12:02,620
+أربعة، أضرب في أربعة وأقسم على أربعة، يمكن أنا شوية
+
+160
+00:12:02,620 --> 00:12:08,480
+أخذتها سريع، هيك، أخذت كذا خطوة في بعض، فهنا أربعة
+
+161
+00:12:08,480 --> 00:12:14,980
+على أربعة، وضربنا في اللي هي الـ term اللي فكينا ده،
+
+162
+00:12:14,980 --> 00:12:20,820
+اللي in fact في الآخر عندنا، تمام، هتوحدهم عشان يطلع
+
+163
+00:12:20,820 --> 00:12:23,460
+معاك الـ term اللي أنت شايفه قدامك، بتهيأ لي بكل
+
+164
+00:12:23,460 --> 00:12:26,620
+ببساطة،
+
+165
+00:12:26,620 --> 00:12:32,200
+بتقدر منها تجمع، مجرد حدود تجمعها، عشان يظهر في
+
+166
+00:12:32,200 --> 00:1
+
+223
+00:16:48,870 --> 00:16:53,750
+المشتركات بينهم طبعا الكلام هذا إحنا ما غيّرناه فيه
+
+224
+00:16:53,750 --> 00:16:56,830
+أي شيء أخذنا الـ a بس، العامل المشترك الـ a كعامل
+
+225
+00:16:56,830 --> 00:17:00,670
+مشترك، بتهيأ لي بكل بساطة ممكن نأخذ r ناقص واحد
+
+226
+00:17:00,670 --> 00:17:06,450
+في الطرفين، فوق وتحت، على أساس أن نوحد المقامات فهي
+
+227
+00:17:06,450 --> 00:17:10,390
+وحدنا مقاماتنا كويس، مادام خلّصنا توحيد المقامات
+
+228
+00:17:10,390 --> 00:17:14,770
+الآن two terms، بدنا نوحدهم بس مع بعضهم، أعتقد واضحة
+
+229
+00:17:14,770 --> 00:17:20,030
+أنها هتكون الآن لو ضربناها جوا، هتصبح زائد اثنين
+
+230
+00:17:20,030 --> 00:17:25,330
+صح؟ وهذا جوا زائد واحد بس بالسالب وهذا بالموجب
+
+231
+00:17:25,330 --> 00:17:31,230
+هيروحوا مع بعض، هتظل الـ R فقط زائد اثنين مع الناقص
+
+232
+00:17:31,230 --> 00:17:37,590
+واحد الأولى مع الناقص واحد الأولى، فكّيتها لكم أكثر
+
+233
+00:17:37,590 --> 00:17:42,770
+فكّيناها بشكل أكبر ليش؟
+
+234
+00:17:42,770 --> 00:17:48,730
+لأنه ببساطة هذه هتطير مع هذه، دلوقت عندك اللي أنت بدك
+
+235
+00:17:48,730 --> 00:17:53,870
+إياه أصلاً، فإذا أثبتناها أنه فعلاً، إذا كانت add k هي
+
+236
+00:17:53,870 --> 00:17:57,230
+is true، بالضرورة هتكون add k زائد واحد برضه is
+
+237
+00:17:57,230 --> 00:18:10,060
+true. تمام، كمان مثال، كمان مثال، هذه الـ route to
+
+238
+00:18:10,060 --> 00:18:15,660
+الـ rational أخذناها طبعاً إحنا بالـ inductive، بالـ
+
+239
+00:18:15,660 --> 00:18:18,600
+... آه بالـ contradiction، بالـ contradiction اللي
+
+240
+00:18:18,600 --> 00:18:22,220
+أنا بدوّيها بالمين؟ بالـ inductive proof، بالـ
+
+241
+00:18:22,220 --> 00:18:25,840
+inductive proof. طيب عشان أقول بالـ inductive proof
+
+242
+00:18:25,840 --> 00:18:29,480
+بدنا نرجع لفكرتها، لاحظ أن إحنا هنا ما فيش عندي N
+
+243
+00:18:29,480 --> 00:18:35,100
+صح؟ زي بالضبط لما رحتوا في عملية الـ contradiction
+
+244
+00:18:35,100 --> 00:18:39,340
+برضه كنتوا محتارين أنه ما فيش طرفين في وجهتها، كنتوا
+
+245
+00:18:39,340 --> 00:18:41,660
+بتقولوا أنه ما فيش طرفين هنا، نفس الجملة، أنا ما عنديش
+
+246
+00:18:41,660 --> 00:18:44,780
+N، الشيء N هذا اللي بدنا نتعامل معاه بكل بساطة
+
+247
+00:18:44,780 --> 00:18:50,060
+إحنا هنولد N، هنعمل N هنا فيها بحيث أني أقول let P
+
+248
+00:18:50,060 --> 00:18:56,340
+of N هي أنه that there is no positive integers B
+
+249
+00:18:56,340 --> 00:19:06,160
+such that root two تساوي N over B، لا يوجد integer
+
+250
+00:19:06,160 --> 00:19:15,040
+كمقام و N مقسومة عليه تعطيني النسبة جذر اثنين
+
+251
+00:19:15,040 --> 00:19:19,460
+النسبة جذر اثنين، والآن بدي أبدأ أقول إيش قيم N
+
+252
+00:19:19,460 --> 00:19:20,200
+الممكنة
+
+253
+00:19:23,490 --> 00:19:27,790
+فولدنا لها n من عندنا، جبنا لها n من عندنا، تمام
+
+254
+00:19:27,790 --> 00:19:31,190
+بهذا الشكل أصبح بكل بساطة بتقدر تتعامل معاها الآن
+
+255
+00:19:31,190 --> 00:19:37,150
+قيمة n المناسبة، تقسم على b عشان تعطي جذر اثنين، إذا
+
+256
+00:19:37,150 --> 00:19:42,710
+والله في قيمة لـ n معناته هي rational، فإحنا الفرضية
+
+257
+00:19:42,710 --> 00:19:45,030
+إيش بتقول؟ is no positive
+
+258
+00:19:47,050 --> 00:19:51,210
+is no positive، ياريت نحط تحتها ثلاثة أربعة خطوط
+
+259
+00:19:51,210 --> 00:19:56,250
+هذه no positive، معناه ذلك أن أنا بتكلم أنه لا يوجد
+
+260
+00:19:56,250 --> 00:19:59,690
+لأن لقدام شوية بدنا نضل نركز إن أنا بتكلم عن
+
+261
+00:19:59,690 --> 00:20:04,490
+لا يوجد، فالإثبات أنه لا يوجد، النفي تبعها بيصير أنه
+
+262
+00:20:04,490 --> 00:20:12,110
+يوجد، خلينا نعدّ النقطة هذه، واضحة واضحة، أيوة true
+
+263
+00:20:12,110 --> 00:20:16,910
+معناته أنه لا positive، الآن لما بدي أقول بدي أفرض
+
+264
+00:20:16,910 --> 00:20:22,190
+عكسها، معناته بدي أقول أنه لأ، هي يوجد، فرضية حتى
+
+265
+00:20:22,190 --> 00:20:24,370
+الآن الـ function اللي إحنا شغالين عليها بدنا
+
+266
+00:20:24,370 --> 00:20:29,350
+نثبتها أن هي P of M، أنه لا يوجد قيمة لـ M نقسمها
+
+267
+00:20:29,350 --> 00:20:37,140
+على integer معين بيطلع لي جذر اثنين. طيب الآن
+
+268
+00:20:37,140 --> 00:20:41,180
+نبدأ بالـ base step، N بتساوي واحد، بتبدأ عند N
+
+269
+00:20:41,180 --> 00:20:46,980
+بتساوي واحد، ثم نثبت بعد ذلك أن الكل زيّه، اللي هو K،
+
+270
+00:20:47,360 --> 00:20:54,780
+K زائد واحد، K زائد اثنين، وكل قيم من واحد لـ K
+
+271
+00:20:54,780 --> 00:21:01,240
+هيحققوا نفس الـ function، اللي هي لا يوجد قيمة نقسمها
+
+272
+00:21:01,240 --> 00:21:06,260
+على بيطلع لي جذر اثنين، اللي هي لا يوجد، تمام، فإذا
+
+273
+00:21:06,260 --> 00:21:11,840
+الـ base step كانت كالتالي، هتصبح بتفترض أن P واحد
+
+274
+00:21:11,840 --> 00:21:18,020
+is true، كيف؟ هقول جذر اثنين هتصبح هنا واحد، مش واحد
+
+275
+00:21:18,020 --> 00:21:21,520
+طب أنا عارف أن جذر اثنين هي أكبر من واحد، من الواحد
+
+276
+00:21:21,520 --> 00:21:25,240
+الصحيح الطبيعي، طيب في نفس الجملة، الواحد الصحيح
+
+277
+00:21:25,240 --> 00:21:31,260
+الطبيعي هو أكبر من أو يساوي واحد على B، على اعتبار
+
+278
+00:21:31,260 --> 00:21:36,880
+أن B positive integer، B positive integer، يعني أقل
+
+279
+00:21:36,880 --> 00:21:41,000
+قيمة له أن يكون واحد، طيب لو كانت واحد على واحد
+
+280
+00:21:41,000 --> 00:21:44,080
+معناته يساوي الواحد، وإحنا عارفين أنه الواحد أقل من
+
+281
+00:21:44,080 --> 00:21:49,760
+جذر اثنين، معناته لا يساوي جذر اثنين، معناته
+
+282
+00:21:49,760 --> 00:21:53,520
+لا يساوي جذر اثنين، صح؟ معناته أنا حققت الحقيقة
+
+283
+00:21:53,520 --> 00:21:59,260
+النظرية هذه، أنه لا يوجد يساوي جذر اثنين، هو فعلاً
+
+284
+00:21:59,260 --> 00:22:03,130
+ما يساويش جذر اثنين، هي عند الواحد، خلّصنا الـ base
+
+285
+00:22:03,130 --> 00:22:07,850
+step حتى اللحظة، هي الـ base step، تمام؟ لكل قيم
+
+286
+00:22:07,850 --> 00:22:11,470
+طبعاً مين بـ B أكبر من أو يساوي واحد، لأنه إذا كانت
+
+287
+00:22:11,470 --> 00:22:14,170
+أكبر من الواحد كمان، معناته بالعكس، صارت fraction
+
+288
+00:22:14,170 --> 00:22:17,670
+يعني كمان أقل من الواحد، فهي بالضرورة أكيد مش هتكون
+
+289
+00:22:17,670 --> 00:22:21,050
+تساوي الاثنين، اللي أنا عارف أن جذر اثنين أكبر من
+
+290
+00:22:21,050 --> 00:22:26,860
+واحد، إحنا مسبقاً عارفين أنه أكبر من واحد، صح؟ فإذا أي
+
+291
+00:22:26,860 --> 00:22:31,260
+كسر واحد على أي رقم positive مستحيل يكون بيساوي
+
+292
+00:22:31,260 --> 00:22:34,480
+جذر الاثنين، لأنه حيكون fraction، فخلّصنا الـ base
+
+293
+00:22:34,480 --> 00:22:39,200
+step، الـ inductive step، الـ inductive step، الآن في
+
+294
+00:22:39,200 --> 00:22:44,920
+الـ inductive step، assume that P of J is true، طيب
+
+295
+00:22:44,920 --> 00:22:50,080
+مين J هذه؟ لكل القيم J أقل من أو يساوي K، strong
+
+296
+00:22:51,190 --> 00:22:55,490
+proof، أنا هنا بتكلم عن الـ strong proof، وهذا النقطة
+
+297
+00:22:55,490 --> 00:22:58,330
+اللي كنتوا بتقولوها صح، الـ strong proof، فإذا أنا
+
+298
+00:22:58,330 --> 00:23:05,050
+بتكلم هنا عن P of J is true، لكل mean J هذه، لكل
+
+299
+00:23:05,050 --> 00:23:09,430
+القيم اللي أقل من K، ابتداءً طبعاً من الـ base، من الـ
+
+300
+00:23:09,430 --> 00:23:12,550
+base step، من الواحد، والاثنين، والثلاثة
+
+301
+00:23:12,550 --> 00:23:16,650
+والأربعة، والخمسة، والستة، والسبعة، والثمانية، والتسعة to K، إذا
+
+302
+00:23:16,650 --> 00:23:23,020
+كلهم فعلاً بيحققوا نفس الفرضية بتاعتنا، أن ولا رقم لو
+
+303
+00:23:23,020 --> 00:23:28,200
+قسمته على P بيساوي جذر اثنين، ولا رقم، معناته بدنا
+
+304
+00:23:28,200 --> 00:23:32,420
+نثبت أن حتى K زائد واحد لو قسمناها على P برضه مش
+
+305
+00:23:32,420 --> 00:23:38,500
+هتساوي كجذر اثنين، جذر اثنين، فمبدئياً حتى الآن
+
+306
+00:23:38,500 --> 00:23:41,440
+الفرضية هذه، اللي هو الـ inductive step اللي بدنا
+
+307
+00:23:41,440 --> 00:23:47,340
+نبني عليها، فإذا معنى ذلك أن جذر اثنين لا يساوي J
+
+308
+00:23:47,340 --> 00:23:53,770
+over P، لأن هذه هي الفرضية اللي أنا أفرضها at k
+
+309
+00:23:53,770 --> 00:24:00,850
+الشيء، أنا جاي هنا بقول أنه الفرضية الصحيحة at k، طب
+
+310
+00:24:00,850 --> 00:24:06,510
+strong proof، معناته at k وكل ما قبلها is true، مادام
+
+311
+00:24:06,510 --> 00:24:12,460
+is true، معناته لا تساوي g over b، لأنه no positive
+
+312
+00:24:12,460 --> 00:24:15,980
+هيتكرر مرة عشان إيه، حطينا عليها ثلاثة خطوط، حطينا
+
+313
+00:24:15,980 --> 00:24:20,200
+تحتها ثلاثة خطوط، جيد، هذا معناته إذا قدرت أقول إن هذا
+
+314
+00:24:20,200 --> 00:24:24,380
+أثبتنا هذا الكلام، إذا هذا صحيح، إذا بالضرورة هتكون
+
+315
+00:24:24,380 --> 00:24:27,880
+هذا الكلام صحيح، الآن بدنا نثبت هذا الموضوع، هل فعلاً
+
+316
+00:24:27,880 --> 00:24:30,680
+صحيح ولا لأ، بس إحنا هنا حطينا النظرية بتاعت من
+
+317
+00:24:30,680 --> 00:24:38,990
+strong mathematical induction، إنه مش أدعياء بس at k
+
+318
+00:24:38,990 --> 00:24:44,750
+وكل ما قبلها، ابتداءً من الـ base case اللي هي من
+
+319
+00:24:44,750 --> 00:24:50,870
+واحد، يعني من واحد لـ k كله، إذا كان كله true، إذا هذه
+
+320
+00:24:50,870 --> 00:24:54,230
+الـ implication، إذا at k زي واحد برضه is true، بس هي
+
+321
+00:24:54,230 --> 00:24:57,130
+كلمة true إيش معناها؟ أنه لا يساوي each other،
+
+322
+00:24:57,130 --> 00:25:01,190
+الاثنين. هي كمان مرة بنعيدها، عشان بنا ما تضيعش
+
+323
+00:25:01,190 --> 00:25:05,330
+منكم الأمور، معناته أنه لا تساوي جذر اثنين، هيك هيك
+
+324
+00:25:05,330 --> 00:25:10,570
+معناه true، حسب الفرضية، حسب الفرضية، تمام، الآن
+
+325
+00:25:10,570 --> 00:25:16,350
+عشان نحسب الكلام ده، نثبته عند k زائد واحد، هنعملها
+
+326
+00:25:16,350 --> 00:25:21,570
+بالـ contradiction، بمعنى أنه بدي أثبت عكسها، لا
+
+327
+00:25:21,570 --> 00:25:29,060
+يحققها، عكسها إيش؟ أنه يوجد، فإذن صارت الـ false الآن
+
+328
+00:25:29,060 --> 00:25:36,260
+أن يوجد، مش هيك؟ إيش يوجد؟ يوجد قيمة، إيش اسمها
+
+329
+00:25:36,260 --> 00:25:42,480
+القيمة هذه؟ K زائد واحد، فإذن الفرضية الآن أن جذر
+
+330
+00:25:42,480 --> 00:25:49,980
+اثنين تساوي K زائد واحد على B، صح؟
+
+331
+00:25:49,980 --> 00:25:56,380
+اللي هو فرضت النفي، فرضنا النفي، طيب متذكرين الـ
+
+332
+00:25:56,380 --> 00:26:00,570
+contradiction؟ أنا بفرض إنه فيه وبخلي الحل
+
+333
+00:26:00,570 --> 00:26:07,510
+يُوصلني للإثبات، فإذن كأنه طلعت جذر 2 تساوي K زائد
+
+334
+00:26:07,510 --> 00:26:13,430
+B، وبعدين مع الحل هاتفاجأ أنه لأ، هي جذر 2 لا تساوي
+
+335
+00:26:13,430 --> 00:26:18,470
+K زائد B، فصارت كأنه أنت بتقول جذر 2 تساوي K زائد B
+
+336
+00:26:18,470 --> 00:26:24,470
+وجذر 2 لا تساوي K زائد B، تناقض على طول، تناقض، تناقض،
+
+337
+00:26:24,470 --> 00:26:28,520
+معناته false، و false معناته أن النظرية من الأساس
+
+338
+00:26:28,520 --> 00:26:32,400
+كانت صحيحة، أنت فرضت عكسها وعكسها طالع متناقض،
+
+339
+00:26:32,400 --> 00:26:37,900
+معناته هي أصلها صحيح، أصلها صحيح، الكلام اللي بنعمله
+
+340
+00:26:37,900 --> 00:26:42,440
+أمتى؟ لأن أنا مش هقدر آخذ كل القيم واحدة واحدة على
+
+341
+00:26:42,440 --> 00:26:47,520
+B، كويس، وأفهم وأثبت أن هي لا تساوي جذر اثنين، فأنت
+
+342
+00:26:47,520 --> 00:26:52,620
+إيش بتقول؟ بدك تفرض أنه لأ هي تساوي، وخلّي الحل يقول لك
+
+343
+00:26:52,620 --> 00:26:56,400
+لا يساوي، لأنه بالـ ... بالـ direct، معناته أنت محتاج
+
+344
+00:26:56,400 --> 00:26:59,280
+تجهد تعوض ... تعوض فيهم كلهم، وهذا الـ cancel
+
+345
+00:26:59,280 --> 00:27:01,580
+introduction، عملناه، أنت مستحيل تجهد تعوض فيهم
+
+346
+00:27:01,580 --> 00:27:06,620
+كلهم، لأ، أنت بدك تثبت أن عكسهم غير صحيح، وقلت لكم
+
+347
+00:27:06,620 --> 00:27:10,660
+إياها قبل هيك، أنت مش بالضرورة أحياناً وفي الحروب
+
+348
+00:27:10,660 --> 00:27:14,660
+الانتخابية مثلاً أنك أنت تركز على مزاياك، أنت ممكن
+
+349
+00:27:14,660 --> 00:27:20,220
+تركز على عيوب خصمك بس، وتكون سبيل لفوزك، فأنت بدون
+
+350
+00:27:20,220 --> 00:27:24,280
+ما تضطر تقول تتكلم عن إنجازات، أنت بتتكلم عن خيبات
+
+351
+00:27:24,280 --> 00:27:30,580
+أمل للخصم، فتعطي حق أن أنت الأفضل، الفكرة نفسها
+
+352
+00:27:30,580 --> 00:27:35,460
+تمام، فهي اللي ... اللي بدنا نصل له الآن، أنه الآن بدأ
+
+353
+00:27:35,460 --> 00:27:40,440
+افترض أن هي لا يوجد، أنه يوجد فعلياً، تمام؟ والله
+
+354
+00:27:40,440 --> 00:27:43,740
+لإجينا أن الحل ظلّ مكمل، أنه ظلّ يوجد، معناته فعلاً
+
+355
+00:27:43,740 --> 00:27:47,440
+في مشكلة عندنا في الحل، لكن الطبيعي الآن واللي أنا
+
+356
+00:27:47,440 --> 00:27:52,980
+متوقعه أنه أثناء الحل هنصل لنقطة أن لأ، إحنا
+
+357
+00:27:52,980 --> 00:27:59,600
+ناقضنا الفرضية بتاعتنا، فالآن هذه فرضية، هذه فرضية مش
+
+358
+00:27:59,600 --> 00:28:02,840
+مسموح أثناء الحل، تفاجأنا أن الفرضية غلط، طب أنا
+
+359
+00:28:02,840 --> 00:28:07,060
+بدي كل شغل عليها، واضحة، تمام؟ هنشوف وين بدنا نصل في
+
+360
+00:28:07,060 --> 00:28:12,820
+الآخر، هذه فرضيتنا، كتبناها على جنب هناك عشان نتطلع
+
+361
+00:28:12,820 --> 00:28:19,440
+قدامها هنا، خلينا نبدأ، هذه الفرضية واللي بدنا ننطلق
+
+362
+00:28:19,440 --> 00:28:21,880
+منها بكل بساطة، نربع الطرفين
+
+363
+00:28:26,570 --> 00:28:30,010
+طيب مشكلة؟ آه، هنصل لنفس النتيجة بس طريقة الإثبات
+
+364
+00:28:30,010 --> 00:28:33,490
+هتختلف في آخرها، ليش؟ لأن أنا بتكلم عن inductive
+
+365
+00:28:33,490 --> 00:28:37,150
+بتكلم مش عن contradiction، لكن السبيل كان هو الـ
+
+366
+00:28:37,150 --> 00:28:41,450
+contradiction نفسها، تمام؟ فهيوصلنا لنفس الفكرة ولو
+
+367
+00:28:41,450 --> 00:28:45,230
+وصلنا فيها لقصة الـ even، متذكرينها، تمام؟ هنصل لنفس
+
+368
+00:28:45,230 --> 00:28:48,830
+الفكرة، فإذا اثنين B تربيع تساوي K زائد واحد
+
+369
+00:28:48,830 --> 00:28:54,040
+تربيع، معناته K زائد واحد تربيع هي even، ومعناه ذلك أن
+
+370
+00:28:54,040 --> 00:28:58,080
+K زائد واحد even، معناه ذلك أن K زائد واحد بقدر
+
+371
+00:28:58,080 --> 00:29:02,500
+أحطه بصيغة اثنين في some integer، في some integer
+
+372
+00:29:02,500 --> 00:29:06,960
+مادام even، مادام طلعت في النهاية even، بكل بساطة
+
+373
+00:29:06,960 --> 00:29:15,720
+أرجع مكانها فوق هنا، فصارت الاثنين T كله تربيع، بكل
+
+374
+00:29:15,720 --> 00:29:20,220
+بساطة تربيع دخله على الطرفين، فصارت أربعة في T تربيع
+
+375
+00:29:20,220 --> 00:29:24,080
+بتقدر ببساطة جداً تختصر الاثنين مع الاثنين، فبتصير B
+
+376
+00:29:24,080 --> 00:29:28,340
+تربيع تساوي اثنين T تربيع، وهذا معناه أن الـ B
+
+377
+00:29:28,340 --> 00:29:37,600
+تربيع even، يعني الـ B even، يعني B even، تمام، الآن
+
+378
+00:29:37,600 --> 00:29:43,920
+جذر اثنين، اللي هي K زائد واحد على B هتساوي اثنين T
+
+379
+00:29:43,920 --> 00:29:52,680
+على اثنين S، يعني T على S، طب حلو جداً، حلو جداً جداً
+
+380
+00:29:52,680 --> 00:30:00,640
+الآن فرضيتنا إيش كانت بتقول؟ أنّه تساوي، بينما فعلياً
+
+381
+00:30:00,640 --> 00:30:09,880
+هنا اللي الـ T هذه طلعت نص قيمة K زائد واحد، صح؟
+
+382
+00:30:10,720 --> 00:30:14,720
+طيب أنا فعلاً بتكلم عن K زائد واحد على B، اتفاجأت و
+
+383
+00:30:14,720 --> 00:30:21,200
+طبعاً كل K و K ناقص واحد لعند ابتداءً من الواحد، هدول
+
+384
+00:30:21,200 --> 00:30:30,120
+أساساً بيحققوا true، فأنت بدل ما تحقق لإن K زائد
+
+385
+00:30:30,120 --> 00:30:34,420
+واحد هي false، روح حطّ مكانها K زائد واحد على
+
+386
+00:30:34,420 --> 00:30:39,160
+اثنين، واللي هي أصلاً مشمولة هنا،
+
+445
+00:35:49,360 --> 00:35:54,480
+اتنين ليست rational أو irrational
+
+446
+00:35:54,480 --> 00:35:57,660
+هذه طريقة و الـ contrapositive طريقة، بس هذا طبعاً
+
+447
+00:35:57,660 --> 00:36:00,900
+طريقة strong وهي واضح أن حتى strong كمان في
+
+448
+00:36:00,900 --> 00:36:01,660
+الأفباد تبعها
+
+449
+00:36:04,300 --> 00:36:08,480
+الـ strong لما تكون أنت أو K زائد واحد لا تعتمد
+
+450
+00:36:08,480 --> 00:36:14,000
+على K فقط عشان تجيبها، لا تعتمد على K فقط، هذه
+
+451
+00:36:14,000 --> 00:36:18,500
+تجيبها لما يكون مثلاً تتكلم عن الـ primes لأن الـ
+
+452
+00:36:18,500 --> 00:36:21,860
+primes أنت عارف أن هي بتعتمد على كل اللي قبلها، مش
+
+453
+00:36:21,860 --> 00:36:26,880
+على اللي قبلها مباشر، لأ على كل اللي قبلها، فهذه
+
+454
+00:36:26,880 --> 00:36:34,100
+بتضطر للـ strong لما تتكلم عن الـ .. الـ .. الـ .. الـ
+
+455
+00:36:34,100 --> 00:36:35,060
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+456
+00:36:35,060 --> 00:36:35,120
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+457
+00:36:35,120 --> 00:36:35,880
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+458
+00:36:35,880 --> 00:36:36,240
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+459
+00:36:36,240 --> 00:36:36,420
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+460
+00:36:36,420 --> 00:36:36,640
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+461
+00:36:36,640 --> 00:36:37,200
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+462
+00:36:37,200 --> 00:36:38,800
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+463
+00:36:38,800 --> 00:36:47,440
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+464
+00:36:47,440 --> 00:36:47,720
+الـ .. الـ .. الـ .. الـ .. الـ
+
+465
+00:36:57,710 --> 00:37:02,250
+معتمد، K زائد واحد معتمد على ما قبل K، ففي الحالة
+
+466
+00:37:02,250 --> 00:37:05,730
+هذه على طول بتفكر في الـ strong مباشرة، بتفكر في مين
+
+467
+00:37:05,730 --> 00:37:09,350
+في الـ strong، أما إذا كان الـ proof K زائد واحد
+
+468
+00:37:09,350 --> 00:37:14,730
+مباشرة معتمد على K، خلص الـ first principle كافي، الـ
+
+469
+00:37:14,730 --> 00:37:16,990
+first principle كافي، لكن هي مش دائماً الدنيا بتكون
+
+470
+00:37:16,990 --> 00:37:20,390
+معاك بهذا الشكل، هي مثل جسم على اتنين، لما تجسم على
+
+471
+00:37:20,390 --> 00:37:23,950
+اتنين مش معناته أنه K زائد واحد لا تعتمد على K فقط،
+
+472
+00:37:24,610 --> 00:37:29,470
+وإنما تعتمد على K زائد واحد على اتنين، واللي احنا
+
+473
+00:37:29,470 --> 00:37:34,030
+أصلًا من الأساس قلنا أنه أقل من K فعلاً، وفي النهاية
+
+474
+00:37:34,030 --> 00:37:38,110
+هي مثبتة أو مثبتة أساسًا ضمن النظرية، فكيف أنا
+
+475
+00:37:38,110 --> 00:37:42,550
+بقول K زائد واحد خارج النظرية وهي معتمدة عليها،
+
+476
+00:37:42,550 --> 00:37:45,690
+تمام
+
+477
+00:37:57,260 --> 00:38:01,520
+كمان مثال هي
+
+478
+00:38:01,520 --> 00:38:06,500
+نفس الفكرة اللي هي مين التكعيب، بس جالك هنا بتساوي
+
+479
+00:38:06,500 --> 00:38:13,840
+حاجة ثانية مختلفة، جالك هنا بتساوي مجموعة الـ ends
+
+480
+00:38:13,840 --> 00:38:20,160
+بدون التكعيب، القيم بدون التكعيب وكله تربيع، فهنا
+
+481
+00:38:20,160 --> 00:38:23,520
+اختلفت عن صيغة التجميع، اختلفت عن صيغة التجميع برضه
+
+482
+00:38:23,520 --> 00:38:28,220
+كيف نشتغل عليها وجاك أنه من أيش بتبدأ، فإذا
+
+483
+00:38:28,220 --> 00:38:32,200
+الـ basis عن تلاتة، الـ basis على طول ببدأ عند مين،
+
+484
+00:38:32,200 --> 00:38:36,560
+عن تلاتة، بدنا نلتزم بمين؟ بـ الـ .. الـ where اللي
+
+485
+00:38:36,560 --> 00:38:39,780
+بكنا نعطيكي إياها، من وين تبدأ؟ فهي عند التلاتة، معناه
+
+486
+00:38:39,780 --> 00:38:43,980
+أنك بدك تأخذ أول three terms هنا و بدك برضه تأخذ
+
+487
+00:38:43,980 --> 00:38:47,890
+أول three terms هنا، فهو الـ three terms: واحد، تمانية
+
+488
+00:38:47,890 --> 00:38:51,710
+و سبعة و عشرين، وهنا واحد زائد اتنين زائد تلاتة
+
+489
+00:38:51,710 --> 00:38:55,050
+كله تربيع، فكله هيطلع سواء هذه أو هذه هيطلع ستة و
+
+490
+00:38:55,050 --> 00:39:01,330
+تلاتين، فإذن أول خطوة صحيحة، الآن الـ inductive step
+
+491
+00:39:01,330 --> 00:39:06,530
+في الحالة هذه بدنا نفرض أن الـ rule true صحيحة at
+
+492
+00:39:06,530 --> 00:39:12,920
+زي ما قلنا k، زي .. at k أو n، تأخذها تأخذها
+
+493
+00:39:12,920 --> 00:39:13,600
+تاخذها تاخذها تاخذها تاخذها تاخذها تاخذها تاخذها
+
+494
+00:39:13,600 --> 00:39:14,640
+تاخذها تاخذها تاخذها تاخذها تاخذها تاخذها تاخذها
+
+495
+00:39:14,640 --> 00:39:17,760
+تاخذها تاخذها تاخذها تاخذها تاخذها تاخذها تاخذها
+
+496
+00:39:17,760 --> 00:39:20,320
+تاخذها تاخذها تاخذها تاخذها تاخذها تاخذها تاخذها
+
+497
+00:39:20,320 --> 00:39:26,160
+تاخذها تاخذها تاخذها تاخذها تاخذها تاخذها تاخذها
+
+498
+00:39:26,160 --> 00:39:35,280
+تاخذها تاخذها تاخذها تاخذها
+
+499
+00:39:40,180 --> 00:39:44,100
+صح؟ مش هيقول فقط، لأن المفروض أنه نضيف لأن زائد
+
+500
+00:39:44,100 --> 00:39:46,960
+واحد وبعدين كله تربيع، بعدين كله تربيع، هذا اللي
+
+501
+00:39:46,960 --> 00:39:51,540
+بدنا نثبته الآن، هذا اللي بدنا نثبته الآن، أساسًا أن
+
+502
+00:39:51,540 --> 00:39:54,460
+أفصل، أقول اللي، معناته بدي أقول أن هي لأن فقط
+
+503
+00:39:54,460 --> 00:40:01,340
+تتفق مع النظرية، هيها زائد إن زائد واحد تكعيب، الـ
+
+504
+00:40:01,340 --> 00:40:05,940
+term اللي انضاف في الطرفين، احنا متفقين أن هذا الـ
+
+505
+00:40:05,940 --> 00:40:19,980
+term يساوي هذا الـ term نظرياً at n، طيب هنضيف K أو n
+
+506
+00:40:19,980 --> 00:40:28,060
+زائد واحد للطرفين، هي هنا مضافة وهي هنا مضافة، هنا
+
+507
+00:40:28,060 --> 00:40:31,020
+أضيفت وهنا أضيفت، طيب عشان أقول أنه فعلاً تم
+
+508
+00:40:31,020 --> 00:40:34,620
+إضافتها والـ rule هتظل صح، المفروض يظهر عندي هذا الـ
+
+509
+00:40:34,620 --> 00:40:34,820
+term
+
+510
+00:40:38,210 --> 00:40:42,590
+مفروض بعد عملية .. عمليات رياضية أعملها يظهر عندي
+
+511
+00:40:42,590 --> 00:40:48,090
+هذا الـ term، هل بنفهم؟ هل احنا .. لازم يظهر عندك؟
+
+512
+00:40:48,090 --> 00:40:53,330
+صح؟ تمام، نمسك الآن الطرف اللي بدنا نبدأ نشتغل عليه،
+
+513
+00:40:53,330 --> 00:41:02,490
+أحول وأغير وأبدل فيه بحيث أنه يطلع هيك بكل
+
+514
+00:41:02,490 --> 00:41:06,090
+بساطة هذا
+
+515
+00:41:06,090 --> 00:41:06,490
+الـ term
+
+516
+00:41:09,270 --> 00:41:13,810
+Euler، رجالنا، جا إيش بيساوي؟
+
+517
+00:41:13,810 --> 00:41:16,890
+صح؟
+
+518
+00:41:16,890 --> 00:41:22,130
+إيش معلق، من واحد to N خلاص، هاي من N واحد لـ N
+
+519
+00:41:22,130 --> 00:41:26,770
+Euler أبو نصر، سجلها لنا، مش أبو نصر سجلها
+
+520
+00:41:26,770 --> 00:41:30,830
+لنا، طيب N في N زائد واحد على اتنين، خلاص، كله
+
+521
+00:41:30,830 --> 00:41:34,290
+بعدين تربيع، okay، ربّعنا التربيع، الآن هذه صارت
+
+522
+00:41:34,290 --> 00:41:39,680
+مشابهة ل المثال اللي أخذناه، ثاني مثال أخذناه، خلاص
+
+523
+00:41:39,680 --> 00:41:44,320
+بتخيّلي واضحة جداً الآن، n زائد واحد هنا، أنت هتدخل
+
+524
+00:41:44,320 --> 00:41:46,920
+التربيع وهتصير على أربعة، أخذناها طويل لسه قبل شوية،
+
+525
+00:41:46,920 --> 00:41:49,700
+ما أخذناها، فصارت زيها زي امتحان سابق له،
+
+526
+00:41:49,700 --> 00:41:54,180
+فالامتحانات بتيجي من بعض، بسمع مع بعض الـ ..
+
+527
+00:41:55,270 --> 00:41:59,550
+modifications، مع بعض التعديلات اللي ممكن نحطها على
+
+528
+00:41:59,550 --> 00:42:03,810
+الـ .. على السؤال الباقي، أمثلة بتاعتي اللي أخذناها
+
+529
+00:42:03,810 --> 00:42:08,630
+سابقا، أصبح ما فيش صعوبة فيه، تكعيب، هذا بتلزمنيش،
+
+530
+00:42:08,630 --> 00:42:15,290
+بتديها تربيع، فحولناها للتربيع ووحدنا المقامات عشان
+
+531
+00:42:15,290 --> 00:42:20,280
+بعدين نرجع لنفس الفكرة الأولى، وصلنا للفكرة لـ N زائد
+
+532
+00:42:20,280 --> 00:42:23,780
+واحد و N زائد اتنين على اتنين، هذا الـ term حسب
+
+533
+00:42:23,780 --> 00:42:29,960
+Euler، هو مجموع لـ عند N زائد واحد، لما تاخد هذا
+
+534
+00:42:29,960 --> 00:42:38,150
+لحاله جوا، لاحظ لما كانت لـ N قلنا N في اللي بعدها in
+
+535
+00:42:38,150 --> 00:42:41,370
+في اللي بعدها على 2، هنا in زائد واحد في اللي بعدها
+
+536
+00:42:41,370 --> 00:42:45,410
+على 2، بنرجع بنستعيد مكانها، معناته أن هنا نتكلم عن
+
+537
+00:42:45,410 --> 00:42:51,790
+summation واحد to n زائد واحد تربيع، هي اللي احنا
+
+538
+00:42:51,790 --> 00:42:57,970
+بدنا هي أساساً استخدمنا
+
+539
+00:42:57,970 --> 00:43:00,050
+Euler track
+
+540
+00:43:02,040 --> 00:43:06,380
+خلاص، أضحك، كمان مثال بالمرة مع نوجت .. اه مع نوجت
+
+541
+00:43:06,380 --> 00:43:10,540
+دي كويس، لأ مسودكوا حرارتكوا أثرة منيحة .. زيادة
+
+542
+00:43:10,540 --> 00:43:11,800
+.. طيب
+
+543
+00:43:16,500 --> 00:43:21,700
+بالـ mathematical induction، المفروض أنه لكل قيم H واللي
+
+544
+00:43:21,700 --> 00:43:26,860
+اللي هي أكبر من minus one، بدنا نثبت أنه واحد زائد
+
+545
+00:43:26,860 --> 00:43:33,880
+N في H دائماً أقل من أو يساوي واحد زائد H كله to
+
+546
+00:43:33,880 --> 00:43:40,580
+the power N for all non negative integers، بمعنى
+
+547
+00:43:40,580 --> 00:43:45,910
+zero، فـ الـ non negative يعني من zero، الـ natural
+
+548
+00:43:45,910 --> 00:43:49,670
+number، من الآخر zero و positive، zero و positive
+
+549
+00:43:49,670 --> 00:43:53,090
+اللي هي الـ natural number، طيب business تبع طول
+
+550
+00:43:53,090 --> 00:43:57,910
+هتكون عند الـ zero، هي أقل قيمة ممكنة، أول قيمة حسب الـ
+
+551
+00:43:57,910 --> 00:44:01,350
+non negative، بنعود فيها، ما أعتقدش هيكون عندنا مشكلة
+
+552
+00:44:01,350 --> 00:44:08,390
+فيها، واحد وهنا صفر، فخلاص هذه دليل واحد، الـ term هنا
+
+553
+00:44:08,390 --> 00:44:13,740
+واحد زائد H، جد ما تكون قيمة H في النهاية، كله بتباري
+
+554
+00:44:13,740 --> 00:44:17,920
+zero يعني واحد، يعني واحد، فبيطلع واحد بيساوي واحد، والـ
+
+555
+00:44:17,920 --> 00:44:22,660
+المساواة هي ضمن الـ rule، فإذا ماشي، إذا الـ business
+
+556
+00:44:22,660 --> 00:44:28,060
+step success، انجحنا فيها، الـ inductive step برضه
+
+557
+00:44:28,060 --> 00:44:32,600
+بكل بساطة، بدنا نتكلم بعدها على N زائد واحد، وهنا
+
+558
+00:44:32,600 --> 00:44:37,120
+برضه N زائد واحد، ونشوف هل الكلام ده صحيح أو .. أو
+
+559
+00:44:37,120 --> 00:44:43,780
+لأ، فهنا هذه، بدأ، افترض أن هي صحيحة، الـ term هذا صحيح
+
+560
+00:44:43,780 --> 00:44:51,840
+لـ عند n، لـ n صحيح، لكل قيم n أكبر من أو يساوي صفر،
+
+561
+00:44:51,840 --> 00:44:58,900
+تمام، الآن بنجرب عند n زائد واحد، و n زائد، أو عفواً
+
+562
+00:44:58,900 --> 00:45:04,240
+فوق، n زائد واحد، أول
+
+563
+00:45:04,240 --> 00:45:09,090
+شغل اللي هنعمله، كلنا عارفين أن واحد زائد H هذه
+
+564
+00:45:09,090 --> 00:45:18,430
+وحسب قيمة H، وين H؟ صح؟ فإذن دائماً أكبر من صفر، H
+
+565
+00:45:18,430 --> 00:45:23,390
+دائماً أكبر من سالب واحد، طيب هي مجموعة مع واحد، يعني
+
+566
+00:45:23,390 --> 00:45:26,850
+دائماً أكبر من صفر، مقتنعين؟ عشان لأنه هذا هنحتاجه
+
+567
+00:45:26,850 --> 00:45:29,910
+في الإثبات، الآن هنحتاجه في الإثبات، فإذا الـ
+
+568
+00:45:29,910 --> 00:45:35,100
+condition هذا مهم جداً، كان في السؤال، مهم جداً كان في
+
+569
+00:45:35,100 --> 00:45:39,420
+السؤال، وكل شغلنا على N، ماحدش يروح يخبط زي ما في
+
+570
+00:45:39,420 --> 00:45:42,520
+وجدها في الأسئلة، لقى أن في هنا متغيرين، في عندك
+
+571
+00:45:42,520 --> 00:45:45,960
+افترضوا أن الـ H كمان متغير، فبدأوا يشتغلوا على الـ H
+
+572
+00:45:45,960 --> 00:45:49,800
+وبدؤوها من سالب واحد، ونسينا أنه لأ، شغلنا على N
+
+573
+00:45:49,800 --> 00:45:55,700
+مش على الـ H، تمام، الآن بكل بساطة هذا الـ term زي ما
+
+574
+00:45:55,700 --> 00:45:59,440
+هو هنا، بتفصلها
+
+575
+00:46:00,800 --> 00:46:03,760
+in لحال، والـ term اللي ضربته فيه، اللي هو نفس الـ
+
+576
+00:46:03,760 --> 00:46:07,940
+term اللي خلاه زائد واحد، اللي خلاه زائد واحد، و
+
+577
+00:46:07,940 --> 00:46:12,040
+كلنا عارفين أن هذا أكبر من صفر، مهمة المعلومة، مهمة
+
+578
+00:46:12,040 --> 00:46:17,860
+جداً المعلومة، عشان في الآخر تقول لي أن الـ in تربيع
+
+579
+00:46:17,860 --> 00:46:21,980
+ناخدها شوية شوية، لأن كلنا عارفين أن واحد زائد h to
+
+580
+00:46:21,980 --> 00:46:27,940
+the power n هتكون أكبر من أو تساوي واحد زائد in h،
+
+581
+00:46:27,940 --> 00:46:35,020
+مدام أنا بتكلم عنه قيمة أكبر من سالب واحد، وبتكلم
+
+582
+00:46:35,020 --> 00:46:40,240
+عن n من صفر، في أكبر يعني positive، القيمة positive
+
+583
+00:46:40,240 --> 00:46:44,220
+بتاعة n، فدائماً هتلاقي أن هذا الـ term صحيح، واحد
+
+584
+00:46:44,220 --> 00:46:50,800
+زائد h to the power n هتكون دائماً أكبر من أو تساوي
+
+585
+00:46:50,800 --> 00:46:55,500
+واحد زائد N في H، في H، هنستفيد منها، هنشوف هنستفيد
+
+586
+00:46:55,500 --> 00:46:58,220
+منها في هذا الـ term اللي موجود عندي هنا، لأنه
+
+587
+00:46:58,220 --> 00:47:02,860
+ببساطة، لو بدك تعوض مكانه، معناته أنت عارف أن هذا
+
+588
+00:47:02,860 --> 00:47:09,580
+الـ term هيكون أكبر، فإذا هاي الـ term هذا هو أكبر من
+
+589
+00:47:09,580 --> 00:47:17,340
+لو استعّدنا عن واحد .. اه مظبوط، واحد زائد H to the
+
+590
+00:47:17,340 --> 00:47:27,220
+power N بواحد زائد N في H، لا هذه  تحالف، ده إثبات؟
+
+591
+00:47:27,220 --> 00:47:33,220
+ليش؟ بدك
+
+592
+00:47:33,220 --> 00:47:36,160
+هيها سالبة؟  جدّيش بدها تكون سالبة؟ هي أكبر من سالب
+
+593
+00:47:36,160 --> 00:47:39,300
+واحد، أكبر من سالب واحد، يعني معناه ذلك أن عندك الـ
+
+594
+00:47:39,300 --> 00:47:41,100
+term ده دائماً أكبر من صفر،
+
+595
+00:47:45,090 --> 00:47:49,070
+هي الفرقية في الـ N هنا، هنا أنت بتتكلم دائماً أكبر
+
+596
+00:47:49,070 --> 00:47:55,710
+من صفر، دائماً أكبر من صفر، فمنتهي الجدل، يعني دائماً
+
+597
+00:47:55,710 --> 00:48:00,430
+أكبر من صفر، معناه ذلك أنه هنا حتى لو بدك تفترض أن
+
+598
+00:48:00,430 --> 00:48:04,630
+هي فيها جزء سالب، فيها جزء سالب، معناته بالعكس، فدي
+
+599
+00:48:04,630 --> 00:48:09,150
+قاعدة بتقول، أنت اللي بهمك هذا الـ term، عشان هيك هو
+
+600
+00:48:09,150 --> 00:48:13,980
+ده اللي علقنا عنه هنا، علقنا فيه، علق عليه، عشان هيك
+
+601
+00:48:13,980 --> 00:48:18,760
+ده اللي علقنا عليه بالأساس، فأنت ضامن أنه جوا الأس
+
+602
+00:48:18,760 --> 00:48:22,940
+لداخل، عشان تقول to the power، أنت ضامن أن هو ده
+
+603
+00:48:22,940 --> 00:48:27,900
+أكبر من صفر، أنت ضامن هو أكبر من صفر، وفي نفس الوجهة
+
+604
+00:48:27,900 --> 00:48:30,480
+بدك تقول لأ، هذه مش بالسالب، لأن بالسالب معناته
+
+605
+00:48:30,480 --> 00:48:35,300
+بالعكس، بتقل قيمتها، متفقين؟ فإذن اللي هي في فترة من
+
+606
+00:48:35,300 --> 00:48:39,580
+سالب واحد لواحد، بالعكس، هذه بتقل أكثر من ما أنت
+
+607
+00:48:39,580 --> 00:48:42,340
+متخيل، لأن بيطلع في term سالب هنا بده ينطرح من
+
+608
+00:48:42,340 --> 00:48:45,900
+الواحد، طيب، هتقول لي لأ، هي فوق الواحد، يعني هي في
+
+609
+00:48:45,900 --> 00:48:48,300
+الجزء الـ positive، هقول لك ماشي، في الجزء الـ
+
+610
+00:48:48,300 --> 00:48:51,220
+positive، فليكن، بس أنت في النهاية، إذا هذه في
+
+611
+00:4
+
+667
+00:53:42,530 --> 00:53:46,410
+كأنك ضربت في K فإذا نضربها في K صارت K factorial
+
+668
+00:53:46,410 --> 00:53:51,890
+على K، صح
+
+669
+00:53:51,890 --> 00:53:59,540
+على K طيب، مقام المقام بصير بسط، فيه أسهل من هيك تخيل
+
+670
+00:53:59,540 --> 00:54:03,780
+أن هذا السؤال هيو عليه خمس درجات، كان هذا السؤال
+
+671
+00:54:03,780 --> 00:54:09,840
+هاي خلصنا، انتهى السؤال، كم سطر؟ هي خمس درجات
+
+672
+00:54:15,250 --> 00:54:19,210
+ملاحظة: تعوض مباشر، يعني أنت بس بتحط تعوض مباشر تبعها
+
+673
+00:54:19,210 --> 00:54:24,510
+تبع الـcombination اللي أنت بتعرفه، هيك نكون خلصنا
+
+674
+00:54:24,510 --> 00:54:28,990
+مجموعة الأسئلة لليوم، المرة الجاية هنحاول نرجع شوية
+
+675
+00:54:28,990 --> 00:54:34,650
+للـencryption، في أكمل فكرة من خلال أسئلتكم، لاحظوا
+
+676
+00:54:34,650 --> 00:54:38,350
+أن أنا بأخد الأسئلة منكم، كمان مرة هنا قلنا نفس
+
+677
+00:54:38,350 --> 00:54:43,840
+الجُملة، فَاللي فهمتوه منكم، أن كان عندكم مشكلة في
+
+678
+00:54:43,840 --> 00:54:50,040
+مشكلة كيف تحسبه، القيمة بتطلع الرقم كبير، فحعمل لكم
+
+679
+00:54:50,040 --> 00:54:52,160
+إياها بشكل رياضي، يعني على السبورة، تحلوها، ما فيش داعي
+
+680
+00:54:52,160 --> 00:54:56,800
+على الكمبيوتر، كويس؟ برضه من الـrules اللي أخذناها
+
+681
+00:54:56,800 --> 00:55:00,280
+في المحاضرة، هجيب لكم rule، أقول لكم إحنا هنستخدم الـrule
+
+682
+00:55:00,280 --> 00:55:03,580
+هذه هتبسط لكم الشغل، و لو عملتها كـsubroutine
+
+683
+00:55:03,580 --> 00:55:06,240
+أريح لكم من إنك أنت تدور على الـfunctions المناسبة
+
+684
+00:55:06,240 --> 00:55:10,420
+للـbig numbers، تمام؟ يعطيكم العافية، و نشوفكم بعد
+
+685
+00:55:10,420 --> 00:55:10,960
+بكره إن شاء الله
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/C8MOQNis1HI_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/C8MOQNis1HI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a84e535ef03acba955440e1e30378a64714510cc
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/C8MOQNis1HI_raw.srt
@@ -0,0 +1,2760 @@
+1
+00:00:05,090 --> 00:00:08,950
+يعطيكوا العفو يا شباب طبعا احنا خلصنا المنهج لكن
+
+2
+00:00:08,950 --> 00:00:13,190
+مكملين مع بعض ان شاء الله تعالى في حل الأسئلة كنوع
+
+3
+00:00:13,190 --> 00:00:17,530
+من أنواع المراجعة لالمثاق و بناء على طلبكم اليوم
+
+4
+00:00:17,530 --> 00:00:19,490
+مابدناش نشتغل في ال inductive مش هيك في ال
+
+5
+00:00:19,490 --> 00:00:24,030
+inductive proof فمجاهزكوا شوية أسئلة اللي هي علاقة
+
+6
+00:00:24,030 --> 00:00:27,430
+برضه بهذا الموضوع اللي هو عملية ال proving بس
+
+7
+00:00:27,430 --> 00:00:31,470
+باستخدام ال mathematical inductive او من موضوع ال
+
+8
+00:00:31,470 --> 00:00:36,390
+induction اللي أخدناه و اتكلمنا فيهفنبدأ على طول و
+
+9
+00:00:36,390 --> 00:00:40,010
+نشوف واحدة من أن الأسئلة اللي كانت جاية في امتحان
+
+10
+00:00:40,010 --> 00:00:43,690
+سابق معظمهم امتحانات سابقة يعني الأسئلة كلها
+
+11
+00:00:43,690 --> 00:00:47,670
+اشتهدنا أنه ندور على كل امتحاناتنا السابقة اللي
+
+12
+00:00:47,670 --> 00:00:50,950
+كنا بنعملها في السنوات الماضية و أشوف إيش الأسئلة
+
+13
+00:00:50,950 --> 00:00:53,430
+اللي كانت إلها علاقة بال mathematical induction
+
+14
+00:00:53,430 --> 00:00:57,830
+بحيث أنه نجيبها و طبعا أجود حلها و أصورلكم إياها
+
+15
+00:00:57,830 --> 00:01:00,170
+عشان نعملكم إياها powerpoint و نزلكم إياها إن شاء
+
+16
+00:01:00,170 --> 00:01:03,520
+الله على ال modelع الموديل هتكون كلها منازلة و في
+
+17
+00:01:03,520 --> 00:01:07,400
+نفس الوقت هي كمحاضرة مصورة موجودة هتكون مع باقي
+
+18
+00:01:07,400 --> 00:01:11,760
+سلسلة المحاضرات نشوف السؤال إيش كان بتكلم؟ بتكلم
+
+19
+00:01:11,760 --> 00:01:14,720
+عن ال mathematical induction to prove that 21
+
+20
+00:01:14,720 --> 00:01:20,940
+divides 4 to the power n plus 1 كله plus 5 to the
+
+21
+00:01:20,940 --> 00:01:26,520
+power 2n minus 1 و whenever n is positive integer
+
+22
+00:01:26,520 --> 00:01:31,620
+فلو كانت ال n هذه positive integer بمعنىin في
+
+23
+00:01:31,620 --> 00:01:37,460
+النهاية in أكبر من zero positive integer كويس
+
+24
+00:01:37,460 --> 00:01:43,640
+فبدنا نوضح ان واحد وعشرين هي divides لأربعة to the
+
+25
+00:01:43,640 --> 00:01:48,440
+power in زائد واحد plus خمسة to the power اتنين in
+
+26
+00:01:48,440 --> 00:01:55,140
+ناقص واحد باستخدام ال inductive step طيب الخطوة
+
+27
+00:01:55,140 --> 00:01:59,960
+الأولى ال business step فيها مشكلة هنبدأ بمين؟
+
+28
+00:02:00,500 --> 00:02:05,240
+بالواحد اللي هو أول positive integer فهنبدأ
+
+29
+00:02:05,240 --> 00:02:10,160
+بالأولى اللى هو ال business تبقى the first number
+
+30
+00:02:10,160 --> 00:02:15,780
+for n اللى هو عند الواحد فبكل بساطة عند الواحد عوض
+
+31
+00:02:15,780 --> 00:02:19,060
+هنا بالواحد وعوض هنا بالواحد وانتهت الجثة شوفها
+
+32
+00:02:19,060 --> 00:02:23,020
+فعلا حققت أول خطوة ولا ماحققتاش أول خطوة فهنجد
+
+33
+00:02:23,020 --> 00:02:27,440
+أربعة to the power اتنين plus خمسة to the power
+
+34
+00:02:27,440 --> 00:02:31,640
+واحدكويس اللي هو اتنين ناقص واحد فبتضل واحد بيسوي
+
+35
+00:02:31,640 --> 00:02:34,180
+واحد و عشرين فواحد و عشرين divided واحد و عشرين
+
+36
+00:02:34,180 --> 00:02:38,480
+اكيد اكيد divided واحد و عشرين و الناتج واحد كويس
+
+37
+00:02:38,480 --> 00:02:45,280
+فهي اول اول جزئية واضحة جدا هتكون عندنا فهنا خلصنا
+
+38
+00:02:45,280 --> 00:02:50,700
+ال bases step لان ال inductive step rule واضح و
+
+39
+00:02:50,700 --> 00:02:56,800
+مافيش فيها كتير مشاكل بدنا assume that انه add in
+
+40
+00:02:56,800 --> 00:03:02,770
+is trueومنها نحاول نجيب at n plus واحد ببساطة جدا
+
+41
+00:03:02,770 --> 00:03:06,030
+يعني الخطوة السهلة والبسيطة فال inductive step بكل
+
+42
+00:03:06,030 --> 00:03:10,550
+بساطة بدنا نثبت k زائد واحد is true إذا كانت at k
+
+43
+00:03:10,550 --> 00:03:14,430
+is true فبكل بساطة خلاص بنعود عند k زائد واحد
+
+44
+00:03:16,660 --> 00:03:19,960
+وبحاول يعني هذه ال strategy اللي انت هتشتغلوها على
+
+45
+00:03:19,960 --> 00:03:23,420
+طول بحط k زائد واحد في المعادلة اللي بدي أعملها
+
+46
+00:03:23,420 --> 00:03:27,020
+أثبات هذه وبعدين بحاول ألعب في الموضوع أعمل شوية
+
+47
+00:03:27,020 --> 00:03:31,920
+ال manipulation الضرورية رياضيا بحيث أني أطلع منها
+
+48
+00:03:31,920 --> 00:03:38,680
+add n تمام فنشوف هل وجدت هذي هي ال total هي هتساوي
+
+49
+00:03:38,680 --> 00:03:43,600
+k زائد اتنينوهنا اتنين K زائد واحد طبعا بعد ما
+
+50
+00:03:43,600 --> 00:03:49,620
+انعوض بدل K تصبح مين؟ طيب، لاحظوا ان احنا يعني
+
+51
+00:03:49,620 --> 00:03:51,780
+برضه من الحاجات اللي بيتلاجوها كتير في الكتب
+
+52
+00:03:51,780 --> 00:03:56,140
+أحيانا بتكلم هنا عن ال N ال general ال equation
+
+53
+00:03:56,140 --> 00:04:00,560
+نفسها، بعدين هنا بتكلم عن K على اساس ان K متغير من
+
+54
+00:04:00,560 --> 00:04:07,200
+واحد لعند ال Nكويس فبكل بساطة بدنا نطلع ال two
+
+55
+00:04:07,200 --> 00:04:11,260
+terms هدولة فبكل بساطة عشان هدي أرجحها ل K بدل K
+
+56
+00:04:11,260 --> 00:04:16,940
+زائد واحد بدي أطلع أربعة منها بدنا نطلع الأربعة
+
+57
+00:04:16,940 --> 00:04:22,940
+منها عساس انه تصبح هدي K زائد واحد in زائد واحد
+
+58
+00:04:22,940 --> 00:04:26,520
+كويس يعني كل اللي محتاجه زائد واحد زائد واحد هدي
+
+59
+00:04:26,520 --> 00:04:30,120
+هطلع على حالها برا هي طلعناها برا فهذا صار جزء من
+
+60
+00:04:30,120 --> 00:04:35,560
+مين من add Kهي طلعنا جزء مبدئيا الناحية التانية
+
+61
+00:04:35,560 --> 00:04:41,660
+عشان أعمل نفس الكرام للخمسة بدنا نطلع اتنين ليش؟
+
+62
+00:04:41,660 --> 00:04:45,820
+لأن مضروبة كانت في اتنين فخمسة في خمسة او خمسة to
+
+63
+00:04:45,820 --> 00:04:49,880
+the power اتنين فهي الخمسة وعشرين اللي دلت فال
+
+64
+00:04:49,880 --> 00:04:52,640
+term هذا وterm هذا هم متناسبين مع هذا الموضوع بس
+
+65
+00:04:52,640 --> 00:04:57,360
+كيف اخدهم اجمحهم مع بعض؟بتفكيره بسيطه عشان اقدر
+
+66
+00:04:57,360 --> 00:05:01,720
+اخد common معناته الخمسة وعشرين هذه بقدر اقول ان
+
+67
+00:05:01,720 --> 00:05:07,380
+هي بتساوي اربع زائد واحد
+
+68
+00:05:07,380 --> 00:05:14,100
+وعشرين مش هيك اربع زائد واحد وعشرين فهي اربع زائد
+
+69
+00:05:14,100 --> 00:05:17,380
+الواحد وعشرين بتهيألي بالان بكل بساطه بنقدر ناخد
+
+70
+00:05:17,380 --> 00:05:22,920
+الاربعة ونطلق الاربعة مع العوامل المشتركة بتاعتها
+
+71
+00:05:22,920 --> 00:05:27,600
+بكل بساطةعلى اعتبار أن الأربعة مضروبة في الأربعة
+
+72
+00:05:27,600 --> 00:05:31,240
+هي to the power of k زائد واحد وفي نفس لغة الأربعة
+
+73
+00:05:31,240 --> 00:05:35,020
+برنا مضروبة في الخمسة to the power of 2k ناقص
+
+74
+00:05:35,020 --> 00:05:39,520
+واحد، مظبوط؟ هي فال term هذا مع ال term هذا
+
+75
+00:05:39,520 --> 00:05:42,480
+أخدناهم مع بعض، بيضل عندي term الواحد وعشرين في
+
+76
+00:05:42,480 --> 00:05:46,520
+خمسة وهذا من واضح جدا أنه بيكسب على واحد وعشرين
+
+77
+00:05:46,520 --> 00:05:50,880
+أنت عندك term مضروب في واحد وعشرين فإذا ان الواحد
+
+78
+00:05:50,880 --> 00:05:56,290
+وعشرين divides this termتمام؟ و نفس القصة ايوة
+
+79
+00:05:56,290 --> 00:06:02,730
+قُطحت مش شايف؟ هذه الآن بدلالة add k فهنا جيبناها
+
+80
+00:06:02,730 --> 00:06:07,340
+k زائد واحد بدلالة ال kفهي طريقة تفكير منطقي
+
+81
+00:06:07,340 --> 00:06:13,260
+المنطقية واحدة ال strategy واحدة الباقي بيظل شطارة
+
+82
+00:06:13,260 --> 00:06:15,760
+كيف الأرقام تستطيع التعامل معاها بس ال strategy
+
+83
+00:06:15,760 --> 00:06:18,540
+واحدة بدنا عشان نخربط ال strategies مع بعض هاي
+
+84
+00:06:18,540 --> 00:06:21,980
+strategy ال inductive بس لا أكثر ولا أقل فهذا ال
+
+85
+00:06:21,980 --> 00:06:24,760
+term كلنا عارفين أن هو نفس ال term هذا اللي هو
+
+86
+00:06:24,760 --> 00:06:31,440
+فعلا بيقسم على 21 او 21 divides it فهذا مدام بيقسم
+
+87
+00:06:31,440 --> 00:06:34,360
+على 21 معناته بكل بساطة بدرجة ان هو 21 في integer
+
+88
+00:06:35,400 --> 00:06:40,180
+في أي sum integer في أي sum integer عشان نقدر نقول
+
+89
+00:06:40,180 --> 00:06:44,560
+في الحالة هذه نعكسهم مع بعض ندخل ال 21 مكان
+
+90
+00:06:44,560 --> 00:06:47,940
+الأربعة و الأربعة مكان ال 21 يعني مين ضرب مين مش
+
+91
+00:06:47,940 --> 00:06:51,500
+هتفرج مين صحيح؟ انت عندك term اتنين تلاتة مضربين
+
+92
+00:06:51,500 --> 00:06:56,080
+في بعض مين جاب المين مش هيفرج معاك فطلحهم عشان تظل
+
+93
+00:06:56,080 --> 00:07:00,720
+21 مع 21 صار 21 مضربة في مين؟ في الأربعة في ال
+
+94
+00:07:00,720 --> 00:07:04,180
+integer هذا ال sum integer plus .. طيب كل هذا ال
+
+95
+00:07:04,180 --> 00:07:08,730
+termبكسم أكيد لأنه أصلا واحد و عشرين واحدة من
+
+96
+00:07:08,730 --> 00:07:15,230
+مشتقاته واحدة من مضرباته فإذا أكيد هيطلع بيكسم على
+
+97
+00:07:15,230 --> 00:07:22,140
+واحد و عشرين sure فإذا أكيد النظرية صحيحةلحظوا إنه
+
+98
+00:07:22,140 --> 00:07:25,060
+إذا كانت اشتغلت من الأساس على فكرة ال two
+
+99
+00:07:25,060 --> 00:07:28,400
+strategies هدول الأساسيات بعوض الخطوة الأولى بعوض
+
+100
+00:07:28,400 --> 00:07:32,140
+الخطوة التانية وانتهت الموضوع .. انتهى الموضوع جيد
+
+101
+00:07:32,140 --> 00:07:39,500
+فإذا 21 فعلا divides this term at k plus واحد وهذا
+
+102
+00:07:39,500 --> 00:07:42,940
+معناه إن عموما النظرية دايما صحيحة أو ال rule ..
+
+103
+00:07:42,940 --> 00:07:47,560
+بدنا عشان نقول theorem ال rule دايما صحيحة طيب
+
+104
+00:07:47,560 --> 00:07:50,480
+واحدة من ال rules اللي أخدناها في ال summation
+
+105
+00:07:51,870 --> 00:07:54,990
+متذكرين في ال summation؟ أخدنا Euler و أخدنا ال
+
+106
+00:07:54,990 --> 00:07:57,590
+geometric و هنتكلم عندنا على ال geometric كمان
+
+107
+00:07:57,590 --> 00:08:01,410
+نثبتها برضه بال inductive الآن كان في عندى التربية
+
+108
+00:08:01,410 --> 00:08:07,090
+.. التكعيب التكعيب و كانت اللي هي زي Euler لكن كله
+
+109
+00:08:07,090 --> 00:08:11,810
+تربيع هي ال Euler term بس كله مربع إذا متذكرين
+
+110
+00:08:11,810 --> 00:08:15,350
+قلناها نفس Euler لكن مربع اللي هو ال summation تبع
+
+111
+00:08:15,350 --> 00:08:20,930
+مين ال cube ل ال termsOkay بكل بساطة inductive
+
+112
+00:08:20,930 --> 00:08:27,830
+step على طول at واحد check من هذه عبارة عن واحد to
+
+113
+00:08:27,830 --> 00:08:31,070
+the power تلاتة زائد اتنين to the power تلاتة زائد
+
+114
+00:08:31,070 --> 00:08:35,410
+تلاتة to the power تلاتة and so on لعند ان to the
+
+115
+00:08:35,410 --> 00:08:40,210
+power تلاتة okay خلاص هنعود فالواحد ال term الأول
+
+116
+00:08:40,210 --> 00:08:43,250
+هو واحد term التكعيب خلاص زي ما هو طب نعود هنا
+
+117
+00:08:43,250 --> 00:08:48,870
+بواحد واحد في اتنين على اتنين واحد تربية يعنييعني
+
+118
+00:08:48,870 --> 00:08:53,290
+كلهما بيساوي واحد بيساوي واحد فكلهما هتلاقوا
+
+119
+00:08:53,290 --> 00:08:58,630
+بيساوي الواحد يعني كلهم هذا او هذا كلهم واحد طيب
+
+120
+00:08:58,630 --> 00:09:03,870
+ال active step برضه بكل أريحية بتعامل مع ان at k
+
+121
+00:09:03,870 --> 00:09:09,310
+هي true و بحاول اجيب at k plus واحد at k plus واحد
+
+122
+00:09:09,310 --> 00:09:17,040
+تمام فهي atن زائد واحد ال term اللي وراه يعني كأنه
+
+123
+00:09:17,040 --> 00:09:21,900
+بتدج مع هذا term افترضنا انه كل هذا term هو صح
+
+124
+00:09:21,900 --> 00:09:28,400
+بدليل انه عوضناها هنا بنفس paint وضفت فقط ال term
+
+125
+00:09:28,400 --> 00:09:34,780
+اللي ضفناه جديد فبدنا نشوف هل هذا term يتفق مع نفس
+
+126
+00:09:34,780 --> 00:09:40,260
+النظرية بس هنا هتكون المفروض ن زائد واحد و هنا
+
+127
+00:09:40,260 --> 00:09:45,990
+هتصبح ن زائد اتنينعشان نتفق ان انا مش في ال term
+
+128
+00:09:45,990 --> 00:09:49,170
+in لأ انا في ال term in زائد واحد هل الكلام ده
+
+129
+00:09:49,170 --> 00:09:54,270
+حقيقه بقدر اطلع من هذا الكلام من ال summation اللي
+
+130
+00:09:54,270 --> 00:09:59,950
+هنا ولا لأ فال strategy حتى الآن ماتغيرتش انا بفهم
+
+131
+00:09:59,950 --> 00:10:05,410
+يعني ماشي في نفس القالية وبنفس الطريقة هات نشتغل
+
+132
+00:10:05,410 --> 00:10:09,480
+عليها تربيه هندخلهعلى ال numerator و ال
+
+133
+00:10:09,480 --> 00:10:14,520
+denominator فهنا هتصبح N زائد N في N زائد 1 كلها
+
+134
+00:10:14,520 --> 00:10:18,580
+تربيع على 4 اللي هي 2 تربيع وهذا ال term بقدر اقول
+
+135
+00:10:18,580 --> 00:10:23,260
+ان هو تربيع في نفسه تكعيب تربيع في نفسه تكعيب فاش
+
+136
+00:10:23,260 --> 00:10:27,380
+كتير إشكالية وهذه بتهيألي استراتيجيا انت بمجرد
+
+137
+00:10:27,380 --> 00:10:31,380
+تطلع فيها أكيد هتفكر فيها ليش؟ لأن انت عندك term
+
+138
+00:10:31,380 --> 00:10:36,160
+تربيعو بدك تجمع ولا تكعيب خلاص بدك التكعيب هذا
+
+139
+00:10:36,160 --> 00:10:39,040
+تخففه للتربيع عشان تقدر تجمع إذا بتقدر تجمع إشي
+
+140
+00:10:39,040 --> 00:10:43,920
+بكل بساطة معناته تربيع مضروب في نفسه فمنطقية يعني
+
+141
+00:10:43,920 --> 00:10:46,800
+ماتهاش كتير زي ما بيقولوا اتفكر فيها كتير في
+
+142
+00:10:46,800 --> 00:10:49,940
+الامتحان و تقول طب من وين بدي أجيبها؟ هي أنت
+
+143
+00:10:49,940 --> 00:10:53,860
+بتحاول تجمع terms معناته أهم حاجة أنك توحد ال
+
+144
+00:10:53,860 --> 00:10:57,840
+termsال order طبعا هيكمل واحد إذا مجمعين علي إيش
+
+145
+00:10:57,840 --> 00:11:00,420
+يكونوا مجمعين علي إيش واحد تقدر تاخد common هذا
+
+146
+00:11:00,420 --> 00:11:04,620
+اللي دايما نفكر فيها كيف أقدر أجمع ال terms أو ال
+
+147
+00:11:04,620 --> 00:11:07,820
+term تبع ال rule مع ال term اللي ضفته تبع n زائد
+
+148
+00:11:07,820 --> 00:11:11,640
+واحد أو k زائد واحد هذي كيف بدي أجمحهم مع بعض طبعا
+
+149
+00:11:11,640 --> 00:11:16,200
+هذا تكعيب طبعا هذا تربيع بسيط جدا هذا حولنا تربيع
+
+150
+00:11:16,200 --> 00:11:22,020
+و خلصنا فهذه أول جزئيةخلصناها صار واضح عندى ان
+
+151
+00:11:22,020 --> 00:11:25,000
+التربيه هذى كمان بتدخل على ال two terms ليش؟ لأنه
+
+152
+00:11:25,000 --> 00:11:28,900
+صار n زائد واحد و هنا في n زائد واحد هنا n زائد
+
+153
+00:11:28,900 --> 00:11:32,100
+واحد تربيه هنا برضه n زائد واحد تربيه بتوحيكك
+
+154
+00:11:32,100 --> 00:11:35,120
+بتخلى زى ما بيقولوا أفكارك تروح في اتجاه انه هذا
+
+155
+00:11:35,120 --> 00:11:39,600
+common بقدر أعمله common لل two terms على طول
+
+156
+00:11:39,600 --> 00:11:46,380
+بيوحيلك المنظر بيوحقش وين رايح جيد فهي بكل بساطة
+
+157
+00:11:46,380 --> 00:11:51,460
+بنقدرنتعامل معاها بهذا الشكل عشان نتوحد هذا term
+
+158
+00:11:51,460 --> 00:11:55,680
+مع الأربعة و تقدر تقول والله ان في حاجات مشتركة
+
+159
+00:11:55,680 --> 00:11:58,920
+بدك توحد المقام معناته أضرب في أربعة و أقسم على
+
+160
+00:11:58,920 --> 00:12:02,620
+أربعة أضرب في أربعة و أقسم على أربعة يمكن أنا شوية
+
+161
+00:12:02,620 --> 00:12:08,480
+أخدتها سريع هيك أخدت كذا خطوة في بعض فهنا أربعة
+
+162
+00:12:08,480 --> 00:12:14,980
+على أربعة و ضربنافي اللي هي ال term اللي فكناها ده
+
+163
+00:12:14,980 --> 00:12:20,820
+اللي in fact في الآخر عندنا تمام هتوحدهم عشان يطلع
+
+164
+00:12:20,820 --> 00:12:23,460
+معاك ال term اللي انت شايفه قدامك بتهيألي بكل
+
+165
+00:12:23,460 --> 00:12:26,620
+ببساطة
+
+166
+00:12:26,620 --> 00:12:32,200
+بتقدر منها اتجمع مجرد حدود اتجمعها عشان يظهر في
+
+167
+00:12:32,200 --> 00:12:36,060
+الآخر ان في حاجات هتختصر مع بعض وين اللي هيختصر مع
+
+168
+00:12:36,060 --> 00:12:39,220
+بعض اللي هيختصر مع بعض ان بعد ما أخدنا ال common
+
+169
+00:12:40,340 --> 00:12:43,680
+نفس الفكرة ال common اللي هي n زائد واحد كله تربيع
+
+170
+00:12:43,680 --> 00:12:49,760
+أخدناها عامل مشترك وهي طلعت هنا فهذه
+
+171
+00:12:49,760 --> 00:12:51,960
+العامل المشترك اللي قلتلكوا عليه من الأول
+
+172
+00:12:51,960 --> 00:12:55,400
+استراتيجيا بدي أطلعه لأن شكله مغري أنه فعلا هذا
+
+173
+00:12:55,400 --> 00:12:59,440
+عامل مشترك ايش اللي بيظل ال n تربيع حقيقية؟
+
+174
+00:13:02,590 --> 00:13:07,490
+وبتظل عندك هنا ال n زائد .. اه عفوا ان ال n زائد
+
+175
+00:13:07,490 --> 00:13:11,510
+واحد بس بعد ما تضرب في أربعة لأنك توحدت المقامات،
+
+176
+00:13:11,510 --> 00:13:16,050
+لإنك توحدت المقامات فهي n زائد واحد في الأربعة على
+
+177
+00:13:16,050 --> 00:13:21,170
+أربعة فكأنه ال term هذا هيك أصبح كامل، هيك، كله
+
+178
+00:13:21,170 --> 00:13:25,750
+على أربعة، كامل على أربعة، بتهيألي مش هيكون عندك
+
+179
+00:13:25,750 --> 00:13:30,790
+إشكالية أنت بدل ما كان جمع صار ضربفصار كأنه كله
+
+180
+00:13:30,790 --> 00:13:36,430
+نفس المقام أتوقع برضه ماعنكاش مشكلة في ال term
+
+181
+00:13:36,430 --> 00:13:39,790
+اللي هناك لأنه و أفتح الأقواص بس فصارت in تربيع
+
+182
+00:13:39,790 --> 00:13:45,250
+زيد أربعة in زائد أربعة هذا بكل بساطة اللي هي in
+
+183
+00:13:45,250 --> 00:13:49,030
+زائد اتنين تربيع يعني in زائد اتنين تربية بتاعي
+
+184
+00:13:49,030 --> 00:13:54,150
+بيبينت خلصت خلصت الحل فهي أصلحت بهذا الشكل هو نفس
+
+185
+00:13:54,150 --> 00:13:59,870
+ال term اللي أنا بتكلم عليه فوق لمانبدأ نجمع ال
+
+186
+00:13:59,870 --> 00:14:04,150
+terms مع بعض و نقول ان هو كله تربيع فهو نفس الفكرة
+
+187
+00:14:04,150 --> 00:14:07,210
+اللي أنا جاهز بقول عليها هذه المفروض يظهر لو انا
+
+188
+00:14:07,210 --> 00:14:14,070
+عن term N زائد 1 تكعيب في اي مشكلة فيها ترتبية و
+
+189
+00:14:14,070 --> 00:14:17,690
+حتى مش ترتبية عشوائية لأ احنا بنفكر وين بدنا نروح
+
+190
+00:14:17,690 --> 00:14:20,750
+فيها يعني احنا جاهزين بنفكر وين بدنا نروح ان احنا
+
+191
+00:14:20,750 --> 00:14:24,670
+نوحد مقامات نوحد ناخد commons هذه الحاجات الأساسية
+
+192
+00:14:24,670 --> 00:14:30,560
+اللي بندور عليهااللي أبسط منها كمان لسه اللي هي
+
+193
+00:14:30,560 --> 00:14:35,320
+مين ال rule اللي أخدناها لل geometric series ال
+
+194
+00:14:35,320 --> 00:14:38,260
+geometric series أخدنا هذا القانون فالأن المطلوب
+
+195
+00:14:38,260 --> 00:14:42,160
+أنه نثبته باستخدام ال inductive أو ال mathematical
+
+196
+00:14:42,160 --> 00:14:45,600
+induction أو ال mathematical induction بكل بساطة
+
+197
+00:14:45,600 --> 00:14:51,160
+الخطوة الأولى ال basis خلاص ال basis عند zero ليش؟
+
+198
+00:14:51,160 --> 00:14:55,370
+لأنه أنا بعيد من zeroفانا بدهاش برضه كتير تفكير
+
+199
+00:14:55,370 --> 00:14:58,590
+أنا بدي من zero فإذا هي ال basis تبعته هي الخطوة
+
+200
+00:14:58,590 --> 00:15:04,150
+الأولى at zero هتصبح هنا A R to the power zero و
+
+201
+00:15:04,150 --> 00:15:11,250
+هنا هيصبح A و عوض في zero فصارت R to the power
+
+202
+00:15:11,250 --> 00:15:15,490
+zero يعني R لحالها ناقص واحد على R ناقص واحد بواحد
+
+203
+00:15:15,490 --> 00:15:19,410
+و ال R to the power zero بواحد فإذا A تساوي A
+
+204
+00:15:19,410 --> 00:15:24,470
+هيطلع في الآخر صحيحإيه زائد ايه يساوي ايه فهي
+
+205
+00:15:24,470 --> 00:15:28,150
+منطقية صحيحة الآن نروح للخطوة التانية او ال
+
+206
+00:15:28,150 --> 00:15:33,270
+inductive step to k plus واحد طيب هذه أسهل من هذيك
+
+207
+00:15:33,270 --> 00:15:36,950
+لأنه بكل بساطة بقدر اطلق at k لحالها هاي at k
+
+208
+00:15:36,950 --> 00:15:41,710
+لحالها و بعوض الصماش اللي مين لk زائد واحد من k
+
+209
+00:15:41,710 --> 00:15:45,250
+زائد واحد لk زاوية واحدواحدة من الحاجات المهارات
+
+210
+00:15:45,250 --> 00:15:49,010
+اللي أخدناها في ال summation فإذا term زيادة بس
+
+211
+00:15:49,010 --> 00:15:52,310
+اللي بينضافي عندك ال term هذا اللي زيادة بدك تجمعه
+
+212
+00:15:52,310 --> 00:15:58,050
+مع المعادلة على اعتبار انه انت بتقول ان at k ال
+
+213
+00:15:58,050 --> 00:16:02,970
+rule is true صح انت بتقول ان هي true انت بدك تثبت
+
+214
+00:16:02,970 --> 00:16:09,650
+at k زائد واحد طيب مدام true معناته بحط قيمتها بحط
+
+215
+00:16:09,650 --> 00:16:13,110
+قيمتها زي ما هي هي بنزلها
+
+216
+00:16:15,420 --> 00:16:19,940
+الآن بنجمع بس وانا عيني على إيش .. إيش المتغير ..
+
+217
+00:16:19,940 --> 00:16:24,320
+إيش اللي ممكن يتغير في القانون من n to n زائد واحد
+
+218
+00:16:24,320 --> 00:16:27,660
+أو من k ل k زائد واحد إن هذا ال term هو اللي
+
+219
+00:16:27,660 --> 00:16:31,340
+هيتغير، الباقي كله ثوابت، هذا ال term المفروض إنه
+
+220
+00:16:31,340 --> 00:16:39,030
+أصبح R n زائد 2مش هيك؟ ايه؟ الطبيعي هيك يصير و
+
+221
+00:16:39,030 --> 00:16:42,070
+كويس فإذا كل الفكرة هيها أني بدي أجمع هذا ال term
+
+222
+00:16:42,070 --> 00:16:48,870
+مع اللي فوق بكل بساطة خد عامل مشترك او خد
+
+223
+00:16:48,870 --> 00:16:53,750
+المشتركات بينهم طبعا الكلام هذا احنا ماغيرناش فيه
+
+224
+00:16:53,750 --> 00:16:56,830
+أي شيء أخدنا ال a بس العامل المشترك ال a كعامل
+
+225
+00:16:56,830 --> 00:17:00,670
+مشترك بتهيألي بكل بساطة ممكن ناخد r زاق ناقص واحد
+
+226
+00:17:00,670 --> 00:17:06,450
+في الطرفينفوق و تحت على اساس ان نوحد المقامات فهي
+
+227
+00:17:06,450 --> 00:17:10,390
+موحدنا مقاماتنا كويس مادام خلصنا توحيد المقامات
+
+228
+00:17:10,390 --> 00:17:14,770
+الان two terms بدنا نوحدهم بس مع بعضهم اعتقد واضحة
+
+229
+00:17:14,770 --> 00:17:20,030
+انها هتكون الان لو هد ضربناها جوا هصبح زائد اتنين
+
+230
+00:17:20,030 --> 00:17:25,330
+صح؟ وهد جوا زائد واحد بس بالسالب وهد بالموجب
+
+231
+00:17:25,330 --> 00:17:31,230
+هيروحوا مع بعض هتظل ال R كتو زائد اتنين مع الناقص
+
+232
+00:17:31,230 --> 00:17:37,590
+واحد الاولىمع الناقص واحد الأولى فكفتلك إياه أكتر
+
+233
+00:17:37,590 --> 00:17:42,770
+هيفكفتناها بشكل أكبر لإيش؟
+
+234
+00:17:42,770 --> 00:17:48,730
+لأنه ببساطة هذه هتطير مع هذه دل عندك اللي أنت بدك
+
+235
+00:17:48,730 --> 00:17:53,870
+إياه أصلا فإذا أثبتناها أنه فعلا إذا كانت add k هي
+
+236
+00:17:53,870 --> 00:17:57,230
+is true بالضرورة هتكون add k زائد واحد برضه is
+
+237
+00:17:57,230 --> 00:18:10,060
+trueتمام، كمان مثل، كمان مثل، هاي ال route to
+
+238
+00:18:10,060 --> 00:18:15,660
+ال rational أخدناها طبعا احنا بال conductive، بال
+
+239
+00:18:15,660 --> 00:18:18,600
+.. اه بال contradiction، بال contradiction اللي
+
+240
+00:18:18,600 --> 00:18:22,220
+انا بدوياها بالمين؟ بال inductive proof، بال
+
+241
+00:18:22,220 --> 00:18:25,840
+inductive proofطيب عشان اقول بال inductive proof
+
+242
+00:18:25,840 --> 00:18:29,480
+بدنا نرجع لفكرتها لاحظ ان احنا هنا مافيش عندي N
+
+243
+00:18:29,480 --> 00:18:35,100
+صح؟ زي بالظبط لما روحتوا في عملية ال contradiction
+
+244
+00:18:35,100 --> 00:18:39,340
+برضه كنتوا محترين انه مافيش طرفين في وجهتها كنتوا
+
+245
+00:18:39,340 --> 00:18:41,660
+بتقولوا انه مافيش طرفين هنا نفس الجسة أنا ماعنديش
+
+246
+00:18:41,660 --> 00:18:44,780
+N الشيء N هذا اللي بدنا نستعامل معاها بكل بساطة
+
+247
+00:18:44,780 --> 00:18:50,060
+احنا هنولد N هنعمل N هنا فيها بحيث اني اقول let P
+
+248
+00:18:50,060 --> 00:18:56,340
+of Nهي انه that there is no positive integers B
+
+249
+00:18:56,340 --> 00:19:06,160
+such that root two تساوي N over B لا يوجد integer
+
+250
+00:19:06,160 --> 00:19:15,040
+كمقام و N مقصومة عليه تعطيني النسبة جذر اتنين
+
+251
+00:19:15,040 --> 00:19:19,460
+النسبة جذر اتنين والان بدي ابدأ اقول ايش قيم N
+
+252
+00:19:19,460 --> 00:19:20,200
+الممكنة
+
+253
+00:19:23,490 --> 00:19:27,790
+فولدنا لها n من عندنا جبنا لها n من عندنا تمام
+
+254
+00:19:27,790 --> 00:19:31,190
+بهذا الشكل أصبح بكل بساطة بتقدر تتعامل معاها الان
+
+255
+00:19:31,190 --> 00:19:37,150
+قيمة n المناسبة تقسم على b عشان تعطي جدر اتنين إذا
+
+256
+00:19:37,150 --> 00:19:42,710
+والله في قيمة ل n معناته هي rational فإحنا الفرضية
+
+257
+00:19:42,710 --> 00:19:45,030
+إيش بتقول is no positive
+
+258
+00:19:47,050 --> 00:19:51,210
+is no positive فياريت نحط تحتها تلتة اربعة خطوط
+
+259
+00:19:51,210 --> 00:19:56,250
+هذه no positive معناه ذلك ان انا بتكلم انه لا يوجد
+
+260
+00:19:56,250 --> 00:19:59,690
+لان لقدام شوية بدنا نضلنا نبركزين ان انا بتكلم عن
+
+261
+00:19:59,690 --> 00:20:04,490
+لا يوجد فالاثبات انه لا يوجد النفي تبعها بيصير انه
+
+262
+00:20:04,490 --> 00:20:12,110
+يوجد جبل ما نعد النقطة هذه واضحة واضحةأيوة true
+
+263
+00:20:12,110 --> 00:20:16,910
+معناته انه لا positive فالان لما بدي اقول بدي افرض
+
+264
+00:20:16,910 --> 00:20:22,190
+عكسها معناته بدي اقول انه لأ هي يوجد فرضية حتى
+
+265
+00:20:22,190 --> 00:20:24,370
+الآن ال function اللي احنا شغالين عليها بدنا
+
+266
+00:20:24,370 --> 00:20:29,350
+نثبتها ان هي P of M انه لا يوجد قيمة ل M اقسمها
+
+267
+00:20:29,350 --> 00:20:37,140
+على integer معين بيه و يطلع ليه جذر اتنينطيب فالان
+
+268
+00:20:37,140 --> 00:20:41,180
+نبدأ بال business step N بتساوي واحد بتبدأ عند N
+
+269
+00:20:41,180 --> 00:20:46,980
+بتساوي واحد ثم نثبت بعد ذلك ان الكل زيه اللي هو K,
+
+270
+00:20:47,360 --> 00:20:54,780
+K زائد واحد, K زائد اتنين وكل قيم من واحد ل K
+
+271
+00:20:54,780 --> 00:21:01,240
+هيحققوا نفس ال function اللي هي لايوجد قيمة نقسمها
+
+272
+00:21:01,240 --> 00:21:06,260
+على بيط و اعطيش اتر اتنيناللي هي لا يوجد تمام فإذا
+
+273
+00:21:06,260 --> 00:21:11,840
+ال business tip كانت تالي هتصبح بتفترض ان بي واحد
+
+274
+00:21:11,840 --> 00:21:18,020
+is true كيف؟ هقول جذر اتنين هتصبح هنا واحد مش واحد
+
+275
+00:21:18,020 --> 00:21:21,520
+طب انا عارف ان جذر اتنين هي اكبر من واحد من الواحد
+
+276
+00:21:21,520 --> 00:21:25,240
+الصحيح الطبيعي طيب في نفس الوجهة الواحد الصحيح
+
+277
+00:21:25,240 --> 00:21:31,260
+الطبيعي هو اكبر من او يسوي واحد على بي على اعتبار
+
+278
+00:21:31,260 --> 00:21:36,880
+ان بي positive integerب positive integer يعني أقل
+
+279
+00:21:36,880 --> 00:21:41,000
+قيمة له أن يكون واحد طيب لو كانت واحد على واحد
+
+280
+00:21:41,000 --> 00:21:44,080
+معناته يساوي الواحد واحنا عارفين أنه الواحد أقل من
+
+281
+00:21:44,080 --> 00:21:49,760
+جذر اتنين معناته لا يساوي جذر اتنين معناته
+
+282
+00:21:49,760 --> 00:21:53,520
+لا يساوي جذر اتنين صح معناته أنا حققت الحقيقة
+
+283
+00:21:53,520 --> 00:21:59,260
+النظرية هذه أنه لا يوجد يساوي جذر اتنين هو فعلا
+
+284
+00:21:59,260 --> 00:22:03,130
+مساويش جذر اتنين هي عند الواحدخلصنا ال business
+
+285
+00:22:03,130 --> 00:22:07,850
+step حتى اللحظة هي ال business step تمام لكل قيم
+
+286
+00:22:07,850 --> 00:22:11,470
+طبعا مين بيه أكبر من أو يساوي واحد لأنه إذا كانت
+
+287
+00:22:11,470 --> 00:22:14,170
+أكبر من الواحد كمان معناته بالعكس صارت fraction
+
+288
+00:22:14,170 --> 00:22:17,670
+يعني كمان أقل من الواحد فهي بالضروري أكيد مش هتكون
+
+289
+00:22:17,670 --> 00:22:21,050
+تساوي الاتنين اللي أنا عارف انه زادر اتنين أكبر من
+
+290
+00:22:21,050 --> 00:22:26,860
+واحدأحنا مسبقا عارفين أنه أكبر من واحد صح؟ فإذا أي
+
+291
+00:22:26,860 --> 00:22:31,260
+كسر واحد على أي رقم positive مستحيل يكون بيساوي
+
+292
+00:22:31,260 --> 00:22:34,480
+ذات الأتنين لأنه حيكون fraction فخلصنا ال business
+
+293
+00:22:34,480 --> 00:22:39,200
+step ال inductive step ال inductive step الآن في
+
+294
+00:22:39,200 --> 00:22:44,920
+ال inductive step assume that P of J is true طيب
+
+295
+00:22:44,920 --> 00:22:50,080
+مين J هذي؟ لكل القيم J أقل من أو يسوى K strong
+
+296
+00:22:51,190 --> 00:22:55,490
+proof أنا هنا بتكلم عن ال strong proof وهذا النقطة
+
+297
+00:22:55,490 --> 00:22:58,330
+اللي كنتوا بتقوليها صح ال strong proof فإذا أنا
+
+298
+00:22:58,330 --> 00:23:05,050
+بتكلم هنا عن P of J is true لكل mean J هذه لكل
+
+299
+00:23:05,050 --> 00:23:09,430
+القيم اللي أقل من K ابتداء طبعا من ال mean من ال
+
+300
+00:23:09,430 --> 00:23:12,550
+business step من الواحد الواحد والاتنين والتلاتة
+
+301
+00:23:12,550 --> 00:23:16,650
+والاربعة والخمسة والستة والتمانية والتسعة to K إذا
+
+302
+00:23:16,650 --> 00:23:23,020
+كلهم فعلا بيحققوا نفسالفرضية بتاعتنا ان ولا رقم لو
+
+303
+00:23:23,020 --> 00:23:28,200
+قصبته على P بساوي جذر اتنين ولا رقم معناته بدنا
+
+304
+00:23:28,200 --> 00:23:32,420
+نثبت ان حتى K زائد واحد لو قصبناها على P برضه مش
+
+305
+00:23:32,420 --> 00:23:38,500
+هتساوي كجذر اتنين جذر اتنين فمبدأيا حتى الآن
+
+306
+00:23:38,500 --> 00:23:41,440
+الفرضية هذه اللي هو ال inductive step اللي بدنا
+
+307
+00:23:41,440 --> 00:23:47,340
+نبني عليها فإذا المعنى ذلك ان جذر اتنين لا يساوي J
+
+308
+00:23:47,340 --> 00:23:53,770
+over Pلأن هذه هي الفرضية اللي أنا أفرضها at k
+
+309
+00:23:53,770 --> 00:24:00,850
+الشيء أنا جاهاد بقول أنه الفرضيتي الصحيحة at k طب
+
+310
+00:24:00,850 --> 00:24:06,510
+strong proof معناته at k وكل ما قبلها is true مدام
+
+311
+00:24:06,510 --> 00:24:12,460
+is true معناته لا تساوي g over bلأنه no positive
+
+312
+00:24:12,460 --> 00:24:15,980
+هيتكمل مرة عشان ايه حطينا عليها تلت خطوط حطينا
+
+313
+00:24:15,980 --> 00:24:20,200
+تحتها تلت خطوط جيد هذا معناته إذا قدرت أقول إن هذا
+
+314
+00:24:20,200 --> 00:24:24,380
+أثبتنا هذا الكلام إذا هذا صحيح إذا بالضرورة هتكون
+
+315
+00:24:24,380 --> 00:24:27,880
+هذا الكلام صحيح الآن بدنا نثبت هذا الموضوع هل فعلا
+
+316
+00:24:27,880 --> 00:24:30,680
+صحيح ولا لأ بس احنا هنا حطينا النظرية تبعت من
+
+317
+00:24:30,680 --> 00:24:38,990
+strong mathematical induction إنه مش أدكيه بسat k
+
+318
+00:24:38,990 --> 00:24:44,750
+وكل ما قبلها ابتداء من ال basis case اللي هي من
+
+319
+00:24:44,750 --> 00:24:50,870
+واحد يعني من واحد ل k كله إذا كان كله true إذا هاي
+
+320
+00:24:50,870 --> 00:24:54,230
+ال implication إذا at k زي واحد برضه is true بس هي
+
+321
+00:24:54,230 --> 00:24:57,130
+كلمة true إيش معناها؟ إنه لا يساوي each other
+
+322
+00:24:57,130 --> 00:25:01,190
+اتنينهي كمان مرة بنعيدها عشان بنا ما تقول ماتضيعش
+
+323
+00:25:01,190 --> 00:25:05,330
+منكوا الأمور معناته انه لا تساوي جذر اتنين هيك هيك
+
+324
+00:25:05,330 --> 00:25:10,570
+معناه true حسب الفرضية اتنى حسب الفرضية تمام الآن
+
+325
+00:25:10,570 --> 00:25:16,350
+عشان نحسب الكلام ده نثبته عند k زائد واحد هنعملها
+
+326
+00:25:16,350 --> 00:25:21,570
+بال contradiction بمعنى أنه بدي أثبت عكسها لا
+
+327
+00:25:21,570 --> 00:25:29,060
+يحققها عكسها أيش أنه يوجدفإذن صارت ال false الآن
+
+328
+00:25:29,060 --> 00:25:36,260
+إن يوجد مش هيك؟ إيش يوجد؟ يوجد قيمة إيش اسمها
+
+329
+00:25:36,260 --> 00:25:42,480
+القيمة هذه؟ K زائد واحد فإذن الفرضية الآن إن جذر
+
+330
+00:25:42,480 --> 00:25:49,980
+اتنين تساوي K زائد واحد على B صح؟
+
+331
+00:25:49,980 --> 00:25:56,380
+اللي هو فرضت النفي فرضنا النفي طيب متذكرين ال
+
+332
+00:25:56,380 --> 00:26:00,570
+contradiction؟أنا بفرض إنه فيه و بخلّي الحل
+
+333
+00:26:00,570 --> 00:26:07,510
+يوصّلني للإثبات فإذن كأنه طلعت جذر 2 تساوي K زائد
+
+334
+00:26:07,510 --> 00:26:13,430
+B و بعدين مع الحل هاتفاجأ أنه لأ هي جذر 2 لا تساوي
+
+335
+00:26:13,430 --> 00:26:18,470
+K زائد B فصارت كأنه أنت بتقول جذر 2 تساوي K زائد B
+
+336
+00:26:18,470 --> 00:26:24,470
+وجذر 2 لا تساوي K زائد B تناقض على طول تناقض تناقض
+
+337
+00:26:24,470 --> 00:26:28,520
+معناته falseو false معناته أن النظرية من الأساس
+
+338
+00:26:28,520 --> 00:26:32,400
+كانت صحيحة أنت فرضت عكسها و عكسها طالع متناقض
+
+339
+00:26:32,400 --> 00:26:37,900
+معناته هي أصلها صحيح أصلها صحيح الكلام اللي بنعمله
+
+340
+00:26:37,900 --> 00:26:42,440
+أمتى لأن أنا مش هقدر أخد كل القيم واحدة واحدة على
+
+341
+00:26:42,440 --> 00:26:47,520
+Bكويس و افقه و اثبت ان هي لا تساوي زدر اتنين فانت
+
+342
+00:26:47,520 --> 00:26:52,620
+اش بتقول بدك تفترض انه لأ هي تساوي و خل الحل يقولك
+
+343
+00:26:52,620 --> 00:26:56,400
+لا يساوي لأنه بال .. بال direct معناته انت محتاج
+
+344
+00:26:56,400 --> 00:26:59,280
+تجهد اتعوض .. اتعوض فيهم كلهم و هذا ال cancel
+
+345
+00:26:59,280 --> 00:27:01,580
+introduction عملناه انت مستحيل تجهد اتعود فيهم
+
+346
+00:27:01,580 --> 00:27:06,620
+كلهم لأ انت بدك تثبت ان عكسهم غير صحيحو قلتلكوا
+
+347
+00:27:06,620 --> 00:27:10,660
+إياها قبل هيك انت مش بالضروري أحيانا و في الحمارات
+
+348
+00:27:10,660 --> 00:27:14,660
+الانتخابية مثلا انك انت تركز على مزاياك انت ممكن
+
+349
+00:27:14,660 --> 00:27:20,220
+تركز على عيوب خاصمك بس و تكون سبيل لفوزك فانت بدون
+
+350
+00:27:20,220 --> 00:27:24,280
+ما تضطر تجول تتكلم عن إنجازات انت بتتكلم عن خيبات
+
+351
+00:27:24,280 --> 00:27:30,580
+أمل للخاصم فتعطي حق أن انت الأفضل الفكرة نفسها
+
+352
+00:27:30,580 --> 00:27:35,460
+تمامفهي اللي .. اللي بدنا نصله الآن انه الآن بدأ
+
+353
+00:27:35,460 --> 00:27:40,440
+افترض ان هي لأ يوجد انه يوجد فعليا، تمام؟ والله
+
+354
+00:27:40,440 --> 00:27:43,740
+لاجينا ان الحل ضال مكمل انه ضالت يوجد معناته فعلا
+
+355
+00:27:43,740 --> 00:27:47,440
+في مشكلة عندنا في الحل لكن الطبيعي الآن و اللي أنا
+
+356
+00:27:47,440 --> 00:27:52,980
+متوقعه أنه أثناء الحل هنصل لنقطة انه لأ احنا
+
+357
+00:27:52,980 --> 00:27:59,600
+ناقضنا الفرضية بتاعتنا فالآن هذه فرضيةهذه فرضية مش
+
+358
+00:27:59,600 --> 00:28:02,840
+مسموح أثناء الحلقة تفاجأة أن الفرضية غلط طب أنا
+
+359
+00:28:02,840 --> 00:28:07,060
+بدي كل شغل عليها واضحة تمام هتنشوف وين بدنا نصل في
+
+360
+00:28:07,060 --> 00:28:12,820
+الآخر هاي فرضيتنا كتبناها على جنب هناك عشان نتضال
+
+361
+00:28:12,820 --> 00:28:19,440
+قدامها هنا خلينا نبدأ هاي الفرضية واللي بدنا ننطلق
+
+362
+00:28:19,440 --> 00:28:21,880
+منها بكل بساطة ربع الطرفين
+
+363
+00:28:26,570 --> 00:28:30,010
+طيب مشكلة؟ اه هنصل لنفس الجديدة بس طريقة الإثبات
+
+364
+00:28:30,010 --> 00:28:33,490
+هتختلف في أخرها ليش؟ لأن أنا بتكلم عن inductive
+
+365
+00:28:33,490 --> 00:28:37,150
+بتكلم مش عن contradiction لكن السبيل كان هو ال
+
+366
+00:28:37,150 --> 00:28:41,450
+contradiction نفسها تمام فهيوصلنا لنفس الفكرة و لو
+
+367
+00:28:41,450 --> 00:28:45,230
+وصلنا فيها لقصة ال even متذكرينها تمام هنصل لنفس
+
+368
+00:28:45,230 --> 00:28:48,830
+الفكرة فإذا اتنين بيه تربيع بتساوي كزائد واحد
+
+369
+00:28:48,830 --> 00:28:54,040
+تربيع معناته كزائد واحد تربيع هيeven ومعناه ذلك ان
+
+370
+00:28:54,040 --> 00:28:58,080
+ك زائد واحد even معناه ذلك ان ك زائد واحد بقدر
+
+371
+00:28:58,080 --> 00:29:02,500
+احطه بصيغة اتنين في some integer في some integer
+
+372
+00:29:02,500 --> 00:29:06,960
+مادام even مادام طلعت في النهاية even بكل بساطة
+
+373
+00:29:06,960 --> 00:29:15,720
+بعود مكانها فوق هنا فصارت الاتنين T كله تربيعبكل
+
+374
+00:29:15,720 --> 00:29:20,220
+بساطة تربيع دخله على الطرفين فصارت أربع في T تربيع
+
+375
+00:29:20,220 --> 00:29:24,080
+بتقدر ببساطة جدا تختصر الاتنين مع الاتنين فبتصير B
+
+376
+00:29:24,080 --> 00:29:28,340
+تربيع بتساوي اتنين T تربيع وهذا معناه ان ال B
+
+377
+00:29:28,340 --> 00:29:37,600
+تربيع even يعني ال B even يعني B even تمام الآن
+
+378
+00:29:37,600 --> 00:29:43,920
+جدر اتنيناللي هي k زائد واحد على b هتساوي اتنين T
+
+379
+00:29:43,920 --> 00:29:52,680
+على اتنين S يعني T على S طب حلو جدا حلو جدا جدا
+
+380
+00:29:52,680 --> 00:30:00,640
+الان فرضيتنا ايش كانت بتقول انها تساوي بينما فعليا
+
+381
+00:30:00,640 --> 00:30:09,880
+هنا اللي ال T هذه طلعت نص قيمة k زائد واحد صح؟
+
+382
+00:30:10,720 --> 00:30:14,720
+طيب أنا فعلا بتكلم عن K زائد واحد على B اتفاجأت و
+
+383
+00:30:14,720 --> 00:30:21,200
+طبعا كل K و K ناقص واحد لعند ابتداء من الواحد هدول
+
+384
+00:30:21,200 --> 00:30:30,120
+أساسا بيحققوا true فانت بدل ما تحقق لإن K زائد
+
+385
+00:30:30,120 --> 00:30:34,420
+واحد هي false روح تحطط لمكانها K زائد واحد على
+
+386
+00:30:34,420 --> 00:30:39,160
+اتنين واللي هي أصلا مشمولة هنا لأنه أكيد أقل من K
+
+387
+00:30:40,980 --> 00:30:48,940
+فضمن ال strong inductive proof لأنها strong معناته
+
+388
+00:30:48,940 --> 00:31:01,040
+add k وكل اللي أقل منها و ال T هي أقل منها فإذا
+
+389
+00:31:01,040 --> 00:31:07,520
+أنت جاهز بتقول أن add T هي تساوي جذر 2 بينما أنا
+
+390
+00:31:07,520 --> 00:31:13,600
+عارف حسب الفرضية الأساسية أنه لأat k فأقل لا يساوي
+
+391
+00:31:13,600 --> 00:31:19,700
+جدر اتنين لا يساوي جدر اتنين مش شكل strong مش شكل
+
+392
+00:31:19,700 --> 00:31:25,020
+strong انه انا بفترض انه النظرية صحيحة لكل القيم
+
+393
+00:31:25,020 --> 00:31:30,160
+ابتدا من ال bases at k لعند k ال theorem is true
+
+394
+00:31:30,160 --> 00:31:35,420
+is true والاهم انا بدي اثبت ان k زائد واحد is true
+
+395
+00:31:35,420 --> 00:31:40,910
+ففرضت عكسهاإن هي false ووصلت معايا إن هي false بس
+
+396
+00:31:40,910 --> 00:31:44,950
+لما جيت أطلع على ال numerator فوق لجيت إن هو مش K
+
+397
+00:31:44,950 --> 00:31:52,210
+زائد واحد أنا اختصرته يعني فعليا ال T لحالها عشان
+
+398
+00:31:52,210 --> 00:31:56,110
+فعلا تكون rational .. تكون rational المفروض ليه
+
+399
+00:31:56,110 --> 00:32:01,250
+مايكونش في عوالمشتركة هي T بس هي نص القيمة طب نص
+
+400
+00:32:01,250 --> 00:32:08,020
+القيمة معناته أكيد أجل من Kأكيد أقل من K طب و أقل
+
+401
+00:32:08,020 --> 00:32:10,540
+من K ما هي كانت بالأساس محطوطة في ال .. في ال ..
+
+402
+00:32:10,540 --> 00:32:15,000
+في الفرضية بتاعتنا أنا قاعد بقولك إن كل اللي أقل
+
+403
+00:32:15,000 --> 00:32:19,620
+من K هو true فانت كيف تروح تقولي false؟ و احنا
+
+404
+00:32:19,620 --> 00:32:24,420
+فرضينه فرض، فرض من عندنا، احنا من الأساس قلنا إن
+
+405
+00:32:24,420 --> 00:32:28,920
+هذه is true فماتيش تقولي false كمان مرة is true
+
+406
+00:32:28,920 --> 00:32:34,200
+معناته إنه لا يوجدis true معناته أنه لا يوجد
+
+407
+00:32:34,200 --> 00:32:39,080
+معناته لا يساوي جذر اتنين عشان هيك حطينا كنا تلت
+
+408
+00:32:39,080 --> 00:32:44,320
+خطوط طوية عليها فرضيتنا أنه لا يوجد integer معناته
+
+409
+00:32:44,320 --> 00:32:49,380
+أنه K هو لا مش integer يقبل القسم على P عشان يعطيك
+
+410
+00:32:49,380 --> 00:32:53,680
+جذر اتنين وكل ما هو أقل منه نفس الكلام بما فيهم T
+
+411
+00:32:53,680 --> 00:33:00,180
+لأنه T أقل من Kصح؟ T أقل من K كلنا متفقين ..
+
+412
+00:33:00,180 --> 00:33:04,660
+خلّيني نعديها نقطة نقطة متفقينش عن النقطة هذه أن T
+
+413
+00:33:04,660 --> 00:33:10,580
+هتطلع أقل من K أكيد طيب احنا فرضيتنا أساسا أن كل
+
+414
+00:33:10,580 --> 00:33:15,900
+القيم اللي أقل من K لما نقسمها على B لا تساوي جذر
+
+415
+00:33:15,900 --> 00:33:21,020
+2 كيف ترجع تقول لي أن لأ تطلعت بتساوي جذر 2 صار
+
+416
+00:33:21,020 --> 00:33:25,330
+تناقض .. تناقض واضح هناهنا تناقض واضح أنت فرض
+
+417
+00:33:25,330 --> 00:33:31,750
+فرضية أثناء الحل طلع عكسها أنت فرض أنه آية T على B
+
+418
+00:33:31,750 --> 00:33:35,450
+لا تساوي جدر اتنين أثناء الحل هيطلعت أن الـ T
+
+419
+00:33:35,450 --> 00:33:42,050
+بتساوي جدر اتنين فإذن لأ هنا في تناقض ف
+
+420
+00:33:42,050 --> 00:33:45,750
+automatically لل J اللي احنا فرضين شغلنا عليها من
+
+421
+00:33:45,750 --> 00:33:52,600
+الأساس لكل J أقل من Kلكل القيم اللي أقل من K بما
+
+422
+00:33:52,600 --> 00:34:00,880
+فيهم K طبعا هي طبعا و كلنا نعلم أن T مدام قسمت على
+
+423
+00:34:00,880 --> 00:34:06,720
+2 أكيد هتكون أقل أو يساوي في أحسن حالتها يعني أنت
+
+424
+00:34:06,720 --> 00:34:09,120
+في أحسن حالتها إذا كان أنا بتكلم عن T زائد 1 اللي
+
+425
+00:34:09,120 --> 00:34:16,930
+هي 2 و K واحدبرضه هتطلع بتساوي K فإذا برضه بظبطش
+
+426
+00:34:16,930 --> 00:34:21,470
+لأنه أنا من الأساس فرض نقات K هي لا يوجد، طلع
+
+427
+00:34:21,470 --> 00:34:28,030
+يوجد، فإذا بال contradiction أو this contradicts
+
+428
+00:34:28,030 --> 00:34:30,810
+the inductive step، ال inductive step اللي اتكلمنا
+
+429
+00:34:30,810 --> 00:34:32,710
+عليها هو هي ال inductive step عشان هيكي جبتلك إيها
+
+430
+00:34:32,710 --> 00:34:34,850
+من ال slide الأولى وحطتلك إيها تاني هنا، هيها
+
+431
+00:34:36,460 --> 00:34:41,580
+هيحطينها جاعت بقولك إذا هذا term أو هذا term لا
+
+432
+00:34:41,580 --> 00:34:48,300
+يساوي جدر اتنين فإذا ال K زائد واحد لا يساوي جدر
+
+433
+00:34:48,300 --> 00:34:51,640
+اتنين انت روحت وقلتلي لأ بدي أعكس هذه okay صحتين
+
+434
+00:34:51,640 --> 00:34:55,540
+بس إذا انعكست هذه حسب ال contrapositive المفروض إن
+
+435
+00:34:55,540 --> 00:34:59,700
+هذه كمان تنعكس صح؟
+
+436
+00:34:59,700 --> 00:35:06,070
+إذا فرضت الجزء هذاوبدي اجيب منه هذا الجزء ماعرفتش
+
+437
+00:35:06,070 --> 00:35:11,070
+اش بروح بسوي بفرض عكس هذا الجزء و بجيب منه عكس هذا
+
+438
+00:35:11,070 --> 00:35:16,210
+الجزء مش هيك ال contrapositive طيب فعليا انا هيك
+
+439
+00:35:16,210 --> 00:35:20,090
+اعملت روحت عكست هذا الجزء بس ماطلعليش عكس هذا
+
+440
+00:35:20,090 --> 00:35:26,310
+الجزء ماطلعليش نفس العكس اللي المفروض متوقعه انا
+
+441
+00:35:26,310 --> 00:35:32,630
+لأ طلعليه قيمة مختلفة تماما طلعلنا مش k زائد واحد
+
+442
+00:35:34,800 --> 00:35:38,860
+يعني أنا بقوله افرضلي at k زائد واحد لما فرض و حل
+
+443
+00:35:38,860 --> 00:35:44,200
+و طلع بتساوي مش at k زائد واحد لأ على قيمة اقل من
+
+444
+00:35:44,200 --> 00:35:49,360
+k زائد واحد و اقل من k كمان فمعنى ذلك انه either
+
+445
+00:35:49,360 --> 00:35:54,480
+اتنين ليست rational او irrational او irrational
+
+446
+00:35:54,480 --> 00:35:57,660
+هذا طريقة و ال contrapositive طريقة بس هذا طبعا
+
+447
+00:35:57,660 --> 00:36:00,900
+طريقة strong و هي واضح ان حتى strong كمان في
+
+448
+00:36:00,900 --> 00:36:01,660
+الأفباد تبعها
+
+449
+00:36:04,300 --> 00:36:08,480
+الـ strong لما تكون انت او K زائد واحد لا تعتمد
+
+450
+00:36:08,480 --> 00:36:14,000
+على K فقط عشان تجيبها لا تعتمد على K فقط هذه
+
+451
+00:36:14,000 --> 00:36:18,500
+بتجيبها لما يكون مثلا تتكلم عن ال primes لأن ال
+
+452
+00:36:18,500 --> 00:36:21,860
+primes انت عارف ان هي بتعتمد على كل اللي جابلها مش
+
+453
+00:36:21,860 --> 00:36:26,880
+على اللي جابلها مباشر لأ على كل اللي جابلها فهذه
+
+454
+00:36:26,880 --> 00:36:34,100
+بتضطر لل strongلما تتكلم عن ال .. ال .. ال .. ال
+
+455
+00:36:34,100 --> 00:36:35,060
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+456
+00:36:35,060 --> 00:36:35,120
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+457
+00:36:35,120 --> 00:36:35,880
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+458
+00:36:35,880 --> 00:36:36,240
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+459
+00:36:36,240 --> 00:36:36,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+460
+00:36:36,420 --> 00:36:36,640
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+461
+00:36:36,640 --> 00:36:37,200
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+462
+00:36:37,200 --> 00:36:38,800
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+463
+00:36:38,800 --> 00:36:38,800
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+464
+00:36:38,800 --> 00:36:47,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+465
+00:36:47,440 --> 00:36:47,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+466
+00:36:47,440 --> 00:36:47,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+467
+00:36:47,440 --> 00:36:47,720
+ال .. ال .. ال .. ال .. ال
+
+468
+00:36:57,710 --> 00:37:02,250
+معتمد K زائد واحد معتمد على ما قبل K ففي الحالة
+
+469
+00:37:02,250 --> 00:37:05,730
+هذه على طول بتفكر في ال strong مباشرة بتفكر في مين
+
+470
+00:37:05,730 --> 00:37:09,350
+في ال strong أما إذا كان ال proof K زائد واحد
+
+471
+00:37:09,350 --> 00:37:14,730
+مباشرة معتمد على K خلص ال first principle كافي ال
+
+472
+00:37:14,730 --> 00:37:16,990
+first principle كافي لكن هي مش دايما الدنيا بتكون
+
+473
+00:37:16,990 --> 00:37:20,390
+معاك بهذا الشكل هي مثل جسم على اتنين لما تجسم على
+
+474
+00:37:20,390 --> 00:37:23,950
+اتنين مش معناته انه K زائد واحد لا تعتمد على K فقط
+
+475
+00:37:24,610 --> 00:37:29,470
+وانما تعتمد على k زائد واحد على اتنين واللي احنا
+
+476
+00:37:29,470 --> 00:37:34,030
+اصلا من الاساس قلنا انه اقل من k فعلا وفي النهاية
+
+477
+00:37:34,030 --> 00:37:38,110
+هي مثبتة او مثبتة بالاساس ضمن النظرية فكيف انا
+
+478
+00:37:38,110 --> 00:37:42,550
+بقول k زائد واحد خارج النظرية وهي معتمدة عليها
+
+479
+00:37:42,550 --> 00:37:45,690
+تمام
+
+480
+00:37:57,260 --> 00:38:01,520
+كمان مثاب هى
+
+481
+00:38:01,520 --> 00:38:06,500
+نفس الفكرة اللى هى مين التكعيب بس جالك هنا بتساوي
+
+482
+00:38:06,500 --> 00:38:13,840
+حاجة تانية مختلفة جالك هنا بتساوي مجموعة ال ends
+
+483
+00:38:13,840 --> 00:38:20,160
+بدون التكعيب القيم بدون التكعيب وكله تربيع فهنا
+
+484
+00:38:20,160 --> 00:38:23,520
+اختلفت عن صيغة التوهي اختلفت عن صيغة التوهي برضه
+
+485
+00:38:23,520 --> 00:38:28,220
+كيف ننشطل عليها وجالك أنه من إيش بتداهاتلاتة، فإذا
+
+486
+00:38:28,220 --> 00:38:32,200
+ال basis عن تلاتة، ال basis على طول ببدأ عند مين،
+
+487
+00:38:32,200 --> 00:38:36,560
+عن تلاتة، بدنا نلتزم بمين ب ال .. ال where اللي
+
+488
+00:38:36,560 --> 00:38:39,780
+بكنا نعطيكيها، من وين تبدأ فهي عند التلاتة، معناه
+
+489
+00:38:39,780 --> 00:38:43,980
+أنك بدك تاخد أول three terms هنا و بدك برضه تاخد
+
+490
+00:38:43,980 --> 00:38:47,890
+أول three terms هنافهو ال three times واحد تمانية
+
+491
+00:38:47,890 --> 00:38:51,710
+و سبعة و عشرين و هنا واحد زائد اتنين زائد تلاتة
+
+492
+00:38:51,710 --> 00:38:55,050
+كله تربيع فكله هيطلع سواء هذه او هذه هيطلع ستة و
+
+493
+00:38:55,050 --> 00:39:01,330
+تلاتين فإذن أول خطوة صحيحة الان ال inductive step
+
+494
+00:39:01,330 --> 00:39:06,530
+في الحالة هذه بدنا نفرض ان ال rule true صحيحة at
+
+495
+00:39:06,530 --> 00:39:12,920
+زي ما قولنا k زي .. at kat k أو n تاخدها تاخدها
+
+496
+00:39:12,920 --> 00:39:13,600
+تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها
+
+497
+00:39:13,600 --> 00:39:13,600
+تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها
+
+498
+00:39:13,600 --> 00:39:13,600
+تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها
+
+499
+00:39:13,600 --> 00:39:14,640
+تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها
+
+500
+00:39:14,640 --> 00:39:17,760
+تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها
+
+501
+00:39:17,760 --> 00:39:20,320
+تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها
+
+502
+00:39:20,320 --> 00:39:26,160
+تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها تاخدها
+
+503
+00:39:26,160 --> 00:39:35,280
+تاخدها تاخدها تاخدها تاخدها
+
+504
+00:39:40,180 --> 00:39:44,100
+صح؟ مش هيقول فقط لإن المفروض أنه نصميش لإن زائد
+
+505
+00:39:44,100 --> 00:39:46,960
+واحد و بعدين كله تربيع بعدين كله تربيع هذا اللي
+
+506
+00:39:46,960 --> 00:39:51,540
+بدنا نثبته الآن هذا اللي بدنا نثبته الآن عساس ان
+
+507
+00:39:51,540 --> 00:39:54,460
+افصلهم اقول اللي معناته بدي اقول ان هي لإن فقط
+
+508
+00:39:54,460 --> 00:40:01,340
+تتفق مع النظرية هيها زائد إن زائد واحد تكيب ال
+
+509
+00:40:01,340 --> 00:40:05,940
+term اللي انضف في الطرفين احنا متفقين ان هذا ال
+
+510
+00:40:05,940 --> 00:40:19,980
+termيساوي هذا ال term نظريا at n طيب هنضيف k او n
+
+511
+00:40:19,980 --> 00:40:28,060
+زائد واحد للطرفين هي هنا مضافة وهي هنا مضافة هنا
+
+512
+00:40:28,060 --> 00:40:31,020
+اضيفت و هنا اضيفت طيب عشان اقول انه فعلا تم
+
+513
+00:40:31,020 --> 00:40:34,620
+اضافتها و ال rule هتظل صح المفروض يظهر عندي هذا ال
+
+514
+00:40:34,620 --> 00:40:34,820
+term
+
+515
+00:40:38,210 --> 00:40:42,590
+مفروض بعد عملية .. عمليات رياضية أعملها يظهر عندي
+
+516
+00:40:42,590 --> 00:40:48,090
+هذا ال term هل بنفهم؟ هل احنا .. لازم يظهر عندك؟
+
+517
+00:40:48,090 --> 00:40:53,330
+صح؟ تمام نمسك الآن الطرف اللي بدنا نبدأ نشتغل عليه
+
+518
+00:40:53,330 --> 00:41:02,490
+أحول و أغير و أبدل فيه بحيث أنه يطلع هيك بكل
+
+519
+00:41:02,490 --> 00:41:06,090
+بساطة هذا
+
+520
+00:41:06,090 --> 00:41:06,490
+ال term
+
+521
+00:41:09,270 --> 00:41:13,810
+Euler رجالنا جا إيش بيساوي؟
+
+522
+00:41:13,810 --> 00:41:16,890
+صح؟
+
+523
+00:41:16,890 --> 00:41:22,130
+إيش معلق، من واحد to N خلاص، هاي من N واحد ل N
+
+524
+00:41:22,130 --> 00:41:26,770
+Euler أبو تنصر سنجلنا إياها، مش أبو تنصر سنجلنا
+
+525
+00:41:26,770 --> 00:41:30,830
+إياها طيب N في N زائد واحد على اتنين، خلاص، كله
+
+526
+00:41:30,830 --> 00:41:34,290
+بعدين تربيع، okay ربّعنا التربيع الأن هذه صارت
+
+527
+00:41:34,290 --> 00:41:39,680
+مشابهة لالمثال اللي أخدناه، تاني مثال أخدناهخلاص
+
+528
+00:41:39,680 --> 00:41:44,320
+بتهيألي واضحة جدا الان n زائد واحد هنا انت هتدخل
+
+529
+00:41:44,320 --> 00:41:46,920
+التربيه و هتصير على أربعة أخدناها طوى لسه قبل شوية
+
+530
+00:41:46,920 --> 00:41:49,700
+ما أخديناها فصارت زيها زي امتحان سابق له
+
+531
+00:41:49,700 --> 00:41:54,180
+فالامتحانات بتيجي من بعض بسمع مع بعض ال ..
+
+532
+00:41:55,270 --> 00:41:59,550
+modifications مع بعض التعديلات اللى ممكن نحطها على
+
+533
+00:41:59,550 --> 00:42:03,810
+ال .. على السؤال الباجي أطبعات بتاعي اللى أخدناها
+
+534
+00:42:03,810 --> 00:42:08,630
+سابقا أصبح مافيش صعوبة فيه تكعيب هدى بتلزمنيش
+
+535
+00:42:08,630 --> 00:42:15,290
+بتديها تربيع فحولناها للتربيع ووحدنا المقامات عشان
+
+536
+00:42:15,290 --> 00:42:20,280
+بعدين نرجع لنفس الفكرة الأولىوصلنا للفكرة ل N زائد
+
+537
+00:42:20,280 --> 00:42:23,780
+واحد و N زائد اتنين على اتنين هذا ال term حسب
+
+538
+00:42:23,780 --> 00:42:29,960
+Euler هو مجموع ل عند N زائد واحد لما تاخد هذا
+
+539
+00:42:29,960 --> 00:42:38,150
+لحاله جوا لاحظ لما كانت ل N قلنا N في اللي بعدهاin
+
+540
+00:42:38,150 --> 00:42:41,370
+في اللي بعدها على 2 هنا in زائد واحد في اللي بعدها
+
+541
+00:42:41,370 --> 00:42:45,410
+على 2 بنرجع بنستعيد مكانها معناته ان هنا نتكلم عن
+
+542
+00:42:45,410 --> 00:42:51,790
+summation واحد to n زائد واحد تربيع هيا اللي احنا
+
+543
+00:42:51,790 --> 00:42:57,970
+بدنا هي أساسا استخدمنا
+
+544
+00:42:57,970 --> 00:43:00,050
+Euler track
+
+545
+00:43:02,040 --> 00:43:06,380
+خلاص اضحكي كمان مثال بالمرة مع نوجت .. اه مع نوجت
+
+546
+00:43:06,380 --> 00:43:10,540
+دي كويس لأ مسوودكوا حرارتكوا أثرة منيحة .. زيادة
+
+547
+00:43:10,540 --> 00:43:11,800
+.. طيب
+
+548
+00:43:16,500 --> 00:43:21,700
+بالmathematical induction المفروض أنه لكل قيم H و
+
+549
+00:43:21,700 --> 00:43:26,860
+اللي هي أكبر من minus one بدنا نثبت أنه واحد زائد
+
+550
+00:43:26,860 --> 00:43:33,880
+N في H دائما أقل من أو يساوي واحد زائد H كله to
+
+551
+00:43:33,880 --> 00:43:40,580
+the power N for all non negative integers بمعنى
+
+552
+00:43:40,580 --> 00:43:45,910
+Zeroف الـ non negative يعني من zero ال natural
+
+553
+00:43:45,910 --> 00:43:49,670
+number من الآخر zero و positive zero و positive
+
+554
+00:43:49,670 --> 00:43:53,090
+اللي هي ال natural number طيب business تبع طول
+
+555
+00:43:53,090 --> 00:43:57,910
+هتكون عند ال zero هي أقل قيمة ممكن أول قيمة حسب ال
+
+556
+00:43:57,910 --> 00:44:01,350
+non negative بنعود فيها ماعتقدش هيكون عندنا مشكلة
+
+557
+00:44:01,350 --> 00:44:08,390
+فيها واحد و هنا صفر فخلاص هذه دلت واحد ال term هنا
+
+558
+00:44:08,390 --> 00:44:13,740
+واحد زائد Hجد ما تكون قيمة H في النهاية كله تتبار
+
+559
+00:44:13,740 --> 00:44:17,920
+Zero يعني واحد يعني واحد فبطلع واحد بيسوا واحد و
+
+560
+00:44:17,920 --> 00:44:22,660
+المساوة هي ضمن ال rule فإذا ماشي إذا ال business
+
+561
+00:44:22,660 --> 00:44:28,060
+step success انجحنا فيها ال inductive step برضه
+
+562
+00:44:28,060 --> 00:44:32,600
+بكل بساطة بدنا نتكلم بعدك على N زائد واحد و هنا
+
+563
+00:44:32,600 --> 00:44:37,120
+برضه N زائد واحد و نشوف هل الكلام ده صحيح او .. او
+
+564
+00:44:37,120 --> 00:44:43,780
+لأفهنا هذه بدأ افترض ان هي صحيحة ال term هذا صحيح
+
+565
+00:44:43,780 --> 00:44:51,840
+ل عند n ل n صحيح لكل قيم n أكبر من أو يساوي صفر
+
+566
+00:44:51,840 --> 00:44:58,900
+تمام الآن بنجرب عند n زائد واحد و n زائد او عفوا
+
+567
+00:44:58,900 --> 00:45:04,240
+فوق n زائد واحد اول
+
+568
+00:45:04,240 --> 00:45:09,090
+شغل اللي هنعملها كلنا عارفين ان واحدزائد H هذه
+
+569
+00:45:09,090 --> 00:45:18,430
+وحسب قيمة H وين H؟ صح؟ فإذن دايما أكبر من صفر H
+
+570
+00:45:18,430 --> 00:45:23,390
+دايما أكبر من سالب واحد طيب هي مجموعة مع واحد يعني
+
+571
+00:45:23,390 --> 00:45:26,850
+دايما أكبر من صفر مقتنعين؟ عشان لأنه هذا حنحتاجه
+
+572
+00:45:26,850 --> 00:45:29,910
+في الإثبات الآن حنحتاجه في الإثبات فإذا ال
+
+573
+00:45:29,910 --> 00:45:35,100
+condition هذا مهم جدا كان في السؤالمهم جدا كان في
+
+574
+00:45:35,100 --> 00:45:39,420
+السؤال وكل شغلنا على N ماحدش يروح الأخبط زي ما في
+
+575
+00:45:39,420 --> 00:45:42,520
+وجدها في الأسئلة لجوا أن في هنا متغيرين في عندك
+
+576
+00:45:42,520 --> 00:45:45,960
+افترضوا أن ال H كمان متغير فبدأوا يشتغلوا على ال H
+
+577
+00:45:45,960 --> 00:45:49,800
+و بدؤوها من سالب واحد و نسينا أنه لأ شغلنا على N
+
+578
+00:45:49,800 --> 00:45:55,700
+مش على ال H تمام الآن بكل بساطة هذا ال term زي ما
+
+579
+00:45:55,700 --> 00:45:59,440
+هو هنا بتفصلهم
+
+580
+00:46:00,800 --> 00:46:03,760
+in لحال و ال term اللي ضربته فيه اللي هو نفس ال
+
+581
+00:46:03,760 --> 00:46:07,940
+term اللي خلاها زائد واحد اللي خلاها زائد واحد و
+
+582
+00:46:07,940 --> 00:46:12,040
+كلنا عارفين ان هذا اكبر من صفر مهمة المعلومة مهمة
+
+583
+00:46:12,040 --> 00:46:17,860
+جدا المعلومة عشان في الآخر تقولي ان ال in تربيع
+
+584
+00:46:17,860 --> 00:46:21,980
+ناخدها شوية شوية لأن كلنا عارفين ان واحد زائد h to
+
+585
+00:46:21,980 --> 00:46:27,940
+the power n هتكون اكبر من او تساوي واحد زائد in h
+
+586
+00:46:27,940 --> 00:46:35,020
+مدام انا بتكلم عنهقيمة أكبر من سالب واحد و باتكلم
+
+587
+00:46:35,020 --> 00:46:40,240
+عن n من صفر في أكبر يعني positive القيمة positive
+
+588
+00:46:40,240 --> 00:46:44,220
+بتاعة n فدائما هتلاقي ان هذا ال term صحيح واحد
+
+589
+00:46:44,220 --> 00:46:50,800
+زائد h to the power nهتكون دايما اكبر من او يساوي
+
+590
+00:46:50,800 --> 00:46:55,500
+واحد زائد N في H في H هنستفيد منها هنشوف هنستفيد
+
+591
+00:46:55,500 --> 00:46:58,220
+منها في هذا ال term اللي موجود عندي هنا لأنه
+
+592
+00:46:58,220 --> 00:47:02,860
+ببساطة لو بدك اتعود مكانه معناته انت عارف انه هذا
+
+593
+00:47:02,860 --> 00:47:09,580
+ال term هيكون اكبر فإذا هاي ال term هذا هو اكبر من
+
+594
+00:47:09,580 --> 00:47:17,340
+لو استعادتعن واحد .. اه مظبوط واحد زائد H to the
+
+595
+00:47:17,340 --> 00:47:27,220
+power N بواحد زائد N في H لا هذي تحالف ده اثبات؟
+
+596
+00:47:27,220 --> 00:47:33,220
+ليش؟ بدك
+
+597
+00:47:33,220 --> 00:47:36,160
+هيها سالبة؟ جدش بدها تكون سالبة؟ هي اكبر من سالب
+
+598
+00:47:36,160 --> 00:47:39,300
+واحد اكبر من سالب واحد يعني معناه ذلك ان عندك ال
+
+599
+00:47:39,300 --> 00:47:41,100
+term ده دايما اكبر من صفر
+
+600
+00:47:45,090 --> 00:47:49,070
+هي الفرقية في ال N هنا هنا انت بتتكلم دائما اكبر
+
+601
+00:47:49,070 --> 00:47:55,710
+من صفر دائما اكبر من صفر فمنتهي الجثة يعني دائما
+
+602
+00:47:55,710 --> 00:48:00,430
+اكبر من صفر معناه ذلك انه هنا حتى لو بدك تفترض ان
+
+603
+00:48:00,430 --> 00:48:04,630
+هي فيها جزء سالب فيها جزء سالب معناته بالعكس فدي
+
+604
+00:48:04,630 --> 00:48:09,150
+قاعدة بتجل انت اللي بهمك هذا ال term عشان هيك هو
+
+605
+00:48:09,150 --> 00:48:13,980
+ده اللي علقنا عنه هنا علقنا فيه علق عليهعشان هيك
+
+606
+00:48:13,980 --> 00:48:18,760
+ده اللي علقنا عليه بالأساس فانت ضامن انه جوا الأُس
+
+607
+00:48:18,760 --> 00:48:22,940
+لداخل عشان تقول to the power انت ضامن ان هو ده
+
+608
+00:48:22,940 --> 00:48:27,900
+أكبر من صفر انت ضامن هو أكبر من صفر وفي نفس الوجهة
+
+609
+00:48:27,900 --> 00:48:30,480
+بدك تقول لأ هذي مش بالسالب لأن بالسالب معناته
+
+610
+00:48:30,480 --> 00:48:35,300
+بالعكس بجل قيمتها متفقين؟ فإذن اللي هي فى فترة من
+
+611
+00:48:35,300 --> 00:48:39,580
+سالب واحد لواحد بالعكس هذي بتجل أكتر من ما انت
+
+612
+00:48:39,580 --> 00:48:42,340
+متخيل لأن بطلع في term سالب هنا بده ينطرح من
+
+613
+00:48:42,340 --> 00:48:45,900
+الواحدطيب، هتقولي لأ، هي فوق الواحد، يعني هي في
+
+614
+00:48:45,900 --> 00:48:48,300
+الجزء ال positive، هقولك ماشي، في الجزء ال
+
+615
+00:48:48,300 --> 00:48:51,220
+positive، فليكن، بس أنت في النهاية، إذا هذه في
+
+616
+00:48:51,220 --> 00:48:53,880
+الجزء ال positive، أنت ضربت في n، هذه في الجزء ال
+
+617
+00:48:53,880 --> 00:48:58,520
+positive، عملت to the power n، و n جديش، بتبدأ من
+
+618
+00:48:58,520 --> 00:49:02,860
+صفر، يعني إذا فرضنا إن هي صفر، معناه ذلك إن هنا
+
+619
+00:49:02,860 --> 00:49:05,360
+بالظبط، هيطلع هنا عندك واحد، و هيطلع عندك هنا
+
+620
+00:49:05,360 --> 00:49:11,240
+واحد، طيب، أكتر من صفر، هيطلع لأ، ال power بتزيد،
+
+621
+00:49:11,980 --> 00:49:15,300
+الpower هتزيدلك ال term اللي هنا فلأ مش محتاج أثبت
+
+622
+00:49:15,300 --> 00:49:18,420
+هي بالعكس إذا أنا مااخد بالي هي إن من النقطة هذه
+
+623
+00:49:18,420 --> 00:49:21,080
+ومااخد بالي إنه ببدأ من ال non negative ومااخد
+
+624
+00:49:21,080 --> 00:49:23,680
+بالي من هذه ال rule اللي احنا حطناها في البداية
+
+625
+00:49:23,680 --> 00:49:28,000
+ومقتنعين فيها لإنه مبني على إنه H أكبر من سالب
+
+626
+00:49:28,000 --> 00:49:31,740
+واحد فمعنى ذلك إنه ال term كله على بعض هذا أكبر من
+
+627
+00:49:31,740 --> 00:49:35,780
+صفر أكيد فانا مطمن هنا إنه هذا ال term ده مانحجون
+
+628
+00:49:35,780 --> 00:49:40,900
+أكبر من هذا ال term تمام وبناء عليه زي ما قلنا
+
+629
+00:49:41,810 --> 00:49:49,770
+بنقدر نعوض بالجزئية هذه تمام عوضنا بالجزئية بهذه
+
+630
+00:49:49,770 --> 00:49:56,110
+الجزئية وخلّيني أقول إن هذه هيك واحد منها
+
+631
+00:49:56,110 --> 00:50:02,490
+بكل بساطة لو جيت عوضت يعني قرنت هذه مع هذه قرننا
+
+632
+00:50:02,490 --> 00:50:07,630
+هذه مع هذه اللي هي هيطلع عندك إيش هي ال term صحيح؟
+
+633
+00:50:07,630 --> 00:50:13,670
+هذا مع هذا أيوة، في مشكلة هدول؟نزلنا زي ما هو تمام
+
+634
+00:50:13,670 --> 00:50:20,230
+الآن هذا ال term اضرب في بعض فبتطلع عندك هاي
+
+635
+00:50:20,230 --> 00:50:26,370
+الواحد وهي ال N وين راحت N خليني احطها هاي واحد
+
+636
+00:50:26,370 --> 00:50:35,910
+زائد N في H وH زائد H في N H تربيع
+
+637
+00:50:38,700 --> 00:50:42,900
+تمام؟ مظبوطة هيك؟ كويس إيش اللي أخدنا عامل مشترك
+
+638
+00:50:42,900 --> 00:50:47,220
+بعد هيكل؟ أخدنا ال H عامل مشترك أخدنا ال H عامل
+
+639
+00:50:47,220 --> 00:50:51,600
+مشترك بحيث أنه يضل عندك هنا واحد و هنا بتاخد N
+
+640
+00:50:51,600 --> 00:50:56,500
+زائد واحد لأ دي التربية حتى بتضل التربية زي ما هي
+
+641
+00:50:56,500 --> 00:51:00,320
+التربية مش هناخدها بتضلها زي ما هي فهنا بتضل واحد
+
+642
+00:51:00,320 --> 00:51:07,090
+زائدtwo terms هدول فقط n زائد واحد في h وهذه زي ما
+
+643
+00:51:07,090 --> 00:51:15,490
+هي هيها صحيحة تمام تمام أمتاز عرفنا أنه هيك اللي
+
+644
+00:51:15,490 --> 00:51:21,550
+بنعمله صح هذا ال term بكل بساطة هيكون أكبر من هذا
+
+645
+00:51:21,550 --> 00:51:27,390
+ال term هي ال واحد واحد وهي ال n هنا في term n في
+
+646
+00:51:27,390 --> 00:51:33,850
+h تربيع هذا term زيادةال term هذا زيادة، معناته
+
+647
+00:51:33,850 --> 00:51:39,070
+أكيد أكبر من هذا ال term لأن هذا جزء منه، هذا جزء
+
+648
+00:51:39,070 --> 00:51:45,150
+منه، فإذا هذا ال term أكيد أكبر من هذا ال term،
+
+649
+00:51:45,150 --> 00:51:50,870
+صح؟ مدام هذا أكبر من term معين و ال term المعين
+
+650
+00:51:50,870 --> 00:51:55,750
+هذا أكبر منه، خلاص، مش هذا هو المطلوب، هو هذا
+
+651
+00:51:55,750 --> 00:52:03,030
+المطلوب، هي عندك فوق، هو هي المطلوبفهي كمان فكرة
+
+652
+00:52:03,030 --> 00:52:09,830
+ده ال inductive proof okay هيك نكون احنا خلصنا و
+
+653
+00:52:09,830 --> 00:52:15,470
+ضايق حاجة أخيرة في الآخر مثال هيك لجيته برضه في
+
+654
+00:52:15,470 --> 00:52:20,030
+واحدة من الأسئلة من الأسئلة اللي اتذكرت انه ماكنش
+
+655
+00:52:20,030 --> 00:52:24,210
+حد نحله كتير لمجرد مع أنه بسيط جدا لمجرد انه لجى
+
+656
+00:52:24,210 --> 00:52:28,090
+في كلمة proof proof that فكلمة proof that بتعمل
+
+657
+00:52:28,090 --> 00:52:29,130
+الظهر عندكم هيك
+
+658
+00:52:32,010 --> 00:52:36,670
+بتعمل عندكم مشكلة فكل الموضوع أنه بدنا نثبت التالي
+
+659
+00:52:36,670 --> 00:52:44,170
+ان K مضروبة في ال combination from N to K تساوي N
+
+660
+00:52:44,170 --> 00:52:49,790
+عكسناهم N في ال combination N ناقص واحد لK ناقص
+
+661
+00:52:49,790 --> 00:52:55,250
+واحد يعني لاحظ التغييرات اللي صارت؟ طيب هل الكلام
+
+662
+00:52:55,250 --> 00:52:58,570
+هذا صحيح؟ ارجع للمعادلة الأصلية تبع ال combination
+
+663
+00:52:59,350 --> 00:53:02,450
+اللي هي ال factorial على factorial factorial على
+
+664
+00:53:02,450 --> 00:53:07,870
+على اتنين factorial تحت خلاص هيها هيها ده مش اكتر
+
+665
+00:53:07,870 --> 00:53:14,730
+من هيك و هناك نفس ال term هناك نفس الجثة كل اللي
+
+666
+00:53:14,730 --> 00:53:21,650
+هنعمله الآن انت عارف مسبقا ان هذه لما
+
+667
+00:53:21,650 --> 00:53:25,310
+تضرب in في in نقص واحد factorial in factorial
+
+668
+00:53:25,310 --> 00:53:31,130
+فهدول هيك مع بعض كلهم مضربين هدول in factorialأيوة
+
+669
+00:53:31,130 --> 00:53:34,770
+هذه بدنا نشتغل عليها شوية هذه رح نشتغل عليها شوية
+
+670
+00:53:34,770 --> 00:53:38,150
+بحيث انه yes ان جول بده أجيبها دلالة ال K
+
+671
+00:53:38,150 --> 00:53:42,530
+factorial فمده أن بدك تحطها K factorial بدك تصبح
+
+672
+00:53:42,530 --> 00:53:46,410
+كأنك ضربت في K فإذا نضربها في K صارت K factorial
+
+673
+00:53:46,410 --> 00:53:51,890
+على K صح
+
+674
+00:53:51,890 --> 00:53:59,540
+على K طيب مقام المقام بصير بسط فيه أسهل من هيكتخيل
+
+675
+00:53:59,540 --> 00:54:03,780
+ان هذا السؤال هيو ها عليه خمس درجات كان هاي السؤال
+
+676
+00:54:03,780 --> 00:54:09,840
+هاي خلصنا انتهى السؤال أكم سطر هي خمس درجات
+
+677
+00:54:15,250 --> 00:54:19,210
+ملاحظ تعوض مباشر يعني انت بس بتحط تعوض مباشر تبعها
+
+678
+00:54:19,210 --> 00:54:24,510
+تبع ال combination اللي انت بتعرفه هات نكون خلصنا
+
+679
+00:54:24,510 --> 00:54:28,990
+مجموعة الأسئلة لليوم المرة الجاية هنحاول نرجع شوية
+
+680
+00:54:28,990 --> 00:54:34,650
+لل encryption في أكمل فكرة من خلال أسئلتكوا لاحظوا
+
+681
+00:54:34,650 --> 00:54:38,350
+أن أنا بأخد الأسئلة منكوا كمان مرة هنا قلنا نفس
+
+682
+00:54:38,350 --> 00:54:43,840
+الجصة فاللي فهمتوا منكوا أن كان عندكم مشكلةفي
+
+683
+00:54:43,840 --> 00:54:50,040
+مشكلة كيف تحسبه القيمة تظبو الرقم كبير فحعملكوا
+
+684
+00:54:50,040 --> 00:54:52,160
+إياها بشكل رياضي يعني على الصبورة تحلوها مافيش ده
+
+685
+00:54:52,160 --> 00:54:56,800
+على الكمبيوتر كويس؟ برضه من ال rules اللي أخدناها
+
+686
+00:54:56,800 --> 00:55:00,280
+في المحاضرة هجيبلك rule أقولك إحنا هنستخدم ال rule
+
+687
+00:55:00,280 --> 00:55:03,580
+هذه هتبسطلك الشغل و لو عملتها ك sub routine
+
+688
+00:55:03,580 --> 00:55:06,240
+أرياحلك من إنك أنت تدور على ال functions المناسبة
+
+689
+00:55:06,240 --> 00:55:10,420
+لل big numbers تمام؟ يعطيكوا العافية و نشوفكم بعد
+
+690
+00:55:10,420 --> 00:55:10,960
+بكرة ان شاء الله
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c52c88944d96090274f20fec4960c5e42e56a0c3
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ.srt
@@ -0,0 +1,2292 @@
+1
+00:00:05,130 --> 00:00:07,950
+طيب بسم الله الرحمن الرحيم يعطيكم العفو يا شباب
+
+2
+00:00:07,950 --> 00:00:13,230
+نكمل اليوم في مساق الـ discrete، اليوم عندنا موضوع
+
+3
+00:00:13,230 --> 00:00:17,290
+جديد بعد ما كنا خلصنا الـ induction، أخذناها المرة
+
+4
+00:00:17,290 --> 00:00:19,710
+اللي فاتت وشوفنا الـ basis step والـ inductive
+
+5
+00:00:19,710 --> 00:00:25,690
+step، ثم تحدثنا منها عن الـ recursion، الـ recursion
+
+6
+00:00:25,690 --> 00:00:28,870
+شوفنا كيف بيصير في recurrence لـ الـ function من
+
+7
+00:00:28,870 --> 00:00:34,660
+نفسها، فاليوم هنتكلم عن الـ counting أو العد، علم
+
+8
+00:00:34,660 --> 00:00:40,780
+العد هو كيف أنا ممكن أعد كويس عدد الطرق لأداء task
+
+9
+00:00:40,780 --> 00:00:45,300
+معينة، فهذا هو المفهوم من كلمة counting أو العد
+
+10
+00:00:45,300 --> 00:00:48,400
+اللي احنا بدنا نتكلم عنه اليوم إن شاء الله تعالى
+
+11
+00:00:48,400 --> 00:00:54,240
+فهو الحقيقة دراسة عدد الطرق أو عدد
+
+12
+00:00:54,240 --> 00:00:59,320
+الطرق اللي ممكن نوضع فيها، خلينا نقول بعض الأشياء
+
+13
+00:00:59,320 --> 00:01:04,200
+في combination معين، في تركيب معين، نقول والله
+
+14
+00:01:04,200 --> 00:01:09,440
+مثال اللي موجود فيه مئة شخص بدهم يتسابقوا، فكم
+
+15
+00:01:09,440 --> 00:01:14,920
+عندي possibilities لفوز الأول عشرة، يعني الأول
+
+16
+00:01:14,920 --> 00:01:18,400
+عشرة من الأوائل، كيف ممكن أعمل؟ ما بديش تسمية
+
+17
+00:01:18,400 --> 00:01:22,280
+احتمالات، ولكن possibilities، أيش الإمكانية أن...
+
+18
+00:01:22,550 --> 00:01:26,750
+أحط combination، تركيبة من عدد المئة شخص هؤلاء
+
+19
+00:01:26,750 --> 00:01:30,990
+بحيث أنه يكونوا هم العشرة اللي هيفوزوا، فكم عدد الـ
+
+20
+00:01:30,990 --> 00:01:36,070
+possibilities هذه، الإمكانيات هذه؟ فطبعاً هنتكلم
+
+21
+00:01:36,070 --> 00:01:39,030
+عنها، وواضح أن أنتم كلكم عارفين هيك الموضوع
+
+22
+00:01:39,030 --> 00:01:42,210
+هذا، فمعنى ذلك أنه المفروض نجري فيه اللي واضح أن
+
+23
+00:01:42,210 --> 00:01:47,140
+أنتم هيك عارفينه، جيد كويس هذا الموضوع، الشغلة
+
+24
+00:01:47,140 --> 00:01:49,720
+الثانية اللي ممكن تكون... خليكم معنا يا شباب
+
+25
+00:01:49,720 --> 00:01:52,720
+الشغلة الثانية اللي ممكن نتكلم فيها في نفس الموضوع في
+
+26
+00:01:52,720 --> 00:01:56,980
+نفس السياق نستفيد منها هي فكرة الـ password، كم
+
+27
+00:01:56,980 --> 00:02:01,140
+أنت ممكن تعمل كـمبرمج، كم ممكن تولد عدد
+
+28
+00:02:01,140 --> 00:02:04,320
+passwords إذا كانت محددة عدد الـ digits اللي أنت
+
+29
+00:02:04,320 --> 00:02:09,300
+بدك تستخدمها للـ password، فبتكون عندك من الأساس عدد
+
+30
+00:02:09,300 --> 00:02:15,080
+أو الـ... كمية أو عدد الـ passwords اللي ممكن توليدها
+
+31
+00:02:15,080 --> 00:02:19,760
+في عدد خانات محددة لكلمة الـ password، فهذا المفروض
+
+32
+00:02:19,760 --> 00:02:23,780
+برضه من أساسيات العد... من أساسيات العد، فلما نقول
+
+33
+00:02:23,780 --> 00:02:27,920
+والله عندك الـ password ممكن تكون من ستة لثمانية
+
+34
+00:02:27,920 --> 00:02:34,100
+letters or digits، ممكن تستخدم إما حروف أو أرقام
+
+35
+00:02:34,100 --> 00:02:40,200
+والـ password أقل شيء من ستة characters أو من ستة
+
+36
+00:02:40,200 --> 00:02:44,800
+حروف أو أرقام لثمانية، فإذا ممكن تكتب الـ password
+
+37
+00:02:44,800 --> 00:02:48,800
+تبعك ستة أو سبعة أو ثمانية حروف أو أرقام، حروف
+
+38
+00:02:48,800 --> 00:02:52,120
+على إيش؟ على أرقام، كم بده يكون عندي عدد passwords
+
+39
+00:02:52,120 --> 00:02:57,190
+ممكنين في الحالة هذه؟ فهذه برضه من خلال موضوعنا
+
+40
+00:02:57,190 --> 00:03:02,450
+لليوم اللي هي الـ basics of counting أو أسس العد،
+
+41
+00:03:02,450 --> 00:03:06,630
+هنستخدمها، هنتكلم عنها، بس نبدأ ندرج شوية شوية، و
+
+42
+00:03:06,630 --> 00:03:11,410
+أنا بتكلم عن أسس العد، بدي أستخدم أو بدي هتكلم عن
+
+43
+00:03:11,410 --> 00:03:16,450
+حاجة كتير مهمة هي الـ two rules كتير بيحكمونا في هذا
+
+44
+00:03:16,450 --> 00:03:19,910
+الموضوع هي الـ sum والـ product... sum وproduct، و
+
+45
+00:03:19,910 --> 00:03:22,330
+هنشوف هذه متى بنستخدمها وهذه متى بنستخدمها حسب
+
+46
+00:03:22,330 --> 00:03:25,210
+منطق السؤال وحسب أنت إيش بدك من السؤال أو كيف بدك
+
+47
+00:03:25,210 --> 00:03:28,850
+...لو بنتكلم عن الـ password... أنت كيف بدك تركب الـ
+
+48
+00:03:28,850 --> 00:03:32,860
+password، فهي مش مجرد إنه عدد الـ digits وخلاص، لأن الـ
+
+49
+00:03:32,860 --> 00:03:37,580
+digits هذه كيف بدك ترتبها؟ كيف بدك تكونها؟ هل لازم
+
+50
+00:03:37,580 --> 00:03:41,800
+يكون كلهم حروف؟ ولا لأ، ممكن يكون كلهم digits؟ ولا
+
+51
+00:03:41,800 --> 00:03:46,100
+لأ، من هذا على هذا؟ طب ممكن تقول حروف لكن ما نقولش
+
+52
+00:03:46,100 --> 00:03:50,330
+عدد الحروف عن اثنين مثلاً من الستة، فأنت ممكن تحط كل
+
+53
+00:03:50,330 --> 00:03:53,110
+الـ rules اللي بدك إياها، ففي الحالة هذه كم يؤثر
+
+54
+00:03:53,110 --> 00:03:57,490
+هذا على عدد الـ passwords الممكنين بحيث أنك أنت
+
+55
+00:03:57,490 --> 00:04:01,050
+ممكن تحاول كمان تزود الـ difficulty تبع الـ
+
+56
+00:04:01,050 --> 00:04:05,900
+password، فأنت لو ما بدك تحدد الـ password هذه بسيطة
+
+57
+00:04:05,900 --> 00:04:09,920
+ولا صعبة ولا normal، فممكن تحدد هؤلاء كم وهؤلاء
+
+58
+00:04:09,920 --> 00:04:14,540
+كم وهؤلاء كم، بناء على مفهومك أنت لإيش يعني
+
+59
+00:04:14,540 --> 00:04:17,020
+صعبة وإيش يعني بسيطة، إيش يعني صعبة وإيش يعني
+
+60
+00:04:17,020 --> 00:04:19,920
+بسيطة، فده كلها هنتكلم عنها، لكن بدنا نفهم شوية
+
+61
+00:04:19,920 --> 00:04:23,300
+basics أساسية في البداية اللي هي الـ sum والـ
+
+62
+00:04:23,300 --> 00:04:26,460
+product، عشان نشرحهم، بدي أفترض أنه في عندي عدد
+
+63
+00:04:26,460 --> 00:04:34,160
+الطرق to do task one، بدي أسميهم مثلاً M way، مميز
+
+64
+00:04:34,160 --> 00:04:40,380
+فعندك عددهم M، عشان أقدر أنفذ الـ task الأولى، طيب لو
+
+65
+00:04:40,380 --> 00:04:44,660
+كان عندك العدد N، هو الـ number of ways to do task 2
+
+66
+00:04:44,660 --> 00:04:48,640
+فأنت صار عندك two tasks بدك تعملها combination مع
+
+67
+00:04:48,640 --> 00:04:51,860
+بعض، بدك تعملها الاثنين مع بعضهم، فهنا أصبح نحن
+
+68
+00:04:51,860 --> 00:04:56,120
+نتكلم عن هذه تحسبها لحالها وهذه تحسبها لحالها،
+
+69
+00:04:56,120 --> 00:04:59,740
+هذه لحالها وهذه لحالها، هأقول الـ letters لحالهم والـ
+
+70
+00:04:59,740 --> 00:05:03,090
+digits لحالهم، طيب وبعدين إيش بدنا نعمل فيهم؟ هنا
+
+71
+00:05:03,090 --> 00:05:08,910
+بتصير كيف، قليلة تركيب الـ password نفسه، إذا والله
+
+72
+00:05:08,910 --> 00:05:14,070
+بدك تعملها مع بعض، هيكون في عندك two ways تشتغل
+
+73
+00:05:14,070 --> 00:05:18,420
+عليها، إما sum تجمعهم، ففي الحالة هذه بيكونوا
+
+74
+00:05:18,420 --> 00:05:23,480
+منفصلين تماماً عن بعض، يا إما letters أو أو أو أو أو
+
+75
+00:05:23,480 --> 00:05:25,120
+أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو
+
+76
+00:05:25,120 --> 00:05:25,140
+أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو
+
+77
+00:05:25,140 --> 00:05:25,200
+أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو
+
+78
+00:05:25,200 --> 00:05:31,000
+أو أو أو أو أو
+
+79
+00:05:31,000 --> 00:05:34,680
+أو، بدنا نقول الـ summation rule، إذا كان أنا الـ task
+
+80
+00:05:34,680 --> 00:05:39,940
+اللي بدي أعملها do either task one or task two، فأنا يا بديهم
+
+81
+00:05:39,940 --> 00:05:44,200
+حروف بس يا بديهم أرقام بس، كويس؟ ففي الحالة هذه
+
+82
+00:05:44,200 --> 00:05:47,500
+طبعاً هي أكيد بالـ password مش منطق أقول الكلام هذا
+
+83
+00:05:47,500 --> 00:05:50,360
+بس في applications ثانية آه منطق جداً، يا هيك يا
+
+84
+00:05:50,360 --> 00:05:52,720
+هيك، زي ما هناخذ أمثلة كتيرة اليوم، هناخذ الأمثلة
+
+85
+00:05:52,720 --> 00:05:53,360
+هتكون كثيرة
+
+86
+00:05:56,360 --> 00:06:01,240
+لكن ما بديش إياها مع بعض، ففي الحالة هذه بنستخدم M
+
+87
+00:06:01,240 --> 00:06:06,940
+plus N، هؤلاء كم عدد الطرق عشان فعلاً أعمل password
+
+88
+00:06:06,940 --> 00:06:12,340
+نفترض من ستة من ستة digits فقط كحروف، كم عددهم؟
+
+89
+00:06:12,340 --> 00:06:16,100
+خلاص بنحسب عددهم وجمعناه وحطيناه كأنه قيمة M، طيب كم
+
+90
+00:06:16,100 --> 00:06:19,960
+عدد الأرقام اللي ممكن أكون منهم password من ستة
+
+91
+00:06:19,960 --> 00:06:23,880
+digits، برضه بنحسب عددهم وبنجمع الاثنين مع بعض،
+
+92
+00:06:23,880 --> 00:06:29,000
+مدام أنا محتاج يا هذا يا هذا، لكن لما بروح للـ
+
+93
+00:06:29,000 --> 00:06:34,020
+product rule، متى؟ لما تكون الـ task اللي بدي أعملها do both
+
+94
+00:06:34,020 --> 00:06:39,080
+task one and task two simultaneously، بمعنى متزامنين
+
+95
+00:06:39,080 --> 00:06:42,020
+مع بعض، بدي أعمل الاثنين مع بعض، ففي الحالة هذه الـ
+
+96
+00:06:42,020 --> 00:06:46,460
+password ممكن يكون من هنا ومن هنا، ساعتها كم من
+
+97
+00:06:46,460 --> 00:06:50,240
+هنا وكم من هنا، أنت بتقدر تكون عندك إمكانية تلعب
+
+98
+00:06:50,240 --> 00:06:53,400
+في الموضوع زي ما بدك، يعني تقول والله بدي أول ثلاثة
+
+99
+00:06:53,400 --> 00:06:57,200
+letters وبعدين ثلاثة digits، أو تقول لأ بديها
+
+100
+00:06:57,200 --> 00:07:00,080
+اثنين وواحد، اثنين وثلاثة، اثنين وخمسة، اعملها بالـ
+
+101
+00:07:00,080 --> 00:07:04,680
+...أقول لك، أقول والله بدي letter digit letter digit
+
+102
+00:07:04,680 --> 00:07:08,280
+letter digit، okay، هذه الـ problem بدك تشتغلها كل
+
+103
+00:07:08,280 --> 00:07:12,820
+واحدة لحالها، تشتغل كل واحدة لحالها وتضربهم مع بعض،
+
+104
+00:07:12,820 --> 00:07:17,160
+في الحالة هذه هنشوف هتتضح طبعاً أكثر، أنت بنستخدم الـ
+
+105
+00:07:17,160 --> 00:07:20,920
+product وأنت بنستخدم الـ sum مع الأمثلة الكثيرة
+
+106
+00:07:20,920 --> 00:07:25,520
+اللي هنقدر نأخذها، لكن الآن عشان أوضح بس أن الفكرة
+
+107
+00:07:25,520 --> 00:07:29,020
+هي برضه ما بعدتش عن حاجة إحنا جاهزين نأخذها
+
+108
+00:07:29,020 --> 00:07:32,860
+باستمرار طول الفصل اللي هي الـ set، الـ set، فأنا بكل
+
+109
+00:07:32,860 --> 00:07:37,140
+بساطة، الـ M هذه، الـ M اللي كانت هي عدد الـ
+
+110
+00:07:37,140 --> 00:07:41,480
+possibilities to do task 1، ممكن أقول عليهم هؤلاء
+
+111
+00:07:41,480 --> 00:07:46,040
+كل way من الـ ways هؤلاء بيتعامل معها كأنها element
+
+112
+00:07:46,040 --> 00:07:52,160
+داخل set كاملة بحيث أني أقول في الآخر الـ A هي الـ
+
+113
+00:07:52,160 --> 00:07:59,340
+set لكل الـ ways to do task one، كل مهمة أو كل حل
+
+114
+00:07:59,340 --> 00:08:02,900
+بقدر أعمله للمهمة الأولى... كل حل ممكن أقدر أعمله
+
+115
+00:08:02,900 --> 00:08:06,220
+للمهمة الأولى بجمعه مع بعضه وبحطه في تافيه set
+
+116
+00:08:06,220 --> 00:08:09,480
+واحدة بسميها set A، فهذه الـ set بتصير هي اللي
+
+117
+00:08:09,480 --> 00:08:13,360
+معطيان كل possibility solutions فعلياً للـ task
+
+118
+00:08:13,360 --> 00:08:18,240
+الأولى، في نفس الكلام برضه بقول عندي الـ set B فهي
+
+119
+00:08:18,240 --> 00:08:21,400
+برضه كل الـ possibilities أو الـ ways أو الـ
+
+120
+00:08:21,400 --> 00:08:26,750
+solutions للـ task 2، للـ task two، فإذا كانت عندي A
+
+121
+00:08:26,750 --> 00:08:32,150
+and B are disjoint، بمعنى أن الحلول هنا مالهاش
+
+122
+00:08:32,150 --> 00:08:36,870
+علاقة بالحلول هنا، A فيها طرق حل مختلفة تماماً عن
+
+123
+00:08:36,870 --> 00:08:41,690
+طرق حل B، ففي الحالة دي بنقدر نقول عشان أعمل
+
+124
+00:08:41,690 --> 00:08:45,190
+either task one or task two، معناته اتحاد الاثنين
+
+125
+00:08:45,190 --> 00:08:49,710
+اتحاد A مع B، فصارت نفس المفهوم اللي أخذناها سابقاً
+
+126
+00:08:49,710 --> 00:08:55,220
+لمين؟ للـ set، للـ set كده، الاتحاد وهذا ينطبق على الـ
+
+127
+00:08:55,220 --> 00:08:58,180
+rule بتاع الـ two اللي هي sum، فهي cardinality لـ A
+
+128
+00:08:58,180 --> 00:09:01,820
+plus cardinality B، يعني معناته M plus N هي نفس الـ
+
+129
+00:09:01,820 --> 00:09:05,680
+sum rule اللي أخذناها، في المقابل عندك برضه
+
+130
+00:09:05,680 --> 00:09:09,780
+إمكانية أن الـ ways to do both task one and task
+
+131
+00:09:09,780 --> 00:09:12,640
+two، سمتين يصل زي ما قلنا اثنين مع بعض، ففي الحالة
+
+132
+00:09:12,640 --> 00:09:18,060
+دي نقدر نقول الـ cardinality لـ A مضروب في الـ
+
+133
+00:09:18,060 --> 00:09:20,900
+cardinality لـ B، فهنا برضه نتكلم عن الـ rule تبع
+
+134
+00:09:20,900 --> 00:09:23,780
+الـ product، الـ product rule لأن بدي أعمل الـ two
+
+135
+00:09:23,780 --> 00:09:27,340
+tasks مع بعض، الـ two tasks مع بعض، في الحالة بتاعتنا
+
+136
+00:09:27,340 --> 00:09:33,440
+طيب نأخذ أمثلة أكيد هتوضح أكثر الكلام النظري اللي
+
+137
+00:09:33,440 --> 00:09:37,780
+قلناه، لو افترض أن الـ student can choose كمبيوتر
+
+138
+00:09:37,780 --> 00:09:41,040
+project في مساق من هالمساقات بتاعتكم، أنطلب منكم
+
+139
+00:09:41,040 --> 00:09:44,100
+تختاروا project، الأستاذ جاب لكم قائمة من الـ
+
+140
+00:09:44,100 --> 00:09:47,200
+projects لكن الـ projects هذه صنف لكم إياها لثلاثة
+
+141
+00:09:47,200 --> 00:09:51,360
+lists، جالكم والله في عندي ثلاثة lists بتحتوي على
+
+142
+00:09:51,360 --> 00:09:55,360
+ثلاثة وعشرين، خمسة عشر، وتسعة عشر possible projects
+
+143
+00:09:55,360 --> 00:09:58,500
+خلينا نقول الثلاثة والعشرون هؤلاء صنف لكم ثلاثة و
+
+144
+00:09:58,500 --> 00:10:02,640
+عشرون project اللي هم علاقة بالـ AI، وخمسة عشر
+
+145
+00:10:02,640 --> 00:10:06,080
+project اللي هم علاقة بالـ networks، وتسعة عشر
+
+146
+00:10:06,080 --> 00:10:08,960
+project اللي هم علاقة بالـ database مثلاً، okay، و
+
+147
+00:10:08,960 --> 00:10:11,860
+جالكم هي في عندكم ثلاث مجموعات، هؤلاء مجموعة الناس
+
+148
+00:10:11,860 --> 00:10:14,120
+اللي بيحبوا يشتغلوا في الـ AI، فليكن هي في عندكم
+
+149
+00:10:14,120 --> 00:10:17,800
+ثلاثة وعشرون مشروع project يختاروا منهم، وهي في
+
+150
+00:10:17,800 --> 00:10:20,720
+اللي بيحب يشتغل في الشبكات هي في خمسة عشر project
+
+151
+00:10:20,720 --> 00:10:24,380
+يختاروا اللي بدكم إياه منهم، واللي بده database
+
+152
+00:10:24,380 --> 00:10:28,880
+هي في عندكم تسعة عشر، How many possible projects
+
+153
+00:10:28,880 --> 00:10:32,900
+are there to choose from؟ يعني لكل طالب منكم الآن
+
+154
+00:10:32,900 --> 00:10:36,300
+هو بالنسبة له كم عدد الـ possibilities للاختيار
+
+155
+00:10:36,300 --> 00:10:41,200
+مجموعة لكل، مش هيك؟ يا بيختار من الثلاثة والعشرين
+
+156
+00:10:41,200 --> 00:10:46,780
+أو الخمسة عشر أو التسعة عشر، مش هيجي يختار من الثلاثة
+
+157
+00:10:46,780 --> 00:10:51,130
+لأنه مش مطلوب أنه يختار project واحد، فإذا في
+
+158
+00:10:51,130 --> 00:10:53,930
+الحالة دي بكل بساطة الـ total هيكون ثلاثة وعشرون
+
+159
+00:10:53,930 --> 00:10:58,210
+خمسة عشر، تسعة عشر، فسبعة وخمسون projects، فأنت عندك
+
+160
+00:10:58,210 --> 00:11:01,050
+سبعة وخمسون possibility to choose your project
+
+161
+00:11:01,050 --> 00:11:05,290
+عشان تختار الـ project تبعك، عندك إمكانية، إمكانيات
+
+162
+00:11:05,290 --> 00:11:10,850
+اختيار بتصل لسبعة وخمسين اختيار، طيب suppose
+
+163
+00:11:10,850 --> 00:11:13,950
+ثانية، suppose، statement labels، محتاجين نعمل
+
+164
+00:11:13,950 --> 00:11:18,270
+label للحالات تبع باستخدام الـ programming
+
+165
+00:11:18,270 --> 00:11:22,510
+language، must be single letter، اللي labels هذه
+
+166
+00:11:22,510 --> 00:11:25,590
+العنوان... العنوان هذا اللي بدك تحطه لمجموعة الـ
+
+167
+00:11:25,590 --> 00:11:30,870
+statements تبعك، إما أن يكون single letter، حرف فقط
+
+168
+00:11:30,870 --> 00:11:36,230
+أو single decimal digit بس... من 0 لـ 9... يا من 0
+
+169
+00:11:36,230 --> 00:11:40,030
+لـ 9 بالضبط 100%، فأنت بتتكلم عن decimal digit و
+
+170
+00:11:40,030 --> 00:11:43,890
+digit واحدة بالـ decimal، يعني نتكلم عن النظام العشري
+
+171
+00:11:43,890 --> 00:11:46,210
+اللي هو من صفر إلى تسعة، فعندك عشرة possibilities
+
+172
+00:11:46,210 --> 00:11:50,450
+له، كويس، فالمطلوب بكل بساطة How many labels are
+
+173
+00:
+
+223
+00:15:48,310 --> 00:15:51,270
+موجودين فيها طب مدام كاملين موجودين فيها معناته
+
+224
+00:15:51,270 --> 00:15:55,950
+عدد الـ possibilities هيصير فيها تبديل بينهم بمعنى
+
+225
+00:15:55,950 --> 00:16:00,550
+أنه هنا يا صفر يا واحد، طيب اللي جنبها لو كنت افترض
+
+226
+00:16:00,550 --> 00:16:04,270
+على جد اتنين برضه هتكون يا صفر يا واحد، صحيح؟ بس
+
+227
+00:16:04,270 --> 00:16:08,090
+لاحظ معنى ذلك أنه كـ string كامل على بعضه إما صفر
+
+228
+00:16:08,090 --> 00:16:15,010
+صفر أو صفر واحد أو واحد صفر أو واحد واحد، فإذن
+
+229
+00:16:15,010 --> 00:16:19,280
+أصبحت مضروب اثنين مضروب الاثنين لأن الاثنين بدهم
+
+230
+00:16:19,280 --> 00:16:23,360
+يتحققوا معاً، لازم يكون في الـ digit الأولى لها رقم
+
+231
+00:16:23,360 --> 00:16:26,920
+لها قيمة، والـ digit الثانية، والـ digit الثانية
+
+232
+00:16:26,920 --> 00:16:29,800
+برضه لها قيمة، والـ digit الثالثة لها قيمة، مش or
+
+233
+00:16:29,800 --> 00:16:34,080
+فإذا كلهم بدهم يتحققوا مع بعض، مدام مع بعض معناته to
+
+234
+00:16:34,080 --> 00:16:38,590
+gether، معناته and، عشان أكون فعلاً عندي string من سبعة
+
+235
+00:16:38,590 --> 00:16:42,290
+digits، وإلا معناته ببطل من سبعة digits، إذا or
+
+236
+00:16:42,290 --> 00:16:46,510
+معناته واحد فقط، أنا بتكلم عن واحد، يهد يهد يهد لأ
+
+237
+00:16:46,510 --> 00:16:49,690
+هو مش يهد يهد، السبعة ببطون دانية هم موجودين، فإذا
+
+238
+00:16:49,690 --> 00:16:56,970
+الأول والثاني والثالث لعند السابع، مدام and، مش
+
+239
+00:16:56,970 --> 00:16:58,890
+or، and خلاص بنضرب
+
+240
+00:17:02,400 --> 00:17:05,180
+ضربناهم في بعض، فمعناته اثنين to the power سبعة أو
+
+241
+00:17:05,180 --> 00:17:10,950
+اثنين متكررة سبع... سبع مرات، خلصنا منها، طيب بدنا
+
+242
+00:17:10,950 --> 00:17:16,170
+نعمل license أو license معين اللي هو password يعني
+
+243
+00:17:16,170 --> 00:17:20,310
+للمنتج تبعكم، license code له بيحتوي على sequence
+
+244
+00:17:20,310 --> 00:17:27,570
+of three letters، من ثلاث حروف، من ثلاث حروف، followed
+
+245
+00:17:27,570 --> 00:17:32,950
+by three digits، ومطبوعين بثلاث digits، فإذا ثلاث
+
+246
+00:17:32,950 --> 00:17:37,270
+حروف وراهم ثلاثة digits اللي هم من صفر لتسعة، كل
+
+247
+00:17:37,270 --> 00:17:43,320
+واحد منهم، فالآن how many different license plates
+
+248
+00:17:43,320 --> 00:17:47,780
+are available، خلاص هي تنحطها برضه بشكلها، الهيكل
+
+249
+00:17:47,780 --> 00:17:50,180
+كيف بده يكون شكلها؟ بده يكون بهذا الشكل
+
+250
+00:17:53,840 --> 00:17:58,580
+فعندي ثلاثة في البداية، هدول عبارة عن letters، كل
+
+251
+00:17:58,580 --> 00:18:01,700
+واحدة منهم letter، الـ letter، ايش الـ possibilities
+
+252
+00:18:01,700 --> 00:18:04,720
+عدد الـ possibilities تبعته؟ ستة وعشرون، فإذا هذا
+
+253
+00:18:04,720 --> 00:18:08,580
+ممكن يكون واحد من ستة وعشرين حرف إحنا عارفينهم
+
+254
+00:18:08,580 --> 00:18:15,400
+و الثاني ستة وعشرون، و الثالث، طيب الجزء الثاني اللي
+
+255
+00:18:15,400 --> 00:18:19,980
+هم الـ three، الـ four by three digits، لـ decimal
+
+256
+00:18:19,980 --> 00:18:23,440
+digits، فإذا إما عشرة، عشرة، عشرة اللي هي من صفر
+
+257
+00:18:23,440 --> 00:18:30,030
+لتسعة، طيب هل هذول المفروض، هل هم or ولا and؟ هنا
+
+258
+00:18:30,030 --> 00:18:33,130
+بنتكلم عن قدر، لأنه بتكلم عن sequence، ما فرجش كثير
+
+259
+00:18:33,130 --> 00:18:36,310
+عن الـ string اللي كنا نحكي عنه، فهو الـ sequence هذا
+
+260
+00:18:36,310 --> 00:18:40,430
+مكوّن من ثلاثة، مطبوعة بثلاثة، يعني لو أقل من ستة مش
+
+261
+00:18:40,430 --> 00:18:44,330
+هيرضى فيه ك... كـ sequence، وكـ license يتعامل معه
+
+262
+00:18:44,330 --> 00:18:48,850
+فإذا هدول اللي لازم يكونوا مع بعض، فإذا مضروبين في
+
+263
+00:18:48,850 --> 00:18:54,660
+بعض، هيكونوا كلهم مضروبين في بعض، طبعاً كويس، فإذا منطق
+
+264
+00:18:54,660 --> 00:18:57,840
+السؤال، أو فهمك لأيش الـ combination اللي أنت بدك
+
+265
+00:18:57,840 --> 00:19:00,300
+تعملها بالظبط هو اللي بيحددلك على طول إن أنت
+
+266
+00:19:00,300 --> 00:19:05,780
+بتتكلم عن الـ sum rule ولا product rule، كمان مثال
+
+267
+00:19:05,780 --> 00:19:10,500
+هنا برضه نفس الكلام، بدنا نعمل statement، label الـ
+
+268
+00:19:10,500 --> 00:19:12,740
+statement اللي عندك، بدك تحطلها label معين، تحطلها
+
+269
+00:19:12,740 --> 00:19:19,900
+ترقيم، الترقيم هذا either a single letter، فإذا جدش
+
+270
+00:19:19,900 --> 00:19:24,740
+بدنا single letter واحدة، أو letter followed by
+
+271
+00:19:24,740 --> 00:19:33,180
+digit، فإذا إما خلصنا من هنا digit
+
+272
+00:19:33,180 --> 00:19:40,780
+واحدة، عبارة عن بديها letter، حروف، فهذه ستة وعشرون، or
+
+273
+00:19:40,780 --> 00:19:48,400
+وبصراحة إنجلك، or، or برضه، single letter followed
+
+274
+00:19:48,400 --> 00:19:55,980
+by digit، فإذا ستة وعشرون وعشرة، مدام followed by
+
+275
+00:19:55,980 --> 00:20:00,780
+digit، معناته مطبوعة، لازم يجوا مع بعض، مدام مع بعض
+
+276
+00:20:00,780 --> 00:20:06,620
+معناته and، الأول and الثاني and، فصارت هذه ستة و
+
+277
+00:20:06,620 --> 00:20:13,880
+عشرين or، مئتين وستين، فإذا نجمعهم بيصير مئتين وثمانية
+
+278
+00:20:13,880 --> 00:20:21,260
+وستين، مئتين وثمانية وستين، صحيح؟ بدأ مقر، فإذا صارت two
+
+279
+00:20:21,260 --> 00:20:25,920
+tasks، متفصلين عن بعض، ووضح لك إياها هذه الـ tasks
+
+280
+00:20:25,920 --> 00:20:29,710
+الأولى، وهذه الـ task الثانية، Okay، هو بتهيألي حل
+
+281
+00:20:29,710 --> 00:20:35,590
+خلصنا من كل هذا، أعملك S على أساس إن هي الـ ست لـ
+
+282
+00:20:35,590 --> 00:20:37,850
+single letter لحالها اللي هي طلعت ستة وعشرون
+
+283
+00:20:37,850 --> 00:20:41,270
+جيبناها، والـ D افترض إن هي single letters followed
+
+284
+00:20:41,270 --> 00:20:46,610
+by digit أو decimal digit، وعملوا لهم اتحاد في
+
+285
+00:20:46,610 --> 00:20:50,390
+الآخر، فوصلنا للمئتين وثمانية وستين اللي طلعناها
+
+286
+00:20:50,390 --> 00:20:52,370
+تمام
+
+287
+00:20:53,930 --> 00:20:59,370
+كمان مثال واضح لهذا الموضوع هو الـ IP address، الـ IP
+
+288
+00:20:59,370 --> 00:21:03,190
+address بيكون له protocol، فبنسميه الـ internet
+
+289
+00:21:03,190 --> 00:21:06,790
+protocol، الـ version 4، وبعدين حالياً صار الـ version
+
+290
+00:21:06,790 --> 00:21:13,630
+6، فخلينا نرجع للـ version 4، الـ version 4 فيه منه
+
+291
+00:21:13,630 --> 00:21:22,760
+classes، فيه منه صنف، عدة أصناف A و B و C و D و E، مصنف
+
+292
+00:21:22,760 --> 00:21:26,200
+لخمس أصناف، بعرفش إذا كان مرة بتعليقه في مساقة أو
+
+293
+00:21:26,200 --> 00:21:30,120
+شيء مهم، إحنا الآن مطلوب مننا في السؤال، ايش مطلوب
+
+294
+00:21:30,120 --> 00:21:34,860
+مننا؟ جدش عدد الـ addresses لثلاث types منهم اللي
+
+295
+00:21:34,860 --> 00:21:39,920
+هو A و B و C، طيب A و B و C هدول بدنا نفهم منهم
+
+296
+00:21:39,920 --> 00:21:45,940
+شغلة إنه عادة هو عبارة عن sequence لـ digits، لمجموعة
+
+297
+00:21:45,940 --> 00:21:50,950
+digits لتعريف الشبكة، والـ host اللي عليها، أو الـ
+
+298
+00:21:50,950 --> 00:21:57,170
+user اللي عليها، تمام، بالإضافة لجزء من الـ sequence
+
+299
+00:21:57,170 --> 00:22:02,430
+هذا عبارة عن one or two or three digits، three bits
+
+300
+00:22:02,430 --> 00:22:06,350
+هدول لتعريف الـ class اللي إحنا بنشتغل عليه، فإذا
+
+301
+00:22:06,350 --> 00:22:10,350
+الـ sequence عندك، واللي هو بالأساس مكوّن بالنسبة
+
+302
+00:22:10,350 --> 00:22:15,770
+للـ version 4، مكوّن من 32 bit، الـ 32 bit هدول بتجسموا
+
+303
+00:22:15,770 --> 00:22:20,470
+حسب كل نوع class، الـ class الأول بناخد منه bit
+
+304
+00:22:20,470 --> 00:22:25,190
+لتعريف الـ class، تعريف الـ class، إذا بدأت بواحد معناها
+
+305
+00:22:25,190 --> 00:22:30,750
+ذلك إني بتكلم عن class A، إذا بدأت بصفر ثم واحد
+
+306
+00:22:30,750 --> 00:22:35,990
+فأنا بتكلم عن class B، إذا كانت صفر صفر واحد class
+
+307
+00:22:35,990 --> 00:22:40,910
+C، فإذا نلاحظ class A أنا استنفذت أول digit أو أول
+
+308
+00:22:40,910 --> 00:22:44,930
+bit لتعريف الـ class نفسه، فبيضل لي واحد وثلاثين
+
+309
+00:22:44,930 --> 00:22:46,710
+واحد وثلاثين، أو واحد وثلاثين بالظبط، واحد و
+
+310
+00:22:46,710 --> 00:22:49,750
+ثلاثين، الواحد والثلاثين هدول بيتم تجسيم، و ليش؟ بيتم
+
+311
+00:22:49,750 --> 00:22:55,080
+تجسيم، ودير بالك لـ users الذين يسمونهم الـ hosts، الـ
+
+312
+00:22:55,080 --> 00:23:00,940
+users هدول أعدادهم لكل small network، خلّيني أو
+
+313
+00:23:00,940 --> 00:23:04,700
+شبكة، بحيث أنه في النهاية الشبكة هذه لها عنوان كمان
+
+314
+00:23:04,700 --> 00:23:09,180
+فأنت الشبكة الأولى، وأنت الـ user الأول فيها، طب هذا
+
+315
+00:23:09,180 --> 00:23:13,400
+ممكن يكون في شبكة ثانية، وليها user أول برضه، يعني
+
+316
+00:23:13,400 --> 00:23:17,700
+ممكن اثنين يكونوا بالنسبة للمجموعة الـ bits اللي
+
+317
+00:23:17,700 --> 00:23:22,100
+خاصة بالـ host نفسه، لكن اختلفوا بمين؟ بعنوان الشبكة
+
+318
+00:23:22,100 --> 00:23:25,520
+فإذا أنا في عندي تجسيم لعنوانين، العنوانين هدول
+
+319
+00:23:25,520 --> 00:23:26,280
+هنسميهم
+
+320
+00:23:28,610 --> 00:23:33,350
+ال... الـ net ID خاصة بالشبكة نفسها، الـ net ID، وفيه
+
+321
+00:23:33,350 --> 00:23:37,550
+عندك الـ host ID، عندك host ID، فكل net لها
+
+322
+00:23:37,550 --> 00:23:41,310
+مجموعة الـ hosts تاعتها، لها مجموعة hosts تاعتها
+
+323
+00:23:41,310 --> 00:23:49,430
+تمام، الآن بالنسبة لـ B، هتكون أول two bits مستنفذين
+
+324
+00:23:49,430 --> 00:23:53,210
+لتعريف الـ class نفسه، فبيضل عندك ثلاثين، فاللي
+
+325
+00:23:53,210 --> 00:23:58,690
+بيبقوا من الثلاثين bit هدول بدنا نجسمهم بين الـ net
+
+326
+00:23:58,690 --> 00:24:06,010
+ID والـ host ID، الثالثة اللي هي C، بيكون عندك three
+
+327
+00:24:06,010 --> 00:24:10,050
+bits لتعريف الـ class نفسه، فبظل عندك تسعة وعشرون
+
+328
+00:24:10,050 --> 00:24:14,350
+بدك تجسمهم ما بين الـ host والـ network، كويس
+
+329
+00:24:14,350 --> 00:24:18,830
+فبتختلف الآن كيف تجسمت، هذا standard بالمناسبة
+
+330
+00:24:18,830 --> 00:24:21,590
+standard يعني إحنا okay عارفين إن في ثلاث حالات و
+
+331
+00:24:21,590 --> 00:24:26,950
+بتختلف تجسيماتهم، هذا standard، خليني نشوف جدش
+
+332
+00:24:26,950 --> 00:24:31,130
+تجسيم كل واحدة منهم، بالنسبة لـ class A، class A
+
+333
+00:24:32,480 --> 00:24:40,160
+بنحسمهم، إن في عندك سبعة bits لتعريف
+
+334
+00:24:40,160 --> 00:24:44,700
+الـ network، جدش بظل من الواحد والثلاثين؟ لأن إحنا
+
+335
+00:24:44,700 --> 00:24:48,080
+قلنا فيه واحد ل... لتعريف الـ class نفسه، وهي سبعة
+
+336
+00:24:48,080 --> 00:24:52,460
+راح، ثمانية، هي ثمانية، جدش ظل للـ host؟ أربعة وعشرون
+
+337
+00:24:52,460 --> 00:24:57,280
+ففي عندك أربعة وعشرون للـ host، معنها ذلك إن كل
+
+338
+00:24:57,280 --> 00:25:02,200
+شبكة في الـ class هذا بتكون بتحمل عدد كبير من الـ
+
+339
+00:25:02,200 --> 00:25:06,840
+users أو الـ hosts من الـ users، طيب أهم شغلة هنا
+
+340
+00:25:06,840 --> 00:25:11,040
+موجودة إنك بالنسبة للـ net ID غير مسموح أن يكونوا
+
+341
+00:25:11,040 --> 00:25:16,470
+السبعة هدول كاملين ones، هذه مش مسموحة فيه، مش مسموحة
+
+342
+00:25:16,470 --> 00:25:20,410
+في الـ class هذا، تمام، أو حتى في الـ classes كلها، طيب
+
+343
+00:25:20,410 --> 00:25:29,250
+الـ class B بيقدر يستوعب ايش؟ 14 bits للـ net، بمعنى إن هنا
+
+344
+00:25:29,250 --> 00:25:33,990
+بيكون عدد الـ nets عليه أكثر، وهذا في المقابل هيخلي
+
+345
+00:25:33,990 --> 00:25:40,380
+عدد الـ users داخل الـ net، كل net لحالها، أقل، هيكون عدد
+
+346
+00:25:40,380 --> 00:25:45,720
+الـ net أقل، تمام، فبتصير عندك 16 بدل ما كانت 24، فأنت
+
+347
+00:25:45,720 --> 00:25:48,620
+شوف جد ايش عدد الـ users اللي ممكن تستخدمهم هنا لكل
+
+348
+00:25:48,620 --> 00:25:53,740
+شبكة، اثنين to the power 24، هنا لأ، هتكون to the
+
+349
+00:25:53,740 --> 00:25:57,100
+power 16، to the power 16، إذا عدد والله الجامعة
+
+350
+00:25:57,100 --> 00:26:00,840
+عددهم مش عدد كبير، لأ، بنجل أكتر من هيك كمان، كويس
+
+351
+00:26:01,590 --> 00:26:05,630
+الآن الـ class، وبالمناسبة هذه أصلاً شغل تجاري، يعني
+
+352
+00:26:05,630 --> 00:26:08,170
+إذا أنا عارف إن الـ area هذه مش هيجيها عدد كبير، ليش
+
+353
+00:26:08,170 --> 00:26:14,030
+أنا أضيع الـ bits في الـ host، طب ما أخليه للشبكة و
+
+354
+00:26:14,030 --> 00:26:17,210
+بضمن إن الشبكات عددهم كبير، وبنجل الشبكات، بخليهم
+
+355
+00:26:18,220 --> 00:26:24,520
+يعني بعيد عن بعض، فب... بغطي area أكبر، بنغطي في
+
+356
+00:26:24,520 --> 00:26:27,680
+الحالة هذه area أكبر، مدام ال... الـ density مش
+
+357
+00:26:27,680 --> 00:26:30,820
+عالية، مدام الـ density مش عالية، بس هذه بتاعت دراسة
+
+358
+00:26:30,820 --> 00:26:37,680
+طبيعية، طيب C... C لاحظ، واحد وعشرون للـ net ID
+
+359
+00:26:37,680 --> 00:26:41,840
+21، وثمانية فقط لمين؟ للـ host، ثمانية للـ host، إذا
+
+360
+00:26:41,840 --> 00:26:46,860
+بنتكلم عن area مافيها capacity عالية، فـ okay بنخلي
+
+361
+00:26:46,860 --> 00:26:51,120
+عدد networks كتير، وكل network تتغذي عدد أقل من الـ
+
+362
+00:26:51,120 --> 00:26:55,100
+host أو من الـ users، تمام، وزي ما اتفقنا الـ two
+
+363
+00:26:55,100 --> 00:27:00,120
+classes بتعرفوا عن بعض بالـ header تبع الـ IP
+
+364
+00:27:00,120 --> 00:27:03,780
+address هذا، من خلال النقل، صفر إذا كان صفر لحالها
+
+365
+00:27:03,780 --> 00:27:09,340
+فأنا بتكلم عن A، إذا واحد، وبعدين الصفر إجا رقم
+
+366
+00:27:09,340 --> 00:27:12,380
+اثنين، فمعنى ذلك هذا B، إذا الصفر إجا رقم ثلاثة
+
+367
+00:27:12,380 --> 00:27:17,620
+فمعناته أنا بتكلم عن C، عن C، كويس، الـ host هنا بده
+
+368
+00:27:17,620 --> 00:27:20,840
+يعطينا شوية characteristics واضحة جداً، بتكون
+
+369
+00:27:20,840 --> 00:27:26,100
+بمستخدمها أنه لا يمكن استخدام الـ host zeros or
+
+370
+00:27:26,100 --> 00:27:30,480
+ones، بمعنى أنه ما فيش user هياخد الـ address zeros
+
+371
+00:27:30,480 --> 00:27:36,600
+في أي شبكة، ولا ones، ولا الـ ones في أي شبكة كانت
+
+372
+00:27:36,600 --> 00:27:40,640
+تمام، فإذا هي هذا أول شرط تتاخدوا بالكم منه، وفي
+
+373
+00:27:40,640 --> 00:27:46,140
+عندي شرط ثاني، كان هنا لمين؟ لل... لل... للـ net ID إن
+
+374
+00:27:46,140 --> 00:27:49,260
+هي بتسمحش بالـ ones، بتسمحش بالـ ones، الآن ايش
+
+375
+00:27:49,260 --> 00:27:54,280
+المطلوب؟ مطلوب جدش عدد الـ addresses الممكنين للـ
+
+376
+00:27:54,280 --> 00:27:56,500
+three classes هدول في الـ system، طبعاً هنا
+
+377
+00:27:56,500 --> 00:28:00,600
+ما تكلمناش إحنا عن مين؟ عن الـ D والـ E، الـ D والـ E
+
+378
+00:28:00,600 --> 00:28:02,880
+بيستخدموهم في الـ broadcasting، في الـ broadcasting
+
+379
+00:28:02,880 --> 00:28:06,820
+اللي هي بياخدوا المدى كله كامل لـ user واحد أو
+
+380
+00:28:06,820 --> 00:28:10,680
+لخدمة واحدة، فبتكون... اه بتكون عددهم كبير في
+
+381
+00:28:10,680 --> 00:28:16,550
+الحالة هذه، تمام، الآن بدنا نشوف جدش عدد الـ
+
+382
+00:28:16,550 --> 00:28:21,490
+possibilities لعدد users، يعني addresses، جدش أنا
+
+383
+00:28:21,490 --> 00:28:25,130
+ممكن أولد addresses بالنظام هذا، بهذا الاستخدام، بكل
+
+384
+00:28:25,130 --> 00:28:28,410
+بساطة، أتوقع ايش بتكون تعمله؟ طبعاً ما حدش هيشتغل
+
+385
+00:28:28,410 --> 00:28:31,330
+بالظبط واحد واحد، لأنه ما حدش هيشتغل في two classes
+
+386
+00:28:31,330 --> 00:28:36,880
+مع بعض، كل واحد له class لحاله، يا A يا B يا C، مش
+
+387
+00:28:36,880 --> 00:28:40,520
+هيك؟ هذه أول شغلة، ممتاز، هذه هلّوجت في التفاصيل،
+
+388
+00:28:40,520 --> 00:28:44,980
+إحنا هلّوجت و حددنا إنه يا A يا B يا C، صحيح؟ A B C،
+
+389
+00:28:44,980 --> 00:28:47,780
+أنا هكون ضمن واحد منهم، مستحيل أكون ضمن أكثر من
+
+390
+00:28:
+
+445
+00:32:56,680 --> 00:32:59,740
+يجوز أن أجمعهم وأسكت خلاص؟ طب أنا في الحالة هذه
+
+446
+00:32:59,740 --> 00:33:04,720
+بالظبط معناه ذلك أن أنا فعليًا في مجموعة ways أو
+
+447
+00:33:04,720 --> 00:33:07,240
+possibilities أجمعهم مرتين: مرة من الـ task الأول و
+
+448
+00:33:07,240 --> 00:33:11,340
+مرة بالنسبة للثانية. أحسنتُوا، فإذا أنا مضطرٌ لأعمل
+
+449
+00:33:14,060 --> 00:33:17,160
+طرحًا لتقاطعهم معنا.. كويس، فهذا هو نفسه الذي
+
+450
+00:33:17,160 --> 00:33:20,260
+سنعمله، وهذا يبين معنا إذا كان عندي.. فعلاً في
+
+451
+00:33:20,260 --> 00:33:26,240
+عندي K ways أقل من..ممكن تكون أقل من أو تساوي..
+
+452
+00:33:26,240 --> 00:33:28,980
+يعني ممكن كل الـ ways التي تنفع لـ task 1 كلها
+
+453
+00:33:28,980 --> 00:33:33,610
+تنفع لـ task 2.. كويس؟ فـ K-Header التي هي ways of
+
+454
+00:33:33,610 --> 00:33:38,410
+doing task one also simultaneously accomplish task
+
+455
+00:33:38,410 --> 00:33:41,510
+two. فإذن هي، رغم أن هي تنفع لـ task one،  بَرْضَهُ
+
+456
+00:33:41,510 --> 00:33:45,410
+بالتزامن مع ذلك، هي بَرْضَهُ تنفع كـ possibilities لـ أو
+
+457
+00:33:45,410 --> 00:33:51,550
+إمكانية لعمل الـ task two أو لأداء الـ task two. تمام.
+
+458
+00:33:51,550 --> 00:33:54,970
+ففي الحالة دي، إيش نسوي؟ نقول بكل بساطة: do either
+
+459
+00:33:54,970 --> 00:33:59,890
+task one or task two، عبارة عن M plus N ناقص K التي
+
+460
+00:33:59,890 --> 00:34:03,290
+قلنا عليها، التي هي التقاطع والاتنين مع بعض، أو الـ
+
+461
+00:34:03,290 --> 00:34:07,330
+ways التي تنفع لكلا الـ tasks. لكلا الـ tasks، task
+
+462
+00:34:07,330 --> 00:34:10,390
+one and task two. وهذه طبعاً لها مرجعية نحن
+
+463
+00:34:10,390 --> 00:34:15,270
+أخذناها لما تكلمنا في الـ sets، لو متذكرين، قلنا الـ
+
+464
+00:34:15,270 --> 00:34:19,430
+cardinality للاتحاد كان يساوي الـ cardinality للأولى
+
+465
+00:34:19,430 --> 00:34:23,150
+plus cardinality الثانية ناقص التقاطع. فالتقاطع هذا
+
+466
+00:34:23,150 --> 00:34:26,810
+معناه أنه ينفع للـ task الأولى، وينفع
+
+467
+00:34:26,810 --> 00:34:28,910
+simultaneously للـ task الثانية بَرْضَهُ في نفس الوقت.
+
+468
+00:34:28,910 --> 00:34:34,550
+فهذا يعتبر تقاطعًا بالنسبة للـ sets. فإذا هنا
+
+469
+00:34:34,550 --> 00:34:38,210
+إذا كانت disjoint، زي الطرق التي كنا نحكيها قبل هيك،
+
+470
+00:34:38,210 --> 00:34:41,710
+لا، ما فيش مشكلة، بيبقى مجموعهم، بس مش هتضطر تعمل طرح
+
+471
+00:34:41,710 --> 00:34:47,540
+لِيش؟ لأن طرحهم هيساوي  الـinteger،  الذي يعني التقاطع، و
+
+472
+00:34:47,540 --> 00:34:54,680
+تباعُهُم، التي هي K، هتكون صفر، فالـset هنا ما فيش، أو صفر.
+
+473
+00:34:54,680 --> 00:35:00,140
+صفر، لا، خمسة، التي هي ما فيش element، ما فيش element
+
+474
+00:35:00,140 --> 00:35:04,280
+zero elements. تمام. هنشوف أمثلة على هذا الموضوع
+
+475
+00:35:04,280 --> 00:35:08,660
+بهذا الشكل. لو بدنا نقول: how many bits strings of
+
+476
+00:35:08,660 --> 00:35:13,540
+length four. تمام. افهمنا. length four. ممتاز. هاي
+
+477
+00:35:13,540 --> 00:35:14,120
+length four.
+
+478
+00:35:16,820 --> 00:35:24,360
+طولها أربعة، ممتاز، بعدين: either start with one or
+
+479
+00:35:24,360 --> 00:35:29,560
+end
+
+480
+00:35:29,560 --> 00:35:30,880
+with double zero.
+
+481
+00:35:33,770 --> 00:35:37,270
+خلص، نمسك واحدة واحدة، مش هنمسكهم واحدة واحدة.
+
+482
+00:35:37,270 --> 00:35:40,070
+ممتاز. نمسكهم واحدة واحدة هالوقت. خليني نبدأ في
+
+483
+00:35:40,070 --> 00:35:44,510
+الأولى، الأولى التي هو جدّش عندي عدد bit string، أو
+
+484
+00:35:44,510 --> 00:35:49,150
+جدّش عدد الـ strings التي ممكن نولّدها من أربعة digit
+
+485
+00:35:49,150 --> 00:35:55,590
+أو أربعة bits. الأولى منهم one. ثمانية، التي هم
+
+486
+00:35:55,590 --> 00:36:00,240
+الخيارات فقط للثلاثة التي ضايلين. دولة ممكن تكون يا
+
+487
+00:36:00,240 --> 00:36:03,320
+صفر، يا واحد، يا صفر، يا واحد، يا صفر، يا واحد. فثنين
+
+488
+00:36:03,320 --> 00:36:10,120
+فثنين، فثنين، فثنين، فثنين، فثنين. خلّصناها. طيب، الـ task
+
+489
+00:36:10,120 --> 00:36:14,260
+الثاني. هذه task one، task
+
+490
+00:36:14,260 --> 00:36:19,900
+two. هدول محكم عليهم خلاص zeros. انتهى هنا. إما zero
+
+491
+00:36:19,900 --> 00:36:24,000
+one zero one. فهذه عددهم أربعة. في الحالة هذه. فثنين
+
+492
+00:36:24,000 --> 00:36:32,030
+فثنين. هذه task two. فصار عندي ثمانية زائد أربعة. طيب،
+
+493
+00:36:32,030 --> 00:36:36,750
+شوية، اصبروا علينا. في تقاطع بينهم. ليش في تقاطع
+
+494
+00:36:36,750 --> 00:36:41,550
+بينهم؟ لأنه هتلاقي مجموعة bit string هي محقّقة
+
+495
+00:36:41,550 --> 00:36:45,850
+الشرطين معاها. محقّقة الشرطين معاها. فهي فعليًا أن عدّت
+
+496
+00:36:45,850 --> 00:36:51,070
+هنا، وأن عدّت هنا. جدّش عددهم؟ نحن لازم نفحصهم، حتى لو
+
+497
+00:36:51,070 --> 00:36:53,730
+طلعوا في النهاية فيه، بس أنا في النهاية لازم أفحصهم.
+
+498
+00:36:53,730 --> 00:36:56,830
+لأنه ممكن يكونوا مُشْتَرَكِين الاتنين مع بعض. طيب، عشان
+
+499
+00:36:56,830 --> 00:36:59,050
+تكون مُشْتَرَكِين الاتنين مع بعض، معناته الأولى هذه محكومة
+
+500
+00:36:59,050 --> 00:37:04,030
+عليها أن تكون one، خلاص، والاثنين
+
+501
+00:37:04,030 --> 00:37:08,950
+الثاني محكوم عليهم خلاص يكونوا zeros. فبقى عندي فقط
+
+502
+00:37:08,950 --> 00:37:13,350
+الخانة الثانية التي ممكن يكون لها possibilities أو
+
+503
+00:37:13,350 --> 00:37:17,590
+ways to do this. فإذا يا صفر يا واحد، في احتمالن.
+
+504
+00:37:17,590 --> 00:37:27,870
+فإذا task one and task two، فالحالة هذه بتساوي
+
+505
+00:37:27,870 --> 00:37:35,070
+اثنين. فإذا ناقص اثنين، ناقص اثنين. جيد. فإذا هتلاقي
+
+506
+00:37:35,070 --> 00:37:38,350
+مين اللي مجموعين في الحالتين؟ التي هي الـ 1 0 0 0، والـ
+
+507
+00:37:38,350 --> 00:37:45,570
+1 1 0 0. هدول الـ two strings. هدول هتلاقيهم موجودين
+
+508
+00:37:45,570 --> 00:37:48,870
+في الحالة الأولى، وفي الثانية، في كلاهما. طبعاً هم
+
+509
+00:37:48,870 --> 00:37:53,630
+هنا، يعني حلّهم كاملين هي الثمانية للأولى، وهي
+
+510
+00:37:53,630 --> 00:37:56,510
+الأربعة للثانية. عشان يكتشف أن الرقم أن هدول
+
+511
+00:37:56,510 --> 00:38:03,410
+متكررين. هي واحد، هي واحد، وهي الثاني مع الثاني. فإذا
+
+512
+00:38:03,410 --> 00:38:07,350
+إذا بدنا نجمعهم، ثمانية زائد أربعة، هتكون الـ 1000
+
+513
+00:38:07,350 --> 00:38:13,490
+انجمع مرتين، والـ 1100 بَرْضَهُ انجمع مرتين. فإذا مضطرين
+
+514
+00:38:13,490 --> 00:38:20,950
+نطرح المرتين تبع التكرار تبعته. الآن نحتاج.. بعض
+
+515
+00:38:20,950 --> 00:38:23,490
+الـ.. نحط بعض الـ rules لـ password على أساس أنه
+
+516
+00:38:23,490 --> 00:38:26,250
+الآن بدنا نعمل توليد لمجموعة passwords. الـ
+
+517
+00:38:26,250 --> 00:38:30,310
+passwords هذه.. هذه لها شروط. أول شرط لها أن الـ
+
+518
+00:38:30,310 --> 00:38:34,610
+password لازم تكون عبارة عن two characters long.
+
+519
+00:38:34,610 --> 00:38:39,710
+فإذا خلّصنا من هذا، ونحط الـ two characters، ونشوف
+
+520
+00:38:39,710 --> 00:38:43,710
+كل الشروط الممكنة له، عشان نقدر نتعامل معه.
+
+521
+00:38:49,810 --> 00:38:53,070
+password من two characters. طبعاً كلمة character أول
+
+522
+00:38:53,070 --> 00:38:56,370
+مرة يتكلم عنها character، أول مرة بيحكي عنها، ليش
+
+523
+00:38:56,370 --> 00:38:59,310
+أول مرة بيحكي عنها؟ لأن character لها مفهوم يا إما
+
+524
+00:38:59,310 --> 00:39:02,410
+letters أو digit، الذي هو decimal digit، أو
+
+525
+00:39:02,410 --> 00:39:05,750
+punctuations، التي هي علامات الترقيم. الـ
+
+526
+00:39:05,750 --> 00:39:10,370
+punctuations هذه، التي هي علامات الترقيم، الـ space،
+
+527
+00:39:10,370 --> 00:39:13,810
+نفسها، الـ $، علامة المائية، العلامة المئوية،
+
+528
+00:39:13,810 --> 00:39:19,430
+كل العلامات الترقيم التي موجودة عندك، دائمًا مع الـ
+
+529
+00:39:19,430 --> 00:39:21,970
+shift، والأرقام التي فوق الـ shift، مع الأرقام التي
+
+530
+00:39:21,970 --> 00:39:27,130
+فوق، كلهم هدول عبارة عن punctuation characters. طيب،
+
+531
+00:39:27,130 --> 00:39:32,310
+فإذا أول شغلة، two، كل password لازم يكون letter,
+
+532
+00:39:32,710 --> 00:39:37,930
+digit or one of ten punctuation. فإذا حكينا ten
+
+533
+00:39:37,930 --> 00:39:42,310
+punctuation، التي هم  عشرة من الأرقام مع الـ shift، على
+
+534
+00:39:42,310 --> 00:39:44,910
+الكمبيوتر، shift مع مجموعة الأرقام التي فوق، التي من
+
+535
+00:39:44,910 --> 00:39:49,570
+واحد للصفر، فبيعطيك مجموعة الـ punctuation هدول. كويس.
+
+536
+00:39:49,570 --> 00:39:52,950
+فعرفنا هنا إيش الـ possibilities التي نحن ممكن
+
+537
+00:39:52,950 --> 00:39:55,970
+نختار منها الـ password تبعنا. إيش password must
+
+538
+00:39:55,970 --> 00:40:03,070
+contain at least digit or punctuation. كل واحد لازم
+
+539
+00:40:03,070 --> 00:40:08,110
+يكون فيه مجموعة يا digit يا punctuation، ضروري.
+
+540
+00:40:08,940 --> 00:40:12,040
+كويس. الثاني، الـ digit الثانية، مش مشكلة، تاخد التي
+
+541
+00:40:12,040 --> 00:40:15,860
+تاخذه، مش إشكال، تاخد التي تَهيّأ. فالآن صار عندي
+
+542
+00:40:15,860 --> 00:40:22,860
+الحقيقة two tasks. task للحالة الأولى، وبعدين
+
+543
+00:40:22,860 --> 00:40:25,700
+بناء عليها نشوف الثانية. بمعنى أن الحالة الأولى هذه
+
+544
+00:40:25,700 --> 00:40:30,000
+بدك تفترض، هل هي أخذت الـ possibilities كلها؟ معناه
+
+545
+00:40:30,000 --> 00:40:34,420
+ذلك أن الثانية لازم تكون الاثنين بس، التي هي إما
+
+546
+00:40:35,570 --> 00:40:39,730
+digit or punctuation، عشان تضمن أن في punctuation.
+
+547
+00:40:39,730 --> 00:40:46,410
+وبعدين بدك تطرح منها، أو تجمعها على العكس تبعها، أن
+
+548
+00:40:46,410 --> 00:40:50,650
+هنا punctuation، وهنا كل الـ letters ممكن تكون التي
+
+549
+00:40:50,650 --> 00:40:53,930
+مسموح فيها letters. إضافي لذلك، بدك تطرح منهم
+
+550
+00:40:53,930 --> 00:40:56,970
+التكرارات التي ممكن تحدث. إيش التكرار الذي ممكن
+
+551
+00:40:56,970 --> 00:41:04,480
+يحدث؟ أن الاثنين يطلعوا digit or punctuation. الاثنين
+
+552
+00:41:04,480 --> 00:41:08,200
+يطلعوا زي بعض، معناته أنا جمعتهم على فرضية أنه
+
+553
+00:41:08,200 --> 00:41:11,780
+الخانة الأولى هي التي هتحكم. ليه؟ digit or
+
+554
+00:41:11,780 --> 00:41:16,500
+punctuation، أو الخانة الثانية، فأنا هأجمع على
+
+555
+00:41:16,500 --> 00:41:18,240
+الخانة الأولى لحالها، والخانة الثانية لحالها، وبعدين
+
+556
+00:41:18,240 --> 00:41:23,640
+أطرح عدد أن الخانتين ظهر فيهم الـ digit or
+
+557
+00:41:23,640 --> 00:41:27,960
+punctuation. هنشوف كيف. فزي ما قلنا، هيها، التي هي جا
+
+558
+00:41:27,960 --> 00:41:31,320
+الـ password. لأ، دي لأ. has digit or punctuation
+
+559
+00:41:31,320 --> 00:41:36,840
+character in position one or two. فإذا الشرط الذي
+
+560
+00:41:36,840 --> 00:41:41,620
+حاكمني شوية أنه لازم يكون فيه رقم أو علامة ترقيم،
+
+561
+00:41:41,620 --> 00:41:44,760
+بتعامل معها، التي هي punctuation، بتعامل معها أنه
+
+562
+00:41:44,760 --> 00:41:49,360
+ممكن تكون ظهرت في الحالة الأولى، أو في التي هي الـ
+
+563
+00:41:49,360 --> 00:41:53,980
+position الأول، أو الـ position الثاني. فعملناهم كإنها
+
+564
+00:41:53,980 --> 00:41:56,920
+two problems. بس بدنا نأخذ بالنا إننا في الحالة هذه
+
+565
+00:41:56,920 --> 00:42:00,060
+لازم أطرح منهم إنه ممكن يظهر في الاثنين مع بعض.
+
+566
+00:42:00,060 --> 00:42:03,220
+بالضبط. فهي التي صار تمامًا. ففرضنا أن الـ position
+
+567
+00:42:03,220 --> 00:42:09,700
+الأول هو الذي يحتوي على الـ digit or punctuation.
+
+568
+00:42:09,700 --> 00:42:15,180
+تمام. مضروبة في مين؟ في الطرف الثاني الذي ممكن يأخذ
+
+569
+00:42:15,800 --> 00:42:20,020
+الثلاث حالات. طيب، خلّصنا منها. طيب، بالنسبة للـ position
+
+570
+00:42:20,020 --> 00:42:23,520
+الثاني، هي الـ position الأول هو ضربهم على طول. هي 21
+
+571
+00:42:23,520 --> 00:42:29,060
+في 46 مباشرة. بالنسبة للـ position الأول، هيعمل نفس
+
+572
+00:42:29,060 --> 00:42:32,280
+الكلام للـ position الثاني. نفس الشيء بَرْضَهُ للـ
+
+573
+00:42:32,280 --> 00:42:36,120
+position الثاني، بحيث أنه يجمعهم مع بعض. فصارت عندك
+
+574
+00:42:36,120 --> 00:42:39,180
+الرقم هذا. جدّش لما نضربه؟ حوالي تسعمئة وشيء، تسعمئة
+
+575
+00:42:39,180 --> 00:42:46,000
+وعشرين. التي هو الـ punctuation أو الـ digit ظهرت في
+
+576
+00:42:46,000 --> 00:42:49,940
+الخانة، أو في الـ position الأول، زائد أنها ظهرت في
+
+577
+00:42:49,940 --> 00:42:53,520
+الـ position الثاني. طيب، استنى، في ناقص أنه ممكن تكون
+
+578
+00:42:53,520 --> 00:42:56,620
+ظهرت في الحالتين، في الـ two positions. فقدّيش
+
+579
+00:42:56,620 --> 00:42:59,720
+احتماليتها هذه؟ احتماليتها، أو possibilities تَعْتُها
+
+580
+00:42:59,720 --> 00:43:01,900
+أن يكون عندي عشرين.
+
+581
+00:43:04,670 --> 00:43:08,810
+وهنا بَرْضَهُ عشرين، فبتطلع ناقص أربع مئة. فبيطلع totally
+
+582
+00:43:08,810 --> 00:43:15,250
+كله على بعض حوالي ألف وأربع مئة وأربعين، كعدد
+
+583
+00:43:15,250 --> 00:43:18,930
+possibilities للـ password في الحالة دي، في الـ
+
+584
+00:43:18,930 --> 00:43:24,530
+password الحالي. طيب، كمان أمثلة. لو عندك مطلوب find
+
+585
+00:43:24,530 --> 00:43:29,520
+the number of three letter initials where none of
+
+586
+00:43:29,520 --> 00:43:33,260
+the letters is repeated. طيب، هذه أبسط منهم، يعني
+
+587
+00:43:33,260 --> 00:43:39,680
+بسيطة جدّاً. ثلاثة لمجموعة حروف، بشرط أنه إذا اخترنا
+
+588
+00:43:39,680 --> 00:43:43,740
+حرف في الخانة الأولى، ما يتكرّر في الثانية، والأول
+
+589
+00:43:43,740 --> 00:43:47,720
+والثاني ما يتكرّر في الثالثة. خلاص. فإذا هنا عندي ستة
+
+590
+00:43:47,720 --> 00:43:51,080
+وعشرين. هنا بتصير الـ possibilities فقط خمسة وعشرين.
+
+591
+00:44:02,770 --> 00:44:09,480
+محتاجة كلام كتير؟ سؤال direct، هذا سريع. قدّيش عدد الـ
+
+592
+00:44:09,480 --> 00:44:14,740
+strings التي بتقدر تاخذها من string طوله أربعة
+
+593
+00:44:14,740 --> 00:44:18,560
+bits؟ اثنين أُسّ أربعة، وانتهت الجثة. طيب، السؤال
+
+594
+00:44:18,560 --> 00:44:22,860
+الذي وراءه: count the number of bit strings length
+
+595
+00:44:22,860 --> 00:44:28,540
+four or less. or less. معناته بدك تجمع. صارت task
+
+596
+00:44:28,540 --> 00:44:33,020
+مختلفة عن بعض. length four، length three، length two،
+
+597
+00:44:33,020 --> 00:44:39,110
+length one. check. بدك تجمعهم مع بعض. فنجمَعُهُم بحيث
+
+598
+00:44:39,110 --> 00:44:43,650
+أنه هيها، إذا كانت الـ length تبعنا واحد، زائد إذا
+
+599
+00:44:43,650 --> 00:44:46,690
+كان الـ length اثنين، زائد إذا كانت ثلاثة، زائد إذا
+
+600
+00:44:46,690 --> 00:44:54,270
+كانت أربعة. بس خلص. تمام. كمان مثال، آه، هذا مثال كويس.
+
+601
+00:44:54,270 --> 00:44:59,510
+هذا مثال منيح. كان ذا 6S of three digit numbers
+
+602
+00:44:59,510 --> 00:45:04,490
+مكوّن من three digit numbers. خليه هو نفس المثال
+
+603
+00:45:04,490 --> 00:45:06,150
+تبعنا. هاي three digit number.
+
+604
+00:45:11,090 --> 00:45:17,470
+إيش مطلوب؟ في three digit number which begin or end
+
+605
+00:45:17,470 --> 00:45:26,410
+with an even digit. بيبدأ أو بينتهي بـ even. بس هي كل
+
+606
+00:45:26,410 --> 00:45:30,670
+المطلوب. فبدنا نعرف قدّيش عدد الأرقام التي مكوّنة من
+
+607
+00:45:30,670 --> 00:45:38,680
+ثلاث خانات، وبتبدأ أو بتنتهي بـ digit أو integer even.
+
+608
+00:45:38,680 --> 00:45:42,620
+الـ integer ده عبارة عن even. خلّيني شوي شوي، نأخذهم
+
+609
+00:45:42,620 --> 00:45:48,560
+نبدأ بالأول والثاني والثالث. نبدأ بالـ begin، لأنه
+
+610
+00:45:48,560 --> 00:45:54,300
+begin هيها begin، وبعدها في or، ثم end with an even.
+
+611
+00:45:54,300 --> 00:45:58,980
+صحيح. فنبدأها or، وبعدها نجمع الاثنين. صحيح؟ نجمع الاثنين.
+
+612
+00:45:58,980 --> 00:46:02,340
+بس بدنا نأخذ بالنا، بدنا نطرح، بعدين نطرح، بس
+
+613
+00:46:02
+
+667
+00:50:49,000 --> 00:50:53,600
+أكبر من B زائد 1، بمعنى أنها من الـ domain و الـ
+
+668
+00:50:53,600 --> 00:50:58,300
+domain هذا هو الـ objects لـ الـ places، و الـ places
+
+669
+00:50:58,300 --> 00:51:01,880
+أقل من الـ a، الـ code domain أقل من الـ a، فمعنى ذلك
+
+670
+00:51:01,880 --> 00:51:04,700
+تقدر تقول أن الـ cardinality لـ a أكبر من أو يساوي
+
+671
+00:51:04,700 --> 00:51:09,960
+الـ cardinality لـ b زائد واحد، فهنا إذا some
+
+672
+00:51:09,960 --> 00:51:16,700
+element of b has more than two or equal to three
+
+673
+00:51:16,700 --> 00:51:22,590
+images under f، أكيد أكيد، فمعنى ذلك أنه دائماً
+
+674
+00:51:22,590 --> 00:51:26,670
+بنظرية الـ pigeonhole principle، أكيد هذه not one
+
+675
+00:51:26,670 --> 00:51:32,230
+to one، أكيد not one to one، هذا sure، تمام، طبعاً هنا
+
+676
+00:51:32,230 --> 00:51:37,090
+شايفين بعض أمثلة الفكرة، طول ما إحنا بنتكلم عن
+
+677
+00:51:37,090 --> 00:51:42,170
+اثنا عشر hole و عندك ثلاثة عشر visions، معنى ذلك أنه
+
+678
+00:51:42,170 --> 00:51:46,450
+لازم هتلاقي two visions at least موجودين في one
+
+679
+00:51:46,450 --> 00:51:47,110
+place.
+
+680
+00:51:49,930 --> 00:51:53,090
+طيب أمثلتها زي أن نقول والله إذا كان في عندنا مئة
+
+681
+00:51:53,090 --> 00:52:02,310
+واحد grades، numerical grades، كويس؟ مش يعني name
+
+682
+00:52:02,310 --> 00:52:06,410
+grades اللي هي a و b و c، لأ numerical، بمعنى واحد
+
+683
+00:52:06,410 --> 00:52:10,460
+ماخد صفر من مئة، واحد من مئة، اثنين من مئة، اللي عندك
+
+684
+00:52:10,460 --> 00:52:15,220
+مئة في المئة، فأنت بتتكلم عن مئة وواحد تقييم رقمي
+
+685
+00:52:15,220 --> 00:52:19,780
+من مئة، فاللي هي من صفر لمئة، ففي الحالة إذا كان
+
+686
+00:52:19,780 --> 00:52:23,920
+عندك أكثر من مئة وواحد students in this class،
+
+687
+00:52:23,920 --> 00:52:27,760
+معناته على الأقل فيه اثنين ماخذين نفس الـ grade، نفس
+
+688
+00:52:27,760 --> 00:52:30,160
+الـ grade، فأنت بتعرف على طول أنه فيه اثنين على الأقل
+
+689
+00:52:30,160 --> 00:52:32,620
+ماخذين نفس الـ grade، طبعاً أكيد الـ function هنا هتكون
+
+690
+00:52:32,620 --> 00:52:36,880
+إيش؟ not one to one، not one-to-one، الكلام بسيط و
+
+691
+00:52:36,880 --> 00:52:40,420
+sit down، وشهد، طيب كمان أمثلة هيك سريعة، among any
+
+692
+00:52:40,420 --> 00:52:44,840
+group of three hundred sixty-seven، إذا كان والله
+
+693
+00:52:44,840 --> 00:52:48,100
+عندك مجموعة فيها من الناس ثلاثمئة وسبعة وستون،
+
+694
+00:52:48,100 --> 00:52:51,960
+معنى ذلك أنه أنت متأكد تماماً أن فيه اثنين على
+
+695
+00:52:51,960 --> 00:52:55,610
+الأقل مولودين في نفس اليوم، مئة بالمئة بالضبط،
+
+696
+00:52:55,610 --> 00:53:00,010
+متأكدين تماماً، طيب إذا كان في عندك سبعة وعشرون group من
+
+697
+00:53:00,010 --> 00:53:03,270
+سبعة وعشرون كلمة بالـ English، معنى ذلك إن أنت
+
+698
+00:53:03,270 --> 00:53:07,870
+ضامن at least في عندك two words بادئين بنفس الحرف،
+
+699
+00:53:07,870 --> 00:53:12,750
+أكيد، طيب how many people must be selected from a
+
+700
+00:53:12,750 --> 00:53:17,010
+collection of fifteen married couples to ensure
+
+701
+00:53:17,010 --> 00:53:22,610
+that at least two of the persons chosen are married to
+
+702
+00:53:22,610 --> 00:53:23,350
+each other.
+
+703
+00:53:27,410 --> 00:53:34,990
+هنا بنتكلم عن خمسة عشر couple، خمسة عشر couple هدول
+
+704
+00:53:34,990 --> 00:53:38,990
+أزواج.
+
+705
+00:53:38,990 --> 00:53:43,750
+أزواج، يعني couples، أنت بتتكلم عن أزواج مع بعض، كويس؟
+
+706
+00:53:43,750 --> 00:53:51,510
+فأنت عندك من واحد، اثنين لعند خمسة عشر، كويس؟ وهتبدأ
+
+707
+00:53:51,510 --> 00:53:56,960
+تعمل لعبة إنك تختار أفراد، تختار أفراد، كويس؟ اخترنا
+
+708
+00:53:56,960 --> 00:54:00,360
+واحد، اثنين، ثلاثة، وإحنا جديد بنطلع اللعبة، مجموعة
+
+709
+00:54:00,360 --> 00:54:03,700
+يلعبوا، طب أنت بتضمن أنه، أو جدّيش عدد الاختيارات
+
+710
+00:54:03,700 --> 00:54:06,920
+اللي لازم تختارها عشان تضمن مائة بالمئة أن اللي
+
+711
+00:54:06,920 --> 00:54:11,960
+اختارتهم فيهم اثنين couple، أكيد، ليش؟ لأنه أسوأ
+
+712
+00:54:11,960 --> 00:54:16,820
+احتمال ممكن أنك أنت قاعد بتختار، وقاعدين بيطلعوا one
+
+713
+00:54:16,820 --> 00:54:20,540
+من الـ couple بس، الأول، الثاني، الثالث، الرابع،
+
+714
+00:54:20,540 --> 00:54:25,790
+عددهم جدّيش؟ خمسة عشر، لسوء حظك إنه قعدت بتختار، طلعوا
+
+715
+00:54:25,790 --> 00:54:31,690
+الخمسة عشر مختلفين عن بعض، رقم ستة عشر، sure، بده يكون الـ
+
+716
+00:54:31,690 --> 00:54:35,810
+couple تبعه اخترناه قبله، مش هيك؟ فإذا أكيد ستة عشر
+
+717
+00:54:35,810 --> 00:54:39,730
+persons، مائة بالمئة هكون ضامن إنه at least في one
+
+718
+00:54:39,730 --> 00:54:45,550
+couple تم اختيارهم، مش هيك؟ منطقي، أكيد، أكيد، أكيد جداً.
+
+719
+00:54:45,550 --> 00:54:51,650
+مش واضحة، عندك خمسة عشر قبل، قبل يعني إيش؟ زوج وزوجة
+
+720
+00:54:51,650 --> 00:54:54,990
+هيّ الموجودين هنا، وهيّ الثاني، وهيّ الثالث، وهيّ الـ
+
+721
+00:54:54,990 --> 00:54:58,410
+...لعندك الخمسة عشر، كويس؟ طبعاً في النهاية لما بدنا
+
+722
+00:54:58,410 --> 00:55:01,990
+نختار، بختار القبل مع بعضه، بختار one person،
+
+723
+00:55:01,990 --> 00:55:07,730
+فمعنى ذلك أن عدد الـ persons جدّيش؟ ثلاثين، ثلاثين،
+
+724
+00:55:07,730 --> 00:55:12,490
+طيب بدأنا نختار أسماء منهم، بالورقة و لها ده و
+
+725
+00:55:12,490 --> 00:55:19,120
+قعدنا نطلع ونسحب، أنت بأضمن أن اللي اخترتهم يوجد
+
+726
+00:55:19,120 --> 00:55:24,360
+فعلاً فيهم at least one couple، طيب أسوأ حاجة إن
+
+727
+00:55:24,360 --> 00:55:29,260
+اختار خمسة عشر واحد، ما فيش ولا واحد couple مع الثاني،
+
+728
+00:55:29,260 --> 00:55:33,020
+الـ 16 إجباري لازم هيكون couple مع واحد من
+
+729
+00:55:33,020 --> 00:55:38,780
+الخمسة عشر اللي اخترتهم، جابته تمام؟ تمام، خلاص، هذه
+
+730
+00:55:38,780 --> 00:55:41,180
+نخليها للمرة القادمة إن شاء الله، بنكملها.
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4f87fda9f79856f0c3ba9e7ad8beba73e0620e2a
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ_postprocess.srt
@@ -0,0 +1,2920 @@
+1
+00:00:05,130 --> 00:00:07,950
+طيب بسم الله الرحمن الرحيم يعطيكوا العفو يا شباب
+
+2
+00:00:07,950 --> 00:00:13,230
+نكمل اليوم في مساق ال discrete اليوم عندنا موضوع
+
+3
+00:00:13,230 --> 00:00:17,290
+جديد بعد ما كنا خلصنا ال induction أخدناها المرة
+
+4
+00:00:17,290 --> 00:00:19,710
+اللي فاتت و شوفنا ال basis step و ال inductive
+
+5
+00:00:19,710 --> 00:00:25,690
+step ثم تحدثنا منها عن ال recursion ال recursion
+
+6
+00:00:25,690 --> 00:00:28,870
+شوفنا كيف بيصير في recurrence ل ال function من
+
+7
+00:00:28,870 --> 00:00:34,660
+نفسها فاليوم هنتكلم عن ال counting أو العدفعلم
+
+8
+00:00:34,660 --> 00:00:40,780
+العد هو كيف انا ممكن اعد كويس عدد الطرق لأداء task
+
+9
+00:00:40,780 --> 00:00:45,300
+معينة فهذا هو المفهوم من كلمة counting او العد
+
+10
+00:00:45,300 --> 00:00:48,400
+اللي احنا بدنا نتكلم عنه اليوم ان شاء الله تعالى
+
+11
+00:00:48,400 --> 00:00:54,240
+فهو الحقيقة دراسة الأعداج او رقم الطرق او عدد
+
+12
+00:00:54,240 --> 00:00:59,320
+الطرق اللي ممكن نوضع فيها خليني نقول بعض الأشياء
+
+13
+00:00:59,320 --> 00:01:04,200
+في combination معين في تركيب معينان نقول والله
+
+14
+00:01:04,200 --> 00:01:09,440
+المثال اللي موجود فيه ميت شخص بدهم يتسابقه فقداش
+
+15
+00:01:09,440 --> 00:01:14,920
+عندي possibilities لفوز الأول عشرة، يعني الأول
+
+16
+00:01:14,920 --> 00:01:18,400
+عشرة الأوائل، كيف ممكن أعمل؟ مابديش تسميه
+
+17
+00:01:18,400 --> 00:01:22,280
+احتمالات، ولكن possibilities، ايش الإمكانية انه ..
+
+18
+00:01:22,550 --> 00:01:26,750
+أحط combination تركيبة من عدد المائة شخص هدولة
+
+19
+00:01:26,750 --> 00:01:30,990
+بحيث انه يكونوا هم العشر اللي هيفوزوا فجدش عدد ال
+
+20
+00:01:30,990 --> 00:01:36,070
+possibilities هدول، الإمكانيات هذه فطبعا هنتكلم
+
+21
+00:01:36,070 --> 00:01:39,030
+عنها و واضح ان انتوا كلكوا عارفين هيكوا الموضوع
+
+22
+00:01:39,030 --> 00:01:42,210
+هذا فمعنى ذلك انه المفروض نجري فيه اللي واضح ان
+
+23
+00:01:42,210 --> 00:01:47,140
+انتوا هيكوا عارفينهفجيد كويس هذا الموضوع الشغلة
+
+24
+00:01:47,140 --> 00:01:49,720
+التانية اللي ممكن تكون .. خلّيكم معنا يا شباب
+
+25
+00:01:49,720 --> 00:01:52,720
+الشغلة التانية اللي ممكن تتكلم في نفس الموضوع في
+
+26
+00:01:52,720 --> 00:01:56,980
+نفس السياق نستفيد منها هي فكرة ال password جدّيش
+
+27
+00:01:56,980 --> 00:02:01,140
+أنت ممكن تعمل كمبرمج جدّيش ممكن تولّد عدد
+
+28
+00:02:01,140 --> 00:02:04,320
+passwords إذا كانت تحددت عدد ال digits اللي أنت
+
+29
+00:02:04,320 --> 00:02:09,300
+بدك تستخدمها لل password فبتكون عندك من الأساس عدد
+
+30
+00:02:09,300 --> 00:02:15,080
+أو ال ..كمية أو عدد ال passwords اللي ممكن توليدها
+
+31
+00:02:15,080 --> 00:02:19,760
+في عدد خنات محددة لكلمة ال password فهذا المفروض
+
+32
+00:02:19,760 --> 00:02:23,780
+برضه من أساسيات العد .. من أساسيات العد فلما نقول
+
+33
+00:02:23,780 --> 00:02:27,920
+والله عندك ال password ممكن تكون من ستة لتمانية
+
+34
+00:02:27,920 --> 00:02:34,100
+letters or and digitsممكن تستخدم إما حروف أو أرقام
+
+35
+00:02:34,100 --> 00:02:40,200
+و ال password أقل شيء من ستة characters أو من ستة
+
+36
+00:02:40,200 --> 00:02:44,800
+حروف أو أرقام لتمانية فإذا ممكن تكتب ال password
+
+37
+00:02:44,800 --> 00:02:48,800
+تبعتك ستة أو سبعة أو تمانية حروف على أرقام حروف
+
+38
+00:02:48,800 --> 00:02:52,120
+على إيش؟ على أرقام جدش بده يكون عندي عدد passwords
+
+39
+00:02:52,120 --> 00:02:57,190
+ممكنين في الحالة هذه فهذه برضهمن خلال موضوعنا
+
+40
+00:02:57,190 --> 00:03:02,450
+لليوم اللي هي ال basics of counting أو أسس العد،
+
+41
+00:03:02,450 --> 00:03:06,630
+هنستخدمها، هنتكلم عنها، بس نبدأ ندرج شوية شوية و
+
+42
+00:03:06,630 --> 00:03:11,410
+أنا بتكلم عن أسس العد، بدي أستخدم أو بدي هتكلم عن
+
+43
+00:03:11,410 --> 00:03:16,450
+حاجة كتير مهمةهي ال two rules كتير بيحكمونا في هذا
+
+44
+00:03:16,450 --> 00:03:19,910
+الموضوع هي ال sum و ال product .. sum و product و
+
+45
+00:03:19,910 --> 00:03:22,330
+هنشوف هدى إمتى بنستخدمها و هدى إمتى بنستخدمها حسب
+
+46
+00:03:22,330 --> 00:03:25,210
+منطق السؤال و حسب إنت إيش بدك من السؤال أو كيف بدك
+
+47
+00:03:25,210 --> 00:03:28,850
+.. لو بنتكلم عن ال password .. إنت كيف بدك تركب ال
+
+48
+00:03:28,850 --> 00:03:32,860
+password فهي مش مجرد إنه عدد ال digits و خلاصلأ ال
+
+49
+00:03:32,860 --> 00:03:37,580
+digits هذه كيف بدك ترتبها؟ كيف بدك تكونها؟ هل لازم
+
+50
+00:03:37,580 --> 00:03:41,800
+يكون كلهم حروف؟ ولا لأ ممكن يكون كلهم digits؟ ولا
+
+51
+00:03:41,800 --> 00:03:46,100
+لأ من هذا على هذا؟ طب ممكن تقول حروف لكن مايقولوش
+
+52
+00:03:46,100 --> 00:03:50,330
+عدد الحروف عن اتنين مثلا من الستةفانت ممكن تحط كل
+
+53
+00:03:50,330 --> 00:03:53,110
+ال rules اللي بدك اياها ففي الحالة هذه جدش بيأثر
+
+54
+00:03:53,110 --> 00:03:57,490
+هذا على عدد ال passwords الممكنين بحيث انك انت
+
+55
+00:03:57,490 --> 00:04:01,050
+ممكن تحاول كمان تزود ال difficulty تبعت ال
+
+56
+00:04:01,050 --> 00:04:05,900
+password فانت لو مابدك تحدد ال password هذهبسيطة
+
+57
+00:04:05,900 --> 00:04:09,920
+ولا صعبة ولا normal فممكن تحدد هدول جديش و هدول
+
+58
+00:04:09,920 --> 00:04:14,540
+جديش و هدول جديش بناء على مفهومك انت لأ إيش يعني
+
+59
+00:04:14,540 --> 00:04:17,020
+صعبة و إيش يعني بسيطة إيش يعني صعبة و إيش يعني
+
+60
+00:04:17,020 --> 00:04:19,920
+بسيطة فده كلها هنتكلم عنها لكن بدنا نفهم شوية
+
+61
+00:04:19,920 --> 00:04:23,300
+basics أساسية في البداية اللي هي ال some way ل
+
+62
+00:04:23,300 --> 00:04:26,460
+product عشان نشرحهم بدي أفترض أنه في عندى عدد
+
+63
+00:04:26,460 --> 00:04:34,160
+الطرق to do task one بدي أسميهم مثلا M wayما مميز
+
+64
+00:04:34,160 --> 00:04:40,380
+فعندك عددهم M عشان أقدر أنفذ ال task الأولى طيب لو
+
+65
+00:04:40,380 --> 00:04:44,660
+كان عندك العدد N هد ال number of ways to do task 2
+
+66
+00:04:44,660 --> 00:04:48,640
+فانت صار عندك two tasks بدك تعملهم combination مع
+
+67
+00:04:48,640 --> 00:04:51,860
+بعض بدك تعملهم الأتنين مع بعضهم فهنا أصبح نحن
+
+68
+00:04:51,860 --> 00:04:56,120
+نتكلم عن هد لحال تحسبها لحالها و هد بتحسبها لحالها
+
+69
+00:04:56,120 --> 00:04:59,740
+هد لحال و هد لحال هقول ال letters لحالهم و ال
+
+70
+00:04:59,740 --> 00:05:03,090
+digits لحالهمطيب و بعدين إيش بدنا نعمل فيهم؟ هنا
+
+71
+00:05:03,090 --> 00:05:08,910
+بتصير كيف قلية تركيب ال password نفسه إذا والله
+
+72
+00:05:08,910 --> 00:05:14,070
+بدك تعملهم مع بعض، هيكون في عندك two ways تشتغل
+
+73
+00:05:14,070 --> 00:05:18,420
+على اما someتجمحهم جامع ففي الحالة هذه بيكونوا
+
+74
+00:05:18,420 --> 00:05:23,480
+منفصلين تماما عن بعض يا اما letters او او او او او
+
+75
+00:05:23,480 --> 00:05:25,120
+او او او او او او او او او او او او او او او او او
+
+76
+00:05:25,120 --> 00:05:25,140
+او او او او او او او او او او او او او او او او او
+
+77
+00:05:25,140 --> 00:05:25,200
+او او او او او او او او او او او او او او او او او
+
+78
+00:05:25,200 --> 00:05:31,000
+او او او او او
+
+79
+00:05:31,000 --> 00:05:34,680
+اوبدنا نقول ال summation rule إذا كان انا ال task
+
+80
+00:05:34,680 --> 00:05:39,940
+سبعتي do either task one or task two فانا يا بديهم
+
+81
+00:05:39,940 --> 00:05:44,200
+حروف بس يا بديهم أرقام بس، كويس؟ ففي الحالة هذه
+
+82
+00:05:44,200 --> 00:05:47,500
+طبعا هي أكيد بال password مش منطق أقول الكلام هذا
+
+83
+00:05:47,500 --> 00:05:50,360
+بس في applications تانية أه منطق جدا، يا هيك يا
+
+84
+00:05:50,360 --> 00:05:52,720
+هيك زي ما هناخد أنفلة كتير اليوم هناخد، الأنفلة
+
+85
+00:05:52,720 --> 00:05:53,360
+هتكون كتيرة
+
+86
+00:05:56,360 --> 00:06:01,240
+لكن بديش اياهم مع بعض ففي الحالة هدى بنستخدم M
+
+87
+00:06:01,240 --> 00:06:06,940
+plus Nهدول جديش عدد الطرق عشان فعلا أعمل password
+
+88
+00:06:06,940 --> 00:06:12,340
+نفترض من ستة من ستة digits فقط كحروف جديش عددهم
+
+89
+00:06:12,340 --> 00:06:16,100
+خلاص يبنى عددهم وجمعناه وحطناه كأنه قيمة M طب جديش
+
+90
+00:06:16,100 --> 00:06:19,960
+عدد الأرقام اللى ممكن أكون منهم password من ستة
+
+91
+00:06:19,960 --> 00:06:23,880
+digits برضه بنحسب عددهم و بنجمع الاتنين مع بعض
+
+92
+00:06:23,880 --> 00:06:29,000
+مدام أنا محتاج يا هذا يا هذا لكن لما بروح لل
+
+93
+00:06:29,000 --> 00:06:34,020
+product rule امتىلما تكون ال task تبعتي do both
+
+94
+00:06:34,020 --> 00:06:39,080
+task one and task two simultaneously بمعنى متزاون
+
+95
+00:06:39,080 --> 00:06:42,020
+مع بعض بدي أعمل اتنين مع بعض ففي الحالة هذه ال
+
+96
+00:06:42,020 --> 00:06:46,460
+password ممكن يكون من هنا و من هنا ساعتها جديش من
+
+97
+00:06:46,460 --> 00:06:50,240
+هنا وجديش من هنا انت بتقدر تكون عندك إمكانية تلعب
+
+98
+00:06:50,240 --> 00:06:53,400
+في الموضوع زي ما بدك يعني تقول والله بدي أول تلاتة
+
+99
+00:06:53,400 --> 00:06:57,200
+letters و بعدين تلاتة digits او تقول لأ بديها
+
+100
+00:06:57,200 --> 00:07:00,080
+اتنين و واحد اتنين و تلاتة اتنين و خمس اعملها بال
+
+101
+00:07:00,080 --> 00:07:04,680
+.. اقولكقول والله بدي letter digit letter digit
+
+102
+00:07:04,680 --> 00:07:08,280
+letter digit okay هذه ال problem بدك تشتغلها كل
+
+103
+00:07:08,280 --> 00:07:12,820
+واحدة لحالها تشتغل كل واحدة تصلحها و تضربهم مع بعض
+
+104
+00:07:12,820 --> 00:07:17,160
+في الحالة هذه حنشوف هتتضح طبعا أكتر أنت بنستخدم ال
+
+105
+00:07:17,160 --> 00:07:20,920
+product و أنت بنستخدم ال some مع الأمثلة الكتيرة
+
+106
+00:07:20,920 --> 00:07:25,520
+اللي هنقدر ناخدهالكن الآن عشان اوضح بس ان الفكرة
+
+107
+00:07:25,520 --> 00:07:29,020
+هي برضه مابعدتش عن حاجة احنا جاهزين ناخدها
+
+108
+00:07:29,020 --> 00:07:32,860
+باستمرار طول الفصل اللي هي ال 6 ال 6 فانا بكل
+
+109
+00:07:32,860 --> 00:07:37,140
+بساطة ال M هذه ال M اللي كانت هي عدد ال
+
+110
+00:07:37,140 --> 00:07:41,480
+possibilities to do task 1 ممكن اقول عليهم هدولة
+
+111
+00:07:41,480 --> 00:07:46,040
+كلWay من ال ways هدول بيتعامل معاها كأنها element
+
+112
+00:07:46,040 --> 00:07:52,160
+داخل set كاملة بحيث أني أقول في الآخر ال A هي ال
+
+113
+00:07:52,160 --> 00:07:59,340
+set لكل ال ways to do task oneكل مهمة او كل حل
+
+114
+00:07:59,340 --> 00:08:02,900
+بقدر اعمله للمهمة الاولى .. كل حل ممكن اقدر اعمله
+
+115
+00:08:02,900 --> 00:08:06,220
+للمهمة الاولى بجمعه مع بعضه و بحطه في تافيه set
+
+116
+00:08:06,220 --> 00:08:09,480
+واحدة بسميها set A فهذه ال set بتصير هي اللي
+
+117
+00:08:09,480 --> 00:08:13,360
+معطياني كل possibility solutions فعليا لل task
+
+118
+00:08:13,360 --> 00:08:18,240
+الاولى في نفس الكلام برضه بقول عندي ال set B فهي
+
+119
+00:08:18,240 --> 00:08:21,400
+برضه كل ال possibilities او ال ways او ال
+
+120
+00:08:21,400 --> 00:08:26,750
+solutions لل task 2لأ ال task two فإذا كانت عند a
+
+121
+00:08:26,750 --> 00:08:32,150
+and b are disjoint بمعنى إن الحلول هنا مالهاش
+
+122
+00:08:32,150 --> 00:08:36,870
+علاقة بالحلول هنا a فيها طرق حل مختلفة تماما عن
+
+123
+00:08:36,870 --> 00:08:41,690
+طرق حل بي ففي الحالة دي بنقدر نقول عشان أعمل
+
+124
+00:08:41,690 --> 00:08:45,190
+either task one or task two معناته اتحاد الأثنين
+
+125
+00:08:45,190 --> 00:08:49,710
+اتحاد a مع بي فصارت نفس المفهوم اللي أخدناها سابقا
+
+126
+00:08:49,710 --> 00:08:55,220
+ل مين لل six ل ال six كدهالتحاد وهذا ينطبق على ال
+
+127
+00:08:55,220 --> 00:08:58,180
+rule بتاع التو اللي هي sum فهي cardinality ل a
+
+128
+00:08:58,180 --> 00:09:01,820
+plus cardinality يعني معناته M plus N هي نفس ال
+
+129
+00:09:01,820 --> 00:09:05,680
+sum rule اللي أخدناها في المقابلة عندك برضه
+
+130
+00:09:05,680 --> 00:09:09,780
+إمكانية ان ال ways to do both task one and task
+
+131
+00:09:09,780 --> 00:09:12,640
+two سمتن يصل زي ما قلنا اتنين مع بعض ففي الحالة
+
+132
+00:09:12,640 --> 00:09:18,060
+نقدر نقولالـ cardinality لـ A مضروب في ال
+
+133
+00:09:18,060 --> 00:09:20,900
+cardinality لـ B فهنا برضه نتكلم عن ال rule تبعت
+
+134
+00:09:20,900 --> 00:09:23,780
+ال product ال product rule لإن بدي أعمل ال two
+
+135
+00:09:23,780 --> 00:09:27,340
+tasks مع بعض ال two tasks مع بعض في الحالة بتاعتنا
+
+136
+00:09:27,340 --> 00:09:33,440
+طيب ناخد أمثلة أكيد هتوضح أكتر الكلام النظري اللي
+
+137
+00:09:33,440 --> 00:09:37,780
+قلناه لو افترض انه ال student can chooseأبكمبيوتر
+
+138
+00:09:37,780 --> 00:09:41,040
+project في مساق من هالمساقات بتاعتكم انطلب منكوا
+
+139
+00:09:41,040 --> 00:09:44,100
+تختاروا project الأستاذ جابلكوا قائمة من ال
+
+140
+00:09:44,100 --> 00:09:47,200
+projects لكن ال projects هذه صنفلكوا إيها ل three
+
+141
+00:09:47,200 --> 00:09:51,360
+lists جالكم والله في عندي three lists بتحتوي على
+
+142
+00:09:51,360 --> 00:09:55,360
+تلتة و عشرين خمستاش و تسعتاش possible projects
+
+143
+00:09:55,360 --> 00:09:58,500
+خليني أقول ال تلتة و عشرين هدولة صنفلكوا تلتة و
+
+144
+00:09:58,500 --> 00:10:02,640
+عشرين project اللي هم علاقة بال AIو خمستاشر
+
+145
+00:10:02,640 --> 00:10:06,080
+project اللي هم علاقة بال networks و تسعتاشر
+
+146
+00:10:06,080 --> 00:10:08,960
+project اللي هم علاقة بال database مثلا okay و
+
+147
+00:10:08,960 --> 00:10:11,860
+جالكم هى في عندكوا تلت مجموعات هدولة مجموعة الناس
+
+148
+00:10:11,860 --> 00:10:14,120
+اللي بيحبوا يشتغلوا في ال AI فليكن هى في عندكوا
+
+149
+00:10:14,120 --> 00:10:17,800
+تلت و عشرين مشروع project يختاروا منهم و هى في
+
+150
+00:10:17,800 --> 00:10:20,720
+اللي بيحب يشتغل في الشبكات هى في خمستاشر project
+
+151
+00:10:20,720 --> 00:10:24,380
+اختاروا اللي بدكوا إياه منهم و اللي بدهوا database
+
+152
+00:10:24,380 --> 00:10:28,880
+هى في عندكوا تسعة عشرHow many possible projects
+
+153
+00:10:28,880 --> 00:10:32,900
+are there to choose from؟ يعني لكل طالب منكم الآن
+
+154
+00:10:32,900 --> 00:10:36,300
+هو بالنسباله جداش عدد ال possibilities للاختيار
+
+155
+00:10:36,300 --> 00:10:41,200
+مجموعة لكل، مش هيك؟ يا بيختار من التلاتة و عشرين
+
+156
+00:10:41,200 --> 00:10:46,780
+أو الخمستاش أو التسعتاش، مش هيجي يختار من التلاتة
+
+157
+00:10:46,780 --> 00:10:51,130
+لأنه مش مطلوب انه يقول لاproject واحد فإذا في
+
+158
+00:10:51,130 --> 00:10:53,930
+الحالة دي بكل بساطة ال total هيكون تلاتة و عشرين
+
+159
+00:10:53,930 --> 00:10:58,210
+خمس عشر تسعتاش فسبعة و خمسين projects فانت عندك
+
+160
+00:10:58,210 --> 00:11:01,050
+سبعة و خمسين possibility to choose your project
+
+161
+00:11:01,050 --> 00:11:05,290
+عشان تختار ال project تبعك عندك إمكانية إمكانيات
+
+162
+00:11:05,290 --> 00:11:10,850
+اختيار بتصل لسبعة و خمسين اختيار طيب suppose
+
+163
+00:11:10,850 --> 00:11:13,950
+فالتاني suppose statement labels محتاجين نعمل
+
+164
+00:11:13,950 --> 00:11:18,270
+labelلأ الحالات بتبعت باستخدام ال programming
+
+165
+00:11:18,270 --> 00:11:22,510
+language must be single letter اللي labels ها دي
+
+166
+00:11:22,510 --> 00:11:25,590
+العنوان .. العنوان هذا اللي بدك تحطه لمجموعة ال
+
+167
+00:11:25,590 --> 00:11:30,870
+statements سبعتك اما ان يكون single letter حرف فقط
+
+168
+00:11:30,870 --> 00:11:36,230
+او single decimal digit بس .. من 0 ل 9 .. يا من 0
+
+169
+00:11:36,230 --> 00:11:40,030
+ل 9 بالضبط 100% فانت بتتكلم عن decimal digit و
+
+170
+00:11:40,030 --> 00:11:43,890
+digit واحدةبال decimal يعني نتكلم عن النظام العشر
+
+171
+00:11:43,890 --> 00:11:46,210
+اللي هو من صفر إلى تسعة فعندك عشرة possibility
+
+172
+00:11:46,210 --> 00:11:50,450
+لإله، كويس، فالمطلوب بكل بساطة how many labels are
+
+173
+00:11:50,450 --> 00:11:54,050
+there، انت عارف مش محتاج كتير لما أقولك والله هي
+
+174
+00:11:54,050 --> 00:11:57,430
+كل statement بتقدر تسميها باسم، والاسم هذا إما أنه
+
+175
+00:11:57,430 --> 00:12:01,520
+يكون حرف أو يكون digit من ال decimal، بسو حرف
+
+176
+00:12:01,520 --> 00:12:05,960
+single فإذا هم السبت عشرين حرف زائد العشرة digits
+
+177
+00:12:05,960 --> 00:12:09,460
+تعوني ال decimal فبطلع عندى ستة و تلاتين
+
+178
+00:12:09,460 --> 00:12:13,980
+possibility لاستخدامهم ك label او لل statement
+
+179
+00:12:13,980 --> 00:12:20,400
+label طيب how many integers between one and one
+
+180
+00:12:20,400 --> 00:12:25,820
+hundred including ال one hundred are even or end
+
+181
+00:12:25,820 --> 00:12:32,320
+with five؟ تماملاحظ الان احنا صرنا نتكلم عن ايش عن
+
+182
+00:12:32,320 --> 00:12:37,060
+or واضحة عندي هنا معناه ذلك ان في عندي two tasks
+
+183
+00:12:37,060 --> 00:12:44,680
+two tasks task قبل ال or فبسميها task one وفي task
+
+184
+00:12:44,680 --> 00:12:50,460
+بعد ال or بسميها task two و بدنا نحسب كل واحدة على
+
+185
+00:12:50,460 --> 00:12:55,080
+حده كل واحدة على حده فانت بتتكلم من صفر لمية اول
+
+186
+00:12:55,080 --> 00:12:59,930
+task ال evenعدد ال even اللي فيها، كلنا عارفين
+
+187
+00:12:59,930 --> 00:13:06,470
+قداش؟ خمسين even، خمسين
+
+188
+00:13:06,470 --> 00:13:14,010
+even بعتبار أنه المشمولة الخمسين، لكن مجلناش أنه
+
+189
+00:13:14,010 --> 00:13:19,090
+اه من الواحد عفواأه لأنه بدي أقولك مش كاتب أن
+
+190
+00:13:19,090 --> 00:13:23,310
+الصفر موجود فهو من واحد فعليا فإذا عندك خمسين طيب
+
+191
+00:13:23,310 --> 00:13:27,850
+ال end with five end with five يعني معناته الأحد
+
+192
+00:13:27,850 --> 00:13:33,110
+تعتها خمسة الأحد تعتها خمسة كده إيش عددهم عشرة
+
+193
+00:13:33,110 --> 00:13:38,950
+ابدأ من الخمسة نفسها خمستعش و هكذا عند الخمسة
+
+194
+00:13:38,950 --> 00:13:45,300
+وتسعين ففعليابدأت من الخمسة صفر خمسة واحد لخمسة
+
+195
+00:13:45,300 --> 00:13:52,200
+تسعة لاحظ العشرات من الصفر للتسعة فعددهم جداش عشرة
+
+196
+00:13:52,200 --> 00:13:56,700
+فبصير خمسة زائد عشرة فانت عندك كمان ال task التاني
+
+197
+00:13:56,700 --> 00:14:03,080
+عشرة اللي هم نقدر نسميهم end with five طيب مربوطين
+
+198
+00:14:03,080 --> 00:14:10,480
+بإيش؟ ب or يعني ستين or يعني معناته هذا مفصل عن
+
+199
+00:14:10,480 --> 00:14:16,470
+هذاهذه هتكون منفصل عن هذه طيب طبعا هنا واضح ان هي
+
+200
+00:14:16,470 --> 00:14:21,770
+منفصل عن بعضبمعنى إن لو في أرقام بتظبط إن هيكونوا
+
+201
+00:14:21,770 --> 00:14:25,390
+الاتنين مع بعض هدخلنا في جثة هنتكلم عنها لكن الان
+
+202
+00:14:25,390 --> 00:14:28,710
+واضح إن ال set أو ال task هذه هي منفصلة تماما عن
+
+203
+00:14:28,710 --> 00:14:32,550
+ال task هذه ليش؟ لأنه مدام هي and with five معناتي
+
+204
+00:14:32,550 --> 00:14:36,370
+هي odd مستحيل تكون even فإذا أنا ضامن إن المجموعة
+
+205
+00:14:36,370 --> 00:14:40,470
+الخمسين هنا مافيش فيهم ولا رقم من العشرة والعشر
+
+206
+00:14:40,470 --> 00:14:43,710
+هدول برضه مافيش فيهم ولا رقم من الخمسين هدول فإذا
+
+207
+00:14:43,710 --> 00:14:47,590
+بنجمحهم لأنه disjoint حتى الآن اللي اتكلمنا عنها
+
+208
+00:14:47,590 --> 00:14:56,430
+اللي هي disjointتمام كمان مثال how
+
+209
+00:14:56,430 --> 00:14:58,890
+many different pit strings .. strings of length
+
+210
+00:14:58,890 --> 00:15:06,610
+seven are there؟ مافيش فيها كتير برضه مشكلة جدش
+
+211
+00:15:06,610 --> 00:15:13,610
+بتعمل عدد strings من عدد digits سبعة
+
+212
+00:15:18,470 --> 00:15:22,370
+كل واحدة منهم لحالهم هدولة إيش ال possibility
+
+213
+00:15:22,370 --> 00:15:25,510
+بتاعتها اتنين، يا صفر يا واحد، فإذا هذه يا صفر يا
+
+214
+00:15:25,510 --> 00:15:28,570
+واحد، فإذا ال possibility بتاعتها اتنين، طيب ال
+
+215
+00:15:28,570 --> 00:15:31,570
+possibility بتاعة التانية برضه يا صفر يا واحد،
+
+216
+00:15:31,570 --> 00:15:34,750
+فإذا برضه اتنين، اتنين، اتنين، اتنين، اتنين،
+
+217
+00:15:34,750 --> 00:15:36,370
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+218
+00:15:36,370 --> 00:15:36,650
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+219
+00:15:36,650 --> 00:15:37,630
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+220
+00:15:37,630 --> 00:15:41,570
+اتنينالـ length كله على بعضه seven فإذا لازم يكون
+
+221
+00:15:41,570 --> 00:15:45,590
+ال combination فيهم ال سبعة digit هدول اللي هم ال
+
+222
+00:15:45,590 --> 00:15:48,310
+binary digit ال binary digit لازم يكونوا كاملين
+
+223
+00:15:48,310 --> 00:15:51,270
+موجودين فيها طب مدام كاملين موجودين فيها معناته
+
+224
+00:15:51,270 --> 00:15:55,950
+عدد ال possibilities هصير فيهاتبديل بينهم بمعنى
+
+225
+00:15:55,950 --> 00:16:00,550
+انه هنا يا صفر يا واحد طيب اللي جنبها لو كنت افترض
+
+226
+00:16:00,550 --> 00:16:04,270
+على جد اتنين برضه هتكون يا صفر يا واحد صحيح؟ بس
+
+227
+00:16:04,270 --> 00:16:08,090
+لاحظ معنى ذلك انه ك string كامل على بعضه اما صفر
+
+228
+00:16:08,090 --> 00:16:15,010
+صفر او صفر واحد او واحد صفر او واحد واحد فإذن
+
+229
+00:16:15,010 --> 00:16:19,280
+أصبحت مضروب لاتنينمضروب الاتنين لإن الاتنين بدهم
+
+230
+00:16:19,280 --> 00:16:23,360
+يتحققوا معاً لازم يكون في ال digit الأولى لها رقم
+
+231
+00:16:23,360 --> 00:16:26,920
+لها قيمة وال digit التانية and ال digit التانية
+
+232
+00:16:26,920 --> 00:16:29,800
+برضه لها قيمة and ال digit التالتة لها قيمة مش or
+
+233
+00:16:29,800 --> 00:16:34,080
+فإذا كلهم بدهم يتحققوا مع بعض مدام مع بعض معناه to
+
+234
+00:16:34,080 --> 00:16:38,590
+endمعناته and عشان أكون فعلا عندي string من سبعة
+
+235
+00:16:38,590 --> 00:16:42,290
+digits وإلا معناته ببطل من سبعة digits إذا or
+
+236
+00:16:42,290 --> 00:16:46,510
+معناته واحد فقط أنا بتكلم عن واحد يهد يهد يهد لأ
+
+237
+00:16:46,510 --> 00:16:49,690
+هو مش يهد يهد السبعة ببطون دانية هم موجودين فإذا
+
+238
+00:16:49,690 --> 00:16:56,970
+الأول و التاني و التالت لعند السابع مدام و and مش
+
+239
+00:16:56,970 --> 00:16:58,890
+or and خلاص بنضرب
+
+240
+00:17:02,400 --> 00:17:05,180
+ضربناهم في بعض فمعناته اتنين to the power سبع او
+
+241
+00:17:05,180 --> 00:17:10,950
+اتنين متكررة سبع .. سبع مرات، خلصنا منهاطيب بدنا
+
+242
+00:17:10,950 --> 00:17:16,170
+نعمل license او license معين اللي هو password يعني
+
+243
+00:17:16,170 --> 00:17:20,310
+للمنتج تبعكوا license code له بيحتوي على sequence
+
+244
+00:17:20,310 --> 00:17:27,570
+of three letters من تلت حروف من تلت حروف followed
+
+245
+00:17:27,570 --> 00:17:32,950
+by three digits ومطبوعين ب three digits فاذا تلت
+
+246
+00:17:32,950 --> 00:17:37,270
+حروف وراهم تلاتة digits اللي هم من صفر لتسعة كل
+
+247
+00:17:37,270 --> 00:17:43,320
+واحد منهم فالانhow many different license plates
+
+248
+00:17:43,320 --> 00:17:47,780
+are available خلاص هي تنحطها برضه بشكلها الهيكل
+
+249
+00:17:47,780 --> 00:17:50,180
+كيف بده يكون شكلها بده يكون بهذا الشكل
+
+250
+00:17:53,840 --> 00:17:58,580
+فعندي تلاتة في البداية هدولة عبارة عن letters كل
+
+251
+00:17:58,580 --> 00:18:01,700
+واحدة منهم letter ال letter ايش ال possibilities
+
+252
+00:18:01,700 --> 00:18:04,720
+عدد ال possibilities تبعته؟ ستة و عشرين فإذا هذا
+
+253
+00:18:04,720 --> 00:18:08,580
+ممكن يكون واحد من ستة و عشرين حرف احنا عارفينهم
+
+254
+00:18:08,580 --> 00:18:15,400
+والتاني ستة و عشرين والتالتطيب الجزء التاني اللي
+
+255
+00:18:15,400 --> 00:18:19,980
+هم ال three ال four by three digits ل decimal
+
+256
+00:18:19,980 --> 00:18:23,440
+digits فإذا إما عشرة عشرة عشرة اللي هي من صفر
+
+257
+00:18:23,440 --> 00:18:30,030
+لتسعة طيب هل وجد هدول المفروض هل هم or ولا andهنا
+
+258
+00:18:30,030 --> 00:18:33,130
+بنتكلم عن قدر لأنه بتكلم عن sequence مافرجش كتير
+
+259
+00:18:33,130 --> 00:18:36,310
+عن ال string اللي كنا نحكي عنه فهو ال sequence هذا
+
+260
+00:18:36,310 --> 00:18:40,430
+مكوّن من تلاتة مطبوعة بتلاتة يعني لو أقل من ستة مش
+
+261
+00:18:40,430 --> 00:18:44,330
+هيرضى فيه ك .. ك sequence و ك license يتعامل معه
+
+262
+00:18:44,330 --> 00:18:48,850
+فإذا هدول اللي لازم يكونوا مع بعض فإذا مضربين في
+
+263
+00:18:48,850 --> 00:18:54,660
+بعض هيكونوا كلهم مضربين في بعضطبعا كويس فإذا منطق
+
+264
+00:18:54,660 --> 00:18:57,840
+السؤال او فهمك لا ايش ال combination اللي انت بدك
+
+265
+00:18:57,840 --> 00:19:00,300
+تعملها بالظبط هو اللي بيحددلك على طول ان انت
+
+266
+00:19:00,300 --> 00:19:05,780
+بتتكلم عن ال some rule ولا product rule كمان مثال
+
+267
+00:19:05,780 --> 00:19:10,500
+هنا برضه نفس الكلام بدنا نعمل statement labelال
+
+268
+00:19:10,500 --> 00:19:12,740
+statement اللي عندك بدك تحطلها label معين تحطلها
+
+269
+00:19:12,740 --> 00:19:19,900
+ترقيم الترقيم هذا either a single letter فإذا جدش
+
+270
+00:19:19,900 --> 00:19:24,740
+بدني single letter واحدة أو letter followed by
+
+271
+00:19:24,740 --> 00:19:33,180
+digit فإذا إما خلصنا من هنا digit
+
+272
+00:19:33,180 --> 00:19:40,780
+واحدة عبارة عن بديها letter حروف فهذه ستة وعشرينor
+
+273
+00:19:40,780 --> 00:19:48,400
+و بصراحة انجلك or or برضه single letter followed
+
+274
+00:19:48,400 --> 00:19:55,980
+by digit فإذا ستة و عشرين و عشرة مادام followed by
+
+275
+00:19:55,980 --> 00:20:00,780
+digit معناته مطبوعة لازم يجوا مع بعض مادام مع بعض
+
+276
+00:20:00,780 --> 00:20:06,620
+معناته and الأول and التاني and فصارت هذه ستة و
+
+277
+00:20:06,620 --> 00:20:13,880
+عشرين orمتين و ستين فإذا تجمحهم بيصير متين تمانية
+
+278
+00:20:13,880 --> 00:20:21,260
+ستة متين ستة و تمانين صحيح؟ بدأ مقر فإذا صارت two
+
+279
+00:20:21,260 --> 00:20:25,920
+task متفاصلين عن بعض و وضح لك إياها هذه ال task
+
+280
+00:20:25,920 --> 00:20:29,710
+الأولى وهذه ال task التانيةOkay هو بتهيألي حل
+
+281
+00:20:29,710 --> 00:20:35,590
+هخلصنا من كل هذا أعملك S على أساس إن هي الست ل
+
+282
+00:20:35,590 --> 00:20:37,850
+single letter لحالها اللي هي طلعت ستة و عشرين
+
+283
+00:20:37,850 --> 00:20:41,270
+جيبناها و ال D افترض إن هي single letters followed
+
+284
+00:20:41,270 --> 00:20:46,610
+by digit او decimal digit وعملوا لهم اتحاد في
+
+285
+00:20:46,610 --> 00:20:50,390
+الآخر فوصلنا ل المتين ستة و تمانين اللي طلعناها
+
+286
+00:20:50,390 --> 00:20:52,370
+تمام
+
+287
+00:20:53,930 --> 00:20:59,370
+كمان مثل واضح لهذا الموضوع هي ال IP address ال IP
+
+288
+00:20:59,370 --> 00:21:03,190
+address بيكون له protocol فبنسميه ال internet
+
+289
+00:21:03,190 --> 00:21:06,790
+protocol ال version 4 و بعدين حاليا صار ال version
+
+290
+00:21:06,790 --> 00:21:13,630
+6 فخلينا نرجع لل version 4 ال version 4 في منه
+
+291
+00:21:13,630 --> 00:21:22,760
+classes في منه صنف لعدة أصناف A وB وC وD وEمصنف
+
+292
+00:21:22,760 --> 00:21:26,200
+لخمس أصناف بعرفش إذا كان مرة بتعليقه في مساقة أو
+
+293
+00:21:26,200 --> 00:21:30,120
+إشي المهم إحنا الآن مطلوب مننا في السؤال إيش مطلوب
+
+294
+00:21:30,120 --> 00:21:34,860
+مننا جدش عدد ال addresses ل three types منهم اللي
+
+295
+00:21:34,860 --> 00:21:39,920
+هو a و b و c طيب a و b و c هدول بدنا نفهم منهم
+
+296
+00:21:39,920 --> 00:21:45,940
+شغلة إنه عادة هو عبارة عن sequence ل digit لمجموعة
+
+297
+00:21:45,940 --> 00:21:50,950
+digits لتعريف الشبكةو ال host اللي عليها او ال
+
+298
+00:21:50,950 --> 00:21:57,170
+user اللي عليها تمام بالاضافة لجزء من ال sequence
+
+299
+00:21:57,170 --> 00:22:02,430
+هذا عبارة عن one or two or three digits three bit
+
+300
+00:22:02,430 --> 00:22:06,350
+هدولة لتعريف ال class اللي احنا بنشتغل عليه فإذا
+
+301
+00:22:06,350 --> 00:22:10,350
+ال sequence عندك و اللي هو بالاساس مكوّن بالنسبة
+
+302
+00:22:10,350 --> 00:22:15,770
+لل version 4 مكوّن من 32بت ال 32 بت هدول بتجسموا
+
+303
+00:22:15,770 --> 00:22:20,470
+حسب كل نوع class ال class الأول بناخد منه بت
+
+304
+00:22:20,470 --> 00:22:25,190
+لتعريف ال classلتعريف ال class إذا بدأت بواحد معنا
+
+305
+00:22:25,190 --> 00:22:30,750
+ذلك إن أنا بتكلم عن class A إذا بدأت بصفر ثم واحد
+
+306
+00:22:30,750 --> 00:22:35,990
+فانا بتكلم عن class B إذا كانت صفر صفر واحد class
+
+307
+00:22:35,990 --> 00:22:40,910
+C فإذا نلاحظ class A أنا استنفذت أول digit أو أول
+
+308
+00:22:40,910 --> 00:22:44,930
+bit لتعريف ال class نفسه فبيضللي واحد و تلاتين
+
+309
+00:22:44,930 --> 00:22:46,710
+واحد و تلاتين او واحد و تلاتين بالظبط واحد و
+
+310
+00:22:46,710 --> 00:22:49,750
+تلاتين الواحد و تلاتين هدول بيتم تجسم و ليش؟ بيتم
+
+311
+00:22:49,750 --> 00:22:55,080
+تجسم و دير بالك ل usersالذين يسمونهم الـ host ال
+
+312
+00:22:55,080 --> 00:23:00,940
+users هدولة أعدادهم لكلsmall network خلّيني او
+
+313
+00:23:00,940 --> 00:23:04,700
+شبكة بحيث انه في النهاية الشبكة هذه لها عنوان كمان
+
+314
+00:23:04,700 --> 00:23:09,180
+فانت الشبكة الأولى وانت ال user الأول فيها طب هذا
+
+315
+00:23:09,180 --> 00:23:13,400
+ممكن يكون في شبكة تانية ويلها user أول برضه يعني
+
+316
+00:23:13,400 --> 00:23:17,700
+ممكن اتنين يكونوا بالنسبة للمجموعة ال bits اللي
+
+317
+00:23:17,700 --> 00:23:22,100
+خاصة بالhost نفسه لكن اختلفوا بمين؟ بعنوان الشبكة
+
+318
+00:23:22,100 --> 00:23:25,520
+فإذا انا في عندي تتجسم لعنوانين العنوانين هدول
+
+319
+00:23:25,520 --> 00:23:26,280
+هنسميهم
+
+320
+00:23:28,610 --> 00:23:33,350
+ال .. ال net ID خاصة بالشبكة نفسها ال net ID و فيه
+
+321
+00:23:33,350 --> 00:23:37,550
+عندك ال host ID عندك host ID فكل net فيه لها
+
+322
+00:23:37,550 --> 00:23:41,310
+مجموعة ال hosts تاعتها لها مجموعة hosts تاعتها
+
+323
+00:23:41,310 --> 00:23:49,430
+تمامالان بالنسبة لـ B هتكون اول two bits مستنفذين
+
+324
+00:23:49,430 --> 00:23:53,210
+لتعريف ال class نفسه فبتضع لعندك تلاتين فاللي
+
+325
+00:23:53,210 --> 00:23:58,690
+بتبقى من التلاتين bit هدولة بدنا نجسمهم بين ال net
+
+326
+00:23:58,690 --> 00:24:06,010
+ID و ال host ID التالتة اللي هي Cبكون عندك three
+
+327
+00:24:06,010 --> 00:24:10,050
+bits لتعريف ال class نفسه فبظل عندك تسعة و عشرين
+
+328
+00:24:10,050 --> 00:24:14,350
+بدك اتجسمهم ما بين ال host و ال network كويس
+
+329
+00:24:14,350 --> 00:24:18,830
+فبتختلف الان كيف اتجسمت هاد standard بالمناسبة
+
+330
+00:24:18,830 --> 00:24:21,590
+standard يعني احنا okay عارفين ان في تلات حالات و
+
+331
+00:24:21,590 --> 00:24:26,950
+بتختلف تجسيماتهم standard هذا خليني نشوف جدش
+
+332
+00:24:26,950 --> 00:24:31,130
+تجسيمة كل واحدة منهم بالنسبة ل class A class A
+
+333
+00:24:32,480 --> 00:24:40,160
+امجسمهم ان في عندك سبعة bit لتعريف
+
+334
+00:24:40,160 --> 00:24:44,700
+ال network جدش بظل من الواحد و التلاتين لان احنا
+
+335
+00:24:44,700 --> 00:24:48,080
+قلنا في واحد لمن لتعريف ال class نفسه وهي في سبعة
+
+336
+00:24:48,080 --> 00:24:52,460
+راح تمانية هاي تمانية جدش ظل ال host اربعة و عشرين
+
+337
+00:24:52,460 --> 00:24:57,280
+ففي عندك اربعة و عشرين لال host معناه ذلك ان كل
+
+338
+00:24:57,280 --> 00:25:02,200
+شبكة في ال class هذا بتكون بتحمل عدد كبير من ال
+
+339
+00:25:02,200 --> 00:25:06,840
+users او ال host من ال users طيب اهم شغلة هنا
+
+340
+00:25:06,840 --> 00:25:11,040
+موجودة انك بالنسبة لل net ID غير مسموح ان يكونوا
+
+341
+00:25:11,040 --> 00:25:16,470
+السبعة هدول كاملين onceهذه مش مسموحة فيه مش مسموحة
+
+342
+00:25:16,470 --> 00:25:20,410
+في ال class هذا تمام او حتى في ال classes كلها طيب
+
+343
+00:25:20,410 --> 00:25:29,250
+ال class B بيقدرس ايش 14 bit ل ال net بمعنى ان هنا
+
+344
+00:25:29,250 --> 00:25:33,990
+بيكون عدد ال nets عليه اكتر وهذا في المقابل هيخلي
+
+345
+00:25:33,990 --> 00:25:40,380
+عدد ال user داخل ال net كل net لحالها اقلهيكون عدد
+
+346
+00:25:40,380 --> 00:25:45,720
+ال net أقل تمام فبتصير عندك 16 بدل ما كانت 24 فانت
+
+347
+00:25:45,720 --> 00:25:48,620
+شوف جد ايش عدد ال users اللي ممكن تستخدمهم هنا لكل
+
+348
+00:25:48,620 --> 00:25:53,740
+شبكة اتنين to the power 24 هنا لأ هتكون to the
+
+349
+00:25:53,740 --> 00:25:57,100
+power 16 to the power 16 اذا عدد والله الجامعة
+
+350
+00:25:57,100 --> 00:26:00,840
+عددهم مش عدد كبير لأ بنجلل اكتر من هيك كمان كويس
+
+351
+00:26:01,590 --> 00:26:05,630
+الان ال class و بالمناسبة هذه اصلا شغل تجاري يعني
+
+352
+00:26:05,630 --> 00:26:08,170
+اذا انا عارف ان ال area هذه مش هيجيها عدد كبير ليش
+
+353
+00:26:08,170 --> 00:26:14,030
+انا اضيع ال bits في ال host طب ما بخليه للشبكة و
+
+354
+00:26:14,030 --> 00:26:17,210
+بضمن ان الشبكات عددهم كبير و بنجل الشبكات بخليهم
+
+355
+00:26:18,220 --> 00:26:24,520
+يعني بععد عن بعض فب .. بغطي area أكبر بنغطي في
+
+356
+00:26:24,520 --> 00:26:27,680
+الحالة هذه area أكبر مدام ال .. ال density مش
+
+357
+00:26:27,680 --> 00:26:30,820
+عالية مدام ال density مش عالية بس هذه بتاع دراسة
+
+358
+00:26:30,820 --> 00:26:37,680
+طبيعية طيب C .. C لاحظ واحد و عشرين لاالـ net ID
+
+359
+00:26:37,680 --> 00:26:41,840
+21 و تمانية فقط لمين؟ لل host تمانية لل host إذا
+
+360
+00:26:41,840 --> 00:26:46,860
+بنتكلم عن area مافيها capacity عالية ف okay بنخلي
+
+361
+00:26:46,860 --> 00:26:51,120
+عدد networks كتير و كل network تتغذي عدد أقل من ال
+
+362
+00:26:51,120 --> 00:26:55,100
+host أو من ال users تمام و زي ما اتفجنا ال two
+
+363
+00:26:55,100 --> 00:27:00,120
+classes بتعرفوا عن بعض بال header تبعالـ IB
+
+364
+00:27:00,120 --> 00:27:03,780
+address هذا من خلال النقل صفر إذا كان صفر لحالها
+
+365
+00:27:03,780 --> 00:27:09,340
+فأنا بتكلم عن إيه إذا واحد و بعدين الصفر إجا رقم
+
+366
+00:27:09,340 --> 00:27:12,380
+اتنين فمعنى ذلك هدي بي إذا الصفر إجا رقم تلاتة
+
+367
+00:27:12,380 --> 00:27:17,620
+فمعناته أنا بتكلم عنهC عن C كويس ال host هنا بده
+
+368
+00:27:17,620 --> 00:27:20,840
+يعطينا شوية characteristic واضحة جدا بتكون
+
+369
+00:27:20,840 --> 00:27:26,100
+بمستخدمها انه لا يمكن استخدام ال host zeros or
+
+370
+00:27:26,100 --> 00:27:30,480
+ones بمعنى انه مافيش user هياخد ال address zeros
+
+371
+00:27:30,480 --> 00:27:36,600
+في أي شبكة ولا ones ولا ال ones في أي شبكة كانت
+
+372
+00:27:36,600 --> 00:27:40,640
+تمام فإذا هي هذا أول شرط تتاخدوا بالكم منه وفي
+
+373
+00:27:40,640 --> 00:27:46,140
+عندي شرط تاني كان هنا لمينلل .. ال .. ال net ID ان
+
+374
+00:27:46,140 --> 00:27:49,260
+هي بتسمحش بال ones بتسمحش بال ones الان ايش
+
+375
+00:27:49,260 --> 00:27:54,280
+المطلوب؟ مطلوب جدش عدد ال addresses الممكنين ل ال
+
+376
+00:27:54,280 --> 00:27:56,500
+three classes هدولة في ال system طبعا هنا
+
+377
+00:27:56,500 --> 00:28:00,600
+ماتكلمناش احنا عن مين؟ عن ال D و ال E ال D و ال E
+
+378
+00:28:00,600 --> 00:28:02,880
+بيستخدموهم في ال broadcasting في ال broadcasting
+
+379
+00:28:02,880 --> 00:28:06,820
+اللي هي بياخدوا المدى كله كامل ل user واحد او
+
+380
+00:28:06,820 --> 00:28:10,680
+لخدمة واحدة فبتكون .. اه بتكون عددهم كبير في
+
+381
+00:28:10,680 --> 00:28:16,550
+الحالة هذه تمامالان بدنا نشوف جداش عدد ال
+
+382
+00:28:16,550 --> 00:28:21,490
+possibilities لعدد users يعني addresses جداش انا
+
+383
+00:28:21,490 --> 00:28:25,130
+ممكن اولد addresses بالنظام هذا بهذا الاستخدام بكل
+
+384
+00:28:25,130 --> 00:28:28,410
+بساطة اتوقع ايش بتكون تعمله طبعا ماحدش هيشتغل
+
+385
+00:28:28,410 --> 00:28:31,330
+بالظبط واحد واحد لانه ماحدش هيشتغل في two classes
+
+386
+00:28:31,330 --> 00:28:36,880
+مع بعض كل واحد له class لحاله يا a يا b يا cمش
+
+387
+00:28:36,880 --> 00:28:40,520
+هيك؟ هذه أول شغلة، ممتاز، هذه هلوجت في التفاصيل،
+
+388
+00:28:40,520 --> 00:28:44,980
+احنا هلوجت وحددنا أنه يا A يا B يا C، صحيح؟ A B C،
+
+389
+00:28:44,980 --> 00:28:47,780
+أنا هكون ضمن واحد منهم، مستحيل أكون ضمن أكتر من
+
+390
+00:28:47,780 --> 00:28:52,960
+هيك، فإذن الأول or التاني or التالت، فإذا تصق أولة
+
+391
+00:28:52,960 --> 00:28:55,940
+تانية تالتة، هدول منفصلين عن بعض، تمسكهم واحدة
+
+392
+00:28:55,940 --> 00:28:59,080
+واحدة الأولمسيكنا الأولى هلو يجي تبدأ نشتغل في
+
+393
+00:28:59,080 --> 00:29:03,080
+شغلتك هنقول ان في عندى واحد و تلاتين الواحد و
+
+394
+00:29:03,080 --> 00:29:06,660
+تلاتين هتجسموا سبعة السبعة هدولة ممكن تكون اتنين
+
+395
+00:29:06,660 --> 00:29:10,780
+to the power seven ناقص واحد لأنه مش مسموح بالones
+
+396
+00:29:10,780 --> 00:29:16,040
+اللي قلتلنا عليها صح؟ ممتاز طيب هدولة ال sequence
+
+397
+00:29:16,040 --> 00:29:21,760
+تبع مين؟ تبع ال address تبع ال network followed by
+
+398
+00:29:21,760 --> 00:29:27,540
+أو with ال host ال host جد يشضلأربعة و عشرين بقى
+
+399
+00:29:27,540 --> 00:29:30,800
+انا ذلك بتكلم عن ال host لحاله اتنين to the power
+
+400
+00:29:30,800 --> 00:29:34,300
+اربعة و عشرين ناقص اتنين احسنته اللي هي ال zeros و
+
+401
+00:29:34,300 --> 00:29:37,540
+ال ones تمام هلوجة الناتج اللي بطلع بضربه في مين
+
+402
+00:29:37,540 --> 00:29:41,860
+في اتنين to the power seven ناقص واحد عشان يعطيني
+
+403
+00:29:41,860 --> 00:29:46,120
+ال sequence كله ل class A فبنكون خلصنا one task
+
+404
+00:29:46,120 --> 00:29:51,980
+بتكمل التانية و التالتة و بتجمع الباقي تقن الأمور
+
+405
+00:29:51,980 --> 00:29:58,070
+فإذا هين بنجمحهمعدد ل class A عدد ال addresses ل
+
+406
+00:29:58,070 --> 00:30:02,470
+class B وعدد ال addresses ل class C وبنبدأ واحد
+
+407
+00:30:02,470 --> 00:30:06,490
+واحد فإذا هنا استخدمنا هنا summation أو some rule
+
+408
+00:30:06,490 --> 00:30:15,610
+some rule okay
+
+409
+00:30:15,610 --> 00:30:22,170
+class A بدنا نشوفالنتوارك الأول، إيش عدد ال valid
+
+410
+00:30:22,170 --> 00:30:25,050
+addresses له ال network، وبعدين ال valid مضروبة
+
+411
+00:30:25,050 --> 00:30:29,130
+لإنه followed with، هذه 31 كاملين ورا بعض، لازم
+
+412
+00:30:29,130 --> 00:30:31,950
+يكونوا كاملين ورا بعض، مانفعش أفصلهم هذا أو هذا،
+
+413
+00:30:31,950 --> 00:30:36,550
+هم الإتنين مع بعض بيشكلوا ال IP address تبعك كجهاز
+
+414
+00:30:36,550 --> 00:30:41,250
+على الشبكةكلاهما مع بعض، بنفعش والله تقول جدش رقمك
+
+415
+00:30:41,250 --> 00:30:45,030
+as a host، بس، لأ as a host وإيش الشبكة اللي أنت
+
+416
+00:30:45,030 --> 00:30:48,330
+ماخد منها، ال address تبع الشبكة كمان، عشان أعرفك
+
+417
+00:30:48,330 --> 00:30:51,490
+على الشبكة العالمية كلها، تمام، فإذا مضربين في
+
+418
+00:30:51,490 --> 00:30:57,280
+بعض، لأ ال valid hostبكل بساطة بالنسبة لل network
+
+419
+00:30:57,280 --> 00:31:00,880
+قلنا 2⁷7-1 وعرفنا ليش ناقص واحد لإن ال ones مش
+
+420
+00:31:00,880 --> 00:31:07,080
+مسموح فيها فبتطلع 127 بالنسبة لل host 2⁷24-2 برضه
+
+421
+00:31:07,080 --> 00:31:10,160
+عرفنا ليش لإن لا ال zeros مسموح فيها ولا ال ones
+
+422
+00:31:10,160 --> 00:31:17,000
+مسموح فيها فبتطلع حوالي 16777214
+
+423
+00:31:17,000 --> 00:31:22,880
+نضرب الاتنين في بعض عشان يطلع ليه total لمينبس
+
+424
+00:31:22,880 --> 00:31:26,700
+بتعيد نفس الكلام لمين؟ ل B و بتعيده كمان ل C و
+
+425
+00:31:26,700 --> 00:31:30,180
+بتجمع التلت أقام اللي بيطلعوا، لاحظوا أنه العدد
+
+426
+00:31:30,180 --> 00:31:32,380
+الأكبر في الغالب الرقم الأكبر بيطلع على class A
+
+427
+00:31:32,380 --> 00:31:38,090
+فالرقمجدش لأ مش هذا الرقم عموما هذا لحاله بطلع
+
+428
+00:31:38,090 --> 00:31:43,510
+تنين مليار تقريبا و إشي بيضل حوالي المليار و نص ل
+
+429
+00:31:43,510 --> 00:31:48,390
+class B و C مع بعض كلاهما مع بعض حسبوها جربوها
+
+430
+00:31:48,390 --> 00:31:52,690
+حسبوها لحالكم عشان يطلع في نهاية total حوالي 3.7
+
+431
+00:31:52,690 --> 00:31:57,830
+billion IP addresses طبعا الرقم هذا ماكانش كافي
+
+432
+00:31:59,340 --> 00:32:02,640
+الرقم هذا ماكانش كافي و عشان هيك كان في version 6
+
+433
+00:32:02,640 --> 00:32:09,560
+عشان هيك انتقلوا ل version 6 لأ احنا بدنا نحدد عدد
+
+434
+00:32:09,560 --> 00:32:13,760
+bits أكبر من اللي كنا مستخدمينه ل 32 لأ محتاجين
+
+435
+00:32:13,760 --> 00:32:17,260
+أكبر من هيك فهتنجرب اشي تاني و فعلا بدأوا ينتقلوا
+
+436
+00:32:17,260 --> 00:32:20,800
+لل system الجديد اللي هو ال IP address او ال
+
+437
+00:32:20,800 --> 00:32:25,120
+internet protocol version 6 اللي حاليا المعظم شغل
+
+438
+00:32:25,120 --> 00:32:26,720
+انتقله
+
+439
+00:32:28,840 --> 00:32:33,860
+تمام الآن كل الكلام اللي فات كويس بس كله كان تحت
+
+440
+00:32:33,860 --> 00:32:38,120
+كلمة كانت مكتوبة هنا disjoint task one and task
+
+441
+00:32:38,120 --> 00:32:42,420
+two are disjoint بمعنى ان هم منفصلين عن بعض مافيش
+
+442
+00:32:42,420 --> 00:32:46,400
+حلول resolutions او possibilities بتنفع لكلاهما
+
+443
+00:32:46,400 --> 00:32:50,480
+معا لكن لو ظهرت هذه الحالة انه لأ والله في حلول
+
+444
+00:32:50,480 --> 00:32:56,680
+بتنفع لل task الأولى والتانيةو انا بدي قر مثلا هل
+
+445
+00:32:56,680 --> 00:32:59,740
+يجوز ان اجمعهم و اسكت خلاص؟ طب انا في الحالة هذه
+
+446
+00:32:59,740 --> 00:33:04,720
+بالظبط معناه ذلك ان انا فعليا في مجموعة ways او
+
+447
+00:33:04,720 --> 00:33:07,240
+possibilities انجمعهم مرتين مرة من ال task الأول و
+
+448
+00:33:07,240 --> 00:33:11,340
+مرة بالنسبة للتانية احسنتوا فإذا ان انا مضطر اعمل
+
+449
+00:33:14,060 --> 00:33:17,160
+طرح لتقاطعهم معانا .. كويس فهذا هو نفسه اللي
+
+450
+00:33:17,160 --> 00:33:20,260
+هنعمله و هذا بيبين معانا إذا كان عندى .. فعلا في
+
+451
+00:33:20,260 --> 00:33:26,240
+عندى K ways أقل من .. ممكن تكون أقل من أو تساوي ..
+
+452
+00:33:26,240 --> 00:33:28,980
+يعني ممكن كل ال ways اللي بتنفع ل task 1 كلها
+
+453
+00:33:28,980 --> 00:33:33,610
+بتنفع ل task 2 .. كويس؟ف K-Header اللي هي ways of
+
+454
+00:33:33,610 --> 00:33:38,410
+doing task one also simultaneously accomplish task
+
+455
+00:33:38,410 --> 00:33:41,510
+two فإذن هي رغم إن هي بتنفع ل task one بس برضه
+
+456
+00:33:41,510 --> 00:33:45,410
+بالتزاون مع ذلك هي برضه بتنفع ك possibilities ل أو
+
+457
+00:33:45,410 --> 00:33:51,550
+إمكانية لعمل ال task two أو لأداء ال task twoتمام
+
+458
+00:33:51,550 --> 00:33:54,970
+ففي الحالة دي إيش بنسوي؟ بنقول بكل بساطة do either
+
+459
+00:33:54,970 --> 00:33:59,890
+task one or task two عبارة عن M plus N ناقص K اللي
+
+460
+00:33:59,890 --> 00:34:03,290
+قلنا عليها اللي هي التقاط والاتنين مع بعض أو ال
+
+461
+00:34:03,290 --> 00:34:07,330
+ways اللي بتنفع لكلا ال tasks لكلا ال tasks task
+
+462
+00:34:07,330 --> 00:34:10,390
+one and task two وهذه طبعا إلها مرجعية احنا
+
+463
+00:34:10,390 --> 00:34:15,270
+أخدناها لما اتكلمنا في ال sets لو متذكرين قلنا ال
+
+464
+00:34:15,270 --> 00:34:19,430
+cardinality للاتحادكان بيسوي ال cardinality للأولى
+
+465
+00:34:19,430 --> 00:34:23,150
+plus cardinality التانية ناقص التقاطع فالتقاطع هذا
+
+466
+00:34:23,150 --> 00:34:26,810
+معناه أنه بينفع لل task الأولى و بينفع
+
+467
+00:34:26,810 --> 00:34:28,910
+simultaneously لل task التانية برضه في نفس الوقت
+
+468
+00:34:28,910 --> 00:34:34,550
+فهذا يعتبر تقاطع بالنسبة لمن ل ال sets فإذا هنا
+
+469
+00:34:34,550 --> 00:34:38,210
+إذا كانت disjoint زي الطرق اللي كنا نحكيها قبل هيك
+
+470
+00:34:38,210 --> 00:34:41,710
+لأ مافيش مشكلة بيبقى مجموحمه بس مش هتطر أعمل طرح
+
+471
+00:34:41,710 --> 00:34:47,540
+ليش لأن طرحهم هيساويفالإنتجريه اللي يعني التقاط و
+
+472
+00:34:47,540 --> 00:34:54,680
+تباحهم اللي هي k هتكون five فالست هنا مفيش أو zero
+
+473
+00:34:54,680 --> 00:35:00,140
+zero لأ five اللي هي مافيش element مافيش element
+
+474
+00:35:00,140 --> 00:35:04,280
+zero elements تمام هاتنشوف أمثلة على هذا الموضوع
+
+475
+00:35:04,280 --> 00:35:08,660
+بهذا الشكل لو بدنا نقول how many bits strings of
+
+476
+00:35:08,660 --> 00:35:13,540
+length four تمام افهمنا length four ممتاز هاي
+
+477
+00:35:13,540 --> 00:35:14,120
+length four
+
+478
+00:35:16,820 --> 00:35:24,360
+طولها أربعة، ممتاز، بعدين either start with one or
+
+479
+00:35:24,360 --> 00:35:29,560
+end
+
+480
+00:35:29,560 --> 00:35:30,880
+with double zero
+
+481
+00:35:33,770 --> 00:35:37,270
+خلص قبنمسك واحدة واحدة مش هنمسكهم واحدة واحدة
+
+482
+00:35:37,270 --> 00:35:40,070
+ممتاز قبنمسكهم واحدة واحدة هالوقت خليني نبدأ في
+
+483
+00:35:40,070 --> 00:35:44,510
+الأولى الأولى اللى هو جدش عندي عدد bit string او
+
+484
+00:35:44,510 --> 00:35:49,150
+جدش عدد ال strings اللى ممكن نولدهم من اربعة digit
+
+485
+00:35:49,150 --> 00:35:55,590
+او اربعة bits الاولى منهم one تمانية اللى هم
+
+486
+00:35:55,590 --> 00:36:00,240
+الخيارات فقط للتلاتة اللى ضايلينهدولة ممكن تكون يا
+
+487
+00:36:00,240 --> 00:36:03,320
+صفر يا واحد يا صفر يا واحد يا صفر يا واحد فتنين
+
+488
+00:36:03,320 --> 00:36:10,120
+فتنين فتنين فتنين فتنين فتنين خلصناها طيب ال task
+
+489
+00:36:10,120 --> 00:36:14,260
+التاني هذه task one task
+
+490
+00:36:14,260 --> 00:36:19,900
+two هدولة محكم عليهم خلاص zeros انتهى هنا إما zero
+
+491
+00:36:19,900 --> 00:36:24,000
+one zero one فهذه عددهم أربعة في الحالة هذه فتنين
+
+492
+00:36:24,000 --> 00:36:32,030
+فتنين هذه taskتو فصار عندى تمانية زائد أربعة طيب
+
+493
+00:36:32,030 --> 00:36:36,750
+شوية اصبروا علينا في تقاطع بينهم ليش في تقاطع
+
+494
+00:36:36,750 --> 00:36:41,550
+بينهم لأنه هتلاقي مجموعة bit string هي محقق
+
+495
+00:36:41,550 --> 00:36:45,850
+الشرطين معاهممحقق الشرطين معاها فهي فعليا ان عدت
+
+496
+00:36:45,850 --> 00:36:51,070
+هنا وان عدت هنا جداش عددهم احنا لازم نفحصهم حتى لو
+
+497
+00:36:51,070 --> 00:36:53,730
+طلعوا في النهاية فيه بس انا في النهاية لازم افحصهم
+
+498
+00:36:53,730 --> 00:36:56,830
+لأنه ممكن يكونوا مشترك الاتنين مع بعض طيب عشان
+
+499
+00:36:56,830 --> 00:36:59,050
+تكون مشترك الاتنين مع بعض معناته الأولى هذه محكوم
+
+500
+00:36:59,050 --> 00:37:04,030
+عليها تكون one خلاص والاتنين
+
+501
+00:37:04,030 --> 00:37:08,950
+التاني محكوم عليهم خلاص يكونوازيروس فبقى لعندي فقط
+
+502
+00:37:08,950 --> 00:37:13,350
+الخانة التانية اللي ممكن يكون لها possibilities او
+
+503
+00:37:13,350 --> 00:37:17,590
+ways to do this فإذا يا صفر يا واحد فيا احتمالين
+
+504
+00:37:17,590 --> 00:37:27,870
+فإذا task one and task two فالحالة هذه بتساوي
+
+505
+00:37:27,870 --> 00:37:35,070
+اتنين فإذا ناقص اتنين ناقص اتنينجيد فإذا هتلاقي
+
+506
+00:37:35,070 --> 00:37:38,350
+مين اللي مجموح في الحالتين اللي هي ال 1 0 0 0 و ال
+
+507
+00:37:38,350 --> 00:37:45,570
+1 1 0 0 هدول ال two strings هدول هتلاقيهم موجودين
+
+508
+00:37:45,570 --> 00:37:48,870
+في الحالة الأولى و في التانية في كلا هما طبعا هم
+
+509
+00:37:48,870 --> 00:37:53,630
+هنا يعني حللك يهم كاملين هي التمانية للأولى وهي
+
+510
+00:37:53,630 --> 00:37:56,510
+الأربعة للتانية عشان يكتشف ان الرقم ان هدوله
+
+511
+00:37:56,510 --> 00:38:03,410
+متكررين هي واحد هي واحد وهي التاني مع التانيفإذا
+
+512
+00:38:03,410 --> 00:38:07,350
+إذا بدنا نجمحهم تمانية زيادة أربعة هتكون ال 1000
+
+513
+00:38:07,350 --> 00:38:13,490
+انجمع مرتين وال1100 برضه انجمع مرتين فإذا مضطرين
+
+514
+00:38:13,490 --> 00:38:20,950
+نطرح المرتين تاعة التكرار تبعتهالان محتاجين .. بعض
+
+515
+00:38:20,950 --> 00:38:23,490
+ال .. نحط بعض ال rules ل password على اساس انه
+
+516
+00:38:23,490 --> 00:38:26,250
+الان بدنا نعمل توليد لمجموعة passwords ال
+
+517
+00:38:26,250 --> 00:38:30,310
+passwords هذه .. هذه إلها شروط أول شرط إلها إن ال
+
+518
+00:38:30,310 --> 00:38:34,610
+password لازم تكون عبارة عن two characters long
+
+519
+00:38:34,610 --> 00:38:39,710
+فإذا خلصنا من هذا و نحط ال two characters و نشوف
+
+520
+00:38:39,710 --> 00:38:43,710
+كل الشروط الممكنة له عشان نقدر نتعامل معاه
+
+521
+00:38:49,810 --> 00:38:53,070
+password من two characters طبعا كلمة character أول
+
+522
+00:38:53,070 --> 00:38:56,370
+مرة يتكلم عنها character أول مرة بيحكي عنها ليش
+
+523
+00:38:56,370 --> 00:38:59,310
+أول مرة بيحكي عنها لأن character لها مفهوم يا إما
+
+524
+00:38:59,310 --> 00:39:02,410
+letters أو digit اللي هو decimal digit أو
+
+525
+00:39:02,410 --> 00:39:05,750
+punctuations اللي هي علامات الترقيم ال
+
+526
+00:39:05,750 --> 00:39:10,370
+punctuations هذه اللي هي علامات الترقيم ال space
+
+527
+00:39:10,370 --> 00:39:13,810
+نفسها ال S دولار العلامة المائية العلامة المئوية
+
+528
+00:39:13,810 --> 00:39:19,430
+كل الالعلامات التقييم اللي موجودة عندك دايما مع ال
+
+529
+00:39:19,430 --> 00:39:21,970
+shift و الأرقام اللي فوق ال shift مع الأرقام اللي
+
+530
+00:39:21,970 --> 00:39:27,130
+فوق كلهم هدولة عبارة عن punctuation characters طيب
+
+531
+00:39:27,130 --> 00:39:32,310
+فإذا أول شغلة two كل password لازم يكون letter,
+
+532
+00:39:32,710 --> 00:39:37,930
+digit or one of ten punctuation فإذا حكملنا ten
+
+533
+00:39:37,930 --> 00:39:42,310
+punctuation اللي هم تعون من الأرقام مع ال shiftعلى
+
+534
+00:39:42,310 --> 00:39:44,910
+الكمبيوتر shift مع مجموعة الأرقام اللي فوق اللي من
+
+535
+00:39:44,910 --> 00:39:49,570
+واحد للصفر فبيعطيك مجموعة ال punctuation هدول كويس
+
+536
+00:39:49,570 --> 00:39:52,950
+فعرفنا هنا ايش ال possibilities اللي احنا ممكن
+
+537
+00:39:52,950 --> 00:39:55,970
+نختار منهم ال password تبعنا ايش password must
+
+538
+00:39:55,970 --> 00:40:03,070
+contain at least digit or punctuation كل واحد لازم
+
+539
+00:40:03,070 --> 00:40:08,110
+يكون فيه مجموعة يا digit يا punctuation ضروري
+
+540
+00:40:08,940 --> 00:40:12,040
+كويس التاني ال digit التانية مش مشكلة تاخد اللي
+
+541
+00:40:12,040 --> 00:40:15,860
+بتاخده مش إشكال تاخد اللي بتهيأ فالآن صار عندي
+
+542
+00:40:15,860 --> 00:40:22,860
+الحقيقة two tasks task لأ الحالة الأولى و بعدين
+
+543
+00:40:22,860 --> 00:40:25,700
+بناء عليها نشوف التانية بمعنى أن الحالة الأولى هذه
+
+544
+00:40:25,700 --> 00:40:30,000
+بدك تفترض هل هي أخدت ال possibilities كلها معناة
+
+545
+00:40:30,000 --> 00:40:34,420
+ذلك أن التانية لازم تكون الاتنين بس اللي هي اما
+
+546
+00:40:35,570 --> 00:40:39,730
+digit or punctuation عشان تضمن ان في punctuation
+
+547
+00:40:39,730 --> 00:40:46,410
+وبعدين بدك تطرح منها او تجمعها على العكس تبعها ان
+
+548
+00:40:46,410 --> 00:40:50,650
+هنا punctuation وهنا كل ال letters ممكن تكون اللي
+
+549
+00:40:50,650 --> 00:40:53,930
+مسموح فيها letters اضافي لذلك بدك تطرح منهم
+
+550
+00:40:53,930 --> 00:40:56,970
+التكرارات اللي ممكن تحدث ايش التكرار اللي ممكن
+
+551
+00:40:56,970 --> 00:41:04,480
+يحدث ان الاتنين يطلعوا digit or punctuationالاتنين
+
+552
+00:41:04,480 --> 00:41:08,200
+يطلعوا زي بعض، معناته أنا جمعتهم على فرضية أنه
+
+553
+00:41:08,200 --> 00:41:11,780
+الخانة الأولى هي اللي هتحكم ليه، digit or
+
+554
+00:41:11,780 --> 00:41:16,500
+punctuation أو الخانة التانية، فانا هجمع على
+
+555
+00:41:16,500 --> 00:41:18,240
+الخانة الأولى لحاله و الخانة التانية لحاله، وبعدين
+
+556
+00:41:18,240 --> 00:41:23,640
+أطرح عدد أن الخالتين ظهر فيهم ال digit or
+
+557
+00:41:23,640 --> 00:41:27,960
+punctuationهنشوف كيف فزي ما قلنا هيها اللي هي جا
+
+558
+00:41:27,960 --> 00:41:31,320
+ال password لأ دي لأ has digit or punctuation
+
+559
+00:41:31,320 --> 00:41:36,840
+character in position one or two فإذا الشرط اللي
+
+560
+00:41:36,840 --> 00:41:41,620
+حاكمني شوية أنه لازم يكون فيه رقم أو علامة ترقيم
+
+561
+00:41:41,620 --> 00:41:44,760
+بتتعامل معها اللي هي punctuation بتتعامل معها أنه
+
+562
+00:41:44,760 --> 00:41:49,360
+ممكن تكون ظهرت في الحالة الأولى أو في اللي هي ال
+
+563
+00:41:49,360 --> 00:41:53,980
+position الأول أو ال position التانىفعملناهم كإنها
+
+564
+00:41:53,980 --> 00:41:56,920
+two problems بس بدنا ناخد بالنا إننا في الحالة هذه
+
+565
+00:41:56,920 --> 00:42:00,060
+لازم أطرح منهم إنه ممكن يظهر في الإتنين مع بعض
+
+566
+00:42:00,060 --> 00:42:03,220
+بالضبط فهي اللي صار تماما ففرضنا إن ال position
+
+567
+00:42:03,220 --> 00:42:09,700
+الأول هو اللي هيحتوي على ال digit or punctuation
+
+568
+00:42:09,700 --> 00:42:15,180
+تمام مضروبة في مين؟ في الطرف التاني اللي ممكن ياخد
+
+569
+00:42:15,800 --> 00:42:20,020
+التلت حالات طيب خلصنا منها طيب بالنسبة لل position
+
+570
+00:42:20,020 --> 00:42:23,520
+التاني هي ال position الأول هو ضربهم على طول هي 21
+
+571
+00:42:23,520 --> 00:42:29,060
+في 46 مباشرة بالنسبة لل position الأول هيعمل نفس
+
+572
+00:42:29,060 --> 00:42:32,280
+الكلام لل position التاني نفس الشيء برضه لل
+
+573
+00:42:32,280 --> 00:42:36,120
+position التاني بحيث انه يجمعهم مع بعض فصارت عندك
+
+574
+00:42:36,120 --> 00:42:39,180
+الرقم هذا جدش لما بدربوا حوالي تسعمية و اشي تسعمية
+
+575
+00:42:39,180 --> 00:42:46,000
+و عشريناللي هو ال punctuation أو ال digit ظهرت في
+
+576
+00:42:46,000 --> 00:42:49,940
+الخانة أو في ال position الأول زائد انها ظهرت في
+
+577
+00:42:49,940 --> 00:42:53,520
+ال position التاني طيب استنى في ناقص انه ممكن تكون
+
+578
+00:42:53,520 --> 00:42:56,620
+ظهرت في الحالتين في ال two positions فقداش
+
+579
+00:42:56,620 --> 00:42:59,720
+احتماليتها هذه احتماليتها او possibilities تعتها
+
+580
+00:42:59,720 --> 00:43:01,900
+ان يكون عندى عشرين
+
+581
+00:43:04,670 --> 00:43:08,810
+وهنا برضه اشرين فبتطلع ناقص اربعمية فبطلع totally
+
+582
+00:43:08,810 --> 00:43:15,250
+كله على بعض حوالي الف واربعمية واربعين كعدد
+
+583
+00:43:15,250 --> 00:43:18,930
+possibilities لل password في الحالة دي في ال
+
+584
+00:43:18,930 --> 00:43:24,530
+password الحالي طيب كمان أمثلة لو عندك مطلوب find
+
+585
+00:43:24,530 --> 00:43:29,520
+the number of three letter initialswhere none of
+
+586
+00:43:29,520 --> 00:43:33,260
+the letters is repeated طيب هذه أبسط منهم يعني
+
+587
+00:43:33,260 --> 00:43:39,680
+بسيطة جدا تلاتة لمجموعة حروف بشرط إنه إذا اخترنا
+
+588
+00:43:39,680 --> 00:43:43,740
+حرف في الخانة الأولى مايتكررش في التانية والأول
+
+589
+00:43:43,740 --> 00:43:47,720
+والتاني مايتكررش في التالتة خلاص فإذا هنا عندي ستة
+
+590
+00:43:47,720 --> 00:43:51,080
+وعشرين هنا بتصير ال possibilities فقط خمسة وعشرين
+
+591
+00:44:02,770 --> 00:44:09,480
+محتاجة كلام كتير؟سؤال direct هذا سريع قداش عدد ال
+
+592
+00:44:09,480 --> 00:44:14,740
+strings اللي بتقدر تاخدهم من string طوله أربعة
+
+593
+00:44:14,740 --> 00:44:18,560
+bits اتنين تثابر أربعة وانتهت الجثة طيب السؤال
+
+594
+00:44:18,560 --> 00:44:22,860
+اللي ورا count the number of bit strings length
+
+595
+00:44:22,860 --> 00:44:28,540
+four or less or less معناته بدك تجمع صارت task
+
+596
+00:44:28,540 --> 00:44:33,020
+مختلف عن بعض length four length three length two
+
+597
+00:44:33,020 --> 00:44:39,110
+length one check بدك تجمحهممع بعض فبنجمحهم بحيث
+
+598
+00:44:39,110 --> 00:44:43,650
+انه هيها اذا كانت ال length تبعنا واحد زائد اذا
+
+599
+00:44:43,650 --> 00:44:46,690
+كان ال length اتنين زائد اذا كانت تلاتة زائد اذا
+
+600
+00:44:46,690 --> 00:44:54,270
+كانت اربعة بس خلص تمام كمان مثال اه هذا مثال كويس
+
+601
+00:44:54,270 --> 00:44:59,510
+هاي مثال منيح كان ذا 6S of three digit numbers
+
+602
+00:44:59,510 --> 00:45:04,490
+مكون من three digit numbers خليا هو نفس المثال
+
+603
+00:45:04,490 --> 00:45:06,150
+تبعنا هاي three digit number
+
+604
+00:45:11,090 --> 00:45:17,470
+أيش مطلوب في three digit number which begin or end
+
+605
+00:45:17,470 --> 00:45:26,410
+with an even digit بيبدأ أو بينتهي ب even بس هي كل
+
+606
+00:45:26,410 --> 00:45:30,670
+المطلوب فبدنا نعرف قداش عدد الأرقام اللي مكونة من
+
+607
+00:45:30,670 --> 00:45:38,680
+ثلاث خانات وبتبدأ أو بتنتهي بdigit او integer even
+
+608
+00:45:38,680 --> 00:45:42,620
+ال integer ده عبارة عن even خلّيني شوي شوي ناخدهم
+
+609
+00:45:42,620 --> 00:45:48,560
+نبدأ بالأول و التاني و التالت نبدأ بال begin لأنه
+
+610
+00:45:48,560 --> 00:45:54,300
+begin هيها begin و بعدها في or ثم end with an even
+
+611
+00:45:54,300 --> 00:45:58,980
+صحيح فنبدأها or و بعدها نجمّل اتنينصحيح؟ انجمّلتن،
+
+612
+00:45:58,980 --> 00:46:02,340
+بس بدنا ناخد بالنا، بدنا نطرح، بعدين تقطحن، بس
+
+613
+00:46:02,340 --> 00:46:07,720
+ناخد حاجة حاجة هالوقت لما نقول بدي أبدأ ب even هل
+
+614
+00:46:07,720 --> 00:46:14,800
+يجوز أني أبدأ بصفر؟ في خانة المئات، في الحالة هذه
+
+615
+00:46:14,800 --> 00:46:19,980
+أنت بطلت three digit number صارت two digit number
+
+616
+00:46:19,980 --> 00:46:24,640
+صحيح؟ بمعنى أنه صفر تسعة وتسعين صفر تسعة وتسعين لأ
+
+617
+00:46:24,640 --> 00:46:30,020
+هي تسعة وتسعينتسعة وتسعين هي فعليا فإذا ماتظبطش
+
+618
+00:46:30,020 --> 00:46:33,900
+إذا ال possibilities لخانة المئات هنا خانة المئات
+
+619
+00:46:33,900 --> 00:46:39,560
+لأ بتبدأ من اتنين فإذا اتنين اربعة ستة تمانية
+
+620
+00:46:39,560 --> 00:46:45,720
+أربعة هاي الأربعة تعتنا مافيش فيها مشكلة هنا
+
+621
+00:46:45,720 --> 00:46:50,760
+العشرة كاملين من الصفر للتسعة صفر للتسعة يجوز و
+
+622
+00:46:50,760 --> 00:46:53,480
+هنا برضه من الصفر للتسعة يجوز مافيش عندي مشكلة
+
+623
+00:46:53,480 --> 00:46:55,220
+فعشرة عشرة
+
+624
+00:46:58,610 --> 00:47:05,890
+هي الحالة الأولى اللى هى begin طيب الحالة التانية
+
+625
+00:47:05,890 --> 00:47:09,830
+اللى
+
+626
+00:47:09,830 --> 00:47:16,450
+هى end with even عشان
+
+627
+00:47:16,450 --> 00:47:22,190
+نقول انتهت ب even أول اشي نفسك هدى تسعة لأن هدى
+
+628
+00:47:22,190 --> 00:47:27,690
+هتكون من واحد لتسعةمن واحد لتسعة فعليا تمام هنا
+
+629
+00:47:27,690 --> 00:47:32,650
+هيكون عندك عشرة فهنا هيكون جداش تسعة مظبوطين وهنا
+
+630
+00:47:32,650 --> 00:47:38,230
+هيكون عددهم خمسة عشان نخلص فيهم فهنا صارت تسعة في
+
+631
+00:47:38,230 --> 00:47:47,110
+عشرة في خمسة هذا اللي هي end with even طيب بين هذا
+
+632
+00:47:47,110 --> 00:47:52,010
+وهذا في أقام اتكررتفي أرقام تكررت معناه ذلك أنه
+
+633
+00:47:52,010 --> 00:47:55,930
+أنا محتاج أطرح منهم محتاجين و لازم نطرح منهم
+
+634
+00:47:55,930 --> 00:48:07,650
+تقاطؤهم بالضبط هذه الأربعة وهذه الخمسة خلاص
+
+635
+00:48:07,650 --> 00:48:10,770
+تضربهم فعلا و تطرحهم من مجموع الدربين اللي قدامك
+
+636
+00:48:10,770 --> 00:48:14,450
+هنا فهذه أربعة في عشرة في خمسة
+
+637
+00:48:20,300 --> 00:48:23,760
+فبطلع هى الأربعة فى عشرة فى خمسة بطلع عندك هنا
+
+638
+00:48:23,760 --> 00:48:31,780
+أربعمية والتانى أربعمية وخمسين والتالتة متين فهدى
+
+639
+00:48:31,780 --> 00:48:37,660
+زائد هدى ناقص هدى فبطلع عندك ستمية وتسعين أقل
+
+640
+00:48:37,660 --> 00:48:45,700
+ستمية وخمسين رقم بيحققوا هذا الشرط تمام الآن فى
+
+641
+00:48:45,700 --> 00:48:49,730
+عندنا حاجة مهمة كتير برضه خلّيكم معناها يا شباببعد
+
+642
+00:48:49,730 --> 00:48:53,490
+ما خلصنا مجموعة أنثى بالعد اتوقع كانت فيها حاجات
+
+643
+00:48:53,490 --> 00:48:59,010
+حلوة مسلية حركت دماغكوا شوية هتننطقل لحاجة اسهل
+
+644
+00:48:59,010 --> 00:49:05,450
+منها كمان ال vision هو ال principle او مبدأ فتحات
+
+645
+00:49:05,450 --> 00:49:11,100
+الحمام ابراج الحمام ابراج الحمام عبارة عن برجسمنتي
+
+646
+00:49:11,100 --> 00:49:13,940
+أو طين أو اشي و بيكون فيه فتحات لمين عشان تتخبى
+
+647
+00:49:13,940 --> 00:49:20,300
+فيه ال .. ال pigeons أو الحمام كويس إذا كان عندى
+
+648
+00:49:20,300 --> 00:49:24,280
+.. هذا طبعا مافيش بنستخدمها كنظرية بنستخدمها إذا
+
+649
+00:49:24,280 --> 00:49:29,060
+كان عندك عدد أكبر من k plus one objects أشياء
+
+650
+00:49:29,060 --> 00:49:33,420
+عددها أكبر من k زائد واحد في حين إن انت عندك عدد k
+
+651
+00:49:33,420 --> 00:49:39,090
+places أو الأماكن عددهم kعددهم K فمعنى ذلك أنت
+
+652
+00:49:39,090 --> 00:49:43,670
+بتكون ضامن هنا أنه على الأقل يوجد مكان فيه أكتر من
+
+653
+00:49:43,670 --> 00:49:47,590
+object مش هيك؟ إذا عدد ال objects أكتر من عدد
+
+654
+00:49:47,590 --> 00:49:52,610
+الأماكن فمعنى ذلك أنه بالضرورة هيكون one object at
+
+655
+00:49:52,610 --> 00:49:57,530
+least فيه at least أكتر من one object ممكن يكون
+
+656
+00:49:57,530 --> 00:50:00,770
+تلتة، خمسة، عشرة جد ما يكون يكون ليش؟ لأنه ممكن
+
+657
+00:50:00,770 --> 00:50:05,800
+يكون في places تانية ومافيش فيها مافيش فيهاو هذا
+
+658
+00:50:05,800 --> 00:50:10,260
+ما ينطبق على فعلًا أبراج الحمام أحيانًا هتلاقي إنه
+
+659
+00:50:10,260 --> 00:50:15,240
+في الصيف هيكونوا بعيد عن بعض كل واحد في hall لحاله
+
+660
+00:50:15,240 --> 00:50:19,840
+لكن في الشتاء هيسيبوا مجموعة halls فاضية و يدفوا
+
+661
+00:50:19,840 --> 00:50:26,880
+بعض لأن الدنيا بارد الدنيا؟ خلاص
+
+662
+00:50:26,880 --> 00:50:32,560
+صح طب كويس أنتوا أدرم إذا إلكوا في الجثة إذا إلكوا
+
+663
+00:50:32,560 --> 00:50:37,680
+في الجثةطيب كيف نقدر نعبر عن هذا الكلام .. هاي
+
+664
+00:50:37,680 --> 00:50:40,060
+شباب .. كيف نقدر نعبر عنه بال function و احنا
+
+665
+00:50:40,060 --> 00:50:43,440
+أخدنا function سابقا نقدر نقول إذا كانت if ال
+
+666
+00:50:43,440 --> 00:50:49,000
+function from A to B .. from A to B بحيث أنه A
+
+667
+00:50:49,000 --> 00:50:53,600
+أكبر من B زائد 1 بمعنى إن هي من ال domain و ال
+
+668
+00:50:53,600 --> 00:50:58,300
+domain هذا هي ال objects لالـ places و ال places
+
+669
+00:50:58,300 --> 00:51:01,880
+أقل من ال a ال code domain أقل من ال a فمعنى ذلك
+
+670
+00:51:01,880 --> 00:51:04,700
+تقدر تقول ان ال cardinality ل a أكبر من أو يساوي
+
+671
+00:51:04,700 --> 00:51:09,960
+ال cardinality ل b plus one plus one فهنا إذا some
+
+672
+00:51:09,960 --> 00:51:16,700
+element of b has more than two or equal to three
+
+673
+00:51:16,700 --> 00:51:22,590
+imagesunder if اكيد اكيد فمعنى ذلك انه دائما
+
+674
+00:51:22,590 --> 00:51:26,670
+بنظرية ال vision hole principle اكيد هذه not one
+
+675
+00:51:26,670 --> 00:51:32,230
+to one اكيد not one to one هذا sure تمام طبعا هنا
+
+676
+00:51:32,230 --> 00:51:37,090
+شايفين بعض امثلة الفكرة طول ما احنا بنتكلم عن
+
+677
+00:51:37,090 --> 00:51:42,170
+اتناشر hole و عندك تلتاشر visions معنى ذلك انه
+
+678
+00:51:42,170 --> 00:51:46,450
+لازم هتلاقي two visions at least موجودين في one
+
+679
+00:51:46,450 --> 00:51:47,110
+place
+
+680
+00:51:49,930 --> 00:51:53,090
+طيب أمثلتها زي أن نقول والله إذا كان في أند مية
+
+681
+00:51:53,090 --> 00:52:02,310
+واحد grades, numerical grades كويس مش يعني name
+
+682
+00:52:02,310 --> 00:52:06,410
+grades اللي هي a و b و c لأ numerical بمعنى واحد
+
+683
+00:52:06,410 --> 00:52:10,460
+ماخد صفر من ميةواحد من مية اتنين من مية اللي عندك
+
+684
+00:52:10,460 --> 00:52:15,220
+مية في المية فانت بتتكلم عن مية و واحد تقييم رقمي
+
+685
+00:52:15,220 --> 00:52:19,780
+من مية فاللي هي من صفر لمية ففي الحالة اذا كان
+
+686
+00:52:19,780 --> 00:52:23,920
+عندك اكتر من مية و واحد students in this class
+
+687
+00:52:23,920 --> 00:52:27,760
+معناته على الاقل فيه اتنين ماخدين نفس ل grade نفس
+
+688
+00:52:27,760 --> 00:52:30,160
+ل grade فانت بتعرف على طول انه فيه اتنين على الاقل
+
+689
+00:52:30,160 --> 00:52:32,620
+ماخدين نفس ل grade طبعا اكيد ال function هنا هتكون
+
+690
+00:52:32,620 --> 00:52:36,880
+ايش not one to onenot one two one الكلام بسيط و
+
+691
+00:52:36,880 --> 00:52:40,420
+sit down و شهد طيب كمان أمثلة هيك سريعة among any
+
+692
+00:52:40,420 --> 00:52:44,840
+group of three hundred sixty seven اذا كان والله
+
+693
+00:52:44,840 --> 00:52:48,100
+عندك مجموعة فيها من الناس تلاتمية سبعة و ستين
+
+694
+00:52:48,100 --> 00:52:51,960
+معناه ذلك انه انت متأكد تماما ان في اتنين على
+
+695
+00:52:51,960 --> 00:52:55,610
+الأقل مولودين في نفس اليوممئة بالمئة بالظبط
+
+696
+00:52:55,610 --> 00:53:00,010
+متأكدين تماما طيب إذا كان في عندك سبعة إجروب من
+
+697
+00:53:00,010 --> 00:53:03,270
+سبعة و عشرين كلمة بال English معناه ذلك إن انت
+
+698
+00:53:03,270 --> 00:53:07,870
+ضامن at least في عندك two words بدئين بنفس الحرف
+
+699
+00:53:07,870 --> 00:53:12,750
+أكيد طيب how many people must be selected from a
+
+700
+00:53:12,750 --> 00:53:17,010
+collection of fifteen married couples to ensure
+
+701
+00:53:17,010 --> 00:53:22,610
+that at least two of persons chosen are married to
+
+702
+00:53:22,610 --> 00:53:23,350
+each other
+
+703
+00:53:27,410 --> 00:53:34,990
+هنا بنتكلم عن خمستاشر couple خمستاشر couple هدولة
+
+704
+00:53:34,990 --> 00:53:38,990
+أزواج
+
+705
+00:53:38,990 --> 00:53:43,750
+أزواج يعني couples انت بتتكلم عن أزواج مع بعض كويس
+
+706
+00:53:43,750 --> 00:53:51,510
+فانت عندك من واحد اتنين لعند خمستاشر كويس و هتبدأ
+
+707
+00:53:51,510 --> 00:53:56,960
+تعمل لعبة انك تختار أفرادتختار أفراد كويس اختارنا
+
+708
+00:53:56,960 --> 00:54:00,360
+واحد اتنين تلاتة و احنا جديد بنطلع اللعبة مجموعة
+
+709
+00:54:00,360 --> 00:54:03,700
+يلعبوا طب انت بتضمن انه او جديش عدد الاختيارات
+
+710
+00:54:03,700 --> 00:54:06,920
+اللي لازم تختارها عشان تضمن مائة بالمائة ان اللي
+
+711
+00:54:06,920 --> 00:54:11,960
+اختارتهم فيهم اتنين couple أكيد ليش لأنه أسوأ
+
+712
+00:54:11,960 --> 00:54:16,820
+احتمال ممكن انك انت جاعد بتختار و جاعدين بتطلع one
+
+713
+00:54:16,820 --> 00:54:20,540
+من ال couple بس ال one الأول التاني التالت الرابع
+
+714
+00:54:20,540 --> 00:54:25,790
+عددهم جديش خمستاشرلسوء حظك إنه قعدت بتختار طلعوا
+
+715
+00:54:25,790 --> 00:54:31,690
+الخمستاش مختلفين عن بعض رقم ستاش sure بده يكون ال
+
+716
+00:54:31,690 --> 00:54:35,810
+couple تبعه اختارناه قبله مش هيك فإذا أكيد ستاشر
+
+717
+00:54:35,810 --> 00:54:39,730
+persons مائة بالمائة حكون ضمنة إنه at least في one
+
+718
+00:54:39,730 --> 00:54:45,550
+couple تم اختيارهم مش هيك منطقي أكيد أكيد أكيد جدا
+
+719
+00:54:45,550 --> 00:54:51,650
+مش واضحةعندك خمستاشر قبل، قبل يعني إيش؟ زوج و زوجة
+
+720
+00:54:51,650 --> 00:54:54,990
+هى الموجودين هنا و هى التانى و هى التالت و هى الخ
+
+721
+00:54:54,990 --> 00:54:58,410
+.. لعندك الخمستاشر، كويس؟ طبعا في النهاية لما بدنا
+
+722
+00:54:58,410 --> 00:55:01,990
+نختار، بختارش القبل مع بعضه، بختار one person
+
+723
+00:55:01,990 --> 00:55:07,730
+فمعنى ذلك أن عدد ال persons جداش؟ تلاتين، تلاتين،
+
+724
+00:55:07,730 --> 00:55:12,490
+طيب بدأنا نختار أسماء منهم، بالورقة و لها ده و
+
+725
+00:55:12,490 --> 00:55:19,120
+قعدنا نطلع و نسحبانت بأضمن ان اللي اخترتهم يوجد
+
+726
+00:55:19,120 --> 00:55:24,360
+فعلا فيهم at least one couple طيب أسوأ حاجة ان
+
+727
+00:55:24,360 --> 00:55:29,260
+اختار خمستاشر واحد مافيش ولا واحد couple مع التاني
+
+728
+00:55:29,260 --> 00:55:33,020
+ال 16 إجباري لازم هيكون couple مع واحد من
+
+729
+00:55:33,020 --> 00:55:38,780
+الخمستاشر اللي اخترتهم جابله تمام؟ تمام خلاص هذه
+
+730
+00:55:38,780 --> 00:55:41,180
+خليها للمرة القادمة ان شاء الله بنكملها
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..cded560c73dede2904e3291ae781187e25e03d72
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3319, "start": 5.13, "end": 33.19, "text": "طيب بسم الله الرحمن الرحيم يعطيكوا العفو يا شباب نكمل اليوم في مساق ال discrete اليوم عندنا موضوع جديد بعد ما كنا خلصنا ال induction أخدناها المرة اللي فاتت و شوفنا ال basis step و ال inductive step ثم تحدثنا منها عن ال recursion ال recursion شوفنا كيف بيصير في recurrence ل ال function من نفسها فاليوم هنتكلم عن ال counting أو العد", "tokens": [9566, 1829, 3555, 4724, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 37495, 9566, 1829, 4117, 14407, 18863, 5172, 2407, 35186, 13412, 3555, 16758, 8717, 24793, 1211, 45595, 20498, 8978, 47524, 995, 4587, 2423, 27706, 45595, 20498, 43242, 8315, 3714, 2407, 11242, 45367, 10874, 16254, 3215, 39182, 19446, 9122, 8315, 16490, 1211, 9381, 8315, 2423, 33371, 5551, 9778, 3215, 8315, 11296, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 4032, 13412, 38688, 8315, 2423, 5143, 1823, 4032, 2423, 31612, 488, 1823, 38637, 2304, 6055, 24401, 12984, 8315, 9154, 11296, 18871, 2423, 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تسعتاش فسبعة و خمسين projects فانت عندك سبعة و خمسين possibility to choose your project عشان تختار ال project تبعك عندك إمكانية إمكانيات اختيار بتصل لسبعة و خمسين اختيار طيب suppose فالتاني suppose statement labels محتاجين نعمل label", "tokens": [4318, 1020, 36764, 24401, 6156, 28814, 15730, 8978, 21542, 6027, 3660, 11778, 1829, 4724, 28820, 4724, 3794, 41193, 3660, 2423, 3217, 39896, 30544, 6055, 1211, 9307, 3660, 4032, 6225, 46309, 9957, 16490, 2304, 3794, 6225, 46309, 6055, 3794, 34268, 33599, 6156, 35457, 27884, 4032, 16490, 2304, 3794, 9957, 4455, 6156, 7649, 2655, 43242, 4117, 8608, 3555, 27884, 4032, 16490, 2304, 3794, 9957, 7959, 281, 2826, 428, 1716, 6225, 8592, 7649, 6055, 46456, 9640, 2423, 1716, 6055, 3555, 3615, 4117, 43242, 4117, 11933, 2304, 41361, 10632, 11933, 2304, 41361, 1829, 9307, 1975, 9778, 31371, 9640, 39894, 36520, 5296, 35457, 27884, 4032, 16490, 2304, 3794, 9957, 1975, 9778, 31371, 9640, 23032, 1829, 3555, 7297, 6156, 6027, 2655, 7649, 1829, 7297, 5629, 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" أو", "probability": 0.87939453125}, {"start": 867.11, "end": 867.21, "word": " ال", "probability": 0.962890625}, {"start": 867.21, "end": 867.45, "word": " task", "probability": 0.88525390625}, {"start": 867.45, "end": 867.73, "word": " هذه", "probability": 0.2412109375}, {"start": 867.73, "end": 867.89, "word": " هي", "probability": 0.3984375}, {"start": 867.89, "end": 868.31, "word": " منفصلة", "probability": 0.9251708984375}, {"start": 868.31, "end": 868.61, "word": " تماما", "probability": 0.986328125}, {"start": 868.61, "end": 868.71, "word": " عن", "probability": 0.8798828125}, {"start": 868.71, "end": 868.77, "word": " ال", "probability": 0.96142578125}, {"start": 868.77, "end": 868.95, "word": " task", "probability": 0.92626953125}, {"start": 868.95, "end": 869.13, "word": " هذه", "probability": 0.91796875}, {"start": 869.13, "end": 869.77, "word": " ليش؟", "probability": 0.7019856770833334}, {"start": 869.77, "end": 870.21, "word": " لأنه", "probability": 0.7450358072916666}, {"start": 870.21, "end": 870.43, "word": " مدام", "probability": 0.7970377604166666}, {"start": 870.43, "end": 870.63, "word": " هي", "probability": 0.798828125}, {"start": 870.63, "end": 871.43, "word": " and", "probability": 0.392578125}, {"start": 871.43, "end": 871.71, "word": " with", "probability": 0.89208984375}, {"start": 871.71, "end": 872.19, "word": " five", "probability": 0.626953125}, {"start": 872.19, "end": 872.55, "word": " معناتي", "probability": 0.8899739583333334}, {"start": 872.55, "end": 872.71, "word": " هي", "probability": 0.408935546875}, {"start": 872.71, "end": 873.09, "word": " odd", "probability": 0.8427734375}, {"start": 873.09, "end": 874.07, "word": " مستحيل", "probability": 0.93505859375}, {"start": 874.07, "end": 874.31, "word": " تكون", "probability": 0.970458984375}, {"start": 874.31, "end": 874.61, "word": " even", "probability": 0.93017578125}, {"start": 874.61, "end": 875.29, "word": " فإذا", "probability": 0.7906901041666666}, {"start": 875.29, "end": 875.49, "word": " أنا", "probability": 0.86865234375}, {"start": 875.49, "end": 875.79, "word": " ضامن", "probability": 0.718505859375}, {"start": 875.79, "end": 875.89, "word": " إن", "probability": 0.7666015625}, {"start": 875.89, "end": 876.37, "word": " المجموعة", "probability": 0.85849609375}, {"start": 876.37, "end": 877.39, "word": " الخمسين", "probability": 0.80413818359375}, {"start": 877.39, "end": 877.67, "word": " هنا", "probability": 0.9853515625}, {"start": 877.67, "end": 878.13, "word": " مافيش", "probability": 0.89990234375}, {"start": 878.13, "end": 878.35, "word": " فيهم", "probability": 0.97509765625}, {"start": 878.35, "end": 878.57, "word": " ولا", "probability": 0.52099609375}, {"start": 878.57, "end": 879.17, "word": " رقم", "probability": 0.99560546875}, {"start": 879.17, "end": 879.33, "word": " من", "probability": 0.99365234375}, {"start": 879.33, "end": 879.79, "word": " العشرة", "probability": 0.95458984375}, {"start": 879.79, "end": 880.47, "word": " والعشر", "probability": 0.7776692708333334}, {"start": 880.47, "end": 880.63, "word": " هدول", "probability": 0.7120768229166666}, {"start": 880.63, "end": 880.87, "word": " برضه", "probability": 0.8704427083333334}, {"start": 880.87, "end": 881.19, "word": " مافيش", "probability": 0.96923828125}, {"start": 881.19, "end": 881.39, "word": " فيهم", "probability": 0.971435546875}, {"start": 881.39, "end": 881.55, "word": " ولا", "probability": 0.83203125}, {"start": 881.55, "end": 881.81, "word": " رقم", "probability": 0.9954427083333334}, {"start": 881.81, "end": 881.95, "word": " من", "probability": 0.99365234375}, {"start": 881.95, "end": 882.77, "word": " الخمسين", "probability": 0.908447265625}, {"start": 882.77, "end": 883.05, "word": " هدول", "probability": 0.8834635416666666}, {"start": 883.05, "end": 883.71, "word": " فإذا", "probability": 0.8732096354166666}, {"start": 883.71, "end": 884.59, "word": " بنجمحهم", "probability": 0.86318359375}, {"start": 884.59, "end": 885.03, "word": " لأنه", "probability": 0.79833984375}, {"start": 885.03, "end": 885.93, "word": " disjoint", "probability": 0.804931640625}, {"start": 885.93, "end": 886.59, "word": " حتى", "probability": 0.9384765625}, {"start": 886.59, "end": 886.77, "word": " الآن", "probability": 0.731689453125}, {"start": 886.77, "end": 886.95, "word": " اللي", "probability": 0.919921875}, {"start": 886.95, "end": 887.39, "word": " اتكلمنا", "probability": 0.9009765625}, {"start": 887.39, "end": 887.59, "word": " عنها", "probability": 0.9912109375}, {"start": 887.59, "end": 887.69, "word": " اللي", "probability": 0.91650390625}, {"start": 887.69, "end": 887.79, "word": " هي", "probability": 0.865234375}, {"start": 887.79, "end": 888.25, "word": " disjoint", "probability": 0.645263671875}], "temperature": 1.0}, {"id": 40, "seek": 91361, "start": 889.01, "end": 913.61, "text": "تمام كمان مثال how many different pit strings .. strings of length seven are there؟ مافيش فيها كتير برضه مشكلة جدش بتعمل عدد strings من عدد digits سبعة", "tokens": [39237, 10943, 9122, 2304, 7649, 50113, 6027, 577, 867, 819, 10147, 13985, 4386, 13985, 295, 4641, 3407, 366, 456, 22807, 19446, 41185, 8592, 8978, 11296, 9122, 2655, 13546, 4724, 43042, 3224, 37893, 28820, 3660, 10874, 3215, 8592, 39894, 25957, 1211, 6225, 3215, 3215, 13985, 9154, 6225, 3215, 3215, 27011, 8608, 3555, 27884], "avg_logprob": -0.16922170036243941, "compression_ratio": 1.3037974683544304, "no_speech_prob": 0.0, "words": [{"start": 889.01, "end": 889.43, "word": "تمام", "probability": 0.93212890625}, {"start": 889.43, "end": 890.55, "word": " كمان", "probability": 0.8059895833333334}, {"start": 890.55, "end": 892.07, "word": " مثال", "probability": 0.90625}, {"start": 892.07, "end": 896.43, "word": " how", "probability": 0.62158203125}, {"start": 896.43, "end": 896.63, "word": " many", "probability": 0.90869140625}, {"start": 896.63, "end": 896.95, "word": " different", "probability": 0.9033203125}, {"start": 896.95, "end": 897.15, "word": " pit", "probability": 0.288330078125}, {"start": 897.15, "end": 897.67, "word": " strings", "probability": 0.82568359375}, {"start": 897.67, "end": 897.69, "word": " ..", "probability": 0.400634765625}, {"start": 897.69, "end": 898.33, "word": " strings", "probability": 0.91796875}, {"start": 898.33, "end": 898.57, "word": " of", "probability": 0.98291015625}, {"start": 898.57, "end": 898.89, "word": " length", "probability": 0.80908203125}, {"start": 898.89, "end": 900.53, "word": " seven", "probability": 0.77099609375}, {"start": 900.53, "end": 901.01, "word": " are", "probability": 0.9658203125}, {"start": 901.01, "end": 902.19, "word": " there؟", "probability": 0.63916015625}, {"start": 902.19, "end": 902.67, "word": " مافيش", "probability": 0.8001302083333334}, {"start": 902.67, "end": 902.85, "word": " فيها", "probability": 0.983642578125}, {"start": 902.85, "end": 903.05, "word": " كتير", "probability": 0.9850260416666666}, {"start": 903.05, "end": 903.29, "word": " برضه", "probability": 0.9622395833333334}, {"start": 903.29, "end": 904.71, "word": " مشكلة", "probability": 0.9290364583333334}, {"start": 904.71, "end": 906.61, "word": " جدش", "probability": 0.7163899739583334}, {"start": 906.61, "end": 907.01, "word": " بتعمل", "probability": 0.9728190104166666}, {"start": 907.01, "end": 907.55, "word": " عدد", "probability": 0.978515625}, {"start": 907.55, "end": 907.99, "word": " strings", "probability": 0.849609375}, {"start": 907.99, "end": 908.31, "word": " من", "probability": 0.99755859375}, {"start": 908.31, "end": 909.81, "word": " عدد", "probability": 0.9879557291666666}, {"start": 909.81, "end": 910.33, "word": " digits", "probability": 0.9306640625}, {"start": 910.33, "end": 913.61, "word": " سبعة", "probability": 0.9220377604166666}], "temperature": 1.0}, {"id": 41, "seek": 93797, "start": 918.47, "end": 937.97, "text": "كل واحدة منهم لحالهم هدولة إيش ال possibility بتاعتها اتنين، يا صفر يا واحد، فإذا هذه يا صفر يا واحد، فإذا ال possibility بتاعتها اتنين، طيب ال possibility بتاعة التانية برضه يا صفر يا واحد، فإذا برضه اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين", "tokens": [28820, 36764, 24401, 3660, 9154, 16095, 5296, 5016, 6027, 16095, 8032, 3215, 12610, 3660, 11933, 1829, 8592, 2423, 7959, 39894, 995, 34268, 11296, 1975, 2655, 1863, 9957, 12399, 35186, 20328, 5172, 2288, 35186, 36764, 24401, 12399, 6156, 28814, 15730, 29538, 35186, 20328, 5172, 2288, 35186, 36764, 24401, 12399, 6156, 28814, 15730, 2423, 7959, 39894, 995, 34268, 11296, 1975, 2655, 1863, 9957, 12399, 23032, 1829, 3555, 2423, 7959, 39894, 995, 27884, 16712, 7649, 10632, 4724, 43042, 3224, 35186, 20328, 5172, 2288, 35186, 36764, 24401, 12399, 6156, 28814, 15730, 4724, 43042, 3224, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 12399, 1975, 2655, 1863, 9957], "avg_logprob": -0.08388888782925076, "compression_ratio": 4.503311258278146, "no_speech_prob": 1.1861324310302734e-05, "words": [{"start": 918.47, "end": 918.87, "word": "كل", "probability": 0.798828125}, {"start": 918.87, "end": 919.41, "word": " واحدة", "probability": 0.9694010416666666}, {"start": 919.41, "end": 919.71, "word": " منهم", "probability": 0.950439453125}, {"start": 919.71, "end": 920.23, "word": " لحالهم", "probability": 0.96142578125}, {"start": 920.23, "end": 921.03, "word": " هدولة", "probability": 0.76904296875}, {"start": 921.03, "end": 921.89, "word": " إيش", "probability": 0.7298177083333334}, {"start": 921.89, "end": 921.99, "word": " ال", "probability": 0.521484375}, {"start": 921.99, "end": 922.37, "word": " possibility", "probability": 0.97119140625}, {"start": 922.37, "end": 922.77, "word": " بتاعتها", "probability": 0.9000244140625}, {"start": 922.77, "end": 923.23, "word": " اتنين،", "probability": 0.683837890625}, {"start": 923.23, "end": 923.35, "word": " يا", "probability": 0.50830078125}, {"start": 923.35, "end": 923.63, "word": " صفر", "probability": 0.95458984375}, {"start": 923.63, "end": 923.73, "word": " يا", "probability": 0.84033203125}, {"start": 923.73, "end": 924.31, "word": " واحد،", "probability": 0.8797200520833334}, {"start": 924.31, "end": 924.55, "word": " فإذا", "probability": 0.88427734375}, {"start": 924.55, "end": 924.79, "word": " هذه", "probability": 0.29638671875}, {"start": 924.79, "end": 924.95, "word": " يا", "probability": 0.8994140625}, {"start": 924.95, "end": 925.27, "word": " صفر", "probability": 0.99072265625}, {"start": 925.27, "end": 925.51, "word": " يا", "probability": 0.9033203125}, {"start": 925.51, "end": 925.91, "word": " واحد،", "probability": 0.9236653645833334}, {"start": 925.91, "end": 926.13, "word": " فإذا", "probability": 0.9659830729166666}, {"start": 926.13, "end": 926.23, "word": " ال", "probability": 0.9248046875}, {"start": 926.23, "end": 926.57, "word": " possibility", "probability": 0.9443359375}, {"start": 926.57, "end": 926.99, "word": " بتاعتها", "probability": 0.9090576171875}, {"start": 926.99, "end": 928.13, "word": " اتنين،", "probability": 0.87216796875}, {"start": 928.13, "end": 928.39, "word": " طيب", "probability": 0.9513346354166666}, {"start": 928.39, "end": 928.57, "word": " ال", "probability": 0.8564453125}, {"start": 928.57, "end": 928.93, "word": " possibility", "probability": 0.98095703125}, {"start": 928.93, "end": 929.21, "word": " بتاعة", "probability": 0.81689453125}, {"start": 929.21, "end": 929.77, "word": " التانية", "probability": 0.9705403645833334}, {"start": 929.77, "end": 930.73, "word": " برضه", "probability": 0.8479817708333334}, {"start": 930.73, "end": 930.87, "word": " يا", "probability": 0.90625}, {"start": 930.87, "end": 931.15, "word": " صفر", "probability": 0.99267578125}, {"start": 931.15, "end": 931.27, "word": " يا", "probability": 0.96533203125}, {"start": 931.27, "end": 931.57, "word": " واحد،", "probability": 0.9386393229166666}, {"start": 931.57, "end": 931.73, "word": " فإذا", "probability": 0.9443359375}, {"start": 931.73, "end": 932.03, "word": " برضه", "probability": 0.98291015625}, {"start": 932.03, "end": 932.91, "word": " اتنين،", "probability": 0.93466796875}, {"start": 932.91, "end": 933.47, "word": " اتنين،", "probability": 0.92255859375}, {"start": 933.47, "end": 933.99, "word": " اتنين،", "probability": 0.98291015625}, {"start": 933.99, "end": 934.35, "word": " اتنين،", "probability": 0.98330078125}, {"start": 934.35, "end": 934.75, "word": " اتنين،", "probability": 0.97939453125}, {"start": 934.75, "end": 935.35, "word": " اتنين،", "probability": 0.96943359375}, {"start": 935.35, "end": 935.89, "word": " اتنين،", "probability": 0.90537109375}, {"start": 935.89, "end": 935.99, "word": " اتنين،", "probability": 0.93798828125}, {"start": 935.99, "end": 936.09, "word": " اتنين،", "probability": 0.95556640625}, {"start": 936.09, "end": 936.37, "word": " اتنين،", "probability": 0.9646484375}, {"start": 936.37, "end": 936.37, "word": " اتنين،", "probability": 0.97080078125}, {"start": 936.37, "end": 936.37, "word": " اتنين،", "probability": 0.97490234375}, {"start": 936.37, "end": 936.37, "word": " اتنين،", "probability": 0.97744140625}, {"start": 936.37, "end": 936.39, "word": " اتنين،", "probability": 0.9791015625}, {"start": 936.39, "end": 936.39, "word": " اتنين،", "probability": 0.9802734375}, {"start": 936.39, "end": 936.39, "word": " اتنين،", "probability": 0.98056640625}, {"start": 936.39, "end": 936.63, "word": " اتنين،", "probability": 0.98037109375}, {"start": 936.63, "end": 936.65, "word": " اتنين،", "probability": 0.98046875}, {"start": 936.65, "end": 936.65, "word": " اتنين،", "probability": 0.9802734375}, {"start": 936.65, "end": 936.65, "word": " اتنين،", "probability": 0.9798828125}, {"start": 936.65, "end": 936.65, "word": " اتنين،", "probability": 0.9798828125}, {"start": 936.65, "end": 936.65, "word": " اتنين،", "probability": 0.9796875}, {"start": 936.65, "end": 936.65, "word": " اتنين،", "probability": 0.97939453125}, {"start": 936.65, "end": 936.65, "word": " اتنين،", "probability": 0.9791015625}, {"start": 936.65, "end": 936.65, "word": " اتنين،", "probability": 0.9791015625}, {"start": 936.65, "end": 937.63, "word": " اتنين،", "probability": 0.97890625}, {"start": 937.63, "end": 937.97, "word": " اتنين", "probability": 0.9769287109375}], "temperature": 1.0}, {"id": 42, "seek": 95353, "start": 938.67, "end": 953.53, "text": "الـ length كله على بعضه seven فإذا لازم يكون ال combination فيهم ال سبعة digit هدول اللي هم ال binary digit ال binary digit لازم يكونوا كاملين موجودين فيها طب مدام كاملين موجودين فيها معناته عدد ال possibilities هصير فيها", "tokens": [6027, 39184, 4641, 28242, 3224, 15844, 45030, 11242, 3224, 3407, 6156, 28814, 15730, 5296, 31377, 2304, 7251, 30544, 2423, 6562, 8978, 16095, 2423, 8608, 3555, 27884, 14293, 8032, 3215, 12610, 13672, 1829, 8032, 2304, 2423, 17434, 14293, 2423, 17434, 14293, 5296, 31377, 2304, 7251, 30544, 14407, 9122, 10943, 1211, 9957, 3714, 29245, 23328, 9957, 8978, 11296, 23032, 3555, 3714, 3215, 10943, 9122, 10943, 1211, 9957, 3714, 29245, 23328, 9957, 8978, 11296, 20449, 8315, 47395, 6225, 3215, 3215, 2423, 12178, 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binary", "probability": 0.93408203125}, {"start": 947.25, "end": 947.47, "word": " digit", "probability": 0.96923828125}, {"start": 947.47, "end": 947.69, "word": " لازم", "probability": 0.9833984375}, {"start": 947.69, "end": 947.93, "word": " يكونوا", "probability": 0.84423828125}, {"start": 947.93, "end": 948.31, "word": " كاملين", "probability": 0.95068359375}, {"start": 948.31, "end": 949.03, "word": " موجودين", "probability": 0.982177734375}, {"start": 949.03, "end": 949.31, "word": " فيها", "probability": 0.989501953125}, {"start": 949.31, "end": 949.71, "word": " طب", "probability": 0.825927734375}, {"start": 949.71, "end": 949.91, "word": " مدام", "probability": 0.7859700520833334}, {"start": 949.91, "end": 950.23, "word": " كاملين", "probability": 0.9786376953125}, {"start": 950.23, "end": 950.61, "word": " موجودين", "probability": 0.988525390625}, {"start": 950.61, "end": 950.89, "word": " فيها", "probability": 0.987548828125}, {"start": 950.89, "end": 951.27, "word": " معناته", "probability": 0.9080403645833334}, {"start": 951.27, "end": 951.57, "word": " عدد", "probability": 0.97314453125}, {"start": 951.57, "end": 951.67, "word": " ال", "probability": 0.91162109375}, {"start": 951.67, "end": 952.43, "word": " possibilities", "probability": 0.9677734375}, {"start": 952.43, "end": 953.17, "word": " هصير", "probability": 0.8045247395833334}, {"start": 953.17, "end": 953.53, "word": " فيها", "probability": 0.99267578125}], "temperature": 1.0}, {"id": 43, "seek": 97711, "start": 954.45, "end": 977.11, "text": "تبديل بينهم بمعنى انه هنا يا صفر يا واحد طيب اللي جنبها لو كنت افترض على جد اتنين برضه هتكون يا صفر يا واحد صحيح؟ بس لاحظ معنى ذلك انه ك string كامل على بعضه اما صفر صفر او صفر واحد او واحد صفر او واحد واحد فإذن أصبحت مضروب لاتنين", "tokens": [2655, 3555, 16254, 1211, 49374, 16095, 4724, 2304, 3615, 1863, 7578, 16472, 3224, 34105, 35186, 20328, 5172, 2288, 35186, 36764, 24401, 23032, 1829, 3555, 13672, 1829, 10874, 1863, 3555, 11296, 45164, 9122, 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يتحققوا معاً لازم يكون في ال digit الأولى لها رقم لها قيمة وال digit التانية and ال digit التانية برضه لها قيمة and ال digit التالتة لها قيمة مش or فإذا كلهم بدهم يتحققوا مع بعض مدام مع بعض معناه to end", "tokens": [2304, 11242, 32887, 3555, 2423, 9307, 1863, 9957, 5296, 28814, 1863, 2423, 9307, 1863, 9957, 47525, 16095, 7251, 2655, 5016, 4587, 4587, 14407, 20449, 995, 14111, 5296, 31377, 2304, 7251, 30544, 8978, 2423, 14293, 16247, 12610, 7578, 5296, 11296, 12602, 4587, 2304, 5296, 11296, 12174, 32640, 3660, 16070, 14293, 16712, 7649, 10632, 293, 2423, 14293, 16712, 7649, 10632, 4724, 43042, 3224, 5296, 11296, 12174, 32640, 3660, 293, 2423, 14293, 16712, 6027, 2655, 3660, 5296, 11296, 12174, 32640, 3660, 37893, 420, 6156, 28814, 15730, 28242, 16095, 47525, 16095, 7251, 2655, 5016, 4587, 4587, 14407, 20449, 45030, 11242, 3714, 3215, 10943, 20449, 45030, 11242, 20449, 8315, 3224, 281, 917], "avg_logprob": -0.21397569058118043, "compression_ratio": 2.1032608695652173, "no_speech_prob": 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تلت حروف من تلت حروف followed by three digits ومطبوعين ب three digits فاذا تلت حروف وراهم تلاتة digits اللي هم من صفر لتسعة كل واحد منهم فالان", "tokens": [9566, 1829, 3555, 47525, 8315, 8717, 25957, 1211, 10476, 1975, 2407, 10476, 20449, 9957, 13672, 1829, 31439, 11524, 37495, 22653, 5296, 19528, 29399, 7435, 6055, 3555, 3615, 4117, 14407, 10476, 3089, 46740, 4724, 1829, 33753, 45865, 15844, 8310, 295, 1045, 7825, 9154, 6055, 1211, 2655, 11331, 32887, 5172, 9154, 6055, 1211, 2655, 11331, 32887, 5172, 6263, 538, 1045, 27011, 4032, 2304, 9566, 3555, 45367, 9957, 4724, 1045, 27011, 6156, 45636, 995, 6055, 1211, 2655, 11331, 32887, 5172, 4032, 23557, 16095, 6055, 1211, 9307, 3660, 27011, 13672, 1829, 8032, 2304, 9154, 20328, 5172, 2288, 5296, 2655, 3794, 27884, 28242, 36764, 24401, 9154, 16095, 6156, 6027, 7649], "avg_logprob": -0.15610259518308459, "compression_ratio": 1.7136752136752136, "no_speech_prob": 9.5367431640625e-07, "words": [{"start": 1030.15, "end": 1030.53, "word": "طيب", 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وهذه ال task التانية", "tokens": [2304, 2655, 9957, 4032, 8608, 2655, 9957, 6156, 28814, 15730, 6055, 7435, 2304, 5016, 16095, 4724, 1829, 9381, 13546, 44650, 9957, 46811, 7649, 10632, 8608, 2655, 3660, 44650, 9957, 8608, 2655, 3660, 4032, 46811, 7649, 9957, 20328, 5016, 1829, 5016, 22807, 47525, 10721, 3714, 4587, 2288, 6156, 28814, 15730, 20328, 9640, 2655, 732, 5633, 44650, 5172, 33546, 1211, 9957, 18871, 45030, 11242, 4032, 4032, 11242, 5016, 5296, 4117, 11933, 25528, 11296, 29538, 2423, 5633, 16247, 12610, 7578, 37037, 24192, 2423, 5633, 16712, 7649, 10632], "avg_logprob": -0.2830882451113533, "compression_ratio": 1.716867469879518, "no_speech_prob": 9.5367431640625e-07, "words": [{"start": 1209.06, "end": 1209.54, "word": "متين", "probability": 0.565673828125}, {"start": 1209.54, "end": 1209.62, "word": " و", "probability": 0.6865234375}, {"start": 1209.62, "end": 1210.12, "word": " ستين", "probability": 0.8489583333333334}, {"start": 1210.12, "end": 1212.08, "word": " فإذا", 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"end": 1785.44, "word": " خلصنا", "probability": 0.9818115234375}, {"start": 1785.44, "end": 1785.66, "word": " one", "probability": 0.93505859375}, {"start": 1785.66, "end": 1786.12, "word": " task", "probability": 0.89013671875}, {"start": 1786.12, "end": 1787.08, "word": " بتكمل", "probability": 0.9493815104166666}, {"start": 1787.08, "end": 1787.46, "word": " التانية", "probability": 0.9581705729166666}, {"start": 1787.46, "end": 1787.56, "word": " و", "probability": 0.853515625}, {"start": 1787.56, "end": 1788.08, "word": " التالتة", "probability": 0.965576171875}, {"start": 1788.08, "end": 1788.36, "word": " و", "probability": 0.91455078125}, {"start": 1788.36, "end": 1789.12, "word": " بتجمع", "probability": 0.97509765625}, {"start": 1789.12, "end": 1790.6, "word": " الباقي", "probability": 0.6886393229166666}, {"start": 1790.6, "end": 1791.74, "word": " تقن", "probability": 0.2381591796875}, {"start": 1791.74, "end": 1791.98, "word": " الأمور", "probability": 0.4800618489583333}, {"start": 1791.98, "end": 1792.26, "word": " فإذا", "probability": 0.7718098958333334}, {"start": 1792.26, "end": 1792.52, "word": " هين", "probability": 0.29058837890625}, {"start": 1792.52, "end": 1793.12, "word": " بنجمحهم", "probability": 0.8787109375}], "temperature": 1.0}, {"id": 81, "seek": 181777, "start": 1794.13, "end": 1817.77, "text": "عدد ل class A عدد ال addresses ل class B وعدد ال addresses ل class C وبنبدأ واحد واحد فإذا هنا استخدمنا هنا summation أو some rule some rule okay class A بدنا نشوف", "tokens": [22488, 3215, 5296, 1508, 316, 6225, 3215, 3215, 2423, 16862, 5296, 1508, 363, 4032, 22488, 3215, 2423, 16862, 5296, 1508, 383, 4032, 3555, 1863, 44510, 10721, 36764, 24401, 36764, 24401, 6156, 28814, 15730, 34105, 44713, 9778, 40448, 8315, 34105, 28811, 34051, 512, 4978, 512, 4978, 1392, 1508, 316, 47525, 8315, 8717, 8592, 38688], "avg_logprob": -0.21325231867807884, "compression_ratio": 1.574468085106383, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1794.13, "end": 1794.73, "word": "عدد", "probability": 0.875732421875}, {"start": 1794.73, "end": 1795.55, "word": " ل", "probability": 0.70703125}, {"start": 1795.55, "end": 1795.99, "word": " class", "probability": 0.44775390625}, {"start": 1795.99, "end": 1796.29, "word": " A", "probability": 0.708984375}, {"start": 1796.29, "end": 1797.31, "word": " عدد", "probability": 0.8346354166666666}, {"start": 1797.31, "end": 1797.41, "word": " ال", "probability": 0.86328125}, {"start": 1797.41, "end": 1797.77, "word": " addresses", "probability": 0.6865234375}, {"start": 1797.77, "end": 1798.07, "word": " ل", "probability": 0.98486328125}, {"start": 1798.07, "end": 1798.37, "word": " class", "probability": 0.89892578125}, {"start": 1798.37, "end": 1798.65, "word": " B", "probability": 0.96923828125}, {"start": 1798.65, "end": 1799.49, "word": " وعدد", "probability": 0.8868815104166666}, {"start": 1799.49, "end": 1799.63, "word": " ال", "probability": 0.96240234375}, {"start": 1799.63, "end": 1800.03, "word": " addresses", "probability": 0.75439453125}, {"start": 1800.03, "end": 1800.27, "word": " ل", "probability": 0.98681640625}, {"start": 1800.27, "end": 1800.59, "word": " class", "probability": 0.919921875}, {"start": 1800.59, "end": 1801.19, "word": " C", "probability": 0.96484375}, {"start": 1801.19, "end": 1802.05, "word": " وبنبدأ", "probability": 0.82275390625}, {"start": 1802.05, "end": 1802.47, "word": " واحد", "probability": 0.867919921875}, {"start": 1802.47, "end": 1802.85, "word": " واحد", "probability": 0.91015625}, {"start": 1802.85, "end": 1803.15, "word": " فإذا", "probability": 0.7158203125}, {"start": 1803.15, "end": 1803.41, "word": " هنا", "probability": 0.89599609375}, {"start": 1803.41, "end": 1804.01, "word": " استخدمنا", "probability": 0.850341796875}, {"start": 1804.01, "end": 1804.27, "word": " هنا", "probability": 0.7099609375}, {"start": 1804.27, "end": 1805.03, "word": " summation", "probability": 0.348876953125}, {"start": 1805.03, "end": 1805.55, "word": " أو", "probability": 0.60009765625}, {"start": 1805.55, "end": 1805.83, "word": " some", "probability": 0.59814453125}, {"start": 1805.83, "end": 1806.49, "word": " rule", "probability": 0.94287109375}, {"start": 1806.49, "end": 1806.85, "word": " some", "probability": 0.41015625}, {"start": 1806.85, "end": 1807.31, "word": " rule", "probability": 0.92529296875}, {"start": 1807.31, "end": 1815.61, "word": " okay", "probability": 0.62548828125}, {"start": 1815.61, "end": 1816.51, "word": " class", "probability": 0.96337890625}, {"start": 1816.51, "end": 1816.79, "word": " A", "probability": 0.9208984375}, {"start": 1816.79, "end": 1817.39, "word": " بدنا", "probability": 0.971435546875}, {"start": 1817.39, "end": 1817.77, "word": " نشوف", "probability": 0.9952799479166666}], "temperature": 1.0}, {"id": 82, "seek": 183713, "start": 1818.53, "end": 1837.13, "text": "النتوارك الأول، إيش عدد ال valid addresses له ال network، وبعدين ال valid مضروبة لإنه followed with، هذه 31 كاملين ورا بعض، لازم يكونوا كاملين ورا بعض، مانفعش أفصلهم هذا أو هذا، هم الإتنين مع بعض بيشكلوا ال IP address تبعك كجهاز على الشبكة", "tokens": [6027, 1863, 2655, 2407, 9640, 4117, 16247, 12610, 12399, 11933, 1829, 8592, 6225, 3215, 3215, 2423, 7363, 16862, 46740, 2423, 3209, 12399, 46599, 22488, 9957, 2423, 7363, 3714, 11242, 32887, 49401, 5296, 28814, 1863, 3224, 6263, 365, 12399, 29538, 10353, 9122, 10943, 1211, 9957, 4032, 23557, 45030, 11242, 12399, 5296, 31377, 2304, 7251, 30544, 14407, 9122, 10943, 1211, 9957, 4032, 23557, 45030, 11242, 12399, 3714, 7649, 5172, 3615, 8592, 5551, 5172, 36520, 16095, 23758, 34051, 23758, 12399, 8032, 2304, 33688, 2655, 1863, 9957, 20449, 45030, 11242, 4724, 1829, 8592, 28820, 14407, 2423, 8671, 2985, 6055, 3555, 3615, 4117, 9122, 7435, 3224, 31377, 15844, 25124, 3555, 4117, 3660], "avg_logprob": -0.19285300912128556, "compression_ratio": 1.6637931034482758, "no_speech_prob": 1.1324882507324219e-06, "words": [{"start": 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0.9052734375}, {"start": 1824.13, "end": 1824.35, "word": " valid", "probability": 0.99267578125}, {"start": 1824.35, "end": 1825.05, "word": " مضروبة", "probability": 0.9642333984375}, {"start": 1825.05, "end": 1825.81, "word": " لإنه", "probability": 0.69000244140625}, {"start": 1825.81, "end": 1826.07, "word": " followed", "probability": 0.869140625}, {"start": 1826.07, "end": 1826.73, "word": " with،", "probability": 0.726806640625}, {"start": 1826.73, "end": 1826.93, "word": " هذه", "probability": 0.73095703125}, {"start": 1826.93, "end": 1827.73, "word": " 31", "probability": 0.65234375}, {"start": 1827.73, "end": 1828.15, "word": " كاملين", "probability": 0.94189453125}, {"start": 1828.15, "end": 1828.29, "word": " ورا", "probability": 0.86572265625}, {"start": 1828.29, "end": 1828.89, "word": " بعض،", "probability": 0.9728190104166666}, {"start": 1828.89, "end": 1829.13, "word": " لازم", "probability": 0.9845377604166666}, {"start": 1829.13, "end": 1829.33, "word": " يكونوا", "probability": 0.9225260416666666}, {"start": 1829.33, "end": 1829.57, "word": " كاملين", "probability": 0.99267578125}, {"start": 1829.57, "end": 1829.71, "word": " ورا", "probability": 0.962646484375}, {"start": 1829.71, "end": 1829.93, "word": " بعض،", "probability": 0.9541015625}, {"start": 1829.93, "end": 1830.13, "word": " مانفعش", "probability": 0.81884765625}, {"start": 1830.13, "end": 1830.55, "word": " أفصلهم", "probability": 0.89111328125}, {"start": 1830.55, "end": 1830.99, "word": " هذا", "probability": 0.66552734375}, {"start": 1830.99, "end": 1831.23, "word": " أو", "probability": 0.9072265625}, {"start": 1831.23, "end": 1831.95, "word": " هذا،", "probability": 0.92333984375}, {"start": 1831.95, "end": 1832.11, "word": " هم", "probability": 0.840576171875}, {"start": 1832.11, "end": 1832.41, "word": " الإتنين", "probability": 0.75323486328125}, {"start": 1832.41, "end": 1832.57, "word": " مع", "probability": 0.99169921875}, {"start": 1832.57, "end": 1832.81, "word": " بعض", "probability": 0.9951171875}, {"start": 1832.81, "end": 1833.71, "word": " بيشكلوا", "probability": 0.883984375}, {"start": 1833.71, "end": 1834.13, "word": " ال", "probability": 0.9755859375}, {"start": 1834.13, "end": 1834.49, "word": " IP", "probability": 0.673828125}, {"start": 1834.49, "end": 1835.03, "word": " address", "probability": 0.91552734375}, {"start": 1835.03, "end": 1835.57, "word": " تبعك", "probability": 0.9749755859375}, {"start": 1835.57, "end": 1836.55, "word": " كجهاز", "probability": 0.9002685546875}, {"start": 1836.55, "end": 1836.69, "word": " على", "probability": 0.92041015625}, {"start": 1836.69, "end": 1837.13, "word": " الشبكة", "probability": 0.98779296875}], "temperature": 1.0}, {"id": 83, "seek": 185383, "start": 1837.77, "end": 1853.83, "text": "كلاهما مع بعض، بنفعش والله تقول جدش رقمك as a host، بس، لأ as a host وإيش الشبكة اللي أنت ماخد منها، ال address تبع الشبكة كمان، عشان أعرفك على الشبكة العالمية كلها، تمام، فإذا مضربين في بعض، لأ ال valid host", "tokens": [4117, 15040, 3224, 15042, 20449, 45030, 11242, 12399, 4724, 1863, 5172, 3615, 8592, 16070, 43761, 6055, 39648, 10874, 3215, 8592, 12602, 4587, 2304, 4117, 382, 257, 3975, 12399, 4724, 3794, 12399, 5296, 10721, 382, 257, 3975, 4032, 28814, 1829, 8592, 25124, 3555, 4117, 3660, 13672, 1829, 14739, 2655, 3714, 47283, 3215, 9154, 11296, 12399, 2423, 2985, 6055, 3555, 3615, 25124, 3555, 4117, 3660, 9122, 2304, 7649, 12399, 6225, 8592, 7649, 5551, 3615, 28480, 4117, 15844, 25124, 3555, 4117, 3660, 18863, 45340, 10632, 28242, 11296, 12399, 46811, 10943, 12399, 6156, 28814, 15730, 3714, 11242, 25513, 9957, 8978, 45030, 11242, 12399, 5296, 10721, 2423, 7363, 3975], "avg_logprob": -0.15580356802259174, "compression_ratio": 1.6911764705882353, "no_speech_prob": 4.0531158447265625e-06, "words": [{"start": 1837.77, "end": 1838.25, "word": "كلاهما", "probability": 0.665130615234375}, {"start": 1838.25, "end": 1838.41, "word": " مع", "probability": 0.98193359375}, {"start": 1838.41, "end": 1839.11, "word": " بعض،", "probability": 0.7869466145833334}, {"start": 1839.11, "end": 1839.47, "word": " بنفعش", "probability": 0.751708984375}, {"start": 1839.47, "end": 1839.67, "word": " والله", "probability": 0.7047119140625}, {"start": 1839.67, "end": 1839.89, "word": " تقول", "probability": 0.9482421875}, {"start": 1839.89, "end": 1840.23, "word": " جدش", "probability": 0.7473958333333334}, {"start": 1840.23, "end": 1841.25, "word": " رقمك", "probability": 0.943115234375}, {"start": 1841.25, "end": 1841.57, "word": " as", "probability": 0.77734375}, {"start": 1841.57, "end": 1841.71, "word": " a", "probability": 0.93212890625}, {"start": 1841.71, "end": 1842.41, "word": " host،", "probability": 0.683837890625}, {"start": 1842.41, "end": 1843.15, "word": " بس،", "probability": 0.9046223958333334}, {"start": 1843.15, "end": 1843.41, "word": " لأ", "probability": 0.954345703125}, {"start": 1843.41, "end": 1843.75, "word": " as", "probability": 0.76220703125}, {"start": 1843.75, "end": 1843.85, "word": " a", "probability": 0.98193359375}, {"start": 1843.85, "end": 1844.11, "word": " host", "probability": 0.97314453125}, {"start": 1844.11, "end": 1844.37, "word": " وإيش", "probability": 0.7281494140625}, {"start": 1844.37, "end": 1844.79, "word": " الشبكة", "probability": 0.9727783203125}, {"start": 1844.79, "end": 1844.89, "word": " اللي", "probability": 0.95263671875}, {"start": 1844.89, "end": 1845.03, "word": " أنت", "probability": 0.655029296875}, {"start": 1845.03, "end": 1845.31, "word": " ماخد", "probability": 0.9581705729166666}, {"start": 1845.31, "end": 1846.07, "word": " منها،", "probability": 0.9153645833333334}, {"start": 1846.07, "end": 1846.13, "word": " ال", "probability": 0.8603515625}, {"start": 1846.13, "end": 1846.35, "word": " address", "probability": 0.90673828125}, {"start": 1846.35, "end": 1846.57, "word": " تبع", "probability": 0.9241536458333334}, {"start": 1846.57, "end": 1846.97, "word": " الشبكة", "probability": 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نجمحهم تمانية زيادة أربعة هتكون ال 1000 انجمع مرتين وال1100 برضه انجمع مرتين فإذا مضطرين نطرح المرتين تاعة التكرار تبعته", "tokens": [5172, 28814, 15730, 11933, 15730, 47525, 8315, 8717, 7435, 2304, 5016, 16095, 46811, 7649, 10632, 30767, 1829, 18513, 3660, 5551, 25513, 27884, 8032, 2655, 30544, 2423, 9714, 16472, 7435, 2304, 3615, 3714, 43500, 9957, 16070, 43435, 15, 4724, 43042, 3224, 16472, 7435, 2304, 3615, 3714, 43500, 9957, 6156, 28814, 15730, 3714, 11242, 9566, 2288, 9957, 8717, 9566, 2288, 5016, 9673, 43500, 9957, 6055, 995, 27884, 16712, 37983, 9640, 6055, 3555, 34268, 3224], "avg_logprob": -0.2476455512112134, "compression_ratio": 1.7122302158273381, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 2283.07, "end": 2283.41, "word": "فإذا", "probability": 0.8240559895833334}, {"start": 2283.41, "end": 2283.57, "word": " إذا", "probability": 0.69921875}, {"start": 2283.57, "end": 2283.73, "word": " بدنا", "probability": 0.9560546875}, {"start": 2283.73, "end": 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"probability": 0.7882486979166666}, {"start": 2395.27, "end": 2395.63, "word": " password", "probability": 0.95751953125}, {"start": 2395.63, "end": 2395.97, "word": " must", "probability": 0.62939453125}, {"start": 2395.97, "end": 2396.67, "word": " contain", "probability": 0.9345703125}, {"start": 2396.67, "end": 2396.99, "word": " at", "probability": 0.96826171875}, {"start": 2396.99, "end": 2397.35, "word": " least", "probability": 0.966796875}, {"start": 2397.35, "end": 2397.91, "word": " digit", "probability": 0.92626953125}, {"start": 2397.91, "end": 2398.53, "word": " or", "probability": 0.9033203125}, {"start": 2398.53, "end": 2400.41, "word": " punctuation", "probability": 0.991455078125}, {"start": 2400.41, "end": 2401.51, "word": " كل", "probability": 0.78759765625}, {"start": 2401.51, "end": 2402.85, "word": " واحد", "probability": 0.9921875}, {"start": 2402.85, "end": 2403.07, "word": " لازم", "probability": 0.990234375}, {"start": 2403.07, "end": 2403.25, "word": " يكون", "probability": 0.98486328125}, {"start": 2403.25, "end": 2403.67, "word": " فيه", "probability": 0.960693359375}, {"start": 2403.67, "end": 2404.17, "word": " مجموعة", "probability": 0.837890625}, {"start": 2404.17, "end": 2404.41, "word": " يا", "probability": 0.57861328125}, {"start": 2404.41, "end": 2405.19, "word": " digit", "probability": 0.92626953125}, {"start": 2405.19, "end": 2405.35, "word": " يا", "probability": 0.9296875}, {"start": 2405.35, "end": 2405.93, "word": " punctuation", "probability": 0.994140625}, {"start": 2405.93, "end": 2408.11, "word": " ضروري", "probability": 0.9122314453125}], "temperature": 1.0}, {"id": 107, "seek": 243442, "start": 2408.94, "end": 2434.42, "text": "كويس التاني ال digit التانية مش مشكلة تاخد اللي بتاخده مش إشكال تاخد اللي بتهيأ فالآن صار عندي الحقيقة two tasks task لأ الحالة الأولى و بعدين بناء عليها نشوف التانية بمعنى أن الحالة الأولى هذه بدك تفترض هل هي أخدت ال possibilities كلها معناة ذلك أن التانية لازم تكون الاتنين بس اللي هي اما", "tokens": [4117, 45865, 3794, 16712, 7649, 1829, 2423, 14293, 16712, 7649, 10632, 37893, 37893, 28820, 3660, 6055, 47283, 3215, 13672, 1829, 39894, 47283, 3215, 3224, 37893, 11933, 8592, 4117, 6027, 6055, 47283, 3215, 13672, 1829, 39894, 3224, 1829, 10721, 6156, 6027, 148, 48506, 20328, 9640, 18871, 16254, 21542, 38436, 28671, 732, 9608, 5633, 5296, 10721, 21542, 6027, 3660, 16247, 12610, 7578, 4032, 39182, 9957, 44945, 16606, 25894, 11296, 8717, 8592, 38688, 16712, 7649, 10632, 4724, 2304, 3615, 1863, 7578, 14739, 21542, 6027, 3660, 16247, 12610, 7578, 29538, 47525, 4117, 6055, 5172, 2655, 43042, 8032, 1211, 39896, 5551, 9778, 3215, 2655, 2423, 12178, 28242, 11296, 20449, 8315, 3660, 29910, 23275, 14739, 16712, 7649, 10632, 5296, 31377, 2304, 6055, 30544, 2423, 9307, 1863, 9957, 4724, 3794, 13672, 1829, 39896, 1975, 15042], "avg_logprob": -0.17066375968992248, "compression_ratio": 1.9450980392156862, "no_speech_prob": 1.2516975402832031e-05, "words": [{"start": 2408.94, "end": 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110, "seek": 251167, "start": 2485.2, "end": 2511.68, "text": "هنشوف كيف فزي ما قلنا هيها اللي هي جا ال password لأ دي لأ has digit or punctuation character in position one or two فإذا الشرط اللي حاكمني شوية أنه لازم يكون فيه رقم أو علامة ترقيم بتتعامل معها اللي هي punctuation بتتعامل معها أنه ممكن تكون ظهرت في الحالة الأولى أو في اللي هي ال position الأول أو ال position التانى", "tokens": [3224, 1863, 8592, 38688, 9122, 33911, 6156, 11622, 1829, 19446, 12174, 1211, 8315, 39896, 11296, 13672, 1829, 39896, 10874, 995, 2423, 11524, 5296, 10721, 11778, 1829, 5296, 10721, 575, 14293, 420, 27006, 16073, 2517, 294, 2535, 472, 420, 732, 6156, 28814, 15730, 25124, 2288, 9566, 13672, 1829, 11331, 995, 24793, 22653, 13412, 2407, 10632, 14739, 3224, 5296, 31377, 2304, 7251, 30544, 8978, 3224, 12602, 4587, 2304, 34051, 11203, 10943, 3660, 6055, 2288, 4587, 32640, 39894, 2655, 3615, 10943, 1211, 20449, 11296, 13672, 1829, 39896, 27006, 16073, 39894, 2655, 3615, 10943, 1211, 20449, 11296, 14739, 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0.514862060546875}, {"start": 3315.3, "end": 3315.92, "word": " بأضمن", "probability": 0.88916015625}, {"start": 3315.92, "end": 3316.44, "word": " ان", "probability": 0.56103515625}, {"start": 3316.44, "end": 3316.66, "word": " اللي", "probability": 0.85595703125}, {"start": 3316.66, "end": 3317.7, "word": " اخترتهم", "probability": 0.919677734375}, {"start": 3317.7, "end": 3319.12, "word": " يوجد", "probability": 0.9697265625}, {"start": 3319.12, "end": 3319.5, "word": " فعلا", "probability": 0.7543131510416666}, {"start": 3319.5, "end": 3319.84, "word": " فيهم", "probability": 0.980712890625}, {"start": 3319.84, "end": 3320.16, "word": " at", "probability": 0.89404296875}, {"start": 3320.16, "end": 3320.42, "word": " least", "probability": 0.9638671875}, {"start": 3320.42, "end": 3320.88, "word": " one", "probability": 0.92529296875}, {"start": 3320.88, "end": 3321.16, "word": " couple", "probability": 0.93896484375}, {"start": 3321.16, "end": 3323.46, "word": " طيب", "probability": 0.70074462890625}, {"start": 3323.46, "end": 3323.94, "word": " أسوأ", "probability": 0.87158203125}, {"start": 3323.94, "end": 3324.22, "word": " حاجة", "probability": 0.9845377604166666}, {"start": 3324.22, "end": 3324.36, "word": " ان", "probability": 0.436767578125}, {"start": 3324.36, "end": 3324.7, "word": " اختار", "probability": 0.8728841145833334}, {"start": 3324.7, "end": 3325.26, "word": " خمستاشر", "probability": 0.83173828125}, {"start": 3325.26, "end": 3325.8, "word": " واحد", "probability": 0.97998046875}, {"start": 3325.8, "end": 3327.72, "word": " مافيش", "probability": 0.9065755208333334}, {"start": 3327.72, "end": 3327.86, "word": " ولا", "probability": 0.8896484375}, {"start": 3327.86, "end": 3328.24, "word": " واحد", "probability": 0.995361328125}, {"start": 3328.24, "end": 3328.58, "word": " couple", "probability": 0.8427734375}, {"start": 3328.58, "end": 3328.76, "word": " مع", "probability": 0.99169921875}, {"start": 3328.76, "end": 3329.26, "word": " التاني", "probability": 0.931640625}, {"start": 3329.26, "end": 3330.42, "word": " ال", "probability": 0.5517578125}, {"start": 3330.42, "end": 3330.74, "word": " 16", "probability": 0.515625}, {"start": 3330.74, "end": 3331.76, "word": " إجباري", "probability": 0.86806640625}, {"start": 3331.76, "end": 3331.98, "word": " لازم", "probability": 0.9866536458333334}, {"start": 3331.98, "end": 3332.24, "word": " هيكون", "probability": 0.89697265625}, {"start": 3332.24, "end": 3332.46, "word": " couple", "probability": 0.833984375}, {"start": 3332.46, "end": 3332.6, "word": " مع", "probability": 0.9794921875}, {"start": 3332.6, "end": 3332.86, "word": " واحد", "probability": 0.9892578125}, {"start": 3332.86, "end": 3333.02, "word": " من", "probability": 0.95556640625}, {"start": 3333.02, "end": 3333.8, "word": " الخمستاشر", "probability": 0.8953125}, {"start": 3333.8, "end": 3333.88, "word": " اللي", "probability": 0.975830078125}, {"start": 3333.88, "end": 3334.24, "word": " اخترتهم", "probability": 0.902099609375}, {"start": 3334.24, "end": 3334.58, "word": " جابله", "probability": 0.75}, {"start": 3334.58, "end": 3335.8, "word": " تمام؟", "probability": 0.67041015625}, {"start": 3335.8, "end": 3338.12, "word": " تمام", "probability": 0.832275390625}, {"start": 3338.12, "end": 3338.52, "word": " خلاص", "probability": 0.90478515625}, {"start": 3338.52, "end": 3338.78, "word": " هذه", "probability": 0.498291015625}, {"start": 3338.78, "end": 3339.24, "word": " خليها", "probability": 0.8694661458333334}, {"start": 3339.24, "end": 3339.56, "word": " للمرة", "probability": 0.9527994791666666}, {"start": 3339.56, "end": 3340.06, "word": " القادمة", "probability": 0.99365234375}, {"start": 3340.06, "end": 3340.3, "word": " ان", "probability": 0.78515625}, {"start": 3340.3, "end": 3340.46, "word": " شاء", "probability": 0.953125}, {"start": 3340.46, "end": 3340.54, "word": " الله", "probability": 0.95849609375}, {"start": 3340.54, "end": 3341.18, "word": " بنكملها", "probability": 0.96533203125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3343.85925, "duration_after_vad": 3225.426249999987}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d788ea129fd0fccefb9ba0db9e89f640a09af38e
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/CizFZ0L5fRQ_raw.srt
@@ -0,0 +1,2928 @@
+1
+00:00:05,130 --> 00:00:07,950
+طيب بسم الله الرحمن الرحيم يعطيكوا العفو يا شباب
+
+2
+00:00:07,950 --> 00:00:13,230
+نكمل اليوم في مساق ال discrete اليوم عندنا موضوع
+
+3
+00:00:13,230 --> 00:00:17,290
+جديد بعد ما كنا خلصنا ال induction أخدناها المرة
+
+4
+00:00:17,290 --> 00:00:19,710
+اللي فاتت و شوفنا ال basis step و ال inductive
+
+5
+00:00:19,710 --> 00:00:25,690
+step ثم تحدثنا منها عن ال recursion ال recursion
+
+6
+00:00:25,690 --> 00:00:28,870
+شوفنا كيف بيصير في recurrence ل ال function من
+
+7
+00:00:28,870 --> 00:00:34,660
+نفسها فاليوم هنتكلم عن ال counting أو العدفعلم
+
+8
+00:00:34,660 --> 00:00:40,780
+العد هو كيف انا ممكن اعد كويس عدد الطرق لأداء task
+
+9
+00:00:40,780 --> 00:00:45,300
+معينة فهذا هو المفهوم من كلمة counting او العد
+
+10
+00:00:45,300 --> 00:00:48,400
+اللي احنا بدنا نتكلم عنه اليوم ان شاء الله تعالى
+
+11
+00:00:48,400 --> 00:00:54,240
+فهو الحقيقة دراسة الأعداج او رقم الطرق او عدد
+
+12
+00:00:54,240 --> 00:00:59,320
+الطرق اللي ممكن نوضع فيها خليني نقول بعض الأشياء
+
+13
+00:00:59,320 --> 00:01:04,200
+في combination معين في تركيب معينان نقول والله
+
+14
+00:01:04,200 --> 00:01:09,440
+المثال اللي موجود فيه ميت شخص بدهم يتسابقه فقداش
+
+15
+00:01:09,440 --> 00:01:14,920
+عندي possibilities لفوز الأول عشرة، يعني الأول
+
+16
+00:01:14,920 --> 00:01:18,400
+عشرة الأوائل، كيف ممكن أعمل؟ مابديش تسميه
+
+17
+00:01:18,400 --> 00:01:22,280
+احتمالات، ولكن possibilities، ايش الإمكانية انه ..
+
+18
+00:01:22,550 --> 00:01:26,750
+أحط combination تركيبة من عدد المائة شخص هدولة
+
+19
+00:01:26,750 --> 00:01:30,990
+بحيث انه يكونوا هم العشر اللي هيفوزوا فجدش عدد ال
+
+20
+00:01:30,990 --> 00:01:36,070
+possibilities هدول، الإمكانيات هذه فطبعا هنتكلم
+
+21
+00:01:36,070 --> 00:01:39,030
+عنها و واضح ان انتوا كلكوا عارفين هيكوا الموضوع
+
+22
+00:01:39,030 --> 00:01:42,210
+هذا فمعنى ذلك انه المفروض نجري فيه اللي واضح ان
+
+23
+00:01:42,210 --> 00:01:47,140
+انتوا هيكوا عارفينهفجيد كويس هذا الموضوع الشغلة
+
+24
+00:01:47,140 --> 00:01:49,720
+التانية اللي ممكن تكون .. خلّيكم معنا يا شباب
+
+25
+00:01:49,720 --> 00:01:52,720
+الشغلة التانية اللي ممكن تتكلم في نفس الموضوع في
+
+26
+00:01:52,720 --> 00:01:56,980
+نفس السياق نستفيد منها هي فكرة ال password جدّيش
+
+27
+00:01:56,980 --> 00:02:01,140
+أنت ممكن تعمل كمبرمج جدّيش ممكن تولّد عدد
+
+28
+00:02:01,140 --> 00:02:04,320
+passwords إذا كانت تحددت عدد ال digits اللي أنت
+
+29
+00:02:04,320 --> 00:02:09,300
+بدك تستخدمها لل password فبتكون عندك من الأساس عدد
+
+30
+00:02:09,300 --> 00:02:15,080
+أو ال ..كمية أو عدد ال passwords اللي ممكن توليدها
+
+31
+00:02:15,080 --> 00:02:19,760
+في عدد خنات محددة لكلمة ال password فهذا المفروض
+
+32
+00:02:19,760 --> 00:02:23,780
+برضه من أساسيات العد .. من أساسيات العد فلما نقول
+
+33
+00:02:23,780 --> 00:02:27,920
+والله عندك ال password ممكن تكون من ستة لتمانية
+
+34
+00:02:27,920 --> 00:02:34,100
+letters or and digitsممكن تستخدم إما حروف أو أرقام
+
+35
+00:02:34,100 --> 00:02:40,200
+و ال password أقل شيء من ستة characters أو من ستة
+
+36
+00:02:40,200 --> 00:02:44,800
+حروف أو أرقام لتمانية فإذا ممكن تكتب ال password
+
+37
+00:02:44,800 --> 00:02:48,800
+تبعتك ستة أو سبعة أو تمانية حروف على أرقام حروف
+
+38
+00:02:48,800 --> 00:02:52,120
+على إيش؟ على أرقام جدش بده يكون عندي عدد passwords
+
+39
+00:02:52,120 --> 00:02:57,190
+ممكنين في الحالة هذه فهذه برضهمن خلال موضوعنا
+
+40
+00:02:57,190 --> 00:03:02,450
+لليوم اللي هي ال basics of counting أو أسس العد،
+
+41
+00:03:02,450 --> 00:03:06,630
+هنستخدمها، هنتكلم عنها، بس نبدأ ندرج شوية شوية و
+
+42
+00:03:06,630 --> 00:03:11,410
+أنا بتكلم عن أسس العد، بدي أستخدم أو بدي هتكلم عن
+
+43
+00:03:11,410 --> 00:03:16,450
+حاجة كتير مهمةهي ال two rules كتير بيحكمونا في هذا
+
+44
+00:03:16,450 --> 00:03:19,910
+الموضوع هي ال sum و ال product .. sum و product و
+
+45
+00:03:19,910 --> 00:03:22,330
+هنشوف هدى إمتى بنستخدمها و هدى إمتى بنستخدمها حسب
+
+46
+00:03:22,330 --> 00:03:25,210
+منطق السؤال و حسب إنت إيش بدك من السؤال أو كيف بدك
+
+47
+00:03:25,210 --> 00:03:28,850
+.. لو بنتكلم عن ال password .. إنت كيف بدك تركب ال
+
+48
+00:03:28,850 --> 00:03:32,860
+password فهي مش مجرد إنه عدد ال digits و خلاصلأ ال
+
+49
+00:03:32,860 --> 00:03:37,580
+digits هذه كيف بدك ترتبها؟ كيف بدك تكونها؟ هل لازم
+
+50
+00:03:37,580 --> 00:03:41,800
+يكون كلهم حروف؟ ولا لأ ممكن يكون كلهم digits؟ ولا
+
+51
+00:03:41,800 --> 00:03:46,100
+لأ من هذا على هذا؟ طب ممكن تقول حروف لكن مايقولوش
+
+52
+00:03:46,100 --> 00:03:50,330
+عدد الحروف عن اتنين مثلا من الستةفانت ممكن تحط كل
+
+53
+00:03:50,330 --> 00:03:53,110
+ال rules اللي بدك اياها ففي الحالة هذه جدش بيأثر
+
+54
+00:03:53,110 --> 00:03:57,490
+هذا على عدد ال passwords الممكنين بحيث انك انت
+
+55
+00:03:57,490 --> 00:04:01,050
+ممكن تحاول كمان تزود ال difficulty تبعت ال
+
+56
+00:04:01,050 --> 00:04:05,900
+password فانت لو مابدك تحدد ال password هذهبسيطة
+
+57
+00:04:05,900 --> 00:04:09,920
+ولا صعبة ولا normal فممكن تحدد هدول جديش و هدول
+
+58
+00:04:09,920 --> 00:04:14,540
+جديش و هدول جديش بناء على مفهومك انت لأ إيش يعني
+
+59
+00:04:14,540 --> 00:04:17,020
+صعبة و إيش يعني بسيطة إيش يعني صعبة و إيش يعني
+
+60
+00:04:17,020 --> 00:04:19,920
+بسيطة فده كلها هنتكلم عنها لكن بدنا نفهم شوية
+
+61
+00:04:19,920 --> 00:04:23,300
+basics أساسية في البداية اللي هي ال some way ل
+
+62
+00:04:23,300 --> 00:04:26,460
+product عشان نشرحهم بدي أفترض أنه في عندى عدد
+
+63
+00:04:26,460 --> 00:04:34,160
+الطرق to do task one بدي أسميهم مثلا M wayما مميز
+
+64
+00:04:34,160 --> 00:04:40,380
+فعندك عددهم M عشان أقدر أنفذ ال task الأولى طيب لو
+
+65
+00:04:40,380 --> 00:04:44,660
+كان عندك العدد N هد ال number of ways to do task 2
+
+66
+00:04:44,660 --> 00:04:48,640
+فانت صار عندك two tasks بدك تعملهم combination مع
+
+67
+00:04:48,640 --> 00:04:51,860
+بعض بدك تعملهم الأتنين مع بعضهم فهنا أصبح نحن
+
+68
+00:04:51,860 --> 00:04:56,120
+نتكلم عن هد لحال تحسبها لحالها و هد بتحسبها لحالها
+
+69
+00:04:56,120 --> 00:04:59,740
+هد لحال و هد لحال هقول ال letters لحالهم و ال
+
+70
+00:04:59,740 --> 00:05:03,090
+digits لحالهمطيب و بعدين إيش بدنا نعمل فيهم؟ هنا
+
+71
+00:05:03,090 --> 00:05:08,910
+بتصير كيف قلية تركيب ال password نفسه إذا والله
+
+72
+00:05:08,910 --> 00:05:14,070
+بدك تعملهم مع بعض، هيكون في عندك two ways تشتغل
+
+73
+00:05:14,070 --> 00:05:18,420
+على اما someتجمحهم جامع ففي الحالة هذه بيكونوا
+
+74
+00:05:18,420 --> 00:05:23,480
+منفصلين تماما عن بعض يا اما letters او او او او او
+
+75
+00:05:23,480 --> 00:05:25,120
+او او او او او او او او او او او او او او او او او
+
+76
+00:05:25,120 --> 00:05:25,120
+او او او او او او او او او او او او او او او او او
+
+77
+00:05:25,120 --> 00:05:25,140
+او او او او او او او او او او او او او او او او او
+
+78
+00:05:25,140 --> 00:05:25,200
+او او او او او او او او او او او او او او او او او
+
+79
+00:05:25,200 --> 00:05:25,200
+او او او او او او او او او او او او او او او او او
+
+80
+00:05:25,200 --> 00:05:31,000
+او او او او او
+
+81
+00:05:31,000 --> 00:05:34,680
+اوبدنا نقول ال summation rule إذا كان انا ال task
+
+82
+00:05:34,680 --> 00:05:39,940
+سبعتي do either task one or task two فانا يا بديهم
+
+83
+00:05:39,940 --> 00:05:44,200
+حروف بس يا بديهم أرقام بس، كويس؟ ففي الحالة هذه
+
+84
+00:05:44,200 --> 00:05:47,500
+طبعا هي أكيد بال password مش منطق أقول الكلام هذا
+
+85
+00:05:47,500 --> 00:05:50,360
+بس في applications تانية أه منطق جدا، يا هيك يا
+
+86
+00:05:50,360 --> 00:05:52,720
+هيك زي ما هناخد أنفلة كتير اليوم هناخد، الأنفلة
+
+87
+00:05:52,720 --> 00:05:53,360
+هتكون كتيرة
+
+88
+00:05:56,360 --> 00:06:01,240
+لكن بديش اياهم مع بعض ففي الحالة هدى بنستخدم M
+
+89
+00:06:01,240 --> 00:06:06,940
+plus Nهدول جديش عدد الطرق عشان فعلا أعمل password
+
+90
+00:06:06,940 --> 00:06:12,340
+نفترض من ستة من ستة digits فقط كحروف جديش عددهم
+
+91
+00:06:12,340 --> 00:06:16,100
+خلاص يبنى عددهم وجمعناه وحطناه كأنه قيمة M طب جديش
+
+92
+00:06:16,100 --> 00:06:19,960
+عدد الأرقام اللى ممكن أكون منهم password من ستة
+
+93
+00:06:19,960 --> 00:06:23,880
+digits برضه بنحسب عددهم و بنجمع الاتنين مع بعض
+
+94
+00:06:23,880 --> 00:06:29,000
+مدام أنا محتاج يا هذا يا هذا لكن لما بروح لل
+
+95
+00:06:29,000 --> 00:06:34,020
+product rule امتىلما تكون ال task تبعتي do both
+
+96
+00:06:34,020 --> 00:06:39,080
+task one and task two simultaneously بمعنى متزاون
+
+97
+00:06:39,080 --> 00:06:42,020
+مع بعض بدي أعمل اتنين مع بعض ففي الحالة هذه ال
+
+98
+00:06:42,020 --> 00:06:46,460
+password ممكن يكون من هنا و من هنا ساعتها جديش من
+
+99
+00:06:46,460 --> 00:06:50,240
+هنا وجديش من هنا انت بتقدر تكون عندك إمكانية تلعب
+
+100
+00:06:50,240 --> 00:06:53,400
+في الموضوع زي ما بدك يعني تقول والله بدي أول تلاتة
+
+101
+00:06:53,400 --> 00:06:57,200
+letters و بعدين تلاتة digits او تقول لأ بديها
+
+102
+00:06:57,200 --> 00:07:00,080
+اتنين و واحد اتنين و تلاتة اتنين و خمس اعملها بال
+
+103
+00:07:00,080 --> 00:07:04,680
+.. اقولكقول والله بدي letter digit letter digit
+
+104
+00:07:04,680 --> 00:07:08,280
+letter digit okay هذه ال problem بدك تشتغلها كل
+
+105
+00:07:08,280 --> 00:07:12,820
+واحدة لحالها تشتغل كل واحدة تصلحها و تضربهم مع بعض
+
+106
+00:07:12,820 --> 00:07:17,160
+في الحالة هذه حنشوف هتتضح طبعا أكتر أنت بنستخدم ال
+
+107
+00:07:17,160 --> 00:07:20,920
+product و أنت بنستخدم ال some مع الأمثلة الكتيرة
+
+108
+00:07:20,920 --> 00:07:25,520
+اللي هنقدر ناخدهالكن الآن عشان اوضح بس ان الفكرة
+
+109
+00:07:25,520 --> 00:07:29,020
+هي برضه مابعدتش عن حاجة احنا جاهزين ناخدها
+
+110
+00:07:29,020 --> 00:07:32,860
+باستمرار طول الفصل اللي هي ال 6 ال 6 فانا بكل
+
+111
+00:07:32,860 --> 00:07:37,140
+بساطة ال M هذه ال M اللي كانت هي عدد ال
+
+112
+00:07:37,140 --> 00:07:41,480
+possibilities to do task 1 ممكن اقول عليهم هدولة
+
+113
+00:07:41,480 --> 00:07:46,040
+كلWay من ال ways هدول بيتعامل معاها كأنها element
+
+114
+00:07:46,040 --> 00:07:52,160
+داخل set كاملة بحيث أني أقول في الآخر ال A هي ال
+
+115
+00:07:52,160 --> 00:07:59,340
+set لكل ال ways to do task oneكل مهمة او كل حل
+
+116
+00:07:59,340 --> 00:08:02,900
+بقدر اعمله للمهمة الاولى .. كل حل ممكن اقدر اعمله
+
+117
+00:08:02,900 --> 00:08:06,220
+للمهمة الاولى بجمعه مع بعضه و بحطه في تافيه set
+
+118
+00:08:06,220 --> 00:08:09,480
+واحدة بسميها set A فهذه ال set بتصير هي اللي
+
+119
+00:08:09,480 --> 00:08:13,360
+معطياني كل possibility solutions فعليا لل task
+
+120
+00:08:13,360 --> 00:08:18,240
+الاولى في نفس الكلام برضه بقول عندي ال set B فهي
+
+121
+00:08:18,240 --> 00:08:21,400
+برضه كل ال possibilities او ال ways او ال
+
+122
+00:08:21,400 --> 00:08:26,750
+solutions لل task 2لأ ال task two فإذا كانت عند a
+
+123
+00:08:26,750 --> 00:08:32,150
+and b are disjoint بمعنى إن الحلول هنا مالهاش
+
+124
+00:08:32,150 --> 00:08:36,870
+علاقة بالحلول هنا a فيها طرق حل مختلفة تماما عن
+
+125
+00:08:36,870 --> 00:08:41,690
+طرق حل بي ففي الحالة دي بنقدر نقول عشان أعمل
+
+126
+00:08:41,690 --> 00:08:45,190
+either task one or task two معناته اتحاد الأثنين
+
+127
+00:08:45,190 --> 00:08:49,710
+اتحاد a مع بي فصارت نفس المفهوم اللي أخدناها سابقا
+
+128
+00:08:49,710 --> 00:08:55,220
+ل مين لل six ل ال six كدهالتحاد وهذا ينطبق على ال
+
+129
+00:08:55,220 --> 00:08:58,180
+rule بتاع التو اللي هي sum فهي cardinality ل a
+
+130
+00:08:58,180 --> 00:09:01,820
+plus cardinality يعني معناته M plus N هي نفس ال
+
+131
+00:09:01,820 --> 00:09:05,680
+sum rule اللي أخدناها في المقابلة عندك برضه
+
+132
+00:09:05,680 --> 00:09:09,780
+إمكانية ان ال ways to do both task one and task
+
+133
+00:09:09,780 --> 00:09:12,640
+two سمتن يصل زي ما قلنا اتنين مع بعض ففي الحالة
+
+134
+00:09:12,640 --> 00:09:18,060
+نقدر نقولالـ cardinality لـ A مضروب في ال
+
+135
+00:09:18,060 --> 00:09:20,900
+cardinality لـ B فهنا برضه نتكلم عن ال rule تبعت
+
+136
+00:09:20,900 --> 00:09:23,780
+ال product ال product rule لإن بدي أعمل ال two
+
+137
+00:09:23,780 --> 00:09:27,340
+tasks مع بعض ال two tasks مع بعض في الحالة بتاعتنا
+
+138
+00:09:27,340 --> 00:09:33,440
+طيب ناخد أمثلة أكيد هتوضح أكتر الكلام النظري اللي
+
+139
+00:09:33,440 --> 00:09:37,780
+قلناه لو افترض انه ال student can chooseأبكمبيوتر
+
+140
+00:09:37,780 --> 00:09:41,040
+project في مساق من هالمساقات بتاعتكم انطلب منكوا
+
+141
+00:09:41,040 --> 00:09:44,100
+تختاروا project الأستاذ جابلكوا قائمة من ال
+
+142
+00:09:44,100 --> 00:09:47,200
+projects لكن ال projects هذه صنفلكوا إيها ل three
+
+143
+00:09:47,200 --> 00:09:51,360
+lists جالكم والله في عندي three lists بتحتوي على
+
+144
+00:09:51,360 --> 00:09:55,360
+تلتة و عشرين خمستاش و تسعتاش possible projects
+
+145
+00:09:55,360 --> 00:09:58,500
+خليني أقول ال تلتة و عشرين هدولة صنفلكوا تلتة و
+
+146
+00:09:58,500 --> 00:10:02,640
+عشرين project اللي هم علاقة بال AIو خمستاشر
+
+147
+00:10:02,640 --> 00:10:06,080
+project اللي هم علاقة بال networks و تسعتاشر
+
+148
+00:10:06,080 --> 00:10:08,960
+project اللي هم علاقة بال database مثلا okay و
+
+149
+00:10:08,960 --> 00:10:11,860
+جالكم هى في عندكوا تلت مجموعات هدولة مجموعة الناس
+
+150
+00:10:11,860 --> 00:10:14,120
+اللي بيحبوا يشتغلوا في ال AI فليكن هى في عندكوا
+
+151
+00:10:14,120 --> 00:10:17,800
+تلت و عشرين مشروع project يختاروا منهم و هى في
+
+152
+00:10:17,800 --> 00:10:20,720
+اللي بيحب يشتغل في الشبكات هى في خمستاشر project
+
+153
+00:10:20,720 --> 00:10:24,380
+اختاروا اللي بدكوا إياه منهم و اللي بدهوا database
+
+154
+00:10:24,380 --> 00:10:28,880
+هى في عندكوا تسعة عشرHow many possible projects
+
+155
+00:10:28,880 --> 00:10:32,900
+are there to choose from؟ يعني لكل طالب منكم الآن
+
+156
+00:10:32,900 --> 00:10:36,300
+هو بالنسباله جداش عدد ال possibilities للاختيار
+
+157
+00:10:36,300 --> 00:10:41,200
+مجموعة لكل، مش هيك؟ يا بيختار من التلاتة و عشرين
+
+158
+00:10:41,200 --> 00:10:46,780
+أو الخمستاش أو التسعتاش، مش هيجي يختار من التلاتة
+
+159
+00:10:46,780 --> 00:10:51,130
+لأنه مش مطلوب انه يقول لاproject واحد فإذا في
+
+160
+00:10:51,130 --> 00:10:53,930
+الحالة دي بكل بساطة ال total هيكون تلاتة و عشرين
+
+161
+00:10:53,930 --> 00:10:58,210
+خمس عشر تسعتاش فسبعة و خمسين projects فانت عندك
+
+162
+00:10:58,210 --> 00:11:01,050
+سبعة و خمسين possibility to choose your project
+
+163
+00:11:01,050 --> 00:11:05,290
+عشان تختار ال project تبعك عندك إمكانية إمكانيات
+
+164
+00:11:05,290 --> 00:11:10,850
+اختيار بتصل لسبعة و خمسين اختيار طيب suppose
+
+165
+00:11:10,850 --> 00:11:13,950
+فالتاني suppose statement labels محتاجين نعمل
+
+166
+00:11:13,950 --> 00:11:18,270
+labelلأ الحالات بتبعت باستخدام ال programming
+
+167
+00:11:18,270 --> 00:11:22,510
+language must be single letter اللي labels ها دي
+
+168
+00:11:22,510 --> 00:11:25,590
+العنوان .. العنوان هذا اللي بدك تحطه لمجموعة ال
+
+169
+00:11:25,590 --> 00:11:30,870
+statements سبعتك اما ان يكون single letter حرف فقط
+
+170
+00:11:30,870 --> 00:11:36,230
+او single decimal digit بس .. من 0 ل 9 .. يا من 0
+
+171
+00:11:36,230 --> 00:11:40,030
+ل 9 بالضبط 100% فانت بتتكلم عن decimal digit و
+
+172
+00:11:40,030 --> 00:11:43,890
+digit واحدةبال decimal يعني نتكلم عن النظام العشر
+
+173
+00:11:43,890 --> 00:11:46,210
+اللي هو من صفر إلى تسعة فعندك عشرة possibility
+
+174
+00:11:46,210 --> 00:11:50,450
+لإله، كويس، فالمطلوب بكل بساطة how many labels are
+
+175
+00:11:50,450 --> 00:11:54,050
+there، انت عارف مش محتاج كتير لما أقولك والله هي
+
+176
+00:11:54,050 --> 00:11:57,430
+كل statement بتقدر تسميها باسم، والاسم هذا إما أنه
+
+177
+00:11:57,430 --> 00:12:01,520
+يكون حرف أو يكون digit من ال decimal، بسو حرف
+
+178
+00:12:01,520 --> 00:12:05,960
+single فإذا هم السبت عشرين حرف زائد العشرة digits
+
+179
+00:12:05,960 --> 00:12:09,460
+تعوني ال decimal فبطلع عندى ستة و تلاتين
+
+180
+00:12:09,460 --> 00:12:13,980
+possibility لاستخدامهم ك label او لل statement
+
+181
+00:12:13,980 --> 00:12:20,400
+label طيب how many integers between one and one
+
+182
+00:12:20,400 --> 00:12:25,820
+hundred including ال one hundred are even or end
+
+183
+00:12:25,820 --> 00:12:32,320
+with five؟ تماملاحظ الان احنا صرنا نتكلم عن ايش عن
+
+184
+00:12:32,320 --> 00:12:37,060
+or واضحة عندي هنا معناه ذلك ان في عندي two tasks
+
+185
+00:12:37,060 --> 00:12:44,680
+two tasks task قبل ال or فبسميها task one وفي task
+
+186
+00:12:44,680 --> 00:12:50,460
+بعد ال or بسميها task two و بدنا نحسب كل واحدة على
+
+187
+00:12:50,460 --> 00:12:55,080
+حده كل واحدة على حده فانت بتتكلم من صفر لمية اول
+
+188
+00:12:55,080 --> 00:12:59,930
+task ال evenعدد ال even اللي فيها، كلنا عارفين
+
+189
+00:12:59,930 --> 00:13:06,470
+قداش؟ خمسين even، خمسين
+
+190
+00:13:06,470 --> 00:13:14,010
+even بعتبار أنه المشمولة الخمسين، لكن مجلناش أنه
+
+191
+00:13:14,010 --> 00:13:19,090
+اه من الواحد عفواأه لأنه بدي أقولك مش كاتب أن
+
+192
+00:13:19,090 --> 00:13:23,310
+الصفر موجود فهو من واحد فعليا فإذا عندك خمسين طيب
+
+193
+00:13:23,310 --> 00:13:27,850
+ال end with five end with five يعني معناته الأحد
+
+194
+00:13:27,850 --> 00:13:33,110
+تعتها خمسة الأحد تعتها خمسة كده إيش عددهم عشرة
+
+195
+00:13:33,110 --> 00:13:38,950
+ابدأ من الخمسة نفسها خمستعش و هكذا عند الخمسة
+
+196
+00:13:38,950 --> 00:13:45,300
+وتسعين ففعليابدأت من الخمسة صفر خمسة واحد لخمسة
+
+197
+00:13:45,300 --> 00:13:52,200
+تسعة لاحظ العشرات من الصفر للتسعة فعددهم جداش عشرة
+
+198
+00:13:52,200 --> 00:13:56,700
+فبصير خمسة زائد عشرة فانت عندك كمان ال task التاني
+
+199
+00:13:56,700 --> 00:14:03,080
+عشرة اللي هم نقدر نسميهم end with five طيب مربوطين
+
+200
+00:14:03,080 --> 00:14:10,480
+بإيش؟ ب or يعني ستين or يعني معناته هذا مفصل عن
+
+201
+00:14:10,480 --> 00:14:16,470
+هذاهذه هتكون منفصل عن هذه طيب طبعا هنا واضح ان هي
+
+202
+00:14:16,470 --> 00:14:21,770
+منفصل عن بعضبمعنى إن لو في أرقام بتظبط إن هيكونوا
+
+203
+00:14:21,770 --> 00:14:25,390
+الاتنين مع بعض هدخلنا في جثة هنتكلم عنها لكن الان
+
+204
+00:14:25,390 --> 00:14:28,710
+واضح إن ال set أو ال task هذه هي منفصلة تماما عن
+
+205
+00:14:28,710 --> 00:14:32,550
+ال task هذه ليش؟ لأنه مدام هي and with five معناتي
+
+206
+00:14:32,550 --> 00:14:36,370
+هي odd مستحيل تكون even فإذا أنا ضامن إن المجموعة
+
+207
+00:14:36,370 --> 00:14:40,470
+الخمسين هنا مافيش فيهم ولا رقم من العشرة والعشر
+
+208
+00:14:40,470 --> 00:14:43,710
+هدول برضه مافيش فيهم ولا رقم من الخمسين هدول فإذا
+
+209
+00:14:43,710 --> 00:14:47,590
+بنجمحهم لأنه disjoint حتى الآن اللي اتكلمنا عنها
+
+210
+00:14:47,590 --> 00:14:56,430
+اللي هي disjointتمام كمان مثال how
+
+211
+00:14:56,430 --> 00:14:58,890
+many different pit strings .. strings of length
+
+212
+00:14:58,890 --> 00:15:06,610
+seven are there؟ مافيش فيها كتير برضه مشكلة جدش
+
+213
+00:15:06,610 --> 00:15:13,610
+بتعمل عدد strings من عدد digits سبعة
+
+214
+00:15:18,470 --> 00:15:22,370
+كل واحدة منهم لحالهم هدولة إيش ال possibility
+
+215
+00:15:22,370 --> 00:15:25,510
+بتاعتها اتنين، يا صفر يا واحد، فإذا هذه يا صفر يا
+
+216
+00:15:25,510 --> 00:15:28,570
+واحد، فإذا ال possibility بتاعتها اتنين، طيب ال
+
+217
+00:15:28,570 --> 00:15:31,570
+possibility بتاعة التانية برضه يا صفر يا واحد،
+
+218
+00:15:31,570 --> 00:15:34,750
+فإذا برضه اتنين، اتنين، اتنين، اتنين، اتنين،
+
+219
+00:15:34,750 --> 00:15:36,370
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+220
+00:15:36,370 --> 00:15:36,650
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+221
+00:15:36,650 --> 00:15:37,630
+اتنين، اتنين، اتنين، اتنين، اتنين، اتنين، اتنين،
+
+222
+00:15:37,630 --> 00:15:41,570
+اتنينالـ length كله على بعضه seven فإذا لازم يكون
+
+223
+00:15:41,570 --> 00:15:45,590
+ال combination فيهم ال سبعة digit هدول اللي هم ال
+
+224
+00:15:45,590 --> 00:15:48,310
+binary digit ال binary digit لازم يكونوا كاملين
+
+225
+00:15:48,310 --> 00:15:51,270
+موجودين فيها طب مدام كاملين موجودين فيها معناته
+
+226
+00:15:51,270 --> 00:15:55,950
+عدد ال possibilities هصير فيهاتبديل بينهم بمعنى
+
+227
+00:15:55,950 --> 00:16:00,550
+انه هنا يا صفر يا واحد طيب اللي جنبها لو كنت افترض
+
+228
+00:16:00,550 --> 00:16:04,270
+على جد اتنين برضه هتكون يا صفر يا واحد صحيح؟ بس
+
+229
+00:16:04,270 --> 00:16:08,090
+لاحظ معنى ذلك انه ك string كامل على بعضه اما صفر
+
+230
+00:16:08,090 --> 00:16:15,010
+صفر او صفر واحد او واحد صفر او واحد واحد فإذن
+
+231
+00:16:15,010 --> 00:16:19,280
+أصبحت مضروب لاتنينمضروب الاتنين لإن الاتنين بدهم
+
+232
+00:16:19,280 --> 00:16:23,360
+يتحققوا معاً لازم يكون في ال digit الأولى لها رقم
+
+233
+00:16:23,360 --> 00:16:26,920
+لها قيمة وال digit التانية and ال digit التانية
+
+234
+00:16:26,920 --> 00:16:29,800
+برضه لها قيمة and ال digit التالتة لها قيمة مش or
+
+235
+00:16:29,800 --> 00:16:34,080
+فإذا كلهم بدهم يتحققوا مع بعض مدام مع بعض معناه to
+
+236
+00:16:34,080 --> 00:16:38,590
+endمعناته and عشان أكون فعلا عندي string من سبعة
+
+237
+00:16:38,590 --> 00:16:42,290
+digits وإلا معناته ببطل من سبعة digits إذا or
+
+238
+00:16:42,290 --> 00:16:46,510
+معناته واحد فقط أنا بتكلم عن واحد يهد يهد يهد لأ
+
+239
+00:16:46,510 --> 00:16:49,690
+هو مش يهد يهد السبعة ببطون دانية هم موجودين فإذا
+
+240
+00:16:49,690 --> 00:16:56,970
+الأول و التاني و التالت لعند السابع مدام و and مش
+
+241
+00:16:56,970 --> 00:16:58,890
+or and خلاص بنضرب
+
+242
+00:17:02,400 --> 00:17:05,180
+ضربناهم في بعض فمعناته اتنين to the power سبع او
+
+243
+00:17:05,180 --> 00:17:10,950
+اتنين متكررة سبع .. سبع مرات، خلصنا منهاطيب بدنا
+
+244
+00:17:10,950 --> 00:17:16,170
+نعمل license او license معين اللي هو password يعني
+
+245
+00:17:16,170 --> 00:17:20,310
+للمنتج تبعكوا license code له بيحتوي على sequence
+
+246
+00:17:20,310 --> 00:17:27,570
+of three letters من تلت حروف من تلت حروف followed
+
+247
+00:17:27,570 --> 00:17:32,950
+by three digits ومطبوعين ب three digits فاذا تلت
+
+248
+00:17:32,950 --> 00:17:37,270
+حروف وراهم تلاتة digits اللي هم من صفر لتسعة كل
+
+249
+00:17:37,270 --> 00:17:43,320
+واحد منهم فالانhow many different license plates
+
+250
+00:17:43,320 --> 00:17:47,780
+are available خلاص هي تنحطها برضه بشكلها الهيكل
+
+251
+00:17:47,780 --> 00:17:50,180
+كيف بده يكون شكلها بده يكون بهذا الشكل
+
+252
+00:17:53,840 --> 00:17:58,580
+فعندي تلاتة في البداية هدولة عبارة عن letters كل
+
+253
+00:17:58,580 --> 00:18:01,700
+واحدة منهم letter ال letter ايش ال possibilities
+
+254
+00:18:01,700 --> 00:18:04,720
+عدد ال possibilities تبعته؟ ستة و عشرين فإذا هذا
+
+255
+00:18:04,720 --> 00:18:08,580
+ممكن يكون واحد من ستة و عشرين حرف احنا عارفينهم
+
+256
+00:18:08,580 --> 00:18:15,400
+والتاني ستة و عشرين والتالتطيب الجزء التاني اللي
+
+257
+00:18:15,400 --> 00:18:19,980
+هم ال three ال four by three digits ل decimal
+
+258
+00:18:19,980 --> 00:18:23,440
+digits فإذا إما عشرة عشرة عشرة اللي هي من صفر
+
+259
+00:18:23,440 --> 00:18:30,030
+لتسعة طيب هل وجد هدول المفروض هل هم or ولا andهنا
+
+260
+00:18:30,030 --> 00:18:33,130
+بنتكلم عن قدر لأنه بتكلم عن sequence مافرجش كتير
+
+261
+00:18:33,130 --> 00:18:36,310
+عن ال string اللي كنا نحكي عنه فهو ال sequence هذا
+
+262
+00:18:36,310 --> 00:18:40,430
+مكوّن من تلاتة مطبوعة بتلاتة يعني لو أقل من ستة مش
+
+263
+00:18:40,430 --> 00:18:44,330
+هيرضى فيه ك .. ك sequence و ك license يتعامل معه
+
+264
+00:18:44,330 --> 00:18:48,850
+فإذا هدول اللي لازم يكونوا مع بعض فإذا مضربين في
+
+265
+00:18:48,850 --> 00:18:54,660
+بعض هيكونوا كلهم مضربين في بعضطبعا كويس فإذا منطق
+
+266
+00:18:54,660 --> 00:18:57,840
+السؤال او فهمك لا ايش ال combination اللي انت بدك
+
+267
+00:18:57,840 --> 00:19:00,300
+تعملها بالظبط هو اللي بيحددلك على طول ان انت
+
+268
+00:19:00,300 --> 00:19:05,780
+بتتكلم عن ال some rule ولا product rule كمان مثال
+
+269
+00:19:05,780 --> 00:19:10,500
+هنا برضه نفس الكلام بدنا نعمل statement labelال
+
+270
+00:19:10,500 --> 00:19:12,740
+statement اللي عندك بدك تحطلها label معين تحطلها
+
+271
+00:19:12,740 --> 00:19:19,900
+ترقيم الترقيم هذا either a single letter فإذا جدش
+
+272
+00:19:19,900 --> 00:19:24,740
+بدني single letter واحدة أو letter followed by
+
+273
+00:19:24,740 --> 00:19:33,180
+digit فإذا إما خلصنا من هنا digit
+
+274
+00:19:33,180 --> 00:19:40,780
+واحدة عبارة عن بديها letter حروف فهذه ستة وعشرينor
+
+275
+00:19:40,780 --> 00:19:48,400
+و بصراحة انجلك or or برضه single letter followed
+
+276
+00:19:48,400 --> 00:19:55,980
+by digit فإذا ستة و عشرين و عشرة مادام followed by
+
+277
+00:19:55,980 --> 00:20:00,780
+digit معناته مطبوعة لازم يجوا مع بعض مادام مع بعض
+
+278
+00:20:00,780 --> 00:20:06,620
+معناته and الأول and التاني and فصارت هذه ستة و
+
+279
+00:20:06,620 --> 00:20:13,880
+عشرين orمتين و ستين فإذا تجمحهم بيصير متين تمانية
+
+280
+00:20:13,880 --> 00:20:21,260
+ستة متين ستة و تمانين صحيح؟ بدأ مقر فإذا صارت two
+
+281
+00:20:21,260 --> 00:20:25,920
+task متفاصلين عن بعض و وضح لك إياها هذه ال task
+
+282
+00:20:25,920 --> 00:20:29,710
+الأولى وهذه ال task التانيةOkay هو بتهيألي حل
+
+283
+00:20:29,710 --> 00:20:35,590
+هخلصنا من كل هذا أعملك S على أساس إن هي الست ل
+
+284
+00:20:35,590 --> 00:20:37,850
+single letter لحالها اللي هي طلعت ستة و عشرين
+
+285
+00:20:37,850 --> 00:20:41,270
+جيبناها و ال D افترض إن هي single letters followed
+
+286
+00:20:41,270 --> 00:20:46,610
+by digit او decimal digit وعملوا لهم اتحاد في
+
+287
+00:20:46,610 --> 00:20:50,390
+الآخر فوصلنا ل المتين ستة و تمانين اللي طلعناها
+
+288
+00:20:50,390 --> 00:20:52,370
+تمام
+
+289
+00:20:53,930 --> 00:20:59,370
+كمان مثل واضح لهذا الموضوع هي ال IP address ال IP
+
+290
+00:20:59,370 --> 00:21:03,190
+address بيكون له protocol فبنسميه ال internet
+
+291
+00:21:03,190 --> 00:21:06,790
+protocol ال version 4 و بعدين حاليا صار ال version
+
+292
+00:21:06,790 --> 00:21:13,630
+6 فخلينا نرجع لل version 4 ال version 4 في منه
+
+293
+00:21:13,630 --> 00:21:22,760
+classes في منه صنف لعدة أصناف A وB وC وD وEمصنف
+
+294
+00:21:22,760 --> 00:21:26,200
+لخمس أصناف بعرفش إذا كان مرة بتعليقه في مساقة أو
+
+295
+00:21:26,200 --> 00:21:30,120
+إشي المهم إحنا الآن مطلوب مننا في السؤال إيش مطلوب
+
+296
+00:21:30,120 --> 00:21:34,860
+مننا جدش عدد ال addresses ل three types منهم اللي
+
+297
+00:21:34,860 --> 00:21:39,920
+هو a و b و c طيب a و b و c هدول بدنا نفهم منهم
+
+298
+00:21:39,920 --> 00:21:45,940
+شغلة إنه عادة هو عبارة عن sequence ل digit لمجموعة
+
+299
+00:21:45,940 --> 00:21:50,950
+digits لتعريف الشبكةو ال host اللي عليها او ال
+
+300
+00:21:50,950 --> 00:21:57,170
+user اللي عليها تمام بالاضافة لجزء من ال sequence
+
+301
+00:21:57,170 --> 00:22:02,430
+هذا عبارة عن one or two or three digits three bit
+
+302
+00:22:02,430 --> 00:22:06,350
+هدولة لتعريف ال class اللي احنا بنشتغل عليه فإذا
+
+303
+00:22:06,350 --> 00:22:10,350
+ال sequence عندك و اللي هو بالاساس مكوّن بالنسبة
+
+304
+00:22:10,350 --> 00:22:15,770
+لل version 4 مكوّن من 32بت ال 32 بت هدول بتجسموا
+
+305
+00:22:15,770 --> 00:22:20,470
+حسب كل نوع class ال class الأول بناخد منه بت
+
+306
+00:22:20,470 --> 00:22:25,190
+لتعريف ال classلتعريف ال class إذا بدأت بواحد معنا
+
+307
+00:22:25,190 --> 00:22:30,750
+ذلك إن أنا بتكلم عن class A إذا بدأت بصفر ثم واحد
+
+308
+00:22:30,750 --> 00:22:35,990
+فانا بتكلم عن class B إذا كانت صفر صفر واحد class
+
+309
+00:22:35,990 --> 00:22:40,910
+C فإذا نلاحظ class A أنا استنفذت أول digit أو أول
+
+310
+00:22:40,910 --> 00:22:44,930
+bit لتعريف ال class نفسه فبيضللي واحد و تلاتين
+
+311
+00:22:44,930 --> 00:22:46,710
+واحد و تلاتين او واحد و تلاتين بالظبط واحد و
+
+312
+00:22:46,710 --> 00:22:49,750
+تلاتين الواحد و تلاتين هدول بيتم تجسم و ليش؟ بيتم
+
+313
+00:22:49,750 --> 00:22:55,080
+تجسم و دير بالك ل usersالذين يسمونهم الـ host ال
+
+314
+00:22:55,080 --> 00:23:00,940
+users هدولة أعدادهم لكلsmall network خلّيني او
+
+315
+00:23:00,940 --> 00:23:04,700
+شبكة بحيث انه في النهاية الشبكة هذه لها عنوان كمان
+
+316
+00:23:04,700 --> 00:23:09,180
+فانت الشبكة الأولى وانت ال user الأول فيها طب هذا
+
+317
+00:23:09,180 --> 00:23:13,400
+ممكن يكون في شبكة تانية ويلها user أول برضه يعني
+
+318
+00:23:13,400 --> 00:23:17,700
+ممكن اتنين يكونوا بالنسبة للمجموعة ال bits اللي
+
+319
+00:23:17,700 --> 00:23:22,100
+خاصة بالhost نفسه لكن اختلفوا بمين؟ بعنوان الشبكة
+
+320
+00:23:22,100 --> 00:23:25,520
+فإذا انا في عندي تتجسم لعنوانين العنوانين هدول
+
+321
+00:23:25,520 --> 00:23:26,280
+هنسميهم
+
+322
+00:23:28,610 --> 00:23:33,350
+ال .. ال net ID خاصة بالشبكة نفسها ال net ID و فيه
+
+323
+00:23:33,350 --> 00:23:37,550
+عندك ال host ID عندك host ID فكل net فيه لها
+
+324
+00:23:37,550 --> 00:23:41,310
+مجموعة ال hosts تاعتها لها مجموعة hosts تاعتها
+
+325
+00:23:41,310 --> 00:23:49,430
+تمامالان بالنسبة لـ B هتكون اول two bits مستنفذين
+
+326
+00:23:49,430 --> 00:23:53,210
+لتعريف ال class نفسه فبتضع لعندك تلاتين فاللي
+
+327
+00:23:53,210 --> 00:23:58,690
+بتبقى من التلاتين bit هدولة بدنا نجسمهم بين ال net
+
+328
+00:23:58,690 --> 00:24:06,010
+ID و ال host ID التالتة اللي هي Cبكون عندك three
+
+329
+00:24:06,010 --> 00:24:10,050
+bits لتعريف ال class نفسه فبظل عندك تسعة و عشرين
+
+330
+00:24:10,050 --> 00:24:14,350
+بدك اتجسمهم ما بين ال host و ال network كويس
+
+331
+00:24:14,350 --> 00:24:18,830
+فبتختلف الان كيف اتجسمت هاد standard بالمناسبة
+
+332
+00:24:18,830 --> 00:24:21,590
+standard يعني احنا okay عارفين ان في تلات حالات و
+
+333
+00:24:21,590 --> 00:24:26,950
+بتختلف تجسيماتهم standard هذا خليني نشوف جدش
+
+334
+00:24:26,950 --> 00:24:31,130
+تجسيمة كل واحدة منهم بالنسبة ل class A class A
+
+335
+00:24:32,480 --> 00:24:40,160
+امجسمهم ان في عندك سبعة bit لتعريف
+
+336
+00:24:40,160 --> 00:24:44,700
+ال network جدش بظل من الواحد و التلاتين لان احنا
+
+337
+00:24:44,700 --> 00:24:48,080
+قلنا في واحد لمن لتعريف ال class نفسه وهي في سبعة
+
+338
+00:24:48,080 --> 00:24:52,460
+راح تمانية هاي تمانية جدش ظل ال host اربعة و عشرين
+
+339
+00:24:52,460 --> 00:24:57,280
+ففي عندك اربعة و عشرين لال host معناه ذلك ان كل
+
+340
+00:24:57,280 --> 00:25:02,200
+شبكة في ال class هذا بتكون بتحمل عدد كبير من ال
+
+341
+00:25:02,200 --> 00:25:06,840
+users او ال host من ال users طيب اهم شغلة هنا
+
+342
+00:25:06,840 --> 00:25:11,040
+موجودة انك بالنسبة لل net ID غير مسموح ان يكونوا
+
+343
+00:25:11,040 --> 00:25:16,470
+السبعة هدول كاملين onceهذه مش مسموحة فيه مش مسموحة
+
+344
+00:25:16,470 --> 00:25:20,410
+في ال class هذا تمام او حتى في ال classes كلها طيب
+
+345
+00:25:20,410 --> 00:25:29,250
+ال class B بيقدرس ايش 14 bit ل ال net بمعنى ان هنا
+
+346
+00:25:29,250 --> 00:25:33,990
+بيكون عدد ال nets عليه اكتر وهذا في المقابل هيخلي
+
+347
+00:25:33,990 --> 00:25:40,380
+عدد ال user داخل ال net كل net لحالها اقلهيكون عدد
+
+348
+00:25:40,380 --> 00:25:45,720
+ال net أقل تمام فبتصير عندك 16 بدل ما كانت 24 فانت
+
+349
+00:25:45,720 --> 00:25:48,620
+شوف جد ايش عدد ال users اللي ممكن تستخدمهم هنا لكل
+
+350
+00:25:48,620 --> 00:25:53,740
+شبكة اتنين to the power 24 هنا لأ هتكون to the
+
+351
+00:25:53,740 --> 00:25:57,100
+power 16 to the power 16 اذا عدد والله الجامعة
+
+352
+00:25:57,100 --> 00:26:00,840
+عددهم مش عدد كبير لأ بنجلل اكتر من هيك كمان كويس
+
+353
+00:26:01,590 --> 00:26:05,630
+الان ال class و بالمناسبة هذه اصلا شغل تجاري يعني
+
+354
+00:26:05,630 --> 00:26:08,170
+اذا انا عارف ان ال area هذه مش هيجيها عدد كبير ليش
+
+355
+00:26:08,170 --> 00:26:14,030
+انا اضيع ال bits في ال host طب ما بخليه للشبكة و
+
+356
+00:26:14,030 --> 00:26:17,210
+بضمن ان الشبكات عددهم كبير و بنجل الشبكات بخليهم
+
+357
+00:26:18,220 --> 00:26:24,520
+يعني بععد عن بعض فب .. بغطي area أكبر بنغطي في
+
+358
+00:26:24,520 --> 00:26:27,680
+الحالة هذه area أكبر مدام ال .. ال density مش
+
+359
+00:26:27,680 --> 00:26:30,820
+عالية مدام ال density مش عالية بس هذه بتاع دراسة
+
+360
+00:26:30,820 --> 00:26:37,680
+طبيعية طيب C .. C لاحظ واحد و عشرين لاالـ net ID
+
+361
+00:26:37,680 --> 00:26:41,840
+21 و تمانية فقط لمين؟ لل host تمانية لل host إذا
+
+362
+00:26:41,840 --> 00:26:46,860
+بنتكلم عن area مافيها capacity عالية ف okay بنخلي
+
+363
+00:26:46,860 --> 00:26:51,120
+عدد networks كتير و كل network تتغذي عدد أقل من ال
+
+364
+00:26:51,120 --> 00:26:55,100
+host أو من ال users تمام و زي ما اتفجنا ال two
+
+365
+00:26:55,100 --> 00:27:00,120
+classes بتعرفوا عن بعض بال header تبعالـ IB
+
+366
+00:27:00,120 --> 00:27:03,780
+address هذا من خلال النقل صفر إذا كان صفر لحالها
+
+367
+00:27:03,780 --> 00:27:09,340
+فأنا بتكلم عن إيه إذا واحد و بعدين الصفر إجا رقم
+
+368
+00:27:09,340 --> 00:27:12,380
+اتنين فمعنى ذلك هدي بي إذا الصفر إجا رقم تلاتة
+
+369
+00:27:12,380 --> 00:27:17,620
+فمعناته أنا بتكلم عنهC عن C كويس ال host هنا بده
+
+370
+00:27:17,620 --> 00:27:20,840
+يعطينا شوية characteristic واضحة جدا بتكون
+
+371
+00:27:20,840 --> 00:27:26,100
+بمستخدمها انه لا يمكن استخدام ال host zeros or
+
+372
+00:27:26,100 --> 00:27:30,480
+ones بمعنى انه مافيش user هياخد ال address zeros
+
+373
+00:27:30,480 --> 00:27:36,600
+في أي شبكة ولا ones ولا ال ones في أي شبكة كانت
+
+374
+00:27:36,600 --> 00:27:40,640
+تمام فإذا هي هذا أول شرط تتاخدوا بالكم منه وفي
+
+375
+00:27:40,640 --> 00:27:46,140
+عندي شرط تاني كان هنا لمينلل .. ال .. ال net ID ان
+
+376
+00:27:46,140 --> 00:27:49,260
+هي بتسمحش بال ones بتسمحش بال ones الان ايش
+
+377
+00:27:49,260 --> 00:27:54,280
+المطلوب؟ مطلوب جدش عدد ال addresses الممكنين ل ال
+
+378
+00:27:54,280 --> 00:27:56,500
+three classes هدولة في ال system طبعا هنا
+
+379
+00:27:56,500 --> 00:28:00,600
+ماتكلمناش احنا عن مين؟ عن ال D و ال E ال D و ال E
+
+380
+00:28:00,600 --> 00:28:02,880
+بيستخدموهم في ال broadcasting في ال broadcasting
+
+381
+00:28:02,880 --> 00:28:06,820
+اللي هي بياخدوا المدى كله كامل ل user واحد او
+
+382
+00:28:06,820 --> 00:28:10,680
+لخدمة واحدة فبتكون .. اه بتكون عددهم كبير في
+
+383
+00:28:10,680 --> 00:28:16,550
+الحالة هذه تمامالان بدنا نشوف جداش عدد ال
+
+384
+00:28:16,550 --> 00:28:21,490
+possibilities لعدد users يعني addresses جداش انا
+
+385
+00:28:21,490 --> 00:28:25,130
+ممكن اولد addresses بالنظام هذا بهذا الاستخدام بكل
+
+386
+00:28:25,130 --> 00:28:28,410
+بساطة اتوقع ايش بتكون تعمله طبعا ماحدش هيشتغل
+
+387
+00:28:28,410 --> 00:28:31,330
+بالظبط واحد واحد لانه ماحدش هيشتغل في two classes
+
+388
+00:28:31,330 --> 00:28:36,880
+مع بعض كل واحد له class لحاله يا a يا b يا cمش
+
+389
+00:28:36,880 --> 00:28:40,520
+هيك؟ هذه أول شغلة، ممتاز، هذه هلوجت في التفاصيل،
+
+390
+00:28:40,520 --> 00:28:44,980
+احنا هلوجت وحددنا أنه يا A يا B يا C، صحيح؟ A B C،
+
+391
+00:28:44,980 --> 00:28:47,780
+أنا هكون ضمن واحد منهم، مستحيل أكون ضمن أكتر من
+
+392
+00:28:47,780 --> 00:28:52,960
+هيك، فإذن الأول or التاني or التالت، فإذا تصق أولة
+
+393
+00:28:52,960 --> 00:28:55,940
+تانية تالتة، هدول منفصلين عن بعض، تمسكهم واحدة
+
+394
+00:28:55,940 --> 00:28:59,080
+واحدة الأولمسيكنا الأولى هلو يجي تبدأ نشتغل في
+
+395
+00:28:59,080 --> 00:29:03,080
+شغلتك هنقول ان في عندى واحد و تلاتين الواحد و
+
+396
+00:29:03,080 --> 00:29:06,660
+تلاتين هتجسموا سبعة السبعة هدولة ممكن تكون اتنين
+
+397
+00:29:06,660 --> 00:29:10,780
+to the power seven ناقص واحد لأنه مش مسموح بالones
+
+398
+00:29:10,780 --> 00:29:16,040
+اللي قلتلنا عليها صح؟ ممتاز طيب هدولة ال sequence
+
+399
+00:29:16,040 --> 00:29:21,760
+تبع مين؟ تبع ال address تبع ال network followed by
+
+400
+00:29:21,760 --> 00:29:27,540
+أو with ال host ال host جد يشضلأربعة و عشرين بقى
+
+401
+00:29:27,540 --> 00:29:30,800
+انا ذلك بتكلم عن ال host لحاله اتنين to the power
+
+402
+00:29:30,800 --> 00:29:34,300
+اربعة و عشرين ناقص اتنين احسنته اللي هي ال zeros و
+
+403
+00:29:34,300 --> 00:29:37,540
+ال ones تمام هلوجة الناتج اللي بطلع بضربه في مين
+
+404
+00:29:37,540 --> 00:29:41,860
+في اتنين to the power seven ناقص واحد عشان يعطيني
+
+405
+00:29:41,860 --> 00:29:46,120
+ال sequence كله ل class A فبنكون خلصنا one task
+
+406
+00:29:46,120 --> 00:29:51,980
+بتكمل التانية و التالتة و بتجمع الباقي تقن الأمور
+
+407
+00:29:51,980 --> 00:29:58,070
+فإذا هين بنجمحهمعدد ل class A عدد ال addresses ل
+
+408
+00:29:58,070 --> 00:30:02,470
+class B وعدد ال addresses ل class C وبنبدأ واحد
+
+409
+00:30:02,470 --> 00:30:06,490
+واحد فإذا هنا استخدمنا هنا summation أو some rule
+
+410
+00:30:06,490 --> 00:30:15,610
+some rule okay
+
+411
+00:30:15,610 --> 00:30:22,170
+class A بدنا نشوفالنتوارك الأول، إيش عدد ال valid
+
+412
+00:30:22,170 --> 00:30:25,050
+addresses له ال network، وبعدين ال valid مضروبة
+
+413
+00:30:25,050 --> 00:30:29,130
+لإنه followed with، هذه 31 كاملين ورا بعض، لازم
+
+414
+00:30:29,130 --> 00:30:31,950
+يكونوا كاملين ورا بعض، مانفعش أفصلهم هذا أو هذا،
+
+415
+00:30:31,950 --> 00:30:36,550
+هم الإتنين مع بعض بيشكلوا ال IP address تبعك كجهاز
+
+416
+00:30:36,550 --> 00:30:41,250
+على الشبكةكلاهما مع بعض، بنفعش والله تقول جدش رقمك
+
+417
+00:30:41,250 --> 00:30:45,030
+as a host، بس، لأ as a host وإيش الشبكة اللي أنت
+
+418
+00:30:45,030 --> 00:30:48,330
+ماخد منها، ال address تبع الشبكة كمان، عشان أعرفك
+
+419
+00:30:48,330 --> 00:30:51,490
+على الشبكة العالمية كلها، تمام، فإذا مضربين في
+
+420
+00:30:51,490 --> 00:30:57,280
+بعض، لأ ال valid hostبكل بساطة بالنسبة لل network
+
+421
+00:30:57,280 --> 00:31:00,880
+قلنا 2⁷7-1 وعرفنا ليش ناقص واحد لإن ال ones مش
+
+422
+00:31:00,880 --> 00:31:07,080
+مسموح فيها فبتطلع 127 بالنسبة لل host 2⁷24-2 برضه
+
+423
+00:31:07,080 --> 00:31:10,160
+عرفنا ليش لإن لا ال zeros مسموح فيها ولا ال ones
+
+424
+00:31:10,160 --> 00:31:17,000
+مسموح فيها فبتطلع حوالي 16777214
+
+425
+00:31:17,000 --> 00:31:22,880
+نضرب الاتنين في بعض عشان يطلع ليه total لمينبس
+
+426
+00:31:22,880 --> 00:31:26,700
+بتعيد نفس الكلام لمين؟ ل B و بتعيده كمان ل C و
+
+427
+00:31:26,700 --> 00:31:30,180
+بتجمع التلت أقام اللي بيطلعوا، لاحظوا أنه العدد
+
+428
+00:31:30,180 --> 00:31:32,380
+الأكبر في الغالب الرقم الأكبر بيطلع على class A
+
+429
+00:31:32,380 --> 00:31:38,090
+فالرقمجدش لأ مش هذا الرقم عموما هذا لحاله بطلع
+
+430
+00:31:38,090 --> 00:31:43,510
+تنين مليار تقريبا و إشي بيضل حوالي المليار و نص ل
+
+431
+00:31:43,510 --> 00:31:48,390
+class B و C مع بعض كلاهما مع بعض حسبوها جربوها
+
+432
+00:31:48,390 --> 00:31:52,690
+حسبوها لحالكم عشان يطلع في نهاية total حوالي 3.7
+
+433
+00:31:52,690 --> 00:31:57,830
+billion IP addresses طبعا الرقم هذا ماكانش كافي
+
+434
+00:31:59,340 --> 00:32:02,640
+الرقم هذا ماكانش كافي و عشان هيك كان في version 6
+
+435
+00:32:02,640 --> 00:32:09,560
+عشان هيك انتقلوا ل version 6 لأ احنا بدنا نحدد عدد
+
+436
+00:32:09,560 --> 00:32:13,760
+bits أكبر من اللي كنا مستخدمينه ل 32 لأ محتاجين
+
+437
+00:32:13,760 --> 00:32:17,260
+أكبر من هيك فهتنجرب اشي تاني و فعلا بدأوا ينتقلوا
+
+438
+00:32:17,260 --> 00:32:20,800
+لل system الجديد اللي هو ال IP address او ال
+
+439
+00:32:20,800 --> 00:32:25,120
+internet protocol version 6 اللي حاليا المعظم شغل
+
+440
+00:32:25,120 --> 00:32:26,720
+انتقله
+
+441
+00:32:28,840 --> 00:32:33,860
+تمام الآن كل الكلام اللي فات كويس بس كله كان تحت
+
+442
+00:32:33,860 --> 00:32:38,120
+كلمة كانت مكتوبة هنا disjoint task one and task
+
+443
+00:32:38,120 --> 00:32:42,420
+two are disjoint بمعنى ان هم منفصلين عن بعض مافيش
+
+444
+00:32:42,420 --> 00:32:46,400
+حلول resolutions او possibilities بتنفع لكلاهما
+
+445
+00:32:46,400 --> 00:32:50,480
+معا لكن لو ظهرت هذه الحالة انه لأ والله في حلول
+
+446
+00:32:50,480 --> 00:32:56,680
+بتنفع لل task الأولى والتانيةو انا بدي قر مثلا هل
+
+447
+00:32:56,680 --> 00:32:59,740
+يجوز ان اجمعهم و اسكت خلاص؟ طب انا في الحالة هذه
+
+448
+00:32:59,740 --> 00:33:04,720
+بالظبط معناه ذلك ان انا فعليا في مجموعة ways او
+
+449
+00:33:04,720 --> 00:33:07,240
+possibilities انجمعهم مرتين مرة من ال task الأول و
+
+450
+00:33:07,240 --> 00:33:11,340
+مرة بالنسبة للتانية احسنتوا فإذا ان انا مضطر اعمل
+
+451
+00:33:14,060 --> 00:33:17,160
+طرح لتقاطعهم معانا .. كويس فهذا هو نفسه اللي
+
+452
+00:33:17,160 --> 00:33:20,260
+هنعمله و هذا بيبين معانا إذا كان عندى .. فعلا في
+
+453
+00:33:20,260 --> 00:33:26,240
+عندى K ways أقل من .. ممكن تكون أقل من أو تساوي ..
+
+454
+00:33:26,240 --> 00:33:28,980
+يعني ممكن كل ال ways اللي بتنفع ل task 1 كلها
+
+455
+00:33:28,980 --> 00:33:33,610
+بتنفع ل task 2 .. كويس؟ف K-Header اللي هي ways of
+
+456
+00:33:33,610 --> 00:33:38,410
+doing task one also simultaneously accomplish task
+
+457
+00:33:38,410 --> 00:33:41,510
+two فإذن هي رغم إن هي بتنفع ل task one بس برضه
+
+458
+00:33:41,510 --> 00:33:45,410
+بالتزاون مع ذلك هي برضه بتنفع ك possibilities ل أو
+
+459
+00:33:45,410 --> 00:33:51,550
+إمكانية لعمل ال task two أو لأداء ال task twoتمام
+
+460
+00:33:51,550 --> 00:33:54,970
+ففي الحالة دي إيش بنسوي؟ بنقول بكل بساطة do either
+
+461
+00:33:54,970 --> 00:33:59,890
+task one or task two عبارة عن M plus N ناقص K اللي
+
+462
+00:33:59,890 --> 00:34:03,290
+قلنا عليها اللي هي التقاط والاتنين مع بعض أو ال
+
+463
+00:34:03,290 --> 00:34:07,330
+ways اللي بتنفع لكلا ال tasks لكلا ال tasks task
+
+464
+00:34:07,330 --> 00:34:10,390
+one and task two وهذه طبعا إلها مرجعية احنا
+
+465
+00:34:10,390 --> 00:34:15,270
+أخدناها لما اتكلمنا في ال sets لو متذكرين قلنا ال
+
+466
+00:34:15,270 --> 00:34:19,430
+cardinality للاتحادكان بيسوي ال cardinality للأولى
+
+467
+00:34:19,430 --> 00:34:23,150
+plus cardinality التانية ناقص التقاطع فالتقاطع هذا
+
+468
+00:34:23,150 --> 00:34:26,810
+معناه أنه بينفع لل task الأولى و بينفع
+
+469
+00:34:26,810 --> 00:34:28,910
+simultaneously لل task التانية برضه في نفس الوقت
+
+470
+00:34:28,910 --> 00:34:34,550
+فهذا يعتبر تقاطع بالنسبة لمن ل ال sets فإذا هنا
+
+471
+00:34:34,550 --> 00:34:38,210
+إذا كانت disjoint زي الطرق اللي كنا نحكيها قبل هيك
+
+472
+00:34:38,210 --> 00:34:41,710
+لأ مافيش مشكلة بيبقى مجموحمه بس مش هتطر أعمل طرح
+
+473
+00:34:41,710 --> 00:34:47,540
+ليش لأن طرحهم هيساويفالإنتجريه اللي يعني التقاط و
+
+474
+00:34:47,540 --> 00:34:54,680
+تباحهم اللي هي k هتكون five فالست هنا مفيش أو zero
+
+475
+00:34:54,680 --> 00:35:00,140
+zero لأ five اللي هي مافيش element مافيش element
+
+476
+00:35:00,140 --> 00:35:04,280
+zero elements تمام هاتنشوف أمثلة على هذا الموضوع
+
+477
+00:35:04,280 --> 00:35:08,660
+بهذا الشكل لو بدنا نقول how many bits strings of
+
+478
+00:35:08,660 --> 00:35:13,540
+length four تمام افهمنا length four ممتاز هاي
+
+479
+00:35:13,540 --> 00:35:14,120
+length four
+
+480
+00:35:16,820 --> 00:35:24,360
+طولها أربعة، ممتاز، بعدين either start with one or
+
+481
+00:35:24,360 --> 00:35:29,560
+end
+
+482
+00:35:29,560 --> 00:35:30,880
+with double zero
+
+483
+00:35:33,770 --> 00:35:37,270
+خلص قبنمسك واحدة واحدة مش هنمسكهم واحدة واحدة
+
+484
+00:35:37,270 --> 00:35:40,070
+ممتاز قبنمسكهم واحدة واحدة هالوقت خليني نبدأ في
+
+485
+00:35:40,070 --> 00:35:44,510
+الأولى الأولى اللى هو جدش عندي عدد bit string او
+
+486
+00:35:44,510 --> 00:35:49,150
+جدش عدد ال strings اللى ممكن نولدهم من اربعة digit
+
+487
+00:35:49,150 --> 00:35:55,590
+او اربعة bits الاولى منهم one تمانية اللى هم
+
+488
+00:35:55,590 --> 00:36:00,240
+الخيارات فقط للتلاتة اللى ضايلينهدولة ممكن تكون يا
+
+489
+00:36:00,240 --> 00:36:03,320
+صفر يا واحد يا صفر يا واحد يا صفر يا واحد فتنين
+
+490
+00:36:03,320 --> 00:36:10,120
+فتنين فتنين فتنين فتنين فتنين خلصناها طيب ال task
+
+491
+00:36:10,120 --> 00:36:14,260
+التاني هذه task one task
+
+492
+00:36:14,260 --> 00:36:19,900
+two هدولة محكم عليهم خلاص zeros انتهى هنا إما zero
+
+493
+00:36:19,900 --> 00:36:24,000
+one zero one فهذه عددهم أربعة في الحالة هذه فتنين
+
+494
+00:36:24,000 --> 00:36:32,030
+فتنين هذه taskتو فصار عندى تمانية زائد أربعة طيب
+
+495
+00:36:32,030 --> 00:36:36,750
+شوية اصبروا علينا في تقاطع بينهم ليش في تقاطع
+
+496
+00:36:36,750 --> 00:36:41,550
+بينهم لأنه هتلاقي مجموعة bit string هي محقق
+
+497
+00:36:41,550 --> 00:36:45,850
+الشرطين معاهممحقق الشرطين معاها فهي فعليا ان عدت
+
+498
+00:36:45,850 --> 00:36:51,070
+هنا وان عدت هنا جداش عددهم احنا لازم نفحصهم حتى لو
+
+499
+00:36:51,070 --> 00:36:53,730
+طلعوا في النهاية فيه بس انا في النهاية لازم افحصهم
+
+500
+00:36:53,730 --> 00:36:56,830
+لأنه ممكن يكونوا مشترك الاتنين مع بعض طيب عشان
+
+501
+00:36:56,830 --> 00:36:59,050
+تكون مشترك الاتنين مع بعض معناته الأولى هذه محكوم
+
+502
+00:36:59,050 --> 00:37:04,030
+عليها تكون one خلاص والاتنين
+
+503
+00:37:04,030 --> 00:37:08,950
+التاني محكوم عليهم خلاص يكونوازيروس فبقى لعندي فقط
+
+504
+00:37:08,950 --> 00:37:13,350
+الخانة التانية اللي ممكن يكون لها possibilities او
+
+505
+00:37:13,350 --> 00:37:17,590
+ways to do this فإذا يا صفر يا واحد فيا احتمالين
+
+506
+00:37:17,590 --> 00:37:27,870
+فإذا task one and task two فالحالة هذه بتساوي
+
+507
+00:37:27,870 --> 00:37:35,070
+اتنين فإذا ناقص اتنين ناقص اتنينجيد فإذا هتلاقي
+
+508
+00:37:35,070 --> 00:37:38,350
+مين اللي مجموح في الحالتين اللي هي ال 1 0 0 0 و ال
+
+509
+00:37:38,350 --> 00:37:45,570
+1 1 0 0 هدول ال two strings هدول هتلاقيهم موجودين
+
+510
+00:37:45,570 --> 00:37:48,870
+في الحالة الأولى و في التانية في كلا هما طبعا هم
+
+511
+00:37:48,870 --> 00:37:53,630
+هنا يعني حللك يهم كاملين هي التمانية للأولى وهي
+
+512
+00:37:53,630 --> 00:37:56,510
+الأربعة للتانية عشان يكتشف ان الرقم ان هدوله
+
+513
+00:37:56,510 --> 00:38:03,410
+متكررين هي واحد هي واحد وهي التاني مع التانيفإذا
+
+514
+00:38:03,410 --> 00:38:07,350
+إذا بدنا نجمحهم تمانية زيادة أربعة هتكون ال 1000
+
+515
+00:38:07,350 --> 00:38:13,490
+انجمع مرتين وال1100 برضه انجمع مرتين فإذا مضطرين
+
+516
+00:38:13,490 --> 00:38:20,950
+نطرح المرتين تاعة التكرار تبعتهالان محتاجين .. بعض
+
+517
+00:38:20,950 --> 00:38:23,490
+ال .. نحط بعض ال rules ل password على اساس انه
+
+518
+00:38:23,490 --> 00:38:26,250
+الان بدنا نعمل توليد لمجموعة passwords ال
+
+519
+00:38:26,250 --> 00:38:30,310
+passwords هذه .. هذه إلها شروط أول شرط إلها إن ال
+
+520
+00:38:30,310 --> 00:38:34,610
+password لازم تكون عبارة عن two characters long
+
+521
+00:38:34,610 --> 00:38:39,710
+فإذا خلصنا من هذا و نحط ال two characters و نشوف
+
+522
+00:38:39,710 --> 00:38:43,710
+كل الشروط الممكنة له عشان نقدر نتعامل معاه
+
+523
+00:38:49,810 --> 00:38:53,070
+password من two characters طبعا كلمة character أول
+
+524
+00:38:53,070 --> 00:38:56,370
+مرة يتكلم عنها character أول مرة بيحكي عنها ليش
+
+525
+00:38:56,370 --> 00:38:59,310
+أول مرة بيحكي عنها لأن character لها مفهوم يا إما
+
+526
+00:38:59,310 --> 00:39:02,410
+letters أو digit اللي هو decimal digit أو
+
+527
+00:39:02,410 --> 00:39:05,750
+punctuations اللي هي علامات الترقيم ال
+
+528
+00:39:05,750 --> 00:39:10,370
+punctuations هذه اللي هي علامات الترقيم ال space
+
+529
+00:39:10,370 --> 00:39:13,810
+نفسها ال S دولار العلامة المائية العلامة المئوية
+
+530
+00:39:13,810 --> 00:39:19,430
+كل الالعلامات التقييم اللي موجودة عندك دايما مع ال
+
+531
+00:39:19,430 --> 00:39:21,970
+shift و الأرقام اللي فوق ال shift مع الأرقام اللي
+
+532
+00:39:21,970 --> 00:39:27,130
+فوق كلهم هدولة عبارة عن punctuation characters طيب
+
+533
+00:39:27,130 --> 00:39:32,310
+فإذا أول شغلة two كل password لازم يكون letter,
+
+534
+00:39:32,710 --> 00:39:37,930
+digit or one of ten punctuation فإذا حكملنا ten
+
+535
+00:39:37,930 --> 00:39:42,310
+punctuation اللي هم تعون من الأرقام مع ال shiftعلى
+
+536
+00:39:42,310 --> 00:39:44,910
+الكمبيوتر shift مع مجموعة الأرقام اللي فوق اللي من
+
+537
+00:39:44,910 --> 00:39:49,570
+واحد للصفر فبيعطيك مجموعة ال punctuation هدول كويس
+
+538
+00:39:49,570 --> 00:39:52,950
+فعرفنا هنا ايش ال possibilities اللي احنا ممكن
+
+539
+00:39:52,950 --> 00:39:55,970
+نختار منهم ال password تبعنا ايش password must
+
+540
+00:39:55,970 --> 00:40:03,070
+contain at least digit or punctuation كل واحد لازم
+
+541
+00:40:03,070 --> 00:40:08,110
+يكون فيه مجموعة يا digit يا punctuation ضروري
+
+542
+00:40:08,940 --> 00:40:12,040
+كويس التاني ال digit التانية مش مشكلة تاخد اللي
+
+543
+00:40:12,040 --> 00:40:15,860
+بتاخده مش إشكال تاخد اللي بتهيأ فالآن صار عندي
+
+544
+00:40:15,860 --> 00:40:22,860
+الحقيقة two tasks task لأ الحالة الأولى و بعدين
+
+545
+00:40:22,860 --> 00:40:25,700
+بناء عليها نشوف التانية بمعنى أن الحالة الأولى هذه
+
+546
+00:40:25,700 --> 00:40:30,000
+بدك تفترض هل هي أخدت ال possibilities كلها معناة
+
+547
+00:40:30,000 --> 00:40:34,420
+ذلك أن التانية لازم تكون الاتنين بس اللي هي اما
+
+548
+00:40:35,570 --> 00:40:39,730
+digit or punctuation عشان تضمن ان في punctuation
+
+549
+00:40:39,730 --> 00:40:46,410
+وبعدين بدك تطرح منها او تجمعها على العكس تبعها ان
+
+550
+00:40:46,410 --> 00:40:50,650
+هنا punctuation وهنا كل ال letters ممكن تكون اللي
+
+551
+00:40:50,650 --> 00:40:53,930
+مسموح فيها letters اضافي لذلك بدك تطرح منهم
+
+552
+00:40:53,930 --> 00:40:56,970
+التكرارات اللي ممكن تحدث ايش التكرار اللي ممكن
+
+553
+00:40:56,970 --> 00:41:04,480
+يحدث ان الاتنين يطلعوا digit or punctuationالاتنين
+
+554
+00:41:04,480 --> 00:41:08,200
+يطلعوا زي بعض، معناته أنا جمعتهم على فرضية أنه
+
+555
+00:41:08,200 --> 00:41:11,780
+الخانة الأولى هي اللي هتحكم ليه، digit or
+
+556
+00:41:11,780 --> 00:41:16,500
+punctuation أو الخانة التانية، فانا هجمع على
+
+557
+00:41:16,500 --> 00:41:18,240
+الخانة الأولى لحاله و الخانة التانية لحاله، وبعدين
+
+558
+00:41:18,240 --> 00:41:23,640
+أطرح عدد أن الخالتين ظهر فيهم ال digit or
+
+559
+00:41:23,640 --> 00:41:27,960
+punctuationهنشوف كيف فزي ما قلنا هيها اللي هي جا
+
+560
+00:41:27,960 --> 00:41:31,320
+ال password لأ دي لأ has digit or punctuation
+
+561
+00:41:31,320 --> 00:41:36,840
+character in position one or two فإذا الشرط اللي
+
+562
+00:41:36,840 --> 00:41:41,620
+حاكمني شوية أنه لازم يكون فيه رقم أو علامة ترقيم
+
+563
+00:41:41,620 --> 00:41:44,760
+بتتعامل معها اللي هي punctuation بتتعامل معها أنه
+
+564
+00:41:44,760 --> 00:41:49,360
+ممكن تكون ظهرت في الحالة الأولى أو في اللي هي ال
+
+565
+00:41:49,360 --> 00:41:53,980
+position الأول أو ال position التانىفعملناهم كإنها
+
+566
+00:41:53,980 --> 00:41:56,920
+two problems بس بدنا ناخد بالنا إننا في الحالة هذه
+
+567
+00:41:56,920 --> 00:42:00,060
+لازم أطرح منهم إنه ممكن يظهر في الإتنين مع بعض
+
+568
+00:42:00,060 --> 00:42:03,220
+بالضبط فهي اللي صار تماما ففرضنا إن ال position
+
+569
+00:42:03,220 --> 00:42:09,700
+الأول هو اللي هيحتوي على ال digit or punctuation
+
+570
+00:42:09,700 --> 00:42:15,180
+تمام مضروبة في مين؟ في الطرف التاني اللي ممكن ياخد
+
+571
+00:42:15,800 --> 00:42:20,020
+التلت حالات طيب خلصنا منها طيب بالنسبة لل position
+
+572
+00:42:20,020 --> 00:42:23,520
+التاني هي ال position الأول هو ضربهم على طول هي 21
+
+573
+00:42:23,520 --> 00:42:29,060
+في 46 مباشرة بالنسبة لل position الأول هيعمل نفس
+
+574
+00:42:29,060 --> 00:42:32,280
+الكلام لل position التاني نفس الشيء برضه لل
+
+575
+00:42:32,280 --> 00:42:36,120
+position التاني بحيث انه يجمعهم مع بعض فصارت عندك
+
+576
+00:42:36,120 --> 00:42:39,180
+الرقم هذا جدش لما بدربوا حوالي تسعمية و اشي تسعمية
+
+577
+00:42:39,180 --> 00:42:46,000
+و عشريناللي هو ال punctuation أو ال digit ظهرت في
+
+578
+00:42:46,000 --> 00:42:49,940
+الخانة أو في ال position الأول زائد انها ظهرت في
+
+579
+00:42:49,940 --> 00:42:53,520
+ال position التاني طيب استنى في ناقص انه ممكن تكون
+
+580
+00:42:53,520 --> 00:42:56,620
+ظهرت في الحالتين في ال two positions فقداش
+
+581
+00:42:56,620 --> 00:42:59,720
+احتماليتها هذه احتماليتها او possibilities تعتها
+
+582
+00:42:59,720 --> 00:43:01,900
+ان يكون عندى عشرين
+
+583
+00:43:04,670 --> 00:43:08,810
+وهنا برضه اشرين فبتطلع ناقص اربعمية فبطلع totally
+
+584
+00:43:08,810 --> 00:43:15,250
+كله على بعض حوالي الف واربعمية واربعين كعدد
+
+585
+00:43:15,250 --> 00:43:18,930
+possibilities لل password في الحالة دي في ال
+
+586
+00:43:18,930 --> 00:43:24,530
+password الحالي طيب كمان أمثلة لو عندك مطلوب find
+
+587
+00:43:24,530 --> 00:43:29,520
+the number of three letter initialswhere none of
+
+588
+00:43:29,520 --> 00:43:33,260
+the letters is repeated طيب هذه أبسط منهم يعني
+
+589
+00:43:33,260 --> 00:43:39,680
+بسيطة جدا تلاتة لمجموعة حروف بشرط إنه إذا اخترنا
+
+590
+00:43:39,680 --> 00:43:43,740
+حرف في الخانة الأولى مايتكررش في التانية والأول
+
+591
+00:43:43,740 --> 00:43:47,720
+والتاني مايتكررش في التالتة خلاص فإذا هنا عندي ستة
+
+592
+00:43:47,720 --> 00:43:51,080
+وعشرين هنا بتصير ال possibilities فقط خمسة وعشرين
+
+593
+00:44:02,770 --> 00:44:09,480
+محتاجة كلام كتير؟سؤال direct هذا سريع قداش عدد ال
+
+594
+00:44:09,480 --> 00:44:14,740
+strings اللي بتقدر تاخدهم من string طوله أربعة
+
+595
+00:44:14,740 --> 00:44:18,560
+bits اتنين تثابر أربعة وانتهت الجثة طيب السؤال
+
+596
+00:44:18,560 --> 00:44:22,860
+اللي ورا count the number of bit strings length
+
+597
+00:44:22,860 --> 00:44:28,540
+four or less or less معناته بدك تجمع صارت task
+
+598
+00:44:28,540 --> 00:44:33,020
+مختلف عن بعض length four length three length two
+
+599
+00:44:33,020 --> 00:44:39,110
+length one check بدك تجمحهممع بعض فبنجمحهم بحيث
+
+600
+00:44:39,110 --> 00:44:43,650
+انه هيها اذا كانت ال length تبعنا واحد زائد اذا
+
+601
+00:44:43,650 --> 00:44:46,690
+كان ال length اتنين زائد اذا كانت تلاتة زائد اذا
+
+602
+00:44:46,690 --> 00:44:54,270
+كانت اربعة بس خلص تمام كمان مثال اه هذا مثال كويس
+
+603
+00:44:54,270 --> 00:44:59,510
+هاي مثال منيح كان ذا 6S of three digit numbers
+
+604
+00:44:59,510 --> 00:45:04,490
+مكون من three digit numbers خليا هو نفس المثال
+
+605
+00:45:04,490 --> 00:45:06,150
+تبعنا هاي three digit number
+
+606
+00:45:11,090 --> 00:45:17,470
+أيش مطلوب في three digit number which begin or end
+
+607
+00:45:17,470 --> 00:45:26,410
+with an even digit بيبدأ أو بينتهي ب even بس هي كل
+
+608
+00:45:26,410 --> 00:45:30,670
+المطلوب فبدنا نعرف قداش عدد الأرقام اللي مكونة من
+
+609
+00:45:30,670 --> 00:45:38,680
+ثلاث خانات وبتبدأ أو بتنتهي بdigit او integer even
+
+610
+00:45:38,680 --> 00:45:42,620
+ال integer ده عبارة عن even خلّيني شوي شوي ناخدهم
+
+611
+00:45:42,620 --> 00:45:48,560
+نبدأ بالأول و التاني و التالت نبدأ بال begin لأنه
+
+612
+00:45:48,560 --> 00:45:54,300
+begin هيها begin و بعدها في or ثم end with an even
+
+613
+00:45:54,300 --> 00:45:58,980
+صحيح فنبدأها or و بعدها نجمّل اتنينصحيح؟ انجمّلتن،
+
+614
+00:45:58,980 --> 00:46:02,340
+بس بدنا ناخد بالنا، بدنا نطرح، بعدين تقطحن، بس
+
+615
+00:46:02,340 --> 00:46:07,720
+ناخد حاجة حاجة هالوقت لما نقول بدي أبدأ ب even هل
+
+616
+00:46:07,720 --> 00:46:14,800
+يجوز أني أبدأ بصفر؟ في خانة المئات، في الحالة هذه
+
+617
+00:46:14,800 --> 00:46:19,980
+أنت بطلت three digit number صارت two digit number
+
+618
+00:46:19,980 --> 00:46:24,640
+صحيح؟ بمعنى أنه صفر تسعة وتسعين صفر تسعة وتسعين لأ
+
+619
+00:46:24,640 --> 00:46:30,020
+هي تسعة وتسعينتسعة وتسعين هي فعليا فإذا ماتظبطش
+
+620
+00:46:30,020 --> 00:46:33,900
+إذا ال possibilities لخانة المئات هنا خانة المئات
+
+621
+00:46:33,900 --> 00:46:39,560
+لأ بتبدأ من اتنين فإذا اتنين اربعة ستة تمانية
+
+622
+00:46:39,560 --> 00:46:45,720
+أربعة هاي الأربعة تعتنا مافيش فيها مشكلة هنا
+
+623
+00:46:45,720 --> 00:46:50,760
+العشرة كاملين من الصفر للتسعة صفر للتسعة يجوز و
+
+624
+00:46:50,760 --> 00:46:53,480
+هنا برضه من الصفر للتسعة يجوز مافيش عندي مشكلة
+
+625
+00:46:53,480 --> 00:46:55,220
+فعشرة عشرة
+
+626
+00:46:58,610 --> 00:47:05,890
+هي الحالة الأولى اللى هى begin طيب الحالة التانية
+
+627
+00:47:05,890 --> 00:47:09,830
+اللى
+
+628
+00:47:09,830 --> 00:47:16,450
+هى end with even عشان
+
+629
+00:47:16,450 --> 00:47:22,190
+نقول انتهت ب even أول اشي نفسك هدى تسعة لأن هدى
+
+630
+00:47:22,190 --> 00:47:27,690
+هتكون من واحد لتسعةمن واحد لتسعة فعليا تمام هنا
+
+631
+00:47:27,690 --> 00:47:32,650
+هيكون عندك عشرة فهنا هيكون جداش تسعة مظبوطين وهنا
+
+632
+00:47:32,650 --> 00:47:38,230
+هيكون عددهم خمسة عشان نخلص فيهم فهنا صارت تسعة في
+
+633
+00:47:38,230 --> 00:47:47,110
+عشرة في خمسة هذا اللي هي end with even طيب بين هذا
+
+634
+00:47:47,110 --> 00:47:52,010
+وهذا في أقام اتكررتفي أرقام تكررت معناه ذلك أنه
+
+635
+00:47:52,010 --> 00:47:55,930
+أنا محتاج أطرح منهم محتاجين و لازم نطرح منهم
+
+636
+00:47:55,930 --> 00:48:07,650
+تقاطؤهم بالضبط هذه الأربعة وهذه الخمسة خلاص
+
+637
+00:48:07,650 --> 00:48:10,770
+تضربهم فعلا و تطرحهم من مجموع الدربين اللي قدامك
+
+638
+00:48:10,770 --> 00:48:14,450
+هنا فهذه أربعة في عشرة في خمسة
+
+639
+00:48:20,300 --> 00:48:23,760
+فبطلع هى الأربعة فى عشرة فى خمسة بطلع عندك هنا
+
+640
+00:48:23,760 --> 00:48:31,780
+أربعمية والتانى أربعمية وخمسين والتالتة متين فهدى
+
+641
+00:48:31,780 --> 00:48:37,660
+زائد هدى ناقص هدى فبطلع عندك ستمية وتسعين أقل
+
+642
+00:48:37,660 --> 00:48:45,700
+ستمية وخمسين رقم بيحققوا هذا الشرط تمام الآن فى
+
+643
+00:48:45,700 --> 00:48:49,730
+عندنا حاجة مهمة كتير برضه خلّيكم معناها يا شباببعد
+
+644
+00:48:49,730 --> 00:48:53,490
+ما خلصنا مجموعة أنثى بالعد اتوقع كانت فيها حاجات
+
+645
+00:48:53,490 --> 00:48:59,010
+حلوة مسلية حركت دماغكوا شوية هتننطقل لحاجة اسهل
+
+646
+00:48:59,010 --> 00:49:05,450
+منها كمان ال vision هو ال principle او مبدأ فتحات
+
+647
+00:49:05,450 --> 00:49:11,100
+الحمام ابراج الحمام ابراج الحمام عبارة عن برجسمنتي
+
+648
+00:49:11,100 --> 00:49:13,940
+أو طين أو اشي و بيكون فيه فتحات لمين عشان تتخبى
+
+649
+00:49:13,940 --> 00:49:20,300
+فيه ال .. ال pigeons أو الحمام كويس إذا كان عندى
+
+650
+00:49:20,300 --> 00:49:24,280
+.. هذا طبعا مافيش بنستخدمها كنظرية بنستخدمها إذا
+
+651
+00:49:24,280 --> 00:49:29,060
+كان عندك عدد أكبر من k plus one objects أشياء
+
+652
+00:49:29,060 --> 00:49:33,420
+عددها أكبر من k زائد واحد في حين إن انت عندك عدد k
+
+653
+00:49:33,420 --> 00:49:39,090
+places أو الأماكن عددهم kعددهم K فمعنى ذلك أنت
+
+654
+00:49:39,090 --> 00:49:43,670
+بتكون ضامن هنا أنه على الأقل يوجد مكان فيه أكتر من
+
+655
+00:49:43,670 --> 00:49:47,590
+object مش هيك؟ إذا عدد ال objects أكتر من عدد
+
+656
+00:49:47,590 --> 00:49:52,610
+الأماكن فمعنى ذلك أنه بالضرورة هيكون one object at
+
+657
+00:49:52,610 --> 00:49:57,530
+least فيه at least أكتر من one object ممكن يكون
+
+658
+00:49:57,530 --> 00:50:00,770
+تلتة، خمسة، عشرة جد ما يكون يكون ليش؟ لأنه ممكن
+
+659
+00:50:00,770 --> 00:50:05,800
+يكون في places تانية ومافيش فيها مافيش فيهاو هذا
+
+660
+00:50:05,800 --> 00:50:10,260
+ما ينطبق على فعلًا أبراج الحمام أحيانًا هتلاقي إنه
+
+661
+00:50:10,260 --> 00:50:15,240
+في الصيف هيكونوا بعيد عن بعض كل واحد في hall لحاله
+
+662
+00:50:15,240 --> 00:50:19,840
+لكن في الشتاء هيسيبوا مجموعة halls فاضية و يدفوا
+
+663
+00:50:19,840 --> 00:50:26,880
+بعض لأن الدنيا بارد الدنيا؟ خلاص
+
+664
+00:50:26,880 --> 00:50:32,560
+صح طب كويس أنتوا أدرم إذا إلكوا في الجثة إذا إلكوا
+
+665
+00:50:32,560 --> 00:50:37,680
+في الجثةطيب كيف نقدر نعبر عن هذا الكلام .. هاي
+
+666
+00:50:37,680 --> 00:50:40,060
+شباب .. كيف نقدر نعبر عنه بال function و احنا
+
+667
+00:50:40,060 --> 00:50:43,440
+أخدنا function سابقا نقدر نقول إذا كانت if ال
+
+668
+00:50:43,440 --> 00:50:49,000
+function from A to B .. from A to B بحيث أنه A
+
+669
+00:50:49,000 --> 00:50:53,600
+أكبر من B زائد 1 بمعنى إن هي من ال domain و ال
+
+670
+00:50:53,600 --> 00:50:58,300
+domain هذا هي ال objects لالـ places و ال places
+
+671
+00:50:58,300 --> 00:51:01,880
+أقل من ال a ال code domain أقل من ال a فمعنى ذلك
+
+672
+00:51:01,880 --> 00:51:04,700
+تقدر تقول ان ال cardinality ل a أكبر من أو يساوي
+
+673
+00:51:04,700 --> 00:51:09,960
+ال cardinality ل b plus one plus one فهنا إذا some
+
+674
+00:51:09,960 --> 00:51:16,700
+element of b has more than two or equal to three
+
+675
+00:51:16,700 --> 00:51:22,590
+imagesunder if اكيد اكيد فمعنى ذلك انه دائما
+
+676
+00:51:22,590 --> 00:51:26,670
+بنظرية ال vision hole principle اكيد هذه not one
+
+677
+00:51:26,670 --> 00:51:32,230
+to one اكيد not one to one هذا sure تمام طبعا هنا
+
+678
+00:51:32,230 --> 00:51:37,090
+شايفين بعض امثلة الفكرة طول ما احنا بنتكلم عن
+
+679
+00:51:37,090 --> 00:51:42,170
+اتناشر hole و عندك تلتاشر visions معنى ذلك انه
+
+680
+00:51:42,170 --> 00:51:46,450
+لازم هتلاقي two visions at least موجودين في one
+
+681
+00:51:46,450 --> 00:51:47,110
+place
+
+682
+00:51:49,930 --> 00:51:53,090
+طيب أمثلتها زي أن نقول والله إذا كان في أند مية
+
+683
+00:51:53,090 --> 00:52:02,310
+واحد grades, numerical grades كويس مش يعني name
+
+684
+00:52:02,310 --> 00:52:06,410
+grades اللي هي a و b و c لأ numerical بمعنى واحد
+
+685
+00:52:06,410 --> 00:52:10,460
+ماخد صفر من ميةواحد من مية اتنين من مية اللي عندك
+
+686
+00:52:10,460 --> 00:52:15,220
+مية في المية فانت بتتكلم عن مية و واحد تقييم رقمي
+
+687
+00:52:15,220 --> 00:52:19,780
+من مية فاللي هي من صفر لمية ففي الحالة اذا كان
+
+688
+00:52:19,780 --> 00:52:23,920
+عندك اكتر من مية و واحد students in this class
+
+689
+00:52:23,920 --> 00:52:27,760
+معناته على الاقل فيه اتنين ماخدين نفس ل grade نفس
+
+690
+00:52:27,760 --> 00:52:30,160
+ل grade فانت بتعرف على طول انه فيه اتنين على الاقل
+
+691
+00:52:30,160 --> 00:52:32,620
+ماخدين نفس ل grade طبعا اكيد ال function هنا هتكون
+
+692
+00:52:32,620 --> 00:52:36,880
+ايش not one to onenot one two one الكلام بسيط و
+
+693
+00:52:36,880 --> 00:52:40,420
+sit down و شهد طيب كمان أمثلة هيك سريعة among any
+
+694
+00:52:40,420 --> 00:52:44,840
+group of three hundred sixty seven اذا كان والله
+
+695
+00:52:44,840 --> 00:52:48,100
+عندك مجموعة فيها من الناس تلاتمية سبعة و ستين
+
+696
+00:52:48,100 --> 00:52:51,960
+معناه ذلك انه انت متأكد تماما ان في اتنين على
+
+697
+00:52:51,960 --> 00:52:55,610
+الأقل مولودين في نفس اليوممئة بالمئة بالظبط
+
+698
+00:52:55,610 --> 00:53:00,010
+متأكدين تماما طيب إذا كان في عندك سبعة إجروب من
+
+699
+00:53:00,010 --> 00:53:03,270
+سبعة و عشرين كلمة بال English معناه ذلك إن انت
+
+700
+00:53:03,270 --> 00:53:07,870
+ضامن at least في عندك two words بدئين بنفس الحرف
+
+701
+00:53:07,870 --> 00:53:12,750
+أكيد طيب how many people must be selected from a
+
+702
+00:53:12,750 --> 00:53:17,010
+collection of fifteen married couples to ensure
+
+703
+00:53:17,010 --> 00:53:22,610
+that at least two of persons chosen are married to
+
+704
+00:53:22,610 --> 00:53:23,350
+each other
+
+705
+00:53:27,410 --> 00:53:34,990
+هنا بنتكلم عن خمستاشر couple خمستاشر couple هدولة
+
+706
+00:53:34,990 --> 00:53:38,990
+أزواج
+
+707
+00:53:38,990 --> 00:53:43,750
+أزواج يعني couples انت بتتكلم عن أزواج مع بعض كويس
+
+708
+00:53:43,750 --> 00:53:51,510
+فانت عندك من واحد اتنين لعند خمستاشر كويس و هتبدأ
+
+709
+00:53:51,510 --> 00:53:56,960
+تعمل لعبة انك تختار أفرادتختار أفراد كويس اختارنا
+
+710
+00:53:56,960 --> 00:54:00,360
+واحد اتنين تلاتة و احنا جديد بنطلع اللعبة مجموعة
+
+711
+00:54:00,360 --> 00:54:03,700
+يلعبوا طب انت بتضمن انه او جديش عدد الاختيارات
+
+712
+00:54:03,700 --> 00:54:06,920
+اللي لازم تختارها عشان تضمن مائة بالمائة ان اللي
+
+713
+00:54:06,920 --> 00:54:11,960
+اختارتهم فيهم اتنين couple أكيد ليش لأنه أسوأ
+
+714
+00:54:11,960 --> 00:54:16,820
+احتمال ممكن انك انت جاعد بتختار و جاعدين بتطلع one
+
+715
+00:54:16,820 --> 00:54:20,540
+من ال couple بس ال one الأول التاني التالت الرابع
+
+716
+00:54:20,540 --> 00:54:25,790
+عددهم جديش خمستاشرلسوء حظك إنه قعدت بتختار طلعوا
+
+717
+00:54:25,790 --> 00:54:31,690
+الخمستاش مختلفين عن بعض رقم ستاش sure بده يكون ال
+
+718
+00:54:31,690 --> 00:54:35,810
+couple تبعه اختارناه قبله مش هيك فإذا أكيد ستاشر
+
+719
+00:54:35,810 --> 00:54:39,730
+persons مائة بالمائة حكون ضمنة إنه at least في one
+
+720
+00:54:39,730 --> 00:54:45,550
+couple تم اختيارهم مش هيك منطقي أكيد أكيد أكيد جدا
+
+721
+00:54:45,550 --> 00:54:51,650
+مش واضحةعندك خمستاشر قبل، قبل يعني إيش؟ زوج و زوجة
+
+722
+00:54:51,650 --> 00:54:54,990
+هى الموجودين هنا و هى التانى و هى التالت و هى الخ
+
+723
+00:54:54,990 --> 00:54:58,410
+.. لعندك الخمستاشر، كويس؟ طبعا في النهاية لما بدنا
+
+724
+00:54:58,410 --> 00:55:01,990
+نختار، بختارش القبل مع بعضه، بختار one person
+
+725
+00:55:01,990 --> 00:55:07,730
+فمعنى ذلك أن عدد ال persons جداش؟ تلاتين، تلاتين،
+
+726
+00:55:07,730 --> 00:55:12,490
+طيب بدأنا نختار أسماء منهم، بالورقة و لها ده و
+
+727
+00:55:12,490 --> 00:55:19,120
+قعدنا نطلع و نسحبانت بأضمن ان اللي اخترتهم يوجد
+
+728
+00:55:19,120 --> 00:55:24,360
+فعلا فيهم at least one couple طيب أسوأ حاجة ان
+
+729
+00:55:24,360 --> 00:55:29,260
+اختار خمستاشر واحد مافيش ولا واحد couple مع التاني
+
+730
+00:55:29,260 --> 00:55:33,020
+ال 16 إجباري لازم هيكون couple مع واحد من
+
+731
+00:55:33,020 --> 00:55:38,780
+الخمستاشر اللي اخترتهم جابله تمام؟ تمام خلاص هذه
+
+732
+00:55:38,780 --> 00:55:41,180
+خليها للمرة القادمة ان شاء الله بنكملها
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/H4ttvdC1eCk.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/H4ttvdC1eCk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3752d1fd4bea1fd91df397844620bfea1bcf95d4
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/H4ttvdC1eCk.srt
@@ -0,0 +1,1991 @@
+1
+00:00:04,960 --> 00:00:07,120
+يعطيكم العفو يا شباب، اليوم إن شاء الله تعالى
+
+2
+00:00:07,120 --> 00:00:12,360
+بنحاول نختم ما تبقى لنا في موضوع letre إن شاء الله
+
+3
+00:00:12,360 --> 00:00:15,380
+الله، بعد ما اتكلمنا عن الـ letre، الـ introduction أخذنا
+
+4
+00:00:15,380 --> 00:00:21,780
+شوية terminology، أخذنا شوية theory المرة الماضية
+
+5
+00:00:21,780 --> 00:00:27,640
+حسبنا الـ edges مقابل الـ nodes مقابل الـ leaves،  جدش
+
+6
+00:00:27,640 --> 00:00:29,860
+الـ number of leaves، وبعدين اتكلمنا في الآخر على
+
+7
+00:00:31,610 --> 00:00:36,150
+ربطهم بالقوانين مع بعض، تمام. واليوم إن شاء الله
+
+8
+00:00:36,150 --> 00:00:39,370
+تعالى نأخذ applications of trees، طبعًا إذا نتكلم
+
+9
+00:00:39,370 --> 00:00:43,310
+عن applications of trees، مش هنخلص فعليًا، حقيقة يعني
+
+10
+00:00:43,310 --> 00:00:48,570
+لأن تطبيقاتها كثيرة جدًا، كمواد علمية، كأبحاث علمية،
+
+11
+00:00:48,570 --> 00:00:52,170
+لها تطبيقات وتطبيقات جدًا كبيرة، اليوم هنقتصر
+
+12
+00:00:52,170 --> 00:00:57,620
+فقط على جد الـ binary search أو الـ search عمومًا لأن
+
+13
+00:00:57,620 --> 00:01:00,300
+زي ما قلنا، هيكون في binary search، وبعدين هناخذ
+
+14
+00:01:00,300 --> 00:01:03,720
+decision trees، decision trees، من اسمها شغلة
+
+15
+00:01:03,720 --> 00:01:06,920
+القرارات، القرارات معناها واضحة جدًا، أن هذه مقدمة
+
+16
+00:01:06,920 --> 00:01:12,200
+لأهميتها للـ AI، هذه المقدمة اللي لأهميتها لأي AI
+
+17
+00:01:12,200 --> 00:01:15,520
+فما فيش حد بيشتغل في الـ AI، في الذكاء الاصطناعي، وما
+
+18
+00:01:15,520 --> 00:01:19,610
+بيعرّف حاجة اسمها decision trees أو كيف أنا ممكن
+
+19
+00:01:19,610 --> 00:01:24,010
+أعمل شجرة القرارات. شجرة القرارات من خلال الـ
+
+20
+00:01:24,010 --> 00:01:26,430
+flow chart، أنتم كلكم عارفينه، بتعرفوا ترسموه، الـ
+
+21
+00:01:26,430 --> 00:01:29,630
+flow chart هذا. فالـ flow chart عبارة عن سؤال و
+
+22
+00:01:29,630 --> 00:01:33,370
+إجابات: يا yes يا no، إجابات yes no، yes no، yes
+
+23
+00:01:33,370 --> 00:01:36,690
+no، ف أنت ممكن تعمل structure لكل الـ systems اللي
+
+24
+00:01:36,690 --> 00:01:40,630
+ممكن تخطر على بالك، بحيث إنك أنت في الآخر بناء على
+
+25
+00:01:40,630 --> 00:01:43,850
+conditions معينة، ممكن الـ consequential conditions
+
+26
+00:01:43,850 --> 00:01:48,430
+تطلع بقرار، تطلع في الآخر بإيش؟ بقرار، وأهمها يمكن
+
+27
+00:01:48,430 --> 00:01:51,810
+الأعراض بتاعة اللي عند الأطباء، في الأمراض، أعراض
+
+28
+00:01:51,810 --> 00:01:56,450
+بيبدأ يسألك عن مجموعة أعراض، عشان يستنتج منها الـ
+
+29
+00:01:56,450 --> 00:02:00,250
+decision المناسب، يستخدم أو يأخذ القرار المناسب.
+
+30
+00:02:00,250 --> 00:02:04,070
+فهذول الـ two applications بس اللي هنتكلم عنهم، لكن
+
+31
+00:02:04,070 --> 00:02:07,510
+زي ما قلت لكم مرة، الـ trees، الـ applications ساعتها
+
+32
+00:02:07,510 --> 00:02:14,730
+ضخمة وكثيرة في الأبحاث العلمية، فهنبدأ بشكل مبسط في
+
+33
+00:02:14,730 --> 00:02:18,590
+الـ binary search trees، شوية، يمكن في آخر الـ slides
+
+34
+00:02:18,590 --> 00:02:21,110
+هأوُصلكم إياها، شوية إنها تصير كمان مش binary، تكون
+
+35
+00:02:21,110 --> 00:02:26,190
+أكثر من binary، ونشوف لنا، نكتب لنا code عليها،
+
+36
+00:02:26,190 --> 00:02:29,610
+أتوقع ممكن تحتاجوها في الـ data structure، قد يجوز
+
+37
+00:02:29,610 --> 00:02:34,070
+مثلًا، أو شيء. فخلينا نشوفها لما نصلها. طيب، هنا الـ
+
+38
+00:02:34,070 --> 00:02:38,630
+binary search، سواء أنا بعمل search direct، مباشرة، الـ
+
+39
+00:02:38,630 --> 00:02:42,110
+search اللي إحنا عارفينه، اللي هو given x، تمام، و
+
+40
+00:02:42,110 --> 00:02:45,550
+ابحث لي عنها بكل بساطة، يعني ما فيش فيها كتير مشكلة.
+
+41
+00:02:45,550 --> 00:02:49,450
+طيب، إذا كانت given بهذا الشكل، فالموضوع كتير
+
+42
+00:02:49,450 --> 00:02:52,730
+سهل عليك، ليش؟ لأنه اتفقنا من المرة الماضية، بكون
+
+43
+00:02:52,730 --> 00:02:58,550
+عامل modeling للـ array تبعتي باستخدام الـ tree، و
+
+44
+00:02:58,550 --> 00:03:04,090
+مجرد فقط عارف إن الـ priority left to right، و الـ
+
+45
+00:03:04,090 --> 00:03:10,330
+left للـ subTree to write subtree، ماشي بس، وإيه
+
+46
+00:03:10,330 --> 00:03:12,870
+ماهي؟ ماهي، مادام أنا عملتها حسب الـ priority،
+
+47
+00:03:12,870 --> 00:03:16,470
+معناته هي ordered، خلاص، يعني معناته مرتبة، هذا عشان
+
+48
+00:03:16,470 --> 00:03:21,220
+أشوف x معينة، وأعرف وين مكانها، وين مكانها، وهل هي
+
+49
+00:03:21,220 --> 00:03:25,900
+موجودة ولا مش موجودة. سؤالين هما بقى: هل هي موجودة،
+
+50
+00:03:25,900 --> 00:03:29,000
+بدي أرجعها، أو أنه لأ، مش موجودة، بدي أرجعها بصفر، وهذا
+
+51
+00:03:29,000 --> 00:03:31,960
+نفس القوانين اللي أخذناها سابقًا، أو الـ rule اللي
+
+52
+00:03:31,960 --> 00:03:38,300
+أخذناها سابقًا. طيب، هذه بكل، بكل بساطة، الآن عشان
+
+53
+00:03:38,300 --> 00:03:42,660
+نتكلم عن هذا الموضوع، محتاجين نعرف، أخذناها سابقًا
+
+54
+00:03:42,660 --> 00:03:48,120
+برضه في الـ binary search، إن الـ order تبعنا أو الـ
+
+55
+00:03:48,120 --> 00:03:53,220
+complexity كانت logarithmic، وهنا نفس الكلام، أنتَ
+
+56
+00:03:53,220 --> 00:03:58,160
+لما يكون في عندك tree بهذا
+
+57
+00:03:58,160 --> 00:04:04,240
+الشكل، هي ثنائية، كلها binary، ومباشرة تيجي تقارن مع
+
+58
+00:04:04,240 --> 00:04:09,120
+أول عنصر، اللي هي الـ root، وتجد إن الـ x أكبر من..
+
+59
+00:04:09,120 --> 00:04:13,640
+معناته أنتَ مبدئيًا كل هذا استثنيته كله مرة واحدة.
+
+60
+00:04:13,640 --> 00:04:17,440
+استثنيته، أنتَ مش محتاج تبحث فيه، فأنتَ linear لأ، هي
+
+61
+00:04:17,440 --> 00:04:21,560
+مش linear، كـ linear، لأ، مش linear. طيب، فعملية الـ
+
+62
+00:04:21,560 --> 00:04:25,200
+search لـ existing item مش فيها مشكلة، لكن إحنا ممكن
+
+63
+00:04:25,200 --> 00:04:32,140
+برضه نستخدم نفس الـ tree to insert a new item. طيب،
+
+64
+00:04:32,140 --> 00:04:35,060
+مادام to insert a new item، معناته من الأساس أنا
+
+65
+00:04:35,060 --> 00:04:38,500
+ممكن أبدأ بأول عنصر، وباقي العناصر في الـ array
+
+66
+00:04:38,500 --> 00:04:40,980
+تبعتنا، نعملها إحنا insertion، يعني كأننا عملنا
+
+67
+00:04:40,980 --> 00:04:45,500
+sorting، كأن إحنا عملنا sorting، وحاضر في المثال برضه
+
+68
+00:04:45,500 --> 00:04:48,900
+على الـ slides اليوم برضه، كيف أنا ممكن أعمل sorting
+
+69
+00:04:48,900 --> 00:04:52,160
+لـ sequence موجود عندك، ده sequence موجود عندك، تمام.
+
+70
+00:04:52,160 --> 00:04:56,040
+فإذا في الحالة دي، إما existing item موجود فأنتَ بدك
+
+71
+00:04:56,040 --> 00:05:01,320
+تبحث عنه، أو بدك تعمل inserting لـ new item، تمام.
+
+72
+00:05:01,320 --> 00:05:07,400
+وكلاهما، لو بدك تعمل sorting، لأنك بدك الـ x اللي أنتَ
+
+73
+00:05:07,400 --> 00:05:10,440
+بدك تحطه في مكانه الصحيح، بدك كأنك بتبحث عنها في
+
+74
+00:05:10,440 --> 00:05:14,560
+البداية، بتبحث عنها، وين المكان اللي المفروض تكون
+
+75
+00:05:14,560 --> 00:05:18,680
+موجودة فيه؟ ما لاقيتهاش قيمتها، بتحطها في المكان اللي لازم
+
+76
+00:05:18,680 --> 00:05:21,440
+تكون موجودة فيه، ما لاقيتهاش بتحطها، إذا لاقيتها خير
+
+77
+00:05:21,440 --> 00:05:24,880
+وبركة، خلاص، معناته موجودة، ما فيش داعية تكررها تاني.
+
+78
+00:05:24,880 --> 00:05:28,720
+تمام، إذا ما كانت موجودة، زي ما قلنا already
+
+79
+00:05:28,720 --> 00:05:33,540
+present، إذا ما كانت موجودة، الآن الأشكالية..
+
+80
+00:05:33,540 --> 00:05:36,000
+الأشكالية الثانية، إنه بعد ما تعمل sorting، أنتَ
+
+81
+00:05:36,000 --> 00:05:41,420
+محتاج تطبع الـ sequence الجديد. طيب، الطباعة لغتها
+
+82
+00:05:41,420 --> 00:05:45,920
+فكرة الـ log، كلكم عارفين إن الـ print هي linear، مش
+
+83
+00:05:45,920 --> 00:05:50,780
+هيك، الـ print process أو operation هي linear، لأن
+
+84
+00:05:50,780 --> 00:05:53,520
+أنتَ هتروح لـ element by element، أنتَ لازم تمر عليهم
+
+85
+00:05:53,520 --> 00:05:55,100
+element by element. فإذا كان والله بدنا نروح للـ
+
+86
+00:05:55,100 --> 00:05:59,500
+printing لكل الـ items، فمعنى ذلك رجعنا لمين؟ للـ
+
+87
+00:05:59,500 --> 00:06:03,320
+linear complexity، linear complexity. أما لأ، إذا
+
+88
+00:06:03,320 --> 00:06:09,500
+مجرد search، خلاص، بدك تروح لمين؟ أكيد هتكون log. طب
+
+89
+00:06:09,500 --> 00:06:15,200
+sorting، لأ، أنتَ لازم تروح لهم واحدة واحدة، لازم
+
+90
+00:06:15,200 --> 00:06:18,080
+تمسكهم واحدة واحدة، معنى ذلك إن هي direct
+
+91
+00:06:18,080 --> 00:06:26,140
+dependent على الـ number of inputs أو الـ arguments، جدش
+
+92
+00:06:26,140 --> 00:06:29,080
+عددهم خمسين، أنتَ لازم تمسكهم واحدة واحدة، الخمسين
+
+93
+00:06:29,080 --> 00:06:33,640
+كامل. فـ search الـ complexity شيء، وـ sorting الـ
+
+94
+00:06:33,640 --> 00:06:38,420
+complexity شيء ثاني، تمام، كويس. ففي أسوأ الأحوال،
+
+95
+00:06:38,420 --> 00:06:43,200
+مادام إن أنا بتعامل مع to insert، أعمل inserting في
+
+96
+00:06:43,200 --> 00:06:46,240
+الـ sequence، في الـ sequence، فعلى طول في الـ worst
+
+97
+00:06:46,240 --> 00:06:50,000
+case، أنا بتكلم عن linear، لأنه همسكهم واحد واحد، مش
+
+98
+00:06:50,000 --> 00:06:54,740
+هعمل زي فكرة مجرد search بس، لأ، هنا insert، يعني
+
+99
+00:06:54,740 --> 00:06:58,860
+sorting، يعني sorting، بتصير linear، انتهى الكلام،
+
+100
+00:06:58,860 --> 00:07:03,440
+لكن في الـ search logarithmic، أنتَ بتقدر بكل بساطة
+
+101
+00:07:03,440 --> 00:07:07,960
+branch كامل تستثنيه من قرارك، فما تبحثش فيه أصلًا،
+
+102
+00:07:07,960 --> 00:07:14,780
+ما تدورّش على عناصره، بتصير linear، آه، لأن أنتَ هتمسكهم
+
+103
+00:07:14,780 --> 00:07:18,320
+واحد واحد. لأ، عملية الـ insert، إذا كان بدك تعملها
+
+104
+00:07:18,320 --> 00:07:25,740
+insert و search مع بعض، بتصير n في log of n، ليش؟
+
+105
+00:07:25,740 --> 00:07:31,920
+لأن كل واحدة.. بالضبط، واضحة؟ كل واحدة هتمسكها
+
+106
+00:07:31,920 --> 00:07:36,390
+لحال، فأنتَ نفترض عندك عشرة elements، عشرة elements،
+
+107
+00:07:36,390 --> 00:07:40,970
+الأولى هتكون هي الـ root، هتحطها، هتبدأ فيها، والباقي
+
+108
+00:07:40,970 --> 00:07:43,930
+بدك تحطه بالنسبة لي، عشان تعمل order في الآخر، الثاني
+
+109
+00:07:43,930 --> 00:07:49,710
+الآن هتعملها كأنك عندك الـ tree موجودة، كويس، وبدك
+
+110
+00:07:49,710 --> 00:07:53,930
+تبحث عن العنصر الثاني. طيب، هذه لحالها الـ order
+
+111
+00:07:53,930 --> 00:07:57,090
+تبعها log، تمام.
+
+112
+00:07:59,030 --> 00:08:02,270
+من الـ in اللي موجودين عندك، هدول من العشرة أو
+
+113
+00:08:02,270 --> 00:08:04,890
+العشرين، أو المية اللي موجودة عندك، يعني صارت log
+
+114
+00:08:04,890 --> 00:08:11,110
+مضروبة في عددهم، صارت n log of n، واضحة؟ فأنتَ بدك
+
+115
+00:08:11,110 --> 00:08:14,990
+تاخد بالك، لما بدك تعمل sorting، هل sorting يعني بدك
+
+116
+00:08:14,990 --> 00:08:17,270
+تعمل search مع sorting مع بعض، المهم أثناء
+
+117
+00:08:17,270 --> 00:08:17,930
+مضروبين في بعض.
+
+118
+00:08:21,330 --> 00:08:24,490
+هي مثال.. المثال بكل بساطة، زي ما قلنا، بنبدأ بالـ
+
+119
+00:08:24,490 --> 00:08:26,990
+root، عشان نصنفها، وإحنا المرة اللي فاتت أصلًا
+
+120
+00:08:26,990 --> 00:08:30,870
+أخذناها وخلصناها. لسه، هذه ببدأها، لما بدي أشوف الـ
+
+121
+00:08:30,870 --> 00:08:34,050
+tree هذه، وأرسم الـ sequence أو أكتب الـ sequence
+
+122
+00:08:34,050 --> 00:08:38,090
+فعليًا، تبحث كيف موجود، هأجد إنه ببدأ من السبعة.
+
+123
+00:08:38,090 --> 00:08:41,830
+السبعة الآن فيها lift؟ آه، فيها lift، فالـ lift أولى
+
+124
+00:08:41,830 --> 00:08:45,770
+الـ priority lift to right، صح؟ فيها lift أولى. طيب،
+
+125
+00:08:45,770 --> 00:08:49,000
+وصلنا للتلاتة، التلاتة فيها lift؟ آه، فيها lift، فيها
+
+126
+00:08:49,000 --> 00:08:53,920
+left، آه، هنا left، ما ضلش left، معناته هنا zero. طيب،
+
+127
+00:08:53,920 --> 00:09:01,360
+zero، بطلع عندي واحد، الواحد أولى right للـ root، بيجي
+
+128
+00:09:01,360 --> 00:09:06,620
+بعده، فـ left to right، واحدة، اثنين، تلاتة، هيها left
+
+129
+00:09:06,620 --> 00:09:11,560
+to right، على جد sub tree. فأنتُم الآن بتتعاملوا مع
+
+130
+00:09:11,560 --> 00:09:16,780
+sub tree، هيها هذه sub tree، ترتيب الـ sub tree لحالها
+
+131
+00:09:16,780 --> 00:09:20,540
+left to right، بما فيهم الـ root تبعها، طبعًا الـ sub
+
+132
+00:09:20,540 --> 00:09:23,380
+root هنا بيصير اسمه مش الـ root الأصلي، تمام.
+
+133
+00:09:23,380 --> 00:09:27,100
+فهدول بهذا الشكل، واحدة، اثنين، تلاتة، واحد، اثنين، صفر،
+
+134
+00:09:27,100 --> 00:09:31,340
+واحد، اثنين. طيب، خلصنا الآن. لاحظ كأنه إيش سويت؟ كأنه
+
+135
+00:09:31,340 --> 00:09:35,440
+هاد الـ sub tree تبعت، خلصت الـ left
+
+136
+00:09:38,660 --> 00:09:43,480
+واللي مثلته بتلات عناصر، فعليًا الآن الـ root ثم
+
+137
+00:09:43,480 --> 00:09:49,260
+اليمين، فصارت إيش؟ تلاتة، خمسة. خلصنا الآن الـ sub tree
+
+138
+00:09:49,260 --> 00:09:56,740
+هذه، كأنها خلصت عنصر شمال بالنسبة للـ tree الأصلية.
+
+139
+00:09:56,740 --> 00:10:00,000
+الآن بدنا نطلع الـ tree هذه، في ضل إيش لفت عليها؟
+
+140
+00:10:00,000 --> 00:10:05,390
+ما ضلّش، فإذا نقعد نرتّبها، السبعة، ثم نبدأ باليمين، الجزء
+
+141
+00:10:05,390 --> 00:10:09,390
+المتبقي يمين. طب، هد فيه إلها شمال كـ sub-tree، فيه
+
+142
+00:10:09,390 --> 00:10:13,630
+إلها شمال. طيب، نبدأ نشوف، جبل ما نبدأ نتعامل مع الـ
+
+143
+00:10:13,630 --> 00:10:16,970
+nodes نفسها، بتعامل مع الـ sub-tree الأول، فهي في sub
+
+144
+00:10:16,970 --> 00:10:21,170
+-tree هد، لأ، هد الـ sub-tree، نخلص الـ sub-tree هد، الـ
+
+145
+00:10:21,170 --> 00:10:29,290
+left، الـ root، الـ 11، اللي هي اليمين تبع الـ subtree
+
+146
+00:10:29,290 --> 00:10:32,370
+خلصت subtree، يعني كأنها بالنسبة للـ 12، خلصت الـ
+
+147
+00:10:32,370 --> 00:10:34,730
+node اللي هنا، كلها باللي فيها، واللي هي في النهاية
+
+148
+00:10:34,730 --> 00:10:37,990
+مش node، هي subtree، شايفها هو بالنسبة له الـ node
+
+149
+00:10:37,990 --> 00:10:47,550
+تمام، 12، ثم 15. ففعليًا هي sorted الـ sequence عندنا
+
+150
+00:10:47,550 --> 00:10:52,630
+هنا sorted، ما فيش فيه أي مشكلة نهائيًا، ترتيب طبعًا
+
+151
+00:10:52,630 --> 00:10:56,470
+العكس صحيح، ممكن تبدأ عملية الترتيب منه، بس في
+
+152
+00:10:56,470 --> 00:11:00,230
+الحالة هذه، عشان تبدأ عملية الترتيب، بدي يكون هو
+
+153
+00:11:00,230 --> 00:11:05,230
+جايك unordered، دائمًا العنصر اللي في الأول هو اللي
+
+154
+00:11:05,230 --> 00:11:09,210
+بيحدد الشبكة أو الـ tree تبعتك، مين العنصر اللي
+
+155
+00:11:09,210 --> 00:11:12,710
+موجود في البداية؟ أنا بفهم إنه كان أول عنصر، لما
+
+156
+00:11:12,710 --> 00:11:17,950
+عملوا construction للـ tree هذي اللي قدامنا، كان فيه
+
+157
+00:11:17,950 --> 00:11:22,920
+السبعة، زي ما قعدنا هنشوف في المثال اللي جاي، هاي
+
+158
+00:11:22,920 --> 00:11:29,220
+مثال، هاي في عندك مثال، بدنا نرتب مجموعة التخصصات
+
+159
+00:11:29,220 --> 00:11:34,940
+هذه حسب اسمها، أو حسب الحروف بتاعتها، حسب حروفها
+
+160
+00:11:34,940 --> 00:11:37,740
+alphabetical يعني. فبدنا نتعامل معاه as a
+
+161
+00:11:37,740 --> 00:11:41,140
+alphabetical sorting، بدنا نعمل sorting بالنسبة للـ
+
+162
+00:11:41,140 --> 00:11:44,660
+alphabetical، في عندك الـ mathematics، خلاص، الـ
+
+163
+00:11:44,660 --> 00:11:47,800
+mathematics هي اللي جيتها في الأول، بحطها في الأول،
+
+164
+00:11:47,800 --> 00:11:52,300
+صارت هي الـ root، بمعنى لو عكستني إياهم وحطيت لي كلمة
+
+165
+00:11:52,300 --> 00:11:56,680
+تانية، حد فيها، فما تقعدش تغلب حالك تعمل search في
+
+166
+00:11:56,680 --> 00:12:02,100
+البداية، لأ، اللي قدامك هـ to مش هيفرج معاك كتير في
+
+167
+00:12:02,100 --> 00:12:06,420
+الآخر، الـ sorting هتطلع معك، هتطلع معك، ما تقلقش،
+
+168
+00:12:06,420 --> 00:12:10,560
+sorting حسب left to right، و الـ left للـ
+
+223
+00:16:45,650 --> 00:16:46,990
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+224
+00:16:46,990 --> 00:16:48,590
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+225
+00:16:48,590 --> 00:16:48,630
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+226
+00:16:48,630 --> 00:16:48,770
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+227
+00:16:48,770 --> 00:16:49,330
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+228
+00:16:49,330 --> 00:16:49,710
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+229
+00:16:49,710 --> 00:16:54,160
+يعني الله يعني الله يعني الله يعني الله يعنى إيه
+
+230
+00:16:54,160 --> 00:17:00,600
+عشان بس أركز معاك، search ولا sort، insert اللي هي
+
+231
+00:17:00,600 --> 00:17:02,840
+بدأت تكون عبارة عن search وبعدين اللي هو تمام
+
+232
+00:17:02,840 --> 00:17:05,900
+تمام ممتاز، يعني عندك تمال sorting مع .. مع عدد ..
+
+233
+00:17:05,900 --> 00:17:11,260
+خلاص سبحان الله، يدرنها من 0 إلى 10، هذه بطلت اسمها
+
+234
+00:17:11,260 --> 00:17:14,620
+الـ worst case بالعكس، هذه الـ worst case وأنا جيت
+
+235
+00:17:14,620 --> 00:17:17,060
+أنا مش عارف إنهم مرتبين أو مش مرتبين، فجيت أضيف
+
+236
+00:17:17,060 --> 00:17:20,160
+شوية، هذي أه؟ إيش .. إيش طالع معاك؟ أضفنا السفر
+
+237
+00:17:20,160 --> 00:17:24,520
+بالأول كويس، بعدين بنضيف الواحد وراح ترمي الاتنين
+
+238
+00:17:24,520 --> 00:17:27,540
+وراح ترمي اتنين، جيت على العملية الـ .. الـ searching
+
+239
+00:17:27,540 --> 00:17:30,980
+بطلنا إحنا ننزل login بس إن إحنا ننزل انصر وانصر
+
+240
+00:17:30,980 --> 00:17:37,440
+صار زي كده إن هي ممكن تلزق، نزل صارت كأنها سطر كامل
+
+241
+00:17:39,700 --> 00:17:42,680
+كويس، بس أنت برضه نفس الجثة، أنت في النهاية بتتعامل
+
+242
+00:17:42,680 --> 00:17:47,140
+مع كل node على أساس إن هي yes no yes no yes no
+
+243
+00:17:47,140 --> 00:17:55,760
+معاك، والله فاهمك فاهمك فاهمت
+
+244
+00:17:55,760 --> 00:17:58,520
+جزدك على أساس إن كلهم مالوا في اتجاه واحد، كلهم
+
+245
+00:17:58,520 --> 00:18:04,760
+أخدوا اتجاه اتجاه واحد، لما بتيجي بتعمل insertion
+
+246
+00:18:07,240 --> 00:18:10,340
+والله هي بدها بحث، يعني مش غلط، خلينا ناخدهم واحدة
+
+247
+00:18:10,340 --> 00:18:15,160
+واحدة، مش هتصبح .. لأ، هي صادفة معاك، انفع أنت مش
+
+248
+00:18:15,160 --> 00:18:20,200
+هتستغل فكرة الـ decision، لأنه دايما هتكون معاك أكبر
+
+249
+00:18:20,200 --> 00:18:21,340
+أو أصغر، ده مش هتكون أصغر
+
+250
+00:18:24,050 --> 00:18:28,030
+أو أكبر، لو كانت بالعكس، لو كانت بالعكس، يعني اتجاه
+
+251
+00:18:28,030 --> 00:18:31,570
+عكسي، اتجاه عكسي، خلينا نبحثها، مش غلط، أقولك خلينا
+
+252
+00:18:31,570 --> 00:18:34,750
+نعتبرها سؤال من الأسئلة المرة القادمة، ونتعامل
+
+253
+00:18:34,750 --> 00:18:37,730
+معها كأنها سؤال مستقل، ونحلها نشوفها إن شاء الله
+
+254
+00:18:37,730 --> 00:18:43,150
+كويس، إحنا كان في chemistry لسه، والله ما إحنا
+
+255
+00:18:43,150 --> 00:18:44,930
+ماخدين بالنا إن في لسه chemistry، إما تقولوا ليه
+
+256
+00:18:44,930 --> 00:18:50,450
+لسه في الـ C، أهو شوفين أنت دخلتنا في الـ .. هي لسه في
+
+257
+00:18:50,450 --> 00:18:56,510
+الـ main and chemistry، الـ C بتحسني مش كتير باينة الـ C
+
+258
+00:18:56,510 --> 00:18:59,410
+هي باينة، أنت قعدت بتقولي كلهم شمال شمال، هي
+
+259
+00:18:59,410 --> 00:19:06,410
+طلعت لك شمال على طول، طيب، تأثرت بكلامك أه؟ طيب نروح
+
+260
+00:19:06,410 --> 00:19:10,660
+لـ decision trees، في الـ decision trees هنا بدنا
+
+261
+00:19:10,660 --> 00:19:14,460
+ناخد قرار، القرار تبعنا بدي يكون مبني على tree
+
+262
+00:19:14,460 --> 00:19:20,100
+بمعنى yes و no، وبدي أوصل لقرار في النهاية، القرار
+
+263
+00:19:20,100 --> 00:19:23,680
+هيكون مبني على situations معينة، أكيد بدي يكون مبني
+
+264
+00:19:23,680 --> 00:19:28,180
+على situations، فكل decision point أو situation
+
+265
+00:19:28,180 --> 00:19:35,600
+تمثل بـ node، تمثل بـ node، زي إنه نقول الـ situation
+
+266
+00:19:35,600 --> 00:19:45,030
+المعينة، هل X أكبر من خمسة؟ فبدي أقول yes or no؟ yes أو
+
+267
+00:19:45,030 --> 00:19:50,530
+no، فهذه هنا الـ situation اللي أنا بسأل عليها، تمثل
+
+268
+00:19:50,530 --> 00:19:56,480
+بشكل node، طيب الـ action اللي بده يصير أو عادة الـ
+
+269
+00:19:56,480 --> 00:20:01,200
+edge، هذي عشان تروح لـ decision، هذي المفروض النتيجة
+
+270
+00:20:01,200 --> 00:20:04,620
+بتاعة الـ situation، الـ action اللي بده يصير، هل بدي
+
+271
+00:20:04,620 --> 00:20:07,720
+يعني بدي أقارن، بدي أفحص الـ situation وبناء على
+
+272
+00:20:07,720 --> 00:20:11,740
+القرر اللي طلع معايا أو النتيجة بدي أقول فعلا
+
+273
+00:20:11,740 --> 00:20:16,360
+متحقق أو غير متحقق، بمثلها بالـ edges عشان أروح
+
+274
+00:20:16,360 --> 00:20:20,480
+للقرارات، القرار هذا ممكن يكون نهائي، فهذه معناته
+
+275
+00:20:20,480 --> 00:20:24,320
+عبارة عن leaf، أو لأ، هي لسه محتاجة كمان فحص تاني
+
+276
+00:20:24,320 --> 00:20:31,180
+فتصبح هي كمان node لـ situation، بدها فحص لـ
+
+277
+00:20:31,180 --> 00:20:33,680
+situation تاني، بدها فحص زي ما نقول أكبر من خمسة
+
+278
+00:20:33,680 --> 00:20:39,830
+طيب هنا X أصغر من اتنين،  عسى اسم اللي بدي أقول، هل هي
+
+279
+00:20:39,830 --> 00:20:44,110
+من 2 إلى 5 مثلا، أقول والله قيمة X من 2 إلى 5، فنفس
+
+280
+00:20:44,110 --> 00:20:47,850
+الكلام، بدي أقول yes or no، فهل بدي أروح للـ terminal
+
+281
+00:20:47,850 --> 00:20:51,070
+فهذه معناته القرار النهائي، أو لأ، لسه محتاج كمان
+
+282
+00:20:51,070 --> 00:20:55,390
+فحص تاني، زي قصة الأعراض، أنا بسألش عن أعراض واحد
+
+283
+00:20:55,390 --> 00:20:58,840
+وخلاص، الطبيب عادة بيسألك عن العرض الأول، ثم العرض
+
+284
+00:20:58,840 --> 00:21:02,180
+التاني، ثم التالت، وهو بيحط في دماغه sequence
+
+285
+00:21:02,180 --> 00:21:06,400
+لمجموعة الأعراض هذه، عشان يجمعهم مع بعض، ويحاول
+
+286
+00:21:06,400 --> 00:21:14,640
+يطلع بقرار معين، تمام، الآن واحدة
+
+287
+00:21:14,640 --> 00:21:17,860
+من الأمثلة الواضحة على هذا الموضوع هي الـ coin
+
+288
+00:21:17,860 --> 00:21:22,060
+weighing problem، اللي هي عندك مجموعة coins، والـ
+
+289
+00:21:22,060 --> 00:21:25,500
+coins هذه، نفترض الخمسين مليم الفلسطيني
+
+290
+00:21:28,130 --> 00:21:34,750
+من عملتنا الفلسطينية، كويس، الخمسين Palestinian مليم
+
+291
+00:21:34,750 --> 00:21:41,170
+أو millions، كويس، عندي تمن قطع، التمن قطع هدولة
+
+292
+00:21:41,170 --> 00:21:47,110
+فيهم واحدة زائفة، كم وزن محتاج بـ free being
+
+293
+00:21:47,110 --> 00:21:54,290
+balanced عشان اكتشف مين الزائفة، طيب الزائفة هذه
+
+294
+00:21:54,290 --> 00:22:01,510
+كيف زائفة؟ هي lighter counterfeit، بمعنى وزنها أقل من
+
+295
+00:22:01,510 --> 00:22:06,810
+الباقي، لأن كلكم عارفين إنه قيمة المعدن نفسه
+
+296
+00:22:06,810 --> 00:22:10,650
+المفروض إنه حسب الوزن من المعدن نفسه، يكون يعطي نفس
+
+297
+00:22:10,650 --> 00:22:15,350
+قيمة العملة، طيب لما أنا آكل شوية منه وآكل من هذا
+
+298
+00:22:15,350 --> 00:22:17,470
+شوية وآكل من هذا شوية وآكل من هذا شوية، بطلت
+
+299
+00:22:17,470 --> 00:22:22,400
+خمسين مليم، صارت لها 45 مليم مثلا، فعليا يعني قيمة
+
+300
+00:22:22,400 --> 00:22:27,120
+المعدن نفسه أصبح بساوي الخمسين بساوي خمسة وأربعين
+
+301
+00:22:27,120 --> 00:22:30,400
+منه، وأنا روحت جمعتها الأكم من واحدة، وحطيتهم في
+
+302
+00:22:30,400 --> 00:22:34,820
+coin جديدة، اربحت فيها خمسين إضافية، تلغشوا هو هيك
+
+303
+00:22:34,820 --> 00:22:42,000
+بتمام، فمعنى ذلك إنه هي أقل وزنا، أقل وزنا، okay، كم
+
+304
+00:22:42,000 --> 00:22:43,160
+ليه؟
+
+305
+00:22:53,630 --> 00:22:59,670
+ممتاز 100%، الآن أنت حللته منطقيا صح، وحلك صح، الآن
+
+306
+00:22:59,670 --> 00:23:02,670
+بدنا نحل الكلام اللي أنت حللته هذا، نحطه في قالب
+
+307
+00:23:02,670 --> 00:23:07,570
+علمي، نحطه في قالب رياضي، القالب الرياضي ببساطة هي
+
+308
+00:23:07,570 --> 00:23:12,790
+الـ height تبعت للـ tree، لأن الـ tree أنا بتعامل أنا
+
+309
+00:23:12,790 --> 00:23:15,990
+مع الـ tree، واللي أنت قلت لنا إياه الآن، أنت قلت
+
+310
+00:23:15,990 --> 00:23:21,610
+tree، بمعنى أنت حطيت decision، عفوا situation، الـ
+
+311
+00:23:21,610 --> 00:23:27,510
+situation هذا حللته كنتائج، إما قاعد يقول إما إن هي
+
+312
+00:23:27,510 --> 00:23:33,610
+متساويين، فمعنى ذلك إن هي عندك هذا situation معينة
+
+313
+00:23:33,610 --> 00:23:36,870
+هي الوزن اللي أنت عملته، إيش الـ possibilities تبعته؟
+
+314
+00:23:36,870 --> 00:23:45,040
+قلت إما يكون متساويين balanced، أو اليمين أعلى، فمعنى
+
+315
+00:23:45,040 --> 00:23:50,240
+ذلك إنه الشمال فيها الزائف، أو الشمال الأعلى، فمعنى
+
+316
+00:23:50,240 --> 00:23:55,900
+ذلك إنه كفة اليمين اللي فيها القطعة الزائفة، اعمل
+
+317
+00:23:55,900 --> 00:24:03,600
+التلاتة، فهنا نصرنا نتكلم عن theory tree، تمام، هذه
+
+318
+00:24:03,600 --> 00:24:10,040
+بكل بساطة أصبحت كأنه بهذا الشكل، هذه المرة الأولى
+
+319
+00:24:10,740 --> 00:24:14,680
+بعدين قلت لنا إن في مرة ثانية، تمام، المرة الثانية
+
+320
+00:24:14,680 --> 00:24:20,060
+المعنى هتكون يا هنا يا هنا يا هنا، برضه في وزنات
+
+321
+00:24:20,060 --> 00:24:29,400
+الوزنات هذه هتكون تلاتة ولا اتنين هنا
+
+322
+00:24:29,400 --> 00:24:32,760
+كنتائج، وزنتين، إذا كانوا balanced، أنا بتكلم عن
+
+323
+00:24:32,760 --> 00:24:37,580
+تمانية، أي
+
+324
+00:24:37,580 --> 00:24:42,260
+ممكن تكون تلاتة، إحنا ممكن نساوي الأخف والأثقل صح
+
+325
+00:24:42,260 --> 00:24:46,560
+لأنه اللي فهمته منك إن أنت ممكن تحط تلاتة مقابل
+
+326
+00:24:46,560 --> 00:24:52,940
+تلاتة، طيب واحدة منهم وزنت، معناته الأخف فيها الزائف
+
+327
+00:24:52,940 --> 00:24:57,520
+خلاص، كل السبعة هدول هي case سليم، التلاتة هدولة
+
+328
+00:24:57,520 --> 00:25:01,580
+بدنا نحط اتنين منهم على وزنة، فهيطلع برضه تلاتة
+
+329
+00:25:01,580 --> 00:25:05,160
+possibilities ممكنين، إنه اليمين أو الشمال أو
+
+330
+00:25:05,160 --> 00:25:07,960
+balanced، فاللي ضلت ما وزنتهاش هي الزائفة، بتصير
+
+331
+00:25:09,050 --> 00:25:12,550
+واضحة؟ فإذا لأ، أنا هنا واحدة منهم هتكون اتنين هم
+
+332
+00:25:12,550 --> 00:25:17,870
+الاتنين في حال اللي ضالوا برا، بمعنى التلاتة والـ
+
+333
+00:25:17,870 --> 00:25:22,350
+تلاتة، رجحوا مع بعض، الاتنين متساويتين، الاتنين
+
+334
+00:25:22,350 --> 00:25:25,750
+اللي برا هم اللي فيهم الزائف، هنا بطلع إشارة يمينا
+
+335
+00:25:25,750 --> 00:25:31,090
+لشمال، خلاص، فهتكون بهذا الشكل
+
+336
+00:25:34,590 --> 00:25:40,430
+أه، طيب كم .. كم level هيطلع معاك؟ هات ناخد أربعة
+
+337
+00:25:40,430 --> 00:25:46,630
+أربعة، هات نحللها بكل بساطة، بدك تشتغل على هنا طبعا
+
+338
+00:25:46,630 --> 00:25:51,330
+إحنا كنا بنتكلم تلاتة مقابل تلاتة، هنا بدك تشتغل
+
+339
+00:25:51,330 --> 00:25:53,090
+على أربعة مقابل أربعة، طيب
+
+340
+00:25:56,450 --> 00:26:00,030
+أه، أنا عارف والله عارف، بس خلينا نـ .. أتبع معاكم
+
+341
+00:26:00,030 --> 00:26:03,450
+ماشي، مش غلط، خلينا نفكر، وخلينا نـ .. ننطلق، أنا
+
+342
+00:26:03,450 --> 00:26:06,770
+أحيانا بكون عارف إنه لأ، هتوصلنا لإش .. مش مش دي
+
+343
+00:26:06,770 --> 00:26:09,470
+لكن لازم نكمل مع بعض، أنت فاكر، مش غلط، أربعات و
+
+344
+00:26:09,470 --> 00:26:14,210
+وزنتين، هي أربعة أربعة، صار عندي هنا أربعة، أنت بتقول
+
+345
+00:26:14,210 --> 00:26:16,390
+في واحدة منهم .. في واحدة منهم يكون مزيف، يبقى فشل
+
+346
+00:26:16,390 --> 00:26:18,510
+بتقول مش هيتفنن، تمام، هل وجد، أنت بتتكلم عن أربعة
+
+347
+00:26:18,510 --> 00:26:23,590
+أربعة، اتنين، بمعنى الرشح هادي، إذا اليمين كانت أخف
+
+348
+00:26:29,200 --> 00:26:33,300
+ماشي معاك والله معاك، هنا فيه إنك أربعة مقابل أربعة
+
+349
+00:26:33,300 --> 00:26:40,440
+صح، هاي الميزان تبعك، تمام، هاي ميزانك، حطيت أربعة
+
+350
+00:26:40,440 --> 00:26:45,440
+مقابل أربعة، هاي هادي نزلت، يعني الأربع هدول فيهم
+
+351
+00:26:45,440 --> 00:26:48,460
+الزائفة، تمام، يعني معنى ذلك إن أنا وصلت للنود
+
+352
+00:26:48,460 --> 00:26:53,090
+الثاني، وفيه في إيدي أربعة، واحدة منهم زائفة، أيوة
+
+353
+00:26:53,090 --> 00:26:57,590
+هاتمنا نكمل معاك، هي اتنين واتنين صحيح؟ طيب هي
+
+354
+00:26:57,590 --> 00:27:00,890
+اتنين هنا واتنين هنا، صار عندي هنا في النهاية
+
+355
+00:27:00,890 --> 00:27:07,050
+اتنين في إيدي، عرفت إن هم زائفين، كيف بدك تعرفه؟
+
+356
+00:27:07,050 --> 00:27:11,490
+صح؟ كم level هنا عملت؟ طيب زميلك جالك كم level؟
+
+357
+00:27:13,750 --> 00:27:17,510
+يعني معنى ذلك أنا لو بدي على كل وزنة أدفع مقابل
+
+358
+00:27:17,510 --> 00:27:24,930
+الجبان هذا، وزن في النهاية جبان، وهذا بتأجر بالوزنة
+
+359
+00:27:24,930 --> 00:27:29,290
+هقول لك والله بدي أه، وبدي أوزن وزنتين، okay، كل وزنة
+
+360
+00:27:29,290 --> 00:27:33,950
+بشكل، أنا هضطر آخذ منه شكلين، بس أنت هضطر آخذ منك
+
+361
+00:27:33,950 --> 00:27:37,890
+تلاتة، هاخد منك تلاتة، لأنك وزنت تلت مرات، صح ولا لأ؟
+
+362
+00:27:39,810 --> 00:27:44,030
+هينمشي معاك، وقولنا إنه حللناها زي ما .. في إشي
+
+363
+00:27:44,030 --> 00:27:47,610
+غلط عملناها؟ مظبوط، زي ما كانت فكرتك، هنا اضطريت
+
+364
+00:27:47,610 --> 00:27:51,970
+أعمل واحدة اتنين تلاتة، هنا عملت اتنين، لأ، اوفرلي
+
+365
+00:27:51,970 --> 00:27:57,610
+الاتنين، اوفرنا الاتنين، لأ لأ، بتطلع بس زي ما أقوله
+
+366
+00:27:57,610 --> 00:28:01,030
+إله، إله حدود، يعني خليكم أصبروا معايا للـ slide
+
+367
+00:28:01,030 --> 00:28:03,530
+اللي جاية، هقول لكم إيه، إمتى بقدر أعمل اللي أنت
+
+368
+00:28:03,530 --> 00:28:07,370
+عملته، أنا ضلت متماشي معاك، ع أساس كنت مستني منك كمان
+
+369
+00:28:07,370 --> 00:28:11,190
+كلمة زيادة، كإن أقول لك أه هيك بتضبط، بس خلينا ..
+
+370
+00:28:11,190 --> 00:28:16,470
+خلينا معاكم، كيف؟ هو جزء بتاخد وزن 2، بس 6 و 8 ليس
+
+371
+00:28:16,470 --> 00:28:20,010
+لوزن 1، فلو كان فردي بتحط فكرة أكثر من كافية، يعني خمسة
+
+372
+00:28:20,010 --> 00:28:21,670
+وأربعة .. ما هي قاعدة بتقول إذا كان فردي .. كيف
+
+373
+00:28:21,670 --> 00:28:22,790
+بدك تضمن هذا الكلام؟
+
+374
+00:28:25,820 --> 00:28:29,040
+واصبروا عليّ، النقاش مازال مستمر هنا، خلينا نبدأ
+
+375
+00:28:29,040 --> 00:28:32,840
+بالفكرة بس، تعتبر البشار المهندس، هاي الفكرة، وبعدين
+
+376
+00:28:32,840 --> 00:28:36,300
+ننتقل لفكرة البشار المهندس برضه، ونشوف إيش اللي
+
+377
+00:28:36,300 --> 00:28:39,840
+اتخلتف عن الأولى، إنّي قولنا والله تلاتة تلاتة، و
+
+378
+00:28:39,840 --> 00:28:43,320
+هذه الإجابة اللي إجتنا في الأول، تلاتة تلاتة، والـ
+
+379
+00:28:43,320 --> 00:28:48,030
+الكتاب عجبته أكتر، إيش نسوي؟ جالك تلاتة تلاتة، فبضل
+
+380
+00:28:48,030 --> 00:28:52,810
+عندي هنا، إما بترجح في الآخر التلاتة بتاعة الشمال
+
+381
+00:28:52,810 --> 00:28:54,990
+فمعنى ذلك إن التلاتة اللي في اليمين هم اللي فيهم
+
+382
+00:28:54,990 --> 00:28:59,630
+الزائف، تمام، مش مشكلة، هنا نفس الكلام اللي رجحت
+
+383
+00:28:59,630 --> 00:29:03,950
+اليمين، فالشمال هي اللي فيها الزائف، أو اللي تساووا
+
+384
+00:29:03,950 --> 00:29:08,390
+فتنتقل لمن وزنوش، هم اللي فيهم الزائف، بعد هيك
+
+385
+00:29:08,390 --> 00:29:11,830
+محتاجين كمان وزنة ثانية، نعمل نفس الفكرة بس في
+
+386
+00:29:11,830 --> 00:29:16,040
+الآخر، من التلاتة هدول، بحط واحدة مقابل واحدة، وبقي
+
+387
+00:29:16,040 --> 00:29:20,360
+عندي واحدة برا، والله اتزنوا، اللي برا هي اللي فيها
+
+
+445
+00:33:31,460 --> 00:33:39,390
+قلت عليه إذا بتسوّي واحد، يعني إذا كانت تتكلم عن عشرة
+
+446
+00:33:39,390 --> 00:33:43,050
+عشرة
+
+447
+00:33:43,050 --> 00:33:49,490
+coins ليش؟ لأن عشرة موديولو تلاتة واحد، اعمل اللي
+
+448
+00:33:49,490 --> 00:33:55,450
+أنتَ قلت عليه، قول والله بتاخد أربعة، أربعة، أي عفواً
+
+449
+00:33:55,450 --> 00:34:02,030
+تلاتة تلاتة، ويضل أربعة في الحالة هذه، تلاتة تلاتة
+
+450
+00:34:02,030 --> 00:34:09,570
+ويضل أكثر منهم، في الحالة هذه بتاخد floor، خد floor
+
+451
+00:34:09,570 --> 00:34:17,030
+لأنه خلّينا نفكر فيها برضه، هاي بدأت بالوزنة الأولى
+
+452
+00:34:17,030 --> 00:34:24,250
+عندك، قلنا تلاتة تلاتة، وهنا أربعة، إذا كان balance
+
+453
+00:34:24,250 --> 00:34:28,700
+بدو يطلع عندك أربعة، صح؟ هيطلع عندك أربعة إذا كان لأ
+
+454
+00:34:28,700 --> 00:34:31,380
+واحدة منهم رجّحت لليمين، فمعناه ذلك أنه في عندي
+
+455
+00:34:31,380 --> 00:34:34,020
+تلاتة هم اللي بيبقى فحصهم، رجّحت للشمال، فيه يضل
+
+456
+00:34:34,020 --> 00:34:37,740
+عندي تلاتة هم اللي بيبقى فحصهم، طيب السيناريو
+
+457
+00:34:37,740 --> 00:34:42,100
+الثاني أنه لأ، نشتغل على ال ceiling، بس معناته بدي
+
+458
+00:34:42,100 --> 00:34:49,600
+أعمل أربعة مقابل أربعة، وبيضل كده؟ اتنين، ممتازة
+
+459
+00:34:49,600 --> 00:34:53,540
+لاحظوا أنه هنا لو رجّحت يمين أو رجّحت شمال، بيضل عندي
+
+460
+00:34:53,540 --> 00:34:55,800
+أربعة، يعني محتاج لها مرتين
+
+461
+00:34:58,150 --> 00:35:02,850
+مصبوط؟ طيب هنا أنا هحتاج برضه مرتين، بس ثلث
+
+462
+00:35:02,850 --> 00:35:11,490
+الاحتمال هنا ثلثين الاحتمال، صح؟
+
+463
+00:35:11,490 --> 00:35:14,870
+أيوة، okay، أنا مقتنع تماماً أن في ال worst case هقول
+
+464
+00:35:14,870 --> 00:35:19,050
+أنهم تلاتة، ما فيش مشكلة، لكن ال practical بجلّي
+
+465
+00:35:19,050 --> 00:35:23,940
+الاحتمالية، التلاتة، Practical بجلّي الاحتمالية أنه
+
+466
+00:35:23,940 --> 00:35:28,100
+يصير معايا تلاتة، فبنقول لأ، تلاتة تلاتة، وبنخلي
+
+467
+00:35:28,100 --> 00:35:34,700
+الاحتمال لأ أني أضطر لوزنتين، حالة من الثلاث حالات
+
+468
+00:35:34,700 --> 00:35:39,280
+مش حالتين من الثلاث حالات، واضح الجزئية كيف أنها
+
+469
+00:35:39,280 --> 00:35:40,640
+عملت؟ تمام، ممتاز
+
+470
+00:35:45,880 --> 00:35:49,260
+فاضطرنا في الآخر نقول أن احنا بتجسم ال coin الأولى
+
+471
+00:35:49,260 --> 00:35:51,920
+و الثانية و الثالثة في كفة، و الرابعة و الخامسة و
+
+472
+00:35:51,920 --> 00:35:56,380
+السادسة في كفة، و نخلي السابعة و الثامنة برا، ففي
+
+473
+00:35:56,380 --> 00:36:01,020
+الحالة هذه إذا كان رجّحت عند، أو اللي كانت أخف
+
+474
+00:36:01,020 --> 00:36:03,620
+الواحد و اثنين و التلاتة، فمعناته بتدوزن واحد مقابل
+
+475
+00:36:03,620 --> 00:36:09,440
+اثنين، كويس، يا بتطلع واحد يا بتطلع اثنين، أو بتطلع
+
+476
+00:36:09,440 --> 00:36:14,340
+اثنين متساويين، فتلاتة هي اللي فيها مشكلة، طيب أو أنه
+
+477
+00:36:14,340 --> 00:36:18,260
+لأ، اللي أخف هي الكفة بتاعة أربعة خمسة ستة، ونفس
+
+478
+00:36:18,260 --> 00:36:22,720
+الكلام، بوزن أربعة مع خمسة، واحدة منهم هترجّح، معناته
+
+479
+00:36:22,720 --> 00:36:28,840
+الأقل وزناً هي الزائفة، أو أنه balance، الاثنين، فبناخد
+
+480
+00:36:28,840 --> 00:36:32,820
+اللي ما انوزنتش منهم، الحالة الثالثة، سبعة مقابل
+
+481
+00:36:32,820 --> 00:36:38,140
+ثمانية، إذا واحد اثنين تلاتة مقابل أربعة خمسة ستة
+
+482
+00:36:39,600 --> 00:36:42,660
+بالنسبة لم يكن هناك واحدة رجعت على الثانية، فإذا
+
+483
+00:36:42,660 --> 00:36:46,200
+المشكلة ستكون في أربعة أو خمسة أو سبعة أو ثمانية
+
+484
+00:36:46,200 --> 00:36:50,760
+بوزنهم مع بعض بطريقة مباشرة، مباشرة، هي تنتج بالبعض
+
+485
+00:36:50,760 --> 00:36:55,190
+واحدة منهم أخف من الثانية، فهي ال counterfeit أو
+
+486
+00:36:55,190 --> 00:37:01,750
+الزائفة، تمام، الآن مدام أننا في نفس الموضوع و في
+
+487
+00:37:01,750 --> 00:37:05,590
+نفس جزئية ال search، في حاجة اسمها ternary search
+
+488
+00:37:05,590 --> 00:37:11,190
+أخذتوها، طيب ternary search، هتنمحي كل اللي احنا
+
+489
+00:37:11,190 --> 00:37:14,990
+عاملينه عشان
+
+490
+00:37:14,990 --> 00:37:20,750
+هذه، هتشمل كذا مفهوم في بعض، يعني هناخد منها ال
+
+491
+00:37:20,750 --> 00:37:24,690
+search اللي أخذناها سابقاً، هناخد نتكلم عن ال
+
+492
+00:37:24,690 --> 00:37:28,690
+complexity، هنتكلم عن ternary، مدام توي أخذناها من
+
+493
+00:37:28,690 --> 00:37:32,290
+واحدة من التطبيقات، هي الجزئية ال search و ال
+
+494
+00:37:32,290 --> 00:37:38,530
+insertion، تمام، هنا بكل بساطة، هاي
+
+495
+00:37:38,530 --> 00:37:44,030
+ال array تبعك، كنا ناخد في ال binary ايش؟ نقطة و
+
+496
+00:37:44,030 --> 00:37:46,270
+نقارن فيها، لأننا هناخد نقطتين
+
+497
+00:37:52,790 --> 00:37:57,930
+عند الثلث و الثلثين، بدنا ناخد قيمتين، واحدة عند
+
+498
+00:37:57,930 --> 00:38:01,410
+الثلث، واحدة عند مين؟ عند الثلثين، وندور على X، وندور
+
+499
+00:38:01,410 --> 00:38:07,110
+على X، أقارن X بالقيمة، بالقيمة مين؟ الثلثين هذه مثلاً
+
+500
+00:38:07,110 --> 00:38:10,350
+إيش احتمالاتها؟ يا أكبر من، يا أصغر من، والله إذا
+
+501
+00:38:10,350 --> 00:38:15,190
+بتساوي، معناته انتهت الجثة، خلصنا، يعني ضربناها، جاءت
+
+502
+00:38:15,190 --> 00:38:19,710
+على طول، هي طبعاً the best case، لكن ممكن تكون أكبر
+
+503
+00:38:19,710 --> 00:38:26,750
+من، أكبر من، عارف أنتَ إيش سويت؟ الثلثين كلهم راحوا، مش
+
+504
+00:38:26,750 --> 00:38:32,210
+هي خلصت الثلثين مرة واحدة، بدأت بالنص، طيب ماصارش
+
+505
+00:38:32,210 --> 00:38:39,590
+الكلام بهذا الشكل، لجيتها أقل من، أقل من ثلثين، أقل
+
+506
+00:38:39,590 --> 00:38:43,950
+من الثلثين، على طول بتقارنها بمين؟ بالثلث، هتقارنها
+
+507
+00:38:43,950 --> 00:38:50,170
+بالثلث، هنا إيش هيطلع؟ هتلاحظ إيش سويت؟ ليش؟ لأن الـ
+
+508
+00:38:50,170 --> 00:38:53,610
+two branches هدول، بناء على إنها طلعت أقل من ..
+
+509
+00:38:53,610 --> 00:38:58,070
+بناء على أساس إنها أقل من الثلثين، فهنا بتجيك
+
+510
+00:38:58,070 --> 00:39:01,910
+احتمالاتها الآن بالنسبة للثلث، يا أقل من، يا أصغر
+
+511
+00:39:01,910 --> 00:39:10,510
+من، إذا كانت X أقل من الثلث، الثلثين راحوا، أو أكبر
+
+512
+00:39:10,510 --> 00:39:14,850
+من الثلث، برضه الثلثين راحوا، لأنه بخلّي الجزء هذا
+
+513
+00:39:14,850 --> 00:39:18,250
+فقط، فبتصير هذه I جديدة، و J جديدة
+
+514
+00:39:20,630 --> 00:39:25,150
+صح؟ برضه، فإذا أنا بدل ما أعمل elimination لنص
+
+515
+00:39:25,150 --> 00:39:30,730
+عملت elimination لثلثين، طبعاً بعدها هي اتحسّنت على
+
+516
+00:39:30,730 --> 00:39:35,590
+الموضوع هذا، وبندرسها أكثر في الماجستير، أنه بنحطها
+
+517
+00:39:35,590 --> 00:39:38,790
+نسبة معيّنة للي بده يشتغل في ال iterations، فبيسموها
+
+518
+00:39:38,790 --> 00:39:42,070
+النسبة الذهبية، اللي هي 0.618 شي
+
+519
+00:39:42,070 --> 00:39:45,450
+ثاني، بس احنا دلوقتي خلينا فيها في الفكرة نفسها
+
+520
+00:39:45,450 --> 00:39:50,640
+اللي هي ال ternary search، أو البحث الثلاثي، البحث
+
+521
+00:39:50,640 --> 00:39:54,260
+الثلاثي هذه من الحاجات اللي ممكن تيجي كأكواد مثلاً
+
+522
+00:39:54,260 --> 00:39:58,360
+في الـ .. في data structure، في شيء اللي هو يلا
+
+523
+00:39:58,360 --> 00:40:02,680
+فكّروا لنا كيف تعملوا لها code، فكّروا كيف تعملوا لها code
+
+524
+00:40:02,680 --> 00:40:06,800
+فعشان نعمل لها code، الفكرة فهمناها بكل بساطة، هتبدأ
+
+525
+00:40:06,800 --> 00:40:11,860
+procedure، ال procedure ده إيش بده؟ بده ال sequence
+
+526
+00:40:11,860 --> 00:40:14,120
+أو ال array اللي أنتَ بدك تدخله إياها، لأنك بتبقى
+
+527
+00:40:14,120 --> 00:40:19,150
+عارف ال array اللي موجودة، كويس، و مجموعة عناصرها من
+
+528
+00:40:19,150 --> 00:40:24,490
+1 to N، و increasing integers، بمعنى أنها ordered
+
+529
+00:40:24,490 --> 00:40:29,210
+بمعنى ordered، جيد، مش ordered، معناته بدك تفهم
+
+530
+00:40:29,210 --> 00:40:33,530
+علامات ال insertion، بدك تبدأ بال search على كل
+
+531
+00:40:33,530 --> 00:40:38,710
+عنصر، ثم بستنى ال search عشان تبدأ، هتبدأ ternary
+
+532
+00:40:38,710 --> 00:40:44,290
+search، مش binary search، هيشتغل على ternary search،
+
+533
+00:40:44,290 --> 00:40:50,530
+جيد، هتقل؟ آه هتقل، لكن ال order هو هو، إيش ال
+
+534
+00:40:50,530 --> 00:40:53,210
+order أو ال complexity بتاعة ال binary؟
+
+535
+00:40:53,210 --> 00:40:55,450
+logarithmic، صح؟ وهذا هتظهر logarithmic، إيش
+
+536
+00:40:55,450 --> 00:41:00,390
+الاختلاف بينهم؟ ال base بس، هذه كانت log2، هذه log3
+
+537
+00:41:00,390 --> 00:41:04,950
+ف log3 احنا عارفين أنه هتقلّ أكثر كقيمة عددية
+
+538
+00:41:04,950 --> 00:41:09,590
+هتعطيني أقل عدد، لكن ك order ضال واحد هو ال
+
+539
+00:41:09,590 --> 00:41:13,410
+algorithmic، ك order، مش يعني ما عملّي، يعني ما طورتش في
+
+540
+00:41:13,410 --> 00:41:17,370
+المسمّى زيادة، لكن على عرض الواقع، آه هتقلّ شوية
+
+541
+00:41:17,370 --> 00:41:21,930
+الأمور كعدد iterations، تمام، فهي أول خطوة، الخطوة
+
+542
+00:41:21,930 --> 00:41:28,790
+الثانية بتحدد البداية و النهاية I و J، على أساس إن
+
+543
+00:41:28,790 --> 00:41:35,670
+هما 1 و N، أول عنصر، ال index الأول و الأخير، عشان
+
+544
+00:41:35,670 --> 00:41:38,690
+نبدأ الآن، نفس الفكرة اللي قلناها في ال binary، في
+
+545
+00:41:38,690 --> 00:41:41,610
+ال binary كنت ببدأ أعمل elimination، وأقلّل ال
+
+546
+00:41:41,610 --> 00:41:46,760
+duration، لما يصبح عندي one element، خلاص، إذا هو ال
+
+547
+00:41:46,760 --> 00:41:50,480
+one element، انتهى، ما ضلّ مجال أفحص فيه، فأنتَ بيبين
+
+548
+00:41:50,480 --> 00:41:53,500
+ال one element، طول ما في عندي I اللي هي البداية
+
+549
+00:41:53,500 --> 00:42:00,120
+أقل من J ناقص واحد، معناته في بينهم لسه قيم، ما زالت
+
+550
+00:42:00,120 --> 00:42:04,500
+في بينهم قيم، إذا ما تحققتش، معناته فعلياً I صارت
+
+551
+00:42:04,500 --> 00:42:10,750
+أكبر من، صارت أكبر من، معناته صاروا بيساوي بعض، إذا
+
+552
+00:42:10,750 --> 00:42:13,630
+ساووا بعض، لاحظ، طالع فيهم، إذا ساووا بعض، طب هي دي
+
+553
+00:42:13,630 --> 00:42:17,710
+أقل، ناقص واحد، صارت فيها الأقل، فتصبح أقل على
+
+554
+00:42:17,710 --> 00:42:21,130
+طول، فإذا بيختلّ ال condition، وإذا اختلّ ال
+
+555
+00:42:21,130 --> 00:42:24,290
+condition، اطلع خارج ال loop، بطّل في مساحة تدور
+
+556
+00:42:24,290 --> 00:42:28,170
+فيها، لأ، بدنا نفترض إن لسه المساحة موجودة، عشان
+
+557
+00:42:28,170 --> 00:42:33,930
+نبدأ نعمل عملية ال lower و ال upper، بدل ما كنت
+
+558
+00:42:33,930 --> 00:42:37,010
+بتتكلم عن ال midpoint، ال lower point و ال upper
+
+559
+00:42:37,010 --> 00:42:40,450
+point، أو اللي هي الثلث و مين؟ و الثلثين، واللي
+
+560
+00:42:40,450 --> 00:42:46,090
+بيقول، بساطة، جدّش المسافة بينهم على تلاتة، مسافة
+
+561
+00:42:46,090 --> 00:42:49,090
+بينهم على تلاتة، أعطتني جدّش، قيمة هذا الكلام، لكن
+
+562
+00:42:49,090 --> 00:42:53,310
+ما أعطتنيش القيمة المطلقة للعنصر، فهنا آه، لأنه أنا في
+
+563
+00:42:53,310 --> 00:42:57,030
+مرحلة و مرحلة، I مش هتكون هي الواحد، هتتغيّر، ما أنا هتكون
+
+564
+00:42:57,030 --> 00:43:03,000
+مرة هعمل elimination، فلأ زائد ال I، منطقة زائد ال I
+
+565
+00:43:03,000 --> 00:43:06,360
+فبعرف أن أنا موجود هنا الآن، هذا قيمة ال lower، ال
+
+566
+00:43:06,360 --> 00:43:13,820
+upper، ثلثين ال upper، عند الثلثين، أو تقدر تعملها
+
+567
+00:43:13,820 --> 00:43:20,720
+برضه ثلث، و تعمل J ناقص الثلث، صح؟ نفس الأشياء، فهي دي
+
+568
+00:43:20,720 --> 00:43:23,520
+كلها أفكار، أي حاجة بتمشي معاك في ال data structure
+
+569
+00:43:23,520 --> 00:43:27,700
+لأن أنتَ مفروض تدرسوا أفكار، تدرسوا أفكار، فنفس
+
+570
+00:43:27,700 --> 00:43:31,500
+الفكرة، بدك تبدأ من الـ .. من بداية الـ .. ال array
+
+571
+00:43:31,500 --> 00:43:39,080
+ولا من نهايتها، مش هتكون مشكلة كبيرة، تمام، الآن بعد
+
+572
+00:43:39,080 --> 00:43:41,240
+ما نكتب ده، الفحص اللي احنا فحصناه هنا، اللي احنا
+
+573
+00:43:41,240 --> 00:43:46,180
+عملناه، اللي هي روح الموضوع تبعنا، ال tree، جزئية ال tree
+
+574
+00:43:46,180 --> 00:43:49,560
+الآن، اللي هي عبارة عن condition، و أفحصه، yes no yes
+
+575
+00:43:49,560 --> 00:43:54,500
+no، يبدأ شوف ال yes و ال no هدول، فهنبدأ، إذا كانت X
+
+576
+00:43:54,500 --> 00:43:58,900
+أكبر من أو يساوي ال A، أبر كأنك بتقارنها بالعنصر
+
+577
+00:43:58,900 --> 00:44:02,340
+اللي موجود هنا، زي ما عملنا، زي ما عملنا بالضبط، أكيد
+
+578
+00:44:02,340 --> 00:44:06,450
+هيكون عندك two possibilities، ال possibility الأولى
+
+579
+00:44:06,450 --> 00:44:10,850
+.. الإمكانية الأولى أنه يكون هنا مثلاً yes، إذا كانت
+
+580
+00:44:10,850 --> 00:44:16,610
+فعلاً x أكبر من .. إذا، إذا yes، على طول I تساوي ال
+
+581
+00:44:16,610 --> 00:44:23,150
+other زائد واحد، الثلثين الشمال راحوا .. الثلثين
+
+582
+00:44:23,150 --> 00:44:26,450
+الشمال راحوا .. ما علينا أي مشكلة فيهم، و لاحظوا أن
+
+583
+00:44:26,450 --> 00:44:30,970
+أكبر من ولا تساوي، أعطتني إمكانية أقول زائد واحد
+
+584
+00:44:32,270 --> 00:44:36,350
+لأنه ضامن إنه مش متساوي، متساوٍش، معناته بروح على
+
+585
+00:44:36,350 --> 00:44:38,950
+الأنصار اللي ورا، نروح على الأنصار اللي ورا،
+
+586
+00:44:38,950 --> 00:44:41,550
+عملناها جابل هيك، ومفهومة، ما أعتقدش إن في عندكم
+
+587
+00:44:41,550 --> 00:44:44,950
+مشكلة فيها، Else، هذه else إيش يعني؟ يعني معناته
+
+588
+00:44:44,950 --> 00:44:50,550
+أنه ما رحتش ل yes، هنا رحت ل no، لأنه ما تحققش إنه
+
+589
+00:44:50,550 --> 00:44:54,650
+أكبر من، ما تحققش إنه أكبر من، فإذا هنا هيكون إيش؟
+
+590
+00:44:54,650 --> 00:45:00,130
+أصغر أو يساوي، خلّوا دائماً في بالكم كلمة أو يساوي
+
+591
+00:45:00,130 --> 00:45:06,590
+أيوة، ف else if، هالوقت صارت كأنّه أخدت ال no مع ال
+
+592
+00:45:06,590 --> 00:45:11,570
+condition كمان، بكلمة else if، أخذنا الاثنتين مع بعض
+
+593
+00:45:11,570 --> 00:45:18,470
+مع ال يساوي، تمام، x أكبر من a lower، فإذا خلّصنا، احنا
+
+594
+00:45:18,470 --> 00:45:23,590
+وصلنا لهنا، فعلياً أنا موجود هنا، وفعلياً أو يساوي
+
+595
+00:45:24,620 --> 00:45:29,280
+لأنه عدينا فكرة إنه هي أكبر من، وقلنا إنه هي no، فأنا
+
+596
+00:45:29,280 --> 00:45:33,920
+الآن هنا، وهذه تحقّقت، روحت لمين؟ لأكبر من ال lower
+
+597
+00:45:33,920 --> 00:45:42,180
+أكبر من ال lower، هنا أنا الآن هنا، ليش؟ هنا لأنه
+
+598
+00:45:42,180 --> 00:45:48,080
+مبدئياً ليست أكبر من ال upper، اللي هي الثلثين، ليست
+
+599
+00:45:48,080 --> 00:45:55,570
+أكبر من الثلثين، وأكبر من ال lower، إيش بنعمل؟
+
+600
+00:46:00,480 --> 00:46:05,780
+معناته هي المنطقة اللي في النص، ف automatically if
+
+601
+00:46:05,780 --> 00:46:10,100
+then، معناته فعلاً تحقق الشرطان، أن هي ليست أكبر من
+
+602
+00:46:10,100 --> 00:46:13,120
+ال other، بينما هي أكبر من ال lower، على طول بروح
+
+603
+00:46:13,120 --> 00:46:21,100
+إيش بسوي؟ بقول ال I هتصبح هي ال lower زائد واحد، ليش؟
+
+604
+00:46:21,100 --> 00:46:24,520
+لأن هنا ما جلتش أو ساوي، فأنا عندي أريحية أقول أكبر
+
+605
+00:46:24,520 --> 00:46:31,630
+أقول زائد واحد، لكن في ال other لأ، أيوة، ليش؟ لأن في
+
+606
+00:46:31,630 --> 00:46:34,850
+القبر، هي جايتنا من وين الآن الحالة؟ جايتنا من إنه
+
+607
+00:46:34,850 --> 00:46:40,590
+ليست أكبر من، طب ليست أكبر من، كنت ساوي، صح؟ فأخدوا
+
+608
+00:46:40,590 --> 00:46:44,410
+بالكم من الحاجات الرفيعة هذه اللي ممكن تعمل لكم
+
+609
+00:46:44
\ No newline at end of file
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@@ -0,0 +1,2652 @@
+1
+00:00:04,960 --> 00:00:07,120
+يعطيكوا العفو يا شباب اليوم ان شاء الله تعالى
+
+2
+00:00:07,120 --> 00:00:12,360
+بنحاول نختم في ما تبقالنا في موضوع letre ان شاء
+
+3
+00:00:12,360 --> 00:00:15,380
+الله بعد ما اتكلمنا عن letre ال introduction أخدنا
+
+4
+00:00:15,380 --> 00:00:21,780
+شوية terminology أخدنا شوية theore المرة الماضية
+
+5
+00:00:21,780 --> 00:00:27,640
+حسبنا ال edges مقابل ال nodes مقابل ال leaves جدش
+
+6
+00:00:27,640 --> 00:00:29,860
+ال number of leaves و بعدين اتكلمنا في الآخر على
+
+7
+00:00:31,610 --> 00:00:36,150
+ربطهم بالقوانين مع بعض تمام و اليوم ان شاء الله
+
+8
+00:00:36,150 --> 00:00:39,370
+تعالى ناخد applications of trees طبعا إذا بنتكلم
+
+9
+00:00:39,370 --> 00:00:43,310
+عن applications of trees مش هنخلص فعليا حقيقة يعني
+
+10
+00:00:43,310 --> 00:00:48,570
+لأن تطبيقاتها كتيرة جدا كمواد علمية كأبحاث علمية
+
+11
+00:00:48,570 --> 00:00:52,170
+لأ لها تطبيقات و تطبيقات جدا كبيرة اليوم هنقتصر
+
+12
+00:00:52,170 --> 00:00:57,620
+فقط على جد ال binary search أو ال search عمومالأن
+
+13
+00:00:57,620 --> 00:01:00,300
+زي ما قلنا هيكون في binary search وبعدين هناخد
+
+14
+00:01:00,300 --> 00:01:03,720
+decision trees decision trees من اسمها شغلة
+
+15
+00:01:03,720 --> 00:01:06,920
+القرارات، القرارات معناته واضحة جدا أن هذه مقدمة
+
+16
+00:01:06,920 --> 00:01:12,200
+لغنى عنها لل AI هذه المقدمة اللي لغنى عنها لأي AI
+
+17
+00:01:12,200 --> 00:01:15,520
+فمافيش حد بيشتغل في ال AI في الذكاء الاصطناعي وما
+
+18
+00:01:15,520 --> 00:01:19,610
+بعرفش حاجة اسمها decision treesأو كيف انا ممكن
+
+19
+00:01:19,610 --> 00:01:24,010
+اعمل شجرة القرارات .. شجرة القرارات من خلال ال
+
+20
+00:01:24,010 --> 00:01:26,430
+flow chart انتوا كلكوا عارفينه بتعرفوا ترسموه ال
+
+21
+00:01:26,430 --> 00:01:29,630
+flow chart هذا فال flow chart عبارة عن سؤال و
+
+22
+00:01:29,630 --> 00:01:33,370
+إجابات يا yes يا no إجابات yes no .. yes no .. yes
+
+23
+00:01:33,370 --> 00:01:36,690
+no فانت ممكن تعمل structure لكل ال systems اللي
+
+24
+00:01:36,690 --> 00:01:40,630
+ممكن تخطر ع بالك بحيث انك انت في الآخر بناء على
+
+25
+00:01:40,630 --> 00:01:43,850
+conditions معينة ممكن ال consequential conditions
+
+26
+00:01:43,850 --> 00:01:48,430
+تطلع بقراربتطلع في الآخر إيش بقرار و أهمها يمكن
+
+27
+00:01:48,430 --> 00:01:51,810
+الأعراض بتاعة اللي عند الأطباء في الأمراض أعراض
+
+28
+00:01:51,810 --> 00:01:56,450
+بيبدأ يسألك عن مجموعة أعراض عشان يستنتج منها ال
+
+29
+00:01:56,450 --> 00:02:00,250
+decision المناسب يستخدم أو ياخد القرار المناسب
+
+30
+00:02:00,250 --> 00:02:04,070
+فهدولة ال two applications بس اللي هنتكلم عنهم لكن
+
+31
+00:02:04,070 --> 00:02:07,510
+زي ما قلتلكم مرة ال trees ال applications ساعتها
+
+32
+00:02:07,510 --> 00:02:14,730
+دخمة و كتيرة في الأبحاث العلمية فهنبدأبشكل مبسط في
+
+33
+00:02:14,730 --> 00:02:18,590
+ال binary search trees شوية يمكن في آخر ال slides
+
+34
+00:02:18,590 --> 00:02:21,110
+هوصلكوا ايها شوية انها تصير كمان مش binary تكون
+
+35
+00:02:21,110 --> 00:02:26,190
+اكتر من binary و نشوف لنا نكتب لنا code عليها
+
+36
+00:02:26,190 --> 00:02:29,610
+اتوقع ممكن تحتاجوها في ال data structure قد يجوز
+
+37
+00:02:29,610 --> 00:02:34,070
+مثلا او شيء فخلينا نشوفها لما نصلها طيب هنا ال
+
+38
+00:02:34,070 --> 00:02:38,630
+binary search سواء انا بعمل searchdirect مباشرة ال
+
+39
+00:02:38,630 --> 00:02:42,110
+search اللي احنا عارفينه اللي هو given x تمام و
+
+40
+00:02:42,110 --> 00:02:45,550
+ابحثلي عنها بكل بساطة يعني مافيش فيها كتير مشكلة
+
+41
+00:02:45,550 --> 00:02:49,450
+طيب إذا كانت given بهذا الشكل فانت الموضوع كتير
+
+42
+00:02:49,450 --> 00:02:52,730
+سهل عليك ليش لأنه اتفقنا من المرة الماضية بكون
+
+43
+00:02:52,730 --> 00:02:58,550
+عامل modeling لل array تبعتي باستخدام ال tree و
+
+44
+00:02:58,550 --> 00:03:04,090
+مجرد فقط عارف ان ال priority left to right و ال
+
+45
+00:03:04,090 --> 00:03:10,330
+left ل ال subTree to write subtree ماشيك بس و ايه
+
+46
+00:03:10,330 --> 00:03:12,870
+ماهي .. ماهي مادام انا عملتها حسب ال priority
+
+47
+00:03:12,870 --> 00:03:16,470
+معناته هي ordered خلاص يعني معناته ممرتبة هذا عشان
+
+48
+00:03:16,470 --> 00:03:21,220
+اشوف X معينة و اعرف وين مكانهاوين مكانها و هل هي
+
+49
+00:03:21,220 --> 00:03:25,900
+موجودة و لا مش موجودة سؤالين هم بقى هل هي موجودة
+
+50
+00:03:25,900 --> 00:03:29,000
+بدي أرجع أو أنه لأ مش موجودة بدي أرجعها بصفر وهذا
+
+51
+00:03:29,000 --> 00:03:31,960
+نفس القوانين اللي أخدناها سابقا أو ال rule اللي
+
+52
+00:03:31,960 --> 00:03:38,300
+أخدناها سابقا طيب هذه بكل بكل بساطة الآن عشان
+
+53
+00:03:38,300 --> 00:03:42,660
+نتكلم عن هذا الموضوع محتاجيننعرف أخدناها سابقا
+
+54
+00:03:42,660 --> 00:03:48,120
+برضه في ال binary search أنه ال order تبعنا أو ال
+
+55
+00:03:48,120 --> 00:03:53,220
+complexity كانت logarithmic و هنا نفس الكلام أنت
+
+56
+00:03:53,220 --> 00:03:58,160
+لما يكون في عندك tree بهذا
+
+57
+00:03:58,160 --> 00:04:04,240
+الشكلهي ثنائية كلها binary و مباشرة تيجي تقارن مع
+
+58
+00:04:04,240 --> 00:04:09,120
+أول أنصر اللي هي ال root وتجد انه ال X أكبر من ..
+
+59
+00:04:09,120 --> 00:04:13,640
+معناته أنت مبدأيا كل هذا استثنيته كله مرة واحدة
+
+60
+00:04:13,640 --> 00:04:17,440
+استثنيته انت مش محتاج تبحث فيه فانت linear لأ هي
+
+61
+00:04:17,440 --> 00:04:21,560
+مش linear ك linear لأ مش linear طيب فعملية ال
+
+62
+00:04:21,560 --> 00:04:25,200
+search ل existing item مش فيها مشكلة لكن احنا ممكن
+
+63
+00:04:25,200 --> 00:04:32,140
+برضه نستخدم نفس ال treeto insert a new item طيب
+
+64
+00:04:32,140 --> 00:04:35,060
+مادام to insert a new item معناته من الأساس انا
+
+65
+00:04:35,060 --> 00:04:38,500
+ممكن ابدأ بأول عنصر و باجي العناصر في ال array
+
+66
+00:04:38,500 --> 00:04:40,980
+تبعتنا نعملها احنا insertion يعني كأننا عملت
+
+67
+00:04:40,980 --> 00:04:45,500
+sortingكأن احنا عملنا sorting وحضر في الكمثال برضه
+
+68
+00:04:45,500 --> 00:04:48,900
+على ال slides اليوم برضه كيف انا ممكن اعمل sorting
+
+69
+00:04:48,900 --> 00:04:52,160
+ل sequence موجود عندك ده sequence موجود عندك تمام
+
+70
+00:04:52,160 --> 00:04:56,040
+فإذا في الحالة دي اما existing item موجود فانت بدك
+
+71
+00:04:56,040 --> 00:05:01,320
+تبحث عنه او بدك تعمل inserting ل new item تمام
+
+72
+00:05:01,320 --> 00:05:07,400
+وكلهما لو بدك تعمل sorting لأنك بدك ال X اللي انت
+
+73
+00:05:07,400 --> 00:05:10,440
+بدك تحطه في مكانها الصحيح بدك كأنك بتبحث عنها في
+
+74
+00:05:10,440 --> 00:05:14,560
+البدايةبتبحث عنها وين المكان اللى المفروض تكون
+
+75
+00:05:14,560 --> 00:05:18,680
+موجودة فيه مالجتش قيمتها بتحطها المكان اللى لازم
+
+76
+00:05:18,680 --> 00:05:21,440
+تكون موجودة فيه مالجتهاش بتحطها إذا لجتها خير
+
+77
+00:05:21,440 --> 00:05:24,880
+وبركة خلاص معناته موجودة مافيش داعية تكررها تاني
+
+78
+00:05:24,880 --> 00:05:28,720
+تمام إذا كان ماكنتش موجودة زى ما قلنا already
+
+79
+00:05:28,720 --> 00:05:33,540
+present إذا ماكنت موجودة الآن الأشكالية ..
+
+80
+00:05:33,540 --> 00:05:36,000
+الأشكالية التانية أنه بعد ما تعمل sorting أنت
+
+81
+00:05:36,000 --> 00:05:41,420
+محتاج تطبعالـ sequence لجديد طيب الطباعة لغتلك
+
+82
+00:05:41,420 --> 00:05:45,920
+فكرة ال log كلكوا عارفين أن ال print هي linear مش
+
+83
+00:05:45,920 --> 00:05:50,780
+هيك ال print process أو operation هي linear لأن
+
+84
+00:05:50,780 --> 00:05:53,520
+انت هتروح ل element by element انت لازم تمر عليهم
+
+85
+00:05:53,520 --> 00:05:55,100
+element by element فإذا كان و الله بدنا نروح لل
+
+86
+00:05:55,100 --> 00:05:59,500
+printing لكل ال items فمعنى ذلك رجعنا لمين؟ لل
+
+87
+00:05:59,500 --> 00:06:03,320
+linear complexity linear complexity أما لأ إذا
+
+88
+00:06:03,320 --> 00:06:09,500
+مجرد سيرشه خلاصبدك تروح لمين؟ اكيد هتكون log طب
+
+89
+00:06:09,500 --> 00:06:15,200
+sorting لأ انت لازم تروحلهم واحدة واحدة لازم
+
+90
+00:06:15,200 --> 00:06:18,080
+تمسكهم واحدة واحدة معناه ذلك ان هي direct
+
+91
+00:06:18,080 --> 00:06:26,140
+dependent علىالنمبر of inputs أو ال arguments جدش
+
+92
+00:06:26,140 --> 00:06:29,080
+عددهم خمسين انت لازم تمسكهم واحدة واحدة الخمسين
+
+93
+00:06:29,080 --> 00:06:33,640
+كامل ف search ال complexity إشي و sorting ال
+
+94
+00:06:33,640 --> 00:06:38,420
+complexity إشي تاني تمام كويس ففي أسوأ الأحوال
+
+95
+00:06:38,420 --> 00:06:43,200
+مدام أن أنا بتعامل مع to insert أعمل inserting في
+
+96
+00:06:43,200 --> 00:06:46,240
+ال sequence في ال sequence فعلى طول في ال worst
+
+97
+00:06:46,240 --> 00:06:50,000
+case أنا بتكلم عن linear لأنه همسكهم واحد واحد مش
+
+98
+00:06:50,000 --> 00:06:54,740
+هعملزي فكرة مجرد search بس، لأ هنا insert يعني
+
+99
+00:06:54,740 --> 00:06:58,860
+sorting، يعني sorting، بتصير linear، انتهى الكلام،
+
+100
+00:06:58,860 --> 00:07:03,440
+لكن في ال search logarithmic، انت بتقدر بكل بساطة
+
+101
+00:07:03,440 --> 00:07:07,960
+branch كامل تستفني من قرارك، فماتبحثش فيه أصلا،
+
+102
+00:07:07,960 --> 00:07:14,780
+ماتدورش على عناصره، بتصير linearأه لإن انت هتمسكهم
+
+103
+00:07:14,780 --> 00:07:18,320
+واحد واحد، لأ عملية ال insert إذا كان بدك تعملها
+
+104
+00:07:18,320 --> 00:07:25,740
+insert و search مع بعض بتصير N في log of N ليش؟
+
+105
+00:07:25,740 --> 00:07:31,920
+لإن كل واحدة .. بالضبط، واضحيت؟ كل واحدة هتمسكها
+
+106
+00:07:31,920 --> 00:07:36,390
+لحال، فانت نفترض عندك عشر elementsعشرة elements
+
+107
+00:07:36,390 --> 00:07:40,970
+الاولى هتكون هي ال root هتحطها هتبدأ فيها والباقى
+
+108
+00:07:40,970 --> 00:07:43,930
+بدك تحطه بالنسبالي عشان تعمل order في الآخر التانى
+
+109
+00:07:43,930 --> 00:07:49,710
+الآن هتعملها كأنك عندك ال tree موجودة كويس و بدك
+
+110
+00:07:49,710 --> 00:07:53,930
+تبحث عن العنصر التانى طيب هذه لحالها ال order
+
+111
+00:07:53,930 --> 00:07:57,090
+تبعها log تمام
+
+112
+00:07:59,030 --> 00:08:02,270
+in من ال in اللي موجودين عندك هدول من العشرة أو
+
+113
+00:08:02,270 --> 00:08:04,890
+العشرين أو المية اللي موجودة عندك يعني صارت log
+
+114
+00:08:04,890 --> 00:08:11,110
+مضروبة في عددهم صارت in log of in واضحيت؟ فانت بدك
+
+115
+00:08:11,110 --> 00:08:14,990
+تاخد بالك لما بدك تعمل sorting هل sorting يعني بدك
+
+116
+00:08:14,990 --> 00:08:17,270
+تعمل search مع sorting مع بعض المهنات الأثناء
+
+117
+00:08:17,270 --> 00:08:17,930
+مضروبين في بعض
+
+118
+00:08:21,330 --> 00:08:24,490
+هي مثال .. المثال بكل بساطة زي ما قلنا بنبدأ بال
+
+119
+00:08:24,490 --> 00:08:26,990
+route عشان نصنفها و احنا المرة اللي فاتت أصلا
+
+120
+00:08:26,990 --> 00:08:30,870
+أخدناها و خلصناها لسه هذه ببدأها لما بدي أشوف ال
+
+121
+00:08:30,870 --> 00:08:34,050
+tree هذه و أرسم ال sequence أو أكتب ال sequence
+
+122
+00:08:34,050 --> 00:08:38,090
+فعليا تبحث كيف موجود هأجد أنه ببدأ من السابعة
+
+123
+00:08:38,090 --> 00:08:41,830
+السابعة الآن فيها lift؟ أه فيها lift فال lift أولى
+
+124
+00:08:41,830 --> 00:08:45,770
+ال priority lift to right صح؟ فيها lift أولى طيب
+
+125
+00:08:45,770 --> 00:08:49,000
+وصلنا للتلاتة التلاتة فيها lift؟ أه فيها liftفيها
+
+126
+00:08:49,000 --> 00:08:53,920
+left اه هنا left ماضلش left معناته هنا zero طيب
+
+127
+00:08:53,920 --> 00:09:01,360
+zero بطلع عندي واحد الواحد اولى right لل root بيجي
+
+128
+00:09:01,360 --> 00:09:06,620
+بعده ف left to right واحدة اتنين تلاتة هيها left
+
+129
+00:09:06,620 --> 00:09:11,560
+to right على جد sub tree فانتوا الان بتتعاملوا مع
+
+130
+00:09:11,560 --> 00:09:16,780
+sub tree هيهاهذه sub tree ترتيب ال sub tree لحالها
+
+131
+00:09:16,780 --> 00:09:20,540
+left to right بما فيهم ال route تبعها طبعا ال sub
+
+132
+00:09:20,540 --> 00:09:23,380
+route هنا بيصير اسمه مش ال route الأصلي تمام
+
+133
+00:09:23,380 --> 00:09:27,100
+فهدولة بهذا الشكل واحدة اتنين تلاتة واحد اتنين صفر
+
+134
+00:09:27,100 --> 00:09:31,340
+واحد اتنين طيب خلصنا الآن لاحظ كأنه اش سويت كأنه
+
+135
+00:09:31,340 --> 00:09:35,440
+هاد ال sub tree تبعت خلصت ال left
+
+136
+00:09:38,660 --> 00:09:43,480
+واللي مثلته بتلات عناصر فعليا الان ال root ثم
+
+137
+00:09:43,480 --> 00:09:49,260
+اليمين فصارت ايش تلاتة خمسة خلصنا الان ال sub tree
+
+138
+00:09:49,260 --> 00:09:56,740
+هذه كأنها خلصت عنصر اشمال بالنسبة لل tree الأصلية
+
+139
+00:09:56,740 --> 00:10:00,000
+الان بدنا نطلع ال tree هذه فى ضل اشي لفت عليها؟
+
+140
+00:10:00,000 --> 00:10:05,390
+مضلش فإذا نقعد نضطبها السبعةثم نبدأ باليمين الجزء
+
+141
+00:10:05,390 --> 00:10:09,390
+المتبقي يمين طب هد فيه إلها شمال ك sub-tree فيه
+
+142
+00:10:09,390 --> 00:10:13,630
+إلها شمال طيب نبدأ نشوف جبل ما نبدأ نتعامل مع ال
+
+143
+00:10:13,630 --> 00:10:16,970
+nodes نفسها بتعامل مع ال sub-tree الأول فهي في sub
+
+144
+00:10:16,970 --> 00:10:21,170
+-tree هد لأ هد ال sub-tree نخلص ال sub-tree هد ال
+
+145
+00:10:21,170 --> 00:10:29,290
+left ال rootالـ 11 اللي هي اليمين تبع الـ subtree
+
+146
+00:10:29,290 --> 00:10:32,370
+خلصت subtree يعني كأنها بالنسبة للـ 12 خلصت ال
+
+147
+00:10:32,370 --> 00:10:34,730
+node اللي هنا كلها باللي فيها و اللي هي في النهاية
+
+148
+00:10:34,730 --> 00:10:37,990
+مش node هي subtree شايفها هو بالنسبة له ال node
+
+149
+00:10:37,990 --> 00:10:47,550
+تمام 12 ثم 15 ففعليا هي sorted ال sequence عندنا
+
+150
+00:10:47,550 --> 00:10:52,630
+هنا sorted مافيش فيه أي مشكلة نهائياكترتيب طبعا
+
+151
+00:10:52,630 --> 00:10:56,470
+العكس صحيح ممكن تبدأ عملية الترتيب منه بس في
+
+152
+00:10:56,470 --> 00:11:00,230
+الحالة هذه عشان تبدأ عملية الترتيب بدي يكون هو
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+153
+00:11:00,230 --> 00:11:05,230
+جايك unordered دائما العنصر اللي في الأول هو اللي
+
+154
+00:11:05,230 --> 00:11:09,210
+بحكمك الشبكة او ال tree تبعتك مين العنصر اللي
+
+155
+00:11:09,210 --> 00:11:12,710
+موجود في البداية انا بفهم انه كان اول عنصر لما
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+156
+00:11:12,710 --> 00:11:17,950
+عملوا construction لل tree هذي اللي قدامنا كان فيه
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+157
+00:11:17,950 --> 00:11:22,920
+السبعةزي ما قعدنا هنشوف في المثال اللي جاي هاي
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+158
+00:11:22,920 --> 00:11:29,220
+مثال هاي في عندك مثال بدنا نرتب مجموعة التخصصات
+
+159
+00:11:29,220 --> 00:11:34,940
+هذه حسب اسمها أو حسب الحروف بتاعتها حسب حروفها
+
+160
+00:11:34,940 --> 00:11:37,740
+alphabetical يعني فبدنا نتعامل معاه as a
+
+161
+00:11:37,740 --> 00:11:41,140
+alphabetical sorting بدنا نعمل sorting بالنسبة لل
+
+162
+00:11:41,140 --> 00:11:44,660
+alphabetical في عندك ال mathematics خلاص ال
+
+163
+00:11:44,660 --> 00:11:47,800
+mathematics هي اللي جيتها في الوجه بحطها في الأول
+
+164
+00:11:47,800 --> 00:11:52,300
+صارت هي ال rootبمعنى لو عكستني إياهم و حطتلي كلمة
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+165
+00:11:52,300 --> 00:11:56,680
+تانية حد فيها فما تقعدش تغلب حالك تعمل search في
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+166
+00:11:56,680 --> 00:12:02,100
+البداية لأ اللي قدامك ه to مش هيفرج معاك كتير في
+
+167
+00:12:02,100 --> 00:12:06,420
+الآخر ال sorting هتطلع معك هتطلع معك ماتجلجشك
+
+168
+00:12:06,420 --> 00:12:10,560
+sorting حسب left to right و ال left ل ال sub tree
+
+169
+00:12:10,560 --> 00:12:13,600
+ل ال right ل ال sub tree هتطلع معاك في جميع
+
+170
+00:12:13,600 --> 00:12:17,920
+الأحوال صحيح يمكن شكلها يتغير من واحد للتاني بس في
+
+171
+00:12:17,920 --> 00:12:21,400
+النهاية لما بتعامل معاها left to right كله هيطلع
+
+172
+00:12:21,400 --> 00:12:27,300
+نفس ال sorted array في الآخر ماتجلجش فحبدأ بمين
+
+173
+00:12:27,300 --> 00:12:29,000
+بالامر
+
+174
+00:12:30,770 --> 00:12:34,890
+خلص نبدأ بال mathematics ثم physics الآن ال
+
+175
+00:12:34,890 --> 00:12:39,070
+physics بالنسبة لل .. لل M مدام أنك بتتعامل معه
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+176
+00:12:39,070 --> 00:12:44,110
+binary معناته أنا عارف أنه فيه طرفين المفروض
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+177
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+الشمال جبل ال M و اليمين بعد ال M ال physics بعد
+
+178
+00:12:50,470 --> 00:12:57,960
+خلاص بنحط مين؟ عاليمين انتهى بنحط مين؟ عاليمينOkay
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+179
+00:12:57,960 --> 00:13:04,680
+مين بعد هيك فيه عنده؟ Geography Geography جيه جبل
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+180
+00:13:04,680 --> 00:13:09,240
+ال M خلاص معناته بتيجي جبل ال M فإذا على شمال ال M
+
+181
+00:13:09,240 --> 00:13:16,320
+إيش فيه بعدها? Zoology اللي هو علم الحيوان زي Z
+
+182
+00:13:16,320 --> 00:13:22,150
+جاية بعد ال P معناته على يمين ال Pعلى اليمين رايحة
+
+183
+00:13:22,150 --> 00:13:28,030
+لأنها بعدها طيب ال metro .. ال metrology اللي هي
+
+184
+00:13:28,030 --> 00:13:32,870
+هذا علم ال .. الأمطار و الأحوال الجوية علم الأحوال
+
+185
+00:13:32,870 --> 00:13:37,930
+الجوية تمام؟ هذا اشمار عليكم طيب علم الأحوال
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+186
+00:13:37,930 --> 00:13:45,270
+الجوية بدأ بإمين بال M طيب ممتاز M هي بعد M طيب A
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+187
+00:13:45,270 --> 00:13:53,680
+هنا E معنى بعدهابعدها بتيجي بعدها مش شايف؟ أكيد
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+188
+00:13:53,680 --> 00:13:56,800
+لازم ييجي بعدها طيب بالنسبة لل P جابلها و لا
+
+189
+00:13:56,800 --> 00:14:01,200
+بعدها؟ جابلها فبتيجي المفروض عن ناحية عن ناحية هذه
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+190
+00:14:01,200 --> 00:14:09,600
+جيد مين ضل؟ إيش التخصص اللي وراها؟ Geology علوم
+
+191
+00:14:09,600 --> 00:14:17,740
+الأرض Geology G و E E O O G L
+
+192
+00:14:20,130 --> 00:14:26,630
+بعدها فإذا هتصير يمين لل node هذه هتصبح يمين لل
+
+193
+00:14:26,630 --> 00:14:33,370
+node هذه تمام إيش ضال؟ Psychology Psychology بس P
+
+194
+00:14:33,370 --> 00:14:40,490
+بعد ال P فهي ال P جينا هنا هتكون بعدها P P S يعني
+
+195
+00:14:40,490 --> 00:14:47,560
+بعد ال H هتيجي هنا المفروض طيب بالنسبة لل Zع
+
+196
+00:14:47,560 --> 00:14:55,500
+الشمال فده بتيجي شمال هنا بتيجي على الشمال انيا ال
+
+197
+00:14:55,500 --> 00:15:02,160
+psychology بدأنا بال P هاي ال P أكيد بالنسبالي
+
+198
+00:15:02,160 --> 00:15:04,320
+دايما كله يبدأ من ال root كله دايما يبدأ من ال
+
+199
+00:15:04,320 --> 00:15:07,360
+root بالنسبالي ال M ال root هذه على يمينها لأنه
+
+200
+00:15:07,360 --> 00:15:11,580
+أكبر منها بجي هنا طب هاي P مع P خلاص بنعديها بناخد
+
+201
+00:15:11,580 --> 00:15:17,930
+الحرف التانيهنا H هنا S لأ ال S بعد معناته هذا ال
+
+202
+00:15:17,930 --> 00:15:21,530
+psychology المفروض تيجي بعد ال physics على يمينها
+
+203
+00:15:21,530 --> 00:15:25,170
+طيب إجينا على يمينها نقارنها بال Z لأ هي جابل ال Z
+
+204
+00:15:25,170 --> 00:15:30,710
+فبتيجي على شمال ال Z طيب لاحظ أنك لو بدأت بأي كلمة
+
+205
+00:15:30,710 --> 00:15:34,770
+تانية هتتغير صح شكلها ل tree بس لما تيجي تاخدها
+
+206
+00:15:34,770 --> 00:15:40,350
+left to right هتطلع مرتبة هتطلع مرتبةعملية ال
+
+207
+00:15:40,350 --> 00:15:43,030
+insertion اللي مفترض لو بناحكي على ال raw files
+
+208
+00:15:43,030 --> 00:15:48,250
+يتكون ان هو في انتي تكون؟ هو في انتي لأن على فرق
+
+209
+00:15:48,250 --> 00:15:51,510
+احنا اول ال raw كان ابعاد اصغر رقم فعفوا احنا
+
+210
+00:15:51,510 --> 00:15:54,790
+عملنا بس من سفر لعشر رقم ده ضفناهم سفر بعدين واحد
+
+211
+00:15:54,790 --> 00:15:57,450
+و اثنين و اثنين لعملية ال insertion كله هيروح
+
+212
+00:15:57,450 --> 00:16:02,990
+اليومين لحظة شوية انت .. انت الآن بتعمل جابل ال
+
+213
+00:16:02,990 --> 00:16:06,370
+search جابل ال .. اعفو ان ال inserting او ال
+
+214
+00:16:06,370 --> 00:16:10,860
+insertion اللي بدك تعملها بدك تعمل searchلازم تعمل
+
+215
+00:16:10,860 --> 00:16:16,460
+search كل أنصر لازم تعمله search صح؟ اه هاي الأنصر
+
+216
+00:16:16,460 --> 00:16:20,520
+الأول عملتله search طيب خلصناه هل وجدت العملية
+
+217
+00:16:20,520 --> 00:16:25,100
+تبعته عمليته اللي هي logarithmic لانه ال search
+
+218
+00:16:25,100 --> 00:16:30,890
+طيب الأنصر التانيبرضه بدك تعمله search جبل ما
+
+219
+00:16:30,890 --> 00:16:34,010
+تعمله insertion .. ال insertion تبعته .. او ال
+
+220
+00:16:34,010 --> 00:16:36,970
+inserting بتعرف وين ما هو احنا عشان احنا نحكي ع
+
+221
+00:16:36,970 --> 00:16:41,410
+worst case فممكن يعني ما تكونش ال agenda بتري تكون
+
+222
+00:16:41,410 --> 00:16:45,650
+انضافة كسطر واحد كله .. كله واحد الله يعني الله
+
+223
+00:16:45,650 --> 00:16:46,990
+يعني الله يعني الله يعني الله يعني الله يعني الله
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+224
+00:16:46,990 --> 00:16:48,590
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+225
+00:16:48,590 --> 00:16:48,630
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+226
+00:16:48,630 --> 00:16:48,770
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+227
+00:16:48,770 --> 00:16:49,330
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+228
+00:16:49,330 --> 00:16:49,710
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+229
+00:16:49,710 --> 00:16:54,160
+يعني الله يعني الله يعني الله يعني الله يعلا إيه
+
+230
+00:16:54,160 --> 00:17:00,600
+عشان بس أركز معاك search ولا sort insert اللي هي
+
+231
+00:17:00,600 --> 00:17:02,840
+بدأت تكون عبارة عن search و بعدين اللي هو تمام
+
+232
+00:17:02,840 --> 00:17:05,900
+تمام ممتاز يعني عندك تمال sorting مع .. مع عدد ..
+
+233
+00:17:05,900 --> 00:17:11,260
+خلاص سبحان الله يدرنها من 0 إلى 10 هذه بطلت اسمها
+
+234
+00:17:11,260 --> 00:17:14,620
+ال worst case بالعكس هذه ال worst caseو انا هجيت
+
+235
+00:17:14,620 --> 00:17:17,060
+انا مش عارف انهم مرتبين او مش مرتبين فجيت اضيفي
+
+236
+00:17:17,060 --> 00:17:20,160
+شويه هذي اه؟ ايش .. ايش طالع معاك؟ اضفنا السفر
+
+237
+00:17:20,160 --> 00:17:24,520
+بالاول كويس بعدين بنضيف الواحد وراح ترمي الاتنين
+
+238
+00:17:24,520 --> 00:17:27,540
+وراح ترمي اتنين هجيت ع العملية ال .. ال searching
+
+239
+00:17:27,540 --> 00:17:30,980
+بطلنا احنا ننزل login بس ان احنا ننزل انصر وانصر
+
+240
+00:17:30,980 --> 00:17:37,440
+فصار زي كده انها ممكن تلز نزل صارت كأنها سطر كامل
+
+241
+00:17:39,700 --> 00:17:42,680
+كويس بس انت برضه نفس الجثة انت في النهاية بتتعامل
+
+242
+00:17:42,680 --> 00:17:47,140
+مع كل node على اساس ان هي yes no yes no yes no
+
+243
+00:17:47,140 --> 00:17:55,760
+معاك والله فاهمك فاهمك فاهمت
+
+244
+00:17:55,760 --> 00:17:58,520
+جزدك على اساس ان كلهم مالوا في اتجاه واحد كلهم
+
+245
+00:17:58,520 --> 00:18:04,760
+اخدوا اتجاه اتجاه واحد لما بتيجي بتعمل insertion
+
+246
+00:18:07,240 --> 00:18:10,340
+والله هي بدها بحث يعني مش غلط خلينا ناخدهم واحدة
+
+247
+00:18:10,340 --> 00:18:15,160
+واحدة مش هتصبح .. لأ هي صادفة معاك انفع انت مش
+
+248
+00:18:15,160 --> 00:18:20,200
+هتستغل فكرة ال decision لأنه دايما هتكون معاك اكبر
+
+249
+00:18:20,200 --> 00:18:21,340
+او اصغر ده مش هتكون اصغر
+
+250
+00:18:24,050 --> 00:18:28,030
+أو أكبر لو كانت بالعكس لو كانت بالعكس يعني اتجاه
+
+251
+00:18:28,030 --> 00:18:31,570
+عكسي اتجاه عكسي خلينا نبحثها مش غلط اقولك خلينا
+
+252
+00:18:31,570 --> 00:18:34,750
+نعتبرها سؤال من الأسئلة المرة القادمة و نتعامل
+
+253
+00:18:34,750 --> 00:18:37,730
+معها كأنها سؤال مستقل و نحلها نشوفها ان شاء الله
+
+254
+00:18:37,730 --> 00:18:43,150
+كويس احنا كان في chemistry لسه والله ما احنا
+
+255
+00:18:43,150 --> 00:18:44,930
+ماخدين بالنا ان في لسه chemistry اما تقولوا ليه
+
+256
+00:18:44,930 --> 00:18:50,450
+لسه في C اه شوفين انت دخلتنا في ال ..هي لسه في
+
+257
+00:18:50,450 --> 00:18:56,510
+main and chemistry ال C بتهيألي مش كتير باينة ال C
+
+258
+00:18:56,510 --> 00:18:59,410
+هي باينة انت قعدت بتقولي كلهم اشمال اشمال هي
+
+259
+00:18:59,410 --> 00:19:06,410
+طلعتلك اشمال على طول طيب تأثرت بكلامك اه؟ طيب نروح
+
+260
+00:19:06,410 --> 00:19:10,660
+لل decision trees في ال decision treesهنا بدنا
+
+261
+00:19:10,660 --> 00:19:14,460
+ناخد قرار القرار تبعنا بدي يكون مبني على three
+
+262
+00:19:14,460 --> 00:19:20,100
+بمعنى yes و no و بدي اصل لقرار في النهاية القرار
+
+263
+00:19:20,100 --> 00:19:23,680
+هيكون مبني على situations معينة اكيد بدي يكون مبني
+
+264
+00:19:23,680 --> 00:19:28,180
+على situations فكل decision point او situation
+
+265
+00:19:28,180 --> 00:19:35,600
+تمثل ب node تمثل ب node زي انه نقول ال situation
+
+266
+00:19:35,600 --> 00:19:45,030
+المعين هل X أكبر من خمسةفبد أقول yes or no؟ yes أو
+
+267
+00:19:45,030 --> 00:19:50,530
+no فهذه هنا ال situation اللي أنا بسأل عليها تمثل
+
+268
+00:19:50,530 --> 00:19:56,480
+بشكل node طيب ال actionاللي بده يصير أو عادة ال
+
+269
+00:19:56,480 --> 00:20:01,200
+edge هذي عشان تروح ل decision هذي المفروض النتيجة
+
+270
+00:20:01,200 --> 00:20:04,620
+بتاعة ال situation ال action اللي بده يصير هل بدي
+
+271
+00:20:04,620 --> 00:20:07,720
+يعني بدي اقارن بدي افحص ال situation وبناء على
+
+272
+00:20:07,720 --> 00:20:11,740
+القرار اللي طلع معايا او النتيجة بدي اقول فعلا
+
+273
+00:20:11,740 --> 00:20:16,360
+متحقق او غير متحقق بمثلها بال edgesعشان أروح
+
+274
+00:20:16,360 --> 00:20:20,480
+للقرارات القرار هذا ممكن يكون نهائي فهذه معناته
+
+275
+00:20:20,480 --> 00:20:24,320
+عبارة عن leaf أو لأ هي لسه محتاجة كمان فحص تاني
+
+276
+00:20:24,320 --> 00:20:31,180
+فتصبح هي كمان node ل situation بدها فحص ل
+
+277
+00:20:31,180 --> 00:20:33,680
+situation تاني بدها فحص زي ما نقول أكبر من خمسة
+
+278
+00:20:33,680 --> 00:20:39,830
+طيب هنا X أصغر من اتنينعسى اسم اللي بدي أقول هل هي
+
+279
+00:20:39,830 --> 00:20:44,110
+من 2 إلى 5 مثلا أقول والله قيمة X من 2 إلى 5 فنفس
+
+280
+00:20:44,110 --> 00:20:47,850
+الكلام بدي أقول yes or no فهل بدي أروح لل terminal
+
+281
+00:20:47,850 --> 00:20:51,070
+فهذه معناته القرار النهائي أو لأ لسه محتاج كمان
+
+282
+00:20:51,070 --> 00:20:55,390
+فحص تاني زي قصة الأعراض أنا بسألش عن أعراض واحد
+
+283
+00:20:55,390 --> 00:20:58,840
+وخلاصالطبيب عادة بيسألك عن العرض الأول ثم العرض
+
+284
+00:20:58,840 --> 00:21:02,180
+التاني ثم التالت و هو بيحط في دماغه sequence
+
+285
+00:21:02,180 --> 00:21:06,400
+لمجموعة الأعراض هذه عشان يجمحهم مع بعض و يحاول
+
+286
+00:21:06,400 --> 00:21:14,640
+يطلع بمين بقرار يطلع القرار معين تمام الان واحدة
+
+287
+00:21:14,640 --> 00:21:17,860
+من الأمثلة الواضحة على هذا الموضوع هي ال coin
+
+288
+00:21:17,860 --> 00:21:22,060
+weighing problem اللي هي عندك مجموعة coins و ال
+
+289
+00:21:22,060 --> 00:21:25,500
+coins هذه نفترض الخمسين مليم الفلسطيني
+
+290
+00:21:28,130 --> 00:21:34,750
+من عملتنا الفلسطينية كويس الخمسين Palestinian مليم
+
+291
+00:21:34,750 --> 00:21:41,170
+او millions كويس عندى تمان قطعة التمن قطع هدولة
+
+292
+00:21:41,170 --> 00:21:47,110
+فيهم واحدة زائفة اكم وزن محتاج ب free being
+
+293
+00:21:47,110 --> 00:21:54,290
+balanced عشان اكتشف مين الزائفة طيب الزائفة هذه
+
+294
+00:21:54,290 --> 00:22:01,510
+كيف زائفة هي lightercounterfeit بمعنى وزنها أقل من
+
+295
+00:22:01,510 --> 00:22:06,810
+الباجي لأنه كلكم عارفين أنه قيمة المعدن نفسه
+
+296
+00:22:06,810 --> 00:22:10,650
+المفروض أنه حسب الوزن من المعدن نفسه يكون يعطي نفس
+
+297
+00:22:10,650 --> 00:22:15,350
+قيمة العملة طيب لما أنا أكل شوية منه و أكل من هذا
+
+298
+00:22:15,350 --> 00:22:17,470
+شوية و أكل من هذا شوية و أكل من هذا شوية بطرت
+
+299
+00:22:17,470 --> 00:22:22,400
+خمسين ملينصارت لها 45 مليم مثلا فعليا يعني قيمة
+
+300
+00:22:22,400 --> 00:22:27,120
+المعدن نفسه أصبح بسويش الخمسين بساوي خمسة واربعين
+
+301
+00:22:27,120 --> 00:22:30,400
+منه و أنا روحت جمعتها الأكم من واحدة و حاطيتهم في
+
+302
+00:22:30,400 --> 00:22:34,820
+coin جديدة اربحت فيها خمسين إضافية تلغشوا هو هيك
+
+303
+00:22:34,820 --> 00:22:42,000
+بتمام فمعنى ذلك أنه هي أقل وزنا أقل وزنا okay أكم
+
+304
+00:22:42,000 --> 00:22:43,160
+ليش؟
+
+305
+00:22:53,630 --> 00:22:59,670
+ممتاز 100% الان انت حللته ننطقيا صح و حلك صح الان
+
+306
+00:22:59,670 --> 00:23:02,670
+بدنا نحل الكلام اللى انت حللته هذا نحطه فى قالب
+
+307
+00:23:02,670 --> 00:23:07,570
+علمى نحطه فى قالب رياضى القالب الرياضى ببساطة هى
+
+308
+00:23:07,570 --> 00:23:12,790
+ال height تبعت لل tree لأن ال tree انا بتعامل انا
+
+309
+00:23:12,790 --> 00:23:15,990
+مع ال tree و اللى انت قلتلنا اياه الان انت قلت
+
+310
+00:23:15,990 --> 00:23:21,610
+tree بمعنى انت حطيتdecision عفوا situation ال
+
+311
+00:23:21,610 --> 00:23:27,510
+situation هذا حللته كنتائج اما قاعد يقول اما انها
+
+312
+00:23:27,510 --> 00:23:33,610
+متساويين فمعنى ذلك ان هي عندك هذا situation معينة
+
+313
+00:23:33,610 --> 00:23:36,870
+هي الوزن اللي انت عملته ايش ال possibilities تبعته
+
+314
+00:23:36,870 --> 00:23:45,040
+قولت اما يكون متساويين balance او اليمين اعلىفمعنى
+
+315
+00:23:45,040 --> 00:23:50,240
+ذلك أنه الشمال فيها الزائف أو الشمال الأعلى فمعنى
+
+316
+00:23:50,240 --> 00:23:55,900
+ذلك أنه كفة اليمين اللي فيها الجطع الزائفة اعمل
+
+317
+00:23:55,900 --> 00:24:03,600
+التلاتة فهنا تصيرنا نتكلم عن theory three تمام هذه
+
+318
+00:24:03,600 --> 00:24:10,040
+بكل بساطة أصبحت كأنه بهذا الشكل هذه المرة الأولى
+
+319
+00:24:10,740 --> 00:24:14,680
+بعدين قلتلنا ان في مرة تانية تمام المرة التانية
+
+320
+00:24:14,680 --> 00:24:20,060
+المعناه هتكون يا هنا يا هنا يا هنا برضه في وزنات
+
+321
+00:24:20,060 --> 00:24:29,400
+الوزنات هذه هتكون تلاتة ولا اتنين هنا
+
+322
+00:24:29,400 --> 00:24:32,760
+كنتائج وزنتين اذا كانوا balance انا بتكلم عن
+
+323
+00:24:32,760 --> 00:24:37,580
+تمانية اي
+
+324
+00:24:37,580 --> 00:24:42,260
+ممكن تكون تلاتةأحنا ممكن نساوي الأخف والأدلال صح
+
+325
+00:24:42,260 --> 00:24:46,560
+لأنه اللي فهمته منك أن أنت ممكن تحط تلاتة مقابل
+
+326
+00:24:46,560 --> 00:24:52,940
+تلاتة طيب واحدة منهم وزنت معناته الأخف فيها الزائف
+
+327
+00:24:52,940 --> 00:24:57,520
+خلاص كل السبعة هدول هي case سليم التلاتة هدولة
+
+328
+00:24:57,520 --> 00:25:01,580
+بدنا نحط تنتين منهم على وزنة فهيطلع برضه تلاتة
+
+329
+00:25:01,580 --> 00:25:05,160
+possibilities ممكنين أنه اليمين أو الشمال أو
+
+330
+00:25:05,160 --> 00:25:07,960
+balanced فاللي ضالت ماوزنتهاش هي الزائفة بتصير
+
+331
+00:25:09,050 --> 00:25:12,550
+واضحت؟ فإذا لأ انا هنا واحدة منهم هتكون تنتين هم
+
+332
+00:25:12,550 --> 00:25:17,870
+التنتين في حال اللي ضالوا برا بمعنى التلاتة و
+
+333
+00:25:17,870 --> 00:25:22,350
+التلاتة رجحوا مع بعض التنتين متساويتين التنتين
+
+334
+00:25:22,350 --> 00:25:25,750
+اللي برا هم اللي فيهم الزائف هنا بطلع انديال يمينا
+
+335
+00:25:25,750 --> 00:25:31,090
+لشمال خلاص فهتكون بهذا الشكل
+
+336
+00:25:34,590 --> 00:25:40,430
+أه طيب أكم .. أكم level هيطلع معاك هات ناخد أربعة
+
+337
+00:25:40,430 --> 00:25:46,630
+أربعة هات نحللها بكل بساطة بدك تشتغل على هنا طبعا
+
+338
+00:25:46,630 --> 00:25:51,330
+احنا كنا بنتكلم تلاتة مقابل تلاتة هنا بدك تشتغل
+
+339
+00:25:51,330 --> 00:25:53,090
+على أربعة مقابل أربعة طيب
+
+340
+00:25:56,450 --> 00:26:00,030
+أه أنا عارف والله عارف بس خلّينا ن .. أتبع معاكم
+
+341
+00:26:00,030 --> 00:26:03,450
+ماشي مش غلط خلّينا نفكر و خلّينا ن .. ننطلق أنا
+
+342
+00:26:03,450 --> 00:26:06,770
+أحيانا بكون عارف أنه لأ هتوصلنا لإش .. مش مش دي
+
+343
+00:26:06,770 --> 00:26:09,470
+لكن لازم نكمل مع بعض انت فاكر مش غلط أربعات و
+
+344
+00:26:09,470 --> 00:26:14,210
+وزمتان هى أربعة أربعة صار عندى هنا أربعة أنت بتقول
+
+345
+00:26:14,210 --> 00:26:16,390
+في واحدة منهم .. في واحدة منهم يكون مزيف يبقى فشل
+
+346
+00:26:16,390 --> 00:26:18,510
+بتقول مش هيتفنون تمام هل وجد أنت بتتكلم عن أربعة
+
+347
+00:26:18,510 --> 00:26:23,590
+أربعة اتنين بمعنى الرشح هادى إذا اليمين كانت أخف
+
+348
+00:26:29,200 --> 00:26:33,300
+ماشي معاك والله معاك هنا فيه أنك أربعة مقابل أربعة
+
+349
+00:26:33,300 --> 00:26:40,440
+صح هاي الميزان تبعك تمام هاي ميزانك حطيت أربعة
+
+350
+00:26:40,440 --> 00:26:45,440
+مقابل أربعة هاي هادي نزلت يعني الأربع هدول فيهم
+
+351
+00:26:45,440 --> 00:26:48,460
+الزائفة تمام يعني معناه ذلك أن أنا وصلت للنود
+
+352
+00:26:48,460 --> 00:26:53,090
+التاني وفيه في إيدي أربعة واحدة منهم زائفةأيوة
+
+353
+00:26:53,090 --> 00:26:57,590
+هاتمنا نكمل معاك هي اتنين و اتنين صحيح؟ طيب هي
+
+354
+00:26:57,590 --> 00:27:00,890
+اتنين هنا و اتنين هنا صار عنده هنا في النهاية
+
+355
+00:27:00,890 --> 00:27:07,050
+اتنين في ايدي عرفت ان هم زائفين، كيف بدك تعرفه؟
+
+356
+00:27:07,050 --> 00:27:11,490
+صح؟ أكم level هنا عملت؟ طيب زميلك جالك أكم level؟
+
+357
+00:27:13,750 --> 00:27:17,510
+يعني معنى ذلك انا لو بدي على كل وزنة ادفع مقابل
+
+358
+00:27:17,510 --> 00:27:24,930
+الجبان هذا وزن في النهاية جبان و هذا بتأجر بالوزنة
+
+359
+00:27:24,930 --> 00:27:29,290
+هقولك والله بدي اه و بدي اوزن وزنتين okay كل وزنة
+
+360
+00:27:29,290 --> 00:27:33,950
+بشكل انا هضطر اخد منه شكلين بس انت هضطر اخد منك
+
+361
+00:27:33,950 --> 00:27:37,890
+تلاتة هاخد منك تلاتة لانك وزنت تلت مرات صح ولا لأ
+
+362
+00:27:39,810 --> 00:27:44,030
+هينمشينا معاك و قولنا انه حللناها زي ما .. في اشي
+
+363
+00:27:44,030 --> 00:27:47,610
+غلط عملناها؟ مظبوط زي ما كانت فكرتك هنا اضطريت
+
+364
+00:27:47,610 --> 00:27:51,970
+اعمل واحدة اتنين تلاتة هنا عملت اتنين لأ اوفرلي
+
+365
+00:27:51,970 --> 00:27:57,610
+الاتنين اوفرنا الاتنينلأ لأ بتطلع بس زي ما أقوله
+
+366
+00:27:57,610 --> 00:28:01,030
+إله إله حدود يعني خلوكوا أصبروا معايا لل slide
+
+367
+00:28:01,030 --> 00:28:03,530
+اللي جاية هقولكوا إيه أمتى بقدر أعمل اللي انت
+
+368
+00:28:03,530 --> 00:28:07,370
+عملته أنا ضلت متماشي معاك عساس كنت مستنى منك كمان
+
+369
+00:28:07,370 --> 00:28:11,190
+كلمة زيادة كأن أقولك أه هيك بتصبط بس خلينا ..
+
+370
+00:28:11,190 --> 00:28:16,470
+خلينا معاكم كيف؟ هو جزء بتاخد وزن 2 بس 6 و 8 ليس
+
+371
+00:28:16,470 --> 00:28:20,010
+لزن 1 فلو كان فردي بتحط فكاف أكثر من كاف يعني خمسة
+
+372
+00:28:20,010 --> 00:28:21,670
+و أربعة .. ما هي جاعة بتقول إذا كان فردي .. كيف
+
+373
+00:28:21,670 --> 00:28:22,790
+بدك تضمن هذا الكلام؟
+
+374
+00:28:25,820 --> 00:28:29,040
+واصبروا عليّ النقاش مازال مستمر هنا خلّينا نبدأ
+
+375
+00:28:29,040 --> 00:28:32,840
+بالفكرة بس تعت البشار المهندس هاي الفكرته و بعدين
+
+376
+00:28:32,840 --> 00:28:36,300
+ننتقل لفكرة البشار المهندس برضه و نشوف إيش اللي
+
+377
+00:28:36,300 --> 00:28:39,840
+اتختلفت عهم الأولة أني قولنا والله تلاتة تلاتة و
+
+378
+00:28:39,840 --> 00:28:43,320
+هذه الإجابة اللي إجتنا في الأول تلاتة تلاتة و
+
+379
+00:28:43,320 --> 00:28:48,030
+الكتاب عجبته أكتر إيش نسوي؟جالك تلاتة تلاتة فبضل
+
+380
+00:28:48,030 --> 00:28:52,810
+عند هنا إما بترجح في الآخر التلاتة بتاعة الشمال
+
+381
+00:28:52,810 --> 00:28:54,990
+فمعنى ذلك أن التلاتة اللي في اليمين هم اللي فيهم
+
+382
+00:28:54,990 --> 00:28:59,630
+الزائف تمام مش مشكلة هنا نفس الكلام اللي رجحت
+
+383
+00:28:59,630 --> 00:29:03,950
+اليمين فالشمال هي اللي فيها الزائف أو اللي تساووا
+
+384
+00:29:03,950 --> 00:29:08,390
+فتنتقن لمن وزنوش هم اللي فيهم الزائف بعد هيك
+
+385
+00:29:08,390 --> 00:29:11,830
+محتاجين كمان وزنة تانية نعمل نفس الفكرة بس في
+
+386
+00:29:11,830 --> 00:29:16,040
+الآخر من التلاتة هدول بحط واحدة مقابل واحدةوبقال
+
+387
+00:29:16,040 --> 00:29:20,360
+عندي واحدة برا والله اتزنوا اللي برا هي اللي فيها
+
+388
+00:29:20,360 --> 00:29:26,860
+مشكلة ومش محتاج اقعد اوزنها تمام ايه كويس الان
+
+389
+00:29:26,860 --> 00:29:29,980
+الفكرة هذه نظريا احنا اخدناها لسه المرة اللي فاتت
+
+390
+00:29:29,980 --> 00:29:33,420
+وختمنا فيها شغلنا لما كنا بنتكلم عن مجموعة ال
+
+391
+00:29:33,420 --> 00:29:37,700
+rules او ال theoremsو آخر حاجة حسبناها الـ height
+
+392
+00:29:37,700 --> 00:29:42,140
+بتاعتنا صح لما قولنا عدد ال leaves بتساوي ال M to
+
+393
+00:29:42,140 --> 00:29:45,380
+the power of H و بعدين قولنا اننا بدي جيب ال H هذه
+
+394
+00:29:45,380 --> 00:29:49,360
+لأن ال H هذه كانت ال complexityطيب ما هي نفس الاشي
+
+395
+00:29:49,360 --> 00:29:54,840
+ال complexity هنا جداش عدد التكرارات للوزن هنا كان
+
+396
+00:29:54,840 --> 00:29:57,420
+عندى تكرارين هنا اضطريت اعمل تلت تكرارات فمعناه
+
+397
+00:29:57,420 --> 00:30:00,520
+ذلك هي عدد التكرارات صارت جداش عدد التكرارات هي ال
+
+398
+00:30:00,520 --> 00:30:02,480
+.. ال .. ال height اللى بدور عليها و احنا جيبناها
+
+399
+00:30:02,480 --> 00:30:05,140
+logarithmic المرة الماضية جيبناها logarithmic بكل
+
+400
+00:30:05,140 --> 00:30:08,860
+بساطة فال H هنا هتكون اكبر من او تساوي ال ceiling
+
+401
+00:30:08,860 --> 00:30:13,040
+لمين ل log M لعدد ال leaves ليش لأنه عدد ال leaves
+
+402
+00:30:13,040 --> 00:30:19,140
+مش بالضرورى يكون واحدة من مضاعفة ال Mصح؟ يعني لو
+
+403
+00:30:19,140 --> 00:30:23,000
+افترضنا اتنين مش بالضروري ان ال tree اللي تطلع
+
+404
+00:30:23,000 --> 00:30:29,580
+عندى تكون full balanced tree مين قال ضروري؟ ماحدش
+
+405
+00:30:29,580 --> 00:30:32,840
+قال ضروري يعني هل معناه ذلك انه تطلع في الآخر لو
+
+406
+00:30:32,840 --> 00:30:37,300
+بوزن اتنين .. لو ال tree عندى binary تطلع عندى
+
+407
+00:30:37,300 --> 00:30:40,220
+تمانية على اعتبار ان تمانية واحدة من المضاعفات
+
+408
+00:30:40,220 --> 00:30:44,220
+اتنين اربعة تمانية ستاشت مش هى المضاعفات لل binary
+
+409
+00:30:44,220 --> 00:30:49,920
+لأ طلع عندى اربعة عشرطلع عندك 14 فإذا عدد ال
+
+410
+00:30:49,920 --> 00:30:53,240
+leaves اللي بتقتصله 14 فهنا بتعود ال 14 بتاخد
+
+411
+00:30:53,240 --> 00:30:57,700
+ceiling لإنه أكيد هيطلع هنا كسر أكيد هيطلع كسر لا
+
+412
+00:30:57,700 --> 00:31:01,220
+هو 8 ولا هو 16 فهو بين ال 8 و ال 16 يعني بتطلع
+
+413
+00:31:01,220 --> 00:31:06,220
+تلاتة و كسر تلاتة و إشي على طول بتاخد للأعلى و
+
+414
+00:31:06,220 --> 00:31:08,980
+بمشي الحاد تمام ففي حالة زي الحالة اللي احنا
+
+415
+00:31:08,980 --> 00:31:14,380
+اشتغلناها هنا كنت بتكلم عن 8 coins أو تمانية من
+
+416
+00:31:14,380 --> 00:31:18,610
+العملة الفلسطينية اللي بالملين من الخمسين ملينكانت
+
+417
+00:31:18,610 --> 00:31:21,530
+موجودة عندى، بدى أفحصهم، أنا عارف إن الميزان
+
+418
+00:31:21,530 --> 00:31:25,830
+بيعطيني branching لتلاتة، يا يمين يا شمال يا
+
+419
+00:31:25,830 --> 00:31:30,090
+balance فإذن بتكلم عن تلاتة، افحصها بيطلع مندك
+
+420
+00:31:30,090 --> 00:31:33,950
+واحد فاصلة اتنين، فإذن أنا بتكلم عن عدد وزنات
+
+421
+00:31:33,950 --> 00:31:40,950
+اتنين، محتاج وزن تان، فقط، تمام okay، الآن نجي
+
+422
+00:31:40,950 --> 00:31:44,820
+للاستراتيجية اللى بدنا نشتغل عليهاكيف انا بدي
+
+423
+00:31:44,820 --> 00:31:47,800
+اشتغل على أرقام تانية لما يكون عندك أرقام تانية
+
+424
+00:31:47,800 --> 00:31:52,200
+بكل بساطة بناخد التلت مادام أنا بتكلم عن ال M
+
+425
+00:31:52,200 --> 00:31:59,360
+تبعتي بتساوي تلاتة حسب التطبيق انا بتكلم عن وزن
+
+426
+00:31:59,360 --> 00:32:03,880
+ميزان الميزان يا يمين يا شمال يا بيرجح okay فإذا
+
+427
+00:32:03,880 --> 00:32:09,240
+باخد التلت و بعملهsealing لأنه مش بالضروري دايما
+
+428
+00:32:09,240 --> 00:32:14,140
+يقسم على تلاتة العدد الأغراض اللي بدي أفحصها هذه
+
+429
+00:32:14,140 --> 00:32:18,460
+أو عدد ال coins مش بالضروري يقسم على التلاتة فإذا
+
+430
+00:32:18,460 --> 00:32:23,550
+بنقول sealing و بنحطهم كل واحدة في مينفي كفة و
+
+431
+00:32:23,550 --> 00:32:29,570
+بنوزن بناء على ذلك إذا والله ال light weight fake
+
+432
+00:32:29,570 --> 00:32:35,170
+coin ظهرت في ال right معناه ذلك إنه ال set بتاعتنا
+
+433
+00:32:35,170 --> 00:32:39,310
+in over three ceiling هي ال coins اللي بدي أعيد
+
+434
+00:32:39,310 --> 00:32:46,030
+فحصهاصحيح؟ تمام، ونفس الكلام إذا كانت في ال lift،
+
+435
+00:32:46,030 --> 00:32:49,630
+برضه التلت، التلت هذا هو اللي محتاج أرجع أعيد فحصه
+
+436
+00:32:49,630 --> 00:32:55,370
+كمان مرة أو إنه ال in total معقس التلتين اللي هم
+
+437
+00:32:55,370 --> 00:33:00,010
+ضايقين، طبعا هم بقول تقريبا تقريبا تقريبا التلت،
+
+438
+00:33:00,010 --> 00:33:03,820
+لكن هو exactly لأ مش التلتبدليل التمانية اللي كنا
+
+439
+00:33:03,820 --> 00:33:07,780
+بتكلم عنها و اللي عملتناها مشكلة و بدنا نتطر ..
+
+440
+00:33:07,780 --> 00:33:11,260
+عيدنا نتكلم عنها و نحل ال .. الاشتباك اللي صار انه
+
+441
+00:33:11,260 --> 00:33:14,200
+لأ ليش نقسم على تلاتة او على اتنين على مش عارف ايش
+
+442
+00:33:14,200 --> 00:33:17,380
+لإنه ظهر عندي تلاتة تلاتة و ضال اتنين مضالش تلاتة
+
+443
+00:33:17,380 --> 00:33:23,060
+فعليا فإذا هي مش تلت exactly تلت تقريبا طيب مش
+
+444
+00:33:23,060 --> 00:33:31,460
+وهندس إذا ال N مد تلاتة بتساوي واحد اعمل اللي انت
+
+445
+00:33:31,460 --> 00:33:39,390
+قلت عليهإذا بتسوي واحد يعني إذا كانت تتكلم عن عشرة
+
+446
+00:33:39,390 --> 00:33:43,050
+عشرة
+
+447
+00:33:43,050 --> 00:33:49,490
+coins ليش؟ لأن عشرة موديولو تلاتة واحد اعمل اللي
+
+448
+00:33:49,490 --> 00:33:55,450
+انت قلت عليه قول والله بتاخد أربعة أربعة اي عفوا
+
+449
+00:33:55,450 --> 00:34:02,030
+تلاتة تلاتة ويضل أربعة في الحالة هذه تلاتة تلاتة
+
+450
+00:34:02,030 --> 00:34:09,570
+ويضل أكتر منهمففي الحالة هذه بتاخد floor خد floor
+
+451
+00:34:09,570 --> 00:34:17,030
+لأنه خلّينا نفكر فيها برضه هاي بدأت بالوزنة الأولى
+
+452
+00:34:17,030 --> 00:34:24,250
+عندك قلنا تلاتة تلاتة وهنا أربعة إذا كان balance
+
+453
+00:34:24,250 --> 00:34:28,700
+بدو يطلع عندك أربعة صح؟هيطلع عندك أربع إذا كان لأ
+
+454
+00:34:28,700 --> 00:34:31,380
+واحدة منهم رجحت لليمين فمعناه ذلك أنه في عندي
+
+455
+00:34:31,380 --> 00:34:34,020
+تلاتة هم اللي بيبقى فحصهم رجحت للشمال ففيه يضل
+
+456
+00:34:34,020 --> 00:34:37,740
+عندي تلاتة هم اللي بيبقى فحصهم طيب السيناريو
+
+457
+00:34:37,740 --> 00:34:42,100
+التاني أنه لأ نشتغل على ال ceiling بس معناته بدي
+
+458
+00:34:42,100 --> 00:34:49,600
+أعمل أربعة مقابل أربعة وبيضل كده؟ اتنين ممتازة
+
+459
+00:34:49,600 --> 00:34:53,540
+لاحظوا أنه هنا لو رجحت يمين أو رجحت شمال بيضل عندي
+
+460
+00:34:53,540 --> 00:34:55,800
+أربعة يعني محتاج لها مرتين
+
+461
+00:34:58,150 --> 00:35:02,850
+مصبوط؟ طيب هنا انا هحتاج برضه مرتين بس تلت
+
+462
+00:35:02,850 --> 00:35:11,490
+الاحتمال هنا تلتين الاحتمال صح؟
+
+463
+00:35:11,490 --> 00:35:14,870
+ايوة okay انا مقتنع تماما ان في ال worst case هقول
+
+464
+00:35:14,870 --> 00:35:19,050
+ان هم تلاتة مافيش مشكلة لكن ال practical بجل
+
+465
+00:35:19,050 --> 00:35:23,940
+الاحتمالية التلاتةPractical بجلّي الاحتمالية انه
+
+466
+00:35:23,940 --> 00:35:28,100
+يصير معايا تلاتة فبنقول لأ تلاتة تلاتة و بنخلي
+
+467
+00:35:28,100 --> 00:35:34,700
+الاحتمال لأ اني اضطر لوزنتين حالة من التلات حالات
+
+468
+00:35:34,700 --> 00:35:39,280
+مش حالتين من التلات حالات واضح الجزئية كيف انها
+
+469
+00:35:39,280 --> 00:35:40,640
+عملت؟ تمام ممتاز
+
+470
+00:35:45,880 --> 00:35:49,260
+فاضطرنا في الآخر يقول ان احنا بتجسم ال coin الأولى
+
+471
+00:35:49,260 --> 00:35:51,920
+و التانية و التالتة في كفة الرابعة و الخمسة و
+
+472
+00:35:51,920 --> 00:35:56,380
+السادسة في كفة و خلي السابعة و التامنة برا ففي
+
+473
+00:35:56,380 --> 00:36:01,020
+الحالة هذه اذا كان رجحت عند او اللي كانت اخف
+
+474
+00:36:01,020 --> 00:36:03,620
+الواحد و اتنين و التلاتة فمعناته بتدوزن واحد مقابل
+
+475
+00:36:03,620 --> 00:36:09,440
+اتنين كويس يا بتطلع واحد يا بتطلع اتنين او بتطلع
+
+476
+00:36:09,440 --> 00:36:14,340
+اتنين متساويين فتلاتة هياللي فيها مشكلة طيب أو انه
+
+477
+00:36:14,340 --> 00:36:18,260
+لأ اللي أخف هي الكفة بتاعة أربعة خمسة ستة و نفس
+
+478
+00:36:18,260 --> 00:36:22,720
+الكلام بوزن أربعة مع خمسة واحدة منهم هترجح معناته
+
+479
+00:36:22,720 --> 00:36:28,840
+الأقل وزنا هي الزائفة أو انه balance تنتين فبناخد
+
+480
+00:36:28,840 --> 00:36:32,820
+اللي ما انوزنتش منهم الحالة التالتة سبعة مقابل
+
+481
+00:36:32,820 --> 00:36:38,140
+تمانية إذا واحد اتنين تلاتة مقابل أربعة خمسة ستة
+
+482
+00:36:39,600 --> 00:36:42,660
+بالنسبة لم يكن هناك واحدة رجعت على التانية فإذا
+
+483
+00:36:42,660 --> 00:36:46,200
+المشكلة ستكون في أربعة أو خمسة أو سبعة أو تمانية
+
+484
+00:36:46,200 --> 00:36:50,760
+بوزنهم جدا بعض بطريق مباشر مباشر هي تنتنج بالبعض
+
+485
+00:36:50,760 --> 00:36:55,190
+واحدة منهم أخف من التانية فهيالcontrafeit او
+
+486
+00:36:55,190 --> 00:37:01,750
+الزائفة تمام الان مدام اننا في نفس الموضوع و في
+
+487
+00:37:01,750 --> 00:37:05,590
+نفس جزئية ال search في حاجة اسمها eternary search
+
+488
+00:37:05,590 --> 00:37:11,190
+أخدتوها طيب eternary search هتنمحى كل اللي احنا
+
+489
+00:37:11,190 --> 00:37:14,990
+عاملينه عشان
+
+490
+00:37:14,990 --> 00:37:20,750
+هذه هتشمل كذا مفهوم في بعض يعني هناخد منها ال
+
+491
+00:37:20,750 --> 00:37:24,690
+search اللي أخدناها سابقا هناخدنتكلم عن ال
+
+492
+00:37:24,690 --> 00:37:28,690
+complexity هنتكلم عن letry مدام توي أخدناها من
+
+493
+00:37:28,690 --> 00:37:32,290
+واحدة من التطبيقات هي الجزئية ال search و ال
+
+494
+00:37:32,290 --> 00:37:38,530
+insertion تمام هنا بكل بساطة هاي
+
+495
+00:37:38,530 --> 00:37:44,030
+ال array تبعك كنا ناخد في ال binary ايش نقطة و
+
+496
+00:37:44,030 --> 00:37:46,270
+نقارن فيها لأننا هناخد نقطتين
+
+497
+00:37:52,790 --> 00:37:57,930
+عند التلت والتلتين بدنا ناخد قيمتين واحدة عند
+
+498
+00:37:57,930 --> 00:38:01,410
+التلت واحدة عند مين عند التلتين وندور على X وندور
+
+499
+00:38:01,410 --> 00:38:07,110
+على X أقارن X بالقيمة بالقيمة مين التلتين هذه مثلا
+
+500
+00:38:07,110 --> 00:38:10,350
+إيش احتمالاتها يا أكبر من يا أصغر من والله إذا
+
+501
+00:38:10,350 --> 00:38:15,190
+بتساوي معناته انتهت الجثة خلصنا يعني ضربناها جاءت
+
+502
+00:38:15,190 --> 00:38:19,710
+على طول هي طبعا the best case لكن ممكن تكون أكبر
+
+503
+00:38:19,710 --> 00:38:26,750
+منأكبر من عارف انت ايش سويت التلتين كلهم راحوا مش
+
+504
+00:38:26,750 --> 00:38:32,210
+هي خلصت التلتين مرة واحدة بدأت النص طيب ماصارش
+
+505
+00:38:32,210 --> 00:38:39,590
+الكلام بهذا الشكل لجيتها أقل من أقل من تلتين أقل
+
+506
+00:38:39,590 --> 00:38:43,950
+من التلتين على طول بتقارنها بمين بالتلت هتقارنها
+
+507
+00:38:43,950 --> 00:38:50,170
+بالتلت هنا ايش هيطلع هتلاحظ ايش سويتليش؟ لأن الـ
+
+508
+00:38:50,170 --> 00:38:53,610
+two branches هدول بناء على إنها طلعت أقل من ..
+
+509
+00:38:53,610 --> 00:38:58,070
+بناء على أساس إن هي أقل من التلتين فهنا بتجيك
+
+510
+00:38:58,070 --> 00:39:01,910
+احتمالاتها الآن بالنسبة للتلت، يا أقل من يا أصغر
+
+511
+00:39:01,910 --> 00:39:10,510
+من إذا كانت X أقل من التلت، التلتين راحوا أو أكبر
+
+512
+00:39:10,510 --> 00:39:14,850
+من التلت، برضه التلتين راحوا لأنه بخل الجزء هذا
+
+513
+00:39:14,850 --> 00:39:18,250
+فقط، فبتصير هذه I جديدة وجيه جديدة
+
+514
+00:39:20,630 --> 00:39:25,150
+صح؟ برضه فإذا أنا بدل ما أعمل elimination لان نص
+
+515
+00:39:25,150 --> 00:39:30,730
+اعملت elimination لتلتين طبعا بعد هي اتحسن على
+
+516
+00:39:30,730 --> 00:39:35,590
+الموضوع هذا و بندرسها أكتر في الماجستير أنه بنحطها
+
+517
+00:39:35,590 --> 00:39:38,790
+نسبة معينة للي بده يشتغل في ال iterations فبيسموها
+
+518
+00:39:38,790 --> 00:39:42,070
+النسبة الذهبية اللي هي فاصلة ستة واحد تمانية اشي
+
+519
+00:39:42,070 --> 00:39:45,450
+تاني بس احنا دلوقتي خلينا فيها في الفكرة نفسها
+
+520
+00:39:45,450 --> 00:39:50,640
+اللي هي الternary search أو البحث الثلاثيالبحث
+
+521
+00:39:50,640 --> 00:39:54,260
+الثلاثي هذه من الحاجات اللي ممكن تيجي كأكواد مثلا
+
+522
+00:39:54,260 --> 00:39:58,360
+في ال .. في data structure في إشي اللي هو يلا
+
+523
+00:39:58,360 --> 00:40:02,680
+فكرولنا كيف تعملولها code فكروا كيف تعملولها code
+
+524
+00:40:02,680 --> 00:40:06,800
+فعشان نعمللها code الفكرة فهمناها بكل بساطة هتبدأ
+
+525
+00:40:06,800 --> 00:40:11,860
+procedure ال procedure ده إيش بده؟ بده ال sequence
+
+526
+00:40:11,860 --> 00:40:14,120
+أو ال array اللي انت بدك تدخله إياها لأنك بتبقى
+
+527
+00:40:14,120 --> 00:40:19,150
+عارف ال array اللي موجودةكويس و مجموعة عناصرها من
+
+528
+00:40:19,150 --> 00:40:24,490
+1 to N و increasing integers بمعنى ان هي ordered
+
+529
+00:40:24,490 --> 00:40:29,210
+بمعنى ordered جيد مش ordered معناته بدك تفهم
+
+530
+00:40:29,210 --> 00:40:33,530
+علامات ال insertion بدك تبدأ بال search على كل
+
+531
+00:40:33,530 --> 00:40:38,710
+عنصر ثم بستنى ال search عشان تبدأ هتبدأ ternary
+
+532
+00:40:38,710 --> 00:40:44,290
+searchمش binary search، هيشتغل على ternary search،
+
+533
+00:40:44,290 --> 00:40:50,530
+جيد، هتقل؟ أه هتقل، لكن ال order هو هو، إيش ال
+
+534
+00:40:50,530 --> 00:40:53,210
+order أو ال complexity بتاعة ال binary؟
+
+535
+00:40:53,210 --> 00:40:55,450
+logarithmic، صح؟ و هذا هتظهر logarithmic، إيش
+
+536
+00:40:55,450 --> 00:41:00,390
+الاختلاف بينهم؟الـ base بس هذه كانت log2 هذه log3
+
+537
+00:41:00,390 --> 00:41:04,950
+فlog3 احنا عارفين انه هتجلل اكتر كقيمة عددية
+
+538
+00:41:04,950 --> 00:41:09,590
+هتعطيني اقل عدد لكن ك order ضال واحد هو ال
+
+539
+00:41:09,590 --> 00:41:13,410
+algorithmic ك order مش يعني ماعملي يعني ماطورتش في
+
+540
+00:41:13,410 --> 00:41:17,370
+المسمة زيادة لكن على عرض الواقع اه هتتجل شوية
+
+541
+00:41:17,370 --> 00:41:21,930
+الأمور كعدد iterations تمام فهي أول خطوة الخطوة
+
+542
+00:41:21,930 --> 00:41:28,790
+التانية بتحدد البداية والنهايةI و J على أساس إن
+
+543
+00:41:28,790 --> 00:41:35,670
+هما 1 و N أول عنصر ال index الأول و الأخير عشان
+
+544
+00:41:35,670 --> 00:41:38,690
+نبدأ الآن نفس الفكرة اللي قولناها في ال binary في
+
+545
+00:41:38,690 --> 00:41:41,610
+ال binary كنت ببدأ أعمل elimination و أجلل ال
+
+546
+00:41:41,610 --> 00:41:46,760
+durationلما يصبح عندى one element خلاص اذا هو ال
+
+547
+00:41:46,760 --> 00:41:50,480
+one element انتهى ماضالش مجال افحص فيه فانت بيبين
+
+548
+00:41:50,480 --> 00:41:53,500
+ال one element طول ما في عندي I اللي هي البداية
+
+549
+00:41:53,500 --> 00:42:00,120
+اقل من j ناقص واحد معناته في بينهم لسه قيم ما زالت
+
+550
+00:42:00,120 --> 00:42:04,500
+في بينهم قيم اذا ما تحققتش معناته فعليا I صارت
+
+551
+00:42:04,500 --> 00:42:10,750
+اكبر من صارت اكبر من معناته صاروا بيساوي بعضإذا
+
+552
+00:42:10,750 --> 00:42:13,630
+سوا بعض، لاحظ طالع فيهم، إذا سوا بعض، طب هي دي
+
+553
+00:42:13,630 --> 00:42:17,710
+أقل، ناقص واحد، صارت فيها الأقل، فتصبح أقل على
+
+554
+00:42:17,710 --> 00:42:21,130
+طول، فإذا بيختل ال condition، وإذا اختل ال
+
+555
+00:42:21,130 --> 00:42:24,290
+condition، اطلع خارج ال loop، بطل في مساحة تدور
+
+556
+00:42:24,290 --> 00:42:28,170
+فيها، لأ، بدنا نفترض إن لسه المساحة موجودة، عشان
+
+557
+00:42:28,170 --> 00:42:33,930
+نبدأ نعمل عمليةالـ lower و ال upper بدل ما كنت
+
+558
+00:42:33,930 --> 00:42:37,010
+بتتكلم عن ال midpoint ال lower point و ال upper
+
+559
+00:42:37,010 --> 00:42:40,450
+point أو اللي هي التلت و مين و التلتين و اللي
+
+560
+00:42:40,450 --> 00:42:46,090
+بيقول بساطة جدش المسافة بينهم على تلاتة مسافة
+
+561
+00:42:46,090 --> 00:42:49,090
+بينهم على تلاتة اعطتني جدش قيمة هذا الكلام لكن
+
+562
+00:42:49,090 --> 00:42:53,310
+ماعطتنيش القيمة المطلقة للعنصر فهنا اه لأنه انا في
+
+563
+00:42:53,310 --> 00:42:57,030
+مرحل و مرحل I مش هتكون هي الواحد هتتغير مانا هتكون
+
+564
+00:42:57,030 --> 00:43:03,000
+مرة هعمل elimination فلأ زائد ال Iمنطقة زائد ال I
+
+565
+00:43:03,000 --> 00:43:06,360
+فبعرف ان انا موجود هنا الان هذا قيمة ال lower ال
+
+566
+00:43:06,360 --> 00:43:13,820
+upper تلتين ال upper عند التلتين او تقدر تعملها
+
+567
+00:43:13,820 --> 00:43:20,720
+برضه تلت وتعمل J ناقص التلت صح؟نفس الأشياء فهي دي
+
+568
+00:43:20,720 --> 00:43:23,520
+كلها أفكار أي حاجة بمشي معاك في ال data structure
+
+569
+00:43:23,520 --> 00:43:27,700
+لإن انت مفروض تدرسوا أفكار تدرسوا أفكار فنفس
+
+570
+00:43:27,700 --> 00:43:31,500
+الفكرة بدك تبدأ من ال .. من بداية ال .. ال array
+
+571
+00:43:31,500 --> 00:43:39,080
+ولا من نهايتها مش هتكون مشكلة كبيرة تمام الآن بعد
+
+572
+00:43:39,080 --> 00:43:41,240
+يكتب ده الفحص اللي احنا فحصناه هنا اللي احنا
+
+573
+00:43:41,240 --> 00:43:46,180
+عملناه اللي هي روح الموضوع تبعنا ال treeجزئية لتري
+
+574
+00:43:46,180 --> 00:43:49,560
+الآن اللي هي عبارة عن condition وافحصه yes no yes
+
+575
+00:43:49,560 --> 00:43:54,500
+no يبدأ شوف ال yes و ال no هدول فهنبدأ إذا كانت X
+
+576
+00:43:54,500 --> 00:43:58,900
+أكبر من أو يساوي ال A أبر كأنك بتقارنها بالعنصر
+
+577
+00:43:58,900 --> 00:44:02,340
+اللي موجود هنا زي ما عملنا زي ما عملنا بالضبط أكيد
+
+578
+00:44:02,340 --> 00:44:06,450
+هيكون عندك two possibilitiesال possibility الأولى
+
+579
+00:44:06,450 --> 00:44:10,850
+.. الإمكانية الأولى أنه يكون هنا مثلا yes إذا كانت
+
+580
+00:44:10,850 --> 00:44:16,610
+فعلا x أكبر من .. إذا إذا yes على طول I تساوي ال
+
+581
+00:44:16,610 --> 00:44:23,150
+other زائد واحد التلتين الشمال راحوا .. التلتين
+
+582
+00:44:23,150 --> 00:44:26,450
+الشمال راحوا .. ماعنا أي مشكلة فيهم و لاحظوا أن
+
+583
+00:44:26,450 --> 00:44:30,970
+أكبر من ولا تساوي أعطتني إمكانية أقول زائد واحد
+
+584
+00:44:32,270 --> 00:44:36,350
+لأنه ضامن إنه مش متساوي، متساويش، معناته بروح على
+
+585
+00:44:36,350 --> 00:44:38,950
+الأنصار اللي ورا، نروح على الأنصار اللي ورا،
+
+586
+00:44:38,950 --> 00:44:41,550
+عملناها جابل هيك ومفهومة، ماعتقدش إن في عندكم
+
+587
+00:44:41,550 --> 00:44:44,950
+مشكلة فيها Else، هذه else إيش يعني؟ يعني معناته
+
+588
+00:44:44,950 --> 00:44:50,550
+إنه ماروحتش ل yes، هنا روحت ل no، لأنه ماتحققش إنه
+
+589
+00:44:50,550 --> 00:44:54,650
+أكبر من، ماتحققش إنه أكبر من، فإذا هنا هيكون إيش؟
+
+590
+00:44:54,650 --> 00:45:00,130
+أصغر أو يساويخلوا دايما في بالكوا كلمة أو يساوي
+
+591
+00:45:00,130 --> 00:45:06,590
+ايوة ف else if هالوقت صارت كأنه أخدت ال no مع ال
+
+592
+00:45:06,590 --> 00:45:11,570
+condition كمان بكلمة else if أخدنا التنتين مع بعض
+
+593
+00:45:11,570 --> 00:45:18,470
+مع السوا تمام x أكبر من a lower فإذا خلصنا احنا
+
+594
+00:45:18,470 --> 00:45:23,590
+وصلنا لهنا فعليا انا موجود هنا و فعليا أو يساوي
+
+595
+00:45:24,620 --> 00:45:29,280
+لأنه عدينا فكرة إنه هي أكبر من وقلنا إن هي no فانا
+
+596
+00:45:29,280 --> 00:45:33,920
+الآن هنا وهذه تحققت روحت لمين؟ لأكبر من ال lower
+
+597
+00:45:33,920 --> 00:45:42,180
+أكبر من ال lower هنا أنا الآن هنا ليش؟ هنا لأنه
+
+598
+00:45:42,180 --> 00:45:48,080
+مبدأيا ليست أكبر من ال upper اللي هي التلتين ليست
+
+599
+00:45:48,080 --> 00:45:55,570
+أكبر من التلتين وأكبر من ال lowerإيش بنعمل؟
+
+600
+00:46:00,480 --> 00:46:05,780
+معناته هي المنطقة اللي في النص ف automatically if
+
+601
+00:46:05,780 --> 00:46:10,100
+then معناته فعلا تحقق الشرطين ان هي ليست اكبر من
+
+602
+00:46:10,100 --> 00:46:13,120
+ال other بينما هي اكبر من ال lower على طول بروح
+
+603
+00:46:13,120 --> 00:46:21,100
+ايش بسوي بقول ال I هتصبح هي ال lower زائد واحد ليش
+
+604
+00:46:21,100 --> 00:46:24,520
+لأن هنا ماجلتش اوي ساوي فانا عندي اريحية اقول اكبر
+
+605
+00:46:24,520 --> 00:46:31,630
+اقول زائد واحد لكن في ال other لأأيوة، ليش؟ لأن في
+
+606
+00:46:31,630 --> 00:46:34,850
+القبر هي جايانة من وين الآن الحالة؟ جايانة من إنه
+
+607
+00:46:34,850 --> 00:46:40,590
+ليست أكبر من طب ليست أكبر من، كنت ساوي، صح؟ فاخدوا
+
+608
+00:46:40,590 --> 00:46:44,410
+بالكم من الحاجات الرفيعة هذه اللي ممكن تعمللكم
+
+609
+00:46:44,410 --> 00:46:48,770
+Logic Error وانت مش عارف حاجات بسيطة زي هيك ممكن
+
+610
+00:46:48,770 --> 00:46:51,610
+تعملك Logic Error إنه إيه؟ إنه لو إجتك القيمة فعلا
+
+611
+00:46:51,610 --> 00:46:55,710
+دي جاية في القبر هتلاقي إن أنت بدك تعمل زائد واحد،
+
+612
+00:46:55,710 --> 00:47:00,750
+ضيعتهاضيعته فعلا فالقيمة موجودة بس ال code تبعك ما
+
+613
+00:47:00,750 --> 00:47:05,710
+جابهاش فأخدنا بالنا ليش بعمل مرات زائد واحد و بنوت
+
+614
+00:47:05,710 --> 00:47:10,850
+زائد واحد حسب ال condition و عكسه ال inverse تبعه
+
+615
+00:47:10,850 --> 00:47:15,890
+مش ال complement أخدنا كذا مرة نقولكم هد غير هدي
+
+616
+00:47:15,890 --> 00:47:19,730
+هد غير هدي هد غير صح تمام واضحت حتى اللحظة حتى
+
+617
+00:47:19,730 --> 00:47:25,170
+اللحظة خلصنا أننا هنا و خلصنا أننا هنا بلت الحالة
+
+618
+00:47:25,170 --> 00:47:32,530
+القلص الأخيرةأيوة else أنا عارف إيش اللي ضلت فخلاص
+
+619
+00:47:32,530 --> 00:47:35,770
+اللي ضلت أن ال j هي اللي تجيهني على من؟ على ال
+
+620
+00:47:35,770 --> 00:47:40,590
+lower معناته أنا هنا في الحالة التالتة اللي هي في
+
+621
+00:47:40,590 --> 00:47:45,110
+البداية معناته اللي هو ال ال ال j هذه حطليها هنا
+
+622
+00:47:45,110 --> 00:47:49,510
+وصرت أن أنا ببحث في الجزء هذا تمام؟
+
+623
+00:47:50,810 --> 00:47:55,470
+خلصنا فالان هيك بنكون عملنا end لمين؟ لل beginning
+
+624
+00:47:55,470 --> 00:47:59,030
+اللي كنت فاتحها فكل هذا بنعمل لكل .. في كل
+
+625
+00:47:59,030 --> 00:48:03,950
+iteration في كل loop .. في كل loop بناء على كل
+
+626
+00:48:03,950 --> 00:48:08,990
+loop بتتغير عندى يا قيمة I يا قيمة J يا قيمة
+
+627
+00:48:08,990 --> 00:48:15,090
+الاتنين صح؟ إما J بتروح للتلت أو I بتروح للتلتين
+
+628
+00:48:15,090 --> 00:48:22,060
+أو J بتروح للتلتين و I بتروح للتلتفحسب التلت اتلت
+
+629
+00:48:22,060 --> 00:48:24,840
+هدوله واحد منهم هو اللي هينتش في النهاية فانا بكون
+
+630
+00:48:24,840 --> 00:48:28,780
+في جميع الأحوال عملت elimination لتلتين بدل نص في
+
+631
+00:48:28,780 --> 00:48:32,800
+ال binary okay في الآخر بنعمل عملية الفحص النهائي
+
+632
+00:48:32,800 --> 00:48:36,820
+بمجرد ما صار عنده I و J نفس القيمة يعني أنا بتكلم
+
+633
+00:48:36,820 --> 00:48:39,220
+في النهاية صفيت على نقطة واحدة النقطة الواحدة هادى
+
+634
+00:48:39,220 --> 00:48:44,140
+بده افحص لحالها هيا X هل تساوي I طب أنا عارف ان I
+
+635
+00:48:44,140 --> 00:48:48,480
+هي الوحيد اللي دلت الآن يا بتسويها يا بتسويهاشهل
+
+636
+00:48:48,480 --> 00:48:52,040
+بتسويها إذا و الله بتسويها إذا نرجع لقيمة I ال
+
+637
+00:48:52,040 --> 00:48:54,600
+index I لأن أنا عرفتها هنا بقولك هي موجودة في ال
+
+638
+00:48:54,600 --> 00:48:58,220
+location العشر في ال array امشي عشر خطوات هتلاقيها
+
+639
+00:48:58,220 --> 00:49:03,920
+هاي القيمة اللي أنت بدك إيها خلصنا طيب else if x j
+
+640
+00:49:03,920 --> 00:49:09,200
+هيظلت عندك I و J التتين اللي ضالة موجودين عندك قد
+
+641
+00:49:09,200 --> 00:49:14,680
+يصبحوا بيساوي بعض أو عكسوا بعض يعني صارت واحدة
+
+642
+00:49:14,680 --> 00:49:18,680
+جابل التانيةلأن هنا برضه أنت عندك احتمال يأمنوا
+
+643
+00:49:18,680 --> 00:49:25,220
+بسوء بعض أو J صارت أصغر من I الاحتمالين وردين فإذا
+
+644
+00:49:25,220 --> 00:49:30,100
+ممكن يطلعوا هم قيمتين مش قيمة اللي ضالوا بدك تفحص
+
+645
+00:49:30,100 --> 00:49:33,940
+التنتين برضه ترجع قيمة الـJ لا هذي حصلت ولا هذي
+
+646
+00:49:33,940 --> 00:49:38,980
+حصلتصفر انا مالجتهش اصلا الرقم هو الرقم اصلا مش
+
+647
+00:49:38,980 --> 00:49:43,820
+موجود ال X هذه مش موجودة و نهينا بال location اللي
+
+648
+00:49:43,820 --> 00:49:50,830
+هيكون يا I يا J يا 0 اذا مش موجودةكيف؟ لمّين
+
+649
+00:49:50,830 --> 00:49:56,190
+المنهج هنا؟ هيك احنا بالظبط خلصنا منهجنا كل عام
+
+650
+00:49:56,190 --> 00:49:59,370
+تبخير الجزء المتبقي زي ما قلنالكم هنعمل مراجعة
+
+651
+00:49:59,370 --> 00:50:02,390
+أسئلة امتحانات على أسئلة من الكتاب من المواضيع
+
+652
+00:50:02,390 --> 00:50:05,430
+اللي انتوا عندكم مشكلة فيها اللي فهمتوا أنه بدكوا
+
+653
+00:50:05,430 --> 00:50:08,730
+حاجة نركز أكتر في ال inductionمن الشباب يعرفت ان
+
+654
+00:50:08,730 --> 00:50:11,450
+ال induction شوية عندكوا فخلينا معناه طول مرة
+
+655
+00:50:11,450 --> 00:50:15,070
+القادمة ان شاء الله الأسبوع القادم هجيب .. نخليها
+
+656
+00:50:15,070 --> 00:50:17,830
+أسئلة عن ال induction في البداية و بعدين نشوف إيش
+
+657
+00:50:17,830 --> 00:50:20,390
+المواضيع اللي عندكم فيها نقص و عندكم فيها مشكلة و
+
+658
+00:50:20,390 --> 00:50:24,010
+نكمل أسئلة الآن أسئلة اللي هي إما من امتحانات و
+
+659
+00:50:24,010 --> 00:50:26,570
+هحط الأولوية للأسئلة تاعة الامتحانات اللي جيبناهم
+
+660
+00:50:26,570 --> 00:50:28,790
+في امتحانات سابقة اللي هي علاقة بال induction و
+
+661
+00:50:28,790 --> 00:50:31,150
+بعدين هنروح للكتاب إيش الأفكار الزيادة اللي ممكن
+
+662
+00:50:31,150 --> 00:50:34,530
+تكون في جزئية ال induction يعطيكوا العافية كل عام
+
+663
+00:50:34,530 --> 00:50:34,970
+انتوا بخير
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/H4ttvdC1eCk_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/H4ttvdC1eCk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2f94da6fffa8f19b728d904d41ce1c490c0fe042
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/H4ttvdC1eCk_raw.srt
@@ -0,0 +1,2660 @@
+1
+00:00:04,960 --> 00:00:07,120
+يعطيكوا العفو يا شباب اليوم ان شاء الله تعالى
+
+2
+00:00:07,120 --> 00:00:12,360
+بنحاول نختم في ما تبقالنا في موضوع letre ان شاء
+
+3
+00:00:12,360 --> 00:00:15,380
+الله بعد ما اتكلمنا عن letre ال introduction أخدنا
+
+4
+00:00:15,380 --> 00:00:21,780
+شوية terminology أخدنا شوية theore المرة الماضية
+
+5
+00:00:21,780 --> 00:00:27,640
+حسبنا ال edges مقابل ال nodes مقابل ال leaves جدش
+
+6
+00:00:27,640 --> 00:00:29,860
+ال number of leaves و بعدين اتكلمنا في الآخر على
+
+7
+00:00:31,610 --> 00:00:36,150
+ربطهم بالقوانين مع بعض تمام و اليوم ان شاء الله
+
+8
+00:00:36,150 --> 00:00:39,370
+تعالى ناخد applications of trees طبعا إذا بنتكلم
+
+9
+00:00:39,370 --> 00:00:43,310
+عن applications of trees مش هنخلص فعليا حقيقة يعني
+
+10
+00:00:43,310 --> 00:00:48,570
+لأن تطبيقاتها كتيرة جدا كمواد علمية كأبحاث علمية
+
+11
+00:00:48,570 --> 00:00:52,170
+لأ لها تطبيقات و تطبيقات جدا كبيرة اليوم هنقتصر
+
+12
+00:00:52,170 --> 00:00:57,620
+فقط على جد ال binary search أو ال search عمومالأن
+
+13
+00:00:57,620 --> 00:01:00,300
+زي ما قلنا هيكون في binary search وبعدين هناخد
+
+14
+00:01:00,300 --> 00:01:03,720
+decision trees decision trees من اسمها شغلة
+
+15
+00:01:03,720 --> 00:01:06,920
+القرارات، القرارات معناته واضحة جدا أن هذه مقدمة
+
+16
+00:01:06,920 --> 00:01:12,200
+لغنى عنها لل AI هذه المقدمة اللي لغنى عنها لأي AI
+
+17
+00:01:12,200 --> 00:01:15,520
+فمافيش حد بيشتغل في ال AI في الذكاء الاصطناعي وما
+
+18
+00:01:15,520 --> 00:01:19,610
+بعرفش حاجة اسمها decision treesأو كيف انا ممكن
+
+19
+00:01:19,610 --> 00:01:24,010
+اعمل شجرة القرارات .. شجرة القرارات من خلال ال
+
+20
+00:01:24,010 --> 00:01:26,430
+flow chart انتوا كلكوا عارفينه بتعرفوا ترسموه ال
+
+21
+00:01:26,430 --> 00:01:29,630
+flow chart هذا فال flow chart عبارة عن سؤال و
+
+22
+00:01:29,630 --> 00:01:33,370
+إجابات يا yes يا no إجابات yes no .. yes no .. yes
+
+23
+00:01:33,370 --> 00:01:36,690
+no فانت ممكن تعمل structure لكل ال systems اللي
+
+24
+00:01:36,690 --> 00:01:40,630
+ممكن تخطر ع بالك بحيث انك انت في الآخر بناء على
+
+25
+00:01:40,630 --> 00:01:43,850
+conditions معينة ممكن ال consequential conditions
+
+26
+00:01:43,850 --> 00:01:48,430
+تطلع بقراربتطلع في الآخر إيش بقرار و أهمها يمكن
+
+27
+00:01:48,430 --> 00:01:51,810
+الأعراض بتاعة اللي عند الأطباء في الأمراض أعراض
+
+28
+00:01:51,810 --> 00:01:56,450
+بيبدأ يسألك عن مجموعة أعراض عشان يستنتج منها ال
+
+29
+00:01:56,450 --> 00:02:00,250
+decision المناسب يستخدم أو ياخد القرار المناسب
+
+30
+00:02:00,250 --> 00:02:04,070
+فهدولة ال two applications بس اللي هنتكلم عنهم لكن
+
+31
+00:02:04,070 --> 00:02:07,510
+زي ما قلتلكم مرة ال trees ال applications ساعتها
+
+32
+00:02:07,510 --> 00:02:14,730
+دخمة و كتيرة في الأبحاث العلمية فهنبدأبشكل مبسط في
+
+33
+00:02:14,730 --> 00:02:18,590
+ال binary search trees شوية يمكن في آخر ال slides
+
+34
+00:02:18,590 --> 00:02:21,110
+هوصلكوا ايها شوية انها تصير كمان مش binary تكون
+
+35
+00:02:21,110 --> 00:02:26,190
+اكتر من binary و نشوف لنا نكتب لنا code عليها
+
+36
+00:02:26,190 --> 00:02:29,610
+اتوقع ممكن تحتاجوها في ال data structure قد يجوز
+
+37
+00:02:29,610 --> 00:02:34,070
+مثلا او شيء فخلينا نشوفها لما نصلها طيب هنا ال
+
+38
+00:02:34,070 --> 00:02:38,630
+binary search سواء انا بعمل searchdirect مباشرة ال
+
+39
+00:02:38,630 --> 00:02:42,110
+search اللي احنا عارفينه اللي هو given x تمام و
+
+40
+00:02:42,110 --> 00:02:45,550
+ابحثلي عنها بكل بساطة يعني مافيش فيها كتير مشكلة
+
+41
+00:02:45,550 --> 00:02:49,450
+طيب إذا كانت given بهذا الشكل فانت الموضوع كتير
+
+42
+00:02:49,450 --> 00:02:52,730
+سهل عليك ليش لأنه اتفقنا من المرة الماضية بكون
+
+43
+00:02:52,730 --> 00:02:58,550
+عامل modeling لل array تبعتي باستخدام ال tree و
+
+44
+00:02:58,550 --> 00:03:04,090
+مجرد فقط عارف ان ال priority left to right و ال
+
+45
+00:03:04,090 --> 00:03:10,330
+left ل ال subTree to write subtree ماشيك بس و ايه
+
+46
+00:03:10,330 --> 00:03:12,870
+ماهي .. ماهي مادام انا عملتها حسب ال priority
+
+47
+00:03:12,870 --> 00:03:16,470
+معناته هي ordered خلاص يعني معناته ممرتبة هذا عشان
+
+48
+00:03:16,470 --> 00:03:21,220
+اشوف X معينة و اعرف وين مكانهاوين مكانها و هل هي
+
+49
+00:03:21,220 --> 00:03:25,900
+موجودة و لا مش موجودة سؤالين هم بقى هل هي موجودة
+
+50
+00:03:25,900 --> 00:03:29,000
+بدي أرجع أو أنه لأ مش موجودة بدي أرجعها بصفر وهذا
+
+51
+00:03:29,000 --> 00:03:31,960
+نفس القوانين اللي أخدناها سابقا أو ال rule اللي
+
+52
+00:03:31,960 --> 00:03:38,300
+أخدناها سابقا طيب هذه بكل بكل بساطة الآن عشان
+
+53
+00:03:38,300 --> 00:03:42,660
+نتكلم عن هذا الموضوع محتاجيننعرف أخدناها سابقا
+
+54
+00:03:42,660 --> 00:03:48,120
+برضه في ال binary search أنه ال order تبعنا أو ال
+
+55
+00:03:48,120 --> 00:03:53,220
+complexity كانت logarithmic و هنا نفس الكلام أنت
+
+56
+00:03:53,220 --> 00:03:58,160
+لما يكون في عندك tree بهذا
+
+57
+00:03:58,160 --> 00:04:04,240
+الشكلهي ثنائية كلها binary و مباشرة تيجي تقارن مع
+
+58
+00:04:04,240 --> 00:04:09,120
+أول أنصر اللي هي ال root وتجد انه ال X أكبر من ..
+
+59
+00:04:09,120 --> 00:04:13,640
+معناته أنت مبدأيا كل هذا استثنيته كله مرة واحدة
+
+60
+00:04:13,640 --> 00:04:17,440
+استثنيته انت مش محتاج تبحث فيه فانت linear لأ هي
+
+61
+00:04:17,440 --> 00:04:21,560
+مش linear ك linear لأ مش linear طيب فعملية ال
+
+62
+00:04:21,560 --> 00:04:25,200
+search ل existing item مش فيها مشكلة لكن احنا ممكن
+
+63
+00:04:25,200 --> 00:04:32,140
+برضه نستخدم نفس ال treeto insert a new item طيب
+
+64
+00:04:32,140 --> 00:04:35,060
+مادام to insert a new item معناته من الأساس انا
+
+65
+00:04:35,060 --> 00:04:38,500
+ممكن ابدأ بأول عنصر و باجي العناصر في ال array
+
+66
+00:04:38,500 --> 00:04:40,980
+تبعتنا نعملها احنا insertion يعني كأننا عملت
+
+67
+00:04:40,980 --> 00:04:45,500
+sortingكأن احنا عملنا sorting وحضر في الكمثال برضه
+
+68
+00:04:45,500 --> 00:04:48,900
+على ال slides اليوم برضه كيف انا ممكن اعمل sorting
+
+69
+00:04:48,900 --> 00:04:52,160
+ل sequence موجود عندك ده sequence موجود عندك تمام
+
+70
+00:04:52,160 --> 00:04:56,040
+فإذا في الحالة دي اما existing item موجود فانت بدك
+
+71
+00:04:56,040 --> 00:05:01,320
+تبحث عنه او بدك تعمل inserting ل new item تمام
+
+72
+00:05:01,320 --> 00:05:07,400
+وكلهما لو بدك تعمل sorting لأنك بدك ال X اللي انت
+
+73
+00:05:07,400 --> 00:05:10,440
+بدك تحطه في مكانها الصحيح بدك كأنك بتبحث عنها في
+
+74
+00:05:10,440 --> 00:05:14,560
+البدايةبتبحث عنها وين المكان اللى المفروض تكون
+
+75
+00:05:14,560 --> 00:05:18,680
+موجودة فيه مالجتش قيمتها بتحطها المكان اللى لازم
+
+76
+00:05:18,680 --> 00:05:21,440
+تكون موجودة فيه مالجتهاش بتحطها إذا لجتها خير
+
+77
+00:05:21,440 --> 00:05:24,880
+وبركة خلاص معناته موجودة مافيش داعية تكررها تاني
+
+78
+00:05:24,880 --> 00:05:28,720
+تمام إذا كان ماكنتش موجودة زى ما قلنا already
+
+79
+00:05:28,720 --> 00:05:33,540
+present إذا ماكنت موجودة الآن الأشكالية ..
+
+80
+00:05:33,540 --> 00:05:36,000
+الأشكالية التانية أنه بعد ما تعمل sorting أنت
+
+81
+00:05:36,000 --> 00:05:41,420
+محتاج تطبعالـ sequence لجديد طيب الطباعة لغتلك
+
+82
+00:05:41,420 --> 00:05:45,920
+فكرة ال log كلكوا عارفين أن ال print هي linear مش
+
+83
+00:05:45,920 --> 00:05:50,780
+هيك ال print process أو operation هي linear لأن
+
+84
+00:05:50,780 --> 00:05:53,520
+انت هتروح ل element by element انت لازم تمر عليهم
+
+85
+00:05:53,520 --> 00:05:55,100
+element by element فإذا كان و الله بدنا نروح لل
+
+86
+00:05:55,100 --> 00:05:59,500
+printing لكل ال items فمعنى ذلك رجعنا لمين؟ لل
+
+87
+00:05:59,500 --> 00:06:03,320
+linear complexity linear complexity أما لأ إذا
+
+88
+00:06:03,320 --> 00:06:09,500
+مجرد سيرشه خلاصبدك تروح لمين؟ اكيد هتكون log طب
+
+89
+00:06:09,500 --> 00:06:15,200
+sorting لأ انت لازم تروحلهم واحدة واحدة لازم
+
+90
+00:06:15,200 --> 00:06:18,080
+تمسكهم واحدة واحدة معناه ذلك ان هي direct
+
+91
+00:06:18,080 --> 00:06:26,140
+dependent علىالنمبر of inputs أو ال arguments جدش
+
+92
+00:06:26,140 --> 00:06:29,080
+عددهم خمسين انت لازم تمسكهم واحدة واحدة الخمسين
+
+93
+00:06:29,080 --> 00:06:33,640
+كامل ف search ال complexity إشي و sorting ال
+
+94
+00:06:33,640 --> 00:06:38,420
+complexity إشي تاني تمام كويس ففي أسوأ الأحوال
+
+95
+00:06:38,420 --> 00:06:43,200
+مدام أن أنا بتعامل مع to insert أعمل inserting في
+
+96
+00:06:43,200 --> 00:06:46,240
+ال sequence في ال sequence فعلى طول في ال worst
+
+97
+00:06:46,240 --> 00:06:50,000
+case أنا بتكلم عن linear لأنه همسكهم واحد واحد مش
+
+98
+00:06:50,000 --> 00:06:54,740
+هعملزي فكرة مجرد search بس، لأ هنا insert يعني
+
+99
+00:06:54,740 --> 00:06:58,860
+sorting، يعني sorting، بتصير linear، انتهى الكلام،
+
+100
+00:06:58,860 --> 00:07:03,440
+لكن في ال search logarithmic، انت بتقدر بكل بساطة
+
+101
+00:07:03,440 --> 00:07:07,960
+branch كامل تستفني من قرارك، فماتبحثش فيه أصلا،
+
+102
+00:07:07,960 --> 00:07:14,780
+ماتدورش على عناصره، بتصير linearأه لإن انت هتمسكهم
+
+103
+00:07:14,780 --> 00:07:18,320
+واحد واحد، لأ عملية ال insert إذا كان بدك تعملها
+
+104
+00:07:18,320 --> 00:07:25,740
+insert و search مع بعض بتصير N في log of N ليش؟
+
+105
+00:07:25,740 --> 00:07:31,920
+لإن كل واحدة .. بالضبط، واضحيت؟ كل واحدة هتمسكها
+
+106
+00:07:31,920 --> 00:07:36,390
+لحال، فانت نفترض عندك عشر elementsعشرة elements
+
+107
+00:07:36,390 --> 00:07:40,970
+الاولى هتكون هي ال root هتحطها هتبدأ فيها والباقى
+
+108
+00:07:40,970 --> 00:07:43,930
+بدك تحطه بالنسبالي عشان تعمل order في الآخر التانى
+
+109
+00:07:43,930 --> 00:07:49,710
+الآن هتعملها كأنك عندك ال tree موجودة كويس و بدك
+
+110
+00:07:49,710 --> 00:07:53,930
+تبحث عن العنصر التانى طيب هذه لحالها ال order
+
+111
+00:07:53,930 --> 00:07:57,090
+تبعها log تمام
+
+112
+00:07:59,030 --> 00:08:02,270
+in من ال in اللي موجودين عندك هدول من العشرة أو
+
+113
+00:08:02,270 --> 00:08:04,890
+العشرين أو المية اللي موجودة عندك يعني صارت log
+
+114
+00:08:04,890 --> 00:08:11,110
+مضروبة في عددهم صارت in log of in واضحيت؟ فانت بدك
+
+115
+00:08:11,110 --> 00:08:14,990
+تاخد بالك لما بدك تعمل sorting هل sorting يعني بدك
+
+116
+00:08:14,990 --> 00:08:17,270
+تعمل search مع sorting مع بعض المهنات الأثناء
+
+117
+00:08:17,270 --> 00:08:17,930
+مضروبين في بعض
+
+118
+00:08:21,330 --> 00:08:24,490
+هي مثال .. المثال بكل بساطة زي ما قلنا بنبدأ بال
+
+119
+00:08:24,490 --> 00:08:26,990
+route عشان نصنفها و احنا المرة اللي فاتت أصلا
+
+120
+00:08:26,990 --> 00:08:30,870
+أخدناها و خلصناها لسه هذه ببدأها لما بدي أشوف ال
+
+121
+00:08:30,870 --> 00:08:34,050
+tree هذه و أرسم ال sequence أو أكتب ال sequence
+
+122
+00:08:34,050 --> 00:08:38,090
+فعليا تبحث كيف موجود هأجد أنه ببدأ من السابعة
+
+123
+00:08:38,090 --> 00:08:41,830
+السابعة الآن فيها lift؟ أه فيها lift فال lift أولى
+
+124
+00:08:41,830 --> 00:08:45,770
+ال priority lift to right صح؟ فيها lift أولى طيب
+
+125
+00:08:45,770 --> 00:08:49,000
+وصلنا للتلاتة التلاتة فيها lift؟ أه فيها liftفيها
+
+126
+00:08:49,000 --> 00:08:53,920
+left اه هنا left ماضلش left معناته هنا zero طيب
+
+127
+00:08:53,920 --> 00:09:01,360
+zero بطلع عندي واحد الواحد اولى right لل root بيجي
+
+128
+00:09:01,360 --> 00:09:06,620
+بعده ف left to right واحدة اتنين تلاتة هيها left
+
+129
+00:09:06,620 --> 00:09:11,560
+to right على جد sub tree فانتوا الان بتتعاملوا مع
+
+130
+00:09:11,560 --> 00:09:16,780
+sub tree هيهاهذه sub tree ترتيب ال sub tree لحالها
+
+131
+00:09:16,780 --> 00:09:20,540
+left to right بما فيهم ال route تبعها طبعا ال sub
+
+132
+00:09:20,540 --> 00:09:23,380
+route هنا بيصير اسمه مش ال route الأصلي تمام
+
+133
+00:09:23,380 --> 00:09:27,100
+فهدولة بهذا الشكل واحدة اتنين تلاتة واحد اتنين صفر
+
+134
+00:09:27,100 --> 00:09:31,340
+واحد اتنين طيب خلصنا الآن لاحظ كأنه اش سويت كأنه
+
+135
+00:09:31,340 --> 00:09:35,440
+هاد ال sub tree تبعت خلصت ال left
+
+136
+00:09:38,660 --> 00:09:43,480
+واللي مثلته بتلات عناصر فعليا الان ال root ثم
+
+137
+00:09:43,480 --> 00:09:49,260
+اليمين فصارت ايش تلاتة خمسة خلصنا الان ال sub tree
+
+138
+00:09:49,260 --> 00:09:56,740
+هذه كأنها خلصت عنصر اشمال بالنسبة لل tree الأصلية
+
+139
+00:09:56,740 --> 00:10:00,000
+الان بدنا نطلع ال tree هذه فى ضل اشي لفت عليها؟
+
+140
+00:10:00,000 --> 00:10:05,390
+مضلش فإذا نقعد نضطبها السبعةثم نبدأ باليمين الجزء
+
+141
+00:10:05,390 --> 00:10:09,390
+المتبقي يمين طب هد فيه إلها شمال ك sub-tree فيه
+
+142
+00:10:09,390 --> 00:10:13,630
+إلها شمال طيب نبدأ نشوف جبل ما نبدأ نتعامل مع ال
+
+143
+00:10:13,630 --> 00:10:16,970
+nodes نفسها بتعامل مع ال sub-tree الأول فهي في sub
+
+144
+00:10:16,970 --> 00:10:21,170
+-tree هد لأ هد ال sub-tree نخلص ال sub-tree هد ال
+
+145
+00:10:21,170 --> 00:10:29,290
+left ال rootالـ 11 اللي هي اليمين تبع الـ subtree
+
+146
+00:10:29,290 --> 00:10:32,370
+خلصت subtree يعني كأنها بالنسبة للـ 12 خلصت ال
+
+147
+00:10:32,370 --> 00:10:34,730
+node اللي هنا كلها باللي فيها و اللي هي في النهاية
+
+148
+00:10:34,730 --> 00:10:37,990
+مش node هي subtree شايفها هو بالنسبة له ال node
+
+149
+00:10:37,990 --> 00:10:47,550
+تمام 12 ثم 15 ففعليا هي sorted ال sequence عندنا
+
+150
+00:10:47,550 --> 00:10:52,630
+هنا sorted مافيش فيه أي مشكلة نهائياكترتيب طبعا
+
+151
+00:10:52,630 --> 00:10:56,470
+العكس صحيح ممكن تبدأ عملية الترتيب منه بس في
+
+152
+00:10:56,470 --> 00:11:00,230
+الحالة هذه عشان تبدأ عملية الترتيب بدي يكون هو
+
+153
+00:11:00,230 --> 00:11:05,230
+جايك unordered دائما العنصر اللي في الأول هو اللي
+
+154
+00:11:05,230 --> 00:11:09,210
+بحكمك الشبكة او ال tree تبعتك مين العنصر اللي
+
+155
+00:11:09,210 --> 00:11:12,710
+موجود في البداية انا بفهم انه كان اول عنصر لما
+
+156
+00:11:12,710 --> 00:11:17,950
+عملوا construction لل tree هذي اللي قدامنا كان فيه
+
+157
+00:11:17,950 --> 00:11:22,920
+السبعةزي ما قعدنا هنشوف في المثال اللي جاي هاي
+
+158
+00:11:22,920 --> 00:11:29,220
+مثال هاي في عندك مثال بدنا نرتب مجموعة التخصصات
+
+159
+00:11:29,220 --> 00:11:34,940
+هذه حسب اسمها أو حسب الحروف بتاعتها حسب حروفها
+
+160
+00:11:34,940 --> 00:11:37,740
+alphabetical يعني فبدنا نتعامل معاه as a
+
+161
+00:11:37,740 --> 00:11:41,140
+alphabetical sorting بدنا نعمل sorting بالنسبة لل
+
+162
+00:11:41,140 --> 00:11:44,660
+alphabetical في عندك ال mathematics خلاص ال
+
+163
+00:11:44,660 --> 00:11:47,800
+mathematics هي اللي جيتها في الوجه بحطها في الأول
+
+164
+00:11:47,800 --> 00:11:52,300
+صارت هي ال rootبمعنى لو عكستني إياهم و حطتلي كلمة
+
+165
+00:11:52,300 --> 00:11:56,680
+تانية حد فيها فما تقعدش تغلب حالك تعمل search في
+
+166
+00:11:56,680 --> 00:12:02,100
+البداية لأ اللي قدامك ه to مش هيفرج معاك كتير في
+
+167
+00:12:02,100 --> 00:12:06,420
+الآخر ال sorting هتطلع معك هتطلع معك ماتجلجشك
+
+168
+00:12:06,420 --> 00:12:10,560
+sorting حسب left to right و ال left ل ال sub tree
+
+169
+00:12:10,560 --> 00:12:13,600
+ل ال right ل ال sub tree هتطلع معاك في جميع
+
+170
+00:12:13,600 --> 00:12:17,920
+الأحوال صحيح يمكن شكلها يتغير من واحد للتاني بس في
+
+171
+00:12:17,920 --> 00:12:21,400
+النهاية لما بتعامل معاها left to right كله هيطلع
+
+172
+00:12:21,400 --> 00:12:27,300
+نفس ال sorted array في الآخر ماتجلجش فحبدأ بمين
+
+173
+00:12:27,300 --> 00:12:29,000
+بالامر
+
+174
+00:12:30,770 --> 00:12:34,890
+خلص نبدأ بال mathematics ثم physics الآن ال
+
+175
+00:12:34,890 --> 00:12:39,070
+physics بالنسبة لل .. لل M مدام أنك بتتعامل معه
+
+176
+00:12:39,070 --> 00:12:44,110
+binary معناته أنا عارف أنه فيه طرفين المفروض
+
+177
+00:12:44,110 --> 00:12:50,470
+الشمال جبل ال M و اليمين بعد ال M ال physics بعد
+
+178
+00:12:50,470 --> 00:12:57,960
+خلاص بنحط مين؟ عاليمين انتهى بنحط مين؟ عاليمينOkay
+
+179
+00:12:57,960 --> 00:13:04,680
+مين بعد هيك فيه عنده؟ Geography Geography جيه جبل
+
+180
+00:13:04,680 --> 00:13:09,240
+ال M خلاص معناته بتيجي جبل ال M فإذا على شمال ال M
+
+181
+00:13:09,240 --> 00:13:16,320
+إيش فيه بعدها? Zoology اللي هو علم الحيوان زي Z
+
+182
+00:13:16,320 --> 00:13:22,150
+جاية بعد ال P معناته على يمين ال Pعلى اليمين رايحة
+
+183
+00:13:22,150 --> 00:13:28,030
+لأنها بعدها طيب ال metro .. ال metrology اللي هي
+
+184
+00:13:28,030 --> 00:13:32,870
+هذا علم ال .. الأمطار و الأحوال الجوية علم الأحوال
+
+185
+00:13:32,870 --> 00:13:37,930
+الجوية تمام؟ هذا اشمار عليكم طيب علم الأحوال
+
+186
+00:13:37,930 --> 00:13:45,270
+الجوية بدأ بإمين بال M طيب ممتاز M هي بعد M طيب A
+
+187
+00:13:45,270 --> 00:13:53,680
+هنا E معنى بعدهابعدها بتيجي بعدها مش شايف؟ أكيد
+
+188
+00:13:53,680 --> 00:13:56,800
+لازم ييجي بعدها طيب بالنسبة لل P جابلها و لا
+
+189
+00:13:56,800 --> 00:14:01,200
+بعدها؟ جابلها فبتيجي المفروض عن ناحية عن ناحية هذه
+
+190
+00:14:01,200 --> 00:14:09,600
+جيد مين ضل؟ إيش التخصص اللي وراها؟ Geology علوم
+
+191
+00:14:09,600 --> 00:14:17,740
+الأرض Geology G و E E O O G L
+
+192
+00:14:20,130 --> 00:14:26,630
+بعدها فإذا هتصير يمين لل node هذه هتصبح يمين لل
+
+193
+00:14:26,630 --> 00:14:33,370
+node هذه تمام إيش ضال؟ Psychology Psychology بس P
+
+194
+00:14:33,370 --> 00:14:40,490
+بعد ال P فهي ال P جينا هنا هتكون بعدها P P S يعني
+
+195
+00:14:40,490 --> 00:14:47,560
+بعد ال H هتيجي هنا المفروض طيب بالنسبة لل Zع
+
+196
+00:14:47,560 --> 00:14:55,500
+الشمال فده بتيجي شمال هنا بتيجي على الشمال انيا ال
+
+197
+00:14:55,500 --> 00:15:02,160
+psychology بدأنا بال P هاي ال P أكيد بالنسبالي
+
+198
+00:15:02,160 --> 00:15:04,320
+دايما كله يبدأ من ال root كله دايما يبدأ من ال
+
+199
+00:15:04,320 --> 00:15:07,360
+root بالنسبالي ال M ال root هذه على يمينها لأنه
+
+200
+00:15:07,360 --> 00:15:11,580
+أكبر منها بجي هنا طب هاي P مع P خلاص بنعديها بناخد
+
+201
+00:15:11,580 --> 00:15:17,930
+الحرف التانيهنا H هنا S لأ ال S بعد معناته هذا ال
+
+202
+00:15:17,930 --> 00:15:21,530
+psychology المفروض تيجي بعد ال physics على يمينها
+
+203
+00:15:21,530 --> 00:15:25,170
+طيب إجينا على يمينها نقارنها بال Z لأ هي جابل ال Z
+
+204
+00:15:25,170 --> 00:15:30,710
+فبتيجي على شمال ال Z طيب لاحظ أنك لو بدأت بأي كلمة
+
+205
+00:15:30,710 --> 00:15:34,770
+تانية هتتغير صح شكلها ل tree بس لما تيجي تاخدها
+
+206
+00:15:34,770 --> 00:15:40,350
+left to right هتطلع مرتبة هتطلع مرتبةعملية ال
+
+207
+00:15:40,350 --> 00:15:43,030
+insertion اللي مفترض لو بناحكي على ال raw files
+
+208
+00:15:43,030 --> 00:15:48,250
+يتكون ان هو في انتي تكون؟ هو في انتي لأن على فرق
+
+209
+00:15:48,250 --> 00:15:51,510
+احنا اول ال raw كان ابعاد اصغر رقم فعفوا احنا
+
+210
+00:15:51,510 --> 00:15:54,790
+عملنا بس من سفر لعشر رقم ده ضفناهم سفر بعدين واحد
+
+211
+00:15:54,790 --> 00:15:57,450
+و اثنين و اثنين لعملية ال insertion كله هيروح
+
+212
+00:15:57,450 --> 00:16:02,990
+اليومين لحظة شوية انت .. انت الآن بتعمل جابل ال
+
+213
+00:16:02,990 --> 00:16:06,370
+search جابل ال .. اعفو ان ال inserting او ال
+
+214
+00:16:06,370 --> 00:16:10,860
+insertion اللي بدك تعملها بدك تعمل searchلازم تعمل
+
+215
+00:16:10,860 --> 00:16:16,460
+search كل أنصر لازم تعمله search صح؟ اه هاي الأنصر
+
+216
+00:16:16,460 --> 00:16:20,520
+الأول عملتله search طيب خلصناه هل وجدت العملية
+
+217
+00:16:20,520 --> 00:16:25,100
+تبعته عمليته اللي هي logarithmic لانه ال search
+
+218
+00:16:25,100 --> 00:16:30,890
+طيب الأنصر التانيبرضه بدك تعمله search جبل ما
+
+219
+00:16:30,890 --> 00:16:34,010
+تعمله insertion .. ال insertion تبعته .. او ال
+
+220
+00:16:34,010 --> 00:16:36,970
+inserting بتعرف وين ما هو احنا عشان احنا نحكي ع
+
+221
+00:16:36,970 --> 00:16:41,410
+worst case فممكن يعني ما تكونش ال agenda بتري تكون
+
+222
+00:16:41,410 --> 00:16:45,650
+انضافة كسطر واحد كله .. كله واحد الله يعني الله
+
+223
+00:16:45,650 --> 00:16:46,990
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+224
+00:16:46,990 --> 00:16:48,590
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+225
+00:16:48,590 --> 00:16:48,590
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+226
+00:16:48,590 --> 00:16:48,630
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+227
+00:16:48,630 --> 00:16:48,770
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+228
+00:16:48,770 --> 00:16:48,770
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+229
+00:16:48,770 --> 00:16:49,330
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+230
+00:16:49,330 --> 00:16:49,710
+يعني الله يعني الله يعني الله يعني الله يعني الله
+
+231
+00:16:49,710 --> 00:16:54,160
+يعني الله يعني الله يعني الله يعني الله يعلا إيه
+
+232
+00:16:54,160 --> 00:17:00,600
+عشان بس أركز معاك search ولا sort insert اللي هي
+
+233
+00:17:00,600 --> 00:17:02,840
+بدأت تكون عبارة عن search و بعدين اللي هو تمام
+
+234
+00:17:02,840 --> 00:17:05,900
+تمام ممتاز يعني عندك تمال sorting مع .. مع عدد ..
+
+235
+00:17:05,900 --> 00:17:11,260
+خلاص سبحان الله يدرنها من 0 إلى 10 هذه بطلت اسمها
+
+236
+00:17:11,260 --> 00:17:14,620
+ال worst case بالعكس هذه ال worst caseو انا هجيت
+
+237
+00:17:14,620 --> 00:17:17,060
+انا مش عارف انهم مرتبين او مش مرتبين فجيت اضيفي
+
+238
+00:17:17,060 --> 00:17:20,160
+شويه هذي اه؟ ايش .. ايش طالع معاك؟ اضفنا السفر
+
+239
+00:17:20,160 --> 00:17:24,520
+بالاول كويس بعدين بنضيف الواحد وراح ترمي الاتنين
+
+240
+00:17:24,520 --> 00:17:27,540
+وراح ترمي اتنين هجيت ع العملية ال .. ال searching
+
+241
+00:17:27,540 --> 00:17:30,980
+بطلنا احنا ننزل login بس ان احنا ننزل انصر وانصر
+
+242
+00:17:30,980 --> 00:17:37,440
+فصار زي كده انها ممكن تلز نزل صارت كأنها سطر كامل
+
+243
+00:17:39,700 --> 00:17:42,680
+كويس بس انت برضه نفس الجثة انت في النهاية بتتعامل
+
+244
+00:17:42,680 --> 00:17:47,140
+مع كل node على اساس ان هي yes no yes no yes no
+
+245
+00:17:47,140 --> 00:17:55,760
+معاك والله فاهمك فاهمك فاهمت
+
+246
+00:17:55,760 --> 00:17:58,520
+جزدك على اساس ان كلهم مالوا في اتجاه واحد كلهم
+
+247
+00:17:58,520 --> 00:18:04,760
+اخدوا اتجاه اتجاه واحد لما بتيجي بتعمل insertion
+
+248
+00:18:07,240 --> 00:18:10,340
+والله هي بدها بحث يعني مش غلط خلينا ناخدهم واحدة
+
+249
+00:18:10,340 --> 00:18:15,160
+واحدة مش هتصبح .. لأ هي صادفة معاك انفع انت مش
+
+250
+00:18:15,160 --> 00:18:20,200
+هتستغل فكرة ال decision لأنه دايما هتكون معاك اكبر
+
+251
+00:18:20,200 --> 00:18:21,340
+او اصغر ده مش هتكون اصغر
+
+252
+00:18:24,050 --> 00:18:28,030
+أو أكبر لو كانت بالعكس لو كانت بالعكس يعني اتجاه
+
+253
+00:18:28,030 --> 00:18:31,570
+عكسي اتجاه عكسي خلينا نبحثها مش غلط اقولك خلينا
+
+254
+00:18:31,570 --> 00:18:34,750
+نعتبرها سؤال من الأسئلة المرة القادمة و نتعامل
+
+255
+00:18:34,750 --> 00:18:37,730
+معها كأنها سؤال مستقل و نحلها نشوفها ان شاء الله
+
+256
+00:18:37,730 --> 00:18:43,150
+كويس احنا كان في chemistry لسه والله ما احنا
+
+257
+00:18:43,150 --> 00:18:44,930
+ماخدين بالنا ان في لسه chemistry اما تقولوا ليه
+
+258
+00:18:44,930 --> 00:18:50,450
+لسه في C اه شوفين انت دخلتنا في ال ..هي لسه في
+
+259
+00:18:50,450 --> 00:18:56,510
+main and chemistry ال C بتهيألي مش كتير باينة ال C
+
+260
+00:18:56,510 --> 00:18:59,410
+هي باينة انت قعدت بتقولي كلهم اشمال اشمال هي
+
+261
+00:18:59,410 --> 00:19:06,410
+طلعتلك اشمال على طول طيب تأثرت بكلامك اه؟ طيب نروح
+
+262
+00:19:06,410 --> 00:19:10,660
+لل decision trees في ال decision treesهنا بدنا
+
+263
+00:19:10,660 --> 00:19:14,460
+ناخد قرار القرار تبعنا بدي يكون مبني على three
+
+264
+00:19:14,460 --> 00:19:20,100
+بمعنى yes و no و بدي اصل لقرار في النهاية القرار
+
+265
+00:19:20,100 --> 00:19:23,680
+هيكون مبني على situations معينة اكيد بدي يكون مبني
+
+266
+00:19:23,680 --> 00:19:28,180
+على situations فكل decision point او situation
+
+267
+00:19:28,180 --> 00:19:35,600
+تمثل ب node تمثل ب node زي انه نقول ال situation
+
+268
+00:19:35,600 --> 00:19:45,030
+المعين هل X أكبر من خمسةفبد أقول yes or no؟ yes أو
+
+269
+00:19:45,030 --> 00:19:50,530
+no فهذه هنا ال situation اللي أنا بسأل عليها تمثل
+
+270
+00:19:50,530 --> 00:19:56,480
+بشكل node طيب ال actionاللي بده يصير أو عادة ال
+
+271
+00:19:56,480 --> 00:20:01,200
+edge هذي عشان تروح ل decision هذي المفروض النتيجة
+
+272
+00:20:01,200 --> 00:20:04,620
+بتاعة ال situation ال action اللي بده يصير هل بدي
+
+273
+00:20:04,620 --> 00:20:07,720
+يعني بدي اقارن بدي افحص ال situation وبناء على
+
+274
+00:20:07,720 --> 00:20:11,740
+القرار اللي طلع معايا او النتيجة بدي اقول فعلا
+
+275
+00:20:11,740 --> 00:20:16,360
+متحقق او غير متحقق بمثلها بال edgesعشان أروح
+
+276
+00:20:16,360 --> 00:20:20,480
+للقرارات القرار هذا ممكن يكون نهائي فهذه معناته
+
+277
+00:20:20,480 --> 00:20:24,320
+عبارة عن leaf أو لأ هي لسه محتاجة كمان فحص تاني
+
+278
+00:20:24,320 --> 00:20:31,180
+فتصبح هي كمان node ل situation بدها فحص ل
+
+279
+00:20:31,180 --> 00:20:33,680
+situation تاني بدها فحص زي ما نقول أكبر من خمسة
+
+280
+00:20:33,680 --> 00:20:39,830
+طيب هنا X أصغر من اتنينعسى اسم اللي بدي أقول هل هي
+
+281
+00:20:39,830 --> 00:20:44,110
+من 2 إلى 5 مثلا أقول والله قيمة X من 2 إلى 5 فنفس
+
+282
+00:20:44,110 --> 00:20:47,850
+الكلام بدي أقول yes or no فهل بدي أروح لل terminal
+
+283
+00:20:47,850 --> 00:20:51,070
+فهذه معناته القرار النهائي أو لأ لسه محتاج كمان
+
+284
+00:20:51,070 --> 00:20:55,390
+فحص تاني زي قصة الأعراض أنا بسألش عن أعراض واحد
+
+285
+00:20:55,390 --> 00:20:58,840
+وخلاصالطبيب عادة بيسألك عن العرض الأول ثم العرض
+
+286
+00:20:58,840 --> 00:21:02,180
+التاني ثم التالت و هو بيحط في دماغه sequence
+
+287
+00:21:02,180 --> 00:21:06,400
+لمجموعة الأعراض هذه عشان يجمحهم مع بعض و يحاول
+
+288
+00:21:06,400 --> 00:21:14,640
+يطلع بمين بقرار يطلع القرار معين تمام الان واحدة
+
+289
+00:21:14,640 --> 00:21:17,860
+من الأمثلة الواضحة على هذا الموضوع هي ال coin
+
+290
+00:21:17,860 --> 00:21:22,060
+weighing problem اللي هي عندك مجموعة coins و ال
+
+291
+00:21:22,060 --> 00:21:25,500
+coins هذه نفترض الخمسين مليم الفلسطيني
+
+292
+00:21:28,130 --> 00:21:34,750
+من عملتنا الفلسطينية كويس الخمسين Palestinian مليم
+
+293
+00:21:34,750 --> 00:21:41,170
+او millions كويس عندى تمان قطعة التمن قطع هدولة
+
+294
+00:21:41,170 --> 00:21:47,110
+فيهم واحدة زائفة اكم وزن محتاج ب free being
+
+295
+00:21:47,110 --> 00:21:54,290
+balanced عشان اكتشف مين الزائفة طيب الزائفة هذه
+
+296
+00:21:54,290 --> 00:22:01,510
+كيف زائفة هي lightercounterfeit بمعنى وزنها أقل من
+
+297
+00:22:01,510 --> 00:22:06,810
+الباجي لأنه كلكم عارفين أنه قيمة المعدن نفسه
+
+298
+00:22:06,810 --> 00:22:10,650
+المفروض أنه حسب الوزن من المعدن نفسه يكون يعطي نفس
+
+299
+00:22:10,650 --> 00:22:15,350
+قيمة العملة طيب لما أنا أكل شوية منه و أكل من هذا
+
+300
+00:22:15,350 --> 00:22:17,470
+شوية و أكل من هذا شوية و أكل من هذا شوية بطرت
+
+301
+00:22:17,470 --> 00:22:22,400
+خمسين ملينصارت لها 45 مليم مثلا فعليا يعني قيمة
+
+302
+00:22:22,400 --> 00:22:27,120
+المعدن نفسه أصبح بسويش الخمسين بساوي خمسة واربعين
+
+303
+00:22:27,120 --> 00:22:30,400
+منه و أنا روحت جمعتها الأكم من واحدة و حاطيتهم في
+
+304
+00:22:30,400 --> 00:22:34,820
+coin جديدة اربحت فيها خمسين إضافية تلغشوا هو هيك
+
+305
+00:22:34,820 --> 00:22:42,000
+بتمام فمعنى ذلك أنه هي أقل وزنا أقل وزنا okay أكم
+
+306
+00:22:42,000 --> 00:22:43,160
+ليش؟
+
+307
+00:22:53,630 --> 00:22:59,670
+ممتاز 100% الان انت حللته ننطقيا صح و حلك صح الان
+
+308
+00:22:59,670 --> 00:23:02,670
+بدنا نحل الكلام اللى انت حللته هذا نحطه فى قالب
+
+309
+00:23:02,670 --> 00:23:07,570
+علمى نحطه فى قالب رياضى القالب الرياضى ببساطة هى
+
+310
+00:23:07,570 --> 00:23:12,790
+ال height تبعت لل tree لأن ال tree انا بتعامل انا
+
+311
+00:23:12,790 --> 00:23:15,990
+مع ال tree و اللى انت قلتلنا اياه الان انت قلت
+
+312
+00:23:15,990 --> 00:23:21,610
+tree بمعنى انت حطيتdecision عفوا situation ال
+
+313
+00:23:21,610 --> 00:23:27,510
+situation هذا حللته كنتائج اما قاعد يقول اما انها
+
+314
+00:23:27,510 --> 00:23:33,610
+متساويين فمعنى ذلك ان هي عندك هذا situation معينة
+
+315
+00:23:33,610 --> 00:23:36,870
+هي الوزن اللي انت عملته ايش ال possibilities تبعته
+
+316
+00:23:36,870 --> 00:23:45,040
+قولت اما يكون متساويين balance او اليمين اعلىفمعنى
+
+317
+00:23:45,040 --> 00:23:50,240
+ذلك أنه الشمال فيها الزائف أو الشمال الأعلى فمعنى
+
+318
+00:23:50,240 --> 00:23:55,900
+ذلك أنه كفة اليمين اللي فيها الجطع الزائفة اعمل
+
+319
+00:23:55,900 --> 00:24:03,600
+التلاتة فهنا تصيرنا نتكلم عن theory three تمام هذه
+
+320
+00:24:03,600 --> 00:24:10,040
+بكل بساطة أصبحت كأنه بهذا الشكل هذه المرة الأولى
+
+321
+00:24:10,740 --> 00:24:14,680
+بعدين قلتلنا ان في مرة تانية تمام المرة التانية
+
+322
+00:24:14,680 --> 00:24:20,060
+المعناه هتكون يا هنا يا هنا يا هنا برضه في وزنات
+
+323
+00:24:20,060 --> 00:24:29,400
+الوزنات هذه هتكون تلاتة ولا اتنين هنا
+
+324
+00:24:29,400 --> 00:24:32,760
+كنتائج وزنتين اذا كانوا balance انا بتكلم عن
+
+325
+00:24:32,760 --> 00:24:37,580
+تمانية اي
+
+326
+00:24:37,580 --> 00:24:42,260
+ممكن تكون تلاتةأحنا ممكن نساوي الأخف والأدلال صح
+
+327
+00:24:42,260 --> 00:24:46,560
+لأنه اللي فهمته منك أن أنت ممكن تحط تلاتة مقابل
+
+328
+00:24:46,560 --> 00:24:52,940
+تلاتة طيب واحدة منهم وزنت معناته الأخف فيها الزائف
+
+329
+00:24:52,940 --> 00:24:57,520
+خلاص كل السبعة هدول هي case سليم التلاتة هدولة
+
+330
+00:24:57,520 --> 00:25:01,580
+بدنا نحط تنتين منهم على وزنة فهيطلع برضه تلاتة
+
+331
+00:25:01,580 --> 00:25:05,160
+possibilities ممكنين أنه اليمين أو الشمال أو
+
+332
+00:25:05,160 --> 00:25:07,960
+balanced فاللي ضالت ماوزنتهاش هي الزائفة بتصير
+
+333
+00:25:09,050 --> 00:25:12,550
+واضحت؟ فإذا لأ انا هنا واحدة منهم هتكون تنتين هم
+
+334
+00:25:12,550 --> 00:25:17,870
+التنتين في حال اللي ضالوا برا بمعنى التلاتة و
+
+335
+00:25:17,870 --> 00:25:22,350
+التلاتة رجحوا مع بعض التنتين متساويتين التنتين
+
+336
+00:25:22,350 --> 00:25:25,750
+اللي برا هم اللي فيهم الزائف هنا بطلع انديال يمينا
+
+337
+00:25:25,750 --> 00:25:31,090
+لشمال خلاص فهتكون بهذا الشكل
+
+338
+00:25:34,590 --> 00:25:40,430
+أه طيب أكم .. أكم level هيطلع معاك هات ناخد أربعة
+
+339
+00:25:40,430 --> 00:25:46,630
+أربعة هات نحللها بكل بساطة بدك تشتغل على هنا طبعا
+
+340
+00:25:46,630 --> 00:25:51,330
+احنا كنا بنتكلم تلاتة مقابل تلاتة هنا بدك تشتغل
+
+341
+00:25:51,330 --> 00:25:53,090
+على أربعة مقابل أربعة طيب
+
+342
+00:25:56,450 --> 00:26:00,030
+أه أنا عارف والله عارف بس خلّينا ن .. أتبع معاكم
+
+343
+00:26:00,030 --> 00:26:03,450
+ماشي مش غلط خلّينا نفكر و خلّينا ن .. ننطلق أنا
+
+344
+00:26:03,450 --> 00:26:06,770
+أحيانا بكون عارف أنه لأ هتوصلنا لإش .. مش مش دي
+
+345
+00:26:06,770 --> 00:26:09,470
+لكن لازم نكمل مع بعض انت فاكر مش غلط أربعات و
+
+346
+00:26:09,470 --> 00:26:14,210
+وزمتان هى أربعة أربعة صار عندى هنا أربعة أنت بتقول
+
+347
+00:26:14,210 --> 00:26:16,390
+في واحدة منهم .. في واحدة منهم يكون مزيف يبقى فشل
+
+348
+00:26:16,390 --> 00:26:18,510
+بتقول مش هيتفنون تمام هل وجد أنت بتتكلم عن أربعة
+
+349
+00:26:18,510 --> 00:26:23,590
+أربعة اتنين بمعنى الرشح هادى إذا اليمين كانت أخف
+
+350
+00:26:29,200 --> 00:26:33,300
+ماشي معاك والله معاك هنا فيه أنك أربعة مقابل أربعة
+
+351
+00:26:33,300 --> 00:26:40,440
+صح هاي الميزان تبعك تمام هاي ميزانك حطيت أربعة
+
+352
+00:26:40,440 --> 00:26:45,440
+مقابل أربعة هاي هادي نزلت يعني الأربع هدول فيهم
+
+353
+00:26:45,440 --> 00:26:48,460
+الزائفة تمام يعني معناه ذلك أن أنا وصلت للنود
+
+354
+00:26:48,460 --> 00:26:53,090
+التاني وفيه في إيدي أربعة واحدة منهم زائفةأيوة
+
+355
+00:26:53,090 --> 00:26:57,590
+هاتمنا نكمل معاك هي اتنين و اتنين صحيح؟ طيب هي
+
+356
+00:26:57,590 --> 00:27:00,890
+اتنين هنا و اتنين هنا صار عنده هنا في النهاية
+
+357
+00:27:00,890 --> 00:27:07,050
+اتنين في ايدي عرفت ان هم زائفين، كيف بدك تعرفه؟
+
+358
+00:27:07,050 --> 00:27:11,490
+صح؟ أكم level هنا عملت؟ طيب زميلك جالك أكم level؟
+
+359
+00:27:13,750 --> 00:27:17,510
+يعني معنى ذلك انا لو بدي على كل وزنة ادفع مقابل
+
+360
+00:27:17,510 --> 00:27:24,930
+الجبان هذا وزن في النهاية جبان و هذا بتأجر بالوزنة
+
+361
+00:27:24,930 --> 00:27:29,290
+هقولك والله بدي اه و بدي اوزن وزنتين okay كل وزنة
+
+362
+00:27:29,290 --> 00:27:33,950
+بشكل انا هضطر اخد منه شكلين بس انت هضطر اخد منك
+
+363
+00:27:33,950 --> 00:27:37,890
+تلاتة هاخد منك تلاتة لانك وزنت تلت مرات صح ولا لأ
+
+364
+00:27:39,810 --> 00:27:44,030
+هينمشينا معاك و قولنا انه حللناها زي ما .. في اشي
+
+365
+00:27:44,030 --> 00:27:47,610
+غلط عملناها؟ مظبوط زي ما كانت فكرتك هنا اضطريت
+
+366
+00:27:47,610 --> 00:27:51,970
+اعمل واحدة اتنين تلاتة هنا عملت اتنين لأ اوفرلي
+
+367
+00:27:51,970 --> 00:27:57,610
+الاتنين اوفرنا الاتنينلأ لأ بتطلع بس زي ما أقوله
+
+368
+00:27:57,610 --> 00:28:01,030
+إله إله حدود يعني خلوكوا أصبروا معايا لل slide
+
+369
+00:28:01,030 --> 00:28:03,530
+اللي جاية هقولكوا إيه أمتى بقدر أعمل اللي انت
+
+370
+00:28:03,530 --> 00:28:07,370
+عملته أنا ضلت متماشي معاك عساس كنت مستنى منك كمان
+
+371
+00:28:07,370 --> 00:28:11,190
+كلمة زيادة كأن أقولك أه هيك بتصبط بس خلينا ..
+
+372
+00:28:11,190 --> 00:28:16,470
+خلينا معاكم كيف؟ هو جزء بتاخد وزن 2 بس 6 و 8 ليس
+
+373
+00:28:16,470 --> 00:28:20,010
+لزن 1 فلو كان فردي بتحط فكاف أكثر من كاف يعني خمسة
+
+374
+00:28:20,010 --> 00:28:21,670
+و أربعة .. ما هي جاعة بتقول إذا كان فردي .. كيف
+
+375
+00:28:21,670 --> 00:28:22,790
+بدك تضمن هذا الكلام؟
+
+376
+00:28:25,820 --> 00:28:29,040
+واصبروا عليّ النقاش مازال مستمر هنا خلّينا نبدأ
+
+377
+00:28:29,040 --> 00:28:32,840
+بالفكرة بس تعت البشار المهندس هاي الفكرته و بعدين
+
+378
+00:28:32,840 --> 00:28:36,300
+ننتقل لفكرة البشار المهندس برضه و نشوف إيش اللي
+
+379
+00:28:36,300 --> 00:28:39,840
+اتختلفت عهم الأولة أني قولنا والله تلاتة تلاتة و
+
+380
+00:28:39,840 --> 00:28:43,320
+هذه الإجابة اللي إجتنا في الأول تلاتة تلاتة و
+
+381
+00:28:43,320 --> 00:28:48,030
+الكتاب عجبته أكتر إيش نسوي؟جالك تلاتة تلاتة فبضل
+
+382
+00:28:48,030 --> 00:28:52,810
+عند هنا إما بترجح في الآخر التلاتة بتاعة الشمال
+
+383
+00:28:52,810 --> 00:28:54,990
+فمعنى ذلك أن التلاتة اللي في اليمين هم اللي فيهم
+
+384
+00:28:54,990 --> 00:28:59,630
+الزائف تمام مش مشكلة هنا نفس الكلام اللي رجحت
+
+385
+00:28:59,630 --> 00:29:03,950
+اليمين فالشمال هي اللي فيها الزائف أو اللي تساووا
+
+386
+00:29:03,950 --> 00:29:08,390
+فتنتقن لمن وزنوش هم اللي فيهم الزائف بعد هيك
+
+387
+00:29:08,390 --> 00:29:11,830
+محتاجين كمان وزنة تانية نعمل نفس الفكرة بس في
+
+388
+00:29:11,830 --> 00:29:16,040
+الآخر من التلاتة هدول بحط واحدة مقابل واحدةوبقال
+
+389
+00:29:16,040 --> 00:29:20,360
+عندي واحدة برا والله اتزنوا اللي برا هي اللي فيها
+
+390
+00:29:20,360 --> 00:29:26,860
+مشكلة ومش محتاج اقعد اوزنها تمام ايه كويس الان
+
+391
+00:29:26,860 --> 00:29:29,980
+الفكرة هذه نظريا احنا اخدناها لسه المرة اللي فاتت
+
+392
+00:29:29,980 --> 00:29:33,420
+وختمنا فيها شغلنا لما كنا بنتكلم عن مجموعة ال
+
+393
+00:29:33,420 --> 00:29:37,700
+rules او ال theoremsو آخر حاجة حسبناها الـ height
+
+394
+00:29:37,700 --> 00:29:42,140
+بتاعتنا صح لما قولنا عدد ال leaves بتساوي ال M to
+
+395
+00:29:42,140 --> 00:29:45,380
+the power of H و بعدين قولنا اننا بدي جيب ال H هذه
+
+396
+00:29:45,380 --> 00:29:49,360
+لأن ال H هذه كانت ال complexityطيب ما هي نفس الاشي
+
+397
+00:29:49,360 --> 00:29:54,840
+ال complexity هنا جداش عدد التكرارات للوزن هنا كان
+
+398
+00:29:54,840 --> 00:29:57,420
+عندى تكرارين هنا اضطريت اعمل تلت تكرارات فمعناه
+
+399
+00:29:57,420 --> 00:30:00,520
+ذلك هي عدد التكرارات صارت جداش عدد التكرارات هي ال
+
+400
+00:30:00,520 --> 00:30:02,480
+.. ال .. ال height اللى بدور عليها و احنا جيبناها
+
+401
+00:30:02,480 --> 00:30:05,140
+logarithmic المرة الماضية جيبناها logarithmic بكل
+
+402
+00:30:05,140 --> 00:30:08,860
+بساطة فال H هنا هتكون اكبر من او تساوي ال ceiling
+
+403
+00:30:08,860 --> 00:30:13,040
+لمين ل log M لعدد ال leaves ليش لأنه عدد ال leaves
+
+404
+00:30:13,040 --> 00:30:19,140
+مش بالضرورى يكون واحدة من مضاعفة ال Mصح؟ يعني لو
+
+405
+00:30:19,140 --> 00:30:23,000
+افترضنا اتنين مش بالضروري ان ال tree اللي تطلع
+
+406
+00:30:23,000 --> 00:30:29,580
+عندى تكون full balanced tree مين قال ضروري؟ ماحدش
+
+407
+00:30:29,580 --> 00:30:32,840
+قال ضروري يعني هل معناه ذلك انه تطلع في الآخر لو
+
+408
+00:30:32,840 --> 00:30:37,300
+بوزن اتنين .. لو ال tree عندى binary تطلع عندى
+
+409
+00:30:37,300 --> 00:30:40,220
+تمانية على اعتبار ان تمانية واحدة من المضاعفات
+
+410
+00:30:40,220 --> 00:30:44,220
+اتنين اربعة تمانية ستاشت مش هى المضاعفات لل binary
+
+411
+00:30:44,220 --> 00:30:49,920
+لأ طلع عندى اربعة عشرطلع عندك 14 فإذا عدد ال
+
+412
+00:30:49,920 --> 00:30:53,240
+leaves اللي بتقتصله 14 فهنا بتعود ال 14 بتاخد
+
+413
+00:30:53,240 --> 00:30:57,700
+ceiling لإنه أكيد هيطلع هنا كسر أكيد هيطلع كسر لا
+
+414
+00:30:57,700 --> 00:31:01,220
+هو 8 ولا هو 16 فهو بين ال 8 و ال 16 يعني بتطلع
+
+415
+00:31:01,220 --> 00:31:06,220
+تلاتة و كسر تلاتة و إشي على طول بتاخد للأعلى و
+
+416
+00:31:06,220 --> 00:31:08,980
+بمشي الحاد تمام ففي حالة زي الحالة اللي احنا
+
+417
+00:31:08,980 --> 00:31:14,380
+اشتغلناها هنا كنت بتكلم عن 8 coins أو تمانية من
+
+418
+00:31:14,380 --> 00:31:18,610
+العملة الفلسطينية اللي بالملين من الخمسين ملينكانت
+
+419
+00:31:18,610 --> 00:31:21,530
+موجودة عندى، بدى أفحصهم، أنا عارف إن الميزان
+
+420
+00:31:21,530 --> 00:31:25,830
+بيعطيني branching لتلاتة، يا يمين يا شمال يا
+
+421
+00:31:25,830 --> 00:31:30,090
+balance فإذن بتكلم عن تلاتة، افحصها بيطلع مندك
+
+422
+00:31:30,090 --> 00:31:33,950
+واحد فاصلة اتنين، فإذن أنا بتكلم عن عدد وزنات
+
+423
+00:31:33,950 --> 00:31:40,950
+اتنين، محتاج وزن تان، فقط، تمام okay، الآن نجي
+
+424
+00:31:40,950 --> 00:31:44,820
+للاستراتيجية اللى بدنا نشتغل عليهاكيف انا بدي
+
+425
+00:31:44,820 --> 00:31:47,800
+اشتغل على أرقام تانية لما يكون عندك أرقام تانية
+
+426
+00:31:47,800 --> 00:31:52,200
+بكل بساطة بناخد التلت مادام أنا بتكلم عن ال M
+
+427
+00:31:52,200 --> 00:31:59,360
+تبعتي بتساوي تلاتة حسب التطبيق انا بتكلم عن وزن
+
+428
+00:31:59,360 --> 00:32:03,880
+ميزان الميزان يا يمين يا شمال يا بيرجح okay فإذا
+
+429
+00:32:03,880 --> 00:32:09,240
+باخد التلت و بعملهsealing لأنه مش بالضروري دايما
+
+430
+00:32:09,240 --> 00:32:14,140
+يقسم على تلاتة العدد الأغراض اللي بدي أفحصها هذه
+
+431
+00:32:14,140 --> 00:32:18,460
+أو عدد ال coins مش بالضروري يقسم على التلاتة فإذا
+
+432
+00:32:18,460 --> 00:32:23,550
+بنقول sealing و بنحطهم كل واحدة في مينفي كفة و
+
+433
+00:32:23,550 --> 00:32:29,570
+بنوزن بناء على ذلك إذا والله ال light weight fake
+
+434
+00:32:29,570 --> 00:32:35,170
+coin ظهرت في ال right معناه ذلك إنه ال set بتاعتنا
+
+435
+00:32:35,170 --> 00:32:39,310
+in over three ceiling هي ال coins اللي بدي أعيد
+
+436
+00:32:39,310 --> 00:32:46,030
+فحصهاصحيح؟ تمام، ونفس الكلام إذا كانت في ال lift،
+
+437
+00:32:46,030 --> 00:32:49,630
+برضه التلت، التلت هذا هو اللي محتاج أرجع أعيد فحصه
+
+438
+00:32:49,630 --> 00:32:55,370
+كمان مرة أو إنه ال in total معقس التلتين اللي هم
+
+439
+00:32:55,370 --> 00:33:00,010
+ضايقين، طبعا هم بقول تقريبا تقريبا تقريبا التلت،
+
+440
+00:33:00,010 --> 00:33:03,820
+لكن هو exactly لأ مش التلتبدليل التمانية اللي كنا
+
+441
+00:33:03,820 --> 00:33:07,780
+بتكلم عنها و اللي عملتناها مشكلة و بدنا نتطر ..
+
+442
+00:33:07,780 --> 00:33:11,260
+عيدنا نتكلم عنها و نحل ال .. الاشتباك اللي صار انه
+
+443
+00:33:11,260 --> 00:33:14,200
+لأ ليش نقسم على تلاتة او على اتنين على مش عارف ايش
+
+444
+00:33:14,200 --> 00:33:17,380
+لإنه ظهر عندي تلاتة تلاتة و ضال اتنين مضالش تلاتة
+
+445
+00:33:17,380 --> 00:33:23,060
+فعليا فإذا هي مش تلت exactly تلت تقريبا طيب مش
+
+446
+00:33:23,060 --> 00:33:31,460
+وهندس إذا ال N مد تلاتة بتساوي واحد اعمل اللي انت
+
+447
+00:33:31,460 --> 00:33:39,390
+قلت عليهإذا بتسوي واحد يعني إذا كانت تتكلم عن عشرة
+
+448
+00:33:39,390 --> 00:33:43,050
+عشرة
+
+449
+00:33:43,050 --> 00:33:49,490
+coins ليش؟ لأن عشرة موديولو تلاتة واحد اعمل اللي
+
+450
+00:33:49,490 --> 00:33:55,450
+انت قلت عليه قول والله بتاخد أربعة أربعة اي عفوا
+
+451
+00:33:55,450 --> 00:34:02,030
+تلاتة تلاتة ويضل أربعة في الحالة هذه تلاتة تلاتة
+
+452
+00:34:02,030 --> 00:34:09,570
+ويضل أكتر منهمففي الحالة هذه بتاخد floor خد floor
+
+453
+00:34:09,570 --> 00:34:17,030
+لأنه خلّينا نفكر فيها برضه هاي بدأت بالوزنة الأولى
+
+454
+00:34:17,030 --> 00:34:24,250
+عندك قلنا تلاتة تلاتة وهنا أربعة إذا كان balance
+
+455
+00:34:24,250 --> 00:34:28,700
+بدو يطلع عندك أربعة صح؟هيطلع عندك أربع إذا كان لأ
+
+456
+00:34:28,700 --> 00:34:31,380
+واحدة منهم رجحت لليمين فمعناه ذلك أنه في عندي
+
+457
+00:34:31,380 --> 00:34:34,020
+تلاتة هم اللي بيبقى فحصهم رجحت للشمال ففيه يضل
+
+458
+00:34:34,020 --> 00:34:37,740
+عندي تلاتة هم اللي بيبقى فحصهم طيب السيناريو
+
+459
+00:34:37,740 --> 00:34:42,100
+التاني أنه لأ نشتغل على ال ceiling بس معناته بدي
+
+460
+00:34:42,100 --> 00:34:49,600
+أعمل أربعة مقابل أربعة وبيضل كده؟ اتنين ممتازة
+
+461
+00:34:49,600 --> 00:34:53,540
+لاحظوا أنه هنا لو رجحت يمين أو رجحت شمال بيضل عندي
+
+462
+00:34:53,540 --> 00:34:55,800
+أربعة يعني محتاج لها مرتين
+
+463
+00:34:58,150 --> 00:35:02,850
+مصبوط؟ طيب هنا انا هحتاج برضه مرتين بس تلت
+
+464
+00:35:02,850 --> 00:35:11,490
+الاحتمال هنا تلتين الاحتمال صح؟
+
+465
+00:35:11,490 --> 00:35:14,870
+ايوة okay انا مقتنع تماما ان في ال worst case هقول
+
+466
+00:35:14,870 --> 00:35:19,050
+ان هم تلاتة مافيش مشكلة لكن ال practical بجل
+
+467
+00:35:19,050 --> 00:35:23,940
+الاحتمالية التلاتةPractical بجلّي الاحتمالية انه
+
+468
+00:35:23,940 --> 00:35:28,100
+يصير معايا تلاتة فبنقول لأ تلاتة تلاتة و بنخلي
+
+469
+00:35:28,100 --> 00:35:34,700
+الاحتمال لأ اني اضطر لوزنتين حالة من التلات حالات
+
+470
+00:35:34,700 --> 00:35:39,280
+مش حالتين من التلات حالات واضح الجزئية كيف انها
+
+471
+00:35:39,280 --> 00:35:40,640
+عملت؟ تمام ممتاز
+
+472
+00:35:45,880 --> 00:35:49,260
+فاضطرنا في الآخر يقول ان احنا بتجسم ال coin الأولى
+
+473
+00:35:49,260 --> 00:35:51,920
+و التانية و التالتة في كفة الرابعة و الخمسة و
+
+474
+00:35:51,920 --> 00:35:56,380
+السادسة في كفة و خلي السابعة و التامنة برا ففي
+
+475
+00:35:56,380 --> 00:36:01,020
+الحالة هذه اذا كان رجحت عند او اللي كانت اخف
+
+476
+00:36:01,020 --> 00:36:03,620
+الواحد و اتنين و التلاتة فمعناته بتدوزن واحد مقابل
+
+477
+00:36:03,620 --> 00:36:09,440
+اتنين كويس يا بتطلع واحد يا بتطلع اتنين او بتطلع
+
+478
+00:36:09,440 --> 00:36:14,340
+اتنين متساويين فتلاتة هياللي فيها مشكلة طيب أو انه
+
+479
+00:36:14,340 --> 00:36:18,260
+لأ اللي أخف هي الكفة بتاعة أربعة خمسة ستة و نفس
+
+480
+00:36:18,260 --> 00:36:22,720
+الكلام بوزن أربعة مع خمسة واحدة منهم هترجح معناته
+
+481
+00:36:22,720 --> 00:36:28,840
+الأقل وزنا هي الزائفة أو انه balance تنتين فبناخد
+
+482
+00:36:28,840 --> 00:36:32,820
+اللي ما انوزنتش منهم الحالة التالتة سبعة مقابل
+
+483
+00:36:32,820 --> 00:36:38,140
+تمانية إذا واحد اتنين تلاتة مقابل أربعة خمسة ستة
+
+484
+00:36:39,600 --> 00:36:42,660
+بالنسبة لم يكن هناك واحدة رجعت على التانية فإذا
+
+485
+00:36:42,660 --> 00:36:46,200
+المشكلة ستكون في أربعة أو خمسة أو سبعة أو تمانية
+
+486
+00:36:46,200 --> 00:36:50,760
+بوزنهم جدا بعض بطريق مباشر مباشر هي تنتنج بالبعض
+
+487
+00:36:50,760 --> 00:36:55,190
+واحدة منهم أخف من التانية فهيالcontrafeit او
+
+488
+00:36:55,190 --> 00:37:01,750
+الزائفة تمام الان مدام اننا في نفس الموضوع و في
+
+489
+00:37:01,750 --> 00:37:05,590
+نفس جزئية ال search في حاجة اسمها eternary search
+
+490
+00:37:05,590 --> 00:37:11,190
+أخدتوها طيب eternary search هتنمحى كل اللي احنا
+
+491
+00:37:11,190 --> 00:37:14,990
+عاملينه عشان
+
+492
+00:37:14,990 --> 00:37:20,750
+هذه هتشمل كذا مفهوم في بعض يعني هناخد منها ال
+
+493
+00:37:20,750 --> 00:37:24,690
+search اللي أخدناها سابقا هناخدنتكلم عن ال
+
+494
+00:37:24,690 --> 00:37:28,690
+complexity هنتكلم عن letry مدام توي أخدناها من
+
+495
+00:37:28,690 --> 00:37:32,290
+واحدة من التطبيقات هي الجزئية ال search و ال
+
+496
+00:37:32,290 --> 00:37:38,530
+insertion تمام هنا بكل بساطة هاي
+
+497
+00:37:38,530 --> 00:37:44,030
+ال array تبعك كنا ناخد في ال binary ايش نقطة و
+
+498
+00:37:44,030 --> 00:37:46,270
+نقارن فيها لأننا هناخد نقطتين
+
+499
+00:37:52,790 --> 00:37:57,930
+عند التلت والتلتين بدنا ناخد قيمتين واحدة عند
+
+500
+00:37:57,930 --> 00:38:01,410
+التلت واحدة عند مين عند التلتين وندور على X وندور
+
+501
+00:38:01,410 --> 00:38:07,110
+على X أقارن X بالقيمة بالقيمة مين التلتين هذه مثلا
+
+502
+00:38:07,110 --> 00:38:10,350
+إيش احتمالاتها يا أكبر من يا أصغر من والله إذا
+
+503
+00:38:10,350 --> 00:38:15,190
+بتساوي معناته انتهت الجثة خلصنا يعني ضربناها جاءت
+
+504
+00:38:15,190 --> 00:38:19,710
+على طول هي طبعا the best case لكن ممكن تكون أكبر
+
+505
+00:38:19,710 --> 00:38:26,750
+منأكبر من عارف انت ايش سويت التلتين كلهم راحوا مش
+
+506
+00:38:26,750 --> 00:38:32,210
+هي خلصت التلتين مرة واحدة بدأت النص طيب ماصارش
+
+507
+00:38:32,210 --> 00:38:39,590
+الكلام بهذا الشكل لجيتها أقل من أقل من تلتين أقل
+
+508
+00:38:39,590 --> 00:38:43,950
+من التلتين على طول بتقارنها بمين بالتلت هتقارنها
+
+509
+00:38:43,950 --> 00:38:50,170
+بالتلت هنا ايش هيطلع هتلاحظ ايش سويتليش؟ لأن الـ
+
+510
+00:38:50,170 --> 00:38:53,610
+two branches هدول بناء على إنها طلعت أقل من ..
+
+511
+00:38:53,610 --> 00:38:58,070
+بناء على أساس إن هي أقل من التلتين فهنا بتجيك
+
+512
+00:38:58,070 --> 00:39:01,910
+احتمالاتها الآن بالنسبة للتلت، يا أقل من يا أصغر
+
+513
+00:39:01,910 --> 00:39:10,510
+من إذا كانت X أقل من التلت، التلتين راحوا أو أكبر
+
+514
+00:39:10,510 --> 00:39:14,850
+من التلت، برضه التلتين راحوا لأنه بخل الجزء هذا
+
+515
+00:39:14,850 --> 00:39:18,250
+فقط، فبتصير هذه I جديدة وجيه جديدة
+
+516
+00:39:20,630 --> 00:39:25,150
+صح؟ برضه فإذا أنا بدل ما أعمل elimination لان نص
+
+517
+00:39:25,150 --> 00:39:30,730
+اعملت elimination لتلتين طبعا بعد هي اتحسن على
+
+518
+00:39:30,730 --> 00:39:35,590
+الموضوع هذا و بندرسها أكتر في الماجستير أنه بنحطها
+
+519
+00:39:35,590 --> 00:39:38,790
+نسبة معينة للي بده يشتغل في ال iterations فبيسموها
+
+520
+00:39:38,790 --> 00:39:42,070
+النسبة الذهبية اللي هي فاصلة ستة واحد تمانية اشي
+
+521
+00:39:42,070 --> 00:39:45,450
+تاني بس احنا دلوقتي خلينا فيها في الفكرة نفسها
+
+522
+00:39:45,450 --> 00:39:50,640
+اللي هي الternary search أو البحث الثلاثيالبحث
+
+523
+00:39:50,640 --> 00:39:54,260
+الثلاثي هذه من الحاجات اللي ممكن تيجي كأكواد مثلا
+
+524
+00:39:54,260 --> 00:39:58,360
+في ال .. في data structure في إشي اللي هو يلا
+
+525
+00:39:58,360 --> 00:40:02,680
+فكرولنا كيف تعملولها code فكروا كيف تعملولها code
+
+526
+00:40:02,680 --> 00:40:06,800
+فعشان نعمللها code الفكرة فهمناها بكل بساطة هتبدأ
+
+527
+00:40:06,800 --> 00:40:11,860
+procedure ال procedure ده إيش بده؟ بده ال sequence
+
+528
+00:40:11,860 --> 00:40:14,120
+أو ال array اللي انت بدك تدخله إياها لأنك بتبقى
+
+529
+00:40:14,120 --> 00:40:19,150
+عارف ال array اللي موجودةكويس و مجموعة عناصرها من
+
+530
+00:40:19,150 --> 00:40:24,490
+1 to N و increasing integers بمعنى ان هي ordered
+
+531
+00:40:24,490 --> 00:40:29,210
+بمعنى ordered جيد مش ordered معناته بدك تفهم
+
+532
+00:40:29,210 --> 00:40:33,530
+علامات ال insertion بدك تبدأ بال search على كل
+
+533
+00:40:33,530 --> 00:40:38,710
+عنصر ثم بستنى ال search عشان تبدأ هتبدأ ternary
+
+534
+00:40:38,710 --> 00:40:44,290
+searchمش binary search، هيشتغل على ternary search،
+
+535
+00:40:44,290 --> 00:40:50,530
+جيد، هتقل؟ أه هتقل، لكن ال order هو هو، إيش ال
+
+536
+00:40:50,530 --> 00:40:53,210
+order أو ال complexity بتاعة ال binary؟
+
+537
+00:40:53,210 --> 00:40:55,450
+logarithmic، صح؟ و هذا هتظهر logarithmic، إيش
+
+538
+00:40:55,450 --> 00:41:00,390
+الاختلاف بينهم؟الـ base بس هذه كانت log2 هذه log3
+
+539
+00:41:00,390 --> 00:41:04,950
+فlog3 احنا عارفين انه هتجلل اكتر كقيمة عددية
+
+540
+00:41:04,950 --> 00:41:09,590
+هتعطيني اقل عدد لكن ك order ضال واحد هو ال
+
+541
+00:41:09,590 --> 00:41:13,410
+algorithmic ك order مش يعني ماعملي يعني ماطورتش في
+
+542
+00:41:13,410 --> 00:41:17,370
+المسمة زيادة لكن على عرض الواقع اه هتتجل شوية
+
+543
+00:41:17,370 --> 00:41:21,930
+الأمور كعدد iterations تمام فهي أول خطوة الخطوة
+
+544
+00:41:21,930 --> 00:41:28,790
+التانية بتحدد البداية والنهايةI و J على أساس إن
+
+545
+00:41:28,790 --> 00:41:35,670
+هما 1 و N أول عنصر ال index الأول و الأخير عشان
+
+546
+00:41:35,670 --> 00:41:38,690
+نبدأ الآن نفس الفكرة اللي قولناها في ال binary في
+
+547
+00:41:38,690 --> 00:41:41,610
+ال binary كنت ببدأ أعمل elimination و أجلل ال
+
+548
+00:41:41,610 --> 00:41:46,760
+durationلما يصبح عندى one element خلاص اذا هو ال
+
+549
+00:41:46,760 --> 00:41:50,480
+one element انتهى ماضالش مجال افحص فيه فانت بيبين
+
+550
+00:41:50,480 --> 00:41:53,500
+ال one element طول ما في عندي I اللي هي البداية
+
+551
+00:41:53,500 --> 00:42:00,120
+اقل من j ناقص واحد معناته في بينهم لسه قيم ما زالت
+
+552
+00:42:00,120 --> 00:42:04,500
+في بينهم قيم اذا ما تحققتش معناته فعليا I صارت
+
+553
+00:42:04,500 --> 00:42:10,750
+اكبر من صارت اكبر من معناته صاروا بيساوي بعضإذا
+
+554
+00:42:10,750 --> 00:42:13,630
+سوا بعض، لاحظ طالع فيهم، إذا سوا بعض، طب هي دي
+
+555
+00:42:13,630 --> 00:42:17,710
+أقل، ناقص واحد، صارت فيها الأقل، فتصبح أقل على
+
+556
+00:42:17,710 --> 00:42:21,130
+طول، فإذا بيختل ال condition، وإذا اختل ال
+
+557
+00:42:21,130 --> 00:42:24,290
+condition، اطلع خارج ال loop، بطل في مساحة تدور
+
+558
+00:42:24,290 --> 00:42:28,170
+فيها، لأ، بدنا نفترض إن لسه المساحة موجودة، عشان
+
+559
+00:42:28,170 --> 00:42:33,930
+نبدأ نعمل عمليةالـ lower و ال upper بدل ما كنت
+
+560
+00:42:33,930 --> 00:42:37,010
+بتتكلم عن ال midpoint ال lower point و ال upper
+
+561
+00:42:37,010 --> 00:42:40,450
+point أو اللي هي التلت و مين و التلتين و اللي
+
+562
+00:42:40,450 --> 00:42:46,090
+بيقول بساطة جدش المسافة بينهم على تلاتة مسافة
+
+563
+00:42:46,090 --> 00:42:49,090
+بينهم على تلاتة اعطتني جدش قيمة هذا الكلام لكن
+
+564
+00:42:49,090 --> 00:42:53,310
+ماعطتنيش القيمة المطلقة للعنصر فهنا اه لأنه انا في
+
+565
+00:42:53,310 --> 00:42:57,030
+مرحل و مرحل I مش هتكون هي الواحد هتتغير مانا هتكون
+
+566
+00:42:57,030 --> 00:43:03,000
+مرة هعمل elimination فلأ زائد ال Iمنطقة زائد ال I
+
+567
+00:43:03,000 --> 00:43:06,360
+فبعرف ان انا موجود هنا الان هذا قيمة ال lower ال
+
+568
+00:43:06,360 --> 00:43:13,820
+upper تلتين ال upper عند التلتين او تقدر تعملها
+
+569
+00:43:13,820 --> 00:43:20,720
+برضه تلت وتعمل J ناقص التلت صح؟نفس الأشياء فهي دي
+
+570
+00:43:20,720 --> 00:43:23,520
+كلها أفكار أي حاجة بمشي معاك في ال data structure
+
+571
+00:43:23,520 --> 00:43:27,700
+لإن انت مفروض تدرسوا أفكار تدرسوا أفكار فنفس
+
+572
+00:43:27,700 --> 00:43:31,500
+الفكرة بدك تبدأ من ال .. من بداية ال .. ال array
+
+573
+00:43:31,500 --> 00:43:39,080
+ولا من نهايتها مش هتكون مشكلة كبيرة تمام الآن بعد
+
+574
+00:43:39,080 --> 00:43:41,240
+يكتب ده الفحص اللي احنا فحصناه هنا اللي احنا
+
+575
+00:43:41,240 --> 00:43:46,180
+عملناه اللي هي روح الموضوع تبعنا ال treeجزئية لتري
+
+576
+00:43:46,180 --> 00:43:49,560
+الآن اللي هي عبارة عن condition وافحصه yes no yes
+
+577
+00:43:49,560 --> 00:43:54,500
+no يبدأ شوف ال yes و ال no هدول فهنبدأ إذا كانت X
+
+578
+00:43:54,500 --> 00:43:58,900
+أكبر من أو يساوي ال A أبر كأنك بتقارنها بالعنصر
+
+579
+00:43:58,900 --> 00:44:02,340
+اللي موجود هنا زي ما عملنا زي ما عملنا بالضبط أكيد
+
+580
+00:44:02,340 --> 00:44:06,450
+هيكون عندك two possibilitiesال possibility الأولى
+
+581
+00:44:06,450 --> 00:44:10,850
+.. الإمكانية الأولى أنه يكون هنا مثلا yes إذا كانت
+
+582
+00:44:10,850 --> 00:44:16,610
+فعلا x أكبر من .. إذا إذا yes على طول I تساوي ال
+
+583
+00:44:16,610 --> 00:44:23,150
+other زائد واحد التلتين الشمال راحوا .. التلتين
+
+584
+00:44:23,150 --> 00:44:26,450
+الشمال راحوا .. ماعنا أي مشكلة فيهم و لاحظوا أن
+
+585
+00:44:26,450 --> 00:44:30,970
+أكبر من ولا تساوي أعطتني إمكانية أقول زائد واحد
+
+586
+00:44:32,270 --> 00:44:36,350
+لأنه ضامن إنه مش متساوي، متساويش، معناته بروح على
+
+587
+00:44:36,350 --> 00:44:38,950
+الأنصار اللي ورا، نروح على الأنصار اللي ورا،
+
+588
+00:44:38,950 --> 00:44:41,550
+عملناها جابل هيك ومفهومة، ماعتقدش إن في عندكم
+
+589
+00:44:41,550 --> 00:44:44,950
+مشكلة فيها Else، هذه else إيش يعني؟ يعني معناته
+
+590
+00:44:44,950 --> 00:44:50,550
+إنه ماروحتش ل yes، هنا روحت ل no، لأنه ماتحققش إنه
+
+591
+00:44:50,550 --> 00:44:54,650
+أكبر من، ماتحققش إنه أكبر من، فإذا هنا هيكون إيش؟
+
+592
+00:44:54,650 --> 00:45:00,130
+أصغر أو يساويخلوا دايما في بالكوا كلمة أو يساوي
+
+593
+00:45:00,130 --> 00:45:06,590
+ايوة ف else if هالوقت صارت كأنه أخدت ال no مع ال
+
+594
+00:45:06,590 --> 00:45:11,570
+condition كمان بكلمة else if أخدنا التنتين مع بعض
+
+595
+00:45:11,570 --> 00:45:18,470
+مع السوا تمام x أكبر من a lower فإذا خلصنا احنا
+
+596
+00:45:18,470 --> 00:45:23,590
+وصلنا لهنا فعليا انا موجود هنا و فعليا أو يساوي
+
+597
+00:45:24,620 --> 00:45:29,280
+لأنه عدينا فكرة إنه هي أكبر من وقلنا إن هي no فانا
+
+598
+00:45:29,280 --> 00:45:33,920
+الآن هنا وهذه تحققت روحت لمين؟ لأكبر من ال lower
+
+599
+00:45:33,920 --> 00:45:42,180
+أكبر من ال lower هنا أنا الآن هنا ليش؟ هنا لأنه
+
+600
+00:45:42,180 --> 00:45:48,080
+مبدأيا ليست أكبر من ال upper اللي هي التلتين ليست
+
+601
+00:45:48,080 --> 00:45:55,570
+أكبر من التلتين وأكبر من ال lowerإيش بنعمل؟
+
+602
+00:46:00,480 --> 00:46:05,780
+معناته هي المنطقة اللي في النص ف automatically if
+
+603
+00:46:05,780 --> 00:46:10,100
+then معناته فعلا تحقق الشرطين ان هي ليست اكبر من
+
+604
+00:46:10,100 --> 00:46:13,120
+ال other بينما هي اكبر من ال lower على طول بروح
+
+605
+00:46:13,120 --> 00:46:21,100
+ايش بسوي بقول ال I هتصبح هي ال lower زائد واحد ليش
+
+606
+00:46:21,100 --> 00:46:24,520
+لأن هنا ماجلتش اوي ساوي فانا عندي اريحية اقول اكبر
+
+607
+00:46:24,520 --> 00:46:31,630
+اقول زائد واحد لكن في ال other لأأيوة، ليش؟ لأن في
+
+608
+00:46:31,630 --> 00:46:34,850
+القبر هي جايانة من وين الآن الحالة؟ جايانة من إنه
+
+609
+00:46:34,850 --> 00:46:40,590
+ليست أكبر من طب ليست أكبر من، كنت ساوي، صح؟ فاخدوا
+
+610
+00:46:40,590 --> 00:46:44,410
+بالكم من الحاجات الرفيعة هذه اللي ممكن تعمللكم
+
+611
+00:46:44,410 --> 00:46:48,770
+Logic Error وانت مش عارف حاجات بسيطة زي هيك ممكن
+
+612
+00:46:48,770 --> 00:46:51,610
+تعملك Logic Error إنه إيه؟ إنه لو إجتك القيمة فعلا
+
+613
+00:46:51,610 --> 00:46:55,710
+دي جاية في القبر هتلاقي إن أنت بدك تعمل زائد واحد،
+
+614
+00:46:55,710 --> 00:47:00,750
+ضيعتهاضيعته فعلا فالقيمة موجودة بس ال code تبعك ما
+
+615
+00:47:00,750 --> 00:47:05,710
+جابهاش فأخدنا بالنا ليش بعمل مرات زائد واحد و بنوت
+
+616
+00:47:05,710 --> 00:47:10,850
+زائد واحد حسب ال condition و عكسه ال inverse تبعه
+
+617
+00:47:10,850 --> 00:47:15,890
+مش ال complement أخدنا كذا مرة نقولكم هد غير هدي
+
+618
+00:47:15,890 --> 00:47:19,730
+هد غير هدي هد غير صح تمام واضحت حتى اللحظة حتى
+
+619
+00:47:19,730 --> 00:47:25,170
+اللحظة خلصنا أننا هنا و خلصنا أننا هنا بلت الحالة
+
+620
+00:47:25,170 --> 00:47:32,530
+القلص الأخيرةأيوة else أنا عارف إيش اللي ضلت فخلاص
+
+621
+00:47:32,530 --> 00:47:35,770
+اللي ضلت أن ال j هي اللي تجيهني على من؟ على ال
+
+622
+00:47:35,770 --> 00:47:40,590
+lower معناته أنا هنا في الحالة التالتة اللي هي في
+
+623
+00:47:40,590 --> 00:47:45,110
+البداية معناته اللي هو ال ال ال j هذه حطليها هنا
+
+624
+00:47:45,110 --> 00:47:49,510
+وصرت أن أنا ببحث في الجزء هذا تمام؟
+
+625
+00:47:50,810 --> 00:47:55,470
+خلصنا فالان هيك بنكون عملنا end لمين؟ لل beginning
+
+626
+00:47:55,470 --> 00:47:59,030
+اللي كنت فاتحها فكل هذا بنعمل لكل .. في كل
+
+627
+00:47:59,030 --> 00:48:03,950
+iteration في كل loop .. في كل loop بناء على كل
+
+628
+00:48:03,950 --> 00:48:08,990
+loop بتتغير عندى يا قيمة I يا قيمة J يا قيمة
+
+629
+00:48:08,990 --> 00:48:15,090
+الاتنين صح؟ إما J بتروح للتلت أو I بتروح للتلتين
+
+630
+00:48:15,090 --> 00:48:22,060
+أو J بتروح للتلتين و I بتروح للتلتفحسب التلت اتلت
+
+631
+00:48:22,060 --> 00:48:24,840
+هدوله واحد منهم هو اللي هينتش في النهاية فانا بكون
+
+632
+00:48:24,840 --> 00:48:28,780
+في جميع الأحوال عملت elimination لتلتين بدل نص في
+
+633
+00:48:28,780 --> 00:48:32,800
+ال binary okay في الآخر بنعمل عملية الفحص النهائي
+
+634
+00:48:32,800 --> 00:48:36,820
+بمجرد ما صار عنده I و J نفس القيمة يعني أنا بتكلم
+
+635
+00:48:36,820 --> 00:48:39,220
+في النهاية صفيت على نقطة واحدة النقطة الواحدة هادى
+
+636
+00:48:39,220 --> 00:48:44,140
+بده افحص لحالها هيا X هل تساوي I طب أنا عارف ان I
+
+637
+00:48:44,140 --> 00:48:48,480
+هي الوحيد اللي دلت الآن يا بتسويها يا بتسويهاشهل
+
+638
+00:48:48,480 --> 00:48:52,040
+بتسويها إذا و الله بتسويها إذا نرجع لقيمة I ال
+
+639
+00:48:52,040 --> 00:48:54,600
+index I لأن أنا عرفتها هنا بقولك هي موجودة في ال
+
+640
+00:48:54,600 --> 00:48:58,220
+location العشر في ال array امشي عشر خطوات هتلاقيها
+
+641
+00:48:58,220 --> 00:49:03,920
+هاي القيمة اللي أنت بدك إيها خلصنا طيب else if x j
+
+642
+00:49:03,920 --> 00:49:09,200
+هيظلت عندك I و J التتين اللي ضالة موجودين عندك قد
+
+643
+00:49:09,200 --> 00:49:14,680
+يصبحوا بيساوي بعض أو عكسوا بعض يعني صارت واحدة
+
+644
+00:49:14,680 --> 00:49:18,680
+جابل التانيةلأن هنا برضه أنت عندك احتمال يأمنوا
+
+645
+00:49:18,680 --> 00:49:25,220
+بسوء بعض أو J صارت أصغر من I الاحتمالين وردين فإذا
+
+646
+00:49:25,220 --> 00:49:30,100
+ممكن يطلعوا هم قيمتين مش قيمة اللي ضالوا بدك تفحص
+
+647
+00:49:30,100 --> 00:49:33,940
+التنتين برضه ترجع قيمة الـJ لا هذي حصلت ولا هذي
+
+648
+00:49:33,940 --> 00:49:38,980
+حصلتصفر انا مالجتهش اصلا الرقم هو الرقم اصلا مش
+
+649
+00:49:38,980 --> 00:49:43,820
+موجود ال X هذه مش موجودة و نهينا بال location اللي
+
+650
+00:49:43,820 --> 00:49:50,830
+هيكون يا I يا J يا 0 اذا مش موجودةكيف؟ لمّين
+
+651
+00:49:50,830 --> 00:49:56,190
+المنهج هنا؟ هيك احنا بالظبط خلصنا منهجنا كل عام
+
+652
+00:49:56,190 --> 00:49:59,370
+تبخير الجزء المتبقي زي ما قلنالكم هنعمل مراجعة
+
+653
+00:49:59,370 --> 00:50:02,390
+أسئلة امتحانات على أسئلة من الكتاب من المواضيع
+
+654
+00:50:02,390 --> 00:50:05,430
+اللي انتوا عندكم مشكلة فيها اللي فهمتوا أنه بدكوا
+
+655
+00:50:05,430 --> 00:50:08,730
+حاجة نركز أكتر في ال inductionمن الشباب يعرفت ان
+
+656
+00:50:08,730 --> 00:50:11,450
+ال induction شوية عندكوا فخلينا معناه طول مرة
+
+657
+00:50:11,450 --> 00:50:15,070
+القادمة ان شاء الله الأسبوع القادم هجيب .. نخليها
+
+658
+00:50:15,070 --> 00:50:17,830
+أسئلة عن ال induction في البداية و بعدين نشوف إيش
+
+659
+00:50:17,830 --> 00:50:20,390
+المواضيع اللي عندكم فيها نقص و عندكم فيها مشكلة و
+
+660
+00:50:20,390 --> 00:50:24,010
+نكمل أسئلة الآن أسئلة اللي هي إما من امتحانات و
+
+661
+00:50:24,010 --> 00:50:26,570
+هحط الأولوية للأسئلة تاعة الامتحانات اللي جيبناهم
+
+662
+00:50:26,570 --> 00:50:28,790
+في امتحانات سابقة اللي هي علاقة بال induction و
+
+663
+00:50:28,790 --> 00:50:31,150
+بعدين هنروح للكتاب إيش الأفكار الزيادة اللي ممكن
+
+664
+00:50:31,150 --> 00:50:34,530
+تكون في جزئية ال induction يعطيكوا العافية كل عام
+
+665
+00:50:34,530 --> 00:50:34,970
+انتوا بخير
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/HU3y5NBu3E8_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/HU3y5NBu3E8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ab958b0b2aa21d5a844721c703e2f2a25fe1d333
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/HU3y5NBu3E8_raw.json
@@ -0,0 +1 @@
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"probability": 0.966796875}, {"start": 164.03, "end": 164.11, "word": " إذا", "probability": 0.6826171875}, {"start": 164.11, "end": 164.27, "word": " كان", "probability": 0.97705078125}, {"start": 164.27, "end": 164.39, "word": " في", "probability": 0.95361328125}, {"start": 164.39, "end": 164.61, "word": " z", "probability": 0.7783203125}, {"start": 164.61, "end": 165.01, "word": " بتجيبوا", "probability": 0.9369140625}, {"start": 165.01, "end": 165.19, "word": " z", "probability": 0.86083984375}, {"start": 165.19, "end": 165.29, "word": " و", "probability": 0.96337890625}, {"start": 165.29, "end": 165.39, "word": " إذا", "probability": 0.84521484375}, {"start": 165.39, "end": 165.53, "word": " كان", "probability": 0.96630859375}, {"start": 165.53, "end": 165.67, "word": " في", "probability": 0.94677734375}, {"start": 165.67, "end": 166.31, "word": " أكتر", "probability": 0.9136962890625}, {"start": 166.31, "end": 166.47, "word": " من", "probability": 0.98046875}, {"start": 166.47, "end": 166.63, "word": " هيك", "probability": 0.779296875}, {"start": 166.63, "end": 167.31, "word": " بتجيبوا", "probability": 0.97060546875}, {"start": 167.31, "end": 167.65, "word": " ال", "probability": 0.91357421875}, {"start": 167.65, "end": 170.31, "word": " equations", "probability": 0.389892578125}, {"start": 170.31, "end": 170.67, "word": " أو", "probability": 0.83544921875}, {"start": 170.67, "end": 171.47, "word": " المتغيرات", "probability": 0.98212890625}, {"start": 171.47, "end": 171.89, "word": " بتاعتكم", "probability": 0.870849609375}, {"start": 171.89, "end": 172.67, "word": " تمام", "probability": 0.7939453125}, {"start": 172.67, "end": 173.99, "word": " ممكن", "probability": 0.896484375}, {"start": 173.99, "end": 174.37, "word": " تكون", "probability": 0.992431640625}, {"start": 174.37, "end": 174.59, "word": " في", "probability": 0.96923828125}, {"start": 174.59, "end": 174.69, "word": " ال", "probability": 0.74462890625}, {"start": 174.69, "end": 174.99, "word": " graphics", "probability": 0.92333984375}], "temperature": 1.0}, {"id": 8, "seek": 19247, "start": 175.97, "end": 192.47, "text": "و ال image processing لما نتكلم في ال graphics او ال image processing اول شغلة هي ال image نفسها تعرف ب 2D array اذا انتم متذكرين في ال برمجة فمعناه ذلك ان هي matrix في النهاية matrix كل element هو عبارة عن", "tokens": [2407, 2423, 3256, 9007, 5296, 15042, 8717, 2655, 4117, 19528, 8978, 2423, 11837, 1975, 2407, 2423, 3256, 9007, 1975, 12610, 13412, 17082, 37977, 39896, 2423, 3256, 8717, 36178, 11296, 37279, 28480, 4724, 568, 35, 10225, 1975, 15730, 16472, 39237, 44650, 8848, 37983, 9957, 8978, 2423, 4724, 2288, 2304, 7435, 3660, 6156, 2304, 3615, 8315, 3224, 29910, 23275, 16472, 39896, 8141, 8978, 28239, 11296, 10632, 8141, 28242, 4478, 31439, 6225, 3555, 9640, 3660, 18871], "avg_logprob": -0.2347972983041325, "compression_ratio": 1.581151832460733, "no_speech_prob": 1.4185905456542969e-05, "words": [{"start": 175.97, "end": 176.31, "word": "و", 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0.97265625}, {"start": 180.83, "end": 181.19, "word": " اول", "probability": 0.833740234375}, {"start": 181.19, "end": 181.55, "word": " شغلة", "probability": 0.7980143229166666}, {"start": 181.55, "end": 181.73, "word": " هي", "probability": 0.8095703125}, {"start": 181.73, "end": 181.85, "word": " ال", "probability": 0.9423828125}, {"start": 181.85, "end": 182.03, "word": " image", "probability": 0.9423828125}, {"start": 182.03, "end": 182.61, "word": " نفسها", "probability": 0.9871419270833334}, {"start": 182.61, "end": 183.79, "word": " تعرف", "probability": 0.909912109375}, {"start": 183.79, "end": 184.07, "word": " ب", "probability": 0.72216796875}, {"start": 184.07, "end": 184.45, "word": " 2D", "probability": 0.6171875}, {"start": 184.45, "end": 184.99, "word": " array", "probability": 0.78857421875}, {"start": 184.99, "end": 185.57, "word": " اذا", "probability": 0.6510009765625}, {"start": 185.57, "end": 185.75, "word": " انتم", "probability": 0.6552734375}, {"start": 185.75, 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to M، to M هذه نتكلم عن الأعمد، الصفوف، نتكلم عن إيش؟ الصفوف، فإذا ال matrix هنا نتعامل معاها M في N، مدام M في N فانا عارف ان ال M هنا للصفوف، لل رو، في ال N اللي هي لل إش، للأعمدة، فهتلاقي أن أكبر رقم في الأعمدة هيكون قيمة ال إيش؟ ال N", "tokens": [2407, 24401, 281, 376, 12399, 281, 376, 29538, 8717, 2655, 4117, 19528, 18871, 16247, 25957, 3215, 12399, 31767, 5172, 38688, 12399, 8717, 2655, 4117, 19528, 18871, 11933, 1829, 8592, 22807, 31767, 5172, 38688, 12399, 6156, 28814, 15730, 2423, 8141, 34105, 8717, 2655, 3615, 10943, 1211, 20449, 995, 11296, 376, 8978, 426, 12399, 3714, 3215, 10943, 376, 8978, 426, 6156, 7649, 995, 6225, 9640, 5172, 16472, 2423, 376, 34105, 24976, 9381, 5172, 38688, 12399, 24976, 12602, 2407, 12399, 8978, 2423, 426, 13672, 1829, 39896, 24976, 11933, 8592, 12399, 24976, 10721, 25957, 41891, 12399, 6156, 3224, 2655, 15040, 38436, 14739, 5551, 4117, 26890, 12602, 4587, 2304, 8978, 16247, 25957, 41891, 39896, 30544, 12174, 32640, 3660, 2423, 11933, 1829, 8592, 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"text": "يعني بدك تبدأ من واحد ماشي بدك تبدو زي ما كنتوا في البرمجة بتبدو ال rate بتبعتكم من zero بمش الحال برضه ك index ببدأ من zero اه ممكن ال pointer تبعك على طول يعمل يكون referring لل zero مباشرة بمش الحال نفس الكلام ال column مشموعة ال columns اللي عندك هي تنتمي ل natural number برضه بتبدأ ايه من صفر او من واحد وبتستمر حسب حجم ال matrix تبعتك حسب حجم ال matrix فهنا هدول ال input اعطيني", "tokens": [40228, 22653, 47525, 4117, 6055, 44510, 10721, 9154, 36764, 24401, 3714, 33599, 1829, 47525, 4117, 6055, 44510, 2407, 30767, 1829, 19446, 9122, 29399, 14407, 8978, 2423, 26890, 2304, 7435, 3660, 39894, 44510, 2407, 2423, 3314, 39894, 3555, 34268, 24793, 9154, 4018, 4724, 2304, 8592, 21542, 6027, 4724, 43042, 3224, 9122, 8186, 4724, 44510, 10721, 9154, 4018, 1975, 3224, 3714, 43020, 2423, 23918, 6055, 3555, 3615, 4117, 15844, 23032, 12610, 7251, 25957, 1211, 7251, 30544, 13761, 24976, 4018, 3714, 3555, 33599, 25720, 4724, 2304, 8592, 21542, 6027, 8717, 36178, 2423, 28820, 10943, 2423, 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"temperature": 1.0}, {"id": 27, "seek": 63767, "start": 610.38, "end": 637.68, "text": "ال location تبع ال row بتاع ال column عشان اعطيك ال value قيمته فقيمته هتكون هي set او عناصر set بس كل عنصر من عناصر ال set هذه معرف بمين بال location تبعه فإذا بقدر أسميها الآن مدام أفهمناها بقدر أقول أن ال function لل matrix A from natural by natural numbers اللي هي ال row by column", "tokens": [6027, 4914, 6055, 3555, 3615, 2423, 5386, 39894, 45761, 2423, 7738, 6225, 8592, 7649, 1975, 3615, 9566, 1829, 4117, 2423, 2158, 12174, 32640, 47395, 6156, 4587, 32640, 47395, 8032, 2655, 30544, 39896, 992, 1975, 2407, 18871, 33546, 2288, 992, 4724, 3794, 28242, 18871, 9381, 2288, 9154, 18871, 33546, 2288, 2423, 992, 29538, 20449, 28480, 4724, 2304, 9957, 20666, 4914, 6055, 3555, 3615, 3224, 6156, 28814, 15730, 4724, 28543, 2288, 5551, 38251, 1829, 11296, 6024, 48506, 3714, 3215, 10943, 5551, 5172, 16095, 8315, 11296, 4724, 28543, 2288, 5551, 39648, 14739, 2423, 2445, 24976, 8141, 316, 490, 3303, 538, 3303, 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code domain أو لل range سبعكم S هذه ال set of elements انهم elements ال elements تبعون ال matrix عناصر ال matrix نفسها لما نقول في عندي matrix بهذا الشكل ال matrix هذه واحد اتنين خمسة سبعة ففعليا العناصر بتاعتنا بنتكلم عن واحد اتنين خمسة سبعة as a S", "tokens": [2655, 4587, 33599, 24976, 3089, 9274, 34051, 24976, 3613, 8608, 3555, 3615, 24793, 318, 29538, 2423, 992, 295, 4959, 16472, 16095, 4959, 2423, 4959, 6055, 3555, 3615, 11536, 2423, 8141, 18871, 33546, 2288, 2423, 8141, 8717, 36178, 11296, 5296, 15042, 8717, 39648, 8978, 18871, 16254, 8141, 39627, 15730, 25124, 28820, 2423, 8141, 29538, 36764, 24401, 1975, 2655, 1863, 9957, 16490, 2304, 3794, 3660, 8608, 3555, 27884, 6156, 5172, 3615, 20292, 995, 18863, 1863, 33546, 2288, 39894, 995, 34268, 8315, 44945, 2655, 4117, 19528, 18871, 36764, 24401, 1975, 2655, 1863, 9957, 16490, 2304, 3794, 3660, 8608, 3555, 27884, 382, 257, 318], "avg_logprob": -0.2250928247329032, "compression_ratio": 1.835680751173709, "no_speech_prob": 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location", "probability": 0.98681640625}, {"start": 678.06, "end": 678.44, "word": " تبعهم", "probability": 0.923583984375}, {"start": 678.44, "end": 678.54, "word": " في", "probability": 0.8447265625}, {"start": 678.54, "end": 678.84, "word": " الحالة", "probability": 0.9117838541666666}, {"start": 678.84, "end": 679.18, "word": " دي", "probability": 0.61474609375}, {"start": 679.18, "end": 679.72, "word": " اذا", "probability": 0.74755859375}, {"start": 679.72, "end": 680.16, "word": " بتكلم", "probability": 0.89208984375}, {"start": 680.16, "end": 680.5, "word": " عن", "probability": 0.98974609375}, {"start": 680.5, "end": 681.98, "word": " مربع", "probability": 0.8068033854166666}, {"start": 681.98, "end": 682.72, "word": " بده", "probability": 0.54736328125}, {"start": 682.72, "end": 683.06, "word": " يكون", "probability": 0.9892578125}, {"start": 683.06, "end": 683.96, "word": " الرقم", "probability": 0.9627278645833334}, {"start": 683.96, "end": 684.24, "word": " تبع", "probability": 0.95947265625}, {"start": 684.24, "end": 684.68, "word": " الصف", "probability": 0.974365234375}, {"start": 684.68, "end": 685.0, "word": " و", "probability": 0.8583984375}, {"start": 685.0, "end": 686.08, "word": " رقم", "probability": 0.817626953125}, {"start": 686.08, "end": 686.66, "word": " العمود", "probability": 0.96044921875}, {"start": 686.66, "end": 687.68, "word": " اعطيني", "probability": 0.90615234375}, {"start": 687.68, "end": 688.42, "word": " رقم", "probability": 0.9943033854166666}, {"start": 688.42, "end": 688.9, "word": " و", "probability": 0.9677734375}, {"start": 688.9, "end": 689.74, "word": " رقم", "probability": 0.98291015625}, {"start": 689.74, "end": 690.3, "word": " ك", "probability": 0.96142578125}, {"start": 690.3, "end": 691.12, "word": " two", "probability": 0.7412109375}, {"start": 691.12, "end": 691.66, "word": " indices", "probability": 0.9404296875}, {"start": 691.66, "end": 692.48, "word": " عشان", "probability": 0.9788411458333334}, 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"تفهم؟ ناقص واحد فبديش و أنت بتقرا و بعدين تتخربط معاكوا لأ لأ نسينا أو يساوي لأ مش أي ساوي لأن احنا بدين بال natural number لما أعرفها من هنا positive okay بتصير أو يساوي لما نعرفها positive integers بتصير يساوي طيب فبنقدر نقول أن ال function ل ال matrix A", "tokens": [2655, 5172, 16095, 22807, 8717, 995, 4587, 9381, 36764, 24401, 6156, 3555, 16254, 8592, 4032, 14739, 2655, 39894, 4587, 23557, 4032, 39182, 9957, 6055, 2655, 34740, 3555, 9566, 20449, 995, 4117, 14407, 5296, 10721, 5296, 10721, 8717, 3794, 1829, 8315, 34051, 7251, 3794, 995, 45865, 5296, 10721, 37893, 36632, 8608, 995, 45865, 5296, 33456, 1975, 5016, 8315, 47525, 9957, 20666, 3303, 1230, 5296, 15042, 5551, 3615, 28480, 11296, 9154, 34105, 3353, 1392, 39894, 9381, 13546, 34051, 7251, 3794, 995, 45865, 5296, 15042, 8717, 3615, 28480, 11296, 3353, 41674, 39894, 9381, 13546, 7251, 3794, 995, 45865, 23032, 1829, 3555, 6156, 3555, 1863, 28543, 2288, 8717, 39648, 14739, 2423, 2445, 5296, 2423, 8141, 316], "avg_logprob": 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0.730712890625}, {"start": 784.37, "end": 784.51, "word": " بال", "probability": 0.8125}, {"start": 784.51, "end": 784.81, "word": " natural", "probability": 0.689453125}, {"start": 784.81, "end": 785.29, "word": " number", "probability": 0.97802734375}, {"start": 785.29, "end": 785.77, "word": " لما", "probability": 0.950439453125}, {"start": 785.77, "end": 786.17, "word": " أعرفها", "probability": 0.8514404296875}, {"start": 786.17, "end": 786.31, "word": " من", "probability": 0.974609375}, {"start": 786.31, "end": 786.55, "word": " هنا", "probability": 0.99560546875}, {"start": 786.55, "end": 787.87, "word": " positive", "probability": 0.9189453125}, {"start": 787.87, "end": 788.33, "word": " okay", "probability": 0.51220703125}, {"start": 788.33, "end": 788.69, "word": " بتصير", "probability": 0.9645182291666666}, {"start": 788.69, "end": 788.85, "word": " أو", "probability": 0.94384765625}, {"start": 788.85, "end": 789.29, "word": " يساوي", "probability": 0.9849853515625}, {"start": 789.29, "end": 789.99, "word": " لما", "probability": 0.947998046875}, {"start": 789.99, "end": 790.33, "word": " نعرفها", "probability": 0.8472900390625}, {"start": 790.33, "end": 790.85, "word": " positive", "probability": 0.89697265625}, {"start": 790.85, "end": 791.69, "word": " integers", "probability": 0.89501953125}, {"start": 791.69, "end": 792.37, "word": " بتصير", "probability": 0.96484375}, {"start": 792.37, "end": 793.09, "word": " يساوي", "probability": 0.987548828125}, {"start": 793.09, "end": 793.81, "word": " طيب", "probability": 0.9117838541666666}, {"start": 793.81, "end": 794.41, "word": " فبنقدر", "probability": 0.93037109375}, {"start": 794.41, "end": 794.71, "word": " نقول", "probability": 0.991455078125}, {"start": 794.71, "end": 795.49, "word": " أن", "probability": 0.468017578125}, {"start": 795.49, "end": 795.61, "word": " ال", "probability": 0.86376953125}, {"start": 795.61, "end": 796.11, "word": " function", "probability": 0.96044921875}, {"start": 796.11, "end": 796.53, "word": " ل", "probability": 0.68115234375}, {"start": 796.53, "end": 796.63, "word": " ال", "probability": 0.416015625}, {"start": 796.63, "end": 796.95, "word": " matrix", "probability": 0.95751953125}, {"start": 796.95, "end": 797.29, "word": " A", "probability": 0.8154296875}], "temperature": 1.0}, {"id": 34, "seek": 81499, "start": 798.41, "end": 814.99, "text": "Given ال location I و J هو العنصر الموجود في I و J فإذا هنا تعريف أزا matrix الآن بعض العملية البسيطة اللي أخدتها سابقا عشان نعمل summation ل ال matrices محتاجين", "tokens": [38, 5709, 2423, 4914, 286, 4032, 508, 31439, 18863, 1863, 9381, 2288, 9673, 29245, 23328, 8978, 286, 4032, 508, 6156, 28814, 15730, 34105, 37279, 16572, 5172, 5551, 11622, 995, 8141, 6024, 48506, 45030, 11242, 18863, 42213, 10632, 29739, 3794, 1829, 9566, 3660, 13672, 1829, 5551, 9778, 3215, 2655, 11296, 8608, 16758, 4587, 995, 6225, 8592, 7649, 8717, 25957, 1211, 28811, 5296, 2423, 32284, 3714, 33753, 26108, 9957], "avg_logprob": -0.2833180076935712, "compression_ratio": 1.4022346368715084, "no_speech_prob": 0.0001558065414428711, "words": [{"start": 798.41, "end": 798.85, "word": "Given", "probability": 0.478271484375}, {"start": 798.85, "end": 799.17, "word": " ال", "probability": 0.259521484375}, {"start": 799.17, "end": 799.57, "word": " location", "probability": 0.9033203125}, {"start": 799.57, "end": 799.93, "word": " I", "probability": 0.7294921875}, {"start": 799.93, "end": 800.13, "word": " و", "probability": 0.59423828125}, {"start": 800.13, "end": 800.35, "word": " J", "probability": 0.497314453125}, {"start": 800.35, "end": 800.73, "word": " هو", "probability": 0.90234375}, {"start": 800.73, "end": 801.65, "word": " العنصر", "probability": 0.9493408203125}, {"start": 801.65, "end": 802.15, "word": " الموجود", "probability": 0.8203125}, {"start": 802.15, "end": 802.27, "word": " في", "probability": 0.92333984375}, {"start": 802.27, "end": 804.31, "word": " I", "probability": 0.9404296875}, {"start": 804.31, "end": 804.87, "word": " و", "probability": 0.93310546875}, {"start": 804.87, "end": 805.03, "word": " J", "probability": 0.71533203125}, {"start": 805.03, "end": 805.39, "word": " فإذا", "probability": 0.4276529947916667}, {"start": 805.39, "end": 805.59, "word": " هنا", "probability": 0.436767578125}, {"start": 805.59, "end": 805.93, "word": " تعريف", "probability": 0.9689127604166666}, {"start": 805.93, "end": 806.25, "word": " أزا", "probability": 0.50732421875}, {"start": 806.25, "end": 806.89, "word": " matrix", "probability": 0.58203125}, {"start": 806.89, "end": 807.57, "word": " الآن", "probability": 0.6087646484375}, {"start": 807.57, "end": 808.27, "word": " بعض", "probability": 0.960693359375}, {"start": 808.27, "end": 808.65, "word": " العملية", "probability": 0.9236653645833334}, {"start": 808.65, "end": 809.25, "word": " البسيطة", "probability": 0.98095703125}, {"start": 809.25, "end": 810.19, "word": " اللي", "probability": 0.8935546875}, {"start": 810.19, "end": 810.69, "word": " أخدتها", "probability": 0.78212890625}, {"start": 810.69, "end": 811.17, "word": " سابقا", "probability": 0.9647216796875}, {"start": 811.17, "end": 811.59, "word": " عشان", "probability": 0.9034830729166666}, {"start": 811.59, "end": 811.99, "word": " نعمل", "probability": 0.9928385416666666}, {"start": 811.99, "end": 812.65, "word": " summation", "probability": 0.9052734375}, {"start": 812.65, "end": 813.19, "word": " ل", "probability": 0.84033203125}, {"start": 813.19, "end": 813.47, "word": " ال", "probability": 0.43603515625}, {"start": 813.47, "end": 813.87, "word": " matrices", "probability": 0.9609375}, {"start": 813.87, "end": 814.99, "word": " محتاجين", "probability": 0.979248046875}], "temperature": 1.0}, {"id": 35, "seek": 84272, "start": 815.9, "end": 842.72, "text": "أول شغلة أن الاتنين بتساوي في الأبعاد فإذا إن لهم نفس ال rows نفس ال columns ثم بعمل الان summation لكل number مع ال corresponding له في ال matrix التانية عشان ينتج أنصر في matrix منتجة أو horizontal matrix المنتجة اللي ناجحة في الآخر تمام ماعتقدش أن فيها مشكلة و الأمثلة كتير واضحة على هذا الموضوع", "tokens": [10721, 12610, 13412, 17082, 37977, 14739, 2423, 9307, 1863, 9957, 39894, 3794, 995, 45865, 8978, 16247, 3555, 3615, 18513, 6156, 28814, 15730, 36145, 5296, 16095, 8717, 36178, 2423, 13241, 8717, 36178, 2423, 13766, 38637, 2304, 4724, 25957, 1211, 2423, 7649, 28811, 5296, 28820, 1230, 20449, 2423, 11760, 46740, 8978, 2423, 8141, 16712, 7649, 10632, 6225, 8592, 7649, 7251, 29399, 7435, 14739, 9381, 2288, 8978, 8141, 9154, 2655, 7435, 3660, 34051, 12750, 8141, 9673, 29399, 7435, 3660, 13672, 1829, 8717, 26108, 5016, 3660, 8978, 6024, 95, 34740, 46811, 10943, 19446, 34268, 28543, 8592, 14739, 8978, 11296, 37893, 28820, 3660, 4032, 16247, 2304, 12984, 37977, 9122, 2655, 13546, 4032, 46958, 5016, 3660, 15844, 23758, 9673, 2407, 11242, 45367], "avg_logprob": -0.19017093507652608, "compression_ratio": 1.7050359712230216, 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product dot product ان انا بدرب vector ب vector ايه ال vector ب ايه ال vector ال vector اللي هو عبارة عن ال role الأولى في ال column التانية role الأولى في ال column التانية هنا أشهر معرفة من ال K فإذا لو قلنا M في K هذه matrix أولى", "tokens": [1211, 19452, 34105, 44945, 2655, 4117, 19528, 18871, 13412, 2407, 10632, 16490, 9381, 2407, 9381, 10632, 8978, 10874, 11622, 19986, 10632, 6024, 114, 25513, 16472, 1975, 5016, 8315, 44945, 2655, 3615, 10943, 1211, 20449, 11331, 26108, 3660, 24525, 2304, 11296, 5893, 1674, 5893, 1674, 16472, 1975, 8315, 47525, 25513, 8062, 4724, 8062, 1975, 1829, 3224, 2423, 8062, 4724, 1975, 1829, 3224, 2423, 8062, 2423, 8062, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 2423, 3090, 16247, 12610, 7578, 8978, 2423, 7738, 16712, 7649, 10632, 3090, 16247, 12610, 7578, 8978, 2423, 7738, 16712, 7649, 10632, 34105, 5551, 8592, 3224, 2288, 20449, 28480, 3660, 9154, 2423, 591, 6156, 28814, 15730, 45164, 12174, 1211, 8315, 376, 8978, 591, 29538, 8141, 5551, 12610, 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"probability": 0.9822591145833334}, {"start": 1379.43, "end": 1379.73, "word": " يكون", "probability": 0.9443359375}, {"start": 1379.73, "end": 1380.63, "word": " المصفوفة", "probability": 0.96982421875}, {"start": 1380.63, "end": 1380.95, "word": " نفسها", "probability": 0.9685872395833334}, {"start": 1380.95, "end": 1381.05, "word": " او", "probability": 0.94189453125}, {"start": 1381.05, "end": 1381.13, "word": " ال", "probability": 0.96337890625}, {"start": 1381.13, "end": 1381.45, "word": " matrix", "probability": 0.982421875}, {"start": 1381.45, "end": 1382.09, "word": " نفسها", "probability": 0.97705078125}, {"start": 1382.09, "end": 1382.35, "word": " هي", "probability": 0.927734375}, {"start": 1382.35, "end": 1382.67, "word": " square", "probability": 0.86083984375}, {"start": 1382.67, "end": 1383.11, "word": " matrix", "probability": 0.9638671875}], "temperature": 1.0}, {"id": 60, "seek": 140021, "start": 1384.27, "end": 1400.21, "text": "أول شرط هي square matrix عشان تفكر تجيب لها ال inverse فمعنى ذلك انه هذا بنتسميه necessary condition شرط ضروري و لحظوا كلمة شرط ضروري مش بالضروري ان هو كافي يعني ممكن تكون", "tokens": [10721, 12610, 13412, 2288, 9566, 39896, 3732, 8141, 6225, 8592, 7649, 6055, 5172, 37983, 6055, 7435, 1829, 3555, 5296, 11296, 2423, 17340, 6156, 2304, 3615, 1863, 7578, 29910, 23275, 16472, 3224, 23758, 4724, 29399, 38251, 1829, 3224, 4818, 4188, 13412, 2288, 9566, 48812, 2288, 13063, 1829, 4032, 5296, 5016, 19913, 14407, 9122, 19528, 3660, 13412, 2288, 9566, 48812, 2288, 13063, 1829, 37893, 20666, 11242, 2288, 13063, 1829, 16472, 31439, 9122, 31845, 1829, 37495, 22653, 3714, 43020, 6055, 30544], "avg_logprob": -0.1509098071086256, "compression_ratio": 1.4293193717277486, "no_speech_prob": 9.119510650634766e-06, "words": [{"start": 1384.27, "end": 1384.67, "word": "أول", "probability": 0.882080078125}, {"start": 1384.67, "end": 1385.29, "word": " شرط", "probability": 0.9378255208333334}, {"start": 1385.29, "end": 1385.81, "word": " هي", 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هذا", "probability": 0.5400390625}, {"start": 1391.51, "end": 1392.07, "word": " بنتسميه", "probability": 0.790673828125}, {"start": 1392.07, "end": 1392.47, "word": " necessary", "probability": 0.81298828125}, {"start": 1392.47, "end": 1393.15, "word": " condition", "probability": 0.9697265625}, {"start": 1393.15, "end": 1393.91, "word": " شرط", "probability": 0.9518229166666666}, {"start": 1393.91, "end": 1394.85, "word": " ضروري", "probability": 0.9554443359375}, {"start": 1394.85, "end": 1395.37, "word": " و", "probability": 0.66748046875}, {"start": 1395.37, "end": 1395.67, "word": " لحظوا", "probability": 0.710205078125}, {"start": 1395.67, "end": 1395.95, "word": " كلمة", "probability": 0.97021484375}, {"start": 1395.95, "end": 1396.21, "word": " شرط", "probability": 0.9763997395833334}, {"start": 1396.21, "end": 1396.79, "word": " ضروري", "probability": 0.9896240234375}, {"start": 1396.79, "end": 1397.15, "word": " مش", "probability": 0.98193359375}, {"start": 1397.15, "end": 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"probability": 0.943359375}, {"start": 1417.39, "end": 1417.81, "word": " هتطلع", "probability": 0.926953125}, {"start": 1417.81, "end": 1417.97, "word": " لها", "probability": 0.6165771484375}, {"start": 1417.97, "end": 1418.05, "word": " ال", "probability": 0.98486328125}, {"start": 1418.05, "end": 1418.27, "word": " inverse", "probability": 0.919921875}], "temperature": 1.0}, {"id": 62, "seek": 144380, "start": 1419.68, "end": 1443.8, "text": "و مش كل المصفوفات المربعة لها inverse في نفس الوقت ليش؟ لأن العملية نفس الحسابية اللي هنشوفها الآن في إنتاج المصفوفة ال inverse أو العكسية هنجد أنه ممكن تطلع undefined ممكن تطلع undefined كويس أما الشرط الوحيد اللي احنا كلنا عارفينه أنه في الآخر ال inverse هذه ال inverse نفسها إذا ضربناها في المصفوفة A", "tokens": [2407, 37893, 28242, 9673, 9381, 5172, 38688, 9307, 9673, 25513, 27884, 5296, 11296, 17340, 8978, 8717, 36178, 2423, 30543, 2655, 32239, 8592, 22807, 5296, 33456, 18863, 42213, 10632, 8717, 36178, 21542, 3794, 16758, 10632, 13672, 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عن", "probability": 0.92626953125}, {"start": 1504.84, "end": 1505.1, "word": " 2", "probability": 0.69482421875}, {"start": 1505.1, "end": 1505.3, "word": " by", "probability": 0.98046875}, {"start": 1505.3, "end": 1505.58, "word": " 2", "probability": 0.9580078125}, {"start": 1505.58, "end": 1506.12, "word": " automatically", "probability": 0.5087890625}, {"start": 1506.12, "end": 1507.02, "word": " ال", "probability": 0.9775390625}, {"start": 1507.02, "end": 1507.62, "word": " diagonal", "probability": 0.8876953125}, {"start": 1507.62, "end": 1508.56, "word": " بتبدل", "probability": 0.97021484375}, {"start": 1508.56, "end": 1509.14, "word": " عناصره", "probability": 0.96728515625}, {"start": 1509.14, "end": 1509.68, "word": " ال", "probability": 0.8203125}, {"start": 1509.68, "end": 1509.92, "word": " co", "probability": 0.5234375}, {"start": 1509.92, "end": 1510.46, "word": "-diagonal", "probability": 0.79638671875}], "temperature": 1.0}, {"id": 66, "seek": 152907, "start": 1511.53, "end": 1529.07, "text": "بتبدل إشارته وبتقسم على ال determinant فال determinant هذه إذا كانت defined هنا وجدنا inverse إذا كانت undefined لأن حيكون في عملية طرح فالطرح هدف إنها إذا وصلنا ل zero ممكن يعمل مشكلة", "tokens": [3555, 2655, 44510, 1211, 11933, 8592, 9640, 47395, 46599, 2655, 4587, 38251, 15844, 2423, 41296, 6156, 6027, 41296, 29538, 11933, 15730, 25961, 2655, 7642, 34105, 49610, 3215, 8315, 17340, 11933, 15730, 25961, 2655, 674, 5666, 2001, 5296, 33456, 11331, 1829, 30544, 8978, 6225, 42213, 10632, 23032, 2288, 5016, 6156, 6027, 9566, 2288, 5016, 8032, 3215, 5172, 36145, 11296, 11933, 15730, 4032, 36520, 8315, 5296, 4018, 3714, 43020, 7251, 25957, 1211, 37893, 28820, 3660], "avg_logprob": -0.18486064229462598, "compression_ratio": 1.5769230769230769, "no_speech_prob": 1.233816146850586e-05, "words": [{"start": 1511.53, "end": 1512.45, "word": "بتبدل", "probability": 0.810791015625}, {"start": 1512.45, "end": 1513.13, "word": " إشارته", "probability": 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بتاعتنا", "probability": 0.8818359375}, {"start": 1531.72, "end": 1532.24, "word": " او", "probability": 0.7139892578125}, {"start": 1532.24, "end": 1533.38, "word": " قيمة", "probability": 0.9847005208333334}, {"start": 1533.38, "end": 1534.3, "word": " المصفوفة", "probability": 0.97861328125}, {"start": 1534.3, "end": 1535.3, "word": " اللي", "probability": 0.418701171875}, {"start": 1535.3, "end": 1535.46, "word": " هو", "probability": 0.454833984375}, {"start": 1535.46, "end": 1535.54, "word": " ال", "probability": 0.94921875}, {"start": 1535.54, "end": 1535.96, "word": " diagonal", "probability": 0.798828125}, {"start": 1535.96, "end": 1536.44, "word": " اضرب", "probability": 0.79052734375}, {"start": 1536.44, "end": 1536.56, "word": " ال", "probability": 0.96435546875}, {"start": 1536.56, "end": 1536.96, "word": " diagonal", "probability": 0.8857421875}, {"start": 1536.96, "end": 1537.54, "word": " ناقص", "probability": 0.888671875}, {"start": 1537.54, "end": 1537.68, "word": " ال", "probability": 0.96728515625}, {"start": 1537.68, "end": 1537.78, "word": " co", "probability": 0.3017578125}, {"start": 1537.78, "end": 1538.14, "word": " diagonal", "probability": 0.45654296875}, {"start": 1538.14, "end": 1541.28, "word": " اذا", "probability": 0.7427978515625}, {"start": 1541.28, "end": 1541.38, "word": " ما", "probability": 0.8525390625}, {"start": 1541.38, "end": 1541.72, "word": " طلعش", "probability": 0.8824462890625}, {"start": 1541.72, "end": 1542.14, "word": " صفر", "probability": 0.9737955729166666}, {"start": 1542.14, "end": 1543.22, "word": " بتقدر", "probability": 0.77392578125}, {"start": 1543.22, "end": 1543.76, "word": " تجيبلها", "probability": 0.9127604166666666}, {"start": 1543.76, "end": 1545.86, "word": " قيمة", "probability": 0.97216796875}, {"start": 1545.86, "end": 1546.16, "word": " لل", "probability": 0.84619140625}, {"start": 1546.16, "end": 1546.58, "word": " inverse", "probability": 0.72412109375}, {"start": 1546.58, "end": 1547.48, 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" co", "probability": 0.828125}, {"start": 1551.38, "end": 1551.68, "word": " diagonal", "probability": 0.875}, {"start": 1551.68, "end": 1552.2, "word": " بدون", "probability": 0.989501953125}, {"start": 1552.2, "end": 1552.28, "word": " ما", "probability": 0.8125}, {"start": 1552.28, "end": 1552.8, "word": " نبدلهم", "probability": 0.9478759765625}], "temperature": 1.0}, {"id": 68, "seek": 157143, "start": 1553.63, "end": 1571.43, "text": "خلاص ناتج هذا العملية هيكون اكيد inverse للمصفوفة اللى عندك طيب ممتاز جدا هي هيكى بنتكلم عن مضروبة في ال inverse تبعها طب ممكن تكون المصفوفة نفسها مضروبة في نفسها زي ان نقول المصفوفة تربية", "tokens": [9778, 1211, 33546, 8717, 9307, 7435, 23758, 18863, 42213, 10632, 39896, 30544, 1975, 4117, 25708, 17340, 5296, 19528, 9381, 5172, 38688, 3660, 13672, 7578, 43242, 4117, 23032, 1829, 3555, 3714, 2304, 2655, 31377, 10874, 28259, 39896, 39896, 4117, 7578, 44945, 2655, 4117, 19528, 18871, 3714, 11242, 32887, 49401, 8978, 2423, 17340, 6055, 3555, 3615, 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{"start": 1893.37, "end": 1893.51, "word": " لما", "probability": 0.91943359375}, {"start": 1893.51, "end": 1893.79, "word": " كنتوا", "probability": 0.9578450520833334}, {"start": 1893.79, "end": 1894.23, "word": " بتعملوا", "probability": 0.9638671875}, {"start": 1894.23, "end": 1895.87, "word": " المعادلات", "probability": 0.9525390625}, {"start": 1895.87, "end": 1896.51, "word": " الكيميائية", "probability": 0.9556640625}, {"start": 1896.51, "end": 1897.13, "word": " و", "probability": 0.8818359375}, {"start": 1897.13, "end": 1897.35, "word": " بدك", "probability": 0.94775390625}, {"start": 1897.35, "end": 1897.95, "word": " تضبط", "probability": 0.96142578125}, {"start": 1897.95, "end": 1898.93, "word": " المعادلة", "probability": 0.989013671875}], "temperature": 1.0}, {"id": 83, "seek": 192830, "start": 1899.72, "end": 1928.3, "text": "مش هيك تضبط عدد ذرات توزنها تعملها عملية توزن فالعملية هذه نفس الكلام برضه في العمليات الحسابية الرياضية لما يكون في عندك matrices لازم تعملها ضبط للمعادلة هل فعلا عملية الضرب لمجموعة ال matrices هذه ممكن لو بهذا الشكل بدك تحطها بهذا الشكل يمكن ما تظبطش فانت بدك تكون عارف مسبقا ان هي بهذا الشكل لما بدك تيجي تضربها في matrix جنبها", "tokens": [2304, 8592, 39896, 4117, 6055, 11242, 3555, 9566, 6225, 3215, 3215, 29910, 2288, 9307, 33427, 11622, 1863, 11296, 6055, 25957, 1211, 11296, 6225, 42213, 10632, 33427, 11622, 1863, 6156, 6027, 25957, 1211, 10632, 29538, 8717, 36178, 2423, 28820, 10943, 4724, 43042, 3224, 8978, 18863, 2304, 20292, 9307, 21542, 3794, 16758, 10632, 2423, 16572, 46958, 10632, 5296, 15042, 7251, 30544, 8978, 43242, 4117, 32284, 5296, 31377, 2304, 6055, 25957, 1211, 11296, 48812, 3555, 9566, 5296, 19528, 3615, 18513, 37977, 8032, 1211, 6156, 3615, 15040, 6225, 42213, 10632, 6024, 114, 25513, 32767, 7435, 2304, 2407, 27884, 2423, 32284, 29538, 3714, 43020, 45164, 39627, 15730, 25124, 28820, 47525, 4117, 6055, 5016, 9566, 11296, 39627, 15730, 25124, 28820, 7251, 43020, 19446, 6055, 19913, 3555, 9566, 8592, 6156, 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"probability": 0.9519856770833334}, {"start": 1904.08, "end": 1904.52, "word": " توزن", "probability": 0.7767740885416666}, {"start": 1904.52, "end": 1905.82, "word": " فالعملية", "probability": 0.944921875}, {"start": 1905.82, "end": 1906.0, "word": " هذه", "probability": 0.50244140625}, {"start": 1906.0, "end": 1906.26, "word": " نفس", "probability": 0.986328125}, {"start": 1906.26, "end": 1906.66, "word": " الكلام", "probability": 0.96875}, {"start": 1906.66, "end": 1906.9, "word": " برضه", "probability": 0.8818359375}, {"start": 1906.9, "end": 1907.06, "word": " في", "probability": 0.88818359375}, {"start": 1907.06, "end": 1908.24, "word": " العمليات", "probability": 0.8826904296875}, {"start": 1908.24, "end": 1908.76, "word": " الحسابية", "probability": 0.988525390625}, {"start": 1908.76, "end": 1909.38, "word": " الرياضية", "probability": 0.8902587890625}, {"start": 1909.38, "end": 1909.86, "word": " لما", "probability": 0.92919921875}, {"start": 1909.86, "end": 1910.06, "word": 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"probability": 0.58026123046875}, {"start": 1921.92, "end": 1922.02, "word": " ما", "probability": 0.366455078125}, {"start": 1922.02, "end": 1922.54, "word": " تظبطش", "probability": 0.91728515625}, {"start": 1922.54, "end": 1923.66, "word": " فانت", "probability": 0.91845703125}, {"start": 1923.66, "end": 1923.86, "word": " بدك", "probability": 0.98046875}, {"start": 1923.86, "end": 1924.08, "word": " تكون", "probability": 0.972900390625}, {"start": 1924.08, "end": 1924.42, "word": " عارف", "probability": 0.98828125}, {"start": 1924.42, "end": 1924.94, "word": " مسبقا", "probability": 0.9158935546875}, {"start": 1924.94, "end": 1925.1, "word": " ان", "probability": 0.65234375}, {"start": 1925.1, "end": 1925.34, "word": " هي", "probability": 0.5888671875}, {"start": 1925.34, "end": 1925.64, "word": " بهذا", "probability": 0.98876953125}, {"start": 1925.64, "end": 1926.06, "word": " الشكل", "probability": 0.988525390625}, {"start": 1926.06, "end": 1926.56, "word": " لما", "probability": 0.946533203125}, {"start": 1926.56, "end": 1926.8, "word": " بدك", "probability": 0.953125}, {"start": 1926.8, "end": 1927.0, "word": " تيجي", "probability": 0.74151611328125}, {"start": 1927.0, "end": 1927.34, "word": " تضربها", "probability": 0.96435546875}, {"start": 1927.34, "end": 1927.46, "word": " في", "probability": 0.95458984375}, {"start": 1927.46, "end": 1927.82, "word": " matrix", "probability": 0.86962890625}, {"start": 1927.82, "end": 1928.3, "word": " جنبها", "probability": 0.9654541015625}], "temperature": 1.0}, {"id": 84, "seek": 194105, "start": 1929.69, "end": 1941.05, "text": "هل في إمكانية هذا الكلام ولا لأ هو الأولى أنها تكون بهذا الشكل عشان تكون عملية الضرب أفضل فبيعمل عملية وزن فبيحطولك T بحيث انه يوزنلك انه في إمكانية عملية الضرب", "tokens": [3224, 1211, 8978, 11933, 2304, 41361, 10632, 23758, 2423, 28820, 10943, 49429, 5296, 10721, 31439, 16247, 12610, 7578, 14739, 11296, 6055, 30544, 39627, 15730, 25124, 28820, 6225, 8592, 7649, 6055, 30544, 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لأ", "probability": 0.845703125}, {"start": 1931.37, "end": 1931.55, "word": " هو", "probability": 0.4775390625}, {"start": 1931.55, "end": 1932.21, "word": " الأولى", "probability": 0.9581705729166666}, {"start": 1932.21, "end": 1932.39, "word": " أنها", "probability": 0.698974609375}, {"start": 1932.39, "end": 1932.65, "word": " تكون", "probability": 0.988525390625}, {"start": 1932.65, "end": 1932.97, "word": " بهذا", "probability": 0.9521484375}, {"start": 1932.97, "end": 1933.39, "word": " الشكل", "probability": 0.99072265625}, {"start": 1933.39, "end": 1933.91, "word": " عشان", "probability": 0.9557291666666666}, {"start": 1933.91, "end": 1934.19, "word": " تكون", "probability": 0.86962890625}, {"start": 1934.19, "end": 1934.53, "word": " عملية", "probability": 0.9733072916666666}, {"start": 1934.53, "end": 1934.91, "word": " الضرب", "probability": 0.8395182291666666}, {"start": 1934.91, "end": 1935.87, "word": " أفضل", "probability": 0.962890625}, {"start": 1935.87, "end": 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عملية تقاطع وعملية اتحاد بالظبط ال meet هي عملية تقاطع فإذا انت بتعمل and كل أنصر مع الأنصر اللي بقابله زي عملية جمع المصففات بالظبط", "tokens": [10721, 15042, 18863, 2304, 20292, 2655, 9957, 13672, 1829, 8978, 16247, 12610, 8032, 3215, 12610, 3660, 5296, 10721, 8032, 3215, 12610, 6225, 2304, 20292, 9307, 6225, 42213, 10632, 6055, 4587, 41193, 3615, 4032, 25957, 1211, 10632, 1975, 2655, 5016, 18513, 20666, 19913, 3555, 9566, 2423, 1677, 39896, 6225, 42213, 10632, 6055, 4587, 41193, 3615, 6156, 28814, 15730, 16472, 2655, 39894, 25957, 1211, 293, 28242, 14739, 9381, 2288, 20449, 16247, 1863, 9381, 2288, 13672, 1829, 4724, 4587, 16758, 43761, 30767, 1829, 6225, 42213, 10632, 10874, 2304, 3615, 9673, 9381, 5172, 5172, 9307, 20666, 19913, 3555, 9566], "avg_logprob": -0.10888671774106722, "compression_ratio": 1.9166666666666667, "no_speech_prob": 1.5497207641601562e-06, "words": [{"start": 2383.85, "end": 2384.29, "word": "أما", "probability": 0.941650390625}, {"start": 2384.29, "end": 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"probability": 0.96142578125}, {"start": 2624.17, "end": 2624.63, "word": " الأول", "probability": 0.96337890625}, {"start": 2624.63, "end": 2626.43, "word": " أول", "probability": 0.81787109375}, {"start": 2626.43, "end": 2626.77, "word": " and", "probability": 0.9697265625}, {"start": 2626.77, "end": 2627.37, "word": " أول", "probability": 0.95166015625}, {"start": 2627.37, "end": 2627.77, "word": " خلاص", "probability": 0.978515625}, {"start": 2627.77, "end": 2628.11, "word": " فإذا", "probability": 0.8312174479166666}, {"start": 2628.11, "end": 2629.25, "word": " and", "probability": 0.94873046875}], "temperature": 1.0}, {"id": 113, "seek": 265367, "start": 2630.77, "end": 2653.67, "text": "مجموحهم او ناتج ال ending or مع العنصرين اللي وراهم or مع العنصرين اللي وراهم و بتجمع بهذا الشكل بتجمع بهذا الشكل هاي هادي في حالة ان انت بتضرب two matrices لمين ل pool يعني okay نفس الكلام اللي قلناه هناك لل power برضه ممكن يكون هنا ال power في ال pool", "tokens": [2304, 7435, 2304, 2407, 5016, 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ناتج", "probability": 0.9591471354166666}, {"start": 2632.31, "end": 2632.47, "word": " ال", "probability": 0.896484375}, {"start": 2632.47, "end": 2632.87, "word": " ending", "probability": 0.91650390625}, {"start": 2632.87, "end": 2633.77, "word": " or", "probability": 0.427978515625}, {"start": 2633.77, "end": 2634.37, "word": " مع", "probability": 0.97705078125}, {"start": 2634.37, "end": 2634.99, "word": " العنصرين", "probability": 0.9646484375}, {"start": 2634.99, "end": 2635.09, "word": " اللي", "probability": 0.763916015625}, {"start": 2635.09, "end": 2635.59, "word": " وراهم", "probability": 0.9827473958333334}, {"start": 2635.59, "end": 2636.11, "word": " or", "probability": 0.377197265625}, {"start": 2636.11, "end": 2636.31, "word": " مع", "probability": 0.88916015625}, {"start": 2636.31, "end": 2636.75, "word": " العنصرين", "probability": 0.9892578125}, {"start": 2636.75, "end": 2636.87, "word": " اللي", "probability": 0.890625}, {"start": 2636.87, "end": 2636.89, "word": " وراهم", "probability": 0.7970377604166666}, {"start": 2636.89, "end": 2636.89, "word": " و", "probability": 0.350341796875}, {"start": 2636.89, "end": 2637.41, "word": " بتجمع", "probability": 0.9266357421875}, {"start": 2637.41, "end": 2637.93, "word": " بهذا", "probability": 0.714111328125}, {"start": 2637.93, "end": 2638.23, "word": " الشكل", "probability": 0.99169921875}, {"start": 2638.23, "end": 2638.65, "word": " بتجمع", "probability": 0.83111572265625}, {"start": 2638.65, "end": 2638.89, "word": " بهذا", "probability": 0.973388671875}, {"start": 2638.89, "end": 2639.25, "word": " الشكل", "probability": 0.986572265625}, {"start": 2639.25, "end": 2640.35, "word": " هاي", "probability": 0.5906982421875}, {"start": 2640.35, "end": 2640.65, "word": " هادي", "probability": 0.6731770833333334}, {"start": 2640.65, "end": 2641.35, "word": " في", "probability": 0.5966796875}, {"start": 2641.35, "end": 2641.65, "word": " حالة", "probability": 0.98974609375}, {"start": 2641.65, "end": 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2653.47, "word": " ال", "probability": 0.59228515625}, {"start": 2653.47, "end": 2653.67, "word": " pool", "probability": 0.59814453125}], "temperature": 1.0}, {"id": 114, "seek": 267389, "start": 2655.75, "end": 2673.89, "text": "بدك تضربهم في بعض و عملية الضرب كلنا عارفين زي ما توشفناها بال O ring الكبيرة لمجموعة ending لمجموعة ending فبدك تضرب اتقول مثلا a to the power to the power و لاحظ ان كتبناها power", "tokens": [3555, 3215, 4117, 6055, 11242, 25513, 16095, 8978, 45030, 11242, 4032, 6225, 42213, 10632, 6024, 114, 25513, 9122, 1211, 8315, 6225, 9640, 5172, 9957, 30767, 1829, 19446, 33427, 8592, 5172, 8315, 11296, 20666, 422, 4875, 33251, 3555, 48923, 5296, 2304, 7435, 2304, 2407, 27884, 8121, 5296, 2304, 7435, 2304, 2407, 27884, 8121, 6156, 3555, 3215, 4117, 6055, 11242, 25513, 1975, 2655, 39648, 50113, 15040, 257, 281, 264, 1347, 281, 264, 1347, 4032, 20193, 5016, 19913, 16472, 9122, 2655, 3555, 8315, 11296, 1347], "avg_logprob": -0.2774849253964711, "compression_ratio": 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2658.93, "end": 2659.63, "word": " توشفناها", "probability": 0.85751953125}, {"start": 2659.63, "end": 2659.91, "word": " بال", "probability": 0.8828125}, {"start": 2659.91, "end": 2660.19, "word": " O", "probability": 0.30078125}, {"start": 2660.19, "end": 2660.51, "word": " ring", "probability": 0.404296875}, {"start": 2660.51, "end": 2661.13, "word": " الكبيرة", "probability": 0.8536783854166666}, {"start": 2661.13, "end": 2663.75, "word": " لمجموعة", "probability": 0.8496907552083334}, {"start": 2663.75, "end": 2664.79, "word": " ending", "probability": 0.93408203125}, {"start": 2664.79, "end": 2665.57, "word": " لمجموعة", "probability": 0.8495279947916666}, {"start": 2665.57, "end": 2666.03, "word": " ending", "probability": 0.95947265625}, {"start": 2666.03, "end": 2666.71, "word": " فبدك", "probability": 0.81048583984375}, {"start": 2666.71, "end": 2667.11, "word": " تضرب", "probability": 0.9920247395833334}, {"start": 2667.11, "end": 2667.65, "word": " اتقول", "probability": 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0.9869791666666666}, {"start": 3002.65, "end": 3002.75, "word": " إن", "probability": 0.4111328125}, {"start": 3002.75, "end": 3002.93, "word": " جول", "probability": 0.6197509765625}, {"start": 3002.93, "end": 3003.13, "word": " هذا", "probability": 0.8564453125}, {"start": 3003.13, "end": 3003.47, "word": " أحسن", "probability": 0.9942626953125}, {"start": 3003.47, "end": 3003.63, "word": " من", "probability": 0.99560546875}, {"start": 3003.63, "end": 3004.33, "word": " هذا،", "probability": 0.966064453125}, {"start": 3004.33, "end": 3004.49, "word": " لأ", "probability": 0.973388671875}, {"start": 3004.49, "end": 3004.65, "word": " هذا", "probability": 0.7939453125}, {"start": 3004.65, "end": 3004.99, "word": " أفضل", "probability": 0.9957275390625}, {"start": 3004.99, "end": 3005.15, "word": " من", "probability": 0.99658203125}, {"start": 3005.15, "end": 3005.39, "word": " هذا", "probability": 0.984375}], "temperature": 1.0}, {"id": 130, "seek": 303026, "start": 3006.26, "end": 3030.26, "text": "بيهمنيش ال language بتهمناش ال language عشان بعدك نبدأ في ال statements بتاعة اللغة و نبدأ ناخد أمثلة يعني بعدك هناخد شوية ال statement و بعدك الجزء الأهم من المحاضرة هيكون تطبيقات .. تطبيقات طب إننا نفكر في كذا هت .. نعمللها code وصفي فشوية المرة القادمة هنروح لل data structure شوية هيك تمام على بركة الله يعطيكوا العافية شباب", "tokens": [21292, 16095, 22653, 8592, 2423, 2856, 39894, 16095, 1863, 33599, 2423, 2856, 6225, 8592, 7649, 39182, 4117, 8717, 44510, 10721, 8978, 2423, 12363, 39894, 995, 27884, 13672, 17082, 3660, 4032, 8717, 44510, 10721, 8717, 47283, 3215, 5551, 2304, 12984, 37977, 37495, 22653, 39182, 4117, 8032, 1863, 47283, 3215, 13412, 2407, 10632, 2423, 5629, 4032, 39182, 4117, 25724, 11622, 38207, 16247, 16095, 9154, 9673, 5016, 46958, 25720, 39896, 30544, 6055, 9566, 21292, 4587, 9307, 4386, 6055, 9566, 21292, 4587, 9307, 23032, 3555, 36145, 8315, 8717, 5172, 37983, 8978, 9122, 15730, 8032, 2655, 4386, 8717, 25957, 1211, 1211, 11296, 3089, 4032, 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{"start": 3008.84, "end": 3009.14, "word": " بعدك", "probability": 0.817626953125}, {"start": 3009.14, "end": 3009.4, "word": " نبدأ", "probability": 0.9676106770833334}, {"start": 3009.4, "end": 3009.48, "word": " في", "probability": 0.7333984375}, {"start": 3009.48, "end": 3009.56, "word": " ال", "probability": 0.9326171875}, {"start": 3009.56, "end": 3010.04, "word": " statements", "probability": 0.95458984375}, {"start": 3010.04, "end": 3010.3, "word": " بتاعة", "probability": 0.9378255208333334}, {"start": 3010.3, "end": 3010.68, "word": " اللغة", "probability": 0.9962565104166666}, {"start": 3010.68, "end": 3011.22, "word": " و", "probability": 0.96337890625}, {"start": 3011.22, "end": 3011.48, "word": " نبدأ", "probability": 0.9562174479166666}, {"start": 3011.48, "end": 3011.72, "word": " ناخد", "probability": 0.9931640625}, {"start": 3011.72, "end": 3012.08, "word": " أمثلة", "probability": 0.9676513671875}, {"start": 3012.08, "end": 3012.72, "word": " يعني", "probability": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/HU3y5NBu3E8_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/HU3y5NBu3E8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2b3dc7f8e4fde47a609ad4c8c8f868e253f7677a
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/HU3y5NBu3E8_raw.srt
@@ -0,0 +1,2764 @@
+1
+00:00:05,350 --> 00:00:09,350
+السلام عليكم و تقولوا عفوا يا شباب نبدأ اليوم ان
+
+2
+00:00:09,350 --> 00:00:13,730
+شاء الله تعالى موضوعنا الجديد و اللي يعتبر اخر
+
+3
+00:00:13,730 --> 00:00:18,110
+section في chapter two بحيث انه من المرة القادمة
+
+4
+00:00:18,110 --> 00:00:20,710
+نبدأ في chapter three اللي هو ال algorithms نبدأ
+
+5
+00:00:20,710 --> 00:00:24,210
+نتحدث عن ال algorithms و اللي شوية فيه من جوانب ال
+
+6
+00:00:24,210 --> 00:00:26,210
+data structure اللي انتوا بتشتغلوا عليها الأيام
+
+7
+00:00:26,210 --> 00:00:29,170
+هذه يعني فيها تقاطعات كتير فهذه للمرة القادمة
+
+8
+00:00:29,170 --> 00:00:32,760
+المهم بدنا نتخلص اليومجزئية ال matrices ال
+
+9
+00:00:32,760 --> 00:00:37,680
+matrices هذه اللي هي جمع ال matrix تفضل ان شاء
+
+10
+00:00:37,680 --> 00:00:43,180
+الله بإذن الله تعالى تمام فالموضوع اللي اليوم هو
+
+11
+00:00:43,180 --> 00:00:45,800
+ال matrix و اللي اتوقع انه هنعدي فيه بسرعة لان
+
+12
+00:00:45,800 --> 00:00:49,060
+انتوا ماخدين ال matrices قبل هيك المصففات قبل هيك
+
+13
+00:00:49,060 --> 00:00:52,400
+انتوا ماخدينها و عارفين ان هي rectangular array هي
+
+14
+00:00:52,400 --> 00:00:56,760
+مجموعة array ولكن بتكونش عبارة عن vectorالاريها دي
+
+15
+00:00:56,760 --> 00:01:00,640
+مربعة أو ربعية خلّيني أقول لإن ممكن مش بالضروري
+
+16
+00:01:00,640 --> 00:01:04,560
+يكون الصفوف زي الأعمدة أو ال raw بتساوي ال columns
+
+17
+00:01:04,560 --> 00:01:07,980
+تبعتها المهم إن هي بتحتوي على مجموعات objects in
+
+18
+00:01:07,980 --> 00:01:14,190
+general in general objects تمام؟عادة بتكون أرقام و
+
+19
+00:01:14,190 --> 00:01:19,110
+لكن ممكن تكون إشي غير الأرقام و نتعامل معها as 2D
+
+20
+00:01:19,110 --> 00:01:24,510
+array أو matrices زي ما قلنا طيب لما أقول بده
+
+21
+00:01:24,510 --> 00:01:29,010
+أعرفها بنعرفها ب M by N ف ال M دايما اللي بتيجي في
+
+22
+00:01:29,010 --> 00:01:33,050
+الأول هدي ل ال rows و ال N دايما بتكون ل ال
+
+23
+00:01:33,050 --> 00:01:38,850
+columns فصفوف و أعمدة و منها ال matrix أو مجموحة
+
+24
+00:01:38,850 --> 00:01:42,720
+matricesبنقدر نعرفها بهذا الشكل مصفوفة زي اللي
+
+25
+00:01:42,720 --> 00:01:46,820
+احنا شايفينها قدامنا عبارة عن مجموعة عناصر ال
+
+26
+00:01:46,820 --> 00:01:49,620
+objects هذه عندي عبارة عن numbers بقدر اسميها
+
+27
+00:01:49,620 --> 00:01:54,520
+three by two matrix فهي بعرف ان الرقم الأول عدد
+
+28
+00:01:54,520 --> 00:01:57,920
+الصفوف الرقم التاني عدد الأعمدة اذا كانوا متساوين
+
+29
+00:01:57,920 --> 00:02:04,320
+فبنسميها square matrix بمعنى مصفوفة مربعة فيها
+
+30
+00:02:04,320 --> 00:02:07,680
+استخدامات استخدامات كتير زي ما هنشوف المصفوفات
+
+31
+00:02:07,680 --> 00:02:12,130
+المربعة ويلها حصوصياتكتب اطباقات ايه اطباقات كتير
+
+32
+00:02:12,130 --> 00:02:16,470
+الحقيقة ال matrix او يمكن انتوا جربتوها مثلا في ال
+
+33
+00:02:16,470 --> 00:02:19,170
+linear equations في ال linear equations عشان تحلوا
+
+34
+00:02:19,170 --> 00:02:24,310
+اي مشكلة خطية مجموعة معادلات فمجموعة متغيرات اكتر
+
+35
+00:02:24,310 --> 00:02:28,770
+من متغير بلزمكوا عدد المعادلات مسوى لعدد المتغيرات
+
+36
+00:02:28,770 --> 00:02:35,850
+فعلى طول بتحطوها ب matrix form او شكلبتحلوها بتكون
+
+37
+00:02:35,850 --> 00:02:40,410
+عبارة عن matrix مضروبة في vector بيساوي vector و
+
+38
+00:02:40,410 --> 00:02:44,110
+بتجيبوا ال inverse لل matrix بتجيبوا x و y و إذا
+
+39
+00:02:44,110 --> 00:02:46,630
+كان في z بتجيبوا z و إذا كان في أكتر من هيك
+
+40
+00:02:46,630 --> 00:02:52,670
+بتجيبوا ال equations أو المتغيرات بتاعتكم تمام
+
+41
+00:02:52,670 --> 00:02:58,570
+ممكن تكون في ال graphicsو ال image processing لما
+
+42
+00:02:58,570 --> 00:03:01,190
+نتكلم في ال graphics او ال image processing اول
+
+43
+00:03:01,190 --> 00:03:05,750
+شغلة هي ال image نفسها تعرف ب 2D array اذا انتم
+
+44
+00:03:05,750 --> 00:03:09,450
+متذكرين في ال برمجة فمعناه ذلك ان هي matrix في
+
+45
+00:03:09,450 --> 00:03:14,110
+النهاية matrix كل element هو عبارة عنبكسل كل
+
+46
+00:03:14,110 --> 00:03:18,150
+element بنسميه بكسل فهي أصلا شكلها أساسا ال image
+
+47
+00:03:18,150 --> 00:03:22,970
+هي matrix طيب الشغلات التانية اللي ممكن استخدام ال
+
+48
+00:03:22,970 --> 00:03:26,090
+matrix فيها في ال graphics أو ال image processing
+
+49
+00:03:26,090 --> 00:03:30,030
+هي عملية التحويل إذا كانت بتكون تلف الصورة أو
+
+50
+00:03:30,030 --> 00:03:34,250
+تعكسوها أو تعملولها rotation فبرضه بتكون من خلال
+
+51
+00:03:34,250 --> 00:03:38,810
+مصفوفات تحويلهي أصلا مصفوفة لما بدي أحولها لشكل
+
+52
+00:03:38,810 --> 00:03:44,870
+آخر عاملها flipping مثلا محتاجة مصفوفة أضربها فيها
+
+53
+00:03:44,870 --> 00:03:50,430
+بحيث أنه يحولها لشكل آخر هو مقابل لشكل الأصلي ال
+
+54
+00:03:50,430 --> 00:03:54,550
+original تبعها زي لما بتكون تعمله mirror حوالين ال
+
+55
+00:03:54,550 --> 00:03:59,560
+x y ال x axis أو ال y axisال X-axis أو ال Y-axis
+
+56
+00:03:59,560 --> 00:04:03,520
+فانتوا كل اللي بتعملوه هتضربوها في matrix حسب
+
+57
+00:04:03,520 --> 00:04:08,740
+الأبعاد بتاعتكوا يعني لو بدنا مثلا نضربها في ال X
+
+58
+00:04:08,740 --> 00:04:13,980
+-axis هضربها في إيش؟ في واحد و سالب واحد واحد صفر
+
+59
+00:04:13,980 --> 00:04:18,120
+صفر سالب واحد لو بده أقول إن هي مربعفالسالب واحدة
+
+60
+00:04:18,120 --> 00:04:21,960
+ده هيعطيني قيم سالبة لمين ل ال Y يعني معناه ذلك ان
+
+61
+00:04:21,960 --> 00:04:26,580
+هي انعكست حوالين ال X و هكذا فالقصد انه عملية ال
+
+62
+00:04:26,580 --> 00:04:31,160
+processing نفسها ممكن تتم من خلال ال matrices طيب
+
+63
+00:04:31,160 --> 00:04:34,840
+و هذا بيقودنا ل computational science علوم
+
+64
+00:04:34,840 --> 00:04:38,920
+الحسابات و الهندسة بشكل عام و اللي بتدخل فيها
+
+65
+00:04:38,920 --> 00:04:43,750
+optimization و بتدخل فيها كل شغلالتحويلات أو ال
+
+66
+00:04:43,750 --> 00:04:47,370
+modeling عملية ال modeling فمهمة جدا ال matrices
+
+67
+00:04:47,370 --> 00:04:51,370
+في الآخر طيب في ال quantum mechanics و ال quantum
+
+68
+00:04:51,370 --> 00:04:56,390
+computing برضه من الحاجات اللي بنقدر نعبر عن طبيعة
+
+69
+00:04:56,390 --> 00:04:59,390
+الذرات و power إذا كانوا متذكرين power و الجدول
+
+70
+00:04:59,390 --> 00:05:04,330
+الدوري تبعه كله عناصره و حركة ال electrons جدروا
+
+71
+00:05:04,330 --> 00:05:08,390
+يعملولها modeling باستخدام ال matrices باستخدامالـ
+
+72
+00:05:08,390 --> 00:05:13,910
+matrices داخل العنصر نفسه فهذه تطبيقات يدوب
+
+73
+00:05:13,910 --> 00:05:19,720
+تعريفاتك بسيطة عننقطة من محيط تطبيقات الـ matrices
+
+74
+00:05:19,720 --> 00:05:23,840
+واللي لاجوا قدامها خلال علوم كو اللي هتقراوها
+
+75
+00:05:23,840 --> 00:05:26,720
+لجدام هتلاجوا انه كتير انها استخدمت نبدأ في ال
+
+76
+00:05:26,720 --> 00:05:30,520
+matrices كماترسيز الان نتكلم عنها ال matrix اولا
+
+77
+00:05:30,520 --> 00:05:33,900
+عشان اقول ان في two matrices equal لبعض هم بيساوي
+
+78
+00:05:33,900 --> 00:05:37,460
+بعض فمعنى ذلك ان ابعادهم لازم يتساوي بعض صفوف
+
+79
+00:05:37,460 --> 00:05:40,640
+تساوي صفوف الأعمدة تساوي الأعمدة زائد كل عنصر
+
+80
+00:05:40,640 --> 00:05:43,880
+يساوي العنصر ال corresponding له او المقابل له في
+
+81
+00:05:43,880 --> 00:05:48,540
+الصف والعمودفإذن كل هذه الشروط لازم تتحقق عشان
+
+82
+00:05:48,540 --> 00:05:52,040
+أقدر أقول أن ال matrices A وB هما equal if and
+
+83
+00:05:52,040 --> 00:05:56,520
+only ifالهم نفس عدد ال rows نفس عدد ال columns و
+
+84
+00:05:56,520 --> 00:06:00,100
+ال corresponding elements ال elements هدولة ال
+
+85
+00:06:00,100 --> 00:06:02,760
+element 11 في المصفوفة الأولى لازم يكون بسوء ال
+
+86
+00:06:02,760 --> 00:06:06,520
+element 11 في المصفوفة التانية and so on و هكذا لو
+
+87
+00:06:06,520 --> 00:06:09,100
+جينا اتكلمنا عن المصفوفة اللي احنا شايفينهم
+
+88
+00:06:09,100 --> 00:06:11,680
+المصففتين التانتين اللي جانتنا رغم ان ال column
+
+89
+00:06:11,680 --> 00:06:16,240
+الأخر zero يعني فعليا انت بتتخيل انه مالوش تأثير
+
+90
+00:06:16,240 --> 00:06:20,250
+لأ هو له تأثيرحلو تأثير فهدولة بيساووش بعض فعليا
+
+91
+00:06:20,250 --> 00:06:24,470
+لإن هنا عندك two columns هنا three columns زائد إن
+
+92
+00:06:24,470 --> 00:06:27,250
+ال corresponding أو ال element هذا مالوش ما يقابله
+
+93
+00:06:27,250 --> 00:06:32,930
+في المصفوفة الأولى فإذا هدول بيساووش بعض طيب ال
+
+94
+00:06:32,930 --> 00:06:38,520
+rule column فعليا تقرأ دائمابالنسبة لل روه من ال
+
+95
+00:06:38,520 --> 00:06:43,420
+top to down to bottom to down بتبدأ من الصف .. من
+
+96
+00:06:43,420 --> 00:06:46,460
+الصف الأول التاني التالت الرابع من الأعلى إلى
+
+97
+00:06:46,460 --> 00:06:50,060
+الأسفل زائد left to right بالنسبة لل إعش لل أعمدة
+
+98
+00:06:50,060 --> 00:06:53,300
+فلما نتكلم هنا هيجي العنصر هذا هو العنصر الأول في
+
+99
+00:06:53,300 --> 00:06:56,480
+مين في ال matrix في المصفوفة على اعتبار أنه الأول
+
+100
+00:06:56,480 --> 00:07:00,520
+بالنسبة للصفوف اللي بتبدأ من فوق لتحت أو بالأعمدة
+
+101
+00:07:00,520 --> 00:07:06,790
+اللي بتبدأ من الشمال لليامين لما نقولوحد to M، to
+
+102
+00:07:06,790 --> 00:07:11,490
+M هذه نتكلم عن الأعمد، الصفوف، نتكلم عن إيش؟
+
+103
+00:07:11,490 --> 00:07:15,590
+الصفوف، فإذا ال matrix هنا نتعامل معاها M في N،
+
+104
+00:07:15,590 --> 00:07:21,070
+مدام M في N فانا عارف ان ال M هنا للصفوف، لل رو،
+
+105
+00:07:21,070 --> 00:07:25,470
+في ال N اللي هي لل إش، للأعمدة، فهتلاقي أن أكبر
+
+106
+00:07:25,470 --> 00:07:31,700
+رقم في الأعمدة هيكون قيمة ال إيش؟ ال Nو أكبر رقم
+
+107
+00:07:31,700 --> 00:07:37,260
+في الصفوف قيمة ال M تمام فبنقدر نقول أن ال matrix
+
+108
+00:07:37,260 --> 00:07:44,120
+A بنحطها bracket فهي كمان أحد الأقواص المهمة جدا
+
+109
+00:07:44,120 --> 00:07:47,760
+اللي بقدر أعرف أن أنا بتعامل هنا مع مين مع matrix
+
+110
+00:07:47,760 --> 00:07:52,040
+ال brackets أو الأقواص الكبيرة هذه اللي هي أكبر
+
+111
+00:07:52,040 --> 00:07:54,340
+حجم من أحجام الأقواص
+
+112
+00:07:57,730 --> 00:08:01,370
+فهذه ال bracket أخدنا سابقا ال curly و قلنا هذه
+
+113
+00:08:01,370 --> 00:08:05,170
+المجموعات لل sets لأ الآن بنتكلم عن ال bracket انه
+
+114
+00:08:05,170 --> 00:08:10,010
+هذا بيستخدم لل arrays او لمصفوفات انك بتقدر نقول
+
+115
+00:08:10,010 --> 00:08:14,670
+عليها ان هي مصفوفة تحتوي على مجموعة عناصر I و J
+
+116
+00:08:14,670 --> 00:08:18,450
+وعارف ان هنا ال I هتكون قيمها ابتدا من ال goal أول
+
+117
+00:08:18,450 --> 00:08:26,590
+ل Mلـ row M الـ J تبدأ من الواحد لل column لأنه
+
+118
+00:08:26,590 --> 00:08:29,430
+دائما الانصر التاني او ال index التاني هي ال
+
+119
+00:08:29,430 --> 00:08:32,610
+column ال index الأولى هي ال row كلام انتوا
+
+120
+00:08:32,610 --> 00:08:36,750
+عارفينه فبنبدأ من واحد to N to N بالنسبة للـ J
+
+121
+00:08:36,750 --> 00:08:42,090
+فالـ J دائما هتكون اصغر او تساوي maximum N كويس
+
+122
+00:08:42,090 --> 00:08:48,150
+هذه تعريفتها طيب ال .. as a function بنقدر نعبر عن
+
+123
+00:08:49,280 --> 00:08:53,000
+الـ matrix as a function على اعتبار ان هي فعليا
+
+124
+00:08:53,000 --> 00:08:57,940
+بنقدر نحطها بشكل مصف بشكل function بحيث انه كل
+
+125
+00:08:57,940 --> 00:09:01,180
+عنصر هو function في مين في ال location تبعه بس ال
+
+126
+00:09:01,180 --> 00:09:06,000
+location ان احنا هنا ال two values او two indices
+
+127
+00:09:06,000 --> 00:09:10,300
+index لل row و index لل column فعشان هيك لما نيجي
+
+128
+00:09:10,300 --> 00:09:16,480
+بدنا نعرفها ال matrix M by Nإن هي كل العناصر I وJ
+
+129
+00:09:16,480 --> 00:09:19,840
+داخل ال bracket هيها فهذه اللي نقدر نقول عليها هي
+
+130
+00:09:19,840 --> 00:09:22,640
+function لل members بس function في مين ال members
+
+131
+00:09:22,640 --> 00:09:24,740
+هدول فعلا؟ ال function في natural number by
+
+132
+00:09:24,740 --> 00:09:32,080
+natural number اللي هي M في N يعني الصفوف في
+
+133
+00:09:32,080 --> 00:09:37,820
+الأعمدة طيب الصفوف هي تنتمي ل natural number أو
+
+134
+00:09:37,820 --> 00:09:41,460
+natural number نقص Zeroيعني بدك تبدأ من واحد ماشي
+
+135
+00:09:41,460 --> 00:09:43,960
+بدك تبدو زي ما كنتوا في البرمجة بتبدو ال rate
+
+136
+00:09:43,960 --> 00:09:47,920
+بتبعتكم من zero بمش الحال برضه ك index ببدأ من
+
+137
+00:09:47,920 --> 00:09:51,360
+zero اه ممكن ال pointer تبعك على طول يعمل يكون
+
+138
+00:09:51,360 --> 00:09:56,020
+referring لل zero مباشرة بمش الحال نفس الكلام ال
+
+139
+00:09:56,020 --> 00:09:59,540
+column مشموعة ال columns اللي عندك هي تنتمي ل
+
+140
+00:09:59,540 --> 00:10:02,120
+natural number برضه بتبدأ ايه من صفر او من واحد
+
+141
+00:10:02,120 --> 00:10:06,220
+وبتستمر حسب حجم ال matrix تبعتك حسب حجم ال matrix
+
+142
+00:10:06,220 --> 00:10:12,080
+فهنا هدول ال input اعطينيال location تبع ال row
+
+143
+00:10:12,080 --> 00:10:17,260
+بتاع ال column عشان اعطيك ال value قيمته فقيمته
+
+144
+00:10:17,260 --> 00:10:22,760
+هتكون هي set او عناصر set بس كل عنصر من عناصر ال
+
+145
+00:10:22,760 --> 00:10:26,660
+set هذه معرف بمين بال location تبعه فإذا بقدر
+
+146
+00:10:26,660 --> 00:10:29,940
+أسميها الآن مدام أفهمناها بقدر أقول أن ال function
+
+147
+00:10:29,940 --> 00:10:34,420
+لل matrix A from natural by natural numbers اللي
+
+148
+00:10:34,420 --> 00:10:41,280
+هي ال row by columnتقاش لل code domain أو لل range
+
+149
+00:10:41,280 --> 00:10:46,860
+سبعكم S هذه ال set of elements انهم elements ال
+
+150
+00:10:46,860 --> 00:10:50,960
+elements تبعون ال matrix عناصر ال matrix نفسها لما
+
+151
+00:10:50,960 --> 00:10:53,940
+نقول في عندي matrix بهذا الشكل ال matrix هذه واحد
+
+152
+00:10:53,940 --> 00:10:59,460
+اتنين خمسة سبعة ففعليا العناصر بتاعتنا بنتكلم عن
+
+153
+00:10:59,460 --> 00:11:10,200
+واحد اتنين خمسة سبعة as a Sلكن هدول عشان اعرفهم
+
+154
+00:11:10,200 --> 00:11:14,920
+بالظبط داخل ال matrix لازم اكون معرف ال location
+
+155
+00:11:14,920 --> 00:11:18,060
+تبعهم لازم نعرف ال location تبعهم فال location
+
+156
+00:11:18,060 --> 00:11:23,060
+تبعهم في الحالة دي اذا بتكلم عن مربع بده يكون
+
+157
+00:11:23,060 --> 00:11:31,120
+الرقم تبع الصف و رقم العمود اعطيني رقم و رقم ك two
+
+158
+00:11:31,120 --> 00:11:36,790
+indices عشان اعطيكما يقابلها من عنصر فبتقدر تحطها
+
+159
+00:11:36,790 --> 00:11:40,690
+بشكل matrix وإلا مش هتقدر تحطها بشكل matrix يعني
+
+160
+00:11:40,690 --> 00:11:44,410
+الواحد وين بدك تحطه هنا انت عارف .. بده افترض ان
+
+161
+00:11:44,410 --> 00:11:49,350
+انت عارف ان هي 2x2 او 3x5 أبعادها عارفهم لكن مش
+
+162
+00:11:49,350 --> 00:11:51,950
+عارف ال location تبع كل واحد منهم فإذا ال location
+
+163
+00:11:51,950 --> 00:11:55,750
+تبع كل واحد منهم هو يعرف بال index وال index ك
+
+164
+00:11:55,750 --> 00:11:58,710
+input لأن هو اللي أنا مستنين منك اعطيني ال input
+
+165
+00:11:58,710 --> 00:12:03,190
+عشان اعطيك العنصرفبيعرف من natural number by
+
+166
+00:12:03,190 --> 00:12:07,330
+natural number على اعتبار ان احنا بنتكلم عن صف أول
+
+167
+00:12:07,330 --> 00:12:09,930
+تاني تاري تامنش هنقول اتنين و نص مافيش حاجة اسم
+
+168
+00:12:09,930 --> 00:12:12,610
+الصف اتنين و نص عشان هيك الأنسب هي نعرفها ب
+
+169
+00:12:12,610 --> 00:12:16,330
+natural number تمام
+
+170
+00:12:16,330 --> 00:12:22,690
+ففي الحالة دايما هنقول I الانصر I هنا دائما لازم
+
+171
+00:12:22,690 --> 00:12:30,930
+تكون mean أقل من Mمن البعد تبع الصفوف و ال j بدها
+
+172
+00:12:30,930 --> 00:12:35,870
+تكون أقل من البعد الأعمدة طيب حد منكم يقول ليه ما
+
+173
+00:12:35,870 --> 00:12:42,670
+قلتش يساوي لبدأ من الصفر أحسنته بدأ من العرف من
+
+174
+00:12:42,670 --> 00:12:45,570
+الأساس natural number فإذا أنا بدأ من الصفر يعني
+
+175
+00:12:45,570 --> 00:12:50,170
+فعليا ال maximum هنا عددهم صحيح الأعمدة مثلا عددهم
+
+176
+00:12:50,170 --> 00:12:55,170
+M بس هم فعليا من الصفر تقام ناقص واحدتفهم؟ ناقص
+
+177
+00:12:55,170 --> 00:12:59,550
+واحد فبديش و أنت بتقرا و بعدين تتخربط معاكوا لأ لأ
+
+178
+00:12:59,550 --> 00:13:04,510
+نسينا أو يساوي لأ مش أي ساوي لأن احنا بدين بال
+
+179
+00:13:04,510 --> 00:13:08,330
+natural number لما أعرفها من هنا positive okay
+
+180
+00:13:08,330 --> 00:13:12,370
+بتصير أو يساوي لما نعرفها positive integers بتصير
+
+181
+00:13:12,370 --> 00:13:17,290
+يساوي طيب فبنقدر نقول أن ال function ل ال matrix A
+
+182
+00:13:18,410 --> 00:13:25,030
+Given ال location I و J هو العنصر الموجود في I و J
+
+183
+00:13:25,030 --> 00:13:29,250
+فإذا هنا تعريف أزا matrix الآن بعض العملية البسيطة
+
+184
+00:13:29,250 --> 00:13:33,470
+اللي أخدتها سابقا عشان نعمل summation ل ال
+
+185
+00:13:33,470 --> 00:13:38,740
+matrices محتاجينأول شغلة أن الاتنين بتساوي في
+
+186
+00:13:38,740 --> 00:13:42,520
+الأبعاد فإذا إن لهم نفس ال rows نفس ال columns ثم
+
+187
+00:13:42,520 --> 00:13:46,140
+بعمل الان summation لكل number مع ال corresponding
+
+188
+00:13:46,140 --> 00:13:51,560
+له في ال matrix التانية عشان ينتج أنصر في matrix
+
+189
+00:13:51,560 --> 00:13:56,900
+منتجة أو horizontal matrix المنتجة اللي ناجحة في
+
+190
+00:13:56,900 --> 00:14:01,060
+الآخر تمام ماعتقدش أن فيها مشكلة و الأمثلة كتير
+
+191
+00:14:01,060 --> 00:14:06,430
+واضحة على هذا الموضوعطيب ال products او عملية ضرب
+
+192
+00:14:06,430 --> 00:14:13,550
+للمصفوفات ماخدينها سابقالكن هنا بنتكلم عن شوية
+
+193
+00:14:13,550 --> 00:14:17,250
+خصوصية في جزئية الضرب ان احنا بنتعامل مع حاجة
+
+194
+00:14:17,250 --> 00:14:21,210
+اسمها dot product dot product ان انا بدرب vector ب
+
+195
+00:14:21,210 --> 00:14:24,110
+vector ايه ال vector ب ايه ال vector ال vector
+
+196
+00:14:24,110 --> 00:14:26,470
+اللي هو عبارة عن ال role الأولى في ال column
+
+197
+00:14:26,470 --> 00:14:30,030
+التانية role الأولى في ال column التانية هنا أشهر
+
+198
+00:14:30,030 --> 00:14:38,570
+معرفة من ال K فإذا لو قلنا M في K هذه matrix أولىو
+
+199
+00:14:38,570 --> 00:14:47,570
+بدنا نضربها في K في M عشان
+
+200
+00:14:47,570 --> 00:14:51,310
+ينتج عندي M في N
+
+201
+00:14:55,170 --> 00:14:59,830
+طيب ليش لازم يكون متساويين عدد الصفوف .. عدد
+
+202
+00:14:59,830 --> 00:15:03,510
+الأعمدة في التانية مع عدد الصفوف في الأولى؟ عشان
+
+203
+00:15:03,510 --> 00:15:06,450
+يتحقق جزئية ال dot product هذه ان انا في النهاية
+
+204
+00:15:06,450 --> 00:15:10,890
+هاخد row by row ده اخد row من الأولى مع column من
+
+205
+00:15:10,890 --> 00:15:15,590
+التانية طب هتنركز عشان اضرب متجاهين في بعض معناته
+
+206
+00:15:15,590 --> 00:15:19,810
+كل عنصر في العنصر المقابل له في المتجه التاني
+
+207
+00:15:19,810 --> 00:15:23,810
+معناه ذلك ان عدد العناصر هنا لازم يكون بيساوي عدد
+
+208
+00:15:23,810 --> 00:15:28,530
+العناصر هناعشان اقدر اقول هدى فى هدى زائد التانى
+
+209
+00:15:28,530 --> 00:15:31,590
+فى التانى زائد التالت فى التالت زائد الرابع فى
+
+210
+00:15:31,590 --> 00:15:34,710
+الرابع طيب عشان نتحقق الكلام معناته ان فعلا عدد
+
+211
+00:15:34,710 --> 00:15:41,480
+العناصر لالأعمدة في الأول لازم يساوي عدد العناصر
+
+212
+00:15:41,480 --> 00:15:47,220
+في الصفوف للتاني عشان فعلا كل عنصر يلاجي مقابله
+
+213
+00:15:47,220 --> 00:15:52,060
+عنصر ينضرب معاه ونجمع نعمل summation فإذا واضح أن
+
+214
+00:15:52,060 --> 00:15:56,700
+أنا جاي أعمل summation صحيح بدرب و بجمع بدرب و
+
+215
+00:15:56,700 --> 00:16:02,940
+بجمع هايا نضرب و نجمع ضربنا و واضح أنه ال counter
+
+216
+00:16:02,940 --> 00:16:06,020
+تبع عملية الضرب الآن هي عناصر
+
+217
+00:16:08,070 --> 00:16:13,810
+متغير لكيه هيبدأ من واحد لما maximum يصل لمن لكيه
+
+218
+00:16:13,810 --> 00:16:16,650
+او من الصفر اذا كنت بده natural number مش هتفرق
+
+219
+00:16:16,650 --> 00:16:19,850
+كتير فهنا المتغير اللي هو ال L
+
+220
+00:16:30,360 --> 00:16:33,740
+مش هتكمل أكتر من هيك لأنه مافيش أعمدة أكتر من هيك،
+
+221
+00:16:33,740 --> 00:16:36,500
+مافيش أعمدة في الأولى ولا صفوف في التانية أكتر من
+
+222
+00:16:36,500 --> 00:16:39,960
+هيك، فإذن حاليًا لما نعملت ال summation من واحد to
+
+223
+00:16:39,960 --> 00:16:44,900
+كيه، وكيه احنا عارفين إنه مشتركهي مشترك عدد أعمد
+
+224
+00:16:44,900 --> 00:16:50,160
+الأول وهي نفس عدد صفوف التاني للأنصر اللي موجود
+
+225
+00:16:50,160 --> 00:17:01,860
+فيه الصف I و العمود J هذا مش هيتغيروا لأنهم ثابتين
+
+226
+00:17:01,860 --> 00:17:06,760
+بالنسبة لل summation بالنسبة لل summation لما فتقت
+
+227
+00:17:06,760 --> 00:17:09,480
+كنا ماخدين ال summation يقولنا ان في الحالة هذه I
+
+228
+00:17:09,480 --> 00:17:18,140
+كأنها freeيعني ثابت فإذا I و J هدول ثابتين وهدول
+
+229
+00:17:18,140 --> 00:17:25,530
+اللي بيعتوني في الآخر عنصرالناتج C I و J طيب هو
+
+230
+00:17:25,530 --> 00:17:28,230
+مين المتغير في الحالة هذه؟ المتغير الحقيقي هي
+
+231
+00:17:28,230 --> 00:17:36,650
+عناصر عمود الصف الأول مع عناصر صفوف العمود التانية
+
+232
+00:17:36,650 --> 00:17:41,010
+اللي هم العناصر هذه اللي بدنا نحكي عنها اللي احنا
+
+233
+00:17:41,010 --> 00:17:46,770
+في المثال اللي وضحنا هنا أربعة تمام فإذا من واحد
+
+234
+00:17:46,770 --> 00:17:50,130
+لأربعة في المثال اللي عندنا اللي هو ل K يعني
+
+235
+00:17:51,310 --> 00:17:55,690
+بالنسبة للتعريف الأعلى فهذه ليش احنا بنفصل فيها
+
+236
+00:17:55,690 --> 00:17:58,430
+انا عارف ان انتوا بتعملوها تلقائيا وبشكل سريع بس
+
+237
+00:17:58,430 --> 00:18:01,650
+انا بفصل فيها لإن هذه عناصر أساسية لما بدك تيجي
+
+238
+00:18:01,650 --> 00:18:06,730
+تشتغل مع الكمبيوتر بدك تكتب الأكواد بعيد و بزيد
+
+239
+00:18:06,730 --> 00:18:09,790
+فيها مش ان انا مش عارف ان انتوا ماخدينها عارف ان
+
+240
+00:18:09,790 --> 00:18:12,530
+انتوا ماخدينها و من زمان ماخدينها بس بنعيد و بنزيد
+
+241
+00:18:12,530 --> 00:18:16,430
+فيها لإنه بدنا نثبت كيف تتعامل مع الأكواد بقرا
+
+242
+00:18:16,430 --> 00:18:20,980
+المعلومة هذه هنصير نقولها على السريعبدنا نكتب code
+
+243
+00:18:20,980 --> 00:18:23,500
+بدك تكون فاهم ان اه ما هي ده عملت ضرب .. ضرب
+
+244
+00:18:23,500 --> 00:18:27,600
+مصفوفات حيكون ال code تلت اربعة أسطور خلاص بدك
+
+245
+00:18:27,600 --> 00:18:32,340
+تكون جاهز انك انت تعديها على السريعمكتوبة كود
+
+246
+00:18:32,340 --> 00:18:36,500
+كأكواد تمام فعشان ذلك لازم تكون فاهمينها كويس لإن
+
+247
+00:18:36,500 --> 00:18:39,020
+هو ده الهدف أصلا من المصاق احنا مش بنقول ان احنا
+
+248
+00:18:39,020 --> 00:18:41,620
+بدنا نعطيكوا علم جديد المصاق اللي عنده الآن مافيش
+
+249
+00:18:41,620 --> 00:18:44,780
+و لا معلومة جديدة بالمناسبة لو جاتت طلعت عليها
+
+250
+00:18:44,780 --> 00:18:47,480
+هتلاقي ان هي معلومات مخدينها كل مرة في سنة من
+
+251
+00:18:47,480 --> 00:18:52,440
+هالسنوات اللي فاتت لكنتترتب بشكل انه يبدأ تهيئك
+
+252
+00:18:52,440 --> 00:18:56,360
+تبرمجها تهيئك بعد هيك لو انطلب منك العملية
+
+253
+00:18:56,360 --> 00:19:01,100
+الحسابية هذه ك code مش تحل على ايدك كأكواد انت
+
+254
+00:19:01,100 --> 00:19:05,020
+جاهز عارف ال .. يعني خليني اقول استراتيجية تاعة
+
+255
+00:19:05,020 --> 00:19:08,500
+العملية نفسها فهي استراتيجية تعملية summation فانت
+
+256
+00:19:08,500 --> 00:19:11,660
+كل عمليتك كبرمجة بتاكي تحولها ل summation أهم شغل
+
+257
+00:19:11,660 --> 00:19:15,480
+هي جزية ال summation هذه اللي هي من I ل J و زي ما
+
+258
+00:19:15,480 --> 00:19:20,520
+قلنا ال L هوال .. ال .. ال bound variable تبعك
+
+259
+00:19:20,520 --> 00:19:26,680
+اللي هو من واحد ل K ل K عشان نعمل ال element I و J
+
+260
+00:19:26,680 --> 00:19:33,080
+في الحالة هذه حسب ما احنا شايفين قدامنا I و J
+
+261
+00:19:33,080 --> 00:19:39,920
+تمام؟ جيد فالحل كأنه انت بتضرب مجموعة vectors مع
+
+262
+00:19:39,920 --> 00:19:43,080
+بعضهم تضرب مجموعة vectors مع .. مع بعضهم
+
+263
+00:19:46,180 --> 00:19:49,500
+تمام الحاجة المهمة بدك تاخد بالك أنه احنا بنتكلم
+
+264
+00:19:49,500 --> 00:19:55,100
+عن ضرب مصففات ضرب المصففات ليست تبدلية ضرب
+
+265
+00:19:55,100 --> 00:20:00,400
+المصففات ليست تبدلية بمعنى لما بقول a في b هي ليست
+
+266
+00:20:00,400 --> 00:20:06,940
+b في a هي ليست b في a تماممثال و اعتقد هذا مش
+
+267
+00:20:06,940 --> 00:20:10,140
+هيكون فيه مشكلة لأن احنا ماعنى مش كتير معنى في
+
+268
+00:20:10,140 --> 00:20:12,920
+العمليات اليدوية جد ما احنا معنين ان احنا فهمنا
+
+269
+00:20:12,920 --> 00:20:15,640
+الاستراتيجية عشان ال algorithm بكرا بعد هيك انت
+
+270
+00:20:15,640 --> 00:20:20,280
+بتضرب زي ما زي ما قلنا صف فعمود فباستخدام ال dot
+
+271
+00:20:20,280 --> 00:20:24,960
+product باستخدام dot product فعنصر فعنصر عنصر
+
+272
+00:20:24,960 --> 00:20:30,850
+فعنصر و بتجمع عشان تشوفأنه فيكتر هذا كان ك raw
+
+273
+00:20:30,850 --> 00:20:36,070
+الأول ك column الأول معناته الأول في الأول أصبح في
+
+274
+00:20:36,070 --> 00:20:41,850
+الناتج هيكون العنصر الأول في الصف مع العنصر الأول
+
+275
+00:20:41,850 --> 00:20:46,910
+في العمود فبيجي هنا مجموعة العملية و هكذا و هكذا
+
+276
+00:20:46,910 --> 00:20:54,760
+تقيص على ذلك مش مشكلة في العملية نفسها طيبعملية
+
+277
+00:20:54,760 --> 00:20:57,700
+الضرب ممكن تقودنا لحاجة اسم ال identity matrices
+
+278
+00:20:57,700 --> 00:21:01,580
+ال matrices هذه لل identity او ال identity
+
+279
+00:21:01,580 --> 00:21:07,960
+matrices هي matrix خلينا نسميها محايدة بمعنى إذا
+
+280
+00:21:07,960 --> 00:21:11,140
+ضربت في أي matrix أخرى هتظل ال matrix أخرى كما هي
+
+281
+00:21:11,140 --> 00:21:16,440
+مش هيتغير معاك شيء فهذا النوع بيكون له خصوصية
+
+282
+00:21:16,440 --> 00:21:21,620
+الخصوصية طبعته طبعا احنا نسميها matrices لأنها مش
+
+283
+00:21:21,620 --> 00:21:27,410
+matrix واحدةإذا كان أول شغلة بتاخد بالك منها ان هي
+
+284
+00:21:27,410 --> 00:21:32,350
+square هي square matrix square matrix مربعة معناه
+
+285
+00:21:32,350 --> 00:21:35,830
+ذلك إن إذا المربعة هي واحد في واحد ولا اتنين في
+
+286
+00:21:35,830 --> 00:21:38,590
+اتنين ولا تلاتة في تلاتة ولا اربعة في اربعة في
+
+287
+00:21:38,590 --> 00:21:41,730
+جميع الأحوال حسب الأنواع اللي واختلفتعتها هي بتتفق
+
+288
+00:21:41,730 --> 00:21:48,910
+في خاصية مهمة جدا انه بغض النظر عنجدش في جدش فهي N
+
+289
+00:21:48,910 --> 00:21:53,550
+وخلاص فبعرف ان هذه ال N اختزلت البعدين الصفوف
+
+290
+00:21:53,550 --> 00:21:58,690
+والاعمدة معاها فبسميها I N فهي من الدرجة N حتى
+
+291
+00:21:58,690 --> 00:22:02,190
+بسميها ال order N وخلاص من الدرجة او ال degree N
+
+292
+00:22:02,190 --> 00:22:07,250
+فهي N في N هي عبارة عن matrix لمجموعة عناصر هسميها
+
+293
+00:22:07,250 --> 00:22:10,510
+دلتة العناصر هذه حسب I وJ ال location تبعها في
+
+294
+00:22:10,510 --> 00:22:14,010
+الصف في العمود بحيث ان الدلتة هذه بتساوي واحد اذا
+
+295
+00:22:14,010 --> 00:22:18,540
+كانوا بيساوي بعضالصف والعمود أو صفر otherwise إذا
+
+296
+00:22:18,540 --> 00:22:24,140
+بيسويش بعض ففي الحالة هذه بنعرفها بهذا الشكل لها
+
+297
+00:22:24,140 --> 00:22:29,560
+قيمتين as a set لكن وين ال location للقيمتين هدولة
+
+298
+00:22:29,560 --> 00:22:34,020
+عشان نحطهم بشكل مرتب diagonal ال diagonal ones
+
+299
+00:22:34,020 --> 00:22:41,480
+otherwise zeros بغض النظر جديش قيمة n فعلى
+
+300
+00:22:41,480 --> 00:22:48,210
+ال diagonal وخلاصعشان ننتج هذه ال identity
+
+301
+00:22:48,210 --> 00:22:52,810
+matrices هتنتج من ان ببدروا بال matrix في ال
+
+302
+00:22:52,810 --> 00:22:58,950
+inverse تبعها ان وجدت ان وجدت طيب عشان يوجد اول
+
+303
+00:22:58,950 --> 00:23:02,090
+شغلة لازم يكون المصفوفة نفسها او ال matrix نفسها
+
+304
+00:23:02,090 --> 00:23:07,350
+هي square matrixأول شرط هي square matrix عشان تفكر
+
+305
+00:23:07,350 --> 00:23:12,070
+تجيب لها ال inverse فمعنى ذلك انه هذا بنتسميه
+
+306
+00:23:12,070 --> 00:23:16,210
+necessary condition شرط ضروري و لحظوا كلمة شرط
+
+307
+00:23:16,210 --> 00:23:21,790
+ضروري مش بالضروري ان هو كافي يعني ممكن تكونمربعة
+
+308
+00:23:21,790 --> 00:23:26,390
+square matrix ومالهاش inverse برضه عادي بس عشان
+
+309
+00:23:26,390 --> 00:23:29,930
+يكون لها inverse أول شرط لازم تكون مربعة فانت لما
+
+310
+00:23:29,930 --> 00:23:33,270
+تش تتطلع تلاقي في عندك matrix ليست مربعة على طول
+
+311
+00:23:33,270 --> 00:23:36,050
+خلاص مافيش ده اتدور على inverse مش هتلاقي ال
+
+312
+00:23:36,050 --> 00:23:40,800
+inverse مش هتطلع لها ال inverseو مش كل المصفوفات
+
+313
+00:23:40,800 --> 00:23:44,580
+المربعة لها inverse في نفس الوقت ليش؟ لأن العملية
+
+314
+00:23:44,580 --> 00:23:48,380
+نفس الحسابية اللي هنشوفها الآن في إنتاج المصفوفة
+
+315
+00:23:48,380 --> 00:23:53,820
+ال inverse أو العكسية هنجد أنه ممكن تطلع undefined
+
+316
+00:23:53,820 --> 00:23:57,100
+ممكن تطلع undefined كويس أما الشرط الوحيد اللي
+
+317
+00:23:57,100 --> 00:24:00,840
+احنا كلنا عارفينه أنه في الآخر ال inverse هذه ال
+
+318
+00:24:00,840 --> 00:24:05,660
+inverse نفسها إذا ضربناها في المصفوفة Aفبيعطيني ال
+
+319
+00:24:05,660 --> 00:24:10,240
+identity و تبادلية الحالة هذه اذا كان المصفوفة ايه
+
+320
+00:24:10,240 --> 00:24:13,520
+في ال inverse تبعها او ال inverse تبعها في ايه في
+
+321
+00:24:13,520 --> 00:24:16,520
+الحالتين بيعطيني ال identity matrix في الحالتين
+
+322
+00:24:16,520 --> 00:24:21,900
+بيعطيني identity matrix طيب تبادلية مافيش فيها
+
+323
+00:24:21,900 --> 00:24:26,710
+مشكلة و دايما بتكون uniqueيعني بمعنى انه كل matrix
+
+324
+00:24:26,710 --> 00:24:30,410
+إذا إلها inverse فهو inverse وحيد، انت متوقعش أنه
+
+325
+00:24:30,410 --> 00:24:33,670
+هيكون لها أكتر من inverse، هي inverse وحيد طيب
+
+326
+00:24:33,670 --> 00:24:37,950
+عملية ال inverse طبعاً إلها قوانين كتيرة وإلها شغل
+
+327
+00:24:37,950 --> 00:24:41,190
+كتير، لكن احنا زي ما قلنا إذا احتجتها، بدك أن تدور
+
+328
+00:24:41,190 --> 00:24:43,970
+على قوانينها عشان تعمل لها برنامج تبعك، فمش هناخد
+
+329
+00:24:43,970 --> 00:24:48,980
+أكتر من اللي هو two by two2 by 2 matrix سهلة و
+
+330
+00:24:48,980 --> 00:24:52,940
+ممكن نتحرك فيها بسهولة ده بالهيك كنا بنحط 3 by 3 و
+
+331
+00:24:52,940 --> 00:24:55,220
+بعدين وجدت انه لأ خلاص ما هي الفكرة ال concept
+
+332
+00:24:55,220 --> 00:24:59,620
+موجود بتظل عملية معادلات مش اشكال المعادلات المهم
+
+333
+00:24:59,620 --> 00:25:02,380
+انه برمجيا احنا فهمنا ايش بدنا نعمل مع الكمبيوتر
+
+334
+00:25:02,380 --> 00:25:06,120
+كويس فال inverse اذا بتكلم عن 2 by 2 automatically
+
+335
+00:25:06,120 --> 00:25:12,450
+ال diagonal بتبدل عناصره ال co-diagonalبتبدل
+
+336
+00:25:12,450 --> 00:25:17,550
+إشارته وبتقسم على ال determinant فال determinant
+
+337
+00:25:17,550 --> 00:25:21,670
+هذه إذا كانت defined هنا وجدنا inverse إذا كانت
+
+338
+00:25:21,670 --> 00:25:25,810
+undefined لأن حيكون في عملية طرح فالطرح هدف إنها
+
+339
+00:25:25,810 --> 00:25:31,040
+إذا وصلنا ل zero ممكن يعمل مشكلةفهي ال determinant
+
+340
+00:25:31,040 --> 00:25:36,440
+بتاعتنا او قيمة المصفوفة اللي هو ال diagonal اضرب
+
+341
+00:25:36,440 --> 00:25:41,280
+ال diagonal ناقص ال co diagonal اذا
+
+342
+00:25:41,280 --> 00:25:47,740
+ما طلعش صفر بتقدر تجيبلها قيمة لل inverse بحيث انه
+
+343
+00:25:47,740 --> 00:25:51,380
+زي ما قلنا بدلنا ال diagonal و عكسنا شرط ال co
+
+344
+00:25:51,380 --> 00:25:55,770
+diagonal بدون ما نبدلهمخلاص ناتج هذا العملية هيكون
+
+345
+00:25:55,770 --> 00:26:01,750
+اكيد inverse للمصفوفة اللى عندك طيب ممتاز جدا هي
+
+346
+00:26:01,750 --> 00:26:07,030
+هيكى بنتكلم عن مضروبة في ال inverse تبعها طب ممكن
+
+347
+00:26:07,030 --> 00:26:10,650
+تكون المصفوفة نفسها مضروبة في نفسها زي ان نقول
+
+348
+00:26:10,650 --> 00:26:15,140
+المصفوفة تربيةاو تكييب او to the power of 4 او to
+
+349
+00:26:15,140 --> 00:26:19,400
+the power of 5 او ال 5 power ففي الحالة هذه نقدر
+
+350
+00:26:19,400 --> 00:26:23,480
+in general نقول ان ممكن اجيب ال inverse او ال
+
+351
+00:26:23,480 --> 00:26:29,570
+power بيلأ المصفوفة A فبسميها A to the power P هذه
+
+352
+00:26:29,570 --> 00:26:35,770
+عبارة عن A في A في A في A P مرة أو P times
+
+353
+00:26:35,770 --> 00:26:39,150
+فضربناها في نفسها كذا مرة بالمناسبة هنا مين هتضرب
+
+354
+00:26:39,150 --> 00:26:43,730
+قبل مين ما هم كلهم زي بعض مش هتفرج مش هتفرج ناخد
+
+355
+00:26:43,730 --> 00:26:48,810
+بالنا بس إنه إذا كان ال P هنا Zeroيعني اي matrix
+
+356
+00:26:48,810 --> 00:26:52,450
+to the bar zero فانا بتكلم عن ال identity نتكلم عن
+
+357
+00:26:52,450 --> 00:26:57,030
+ال identity ت automatic بتحطها ال identity بنفس ال
+
+358
+00:26:57,030 --> 00:27:01,920
+order تبعها in معناته ال identity inطبعا لما نجيب
+
+359
+00:27:01,920 --> 00:27:06,260
+انه نضرب matrix بهذا الشكل to the power 3 هي في
+
+360
+00:27:06,260 --> 00:27:09,860
+نفسها تلت مرات الان مش هيفرق معاك تضرب التنتين
+
+361
+00:27:09,860 --> 00:27:13,200
+اللي في الأول والناتج تضرب في التانية ولا التنتين
+
+362
+00:27:13,200 --> 00:27:15,940
+اللي في الآخر والناتج تضرب في الأولى مش هتفرق ده
+
+363
+00:27:15,940 --> 00:27:19,960
+من هيطلع معاك نفس الناتج نفس الجواب او نفس الناتج
+
+364
+00:27:20,770 --> 00:27:23,930
+فجزئية زيها دي برمج ايه ماتغلبش حالك انه مين جابل
+
+365
+00:27:23,930 --> 00:27:27,630
+مين خلاص مين ماينضرب مش هتفرج معاك المهم انه ينضرب
+
+366
+00:27:27,630 --> 00:27:38,250
+لها بحسب عدد المرات اللي هي ال P times لإن
+
+367
+00:27:38,250 --> 00:27:41,950
+هو اليو ستفير جاي انه احنا ضربنا عدد موت يا فسار
+
+368
+00:27:41,950 --> 00:27:44,650
+بتضرب هطلع بالأهل نفسنا لأ احنا ماضربناش نفسنا بل
+
+369
+00:27:44,650 --> 00:27:48,270
+احنا ضربنا في نفسه احنا يعني بنتكلم العنصر في نفسه
+
+370
+00:27:49,290 --> 00:27:53,430
+ال matrix في نفسها ما طلبناش بال inverse يعني احنا
+
+371
+00:27:53,430 --> 00:27:56,830
+ما طلبنا .. حتى اللحظة احنا ما طلبناش inverse في
+
+372
+00:27:56,830 --> 00:28:00,970
+ال power هنا احنا ما طلبناش نجيب ال inverse مصفوفة
+
+373
+00:28:00,970 --> 00:28:04,890
+to the power جديش to the power صفر خلاص identity
+
+374
+00:28:04,890 --> 00:28:10,410
+بس تكون مربعة تكون مربعة ال determinant تبعها مش
+
+375
+00:28:10,410 --> 00:28:13,330
+هيفرج معنا الآن لإن أنا مش رايح في اتجاه ان اجيب
+
+376
+00:28:13,330 --> 00:28:17,750
+inverseمش رايح في اتجاه هنا جيب inverse okay ال
+
+377
+00:28:17,750 --> 00:28:20,870
+identity يعني عفوًا ال matrix to the power 0 هي
+
+378
+00:28:20,870 --> 00:28:25,130
+identity بس هي بحث ذاتها إلها inverse بعرفش يمكن
+
+379
+00:28:25,130 --> 00:28:30,010
+أو يمكن لأ ماروحناش نجيب inverse إثبات أنه أي عدد
+
+380
+00:28:30,010 --> 00:28:33,650
+السفر متساوي zero متساوي واحد يعني على ال identity
+
+381
+00:28:33,650 --> 00:28:37,750
+يجب إننا ضربنا العدل نفسه في اللي هو ال .. لحظة
+
+382
+00:28:37,750 --> 00:28:41,330
+ماشي أنت لاحظ هنا to the power 0 يعني أنت ماضربتاش
+
+383
+00:28:41,330 --> 00:28:46,860
+في إشيانت مش ضريبة في اشي انت كل ما خاصية عندك زي
+
+384
+00:28:46,860 --> 00:28:51,900
+one million او كل هذا هيك to the power صفر هذا ايش
+
+385
+00:28:51,900 --> 00:28:55,940
+بيفرجش معانا كتير ومش هيفرج معاك كتير بمعنى ان
+
+386
+00:28:55,940 --> 00:28:58,680
+احنا مش رايحين نجيب ال inverse لان في الآخر انا
+
+387
+00:28:58,680 --> 00:29:03,720
+بدي اضربه في ال inverse يطلع ال identity فاهم
+
+388
+00:29:03,720 --> 00:29:08,040
+قصدي؟ بمعنى انا هنا ال a to the power zeroأنت
+
+389
+00:29:08,040 --> 00:29:10,800
+بتكون بدربها في إيش إيه؟ لما قولتوا ثبار اتنين
+
+390
+00:29:10,800 --> 00:29:14,280
+اللي هي ثورات تربيعية يعني معناته في مصفوفة في نفس
+
+391
+00:29:14,280 --> 00:29:17,980
+.. في مصفوفة تانية أو في نفسها بمعنى أنتوا لما
+
+392
+00:29:17,980 --> 00:29:22,380
+بتقول لأي معادلة أن هي تربيعية بتكون x تربيع أو
+
+393
+00:29:22,380 --> 00:29:27,560
+إذا كانت أكتر من متغير x و y فهنا برضه حتى هذه ال
+
+394
+00:29:27,560 --> 00:29:31,720
+order هذه بتسميه تربيعيأي معادلة بهذا الشكل نسميها
+
+395
+00:29:31,720 --> 00:29:35,700
+quadratic .. quadratic form طيب فإذا مصفوفة خلّينا
+
+396
+00:29:35,700 --> 00:29:38,360
+نسميها مصفوفة تانية أنا ماعنديش هنا مصفوفة تانية
+
+397
+00:29:38,360 --> 00:29:41,720
+مضربة فيها احنا ماتكلمش عن مصفوفة تانية مضربة فيها
+
+398
+00:29:41,720 --> 00:29:46,880
+just إنه power مافيش أي شرط هنا يعطيني إنه لابد
+
+399
+00:29:46,880 --> 00:29:50,740
+أكون لها inverse المهم إنها تكون مربعة خلاص إذا
+
+400
+00:29:50,740 --> 00:29:55,260
+مربعت و the power صفر identityidentity matrix تمام
+
+401
+00:29:55,260 --> 00:29:59,640
+بعد هيك بدك تضرب اكتر okay بتضرب مش مشكلة في عملية
+
+402
+00:29:59,640 --> 00:30:04,320
+الضرب كعملية ضرب طيب Transpose او Transposition
+
+403
+00:30:04,320 --> 00:30:09,760
+اللي هي المحور
+
+404
+00:30:09,760 --> 00:30:15,740
+او المحور لل matrix هي من شكلها بتعمل حوالين
+
+405
+00:30:15,740 --> 00:30:19,960
+المحور بتعمل flip بتعمل flip فبتعكس الصفوف اعمدة
+
+406
+00:30:19,960 --> 00:30:24,730
+بتعمل لل اعمدة صفوفطيب هذه اللي هي تطبيقات .. اللي
+
+407
+00:30:24,730 --> 00:30:27,910
+هي تطبيقات كتيرة الحقيقة في عملية ضبط وزن
+
+408
+00:30:27,910 --> 00:30:31,550
+المعادلات في كتير بتستخدم في عملية ضبط وزن
+
+409
+00:30:31,550 --> 00:30:33,870
+المعادلة لما يكون في عندك vector مضروب داخل
+
+410
+00:30:33,870 --> 00:30:37,710
+المعادلة أحيانا و by default ال vector هو في الآخر
+
+411
+00:30:37,710 --> 00:30:42,010
+بيكون عبارة عن column هو عبارة عن column بالأساس
+
+412
+00:30:42,010 --> 00:30:46,330
+يعني أنت لما بتقول ال vector كذا ال vector في معظم
+
+413
+00:30:46,330 --> 00:30:51,150
+تطبيقات الرياضيات بيسموه .. بيكون بهذا الشكلهذا هو
+
+414
+00:30:51,150 --> 00:30:54,790
+ال vector على عكس ما احنا نتخيل ان انتوا بتتخيلوا
+
+415
+00:30:54,790 --> 00:30:58,610
+ان ال vector بهذا الشكل اللي بتكتبوه شكل كصف هو
+
+416
+00:30:58,610 --> 00:31:03,570
+فعلا عمود هو فعلا عمود فمعظم الكتب اللي عارفها
+
+417
+00:31:03,570 --> 00:31:05,950
+الكلام هذا المفروض انه لما بيحطوه بهذا الشكل اش
+
+418
+00:31:05,950 --> 00:31:12,470
+ممكن فوقه بيحط فوق علامة Tاللي هي Transpose بمعنى
+
+419
+00:31:12,470 --> 00:31:15,710
+Transpose ال vector لأن ال vector هو هيك بهذا
+
+420
+00:31:15,710 --> 00:31:20,310
+الشكل أصلا صفوف أعمدة و أعمدة صفوف فهذا يتوفر
+
+421
+00:31:20,310 --> 00:31:24,730
+أحيانا في الورق في عملية الطباعة بدل ما أحطهم
+
+422
+00:31:24,730 --> 00:31:29,550
+column بحط رو و بمشي الحال طيب في عملية ضبط
+
+423
+00:31:29,550 --> 00:31:33,790
+المعادلات بتيجيك كتير معادلات متذكرين لما كنتوا
+
+424
+00:31:33,790 --> 00:31:39,960
+بتعملوا المعادلات الكيميائية و بدك تضبط المعادلةمش
+
+425
+00:31:39,960 --> 00:31:44,520
+هيك تضبط عدد ذرات توزنها تعملها عملية توزن
+
+426
+00:31:44,520 --> 00:31:48,760
+فالعملية هذه نفس الكلام برضه في العمليات الحسابية
+
+427
+00:31:48,760 --> 00:31:53,040
+الرياضية لما يكون في عندك matrices لازم تعملها ضبط
+
+428
+00:31:53,040 --> 00:31:57,000
+للمعادلة هل فعلا عملية الضرب لمجموعة ال matrices
+
+429
+00:31:57,000 --> 00:32:01,920
+هذه ممكن لو بهذا الشكل بدك تحطها بهذا الشكل يمكن
+
+430
+00:32:01,920 --> 00:32:06,060
+ما تظبطش فانت بدك تكون عارف مسبقا ان هي بهذا الشكل
+
+431
+00:32:06,060 --> 00:32:10,450
+لما بدك تيجي تضربها في matrix جنبهاهل في إمكانية
+
+432
+00:32:10,450 --> 00:32:13,390
+هذا الكلام ولا لأ هو الأولى أنها تكون بهذا الشكل
+
+433
+00:32:13,390 --> 00:32:17,430
+عشان تكون عملية الضرب أفضل فبيعمل عملية وزن
+
+434
+00:32:17,430 --> 00:32:20,710
+فبيحطولك T بحيث انه يوزنلك انه في إمكانية عملية
+
+435
+00:32:20,710 --> 00:32:21,050
+الضرب
+
+436
+00:32:23,790 --> 00:32:27,550
+فال Transposition من الحاجات اللي مهمة ان اقول
+
+437
+00:32:27,550 --> 00:32:32,690
+Transpose of Matrix A مثلا هي بكل بساطة ممكن
+
+438
+00:32:32,690 --> 00:32:37,470
+نسميها Transpose of A او A to the power T capital
+
+439
+00:32:37,470 --> 00:32:40,890
+او small في الحالتين مفهومة ان هو ده Transpose في
+
+440
+00:32:40,890 --> 00:32:46,010
+الحالتين مفهومة فبدل ما بتكون M في N بتصير N في M
+
+441
+00:32:46,680 --> 00:32:51,580
+بس فبتعكس صفوف اعمد او اعمدة صفوف زي هذا الشكل لو
+
+442
+00:32:51,580 --> 00:32:59,080
+مثلا حطيت سيخ قطري و لفته هتلاقي تشجلب صفوف اعمد
+
+443
+00:32:59,080 --> 00:33:06,960
+او اعمدة صفوف فصرت بتتكلم عن matrix B I و J تبعها
+
+444
+00:33:06,960 --> 00:33:12,800
+هي نفس A J و I عكسنا صفوف اعمد او اعمدة صفوف مش
+
+445
+00:33:12,800 --> 00:33:18,250
+اكتر من هيكطيب إذا وصلنا لمرحلة إنه بعد ما عملنا
+
+446
+00:33:18,250 --> 00:33:22,190
+العكس فوجدنا إنه ال matrix و ال transpose طبعها
+
+447
+00:33:22,190 --> 00:33:26,830
+متساوين فبنسميها symmetric بنسميها symmetric كويس
+
+448
+00:33:26,830 --> 00:33:30,550
+ففي الحالة هذه إذا كان square وهذا أهم شرط فيها
+
+449
+00:33:30,550 --> 00:33:33,670
+إذا كان هي square فممكن تكون symmetric otherwise
+
+450
+00:33:33,670 --> 00:33:37,630
+لأ لأن إذا ماكنتش square معناته عدد صفوف لا يسووا
+
+451
+00:33:37,630 --> 00:33:41,150
+عدد الأعمدة وفي الحالة هذه لو عكستها مستحيل يقلعوا
+
+452
+00:33:41,150 --> 00:33:44,570
+يسووا بعضبتطلع عدد الصفوف هنا مخالف لعدد الصفوف
+
+453
+00:33:44,570 --> 00:33:49,290
+هنا تمام فأول شرط عشان والله ممكن تكون symmetric
+
+454
+00:33:49,290 --> 00:33:52,510
+اي matrix ان عدد الصفوف هتسوى عدد الأعمد بتاعتها
+
+455
+00:33:52,510 --> 00:33:56,850
+تمام بعد هيك بتشوف ال diagonal تعمل خط على ال
+
+456
+00:33:56,850 --> 00:34:00,310
+diagonal و بتشوف ال upper و ال lower لل diagonal
+
+457
+00:34:00,310 --> 00:34:03,570
+ليه بيسووا بعض أو بيسووش بعض ك mirror حوالين ال
+
+458
+00:34:03,570 --> 00:34:08,870
+diagonal يعني
+
+459
+00:34:08,870 --> 00:34:11,070
+بتفترض كأن ال diagonal أصبح هو المراية
+
+460
+00:34:13,800 --> 00:34:17,020
+بهذا الشكل المراية فالمراية هذه كل عنصر هنا
+
+461
+00:34:17,020 --> 00:34:21,940
+بالنسبة للمراية في نفس الاتجاه و بنفس المسافة
+
+462
+00:34:21,940 --> 00:34:25,660
+المفروض ان نفس العنصر يكون هو هو بنفس الاتجاه و
+
+463
+00:34:25,660 --> 00:34:28,800
+نفس المسافة بشكل عمودي على ال diagonal المفروض ان
+
+464
+00:34:28,800 --> 00:34:32,680
+يطلعوا بسوء بعض هنا و هنا هنا و هنا و هنا كأن ال
+
+465
+00:34:32,680 --> 00:34:37,460
+diagonal فعلا mirror مستوية ايش يعني mirror مستوية
+
+466
+00:34:37,460 --> 00:34:39,900
+انت بتطلع على المراية فانت شايف البعد الحقيقي لك
+
+467
+00:34:39,900 --> 00:34:44,600
+عنهامش مقعرة ولا محدبة اللي هي convex ولا هي
+
+468
+00:34:44,600 --> 00:34:48,380
+concave لأنه convex او concave معناته ايش هتعمل؟
+
+469
+00:34:48,380 --> 00:34:53,920
+اللي هي مقعرة او محدة؟ هيعملك انعكاس خاطئ للمسافة
+
+470
+00:34:53,920 --> 00:34:57,180
+أما لإني بقولك هنا مستوية بمعنى ان نفس المسافة هنا
+
+471
+00:34:57,180 --> 00:35:01,060
+مقابل هنا فلأن لو جينا اتكلمنا عن مجموعة العناصر
+
+472
+00:35:01,060 --> 00:35:09,510
+اللي هنا لكل I و J أقل من N و لاحظ ماقلتش Mلأن أول
+
+473
+00:35:09,510 --> 00:35:12,870
+شرط هي تكون square أصلا وإلا ما هي من الأساس مش
+
+474
+00:35:12,870 --> 00:35:17,930
+symmetrical A I و J بيساوي A J و I خلاص معناته
+
+475
+00:35:17,930 --> 00:35:23,650
+symmetrical لكل I و J لكل I و J أنصر زي هذا أو
+
+476
+00:35:23,650 --> 00:35:28,570
+matrix زي هذه ليش؟ لأن أول شلية مش مربعة من الأساس
+
+477
+00:35:28,570 --> 00:35:34,410
+هي مش مربعة فهذه لأ هي خارج الحسبةSymmetric لاحظ
+
+478
+00:35:34,410 --> 00:35:39,790
+لما تعمل هي الخط هذه بعيدة مسافة نفسها هو نفس
+
+479
+00:35:39,790 --> 00:35:43,990
+العنصر هذه نفس الكلام نفسها نفس العنصر نفس العنصر
+
+480
+00:35:43,990 --> 00:35:48,770
+فإذا نقدر نقول عليها symmetric اه symmetric جبلها
+
+481
+00:35:48,770 --> 00:35:52,310
+transpose المفروض يطلع بيساوي نفس ال a نفس ال a
+
+482
+00:35:52,310 --> 00:35:58,890
+التالتة not symmetric لعنصر واحد بس هدولة بهدون
+
+483
+00:35:58,890 --> 00:36:01,790
+بيساوي بعض هدول بيساوي بعض بس هنا لأ بيساووش بعض
+
+484
+00:36:01,790 --> 00:36:02,410
+في التالتة
+
+485
+00:36:08,090 --> 00:36:11,870
+هذا الكلام كتير هنحتاجه بكرة لما نروح لل relations
+
+486
+00:36:11,870 --> 00:36:13,630
+و لل graph
+
+487
+00:36:20,550 --> 00:36:23,770
+الـ 01 matrices في نوع من أنواع ال matrices اللي
+
+488
+00:36:23,770 --> 00:36:27,270
+هو ممكن نسميه 01 matrices هذي واضح من اسمه ان انا
+
+489
+00:36:27,270 --> 00:36:33,970
+بتكلم عن كل عناصر هي 01 او 10 فهي كل عناصره أصفر و
+
+490
+00:36:33,970 --> 00:36:37,170
+وحيد مناسبة جدا لل logic اللي أخدناها سابقا بحيث
+
+491
+00:36:37,170 --> 00:36:40,310
+ان هي false و true فإذا حتى ال false و true بقدر
+
+492
+00:36:40,310 --> 00:36:44,560
+امثله بشكل matricesبحيث أن الصفر زي ما انتوا
+
+493
+00:36:44,560 --> 00:36:46,980
+عارفين هو force الواحد زي ما انتوا برضه عارفين هو
+
+494
+00:36:46,980 --> 00:36:50,800
+true و بنخلص عليه ال operations اللي ممكن نستخدمها
+
+495
+00:36:50,800 --> 00:36:58,420
+أول شغلة ال mate المقابلة بين a و b mate اللي هي
+
+496
+00:36:58,420 --> 00:37:01,440
+المقابلة إذا كان والله ال matrix a و ال matrix b
+
+497
+00:37:01,440 --> 00:37:03,880
+بيقابلوا بعض أو بيقابلوش بعض فمعنى ذلك أنه ممكن
+
+498
+00:37:03,880 --> 00:37:07,720
+يكون أهم شرط عشان تعمل هذه العملية عملية ال mate
+
+499
+00:37:07,720 --> 00:37:12,620
+أنه يكونوا ال two matrices بيسووا بعضمش بيساووا
+
+500
+00:37:12,620 --> 00:37:15,820
+بعض في ال elements بيساووا بعض في الأبعاد في ال
+
+501
+00:37:15,820 --> 00:37:18,740
+directions بمعنى لهم نفس ال rows نفس ال columns
+
+502
+00:37:18,740 --> 00:37:22,700
+هاي أول شرط ان التنتين بيساووا بعض حجما فلازم
+
+503
+00:37:22,700 --> 00:37:27,180
+يساووا بعض حجما عشان تمسك كل عنصر zero او one مع
+
+504
+00:37:27,180 --> 00:37:33,300
+ال corresponding له و تعمل and فبتعمل
+
+505
+00:37:33,300 --> 00:37:38,010
+ايش العناصر اللي متساوية بين هنا و هنافبتعمل
+
+506
+00:37:38,010 --> 00:37:41,270
+meeting كأنك عملت مقابلة مين اللي أجوا على
+
+507
+00:37:41,270 --> 00:37:46,110
+المقابلة فالعنصر خلينا الصف الأول والعمود الأول في
+
+508
+00:37:46,110 --> 00:37:48,730
+ال matrix الأولى الصف الأول والعمود الأول في ال
+
+509
+00:37:48,730 --> 00:37:51,550
+matrix التانية إذا الإتنين one one معناته true
+
+510
+00:37:51,550 --> 00:37:56,430
+true الإتنين موجودين في مقابلة واحد منهم صفر مافيش
+
+511
+00:37:56,430 --> 00:38:01,760
+مقابلةمش share؟ انت اجيت بس اللي وعدك ماجهاش،
+
+512
+00:38:01,760 --> 00:38:04,220
+راحت، مافيش مقابلة، فعليا meet؟ لأ مافيش meet،
+
+513
+00:38:04,220 --> 00:38:09,680
+تمام ففي الحالة هذه بنعمل كأننا عملناها and إذا
+
+514
+00:38:09,680 --> 00:38:15,290
+كان طلب منك meet a and bعلى طول and كل عنصر مع
+
+515
+00:38:15,290 --> 00:38:17,890
+عنصر اللي قابله .. كل عنصر مع عنصر اللي قابله و
+
+516
+00:38:17,890 --> 00:38:21,150
+انتهين على هيك خلصت الأمور ممكن كتابتها بهذا الشكل
+
+517
+00:38:21,150 --> 00:38:25,330
+مباشرة كأنها dot كأنها dot كأنها ضرب عادي فبتفهم
+
+518
+00:38:25,330 --> 00:38:30,670
+منها ضرب عادي ان انت بتعمل conjunction او and او
+
+519
+00:38:30,670 --> 00:38:36,100
+and العملية التانية هي ال joinالـ join تجميع أنت
+
+520
+00:38:36,100 --> 00:38:40,120
+بتجمع هي الأثنين هاملوا join مع بعض اتحاد مع بعض ل
+
+521
+00:38:40,120 --> 00:38:43,580
+a و b معناته automatically أخدنا الاتحاد إيش بنعبر
+
+522
+00:38:43,580 --> 00:38:49,340
+عنه بال or أو ال disjunction فإذا بنعملها a أي و j
+
+523
+00:38:49,340 --> 00:38:56,360
+disjunction مع b أي و j فهد ال join و هد ال meet
+
+524
+00:38:56,360 --> 00:39:03,000
+بحيث أنه تمتجلنا أنصر جديدما دام روحت لفكرة انه 01
+
+525
+00:39:03,000 --> 00:39:06,460
+و بعمل هنا and و or معناته خلاص بنروح لل poly
+
+526
+00:39:06,460 --> 00:39:11,380
+product برضه بدنا نعمل عملية انه ممكن اضرب مصففتين
+
+527
+00:39:11,380 --> 00:39:16,760
+مع بعض و المصففتين هدولة هدولة 01 matrices و true
+
+528
+00:39:16,760 --> 00:39:21,300
+false زي ما احنا اتكلمنا ان هدولة يمثلوا false و
+
+529
+00:39:21,300 --> 00:39:26,280
+true اللي هو 01 false و true معناه ذلك انه مقدرش
+
+530
+00:39:26,280 --> 00:39:31,410
+اروح اضرب ضرب عادي لأ هنا بصير نتكلم عن logicهيو
+
+531
+00:39:31,410 --> 00:39:40,250
+جالك bullion products اتفضل هديك
+
+532
+00:39:40,250 --> 00:39:42,570
+عملية الضرب اللي احنا لسه بنتكلم فيها هى هى ال
+
+533
+00:39:42,570 --> 00:39:46,130
+bullion productأما العمليتين اللي في الأول هدولة
+
+534
+00:39:46,130 --> 00:39:53,430
+لأ هدول عمليات عملية تقاطع وعملية اتحاد بالظبط ال
+
+535
+00:39:53,430 --> 00:39:58,870
+meet هي عملية تقاطع فإذا انت بتعمل and كل أنصر مع
+
+536
+00:39:58,870 --> 00:40:03,670
+الأنصر اللي بقابله زي عملية جمع المصففات بالظبطجمع
+
+537
+00:40:03,670 --> 00:40:08,030
+المصففات جمع المصففات انت مش محتاج تضرب ضرب vector
+
+538
+00:40:08,030 --> 00:40:11,270
+مع vector لسه ماوصلناش في ال boolean product هو
+
+539
+00:40:11,270 --> 00:40:14,510
+اللي هنتكلم عنه العملية اللي بتحكي عنها بس حتى لأن
+
+540
+00:40:14,510 --> 00:40:17,650
+العمليتين اللي شرحناهم الآن اللي هو ال meet و ال
+
+541
+00:40:17,650 --> 00:40:21,330
+join عنصر مقابل عنصر خلصنا العملية عنصر مقابل عنصر
+
+542
+00:40:21,330 --> 00:40:25,470
+خلصت عنصر مقابل عنصر خلصت مافيش summation مش طولش
+
+543
+00:40:25,470 --> 00:40:27,690
+على ال summation في ال boolean product هذا اللي
+
+544
+00:40:27,690 --> 00:40:30,970
+هنتكلم فيه عن ال summationهناك كنا بنتكلم
+
+545
+00:40:30,970 --> 00:40:37,250
+summation لعملية ضرب ال summation هنا مش هي نفسها
+
+546
+00:40:37,250 --> 00:40:42,270
+عملية ال or لما بجمع ماهي or اللي هي ال join يعني
+
+547
+00:40:42,270 --> 00:40:49,270
+اذا كانت big summation بده يقابلها big oring
+
+548
+00:40:49,270 --> 00:40:53,230
+لعناصر
+
+549
+00:40:53,230 --> 00:40:56,830
+مضروبة في بعض هنا بيصير عناصر
+
+550
+00:40:59,450 --> 00:41:03,910
+ending مع بعض بس هي كل الفرق فإذا هاتنشوف كيف
+
+551
+00:41:03,910 --> 00:41:12,110
+هيصير الشكل اللي عانت بحها بنكتبها بهذا الشكل A
+
+552
+00:41:12,110 --> 00:41:17,610
+Boolean product B عامل زي بالظبط السهم اللي طالع
+
+553
+00:41:17,610 --> 00:41:21,030
+من الصبورة علامة السهم اللي طالع من الصبورة طب
+
+554
+00:41:21,030 --> 00:41:23,670
+علامة السهم اللي داخل الصبورة عارفين كده اللي هي
+
+555
+00:41:23,670 --> 00:41:30,570
+علامة ال Xكمان ممتاز فإذا هذه العلامة بنعرف ان انا
+
+556
+00:41:30,570 --> 00:41:34,610
+بتكلم عن pull in product اللي انا هتطلع من الصبورة
+
+557
+00:41:34,610 --> 00:41:37,110
+في اتجاه اللي طلع من الصبورة مش داخلة على الصبورة
+
+558
+00:41:37,110 --> 00:41:43,110
+تمام جيد جدا كويس ان انتوا متذكريهم فلما بقول pull
+
+559
+00:41:43,110 --> 00:41:47,690
+in product هي بتسوية بتبقى المفروض تطلع ليه C C
+
+560
+00:41:47,690 --> 00:41:52,110
+هذه matrix جديدة طيب نفس الكلام اللي قلناه سابقا
+
+561
+00:41:52,110 --> 00:41:53,810
+لازم في الآخر يكون في عنده
+
+562
+00:41:57,120 --> 00:41:59,260
+compatibility between them، إيش يعني
+
+563
+00:41:59,260 --> 00:42:02,460
+compatibility؟ في توافق عشان أقدر أجيب عملية
+
+564
+00:42:02,460 --> 00:42:08,360
+الضرب، التوافق هذا في جزئية الأعمدة مع الصفوف، K
+
+565
+00:42:08,360 --> 00:42:14,190
+برضه بدها تكون Kتوافقية لازم وإلا عملية حتى كلمة
+
+566
+00:42:14,190 --> 00:42:18,330
+product لازم هتوافقية مباشرة فإذن بحيث أنه لما أجي
+
+567
+00:42:18,330 --> 00:42:21,330
+أعمل عملية ضرب أنا هنا عامل خمسة برضه خليهم خمسة
+
+568
+00:42:21,330 --> 00:42:24,750
+لازم نكون متوافقين مع بعض فإذن العنصر الأول مضروب
+
+569
+00:42:24,750 --> 00:42:28,030
+في الأول هي اللي كنا نعمل زائد التاني مضروب في
+
+570
+00:42:28,030 --> 00:42:31,790
+التاني طب ال and نغير شوية كلمة مضروب بيدقول and
+
+571
+00:42:31,790 --> 00:42:38,370
+وكلمة زائد بيدقول or معناته بيدقول الأول and الأول
+
+572
+00:42:38,370 --> 00:42:46,200
+or التانيand التاني or التالت and التالت or
+
+573
+00:42:46,200 --> 00:42:52,000
+لاحظتوا كيف صارت؟ بغير بس مصطلحات عشان تتوافق مع
+
+574
+00:42:52,000 --> 00:42:56,720
+ال pollen الشفرة كويس الرابع مع الرابع و الخمس مع
+
+575
+00:42:56,720 --> 00:43:01,420
+الخمس و هكذا صارت فعليا العملية عندي orange كبيرة
+
+576
+00:43:01,420 --> 00:43:11,200
+لمين؟ لأكم عدد من واحد ل Kمن واحد ل K فعليا تبدأ
+
+577
+00:43:11,200 --> 00:43:17,080
+من واحد ل K لاقى العناصر اللى موجودة عنده في I و J
+
+578
+00:43:17,080 --> 00:43:20,600
+و I زى ما قلنا هنا بدي احدها اقول ان هد I خلاص و
+
+579
+00:43:20,600 --> 00:43:28,340
+هد J فإذا الصف مع العمود صف مع العمود عشان يعطيني
+
+580
+00:43:28,340 --> 00:43:36,110
+العنصرI و J answer I و J تمام في الحالة هذه I A A
+
+581
+00:43:36,110 --> 00:43:43,950
+I ال and لأنه قولنا الأول and التاني عفوا أن الأول
+
+582
+00:43:43,950 --> 00:43:52,310
+and الأول أول and أول خلاص فإذا andمجموحهم او ناتج
+
+583
+00:43:52,310 --> 00:43:56,750
+ال ending or مع العنصرين اللي وراهم or مع العنصرين
+
+584
+00:43:56,750 --> 00:44:00,350
+اللي وراهم و بتجمع بهذا الشكل بتجمع بهذا الشكل هاي
+
+585
+00:44:00,350 --> 00:44:06,510
+هادي في حالة ان انت بتضرب two matrices لمين ل pool
+
+586
+00:44:06,510 --> 00:44:12,210
+يعني okay نفس الكلام اللي قلناه هناك لل power برضه
+
+587
+00:44:12,210 --> 00:44:16,870
+ممكن يكون هنا ال power في ال poolبدك تضربهم في بعض
+
+588
+00:44:16,870 --> 00:44:20,190
+و عملية الضرب كلنا عارفين زي ما توشفناها بال O
+
+589
+00:44:20,190 --> 00:44:26,710
+ring الكبيرة لمجموعة ending لمجموعة ending فبدك
+
+590
+00:44:26,710 --> 00:44:33,050
+تضرب اتقول مثلا a to the power to the power و لاحظ
+
+591
+00:44:33,050 --> 00:44:38,310
+ان كتبناها powerوحطناها داخل brackets عشان نعرف
+
+592
+00:44:38,310 --> 00:44:43,170
+اننا بنتكلم عن boolean products فبنضربهم بهذا
+
+593
+00:44:43,170 --> 00:44:45,910
+الشكل boolean product .. boolean product ..
+
+594
+00:44:45,910 --> 00:44:47,010
+boolean product .. boolean product .. boolean
+
+595
+00:44:47,010 --> 00:44:47,510
+product .. boolean product .. boolean product ..
+
+596
+00:44:47,510 --> 00:44:47,770
+boolean product .. boolean product .. boolean
+
+597
+00:44:47,770 --> 00:44:48,230
+product .. boolean product .. boolean product ..
+
+598
+00:44:48,230 --> 00:44:48,990
+boolean product .. boolean product .. boolean
+
+599
+00:44:48,990 --> 00:44:49,690
+product .. boolean product .. boolean product ..
+
+600
+00:44:49,690 --> 00:44:52,610
+boolean product .. boolean product .. boolean
+
+601
+00:44:52,610 --> 00:44:54,830
+product .. boolean product .. boolean product ..
+
+602
+00:44:54,830 --> 00:44:54,890
+boolean product .. boolean product .. boolean
+
+603
+00:44:54,890 --> 00:44:54,890
+product .. boolean product .. boolean product ..
+
+604
+00:44:54,890 --> 00:44:54,950
+boolean product .. boolean product .. boolean
+
+605
+00:44:54,950 --> 00:44:54,990
+product .. boolean product .. boolean product ..
+
+606
+00:44:54,990 --> 00:44:56,090
+boolean product .. boolean product .. boolean
+
+607
+00:44:56,090 --> 00:44:58,290
+product .. boolean product .. boolean product ..
+
+608
+00:44:58,290 --> 00:45:02,890
+boolean
+
+609
+00:45:04,500 --> 00:45:10,600
+جيد بتهيري خلصنا اه اوكي فإذن الكويس ان احنا خلصنا
+
+610
+00:45:10,600 --> 00:45:17,020
+الجزء اللي كان ضايقنا من جزئية ال chapter اتنين
+
+611
+00:45:17,020 --> 00:45:22,540
+يكون هيك خلصناها بحيث انه المرة القادمة ممكن نبدأ
+
+612
+00:45:22,540 --> 00:45:27,160
+مباشرة في ال algorithm بس بدنا المرة القادمة نبدأ
+
+613
+00:45:27,160 --> 00:45:32,320
+when بدي أبدأ مباشرة في ال structure للأكواد بمعنى
+
+614
+00:45:32,320 --> 00:45:42,980
+انه هنبدأمن .. من code بدنا نكتبهcode بدنا نكتبه
+
+615
+00:45:42,980 --> 00:45:45,940
+بمعنى ان المقدمات انا مش محتاج ادخلكوا في مقدمات
+
+616
+00:45:45,940 --> 00:45:48,860
+كتيرة او يعني خليني اقول اوضحلكوا ايش أهمية
+
+617
+00:45:48,860 --> 00:45:52,640
+البرمجة و ليش في احنا محتاجين برمجة و ال algorithm
+
+618
+00:45:52,640 --> 00:45:56,280
+ايش يعني algorithm فكتير كويس ان أول سلايدين
+
+619
+00:45:56,280 --> 00:46:00,060
+تقرؤوهم لأنه مقدمة ايش يعني algorithm ال algorithm
+
+620
+00:46:00,060 --> 00:46:03,460
+و ايش أهميته و ايش معناه التعريف تبعه ان انا بدي
+
+621
+00:46:03,460 --> 00:46:05,480
+اعمل أحل task معينة
+
+622
+00:46:07,730 --> 00:46:11,410
+بطريقة معينة بدنا نتكلم انه والله في حاجة اسمها
+
+623
+00:46:11,410 --> 00:46:15,330
+language programming language احنا في المصادق
+
+624
+00:46:15,330 --> 00:46:19,230
+تبعنا بهمناش ال language اللي هتستخدمها انت بتحب
+
+625
+00:46:19,230 --> 00:46:21,630
+ال Java okay اشتغل على ال Java انا بدي Python okay
+
+626
+00:46:21,630 --> 00:46:25,730
+بشتغل ال Python انت بدك C++ اشتغل C++ مش هتفرج
+
+627
+00:46:25,730 --> 00:46:29,970
+معانا لكن في النهاية كمجموع مبرمجين المفروض انه في
+
+628
+00:46:29,970 --> 00:46:35,100
+الأفكار نفهم بعض انا مش متعلم Java مثلاأنت ليش بت
+
+629
+00:46:35,100 --> 00:46:38,720
+.. بالظبط ليش تلزمني أني أفهم أشياء .. كيف طبيعة
+
+630
+00:46:38,720 --> 00:46:41,380
+ال structure أو ال expression بتاعة ال Java؟ أنا
+
+631
+00:46:41,380 --> 00:46:47,430
+مش محتاجها، فعشان هيك بدنا نعرف أن أحنا هنوحدسواء
+
+632
+00:46:47,430 --> 00:46:51,290
+ان انت بتشتغل على newer programming language زي ال
+
+633
+00:46:51,290 --> 00:46:57,050
+Java, C++, C Visual ال Android كل هذه الجديدة او
+
+634
+00:46:57,050 --> 00:47:00,950
+من الحاجات القديمة، واحد يعني خليني نقول متعلم من
+
+635
+00:47:00,950 --> 00:47:03,670
+ال versions القديمة اكيد طبعا انتوا بتسمعوها شهر
+
+636
+00:47:03,670 --> 00:47:07,850
+واحدة ال Fortran او ال Copal او ال Basic الأصلية
+
+637
+00:47:07,850 --> 00:47:10,980
+اللي كانت UnderDOSالذكرين ال .. ال underdose أنتوا
+
+638
+00:47:10,980 --> 00:47:12,820
+ماشيفتهوش طبعا ال underdose دخلتوا على ال windows
+
+639
+00:47:12,820 --> 00:47:15,900
+على طول لأ ال underdose اللي هي على الشاشة السوداء
+
+640
+00:47:15,900 --> 00:47:18,780
+مباشرة كنا نشتغل مباشرة على الشاشة السوداء الكتابة
+
+641
+00:47:18,780 --> 00:47:23,700
+كتبت البرامج كويس سواء القليمة أو الجديدة أو ال
+
+642
+00:47:23,700 --> 00:47:27,260
+simple حتى language اللي هي ال low level coding
+
+643
+00:47:27,260 --> 00:47:30,860
+أنا في النهاية بهمن الفكرة بهمنيش أنت كيف هتطبقها
+
+644
+00:47:30,860 --> 00:47:34,760
+لأن عملتي التطبيق سهلة و كلكم بتعرفوا أن الآن لغات
+
+645
+00:47:34,760 --> 00:47:40,150
+البرمجة أصبحت قوالببمعنى ان هو tools جاهزة tools
+
+646
+00:47:40,150 --> 00:47:43,150
+أصبحت جاهزة انت مش محتاج تكتب ال .. تكتب مثلا كيف
+
+647
+00:47:43,150 --> 00:47:46,810
+ده تجيب ال .. ال .. ال max number لأ انت بتكتب
+
+648
+00:47:46,810 --> 00:47:49,390
+أحيان ال max و بت .. و بتحطوله بس ال array هو
+
+649
+00:47:49,390 --> 00:47:52,690
+بجيبلك ال maximum بتوعاته و خلصناه ف زمان لأ احنا
+
+650
+00:47:52,690 --> 00:47:57,170
+كنا زمان احنا لنضطر نكتب ال sub routine هذا ال sub
+
+651
+00:47:57,170 --> 00:48:00,090
+routine اللي هو الجزء هذا لازم ينكتب جد ما ياخد
+
+652
+00:48:00,090 --> 00:48:03,310
+ياخد عشان بس أقول ان خلصتها يعني الجزء الأول من
+
+653
+00:48:03,310 --> 00:48:05,590
+البرنامج و أكمل البرنامج .. الآن لأ صارت كلها
+
+654
+00:48:05,590 --> 00:48:09,210
+جاهزةال Laravel ومال Laravel وكل ال versions
+
+655
+00:48:09,210 --> 00:48:12,270
+الجديدة هالوجت هي بتعتمد بشكل أساس إن هي platform
+
+656
+00:48:12,270 --> 00:48:16,490
+ل language تانية تحتها فهذه قوالب .. هذه بتسهل
+
+657
+00:48:16,490 --> 00:48:19,970
+عليك إن هي بتعطيك قوالب جاهزة مش أكتر من هيك فهي
+
+658
+00:48:19,970 --> 00:48:23,910
+ماتجلجوش ولا تخافوا حتى منها هي ليست لغة بحد ذاتها
+
+659
+00:48:24,680 --> 00:48:27,480
+يعني ماحدش يخطبك بكرا يقولك والله أنا بدي مبرمج
+
+660
+00:48:27,480 --> 00:48:32,220
+Laravel أو مبرمج .. انت قادر و بسيطة و مش هالجثة
+
+661
+00:48:32,220 --> 00:48:35,980
+الكبيرة لإن هي زي ما بقوله قوالب انت بس بدك تتعامل
+
+662
+00:48:35,980 --> 00:48:40,780
+معاها مش أكتر من هيكEquals انت بتحسها انها لغة
+
+663
+00:48:40,780 --> 00:48:43,580
+تانية انا مش قاعد بقولك اذا خوفت حالك منها هتحس
+
+664
+00:48:43,580 --> 00:48:46,320
+انها لغة تانية بس اذا انت عارف ان هي مجرد قوالب بس
+
+665
+00:48:46,320 --> 00:48:49,180
+افهم ايش القوالب او ايش ال tools هذه كيف تستخدم ال
+
+666
+00:48:49,180 --> 00:48:53,220
+tools انتهت خلصها المرة القادمة مباشرة هندب مين
+
+667
+00:48:53,220 --> 00:48:56,860
+بال pseudo code اللي هو pseudo كلمة pseudo اللي هو
+
+668
+00:48:56,860 --> 00:49:01,520
+بمعنى مزيف او شبح شبيه شبيه ال code اللي هو بنسميه
+
+669
+00:49:01,520 --> 00:49:05,380
+في الآخر description codeالـ code الوصفي إنه
+
+670
+00:49:05,380 --> 00:49:09,180
+هتنفهم كيف ممكن نفكر في حل المشكلة فممكن نحطها
+
+671
+00:49:09,180 --> 00:49:14,060
+بشكل algorithm زي مجالنا الخوارزمة، الخوارزمة من
+
+672
+00:49:14,060 --> 00:49:18,560
+ألف سنين جالا كتبها، كيف كتبها، خطوات، فكل عملية
+
+673
+00:49:18,560 --> 00:49:20,760
+بيعملها بشكل إنه عشان نعملها بنعمل واحد، اتنين،
+
+674
+00:49:20,760 --> 00:49:24,220
+تلاتة، أربعة، بهمنش انت بعدين كيف تشتغل اللغة اللي
+
+675
+00:49:24,220 --> 00:49:28,940
+تشتغلها، اشتغل اللغة اللي بدك إياهاالمهم طريقة
+
+676
+00:49:28,940 --> 00:49:33,040
+التفكير هذا اللى هنشتغل عليه نكتبها بشكل وصفى فمن
+
+677
+00:49:33,040 --> 00:49:38,580
+المرة القادمة هتبدأ من مثال نحطه هنا وصفنا حل
+
+678
+00:49:38,580 --> 00:49:43,240
+المشكلة هنوصف حل المشكلة و نجف عشان نبدأ نشوف كيف
+
+679
+00:49:43,240 --> 00:49:47,590
+تطبيقها هيتم ثمال characteristics بتاعة ال
+
+680
+00:49:47,590 --> 00:49:51,130
+algorithm، هذه الحاجة الأهم اللي بدك إياها، إيش
+
+681
+00:49:51,130 --> 00:49:54,230
+العناصر اللي إنت لما تجيبلي code و هو يجيبلي code،
+
+682
+00:49:54,230 --> 00:49:57,650
+هدور عليها، بغض النظر إيش اللغات اللي بتشتغلوها،
+
+683
+00:49:57,650 --> 00:50:01,650
+أنا هدور على مجموعة أشياء، في characteristics، هذه
+
+684
+00:50:01,650 --> 00:50:04,650
+اللي هندور عليها، إن جول هذا أحسن من هذا، لأ هذا
+
+685
+00:50:04,650 --> 00:50:08,580
+أفضل من هذابيهمنيش ال language بتهمناش ال language
+
+686
+00:50:08,580 --> 00:50:11,480
+عشان بعدك نبدأ في ال statements بتاعة اللغة و نبدأ
+
+687
+00:50:11,480 --> 00:50:14,460
+ناخد أمثلة يعني بعدك هناخد شوية ال statement و
+
+688
+00:50:14,460 --> 00:50:18,480
+بعدك الجزء الأهم من المحاضرة هيكون تطبيقات ..
+
+689
+00:50:18,480 --> 00:50:22,280
+تطبيقات طب إننا نفكر في كذا هت .. نعمللها code
+
+690
+00:50:22,280 --> 00:50:25,660
+وصفي فشوية المرة القادمة هنروح لل data structure
+
+691
+00:50:25,660 --> 00:50:30,260
+شوية هيك تمام على بركة الله يعطيكوا العافية شباب
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Hz7u2ePwdBo_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Hz7u2ePwdBo_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..99314e71b373e68c7b29e485147f1f2956e6085e
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Hz7u2ePwdBo_postprocess.srt
@@ -0,0 +1,2388 @@
+1
+00:00:05,090 --> 00:00:08,230
+طيب حطيكوا العفو يا شباب اليوم ان شاء الله تعالى
+
+2
+00:00:08,230 --> 00:00:12,550
+نكمل موضوع ال set اتكلمنا فيه من المرة الماضية
+
+3
+00:00:12,550 --> 00:00:17,790
+فتحنا موضوع ال sets و المجموعات وصلنا فيه لجزئية
+
+4
+00:00:17,790 --> 00:00:23,730
+ال tables وقلنا ان هد فيها اختلاف عن ال setليش؟
+
+5
+00:00:23,730 --> 00:00:27,730
+لأنه هذه مهم فيها الترتيب فهذه ordered على عكس ما
+
+6
+00:00:27,730 --> 00:00:31,610
+كنا نتحدث في بداية المحاضرة السابقة أن ال set هي
+
+7
+00:00:31,610 --> 00:00:38,290
+unordered set أو unordered group من ال objects بغض
+
+8
+00:00:38,290 --> 00:00:40,630
+النظر إيش ال object بتاع اللي قولنا الكلام هذا بغض
+
+9
+00:00:40,630 --> 00:00:45,670
+النظر إيش هي ال object أرقام أو أعداد أو أي شيء
+
+10
+00:00:45,670 --> 00:00:49,670
+متعدد حوالينا ممكن نحطه ك objects داخل مجموعة
+
+11
+00:00:50,420 --> 00:00:54,920
+تحدثنا عن موضوع الأزواج المرتبة تجاوزا بنسميها
+
+12
+00:00:54,920 --> 00:00:57,100
+الأزواج المرتبة لأن زوج مرتب معناته يحتوي على
+
+13
+00:00:57,100 --> 00:01:00,660
+عنصرين فقط لأ هي ممكن تكون أكتر من عنصرين و تحدثنا
+
+14
+00:01:00,660 --> 00:01:04,160
+عن هذا الموضوع و ممكن تكون مرتبة و لازامة لازم
+
+15
+00:01:04,160 --> 00:01:08,140
+تكون مرتبة و عشان هيك ماعطيناهاش ال curly braces
+
+16
+00:01:08,140 --> 00:01:12,780
+اللي احنا متعارف عليها للمجموعة بحيث انه العناصر
+
+17
+00:01:12,780 --> 00:01:17,860
+داخلها بفرقش الترتيببفرجش معانا ترتيبها، لكن في ال
+
+18
+00:01:17,860 --> 00:01:20,780
+intables .. في ال intables لأ بفرج الترتيب، في ال
+
+19
+00:01:20,780 --> 00:01:26,940
+intables لما باش باتكلم عن ضرب two .. خلينا نسميهم
+
+20
+00:01:26,940 --> 00:01:33,360
+two tuples متعددين و أزواج .. و مرتبةبغض النظر يا
+
+21
+00:01:33,360 --> 00:01:39,000
+أزواج فعلا زوج زوج ولا أكتر، بيكون مهم الترتيب حتى
+
+22
+00:01:39,000 --> 00:01:42,540
+في الناتج تبعهم، في الناتج تبعهم، فهذه بيسموها ال
+
+23
+00:01:42,540 --> 00:01:46,800
+Cartesian products عملية ضرب الكارتيزي، في ال
+
+24
+00:01:46,800 --> 00:01:50,940
+Cartesian product لما يكون عندي A Cartesian
+
+25
+00:01:50,940 --> 00:01:56,980
+productB هذي مكافئة ل set أنا مستخدم بعرف set على
+
+26
+00:01:56,980 --> 00:01:59,940
+اعتبار ان ال A و ال B هم sets وهذا اللي خلنا
+
+27
+00:01:59,940 --> 00:02:04,680
+تطرقناها الماضية لأنه هستخدمها في ال sets ال A و
+
+28
+00:02:04,680 --> 00:02:09,980
+ال B هم sets عادي جدا فإذا عناصر كل واحدة لحال
+
+29
+00:02:09,980 --> 00:02:14,380
+بهمنش فيها ترتيبكل واحدة لحاله، لكن لما بقول
+
+30
+00:02:14,380 --> 00:02:21,060
+Cartesian product ل 6A مع 6B، هيقيني 6، okay مافيش
+
+31
+00:02:21,060 --> 00:02:26,220
+مشكلة، بس 6 لإيش؟ لأزواج مرتبة، الأزواج المرتبة دي
+
+32
+00:02:26,220 --> 00:02:30,360
+مهم فيها الترتيب، لكن أنهي زوج جابلة تاني بيفرجش
+
+33
+00:02:31,230 --> 00:02:36,410
+لأن هم داخل set بينما تركيب ال set للزوج المرتب هو
+
+34
+00:02:36,410 --> 00:02:40,930
+اللي بهمني بحيث أن العنصر الأول في ال set من
+
+35
+00:02:40,930 --> 00:02:44,810
+المجموعة الأولى والعنصر التاني من المجموعات
+
+36
+00:02:44,810 --> 00:02:52,160
+التانية، مانفعش هناكسه، مانفعش هناكسههي مجموعة
+
+37
+00:02:52,160 --> 00:02:57,860
+أزواج مرتبة a و b بحيث ان small a هو belong to
+
+38
+00:02:57,860 --> 00:03:02,460
+capital A فهو جايين من ال group الأول أو من ال set
+
+39
+00:03:02,460 --> 00:03:10,680
+الأولى و b and b من ال set التانيةتعكس غلط حيبطل
+
+40
+00:03:10,680 --> 00:03:13,280
+اسمه Cartesian product حيبطل اسمه Cartesian
+
+41
+00:03:13,280 --> 00:03:16,500
+product فكلمة Cartesian product معناته ان هي مرتبة
+
+42
+00:03:16,500 --> 00:03:21,620
+حسب عناصر او ترتيب المجموعتين فبناخد عناصر الاولى
+
+43
+00:03:21,620 --> 00:03:25,480
+كل عنصر من الاولى مع كل عنصر من التانية بنفس
+
+44
+00:03:25,480 --> 00:03:29,580
+ترتيبهم في ال Cartesian product تمام كمثال ممكن
+
+45
+00:03:29,580 --> 00:03:37,520
+يكون عند ال set a,b Cartesian product of6 1 2 فهنا
+
+46
+00:03:37,520 --> 00:03:43,900
+أكيد هيعطينا مجموعة من أزواج مرتبة الأزواج المرتبة
+
+47
+00:03:43,900 --> 00:03:47,860
+هذه هيكون فيها زوج مرتب الزوج المرتب هذا العنصر
+
+48
+00:03:47,860 --> 00:03:51,520
+الأول فيه من المجموعة الأولى والعنصر التاني من
+
+49
+00:03:51,520 --> 00:04:00,660
+المجموعة التانية فهيكون A و 1 A و 2 B 1 B و 2 أربع
+
+50
+00:04:00,660 --> 00:04:07,830
+هذه الأربعهي الأربعة تمام؟ كويس الآن إذا كانت ال
+
+51
+00:04:07,830 --> 00:04:13,770
+two sets هم finite بمعنى limited معروف جداش عدد ال
+
+52
+00:04:13,770 --> 00:04:16,250
+elements تعونهم بكل بساطة بقدر أقول إن ال
+
+53
+00:04:16,250 --> 00:04:19,150
+cardinality بتاعتهم هي فعليا تساوي ال cardinality
+
+54
+00:04:19,150 --> 00:04:22,910
+للأولى للست الأولى في ال cardinality للست التانية
+
+55
+00:04:22,910 --> 00:04:27,370
+كانوا اتنينو هنا اتنين اتنين فى اتنين اربعة اه
+
+56
+00:04:27,370 --> 00:04:32,210
+فعلا الناتج بيطلع اربعة على ال Cartesian طيب في ال
+
+57
+00:04:32,210 --> 00:04:35,630
+Cartesian زى ما قلنا مدام الترتيب مهم معناه ذلك
+
+58
+00:04:35,630 --> 00:04:39,850
+انه ليس بالضروري و ليس فى كل الحالات و ليس for all
+
+59
+00:04:39,850 --> 00:04:46,710
+a و b Cartesian a فى b يساوي b فا قد تصدف فى حالات
+
+60
+00:04:46,710 --> 00:04:53,890
+نادرة او فى حالات قليلة لكن بصفة عامة ليسللكل ليس
+
+61
+00:04:53,890 --> 00:04:56,870
+للكل انه ممكن تكون A Cartesian B تسوي B Cartesian
+
+62
+00:04:56,870 --> 00:05:01,910
+A الا اذا كانوا الاتنين فيهم نفس العناصر فلو
+
+63
+00:05:01,910 --> 00:05:07,770
+انعكسه تظبط هي هي تمام فهذه مهمة جدا نقدر نعمل
+
+64
+00:05:07,770 --> 00:05:11,150
+extension لنفس الفكرة ال concept انه ممكن تكون A1
+
+65
+00:05:11,150 --> 00:05:15,770
+Cartesian A2 Cartesian A3 to AN فهذا بطل زوج مرتبة
+
+66
+00:05:15,770 --> 00:05:23,760
+صار and doubles and doubles بمعنى انه هتصبحA1, A2
+
+67
+00:05:23,760 --> 00:05:30,160
+و AN كترتيب
+
+68
+00:05:30,160 --> 00:05:34,880
+intables او intable أولى هناخد intable تانية بحيث
+
+69
+00:05:34,880 --> 00:05:42,960
+انه A1 من الست capital A1 small a2 لازم تكون احد
+
+70
+00:05:42,960 --> 00:05:49,710
+عناصر capital A2 و هكذاان بالsmall هتكون احد عناصر
+
+71
+00:05:49,710 --> 00:05:55,470
+capital A N أو الست A N تمام؟ وفي الحالة هذه بنشوف
+
+72
+00:05:55,470 --> 00:05:59,850
+جدش ال cardinality ل A واحد جدش ال cardinality ل A
+
+73
+00:05:59,850 --> 00:06:03,030
+اتنين جدش ال cardinality ل A تلاتة جدش ال
+
+74
+00:06:03,030 --> 00:06:06,470
+cardinality ل A N كلهم هندروفوا في بعض عشان يطلع
+
+75
+00:06:06,470 --> 00:06:09,830
+جدش عدد الأزواج المرتبة تجاوزاً .. هقول أزواج
+
+76
+00:06:09,830 --> 00:06:13,330
+مرتبة جدش تجاوزاً عدد الأزواج المرتبة اللي ممكن
+
+77
+00:06:13,330 --> 00:06:17,000
+نعملهم generation منهامن ال kartesian بتاعتهم ..
+
+78
+00:06:17,000 --> 00:06:20,300
+من ال kartesian بتاعتهم بمعنى لما يكون في عندك
+
+79
+00:06:20,300 --> 00:06:23,580
+اتنين و اتنين و اتنين هنا مثلا اتنين و اتنين و
+
+80
+00:06:23,580 --> 00:06:27,060
+رحنا عملنا kartesian في كمان ست مكونة من اتنين
+
+81
+00:06:27,060 --> 00:06:32,900
+فالمتوقع انه كم عنصر هيطلع عنده اتنين في اتنين في
+
+82
+00:06:32,900 --> 00:06:38,180
+اتنين فغالبا تمانية هيطلع عندك تمانية هيطلع عندك
+
+83
+00:06:38,180 --> 00:06:43,830
+تمانية تمامطيب نيجي الحاول الآن نسرق شوية في حاجات
+
+84
+00:06:43,830 --> 00:06:46,470
+operations انتوا أخدتوها سابقا في أول operator رح
+
+85
+00:06:46,470 --> 00:06:50,030
+ناخده هو ال union او الاتحاد الاتحاد او ال union
+
+86
+00:06:50,030 --> 00:06:55,790
+فلو كان عند ال set A و B ف ال union تبعتهم و بتاخد
+
+87
+00:06:55,790 --> 00:07:01,810
+حرف ال U تقريبا شبه هيك بحرف ال U A union B تقرأ
+
+88
+00:07:01,810 --> 00:07:06,130
+هذه عبارة عن set بتحتوي على كل ال elementsthat are
+
+89
+00:07:06,130 --> 00:07:15,170
+either in a or b or b or both او في كلاهما برضه
+
+90
+00:07:15,170 --> 00:07:18,970
+موجودة بتنحسب او في كلاهما of course in both طيب
+
+91
+00:07:18,970 --> 00:07:27,090
+formally for all a و b لكل ال six أي two six لكل
+
+92
+00:07:27,090 --> 00:07:34,370
+الحالات الأولى اتحاد التانية يعطيني six برضه six
+
+93
+00:07:35,450 --> 00:07:42,430
+لعناصر، العناصر هذه لازم تكون ضمن الست الأولى أو
+
+94
+00:07:42,430 --> 00:07:47,850
+الست التانية أو الست التانية، منطقش التانية، عارفة
+
+95
+00:07:47,850 --> 00:07:53,670
+طيب، هلاحظ أنه الاتحاد A اتحاد B أو A union B
+
+96
+00:07:53,670 --> 00:07:58,230
+تحتوي على كل ال elements of A and كل ال elements
+
+97
+00:07:58,230 --> 00:08:03,650
+of Bأكيد لازم تكون محتوى على الجميع على الكل و في
+
+98
+00:08:03,650 --> 00:08:07,710
+الحالة دي بنقدر نقول for all a و b for all معناته
+
+99
+00:08:07,710 --> 00:08:12,410
+لكل الحالات اللي ممكن تختار فيهم two sets أي two
+
+100
+00:08:12,410 --> 00:08:16,050
+sets هتختارهم هنطبق عليهم التعريف اللي هيجي لكل
+
+101
+00:08:16,050 --> 00:08:22,870
+two sets مع بعض هيكون فيه عندك a union b هو super
+
+102
+00:08:22,870 --> 00:08:27,930
+set of a لحالها و هو super set of b لحالها ليش لأن
+
+103
+00:08:27,930 --> 00:08:32,810
+هو أكيد أكبر منهافي أسوأ الحوار هيكون بيسويها لأنه
+
+104
+00:08:32,810 --> 00:08:38,150
+لازم يحتوي على كل عناصر A الشيخ و في نفس الوجد
+
+105
+00:08:38,150 --> 00:08:42,530
+لازم يحتوي على كل عناصر B فإذا الاتحاد نفسه هو
+
+106
+00:08:42,530 --> 00:08:50,410
+super set من كل set لحالها من كل set لحالهاطيب
+
+107
+00:08:50,410 --> 00:08:55,510
+أمثل عليها زي الأمثل اللي احنا شايفينها ABC union
+
+108
+00:08:55,510 --> 00:08:58,530
+اتنين و تلاتة مافيش فيها مشكلة هذه على طول بناخدهم
+
+109
+00:08:58,530 --> 00:09:01,850
+مباشرة لأن هم اصلا distinguished عن بعض مختلفين
+
+110
+00:09:01,850 --> 00:09:04,850
+مافيش اي تشابه بينهم لكن في الحالة التانية اتنين
+
+111
+00:09:04,850 --> 00:09:09,330
+تلاتة خمسة اتحاد تلاتة خمسة سبعة في الحالة هذه انت
+
+112
+00:09:09,330 --> 00:09:12,310
+هتكتبهم بهذا الشكل بس مش هذا المطلوب ولا هذا
+
+113
+00:09:12,310 --> 00:09:18,540
+المرغوب المطلوب هو الاتنينتلاتة، خمسة، سبعة بدنا
+
+114
+00:09:18,540 --> 00:09:22,180
+ال distinct أو ال different elements ال different
+
+115
+00:09:22,180 --> 00:09:24,600
+elements هي اللي اتضالى عشان حتى لما بدنا بعدين
+
+116
+00:09:24,600 --> 00:09:28,140
+نحط cardinality ال cardinality يكون عددها صح عددها
+
+117
+00:09:28,140 --> 00:09:31,800
+يكون صحيح فعليا اتحادهم مع بعض ال cardinality له
+
+118
+00:09:31,800 --> 00:09:40,060
+هيطلع أربعة هيطلع أربعة بهذا الشكل مش ستة مش ستة
+
+119
+00:09:40,060 --> 00:09:45,470
+فإذا بدنا نقول هنا الاتحادمعنى انا اكتب هو هيطلع
+
+120
+00:09:45,470 --> 00:09:51,730
+اربعة not six بده اخليها هنا محطوطة على جنب عشان
+
+121
+00:09:51,730 --> 00:09:57,630
+هدنا هنحتاجها هنحتاج الكلمة هذيOkay هاي مثال إلها
+
+122
+00:09:57,630 --> 00:10:03,350
+فمعنا ذلك بناخد كل الاتحاد كامل أخدتم انتوا الكلام
+
+123
+00:10:03,350 --> 00:10:05,710
+هذا طيب النوع التاني هو ال intersection أو التقاطع
+
+124
+00:10:05,710 --> 00:10:09,990
+التقاطع و ال intersection لأي two sets A و B ال
+
+125
+00:10:09,990 --> 00:10:14,410
+intersection between A و B هي عبارة عن set برضه
+
+126
+00:10:14,410 --> 00:10:18,170
+containing أو بتحتوي على كل ال elements that are
+
+127
+00:10:18,170 --> 00:10:23,090
+simultaneously in A and B في نفس الوقت هي موجودة
+
+128
+00:10:23,090 --> 00:10:28,400
+في A و B مع بعضموجودة في A؟ لا يكفي، موجودة في B؟
+
+129
+00:10:28,400 --> 00:10:30,880
+لا يكفي، لأ، موجودة في الإتنين معاها، في الإتنين
+
+130
+00:10:30,880 --> 00:10:33,820
+مع بعضهم، ففي الحالة هذه بنقدر نقول for all A وB
+
+131
+00:10:33,820 --> 00:10:38,580
+لأي two sets A وB، لكل ال two sets A وB، إيش ما
+
+132
+00:10:38,580 --> 00:10:43,020
+يكون نوع A وإيش ما يكون نوع B A intersection B هو
+
+133
+00:10:43,020 --> 00:10:49,600
+عبارة عن set لمجموعة عناصر، بحيث إن كل عنصر هو
+
+134
+00:10:49,600 --> 00:10:56,250
+ينتمي ل A و .. هنا و بدل orهنا صارت and بدل or،
+
+135
+00:10:56,250 --> 00:11:00,490
+and هو نفسه ينتمي له بيه، بس هاي كل الاختلاف
+
+136
+00:11:00,490 --> 00:11:04,310
+الوحيد في ال and و ال or اللي موجودة عندنا هنا ال
+
+137
+00:11:04,310 --> 00:11:09,150
+A intersection بي هي بعكس هناك، هنا بتصير subset
+
+138
+00:11:09,150 --> 00:11:14,160
+من A لحالهاأو subset من B لحقها و subset حتى من B
+
+139
+00:11:14,160 --> 00:11:18,620
+لحقها فبنقدر نقول أنه ال intersection هو عبارة عن
+
+140
+00:11:18,620 --> 00:11:22,440
+subset من ال set الأولى و ال intersection برضه هو
+
+141
+00:11:22,440 --> 00:11:25,680
+subset من ال set التانية منطق جدا لأنه أكيد هو
+
+142
+00:11:25,680 --> 00:11:30,960
+هيكون أقل منهم أو يسوى واحدة منهم بحيث أن الواحدة
+
+143
+00:11:30,960 --> 00:11:36,480
+هذه هي مشمولة في التانية صح تمام زي الأمثلة اللي
+
+144
+00:11:36,480 --> 00:11:41,850
+موجودة عندنا ABCIntersection اتنين و تلاتة فاي
+
+145
+00:11:41,850 --> 00:11:46,670
+طبيعي مافيش اصلا طيب اتنين اربعة ستة تلاتة اربعة
+
+146
+00:11:46,670 --> 00:11:50,110
+ستة فهيكون في عند الاربعة فقط زي اتقاطوا الطرق
+
+147
+00:11:50,110 --> 00:11:55,230
+هيكي لما تقول والله هي شارع وهي شارع طب المربع
+
+148
+00:11:55,230 --> 00:11:57,230
+اللي في النص ال square اللي في النص هو يتبع لأي
+
+149
+00:11:57,230 --> 00:12:01,300
+شارع هو للاتنين الحقيقةهتقول عليه في الشارع A و لا
+
+150
+00:12:01,300 --> 00:12:04,420
+في الشارع B؟ هو الحقيقة جاية في الاتنين فهو ال
+
+151
+00:12:04,420 --> 00:12:07,840
+intersection بين الشارعين بالظبط عاملين زي الرسم
+
+152
+00:12:07,840 --> 00:12:10,020
+اللي احنا رسمينها
+
+153
+00:12:13,200 --> 00:12:18,140
+طيب ال disjointedness ال .. ال .. ال disjoint اللي
+
+154
+00:12:18,140 --> 00:12:21,660
+هو انك انت بدك تعمل intersection و يطلع في زي
+
+155
+00:12:21,660 --> 00:12:25,760
+المثال اللي اتواخدناه فلما تيجي تطلع على هذا
+
+156
+00:12:25,760 --> 00:12:29,740
+المثال معناه ذلك انه هادي disjoint من هادي هم
+
+157
+00:12:29,740 --> 00:12:34,850
+منفصلين اصلاهما منفصلين أساسا في انفصال هما مافيش
+
+158
+00:12:34,850 --> 00:12:37,630
+بينهم اي intersection فعشان اقول والله ال two sets
+
+159
+00:12:37,630 --> 00:12:43,890
+منفصلين او disjoint او unjoined .. unjoined مافيش
+
+160
+00:12:43,890 --> 00:12:47,390
+تلاقي بينهم غير متلاقتين معناه ذلك ان هذا الكلام
+
+161
+00:12:47,390 --> 00:12:50,050
+يحدث if and only if ال intersection between them
+
+162
+00:12:50,050 --> 00:12:54,560
+is emptyانه تقاطحهم او ال intersection between
+
+163
+00:12:54,560 --> 00:12:59,420
+them هو فاي هو فاي فبنقول خلاص هم منفصلين زي
+
+164
+00:12:59,420 --> 00:13:05,020
+بالظبط مجموعة الاعداد ال even و ال odd هم اكيد set
+
+165
+00:13:05,020 --> 00:13:09,960
+of even integers is disjoint with the set of odd
+
+166
+00:13:09,960 --> 00:13:15,390
+integers منطقى هتلاقي فيه اي عنصر هيك و هيكو لا
+
+167
+00:13:15,390 --> 00:13:19,670
+يمكن الزوجي لحاله و الفردي لحاله .. زوجي لحاله و
+
+168
+00:13:19,670 --> 00:13:23,810
+الفردي لحاله فهدول disjoint لبعض .. منفصلين عن بعض
+
+169
+00:13:23,810 --> 00:13:29,530
+okay ال inclusion .. its inclusion principle
+
+170
+00:13:29,530 --> 00:13:36,630
+هالوقت لما أقول بدي الاتحاد و بدي أجيبله a union b
+
+171
+00:13:36,630 --> 00:13:44,400
+و بدنا نجيب العدد العدد توه ماطلعش ستة صح؟بمعنى
+
+172
+00:13:44,400 --> 00:13:48,560
+إنه ماكانش بكل بساطة Cardinality A زائد
+
+173
+00:13:48,560 --> 00:13:52,740
+Cardinality B خلصنا هذي كانت تعبّق في المثال تبعته
+
+174
+00:13:52,740 --> 00:13:56,080
+كان يعبّر عنها برقم ستة مش هيك كان عددهم ستة بس
+
+175
+00:13:56,080 --> 00:14:03,140
+فعليا مش صح فعليا مش صحيح الكلام هذا بمعنى إنه لأ
+
+176
+00:14:03,140 --> 00:14:09,480
+أنا في بعض عناصر جمعتهم مرتينبالظبط ناقص التقاطة
+
+177
+00:14:09,480 --> 00:14:12,200
+وهذا المهم ليش؟ لأنه في بعض عناصر انجمعتهم مرتين
+
+178
+00:14:12,200 --> 00:14:16,180
+طيب مين اللي انجمع مرتين هو التقاطة بينهم ليش
+
+179
+00:14:16,180 --> 00:14:20,060
+التقاطة بينهم؟ لأنه انجمع كأنه مع A وانجمع هو نفس
+
+180
+00:14:20,060 --> 00:14:23,240
+الأنصر كأنه مع B فمعناه ذلك انه مرتين محتاجين
+
+181
+00:14:23,240 --> 00:14:27,520
+نطلحوا مرة عشان يظللوا مرة واحدة في العد عشان هيك
+
+182
+00:14:27,520 --> 00:14:30,640
+مين اللي بتنطبق عليهم هذه الحالة انه انجمع مرتين
+
+183
+00:14:30,640 --> 00:14:34,160
+هم فقط ال intersection elementsاللي هي عناصر
+
+184
+00:14:34,160 --> 00:14:38,420
+التقاطع فمعنادلك لابد انه نعمل minus في الآخر لل
+
+185
+00:14:38,420 --> 00:14:47,060
+intersection ال intersection ل ال two sets فهو هذا
+
+186
+00:14:47,060 --> 00:14:51,200
+بالظبط اللي احنا بنحكيه واخدته اكيد برضه ايام ما
+
+187
+00:14:51,200 --> 00:14:54,680
+اخدته ال sets طيب أمثلة طبعا الأمثلة كتير على هذا
+
+188
+00:14:54,680 --> 00:14:59,650
+الكلام أمثلة الموضوع هذا كتيرممكن زي ما بيقولوا
+
+189
+00:14:59,650 --> 00:15:03,290
+التلاعب فيها بشكل كتير كبير و نعمل منها أسئلة كتير
+
+190
+00:15:03,290 --> 00:15:07,710
+.. كتير أسئلة ممكن تنعمل من ورا هذا القضم لو
+
+191
+00:15:07,710 --> 00:15:12,970
+افترضنا انه انتوا كطلاب مسجلين ال discrete و في
+
+192
+00:15:12,970 --> 00:15:16,830
+نفس الوقت مسجلين data structure تمام؟ طيب لو بده
+
+193
+00:15:16,830 --> 00:15:19,590
+اقول جدش عدد الطلاب اللي مسجلين discrete and data
+
+194
+00:15:19,590 --> 00:15:24,680
+structureمسجلين يا هادي يا هادي مين جدش عدد الطلاب
+
+195
+00:15:24,680 --> 00:15:28,300
+اللي مسجلين هادي و هادي هنقول والله جدش عدد الطلاب
+
+196
+00:15:28,300 --> 00:15:33,140
+عندي وفي ال data structure جدش عدد الطلاب و اجمعهم
+
+197
+00:15:33,140 --> 00:15:41,520
+لأ استنى انتهك في ناس و غالبا ناس كتير اتكرروا
+
+198
+00:15:41,520 --> 00:15:45,240
+جمعتهم مرتين عديتهم مرتين فمعنى ذلك بدك تشوف مين
+
+199
+00:15:45,240 --> 00:15:48,820
+الناس هدول طب انا مين اللي عديته مرتين اللي هو ال
+
+200
+00:15:48,820 --> 00:15:52,470
+intersectionاللي فعلا هو مسجل هنا ومسجل هنا فهدول
+
+201
+00:15:52,470 --> 00:15:56,570
+لازم ينطرحوا مرة عشان يكونوا انجمعوا مرة كويس فهذه
+
+202
+00:15:56,570 --> 00:16:01,510
+بكل بساطة الفكرة how many students are study
+
+203
+00:16:01,510 --> 00:16:05,650
+discrete or data structure ففي الحالة لو افترضنا
+
+204
+00:16:05,650 --> 00:16:09,730
+ان ال set S هي عبارة عن اتحاد discrete مع data
+
+205
+00:16:09,730 --> 00:16:12,090
+structure مش عارف ليش حطيتها بيه انا
+
+206
+00:16:15,630 --> 00:16:20,550
+هي problem؟ طيب ال data structure و B هنقول ان هي
+
+207
+00:16:20,550 --> 00:16:23,610
+لا ال data structure ف ال discrete يمكن انها
+
+208
+00:16:23,610 --> 00:16:29,290
+مختلفة بتطلعوا دي دي هيك المهم ال D هي مجموعة كل
+
+209
+00:16:29,290 --> 00:16:34,490
+الطلاب بشرط ان الطالب هو مسجل data structureبمعنى
+
+210
+00:16:34,490 --> 00:16:38,130
+هاللغة لما بدي أجي أخد الحضور غيابه و أجمعهم هقول
+
+211
+00:16:38,130 --> 00:16:42,090
+اه كل الطلاب بشرط انه يكون مسجل طب إذا مش مسجل
+
+212
+00:16:42,090 --> 00:16:45,230
+خليك جاعد احضر أنا ماعنديش مشكلة بس مش حتى باسمك
+
+213
+00:16:45,230 --> 00:16:48,030
+ان انت مسجل المادة بديك تبقى اللي جاعد خليك جاعد،
+
+214
+00:16:48,030 --> 00:16:52,890
+كويس؟ فهنا الشرط مهم انه لا ال .. مين اللي هيقيد
+
+215
+00:16:52,890 --> 00:16:55,770
+انه والله مسجل هو فقط اللي مسجل هو مش بالضرورة هو
+
+216
+00:16:55,770 --> 00:17:02,580
+اللي جاعد يعني تمام، الآن بعض الطلابهم فعليا
+
+217
+00:17:02,580 --> 00:17:08,360
+مسجلين الاتنين فلما بدي اخد ال cardinality العدد ك
+
+218
+00:17:08,360 --> 00:17:13,280
+total بدي اجمع مجموع المسجلين discrete زي مجموع
+
+219
+00:17:13,280 --> 00:17:18,280
+المسجلين data structure ناقص تقطعهم مفهومة و مافيش
+
+220
+00:17:18,280 --> 00:17:24,070
+فيها كتير مشكلة ان شاء الله ال set differenceلما
+
+221
+00:17:24,070 --> 00:17:27,950
+بقول set difference بمعنى الفرق بين المجموعتين في
+
+222
+00:17:27,950 --> 00:17:31,690
+اندي مجموعتين و بتجيب الفرق ما بينهم بحيث اني اقول
+
+223
+00:17:31,690 --> 00:17:35,390
+A difference B A difference B معناته ان العنصر
+
+224
+00:17:35,390 --> 00:17:39,610
+موجود في A و غير موجود في B و غير موجود في B ففي
+
+225
+00:17:39,610 --> 00:17:43,170
+الحالة هذي بنكتبه A difference B هو عبارة عن set
+
+226
+00:17:43,170 --> 00:17:47,750
+برضه بحيث انه كل عنصر داخل ال set هذي هو موجود في
+
+227
+00:17:47,750 --> 00:17:54,750
+A و غير موجود في B أوهو كل أنصر غير موجود في A
+
+228
+00:17:54,750 --> 00:18:00,510
+بيضمن لوجوده في B بمعنى إذا موجود في A إذا هو
+
+229
+00:18:00,510 --> 00:18:04,790
+موجود في B لأ أنا بديش إياها هيك أنا بديها إذا
+
+230
+00:18:04,790 --> 00:18:08,930
+موجود في A مش موجود في B مش موجود في B فمعنى ذلك
+
+231
+00:18:08,930 --> 00:18:14,010
+أنه صار negation ال implication meaning of
+
+232
+00:18:14,010 --> 00:18:19,960
+implication كانت falsetrue false مش هي true false
+
+233
+00:18:19,960 --> 00:18:24,380
+هي دي اللي بديها true false ان هو موجود في a و غير
+
+234
+00:18:24,380 --> 00:18:28,900
+موجود في b true false ففعلا هذه الحالة الوحيدة
+
+235
+00:18:28,900 --> 00:18:32,040
+اللي بدي أقول عليها ينطبق عليها a difference بي
+
+236
+00:18:32,040 --> 00:18:36,720
+ففي الحالة هذه بنقدر نقول ان بي هلوقت بنعرف حاجة
+
+237
+00:18:36,720 --> 00:18:41,460
+إضافية لبي بالنسبة لإيه أصبحت أصبحت هنا بي هي او
+
+238
+00:18:41,460 --> 00:18:46,680
+الناتج بنصير هو ال complement of بيwith respect to
+
+239
+00:18:46,680 --> 00:18:51,880
+a بالنسبة ل a with respect ل a عشان نوضحها هناخدها
+
+240
+00:18:51,880 --> 00:18:56,040
+عدنا لأن هيك هيك لازم هرجعلها with respect to a
+
+241
+00:18:56,040 --> 00:19:00,960
+هذه بس خليني أخد المثال لو قلنا اندي six of from
+
+242
+00:19:00,960 --> 00:19:07,460
+one to six minus الأعداد ال .. ال .. ال primes
+
+243
+00:19:07,460 --> 00:19:11,400
+minus ال primes لاحظته فإذا ال difference بين
+
+244
+00:19:11,400 --> 00:19:16,040
+الأعداد من واحد لستةمخصوم منها او difference of
+
+245
+00:19:16,040 --> 00:19:24,840
+the primes for eleven ففي الحالة دي إيش بتدور انت؟
+
+246
+00:19:24,840 --> 00:19:29,440
+بتدور على أعداد موجودة في الأول و غير موجودة في
+
+247
+00:19:29,440 --> 00:19:34,520
+الثاني فبتتكلم عن الواحد أه موجود هنا غير موجود
+
+248
+00:19:34,520 --> 00:19:42,610
+هنا، الأتنين لأتلاتة لأ اربعة ماشي خمسة لأ ستة
+
+249
+00:19:42,610 --> 00:19:48,130
+ماشي فهي انتهت الواحد واربعة وستة بحيث انها موجودة
+
+250
+00:19:48,130 --> 00:19:52,190
+في ال a وغير موجودة في مين في b وهنا بدأنا نختصر
+
+251
+00:19:52,190 --> 00:19:57,890
+العناصر اللي موجودة فعلا في كلاهما عشان نصل النتج
+
+252
+00:19:57,890 --> 00:20:05,070
+طيب الآن z ناقص b يعني ناقص n اللي هو ال integers
+
+253
+00:20:05,070 --> 00:20:10,800
+ناقص ال natural numbersهى عبارة عن من minus one او
+
+254
+00:20:10,800 --> 00:20:14,300
+من minus infinity حقيقة في مجموعة ellipses عندى
+
+255
+00:20:14,300 --> 00:20:17,660
+هنا معناته جاء من minus infinity ومجموعة ellipses
+
+256
+00:20:17,660 --> 00:20:21,340
+هنا to infinity فمن minus infinity to infinity
+
+257
+00:20:23,790 --> 00:20:27,290
+zero to infinity أكيد هيعطيني ال negative أو
+
+258
+00:20:27,290 --> 00:20:32,250
+هيعطيني set of numbers بحيث أنه ال numbers هذه هي
+
+259
+00:20:32,250 --> 00:20:37,590
+integers لكن ليست natural numbers معناته ليست من
+
+260
+00:20:37,590 --> 00:20:40,550
+الأعداد الطبيعية هذا معناته هيعطيني أنه هي فعليا
+
+261
+00:20:40,550 --> 00:20:45,650
+set of integers بحيث أنه كل integer هو عبارة عن
+
+262
+00:20:45,650 --> 00:20:50,790
+negative integer هو negative integerلا هو صفر ولا
+
+263
+00:20:50,790 --> 00:20:53,730
+هو الموجب لأن صفر وموجب هي ال natural number فإذا
+
+264
+00:20:53,730 --> 00:20:57,350
+بدنا نشيها natural number فأصبح من minus infinity
+
+265
+00:20:57,350 --> 00:21:03,190
+to minus one وبنوقف بسيطة وسهلة مافيش فيها أشكالية
+
+266
+00:21:03,190 --> 00:21:09,330
+مقدمة للي جاي هاي بهذا الشكل فتصبح ال set A ناقص B
+
+267
+00:21:09,330 --> 00:21:14,650
+بال Venn Diagram بهذا الشكل كأنه التقاطع بينهم B
+
+268
+00:21:14,650 --> 00:21:19,190
+أكلته فإيش اللي ضال ل A بضل كأنه ال difference ل A
+
+269
+00:21:20,880 --> 00:21:24,360
+Okay الان ال difference ده فتحلنا موضوع تاني اللي
+
+270
+00:21:24,360 --> 00:21:28,020
+هو ال compliment ال set compliments ال set
+
+271
+00:21:28,020 --> 00:21:30,560
+compliments لما يكون في عندي universe of discourse
+
+272
+00:21:30,560 --> 00:21:38,580
+كبير فضاء عينة كبير في شغلنا بقدر افترضإن اسم you
+
+273
+00:21:38,580 --> 00:21:42,340
+من universe of discourse، هفترض إن اسمه you، هذا
+
+274
+00:21:42,340 --> 00:21:44,720
+هو الفضاء العيني كله، هذا قاعدة البيانات كاملة
+
+275
+00:21:44,720 --> 00:21:49,720
+مثلا، العدد الكامل، ففي الحالة هذه، بيكون واضح جدا
+
+276
+00:21:49,720 --> 00:21:53,920
+إن هو ال universe of discourse الطبيعي عندي، خلاص
+
+277
+00:21:53,920 --> 00:21:59,120
+بتعامل معاه كإن هو كل الشغل تبعي، أي sets أخرى هي
+
+278
+00:21:59,120 --> 00:22:03,070
+داخله، هي داخله إذا سميته youفهذا ال universe of
+
+279
+00:22:03,070 --> 00:22:06,030
+discourse فضاء العينة اللي بفترض ان مافيش شيء برا
+
+280
+00:22:06,030 --> 00:22:13,330
+مافيش شيء خارجه فبنقدر منه ان اعرف اذا كانت A هي
+
+281
+00:22:13,330 --> 00:22:17,650
+subset من U فهي مجموعة جزئية من ال universe of
+
+282
+00:22:17,650 --> 00:22:22,090
+discourse من فضاء العينة اسمها A بقدر اقول منها ان
+
+283
+00:22:22,090 --> 00:22:28,320
+ال complement of A هسميها A barComplement of A هي
+
+284
+00:22:28,320 --> 00:22:34,520
+هذي بنقدر ببساطة نقول إن هي عبارة عن U ناقص A وإن
+
+285
+00:22:34,520 --> 00:22:38,420
+العناصر اللي كانت تنتمي ل A بشيلها إيش المتبقى هو
+
+286
+00:22:38,420 --> 00:22:44,340
+ال complement ل A بمعنى هو مكمل A with respect to
+
+287
+00:22:44,340 --> 00:22:49,700
+U بالنسبة ل U بالنسبة لفضاء العين اللي احنا بنتكلم
+
+288
+00:22:49,700 --> 00:22:53,560
+فيه ال A دي لو راحت لفضاء عين تاني أكيد ال
+
+289
+00:22:53,560 --> 00:22:58,380
+complement هيختلفصحيح إذا ال two universe of
+
+290
+00:22:58,380 --> 00:23:02,000
+discourses هدولة مختلفين عن بعض في الحجم تمام
+
+291
+00:23:02,000 --> 00:23:08,600
+فبنقدر زي ما قلنا تسميها U difference A ف
+
+292
+00:23:08,600 --> 00:23:14,690
+automatically أصبحتالناتج تبحى تبع ال difference
+
+293
+00:23:14,690 --> 00:23:18,710
+هي ال complement of a مثال لو قلنا ال U هي ال
+
+294
+00:23:18,710 --> 00:23:21,250
+natural number كل natural number من صفر to
+
+295
+00:23:21,250 --> 00:23:27,210
+positive infinity بدنا نجيب ال complement of three
+
+296
+00:23:27,210 --> 00:23:32,690
+five بسيط عيب ده هاي صفر واحد اتنين بدناش التلاتة
+
+297
+00:23:32,690 --> 00:23:36,610
+اربعة الخمسة بدناش ياه وكمل خلاص الباقي فهدول هم
+
+298
+00:23:36,610 --> 00:23:42,630
+العناصر المكملينلأ ال set with respect to universe
+
+299
+00:23:42,630 --> 00:23:45,170
+of discourse بالنسبة لل universe of discourse
+
+300
+00:23:45,170 --> 00:23:50,070
+بالنسبة لل universe طيب مثالها برضه نفس الكلام ال
+
+301
+00:23:50,070 --> 00:23:54,630
+complement هنا بنقدر نعبر عنه أن هو set of X such
+
+302
+00:23:54,630 --> 00:23:59,330
+that X not belong to A not belong to A with
+
+303
+00:23:59,330 --> 00:24:03,450
+respect to U بمعنى أنه إيش فضاء العين اللي أنت
+
+304
+00:24:03,450 --> 00:24:10,030
+بدأت تختار منه ال X set هذي ال Uالـ U هذه الإكسات
+
+305
+00:24:10,030 --> 00:24:14,350
+اللي بدك تجرب عليها مين اللي لا ينتمي لإيه هي الكل
+
+306
+00:24:14,350 --> 00:24:17,930
+ما هو ينتمي لمين لل U يعني داخل ال universe of
+
+307
+00:24:17,930 --> 00:24:21,850
+discourse فأصبحت كأنه ينتمي ل U و لا ينتمي ل A
+
+308
+00:24:21,850 --> 00:24:25,590
+بالظبط هاي اللي احنا بنحكيه هذه هي ال set
+
+309
+00:24:25,590 --> 00:24:28,190
+complement بمعنى أنه لو كانت عند ال U بهذا الشكل
+
+310
+00:24:28,190 --> 00:24:31,950
+فين دياجرام where مجموعة عناصر A بهذا الشكل
+
+311
+00:24:31,950 --> 00:24:37,730
+بنشيلها والباقيهيكون هو ال a compliment بحيث انه
+
+312
+00:24:37,730 --> 00:24:41,870
+هد فاضي خلاص هنا هد فاضا طلعناها ال a كلها غير
+
+313
+00:24:41,870 --> 00:24:50,950
+موجودة غير موجودة المتبقى هو ال compliment طيب بعض
+
+314
+00:24:50,950 --> 00:24:58,570
+ال notations او ال rules اللى ممكن نستخدمها مع ال
+
+315
+00:24:58,570 --> 00:25:03,990
+setsال identity أو بمعنى المحايد المحايد عندك ال
+
+316
+00:25:03,990 --> 00:25:07,970
+في هي محايد في إيش؟ في الاتحاد في ال union لإن في
+
+317
+00:25:07,970 --> 00:25:12,890
+اتحاد أي شيء هيظل نفس الشيء الست مش هتتغير طيب و
+
+318
+00:25:12,890 --> 00:25:18,310
+ال universe of discourse تقاطع أي ست داخله هتظل
+
+319
+00:25:18,310 --> 00:25:22,730
+نفس الست هتظل نفس الست اللي بنتكلم عنها فإذا هذا
+
+320
+00:25:22,730 --> 00:25:29,170
+أي أول محايد عندكالعكس تبعهم الهيمنة إذا كان قولنا
+
+321
+00:25:29,170 --> 00:25:36,890
+والله you اتحاد أي subset داخلها هيطلع you هتهيمن
+
+322
+00:25:36,890 --> 00:25:39,770
+على أي subset داخلها في الاتحاد بينما ال five
+
+323
+00:25:39,770 --> 00:25:43,090
+هتهيمن في معملية ال intersection five intersection
+
+324
+00:25:43,090 --> 00:25:47,330
+أي حاجة على طول five five بغض النظر أيش اللي موجود
+
+325
+00:25:47,330 --> 00:25:54,020
+كويس العنصر مع نفسه setاتحاد نفس ال set أو تقاطع
+
+326
+00:25:54,020 --> 00:25:57,160
+نفس ال set هتبقى نفس ال set هتبقى نفس ال set ال
+
+327
+00:25:57,160 --> 00:26:01,740
+double compliment compliment of compliment هيرجع
+
+328
+00:26:01,740 --> 00:26:07,120
+لنفس ال set هترجع لنفس ال set التبديل ال
+
+329
+00:26:07,120 --> 00:26:11,600
+commutative property هنا a union b هي نفس b union
+
+330
+00:26:11,600 --> 00:26:15,080
+a ونفس الكلام في ال intersection الأولى تقاطع
+
+331
+00:26:15,080 --> 00:26:19,290
+التانية هي نفس التانية تقاطع الأولى مختلفش اشيطيب
+
+332
+00:26:19,290 --> 00:26:23,710
+ال associative بمعنى مين جاب المين هذا بنعملها لما
+
+333
+00:26:23,710 --> 00:26:27,010
+يكون في عندك اكتر من intersection او اكتر من union
+
+334
+00:26:27,010 --> 00:26:33,030
+A union B union C مين الاتنين اللي هتاخدهم union
+
+335
+00:26:33,030 --> 00:26:35,530
+في الأول و بعدين الناتج تعمل union مع التالت مش
+
+336
+00:26:35,530 --> 00:26:40,750
+هتفرج B مع C في الأول او A مع B في الأول مافيش
+
+337
+00:26:40,750 --> 00:26:45,040
+مشكلة او A مع C في الأول برضه مافيش مشكلةمش هيفرج،
+
+338
+00:26:45,040 --> 00:26:48,600
+نفس الكلام في مين؟ في ال intersection، نفس الموضوع
+
+339
+00:26:48,600 --> 00:26:52,540
+في ال intersection دي مورغان، دي مورغان برضه لحجنا
+
+340
+00:26:52,540 --> 00:26:57,900
+لحجنا حتى في ال .. في ال sets فلما يكون في عندي A
+
+341
+00:26:57,900 --> 00:27:02,860
+union B ال complement لهفعليا ال compliment لكل
+
+342
+00:27:02,860 --> 00:27:06,640
+واحدة مع ال intersection مش مع ال union والعكس
+
+343
+00:27:06,640 --> 00:27:10,220
+صحيح إذا ال compliment لكل ناتج ال intersection
+
+344
+00:27:10,220 --> 00:27:15,780
+فهو فعليا اتحاد ال compliment لكل set مع بعضه
+
+345
+00:27:15,780 --> 00:27:19,960
+اتحاد لل compliment ل ال two sets compliment ال
+
+346
+00:27:19,960 --> 00:27:25,180
+set الأولى مع compliment ال set التاني لعندي
+
+347
+00:27:25,180 --> 00:27:27,680
+الأن هي نفسها هو حتى اللحظة نفسها
+
+348
+00:27:30,370 --> 00:27:33,910
+وببساطة جدا عارف ليش؟ لأن أساسا لما عرفنا ال union
+
+349
+00:27:33,910 --> 00:27:37,310
+هي كانت or و لما عرفنا ال intersection كانت and
+
+350
+00:27:37,310 --> 00:27:45,470
+فهي هي and و or تمام، الآن هنبدأ في الجد شوية لما
+
+351
+00:27:45,470 --> 00:27:48,830
+يكون في عندي approving ل ال set identities بدنا
+
+352
+00:27:48,830 --> 00:27:52,890
+نثبت أن ال two sets هدولة هم identity لبعض هم
+
+353
+00:27:52,890 --> 00:27:57,250
+مكافئين لبعض في أننا ال three methods عشان نشتغل
+
+354
+00:27:57,250 --> 00:28:04,390
+الكلام هذا يعني بمعنىE1 بدي أثبت أنها تساوي E2 أول
+
+355
+00:28:04,390 --> 00:28:07,910
+طريقة أني أفرض أن كل واحدة منهم هي subset من
+
+356
+00:28:07,910 --> 00:28:15,170
+التانية أفرض أنه أحاول أثبت أن E1 هي subset من E2
+
+357
+00:28:15,170 --> 00:28:20,130
+and E2
+
+358
+00:28:20,130 --> 00:28:25,530
+هي subset من E1 إذا قدرنا نصل لأثبات المعادلتين مع
+
+359
+00:28:25,530 --> 00:28:30,060
+بعض فالاتنين بتساويطيب أو باستخدام ال set builder
+
+360
+00:28:30,060 --> 00:28:35,620
+notation و هي حتى أنا كتبت logical equivalence
+
+361
+00:28:35,620 --> 00:28:38,260
+فإذا هو مسميها المعادلة التاعته و ال rules تاعته
+
+362
+00:28:38,260 --> 00:28:42,400
+هي logical هي logical فإذا ممكن نستخدم ال logical
+
+363
+00:28:42,400 --> 00:28:45,760
+زي ما أعملنا الإثبات في ال logic هنرجع نعمل إثبات
+
+364
+00:28:45,760 --> 00:28:48,960
+برضه لل sets بنفس القالية فهذه الطريقة التانية أو
+
+365
+00:28:48,960 --> 00:28:52,930
+استخدام أبسط شغلةالـ Membership Table مدام أنا
+
+366
+00:28:52,930 --> 00:28:56,330
+متعامل معاه على أساس ان هي زي ال logic طب معناته
+
+367
+00:28:56,330 --> 00:28:59,090
+بدي أقول إذا كان تنتمي بتعتبرها واحد وإذا كان لا
+
+368
+00:28:59,090 --> 00:29:01,950
+تنتمي بتعتبرها صفر وأتعامل معاها صفر وواحد وخلاص
+
+369
+00:29:01,950 --> 00:29:04,910
+وأحط الجدول ال truth table تبعناه وأمشي عليه
+
+370
+00:29:04,910 --> 00:29:08,290
+وانتهينا هذه تلات طرق بس طبعا الأخير تستخدمه لما
+
+371
+00:29:08,290 --> 00:29:12,330
+تكون حجم ال problem تبعتك صغيرة و بتقدر تحط ال
+
+372
+00:29:12,330 --> 00:29:16,230
+rules تبعتك بأرياحية و ال columns مش معقدة ال
+
+373
+00:29:16,230 --> 00:29:21,400
+columns تبعتك مش معقدة هناخد أنفلة طبعاهي مثال ..
+
+374
+00:29:21,400 --> 00:29:32,780
+هى مثال مطلوب نثبت انه A intersection of B union C
+
+375
+00:29:32,780 --> 00:29:39,080
+equivalent to ايش؟ to A intersection B union مع A
+
+376
+00:29:39,080 --> 00:29:43,500
+intersection C كويس؟
+
+377
+00:29:43,500 --> 00:29:50,430
+طبعا هذه distribution ماقولناهاش تويبس هي موجودة
+
+378
+00:29:50,430 --> 00:29:54,430
+طالب مننا احنا نثبتها ما كتبناها اش توي صح بس
+
+379
+00:29:54,430 --> 00:29:58,530
+مطلوب نثبتها طيب هنشتغل على اللي هو ال mutual
+
+380
+00:29:58,530 --> 00:30:03,630
+subset mutual subset بمعنى ان كل منهم هو ال subset
+
+381
+00:30:03,630 --> 00:30:06,770
+تبادلي كل واحدة منهم هي subset من التاني okay
+
+382
+00:30:06,770 --> 00:30:10,410
+هتشوف فبدي افرض الفرضية الأولى ان الأول subset من
+
+383
+00:30:10,410 --> 00:30:14,570
+التاني وعدنا هنكمل نعمل العكس ان التاني هو subset
+
+384
+00:30:14,570 --> 00:30:18,250
+من الأول نبدأ بخطوة الأولى فهذه رقم واحدهذه الرقم
+
+385
+00:30:18,250 --> 00:30:21,810
+واحد اللي بدنا نبدأ نثبتها بدنا نثبت ان a
+
+386
+00:30:21,810 --> 00:30:25,730
+intersection b union c هي subset من هذا ال term
+
+387
+00:30:25,730 --> 00:30:30,970
+معناه ذلك انه بدى الآن اقول ان كل عنصر ينتمي لهذا
+
+388
+00:30:30,970 --> 00:30:35,490
+الطرف بالضرورة لازم يكون موجود في الطرف التاني هي
+
+389
+00:30:35,490 --> 00:30:39,690
+اللي بدنا نثبته حاليا okay ف assume that ان x هي
+
+390
+00:30:39,690 --> 00:30:44,110
+ينتمي للطرف اللي أنا فرضه subset
+
+391
+00:30:45,890 --> 00:30:49,230
+عشان أثبت بعدين إنه مدام هو ينتمي لهذا الطرف هو
+
+392
+00:30:49,230 --> 00:30:52,030
+بالضروري لازم ينتمي للطرف الآخر بنكون جيبنا subset
+
+393
+00:30:52,030 --> 00:30:55,350
+إن الأولى هي subset من التانية خلّيني نشوف assume
+
+394
+00:30:55,350 --> 00:31:01,630
+X belong to A intersection B union C هذا
+
+395
+00:31:01,630 --> 00:31:05,050
+intersection إيش يعني intersection؟ يعني إذا كان X
+
+396
+00:31:05,050 --> 00:31:12,990
+هو ينتمي ل A intersection B union C فهو بالضروري
+
+397
+00:31:12,990 --> 00:31:14,030
+ينتمي للطرفين
+
+398
+00:31:16,480 --> 00:31:19,380
+ما دام ينتمي لل intersection بينهم يعني هو موجود
+
+399
+00:31:19,380 --> 00:31:28,620
+في الطرفين الطرف A والطرف B union C فإذا بكل بساطة
+
+400
+00:31:28,620 --> 00:31:35,980
+بقدر أقول أن X هو ينتمي بالضرورة ل A and X هو برضه
+
+401
+00:31:35,980 --> 00:31:41,820
+ينتمي بالضرورة ل B union Cطيب عند union C ماقدرش
+
+402
+00:31:41,820 --> 00:31:45,840
+أقول إن هو ينتمي للإتنين هو في أسوأ الأحوال ينتمي
+
+403
+00:31:45,840 --> 00:31:49,000
+لواحد منهم في أسوأ الأحوال هو ينتمي لواحد منهم
+
+404
+00:31:49,000 --> 00:31:55,020
+هنحط ال two خلينا نسميها premises بتاعوننا
+
+405
+00:31:55,020 --> 00:31:59,060
+الفرضيات بتاعتنا بدأ أفترض إن هو ينتمي لل B الأول
+
+406
+00:31:59,060 --> 00:32:02,320
+و أشوف هل الكلام بيطلع صح و بعدين هفترض إن هو
+
+407
+00:32:02,320 --> 00:32:05,400
+ينتمي لل C هل فعلا برضه الكلام بيطلع صح ولا لأ
+
+408
+00:32:05,400 --> 00:32:13,340
+هنبدأ حاجة حاجة فالفرضية الأولى FX تنتمي للـ B
+
+409
+00:32:13,340 --> 00:32:19,320
+فإذا الأن أصبح هنا ينتمي ل A و B أصبح ينتمي ل A و
+
+410
+00:32:19,320 --> 00:32:24,520
+ل B في الحالة هذه إذا بينتمي ل A و ل B هذا يؤكدنا
+
+411
+00:32:24,520 --> 00:32:36,740
+أو بيعطيني إن X ينتمي ل A intersection B تمام؟
+
+412
+00:32:36,740 --> 00:32:43,390
+كويس هي موجودة فعلا هناأو موجودة اتحاد مع others
+
+413
+00:32:43,390 --> 00:32:47,970
+set others set خلاص إيش ما تكون ال set هذه .. هذا
+
+414
+00:32:47,970 --> 00:32:53,570
+اتحاد صح؟ تفهمين إيش يعني هذا اتحاد؟ يعني معناه
+
+415
+00:32:53,570 --> 00:32:56,590
+ذلك ينتمي للجزء الأول من الاتحاد فهو أكيد ينتمي
+
+416
+00:32:56,590 --> 00:33:03,510
+للكل Union Union خلاص فإذا الفرضية الأولى إذا كان
+
+417
+00:33:03,510 --> 00:33:08,310
+ينتمي ل B فهو أكيد هينتمي لكل ال term هذا طيب
+
+418
+00:33:08,310 --> 00:33:15,300
+الفرضية التانيةف X ينتمي ل C وهذا معناه ان X تنتمي
+
+419
+00:33:15,300 --> 00:33:22,700
+ل A intersection C اللي هو الطرف التاني و إذا
+
+420
+00:33:22,700 --> 00:33:27,420
+انتمت للطرف التاني مش هيفرج إيش الطرف الأول لإن
+
+421
+00:33:27,420 --> 00:33:34,080
+اتحاد برضه خلاص بالظبط true or أي حاجة true or
+
+422
+00:33:35,350 --> 00:33:38,910
+nothing مش فارقة معناه إيش هي بالظبط مش فارقة إيش
+
+423
+00:33:38,910 --> 00:33:42,390
+هيكون الطرف الآخر فإذا هي أثباتها طبعا هنا مفصل
+
+424
+00:33:42,390 --> 00:33:45,530
+أكتر احنا شرحنا بحيث انه على طول مباشرة مني لإلك
+
+425
+00:33:45,530 --> 00:33:50,930
+على طول هي وصلتك تمام الآن مخلصناش لسه الطرف
+
+426
+00:33:50,930 --> 00:33:55,070
+التاني اللي بدنا الطرف التاني هو subset من الطرف
+
+427
+00:33:55,070 --> 00:34:00,470
+الأول الطرف التاني هو subset من الطرف الأول وهذه
+
+428
+00:34:00,470 --> 00:34:08,270
+بكل بساطة بتقدر تقول مدام هذا اتحادتشهد اتحاد هذه
+
+429
+00:34:08,270 --> 00:34:18,390
+واضحة و هي مكتوبة عندك هتشوف الطرف الآخر X تنتمي ل
+
+430
+00:34:18,390 --> 00:34:29,550
+A intersection B اتحاد A intersection C فرضية أولى
+
+431
+00:34:30,410 --> 00:34:35,150
+لأنه هذا اتحاد، فهو إما ينتمي لهذا ال term أو لهذا
+
+432
+00:34:35,150 --> 00:34:38,410
+ال term أو كلاهما، بس احنا بناخد بالأسوأ، بأسوأ
+
+433
+00:34:38,410 --> 00:34:41,530
+الاحتمالات أنه مش موجود في كلا الطرفين، هو في واحد
+
+434
+00:34:41,530 --> 00:34:45,010
+منهم، فإذا في الحالة هذه X belonging الحالة الأولى
+
+435
+00:34:45,010 --> 00:34:49,290
+اللي هفرضها، أنه لأ هو ماينتميش لهنا، ينتمي ل A
+
+436
+00:34:49,290 --> 00:34:55,650
+intersection Bما دام ينتمي ل A intersection B فهو
+
+437
+00:34:55,650 --> 00:34:59,650
+بالضروري ينتمي ل كلهما بالضروري ينتمي ل كلهما إذا
+
+438
+00:34:59,650 --> 00:35:08,270
+X ينتمي ل A و X ينتمي ل B بالضرورة طيب نبدأ شوية
+
+439
+00:35:08,270 --> 00:35:16,550
+شوية من هذا الكلام بقدر أقول في الحالة هذه نبدأ
+
+440
+00:35:16,550 --> 00:35:23,620
+نشتغل هنا ينتمي ل A و ل B صح؟ ينتمي ل Aوينتمي ل B
+
+441
+00:35:23,620 --> 00:35:29,160
+طيب B اتحاد أي شيء true خلاص نعم طيب intersection
+
+442
+00:35:29,160 --> 00:35:33,700
+true مع true true فخلاص هذه صحيحة ناخد الفرضية
+
+443
+00:35:33,700 --> 00:35:37,720
+التانية إذا هو لأ لا ينتمي لهذا ال term ينتمي لل
+
+444
+00:35:37,720 --> 00:35:44,360
+term التاني X belong to A intersection C فبالضرورة
+
+445
+00:35:44,360 --> 00:35:48,600
+X هينتمي ل A و X هينتمي ل C
+
+446
+00:35:54,810 --> 00:36:00,390
+طيب، ينتمي لـ A و ينتمي لـ C فهو أكيد ينتمي لـ C
+
+447
+00:36:00,390 --> 00:36:05,710
+خلاص اتحاد أي مجموعة لا ينتمي لها حتى فهو موجود من
+
+448
+00:36:05,710 --> 00:36:09,550
+الاتحاد بغض النظر هو موجود في B و لا مش موجود في B
+
+449
+00:36:09,550 --> 00:36:12,850
+طيب، معناه ذلك أنه في الاتحاد هو موجود أصبح موجود
+
+450
+00:36:12,850 --> 00:36:17,370
+في هذه ال .. ال set اللي تم إنتاجها من الاتحاد set
+
+451
+00:36:17,370 --> 00:36:20,250
+هو موجود فيها مع set هو موجود فيها intersection
+
+452
+00:36:20,250 --> 00:36:24,690
+أكيد هيكون موجود في ال intersectionفهي عملنا
+
+453
+00:36:24,690 --> 00:36:30,890
+الإثبات للحالتين اللي هي كل واحدة منهم subset من
+
+454
+00:36:30,890 --> 00:36:34,490
+التانية، كل واحدة منهم subset من التانية، تمام
+
+455
+00:36:37,550 --> 00:36:43,110
+Okay طبعا ممكن نعمل من خلال ال truth table زي ما
+
+456
+00:36:43,110 --> 00:36:45,630
+احنا شايفين بس هنسميه هنا ال membership table
+
+457
+00:36:45,630 --> 00:36:49,370
+membership table لأن هي مش truth or false هي ينتمي
+
+458
+00:36:49,370 --> 00:36:53,170
+ولا لا ينتمي فهي membership هي membership لو قولنا
+
+459
+00:36:53,170 --> 00:36:59,060
+بدنا نثبت ان a union bdifference B هو equal to A
+
+460
+00:36:59,060 --> 00:37:03,840
+difference B مباشرة الكلام هذا بنقدر نحطه مباشرة
+
+461
+00:37:03,840 --> 00:37:09,140
+بحيث انه ينتمي و لا ينتمي فهنا هنقول لا ينتمي لا
+
+462
+00:37:09,140 --> 00:37:13,620
+ينتمي لا ينتمي ينتمي ينتمي لا ينتمي ينتمي ينتمي
+
+463
+00:37:13,620 --> 00:37:18,800
+belong to belong to فالاتحاد تبعهمالاتحاد هو غير
+
+464
+00:37:18,800 --> 00:37:20,940
+موجود لا في a ولا في b فهو مش موجود في الاتحاد
+
+465
+00:37:20,940 --> 00:37:24,700
+اكيد طب هو مش موجود في a لكن موجود في b موجود في
+
+466
+00:37:24,700 --> 00:37:31,220
+الاتحاد هي or تمام
+
+467
+00:37:31,220 --> 00:37:36,620
+فهي كائنها or الناتج هذا ناقص b بمعنى ان هو موجود
+
+468
+00:37:36,620 --> 00:37:43,260
+هنا و غير موجود في b موجود و غير موجود لأ موجود و
+
+469
+00:37:43,260 --> 00:37:47,650
+غير لأ برضه لأموجود و غير .. اه هيها موجود و غير
+
+470
+00:37:47,650 --> 00:37:53,310
+موجود موجود في الأول و غير موجود في التاني هي ال
+
+471
+00:37:53,310 --> 00:37:56,350
+difference check ال difference تمام فإذا هي الحالة
+
+472
+00:37:56,350 --> 00:37:59,210
+الوحيدة موجود و غير موجود هنا موجود موجود لأ صفر
+
+473
+00:37:59,210 --> 00:38:07,950
+هي أول term عندى التانية ايهdifference B موجود
+
+474
+00:38:07,950 --> 00:38:14,210
+موجود لأ غير موجود غير موجود غير موجود موجود موجود
+
+475
+00:38:14,210 --> 00:38:18,190
+هى هى هنا موجود في A و غير موجود في B عشان يحقق ال
+
+476
+00:38:18,190 --> 00:38:23,350
+A minus B كمان فهذه هي الواحد تعالى تطلع على ال
+
+477
+00:38:23,350 --> 00:38:30,110
+two columns هدول فإذا فعلا هذه equivalent لهذه هذه
+
+478
+00:38:30,110 --> 00:38:32,550
+equivalent لهذه زيها زي ال truth table اللى كنتوا
+
+479
+00:38:32,550 --> 00:38:44,210
+تاخدوه سابقاهذه الطريقة التانية تقدر
+
+480
+00:38:44,210 --> 00:38:47,570
+طبعا تكبروا الموضوع موجود عندكم هذا مش محلول
+
+481
+00:38:47,570 --> 00:38:51,330
+بتهيألي صح؟ خلاص okay جربوا حلو عندكم اشتغلوا عليه
+
+482
+00:38:51,330 --> 00:38:55,070
+بنفس القالية بنفس الفكرة ماخدينه كذا مرة في ال
+
+483
+00:38:55,070 --> 00:38:57,930
+logic خدتوها هنا خدتوها يعني بتهيألي مش هيكون كتير
+
+484
+00:38:57,930 --> 00:39:04,420
+صعب عملية حلو يعنيتمام الان نعمل نشوف ال
+
+485
+00:39:04,420 --> 00:39:08,380
+generalization ل ال two operators اللي أخدناهم ل
+
+486
+00:39:08,380 --> 00:39:10,480
+ال two operators اللي أخدناهم في عندي ال
+
+487
+00:39:10,480 --> 00:39:13,820
+generalized union بمعنى أن ال union هو مش بالضروري
+
+488
+00:39:13,820 --> 00:39:17,720
+ل two sets فقط لأنه ممكن نعمله أكتر من two sets
+
+489
+00:39:17,720 --> 00:39:21,660
+ممكن نعمله أكتر من two sets و نسميه N array union
+
+490
+00:39:21,660 --> 00:39:33,640
+N .. N set فإذا A1 union A2 union A3 to ANالآن زي
+
+491
+00:39:33,640 --> 00:39:37,000
+ما توي شفنا في ال .. ال competitive مين جاب المين
+
+492
+00:39:37,000 --> 00:39:41,190
+مش هيفرجأو في ال association في ال association
+
+493
+00:39:41,190 --> 00:39:44,770
+المشاركة مين هنشاركه مع مين مش هتفرج معانا يعني
+
+494
+00:39:44,770 --> 00:39:48,950
+واحد هيقول بتاخد ا واحد اتحاد اتنين والناتج اعمل
+
+495
+00:39:48,950 --> 00:39:52,870
+اتحاد am والناتج ا بعدين ارجع ل اي تلقاء انت حر
+
+496
+00:39:52,870 --> 00:39:57,650
+المهم ان في الآخر تعمل اتحاد ال n sits كلهم مع بعض
+
+497
+00:39:57,650 --> 00:40:01,230
+تمام او تعمل عملية ال grouping عملية ال grouping
+
+498
+00:40:01,230 --> 00:40:05,070
+انت حر فيها ال order للعملية ال grouping انت برضه
+
+499
+00:40:05,070 --> 00:40:10,300
+حر فيهاunrelevant بمعنى
+
+500
+00:40:10,300 --> 00:40:14,420
+انت اشتغلها مين جاب المين مش هتفرج، الان هذه كيف
+
+501
+00:40:14,420 --> 00:40:17,800
+ممكن نكتبها عشان ماقعدش اكتب terms كتيرة بنكتبها
+
+502
+00:40:17,800 --> 00:40:23,180
+big U زي ال summation ليش لو كنت تعمل جمع جمع جمع
+
+503
+00:40:23,180 --> 00:40:27,780
+انت بتعمل summation وخلاص وخلاصطيب او ال product
+
+504
+00:40:27,780 --> 00:40:32,120
+ليش تعمل product انت بتعمل buy و بتحدد ال limits
+
+505
+00:40:32,120 --> 00:40:35,200
+ساعتها و خلاص بتحدد ال limits نفس الكلام برضه في
+
+506
+00:40:35,200 --> 00:40:39,820
+ال 6 بنعمله big U فهذه ال notation عبارة عن big U
+
+507
+00:40:39,820 --> 00:40:47,060
+from I equal to 1 to N و AI فأصبحت كأنها اتحاد A 1
+
+508
+00:40:47,060 --> 00:40:54,560
+2 3 4 to N خلصنا منهانفس الكلام هذه مميزة ل finite
+
+509
+00:40:54,560 --> 00:40:58,600
+ممكن تكون infinite او ممكن تكون infinite ممكن تكون
+
+510
+00:40:58,600 --> 00:41:02,560
+infinite لكن انا مش هقدر اجيب الحاصل الحاصل ال
+
+511
+00:41:02,560 --> 00:41:06,060
+union نفسه او ال result of union مش هقدر اجيبه
+
+512
+00:41:06,060 --> 00:41:10,840
+لانه to infinity لكن ممكن تنكتب انعبر عنها بهذا
+
+513
+00:41:10,840 --> 00:41:15,180
+الشكل ك infinite set ممكن نقول you from one to
+
+514
+00:41:15,180 --> 00:41:21,180
+infinity to infinity ل a i و بس كتعبير عن الحالة
+
+515
+00:41:21,180 --> 00:41:25,630
+اللي موجودةالكلام هو هو لمين لل intersection نفس
+
+516
+00:41:25,630 --> 00:41:29,670
+الجثة ال intersection ممكن نحطه بنفس القالية و مين
+
+517
+00:41:29,670 --> 00:41:35,010
+جاب المين بفرجش تفرجش معناه ممكن نعملها big arc
+
+518
+00:41:35,010 --> 00:41:41,750
+اللي هو القص الكبير للتعبير عن ال big او اللي هو
+
+519
+00:41:41,750 --> 00:41:46,210
+ال intersection لأكتر من twoset من two sets من
+
+520
+00:41:46,210 --> 00:41:49,170
+واحد to one و نفس الكلام ممكن نعملها لل infinite
+
+521
+00:41:49,170 --> 00:41:53,950
+او لل for infinity بتوعيش from one to infinity و
+
+522
+00:41:53,950 --> 00:42:03,130
+بيمشي الحال كتعبير عن infinite sets تمام الآن
+
+523
+00:42:03,130 --> 00:42:07,130
+عملية التمثيل باستخدام ال bit string باستخدام ال
+
+524
+00:42:07,130 --> 00:42:12,540
+bit string ممكن نقوللو افترضت عندى U هي ال natural
+
+525
+00:42:12,540 --> 00:42:18,640
+number و عندى 6 S هي عبارة عن اتنين، تلاتة، خمسة،
+
+526
+00:42:18,640 --> 00:42:24,350
+سبعة، احداش ممكن نعبر عنها بال bit stringك bit
+
+527
+00:42:24,350 --> 00:42:28,410
+string sequence من مجموعة bits وكلمة bits احنا
+
+528
+00:42:28,410 --> 00:42:32,150
+عارفين جاي من binary من كلمة binary معنى ذلك انه
+
+529
+00:42:32,150 --> 00:42:36,030
+اثنائية يعني معنى ذلك انه يا صفر يا واحد يا صفر يا
+
+530
+00:42:36,030 --> 00:42:38,650
+واحد بنقدر نتمثل فيها الاعدادات او بنقدر نتمثل
+
+531
+00:42:38,650 --> 00:42:43,070
+فيها الاعدادات اذا افترضنا انه كترتيب natural
+
+532
+00:42:43,070 --> 00:42:46,790
+number بيبدأ من الصفر مش هيك فبنمثل ال location
+
+533
+00:42:46,790 --> 00:42:50,990
+نفسه هو ال natural number ال location نفسه هذا ال
+
+534
+00:42:50,990 --> 00:42:55,400
+location تبع الصفر هل الصفر موجود؟لا مش موجود،
+
+535
+00:42:55,400 --> 00:43:00,480
+معناته صفر طيب الواحد موجود، الأتنين موجودة،
+
+536
+00:43:00,480 --> 00:43:05,900
+بعطيها واحد، مهي membership هو ينتمي ولا لا ينتمي؟
+
+537
+00:43:05,900 --> 00:43:09,900
+ينتمي هنا بصبح، مش لل set، ينتمي ل ال bit string
+
+538
+00:43:09,900 --> 00:43:13,620
+ولا لا ينتمي لل string؟ هل هو ينتمي لل string؟ أه
+
+539
+00:43:13,620 --> 00:43:16,520
+ينتمي، طب في أي location، بتعامل مع ال location
+
+540
+00:43:16,520 --> 00:43:21,300
+كأنه هذا natural number كأنها natural number، ببدأ
+
+541
+00:43:21,300 --> 00:43:25,520
+من مين؟ من الصفرصفر واحد اتنين اه الاتنين موجودة
+
+542
+00:43:25,520 --> 00:43:28,020
+التلاتة موجودة حتى بدون ما اشوفها هنا اذا كان
+
+543
+00:43:28,020 --> 00:43:30,720
+تمثيلهم صح بقدر من هنا على طول اعرف ايش العرقام
+
+544
+00:43:30,720 --> 00:43:34,800
+اللي موجودة من خلال sequence بهذا الشكل الطريقة
+
+545
+00:43:34,800 --> 00:43:38,840
+هذه سهلة جدا تمثيل المجموعات اذا كانت natural
+
+546
+00:43:38,840 --> 00:43:44,920
+number للكمبيوتر مش هيك؟ متخيل انت تكتب المجموعة و
+
+547
+00:43:44,920 --> 00:43:47,960
+تخزينها على ال hard disk بهذا الشكل ك hardware ولا
+
+548
+00:43:47,960 --> 00:43:52,240
+تخزينها bit string واحد يعبرلك عن المجموعة و خلاص
+
+549
+00:43:53,650 --> 00:43:57,510
+ملاحظين جدش بتسهل علينا إذا كان نوعية البيانات هي
+
+550
+00:43:57,510 --> 00:44:01,070
+natural number إذا كان البيانات اللي داخلها أو ال
+
+551
+00:44:01,070 --> 00:44:03,750
+data اللي جواها هي عبارة عن أرقام و الأرقام هذه هي
+
+552
+00:44:03,750 --> 00:44:06,370
+natural number فخلاص بعرف إن هي صفر واحد اتنين
+
+553
+00:44:06,370 --> 00:44:10,670
+تلاتة ترتيبا و بشوف جدش اللي ماطينيها و بشتغل عليه
+
+554
+00:44:10,670 --> 00:44:14,350
+باستخدام ال union أو ال intersection أو حتى ال
+
+555
+00:44:14,350 --> 00:44:20,050
+complement كلها عادي جدا كأنها or and و negation
+
+556
+00:44:21,170 --> 00:44:26,590
+كيف الكلام هذا؟ هنشوف كيف هي مثال عشان يوضحلنا
+
+557
+00:44:26,590 --> 00:44:30,430
+الموضوع لو افترضنا ان ال union او ال universe of
+
+558
+00:44:30,430 --> 00:44:33,410
+discourse ال U او ال universe of discourse هي
+
+559
+00:44:33,410 --> 00:44:37,870
+الأرقام ال natural number من واحد لعشرة من واحد
+
+560
+00:44:37,870 --> 00:44:40,830
+لعشرة فهذه هي ال universe of discourse طبعاً بدنا
+
+561
+00:44:40,830 --> 00:44:46,370
+نمثل الرقم اللي قدامنا هنا بهذا الشكل الطبيعي هروح
+
+562
+00:44:46,370 --> 00:44:52,560
+احطه كstring و بدنا نبدأ نشتغل عليه فممكن اقول صفر
+
+563
+00:44:52,560 --> 00:44:57,300
+صفر واحد واحد واحد صفر صفر مابقدش صرنا هيك اتنين
+
+564
+00:44:57,300 --> 00:45:02,420
+تلاتة اربعة خمسة ستة سبعة امانية تسعة عشرة and so
+
+565
+00:45:02,420 --> 00:45:10,100
+on بتكون كيف؟ تبدأ من صفر اه بدك تبدأ من صفر هنا
+
+566
+00:45:10,100 --> 00:45:14,140
+اه لأ حسب ال universe of discourse اه هناك لاحظ
+
+567
+00:45:14,140 --> 00:45:21,170
+هناك ايش حددلك إياها؟ف ال U هي اللي بتحدد نقاش ال
+
+568
+00:45:21,170 --> 00:45:25,450
+.. كيف نبدأ هنا ال U حددلكيها من الأول جالك ال U
+
+569
+00:45:25,450 --> 00:45:32,370
+تبعتي واحد ابدا من واحد لعشرة كويس العكس صحيح برضه
+
+570
+00:45:32,370 --> 00:45:35,510
+نفس الكلام translation بالعكس برضه بدك تقول هنا
+
+571
+00:45:35,510 --> 00:45:43,670
+عبارة عن واحد هتنكتب المجموعة اتنين تلاتة اربعة
+
+572
+00:45:43,670 --> 00:45:49,010
+سبعة تمانية تسعة عشرة
+
+573
+00:45:52,920 --> 00:45:56,960
+خلاص الباقي نفس الجثة بتقدر تعمله نفس الشيء طيب
+
+574
+00:45:56,960 --> 00:46:00,880
+انا معنى شوية بس اكمل ات .. اكملي لنا واحدة من
+
+575
+00:46:00,880 --> 00:46:08,780
+التنتين هدولة هات نعمل هذه هنا نبدأ من اتنين اربعة
+
+576
+00:46:08,780 --> 00:46:16,760
+خمسة ستة وفي سبعة كمان تمانية تسعة عشرة مش موجودين
+
+577
+00:46:16,760 --> 00:46:17,580
+خلاص لا هيك
+
+578
+00:46:20,910 --> 00:46:35,410
+طيب اتخيلولا بدنا نعمل intersection اربعة
+
+579
+00:46:35,410 --> 00:46:42,590
+موجودة صحيح okay هذه intersection طب بدنا نعمل
+
+580
+00:46:42,590 --> 00:46:42,910
+union
+
+581
+00:46:50,410 --> 00:46:57,930
+لأ الخمسة موجودة والستة موجودة خلاص معنا ذلك
+
+582
+00:46:57,930 --> 00:47:05,170
+اتحادهم هيطلع ال ال you طيب ممتاز هتلنا نعمل
+
+583
+00:47:05,170 --> 00:47:08,170
+الكلام هذا انسال اللي موجود هنا و هدولة التنتين
+
+584
+00:47:08,170 --> 00:47:13,450
+نعملهم متذاكرين ال ال bitwise ال bitwise
+
+585
+00:47:13,450 --> 00:47:18,970
+intersection او unionهتنعمل ال .. union ما هي
+
+586
+00:47:18,970 --> 00:47:22,870
+بالظبط intersection and union هى بتعمل or ولا and
+
+587
+00:47:22,870 --> 00:47:31,310
+بدنا نعمل and هى عندي واحدة هى تنتين وهى تلاتة
+
+588
+00:47:31,310 --> 00:47:35,130
+هدول ايش مواقعهم اتنين واربعة وسبعة هى اتنين
+
+589
+00:47:35,130 --> 00:47:39,250
+واربعة وسبعة مهم انت تشايفيهم اصلا طيب بدك تعمل
+
+590
+00:47:39,250 --> 00:47:46,060
+اتحاد اتحاد مافيش صفرين بالبعضotherwise كله ones
+
+591
+00:47:46,060 --> 00:47:52,860
+يعني على الأقل في واحد في واحد ال two strings خلاص
+
+592
+00:47:52,860 --> 00:47:57,940
+معناته اليوم كلها كلهم موجودين فهي نفس الفكرة
+
+593
+00:47:57,940 --> 00:48:03,260
+بتعمل intersection بتعملunion بنفس القالية يلا
+
+594
+00:48:03,260 --> 00:48:06,180
+اعطيكوا العافية خلصنا احنا ال sets و اليوم كان في
+
+595
+00:48:06,180 --> 00:48:10,160
+عندنا set operations و خلصناها المرة القادمة هيكون
+
+596
+00:48:10,160 --> 00:48:13,440
+في الجزئية اللي ضايلة اللي هي ال function لإن
+
+597
+00:48:13,440 --> 00:48:15,480
+الأسبوع حدث في جزئية ال function لسه ما خلصناهاش
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/KAeoVdmcXOE.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/KAeoVdmcXOE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..03fff7377e020460b36d89e4fdb8a74cc9c3c952
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/KAeoVdmcXOE.srt
@@ -0,0 +1,2010 @@
+
+1
+00:00:05,230 --> 00:00:08,630
+السلام عليكم، يا أعطاكم الله العفو يا شباب، نبدأ اليوم
+
+2
+00:00:08,630 --> 00:00:12,850
+إن شاء الله تعالى في درس جديد، وهو الـ theory of
+
+3
+00:00:12,850 --> 00:00:18,050
+sets أو الـ set theory، فسنَتَكلم عن نظرية المجموعات
+
+4
+00:00:18,050 --> 00:00:24,050
+ونتحدث عنها وعن خصائصها، على اعتبار أن المجموعات هي
+
+5
+00:00:24,050 --> 00:00:27,310
+الجزء
+
+6
+00:00:27,310 --> 00:00:29,710
+الأهم في الـ universe of discourse، باعتبار أنه
+
+7
+00:00:29,710 --> 00:00:35,340
+المدخل لقواعد البيانات، فلما نجي نتكلم عن الـ set
+
+8
+00:00:35,340 --> 00:00:40,780
+فهي عبارة عن structure أو بناء يمثل لنا unordered
+
+9
+00:00:42,020 --> 00:00:47,800
+collection أو group، فأي مجموعة أو تجمع من الأرقام
+
+10
+00:00:47,800 --> 00:00:53,900
+أو العناصر بشكل عام، objects غير مرتبة، فالمجموعة هي
+
+11
+00:00:53,900 --> 00:00:56,720
+بشكل أو بآخر هي بتكون غير مرتبة، فلما نتكلم عن
+
+12
+00:00:56,720 --> 00:00:59,940
+مجموعة طلبة الـ discrete، فهم ليس بالضروري دائماً
+
+13
+00:00:59,940 --> 00:01:02,400
+يكونوا بنفس الترتيب، ونفس الجُملة اللي قاعدينها
+
+14
+00:01:02,400 --> 00:01:07,320
+ولكن في النهاية هم نفس المجموعة، ونفس الـ objects
+
+15
+00:01:07,320 --> 00:01:12,550
+بالنسبة لكشف الحضور والغياب مثلاً، أو كشف آخر العام
+
+16
+00:01:12,550 --> 00:01:17,390
+أو آخر الفصل اللي بده يعطيه درجات، فبيكون نفس العدد
+
+17
+00:01:17,390 --> 00:01:20,870
+أجل، ولكن الترتيب ليس بالضروري دائماً يكون نفس الترتيب
+
+18
+00:01:20,870 --> 00:01:24,870
+ليس بالضروري يكون نفس الترتيب، فهذا ممكن يكون zero
+
+19
+00:01:24,870 --> 00:01:29,530
+objects، ممكن يكون nothing، اللي هو دائماً بتسموها
+
+20
+00:01:29,530 --> 00:01:34,010
+المجموعة الخالية، كنتوا تعرفوها بالـ  Φ (فاي)، فإما zero أو more
+
+21
+00:01:34,010 --> 00:01:37,550
+distinct أو different objects، فبتكون مجموعة
+
+22
+00:01:37,550 --> 00:01:41,350
+objects، واللي سميناها objects، ليس بالضروري نسميها
+
+23
+00:01:41,350 --> 00:01:44,950
+numbers، ليس بالضروري نسميها numbers، لأنها أي
+
+24
+00:01:44,950 --> 00:01:48,710
+شيء في الدنيا ممكن تكون sets، ممكن تكون sets، وزي
+
+25
+00:01:48,710 --> 00:01:54,250
+ما قلنا هنا، تكلمنا عن المسجلين لمُصَاق معين، هم أصلاً
+
+26
+00:01:54,250 --> 00:01:58,730
+ضمن مجموعة المسجلين لهذا المُصَاق، بغض النظر عن
+
+27
+00:01:58,730 --> 00:02:02,320
+ترتيبهم، كل الـ mathematics من تعريفنا البسيط ده، كل
+
+28
+00:02:02,320 --> 00:02:04,740
+الـ mathematics اللي ممكن تخطر على بالكم، هي ممكن
+
+29
+00:02:04,740 --> 00:02:09,160
+تُعبَّر بـ ... كـ sets، ليش؟ لأن أي mathematics أنتَ
+
+30
+00:02:09,160 --> 00:02:13,160
+بتتخيلها في الدنيا، أكيد محتاج تعطيها قيم، أو القيم
+
+31
+00:02:13,160 --> 00:02:16,240
+هذه، ليس بالضروري تكون عددية أو رقمية، زي ما قلنا، ليس
+
+32
+00:02:16,240 --> 00:02:18,980
+بالضرورة تكون رقمية أو عددية، زي مثلاً الـ false، true
+
+33
+00:02:18,980 --> 00:02:22,540
+اللي كنا بناخذه من أول الفصل حتى الآن، هذه ليست
+
+34
+00:02:22,540 --> 00:02:26,040
+عددية، هي إما true، إما false، صح أو خطأ، فهذه برضه
+
+35
+00:02:26,040 --> 00:02:30,080
+نفس الشيء، ممكن تتعامل معها as a set، as a set، الـ set
+
+36
+00:02:30,080 --> 00:02:35,000
+هذه تحتوي على two elements، فأنا محتاج أعطي قيمة من
+
+37
+00:02:35,000 --> 00:02:37,680
+الـ universe of discourse، فمادام في حاجة اسمها
+
+38
+00:02:37,680 --> 00:02:40,440
+universe of discourse، وهذه الـ predicate برضه
+
+39
+00:02:40,440 --> 00:02:45,140
+اتكلمنا عنها، والـ predicate هي نفس فكرة الـ
+
+40
+00:02:45,140 --> 00:02:49,940
+function، هي بتتعامل مع قيمة للـ object أو للـ
+
+41
+00:02:49,940 --> 00:02:52,820
+subject من الـ universe of discourse، طب الـ universe of
+
+42
+00:02:52,820 --> 00:02:56,640
+discourse هذا هو عبارة عن collection أو group of
+
+43
+00:02:56,640 --> 00:03:00,700
+elements، group of elements، لما نتكلم عن الـ X،  جد أيش
+
+44
+00:03:00,700 --> 00:03:04,900
+القيم اللي ممكن تأخذها، فهي ممكن تأخذ أي قيمة من الـ
+
+45
+00:03:04,900 --> 00:03:08,300
+X axis، طيب الـ X axis، القيم نفسها اللي موجودة على
+
+46
+00:03:08,300 --> 00:03:11,980
+الـ X axis هذه، طب ما هي برضه elements، هي مجموعة
+
+47
+00:03:11,980 --> 00:03:17,060
+elements، فبنقدر نقول إن X ممكن يأخذ أي قيمة من الـ
+
+48
+00:03:17,060 --> 00:03:21,800
+set هذه، من الـ set هذه اللي بتحتوي على مجموعة الـ
+
+49
+00:03:21,800 --> 00:03:26,670
+elements، تمام، بعض الـ mutations الأساسية، كلنا
+
+50
+00:03:26,670 --> 00:03:31,050
+بنتعامل مع الـ set كمسمى للـ set، والـ elements بتاعت
+
+51
+00:03:31,050 --> 00:03:35,730
+الـ set بشكل بسيط، وصريح، وواضح، عادة الـ set نفسها
+
+52
+00:03:35,730 --> 00:03:40,270
+كمتغير، بنحطها capital، بنعطيها قيمة capital، فممكن
+
+53
+00:03:40,270 --> 00:03:46,810
+أقول الـ set لـ الـ discrete دي، هذه بتحتوي على كل الـ
+
+54
+00:03:46,810 --> 00:03:52,110
+elements، والآن بنحطها، بتعرف بالـ curly braces أو
+
+55
+00:03:52,110 --> 00:03:56,750
+الأقواس المجعدة، اللي بالشكل هذا، تعرف إن مدبها
+
+56
+00:03:56,750 --> 00:04:00,470
+بداخله هي الـ elements، والـ elements بتاعتها بتعطى قيم
+
+57
+00:04:00,470 --> 00:04:01,190
+small
+
+58
+00:04:04,520 --> 00:04:09,280
+تمام؟ بتعطى قيم small، فإذا capital لاسم الـ group
+
+59
+00:04:09,280 --> 00:04:14,280
+كله، أو الـ set الكبيرة ككل، والـ elements داخلها
+
+60
+00:04:14,280 --> 00:04:19,220
+بتعطى small letters، فـ... وهي بتكون محصورة داخل الـ
+
+61
+00:04:19,220 --> 00:04:22,680
+curly braces، فأنا بعرف إن الـ curly هاد للـ sets
+
+62
+00:04:22,680 --> 00:04:26,680
+... لمين؟ للـ sets، وإذا curly، معناته ليس بالضروري
+
+63
+00:04:26,680 --> 00:04:31,240
+اللي جوا يكون مرتباً، ليس بالضروري أكون مرتباً، بخلاف
+
+64
+00:04:31,240 --> 00:04:34,880
+الأقواس اللي كنتوا بتاخدوها للأزواج المرتبة، كنتوا
+
+65
+00:04:34,880 --> 00:04:38,100
+بتاخدوا الأقواس، إذا أخذناها بهذا الشكل، فهذا قوس
+
+66
+00:04:38,100 --> 00:04:44,900
+مرتّب، قوس مرتّب، بغض النظر هو زوج أو أكثر، يعني هنا لو
+
+67
+00:04:44,900 --> 00:04:50,100
+ثلاثة، ممكن نحطهم A، وB، وC، أنا بعرف إن هدول مرتبين
+
+68
+00:04:50,100 --> 00:04:54,740
+بمعنى X، Y، Z،  محاولة X، Y، Z، فهذا بيعطينا نقطة إحداثية
+
+69
+00:04:54,740 --> 00:05:00,920
+ما بنفعش نقول B، وA، بتصير نقطة مختلفة تماماً، فنقطة تماماً
+
+70
+00:05:00,920 --> 00:05:04,780
+مختلفة، أما هنا أقول B، A، C، بيمشي الحال، هي نفس الـ
+
+71
+00:05:04,780 --> 00:05:08,560
+group، الـ group أو الـ set، هي هي، ظلت نفس القيمة، نفس
+
+72
+00:05:08,560 --> 00:05:13,490
+الـ set، طيب، الطرق اللي بنوصف فيها الـ sets، من أهمها
+
+73
+00:05:13,490 --> 00:05:17,690
+إما أني أكتبها كاملة، وليس بالضروري دائماً هذه
+
+74
+00:05:17,690 --> 00:05:21,550
+تسعفني، لأن أحياناً بتكون الـ set، مجموعة الـ element
+
+75
+00:05:21,550 --> 00:05:26,250
+عددها كبير، عددها كبير، فما بقدر أكتبهم as a
+
+76
+00:05:26,250 --> 00:05:30,290
+sequence، كلهم هيك، أحطهم على بعض وأكتبهم، ويأخذوا
+
+77
+00:05:30,290 --> 00:05:33,670
+مني الصبورة ثلاث أربع مرات، ليس بالضروري دائماً بيصير
+
+78
+00:05:33,670 --> 00:05:36,410
+معاك، لأ، ممكن أن نستخدم حاجة اسمها set builder
+
+79
+00:05:36,410 --> 00:05:42,370
+notation، set builder notation، اللي هو اختصارات أو
+
+80
+00:05:42,370 --> 00:05:49,030
+علامات أو symbols، تبع البناء، أو بناء المجموعة، و
+
+81
+00:05:49,030 --> 00:05:52,090
+اللي هي ممكن نكتبها as a function، ممكن تكتب as a
+
+82
+00:05:52,090 --> 00:05:56,450
+function، نقول والله عندي set أو proposition P of X
+
+83
+00:05:56,940 --> 00:05:59,920
+الـ P of X هذا بدنا نعرفه على الـ universe of
+
+84
+00:05:59,920 --> 00:06:04,060
+discourse، فممكن نعرف الـ set كأنها هي الـ elements
+
+85
+00:06:04,060 --> 00:06:07,540
+اللي حناخد منها الـ universe of discourse، حناخد
+
+86
+00:06:07,540 --> 00:06:13,380
+أمثلة عليها جاية، هي مجموعة أمثلة شوية شوية لعند ما
+
+87
+00:06:13,380 --> 00:06:16,880
+نصل للـ builder أو الـ set builder اللي حنتكلم عن
+
+88
+00:06:16,880 --> 00:06:21,300
+ها، طيب الـ set، أكد على unordered، هي مش مرتبة
+
+89
+00:06:21,300 --> 00:06:27,300
+فمعنى ذلك ABC هي نفسها ACB، whatever، بدّلوا شغلّب
+
+90
+00:06:27,300 --> 00:06:29,720
+فيهم زي ما بدك، واعملوا كل الـ possibilities
+
+91
+00:06:29,720 --> 00:06:33,720
+الممكنة لترتيبهم، مش هيفرق معانا، كلهم نفس الشيء
+
+92
+00:06:33,720 --> 00:06:38,160
+بعرف من الـ curly braces إن هدول مجموعة في النهاية
+
+93
+00:06:38,160 --> 00:06:41,640
+هدول مجموعة، ما تقوليش ما أنا عاملها أقواس مرتبة، لأ
+
+94
+00:06:41,640 --> 00:06:45,340
+هذا ليس أقواس مرتبة، هذا أقواس المجموعة، أقواس المجموعة
+
+95
+00:06:45,340 --> 00:06:49,760
+ما بيفرقش كيف الترتيب جوا، بمعنى هذه زي هذه زي هذه، كلهم
+
+96
+00:06:49,760 --> 00:06:55,240
+نفس الشيء، ما بيفرقش معانا، طيب شغل ثانية، unequal
+
+97
+00:06:55,240 --> 00:07:00,800
+بمعنى، ما تقوليش ما هو زي العدد، لما نقول مثلاً في
+
+98
+00:07:00,800 --> 00:07:05,460
+الزوج المرتب واحد واحد، هذه معناته نقطة واحد
+
+99
+00:07:05,460 --> 00:07:09,920
+واحد، بس لما أقول مجموعة واحد واحد، ما فيش حاجة
+
+100
+00:07:09,920 --> 00:07:15,260
+اسمها هيك، هذا اسمه تكرار، تكرار، لأ هذه فعلياً
+
+101
+00:07:15,260 --> 00:07:20,080
+الأولى أنها تُكتب مجموعة واحد بس، لأن التكرار لا
+
+102
+00:07:20,080 --> 00:07:25,000
+يُعتد به، فهي لازم تكون الـ order، الـ set unequal
+
+103
+00:07:25,850 --> 00:07:29,670
+ما يكونش فيها elements متساوية، الـ element يمثل مرة
+
+104
+00:07:29,670 --> 00:07:34,130
+واحدة فقط، فمعنى ذلك أنه إذا كانت a و b بيساووا بعض، a
+
+105
+00:07:34,130 --> 00:07:39,870
+,b,c هذه زيادة على الفاضي، هذه زيادة على الفاضي، الصح أن
+
+106
+00:07:39,870 --> 00:07:45,710
+أقول a,c وبس، أو b,c وبس، على اعتبار أن a و b هم زي
+
+107
+00:07:45,710 --> 00:07:50,630
+بعض، هم زي بعض، زي عندما أقول a,a,b,a,b,c,c هذه كلها
+
+108
+00:07:51,450 --> 00:07:55,470
+طويلة عريضة على الفاضي، هذه كلها a, b, c وخلاص، أو a, c
+
+109
+00:07:55,470 --> 00:08:00,070
+مادام a وb بيساووا بعض، فهذه فعلياً لا تمثل بهذا الشكل
+
+110
+00:08:00,070 --> 00:08:03,890
+ما تكتبهاش، أي مجموعة بهذا الشكل فيها تكرارات، ولو
+
+111
+00:08:03,890 --> 00:08:08,470
+أنت عارف إن فيه two elements بيساووا بعض، اختصر الـ set ده
+
+112
+00:08:08,470 --> 00:08:12,170
+بتكون بأصغر صورة ممكنة، بحيث يكون distanced أو
+
+113
+00:08:12,170 --> 00:08:15,390
+different elements، زي تعريفنا أول ما بدأنا
+
+114
+00:08:15,390 --> 00:08:18,070
+different elements، لازم يكونوا مختلفين عن بعض
+
+115
+00:08:18,070 --> 00:08:24,330
+ما بنفعش تتعامل معها كزوج مرتب، الموضع بيفرق، حتى لو
+
+116
+00:08:24,330 --> 00:08:27,550
+نفس القيمة، هنا واحد وهنا واحد، لأ، مختلفين عن بعض
+
+117
+00:08:27,550 --> 00:08:31,980
+هدول الـ two ones، هدول مختلفين تماماً عن بعض، لما
+
+118
+00:08:31,980 --> 00:08:34,620
+بتكلم عن الـ curly braces، لأ، أنا بتكلم عن مجموعة
+
+119
+00:08:34,620 --> 00:08:42,020
+المجموعة، لازم تختصر كل المتشابه تمام، فإذا لما نيجي
+
+120
+00:08:42,020 --> 00:08:45,740
+نتكلم عن الـ equality، الـ equality للـ sets أو
+
+121
+00:08:45,740 --> 00:08:51,500
+المساواة للمجموعات، بدها تحكمها نفس المجموعة الـ
+
+122
+00:08:51,500 --> 00:08:55,620
+rules اللي أخذناها سابقاً، الـ inequality للمجموعة الـ
+
+123
+00:08:55,620 --> 00:08:58,560
+elements ساعتها، والـ unordered في حالتنا
+
+124
+00:08:58,560 --> 00:09:02,120
+بمعنى، إذا كان أنت قدرت تعرف مجموعة بطريقة، وأنا
+
+125
+00:09:02,120 --> 00:09:05,080
+عرفتُها بطريقة ثانية، حتى لو كانت عكسية، بس في النهاية
+
+126
+00:09:05,080 --> 00:09:08,960
+نفس الـ elements موجودين في المجموعتين، فبقول إن الـ
+
+127
+00:09:08,960 --> 00:09:12,680
+two sets متساويين، بغض النظر كيف ترتيبهم، بغض
+
+128
+00:09:12,680 --> 00:09:17,300
+النظر كيف ترتيبهم، فإذا بقول إن الـ two sets هما
+
+129
+00:09:17,300 --> 00:09:23,230
+equal لبعض، if and only if they contain exactly the
+
+130
+00:09:23,230 --> 00:09:26,730
+same elements، إذا، اللهم نفس الـ elements، ما تكلمتش
+
+131
+00:09:26,730 --> 00:09:29,750
+عن ordered، ordered elements، لأ، مش ordered elements
+
+132
+00:09:29,750 --> 00:09:34,230
+الـ elements وبس، زي ما قلنا، المجموعة بتاعتنا لليوم
+
+133
+00:09:34,230 --> 00:09:37,150
+هي نفس المجموعة تاعت يوم الأربعاء، لحضرة يوم الأربعاء
+
+134
+00:09:37,150 --> 00:09:40,310
+بغض النظر أنتم كيف كنتوا قاعدين، بغض النظر عن
+
+135
+00:09:40,310 --> 00:09:46,550
+الترتيب، ما لهاش علاقة بالترتيب تمام، فبدون زي ما
+
+136
+00:09:46,550 --> 00:09:50,150
+قلنا order، بدون الاهتمام إلى كيف الـ set تمّت
+
+137
+00:09:50,150 --> 00:09:54,810
+تعريفها، أو تم الإشارة إليها، بمعنى هل وقت هنشوف هاي
+
+138
+00:09:54,810 --> 00:09:59,160
+set builder، وكل مرة الـ builder...الـ builder مختلف
+
+139
+00:09:59,160 --> 00:10:02,800
+عن الثاني، كل مرة هنحط نفس المجموعة، ولكن تعريف مختلف
+
+140
+00:10:02,800 --> 00:10:06,320
+عن الثاني، فـ for example، لو افترضنا أن الـ set واحد
+
+141
+00:10:06,320 --> 00:10:10,960
+اثنين، ثلاثة، أربعة، هذا تعريف صريح، تعريف صريح للـ set
+
+142
+00:10:10,960 --> 00:10:15,240
+كويس، لكن ما هي نفس الـ set هذه، ممكن أن أعرفها set
+
+143
+00:10:15,240 --> 00:10:18,840
+builder بطريقة مختلفة تماماً، أن أقول هيّا بدأنا بأول
+
+144
+00:10:18,840 --> 00:10:21,950
+الـ curly braces، معنى ذلك إن أنا بعرف إن التعريف
+
+145
+00:10:21,950 --> 00:10:27,470
+الآن داخل الأقواس المجعدة هذه، هو لـ elements داخل
+
+146
+00:10:27,470 --> 00:10:31,430
+set، elements داخل...ما كتبناش الأقواس العادية
+
+147
+00:10:31,430 --> 00:10:37,490
+الأقواس المجعدة، معنى ذلك إن بقول set على طول، شوفتوا
+
+148
+00:10:37,490 --> 00:10:43,890
+على طول بعرف it's a set of elements x such that، أو
+
+149
+00:10:43,890 --> 00:10:49,690
+إذا كان x هو عبارة عن integer، ما بين الصفر، أكبر من
+
+150
+00:10:49,690 --> 00:10:53,110
+الصفر، وأقل من خمسة، طب لما نَمثّل هذا الكلام، حيطلع
+
+151
+00:10:53,110 --> 00:10:57,010
+برضه واحد، اثنين، ثلاثة، أربعة، حيختلف شيء؟ لأ، مش
+
+152
+00:10:57,010 --> 00:11:00,090
+حيختلف شيء، حيجي واحد يقول لك لأ، طب أنا بدي أعرفها
+
+153
+00:11:00,090 --> 00:11:02,870
+بطريقة مختلفة، وبرضه يعمل لي braces، خلاص معناته هو
+
+154
+00:11:02,870 --> 00:11:07,110
+عرف لي إن هو دي set، فهمت منه إنه set، مادام حط لي الـ
+
+155
+00:11:07,110 --> 00:11:11,810
+braces، الـ curly braces، أو الأقواس المجعدة، ده بعرف
+
+156
+00:11:11,810 --> 00:11:16,930
+إن هو دي مجموعة، مجموعة الـ elements X بشرط أن X هي
+
+157
+00:11:16,930 --> 00:11:22,610
+عبارة عن الـ positive integers، واللي قيمتها بين
+
+158
+00:11:22,610 --> 00:11:28,890
+الصفر و25، طيب بين الصفر و25، كم عنصر ممكن يتربع
+
+159
+00:11:28,890 --> 00:11:33,770
+معاه؟ طب نلاحظ أنه أقل من 25، أربعة عناصر، اللي هو 1,2
+
+160
+00:11:33,770 --> 00:11:37,670
+,3,4، أو قيمتهم، مش هيك بس، هو حدّد لمين؟
+
+161
+00:11:37,670 --> 00:11:41,970
+positive، positive، معناته 1,2,3,4، يعني كأنه رجع
+
+162
+00:11:41,970 --> 00:11:46,840
+أعرف لنفس الـ set، هي هيُعرف نفس الـ set كما هي، طيب في
+
+163
+00:11:46,840 --> 00:11:50,500
+الآخر، نفس الـ elements واحدة، رغم أن التعريف اختلف
+
+164
+00:11:50,500 --> 00:11:53,760
+والـ set builders اختلفت، لكن في الحالة هنا بقول إن
+
+165
+00:11:53,760 --> 00:11:58,770
+الثلاث هم equal لبعض، تفرّج في نفسك، الاثنين فيهم نفس
+
+166
+00:11:58,770 --> 00:12:01,750
+العناصر، يعني الاثنين فيهم عناصر متشابهة، لكن واحدة
+
+167
+00:12:01,750 --> 00:12:05,070
+بتحتوي على عناصر أكثر، لكن هي...أجل لأ، هنا لا يساووا
+
+168
+00:12:05,070 --> 00:12:08,330
+بعض، لأ، ما بيساووش بعض، هذه إلها علاقة مختلفة، حناخدها
+
+169
+00:12:08,330 --> 00:12:13
+
+223
+00:16:07,140 --> 00:16:11,420
+integers أقل من عشرة أو من واحد لعشرة أقل من عشرة
+
+224
+00:16:11,420 --> 00:16:15,220
+فخلاص بتكلم عن هذه المجموعة، إيش في عندي مجموعات
+
+225
+00:16:15,220 --> 00:16:18,400
+ثانية؟ ممكن مش عارف حيبدأ هو بالـ ... بس بقى باينة
+
+226
+00:16:18,400 --> 00:16:22,780
+عندي أن ممكن آخذ مثلاً مجموعة الأرقام الزوجية
+
+227
+00:16:22,780 --> 00:16:27,880
+... الفردية ... الزوجية عفواً، وهذه الفردية ... هذه
+
+228
+00:16:27,880 --> 00:16:33,730
+هيك الفردية، ونتكلم عن مجموعة الـ even integers
+
+229
+00:16:33,730 --> 00:16:37,730
+ومجموعة الـ odd integers، بالإضافة أنه ممكن بترتيب
+
+230
+00:16:37,730 --> 00:16:42,610
+معين نحط هذه الأرقام مع بعض، ونقول الـ brines اللي
+
+231
+00:16:42,610 --> 00:16:47,740
+أقل من عشرة مثلاً، أقل من عشرة أو أقل من 11، مش هيك؟
+
+232
+00:16:47,740 --> 00:16:51,460
+أقل من عشر أو أقل من أحد عشر، ماشي الحال تمام، فلاحظ
+
+233
+00:16:51,460 --> 00:16:54,600
+أن الـ Venn diagram  جدرنا أن نرتب مجموعة العناصر
+
+234
+00:16:54,600 --> 00:16:58,060
+بحيث أن هي تشمل أكثر من مجموعة في نفس الوقت، وأن
+
+235
+00:16:58,060 --> 00:17:03,000
+نرتبها بأكثر من مجموعة من مجموعة، فهذه طريقة الـ
+
+236
+00:17:03,000 --> 00:17:06,000
+Venn diagrams، أن أنا ممكن أحط مجموعات مع بعض، أعمل
+
+237
+00:17:06,000 --> 00:17:09,340
+تقاطعاتهم مع بعض، لأن واضح أن هنا صار في تقاطعات
+
+238
+00:17:09,340 --> 00:17:15,330
+تقاطع، لما أتكلم عن تقاطع الـ even مع الـ prime، واضح
+
+239
+00:17:15,330 --> 00:17:19,790
+أنه في رقم واحد جاء في كلاهما، فهذا بقول عليه رقم
+
+240
+00:17:19,790 --> 00:17:23,350
+متقاطع بين الاثنين، يعني هو ينتمي للمجموعة هذه
+
+241
+00:17:23,350 --> 00:17:28,910
+وينتمي للمجموعة هذه، ينتمي، فإذاً من ناحية تمثيل مرئي
+
+242
+00:17:28,910 --> 00:17:32,550
+الـ Venn diagram أعطتني إمكانية كثيرة عالية أن أشوف
+
+243
+00:17:32,550 --> 00:17:37,630
+تمثيل البيانات قدامي لمجموعة الـ sets أو للمجموعات
+
+244
+00:17:37,630 --> 00:17:41,290
+بصفة عامة، فهذه واحدة من الطرق المستخدمة اللي
+
+245
+00:17:41,290 --> 00:17:44,410
+أخذتوها أكيد طبعاً أنتم في الزمان، يمكن كمان مش في
+
+246
+00:17:44,410 --> 00:17:49,250
+توجيهي، يمكن أخذتوها في إعدادي، أظن أعتقد، يمكن في
+
+247
+00:17:49,250 --> 00:17:57,550
+إعدادي، بقى أذكر أن هذه شغل إعدادي كانت، تماماً، الآن
+
+248
+00:17:57,550 --> 00:18:01,390
+بعض العلاقات داخل الـ sets اللي ممكن نتعامل
+
+249
+00:18:01,390 --> 00:18:06,190
+معها مع الـ sets، أهمها وأولها هي الـ membership أو
+
+250
+00:18:06,190 --> 00:18:10,870
+العضوية، العضوية هذه اللي هي ينتمي إلى، إذا كان
+
+251
+00:18:10,870 --> 00:18:14,410
+والله العنصر ينتمي للمجموعة أو هو عضو في المجموعة
+
+252
+00:18:14,410 --> 00:18:17,190
+زي لما توقفنا، تكلمنا عن الاثنين، الاثنين هو عضو في
+
+253
+00:18:17,190 --> 00:18:21,850
+مجموعة الأرقام الزوجية، فإذاً هو ينتمي للأرقام
+
+254
+00:18:21,850 --> 00:18:28,990
+الزوجية، أو بنسميه element، فبنعطيه حرف الـ E كأنه يمثل
+
+255
+00:18:28,990 --> 00:18:33,630
+أو ينتمي إلى، فيأخذ بهذا الشكل، طيب ينتمي إلى
+
+256
+00:18:33,630 --> 00:18:39,690
+معناته أنا بتكلم عن، زي ما قلنا element، نتكلم عن
+
+257
+00:18:39,690 --> 00:18:44,810
+element، يعني بمعنى أن ما قبل هذه العلامة هو عنصر
+
+258
+00:18:44,810 --> 00:18:49,790
+هو إيش؟ عنصر، نأخذ بالنا من هذا الكلام لأنه بعدين
+
+259
+00:18:49,790 --> 00:18:53,390
+هناخذ notations ثانية، ما قبلها مش بالضروري تكون
+
+260
+00:18:53,390 --> 00:18:57,910
+عنصر، ما قبلها بيكونش عنصر، فالعنصر، إذا أنا بدي أشوف
+
+261
+00:18:57,910 --> 00:19:03,370
+علاقة الـ ما قبل هذه العلامة بيكون عبارة عن element
+
+262
+00:19:03,370 --> 00:19:07,110
+فردي، عنصر هو عنصر داخل المجموعة، تمام
+
+263
+00:19:09,890 --> 00:19:13,790
+وبده يكون distinct أو مميز، هو different عن باقي
+
+264
+00:19:13,790 --> 00:19:17,110
+العناصر، عشان نقدر نقول أنه عنصر، زي ما توي قلنا
+
+265
+00:19:17,110 --> 00:19:19,750
+إذا كان والله متشابه مع غيره، معناته لازم يختصر هو
+
+266
+00:19:19,750 --> 00:19:24,090
+وغيره، إذا كان بيساووا بيساووا بعض، بدنا نختار واحد
+
+267
+00:19:24,090 --> 00:19:29,620
+منهم بحيث أنه يظل واحد distinct element، Okay، لما
+
+268
+00:19:29,620 --> 00:19:33,780
+أقول ثلاثة belong to to N، to capital N، معناته أنه
+
+269
+00:19:33,780 --> 00:19:37,380
+ثلاثة هينتمي لأعداد الطبيعية، مش شايف الـ natural
+
+270
+00:19:37,380 --> 00:19:44,360
+number، طيب لما أقول a هو ينتمي لـ set of X بشرط أو
+
+271
+00:19:44,360 --> 00:19:49,860
+إذا كان X هو letter of alphabet، إذا كان الـ X هذه
+
+272
+00:19:49,860 --> 00:19:54,580
+حرف من حروف الأبجدية، معناته صحيح برضه، بقول صحيح
+
+273
+00:19:54,580 --> 00:19:57,880
+لأنه فعلاً الـ a هو واحد من حروف الأبجدية، هو أحد
+
+274
+00:19:57,880 --> 00:20:02,140
+الحروف، فبقدر أقول أن a هو يمثل أحد الـ axis اللي
+
+275
+00:20:02,140 --> 00:20:06,600
+موجودة داخل هذه المجموعة، فبهذه الطريقة بيمشي الحال
+
+276
+00:20:06,600 --> 00:20:11,280
+بالـ set builder أو بهذه الطريقة المباشرة، أن اسميه
+
+277
+00:20:11,280 --> 00:20:16,810
+ينتمي لمجموعة واضحة ومعروفة مسبقاً، طيب بنقدر نعرف الـ
+
+278
+00:20:16,810 --> 00:20:22,330
+equality، لأن in term of belonging to باستخدام أنه
+
+279
+00:20:22,330 --> 00:20:27,370
+لو for all capital هدول صحيح؟ يعني إيش بتكلم؟ sets
+
+280
+00:20:27,370 --> 00:20:33,370
+باتكلمش عن elements هنا، فإذاً for all sets S و T
+
+281
+00:20:33,370 --> 00:20:38,810
+two sets، يعني عندي لكل المجموعات، المجموعة S تساوي
+
+282
+00:20:38,810 --> 00:20:45,890
+المجموعة T if and only if، for all x small، لكل
+
+283
+00:20:45,890 --> 00:20:51,730
+العناصر هنا، بنتكلم لكل العناصر، العنصر x ينتمي لـ S
+
+284
+00:20:51,730 --> 00:20:58,070
+إذاً وإذا فقط هو ينتمي لـ T، يعني كأنه بينتمي لـ S و
+
+285
+00:20:58,070 --> 00:21:05,420
+ينتمي لـ T، كويس، لكل العناصر والعكس صحيح، هو مش فقط
+
+286
+00:21:05,420 --> 00:21:09,780
+إذا بينتمي لـ S هو بينتمي لـ T، لأ، وكمان إذا بينتمي
+
+287
+00:21:09,780 --> 00:21:15,480
+لـ T ينتمي لـ S، عشان هيك بالـ implication بتظبطش، لازم
+
+288
+00:21:15,480 --> 00:21:19,740
+if and only if، لازم إذا بينتمي للأولى بالضرورة
+
+289
+00:21:19,740 --> 00:21:23,200
+ينتمي للثانية، أو إذا بينتمي للثانية بالضرورة يجب
+
+290
+00:21:23,200 --> 00:21:27,440
+أن ينتمي للأولى، عشان أقول إن هم متساويتين في عدد
+
+291
+00:21:27,440 --> 00:21:32,730
+الـ elements، وكلّهم يحتووا على الـ elements x، for all
+
+292
+00:21:32,730 --> 00:21:37,710
+x، لكل العناصر x، ففي الحالة دي بنقول أنه في
+
+293
+00:21:37,710 --> 00:21:43,730
+equality واضحة بين الـ set S والـ set T، تمام، فالـ
+
+294
+00:21:43,730 --> 00:21:48,670
+two sets are equal if and only if they have all the
+
+295
+00:21:48,670 --> 00:21:53,930
+same members، كل العناصر المتشابهة هي موجودة هنا
+
+296
+00:21:53,930 --> 00:22:00,850
+وموجودة هنا، x not belong to S، هذه الـ negation
+
+297
+00:22:00,850 --> 00:22:08,070
+بتاعة belong، معناته أنها لا تنتمي للـ set، معناته ذلك أن
+
+298
+00:22:08,070 --> 00:22:13,730
+x ليست موجودة ضمن الـ set، x هذه مكافئة لـ negation x
+
+299
+00:22:13,730 --> 00:22:18,450
+belong to S، إذا والله x هي تنتمي لـ S، لأ، الـ false
+
+300
+00:22:18,450 --> 00:22:22,490
+تبعها أنها لا تنتمي لـ x، واضح جداً، فليس فيها مشكلة في
+
+301
+00:22:22,490 --> 00:22:30,030
+x is not in set S، okay، المجموعات الخاصة بعض
+
+302
+00:22:30,030 --> 00:22:32,750
+المجموعات الخاصة اللي تعاملنا معها واللي
+
+303
+00:22:32,750 --> 00:22:37,120
+تعاملتوا معها سابقاً هي الـ Phi أو المجموعة الخالية
+
+304
+00:22:37,120 --> 00:22:40,440
+أو الـ empty set أو الـ null، الـ null اللي هي nothing
+
+305
+00:22:40,440 --> 00:22:44,680
+اللي هي صفر، مصفرة يعني ما فيش لها قيمة، فهذه
+
+306
+00:22:44,680 --> 00:22:49,100
+unique set، هذه حالة فريدة من حالات المجموعات، واللي
+
+307
+00:22:49,100 --> 00:22:54,080
+تحتوي على no elements، بغض النظر مهما كان، يعني مهما
+
+308
+00:22:54,080 --> 00:22:57,340
+كانت الـ universe of discourse تبعك، هي عناصر، هي
+
+309
+00:22:57,340 --> 00:23:02,660
+أرقام، هي أشخاص، هي أسماء، بغض النظر إيش نوعها، بس
+
+310
+00:23:02,660 --> 00:23:06,400
+هي no elements، no elements بمعنى، هي عبارة عن
+
+311
+00:23:06,400 --> 00:23:11,820
+مجموعة فارغة، عشان إنك تسميها مجموعة خالية، braces
+
+312
+00:23:11,820 --> 00:23:14,400
+لازم نحط الـ braces، لأن الـ braces هاد اللي بتعطيني
+
+313
+00:23:14,400 --> 00:23:18,500
+التعريف الأساسي اللي هو بقول منه set، كلمة set
+
+314
+00:23:18,500 --> 00:23:22,120
+بفهمها على طول من الـ braces هدول، اللي هو الـ curly
+
+315
+00:23:22,120 --> 00:23:25,400
+braces، بمجرد ما بشوفهم بقول إن أنا بتكلم عن مجموعة
+
+316
+00:23:25,400 --> 00:23:28,540
+طيب إيش فيه جواها؟ صفر، nothing، خالية، فإذاً بقول
+
+317
+00:23:28,540 --> 00:23:32,980
+مجموعة خالية، تمام، فدايماً إنك تكتبها، ما تسيبهاش
+
+318
+00:23:32,980 --> 00:23:36,160
+فارغة، ما تسيبهاش فارغة، لإنه مش حافظ إن أنت بتتكلم
+
+319
+00:23:36,160 --> 00:23:38,360
+عن element ولا بتتكلم عن function ولا بتتكلم عن
+
+320
+00:23:38,360 --> 00:23:42,100
+إيش بالظبط، لما تحط لي الـ curly braces، بفرض بتتكلم عن
+
+321
+00:23:42,100 --> 00:23:49,280
+set، لأ، هذه ما فيش صفر أصلاً، الصفر element، هيقول لك
+
+322
+00:23:49,280 --> 00:23:53,180
+الصفر هو element بحد ذاته، هنا ما فيش الصفر قيمة
+
+323
+00:23:53,180 --> 00:23:56,940
+الصفر نفسه، عشان تقول والله بدي أحط صفر، أنت هنا
+
+324
+00:23:56,940 --> 00:24:01,160
+حطيت فعلياً قيمة، والـ set هنا أصبح تحتوي على one
+
+325
+00:24:01,160 --> 00:24:05,420
+element، لأ، هي فعلياً لا تحتوي حتى على الصفر، لا
+
+326
+00:24:05,420 --> 00:24:10,800
+تحتوي، أيوة، الصفر الخوارزمي جالنا أنه قيمة، أنه
+
+327
+00:24:10,800 --> 00:24:15,160
+object بحد ذاته، الصفر object بحد ذاته، ولو لأنه
+
+328
+00:24:15,160 --> 00:24:17,420
+object بحد ذاته، كان ما اخترعناش كل هالاختراعات
+
+329
+00:24:17,420 --> 00:24:20,880
+اللي وصلتنا للأيام هذه، فلو الخوارزمي باختراع الـ
+
+330
+00:24:20,880 --> 00:24:25,120
+zero تبعه كان ما وصلنا للي إحنا فيه من علوم، إيش
+
+331
+00:24:25,120 --> 00:24:28,700
+مديش أقول لك الرياضيات، من علوم الحاسوب، من اختراع
+
+332
+00:24:28,700 --> 00:24:34,860
+الحاسوب نفسه، طيب فهي عبارة عن set تحتوي على x، وx
+
+333
+00:24:34,860 --> 00:24:41,310
+false، يعني ما فيش x، x false، لا يوجد x، فإذاً no matter
+
+334
+00:24:41,310 --> 00:24:44,690
+the domain of this course، بغض النظر إيش الـ domain
+
+335
+00:24:44,690 --> 00:24:48,130
+أو إيش المجال اللي أنا بتكلم عنه، لفضاء العينة، أنا
+
+336
+00:24:48,130 --> 00:24:52,750
+قلت لكم عناصر، العناصر هذه إيش؟ أرقام، أسماء، أشخاص
+
+337
+00:24:52,750 --> 00:24:59,140
+تفرقش، بغض النظر الشيء، we have the axiom، مسلمة
+
+338
+00:24:59,140 --> 00:25:05,000
+عندنا شيء بديهي، أنه there is no exist x، x belong
+
+339
+00:25:05,000 --> 00:25:10,600
+to phi، لا يوجد x، لا يوجد عنصر ينتمي للمجموعة phi
+
+340
+00:25:10,600 --> 00:25:18,080
+ولا الصفر، لأنه صفر عنصر، تمام، آه تمام، الآن بدأنا في
+
+341
+00:25:18,080 --> 00:25:23,970
+علامة جديدة، S، وأعطاني هالـ notation هذه قدامي، وجاء لي
+
+342
+00:25:23,970 --> 00:25:28,510
+T، لاحظ أول شغلة هنا، تقريباً لما كنا بنتكلم عن x
+
+343
+00:25:28,510 --> 00:25:37,310
+belonged to S، مثلاً، هنا كانت small، يعني element، هنا
+
+344
+00:25:37,310 --> 00:25:41,370
+كانت belonged to تستخدم للـ elements فقط، هنا كانت
+
+345
+00:25:41,370 --> 00:25:45,630
+capital، في هذه معروفة أنها set، الآن أنا بتكلم عن
+
+346
+00:25:45,630 --> 00:25:51,510
+capital relation مع capital set و set، الاثنين هم
+
+347
+00:25:51,510 --> 00:25:56,690
+عبارة عن two sets، طيب ضلت الـ notation اللي بينهم
+
+348
+00:25:56,690 --> 00:26:01,070
+الـ notation اللي بينهم فقط لتمييز المجموعات، لتمييز
+
+349
+00:26:01,070 --> 00:26:05,850
+المجموعات، لكن هي بتشبهها تماماً زي أصغر أو يساوي
+
+350
+00:26:05,850 --> 00:26:11,650
+لاحظ لو غيرتها شوية، هيك صارت إيش؟ كأنه أصغر أو يساوي
+
+351
+00:26:11,650 --> 00:26:15,970
+بس للمجموعات، فعشان نميزها للمجموعات، لإنه نعطيها
+
+352
+00:26:15,970 --> 00:26:20,280
+شوية الـ curve بتاعتها، بحيث أن أنا عارف أن ما قبلها
+
+353
+00:26:20,280 --> 00:26:25,220
+هيكون أصغر أو يساوي ما بعدها، فهي عبارة عن set تحتوي
+
+354
+00:26:25,220 --> 00:26:31,620
+على عناصر، كل هذه العناصر موجودة في الـ set T، وبس، و
+
+355
+00:26:31,620 --> 00:26:37,670
+بس، طيب هل العكس صحيح؟ لأ، ليس ضروري، فإذا أصغر
+
+356
+00:26:37,670 --> 00:26:43,810
+منها أو تساويها، فبنسميها subset أو مجموعة جزئية،
+
+357
+00:26:43,810 --> 00:26:48,390
+مجموعة جزئية منها، فهذا معناه إنه كل الـ elements of
+
+358
+00:26:48,390 --> 00:26:54,730
+S هو عبارة عن elements of T، بنسميها S subset of T
+
+359
+00:26:54,730 --> 00:26:59,110
+تمام؟ كويس، هذا if and only if، for all X، X
+
+360
+00:26:59,110 --> 00:27:04,820
+belong to S، مش if and only if، employees that
+
+361
+00:27:04,820 --> 00:27:10,460
+بيضمن لنا أن X هي تنتمي لـ T، العكس مش بالضروري، وليس
+
+362
+00:27:10,460 --> 00:27:16,640
+صحيحاً، فـ phi هي subset من كل المجموعات الثانية، هي phi
+
+363
+00:27:16,640 --> 00:27:21,080
+فعلياً هي subset من أي مجموعة أخرى، أي مجموعة هي
+
+364
+00:27:21,080 --> 00:27:25,340
+subset من نفسها، subset ليش؟ لأنه لاحظ، في عالم أو
+
+365
+00:27:25,340 --> 00:27:31,620
+يساوي، أو يساوي هنا subset، معناته أنها أصغر منها أو
+
+366
+00:27:31,620 --> 00:27:38,660
+تساويها، فمعنى ذلك أن كل مجموعة هي تساوي نفسها، فهي
+
+367
+00:27:38,660 --> 00:27:44,390
+subset من نفسها، العكس تبعها superset، ولاحظ
+
+368
+00:27:44,390 --> 00:27:47,290
+العلامة، كأنها أكبر منه، فهي الفتحة، دائماً
+
+369
+00:27:47,290 --> 00:27:50,510
+بتروح مع الأكبر، مع الأكبر، معناته الـ S هنا هي
+
+370
+00:27:50,510 --> 00:27:54,770
+الأكبر، بنسميها هنا superset، اسمها superset of T
+
+371
+00:27:54,770 --> 00:27:58,410
+بمعنى
+
+372
+00:27:58,410 --> 00:28:02,510
+أنه العكس صحيح، الآن كل عنصر موجود في T هو موجود في
+
+373
+00:28:02,510 --> 00:28:08,880
+S، والعكس مش بالضروري، العكس، T جزئية من S، بالظبط
+
+374
+00:28:08,880 --> 00:28:13,300
+دائماً الأصغر هي اللي ماخدة بوز الأصغر من أو الأكبر
+
+375
+00:28:13,300 --> 00:28:16,640
+من، زي الأرقام العادية، أنت تخيلها بالظبط زي الأرقام
+
+376
+00:28:16,640 --> 00:28:20,400
+العادية، لكن ماخدة الـ curve عشان نميز مجموعات وليس
+
+377
+00:28:20,400 --> 00:28:24,240
+أرقام، عشان نميزها كمجموعات وليس أرقام، فنفس الفكرة
+
+378
+00:28:24,240 --> 00:28:27,520
+اللي كانت في الـ elements هي هي نفسها في الـ sets
+
+379
+00:28:27,520 --> 00:28:33,380
+طيب هذا بيقودنا لشغلة، أن S ممكن أقول أن هي تساوي T
+
+380
+00:28:33,380 --> 00:28:36,520
+if and only if، كل واحدة منهم هي subset من الثانية
+
+381
+00:28:37,940 --> 00:28:41,980
+هي subset من الثانية، تمام؟ ليش؟ لأنه بيظل العامل
+
+382
+00:28:41,980 --> 00:28:46,180
+المشترك بين الأكبر من والأصغر من، هي أو يساوي، فإذا
+
+383
+00:28:46,180 --> 00:28:49,520
+كانت تحقق الأكبر من أو يساوي، والأصغر من أو يساوي
+
+384
+00:28:49,520 --> 00:28:53,520
+أكيد معناته اللي يساوي هو اللي عمل التحقق هذا، لأنه
+
+385
+00:28:53,520 --> 00:28:57,020
+مستحيل يكون أكبر من وأصغر من في نفس الوقت، لكن
+
+386
+00:28:57,020 --> 00:28:59,520
+أكبر من أو يساوي، وأصغر من أو يساوي، تحقق، معناته
+
+387
+00:28:59,520 --> 00:29:02,960
+اللي يساوي هي اللي شبكت بينهم، فإذا اليساوي وهذا
+
+388
+00:29:02,960 --> 00:29:08,050
+and، فإذا هما فعلاً ب
+
+445
+00:33:42,470 --> 00:33:46,270
+الطلاب لباقي طلاب الجامعة هي مجموعة طلاب كلية
+
+446
+00:33:46,270 --> 00:33:51,480
+الهندسة لكن هي نفسها عبارة عن مجموعات مجسمة. جوا كل
+
+447
+00:33:51,480 --> 00:33:55,740
+مجموعة هو element داخل مجموعة كلية الهندسة element.
+
+448
+00:33:55,740 --> 00:34:00,040
+داخل مجموعة كلية الهندسة. واضحة؟ فإذا ممكن أقول في
+
+449
+00:34:00,040 --> 00:34:02,440
+الآخر هذه الهندسة .. هذه مجموعة طلاب الهندسة
+
+450
+00:34:02,440 --> 00:34:05,640
+الـ هندسة الحسوب، الهندسة المدنية، الهندسة
+
+451
+00:34:05,640 --> 00:34:09,330
+المعمارية، and so on. نكمل كل المجموعات. طيب، داخل نفس
+
+452
+00:34:09,330 --> 00:34:12,610
+المجموع، نجسمهم حسب الـ level. هذا مازال في الـ level
+
+453
+00:34:12,610 --> 00:34:15,310
+الأول، هذا في الـ level الثاني، هذا في الخامس، وهكذا.
+
+454
+00:34:15,310 --> 00:34:20,250
+حسب طبعًا عدد الساعات اللي مخلصهم. كويس؟ فإذا هو نفسه
+
+455
+00:34:20,250 --> 00:34:25,270
+نفسها كمجموعة، ممكن أتعامل معاها as a element. فممكن
+
+456
+00:34:25,270 --> 00:34:30,450
+نقول والله S هنا هي نفسها زي ما قلنا. S هنا ممكن
+
+457
+00:34:30,450 --> 00:34:38,230
+تكون هي الـ subset of x. كتبناها small بمعنى element بحيث
+
+458
+00:34:38,230 --> 00:34:43,190
+أن الـ element هذا، اه شوف ايش كتبناه، subset. طب أنا
+
+459
+00:34:43,190 --> 00:34:47,190
+عارف أن الـ subset للمجموعات مش هيك؟ احنا بنعرف أنه
+
+460
+00:34:47,190 --> 00:34:50,850
+الـ subset للمجموعات. فإذا كأنه بده يقول إن الـ
+
+461
+00:34:50,850 --> 00:34:56,490
+element هذا هو بالأساس مجموعة داخل المجموعة S. طيب،
+
+462
+00:34:56,490 --> 00:35:01,550
+المجموعة هذه عبارة عن إيش؟ عبارة عن subset من واحد
+
+463
+00:35:01,550 --> 00:35:04,650
+اتنين تلاتة. معناته الآن بتتخيل أن الـ S هذه أي
+
+464
+00:35:04,650 --> 00:35:07,790
+مجموعة قد تصلح أن هي تكون subset من واحد اتنين
+
+465
+00:35:07,790 --> 00:35:12,600
+تلاتة. في؟ اه، في. بيمشي الحال. واحد، اه بيمشي الحال. واحد
+
+466
+00:35:12,600 --> 00:35:15,440
+و اتنين بيمشي الحال، واحد و تلاتة بيمشي الحال،
+
+467
+00:35:15,440 --> 00:35:18,440
+اتنين و تلاتة بيمشي الحال، اتنين لحالها بيمشي الحال،
+
+468
+00:35:18,440 --> 00:35:20,680
+تلاتة لحالها بيمشي الحال، واحد و اتنين تلاتة نفسها
+
+469
+00:35:20,680 --> 00:35:26,500
+بيمشي الحال لأنه أو يساوي. لاحظت؟ فـ S هنا معناته ممكن
+
+470
+00:35:26,500 --> 00:35:34,640
+تأخذ set of مجموعة sets. نروها كأنه كل set داخلها
+
+471
+00:35:34,640 --> 00:35:38,680
+هو كأنه element بالنسبة لها. صحيح، هو مجموعة بالنسبة
+
+472
+00:35:38,680 --> 00:35:44,640
+للـ elements تبعها. نفسها زي لما أقول والله هي طلاب
+
+473
+00:35:44,640 --> 00:35:48,820
+هندسة الحسوب. طيب، في الآخر طلاب هندسة الحسوب ممكن
+
+474
+00:35:48,820 --> 00:35:52,000
+أصنفهم: المستوى الأول، والثاني، والثالث، والرابع، and
+
+475
+00:35:52,000 --> 00:35:56,260
+so on. طيب، كل مستوى هحطه داخل مجموعة رغم أنه
+
+476
+00:35:56,260 --> 00:36:02,720
+كمجموعة، هي عنصر داخل مجموعة هندسة الحسوب أو طلاب
+
+477
+00:36:02,720 --> 00:36:08,190
+هندسة الحسوب ككل. بهذا الشكل ممكن نقول أنه الـ set هي
+
+478
+00:36:08,190 --> 00:36:14,510
+subset، هي element داخل set أكبر منها. لما نقول الآن في
+
+479
+00:36:14,510 --> 00:36:21,010
+الحالة هذه، واحد أكيد لا تساوي set تحتوي على العنصر
+
+480
+00:36:21,010 --> 00:36:28,290
+واحد. هذه واحد element لحاله. هنا لأ، هذه set تحتوي
+
+481
+00:36:28,290 --> 00:36:33,250
+على العنصر واحد. طيب، هنا لا تساوي برضه set تحتوي
+
+482
+00:36:33,250 --> 00:36:38,950
+على set. فإذا الـ set هذه ليست الـ set هذه، هذه set
+
+483
+00:36:38,950 --> 00:36:42,810
+تحتوي على element بس، عنصر، هذه لأ، الـ set تحتوي
+
+484
+00:36:42,810 --> 00:36:47,560
+على set أخرى. تمام؟ بغض النظر إيش اللي جوا الـ set
+
+485
+00:36:47,560 --> 00:36:52,100
+الأخرى. لإنه هنا صارت كأنه بدي أقول هذه الـ set خلاص
+
+486
+00:36:52,100 --> 00:36:55,060
+هي، عرفناها، هي الـ set. هل الـ elements اللي جوا
+
+487
+00:36:55,060 --> 00:36:57,780
+بيساوي بعض؟ لأ، ما احنا رجعناها إن الـ element هو
+
+488
+00:36:57,780 --> 00:37:00,160
+element داخل الـ set. أما هذه الـ set داخل الـ set
+
+489
+00:37:00,160 --> 00:37:06,500
+بيساوي بعض كيف؟
+
+490
+00:37:06,500 --> 00:37:15,140
+اه، تنتمي للـ set الأكبر اللي هي هذه كاملة على بعضها.
+
+491
+00:37:16,850 --> 00:37:23,070
+بهذا الشكل، بس بدها تكون واضحة أنه هي subset من شيء
+
+492
+00:37:23,070 --> 00:37:27,490
+ثاني طبعًا.
+
+493
+00:37:27,490 --> 00:37:32,370
+لا تساوي، هو ما يساوي، بالعكس، هو ما ساوى، هو بالعكس
+
+494
+00:37:32,370 --> 00:37:36,670
+بيقول لك لا تساوي. هو بيقول لك يعني الكتاب بيقول لك أنت
+
+495
+00:37:36,670 --> 00:37:42,450
+لا تساوي answer بمجموعة. فلأ هو ما ساوى أبدًا. أي
+
+496
+00:37:42,450 --> 00:37:46,090
+واحد مثلًا، جزء، جزء من المجموعة الثالثة أو أي
+
+497
+00:37:46,090 --> 00:37:51,390
+واحد .. أي واحد الأول هو ولا إله أي علاقة بأي بنـ
+
+498
+00:37:51,390 --> 00:37:56,050
+اللي باقي، ولا إله أي علاقة ولا بأي حالة من الحالات.
+
+499
+00:37:56,050 --> 00:38:00,670
+مالوش علاقة. علاقته الوحيدة إني أقدر أقول هنا أنه
+
+500
+00:38:00,670 --> 00:38:06,710
+واحد belong to واحد بس. هي علاقته. أما لا يساوي
+
+501
+00:38:06,710 --> 00:38:11,010
+للثالثة.
+
+502
+00:38:11,010 --> 00:38:16,700
+أكيد لأ أبدًا. أكيد لأ. عارف أنت بنفع في حالة واحدة
+
+503
+00:38:16,700 --> 00:38:23,180
+إذا كانت المجموعة بهذا الشكل، وواحد. أما هي مش هيك.
+
+504
+00:38:23,180 --> 00:38:30,220
+ففكرة إني أقول واحد ينتمي إلى هذه اه صح، لكن أشيله
+
+505
+00:38:30,220 --> 00:38:38,660
+لأ، not belong. لازم تكون equal فعلاً هو بيساوي حقيقة
+
+506
+00:38:38,660 --> 00:38:42,480
+distinct element. تمام.
+
+507
+00:38:48,010 --> 00:38:52,610
+الـ cardinality. في حاجة اسمها cardinality والعلامة
+
+508
+00:38:52,610 --> 00:38:54,850
+بتاعتها عاملة زي الـ absolute. absolute معناته
+
+509
+00:38:54,850 --> 00:39:00,250
+القيمة المطلقة. مش هيك؟ لما أحطها لمجموعة، احنا
+
+510
+00:39:00,250 --> 00:39:02,550
+عارفين إن المجموعة هذه ما فيش مجموعة بالسالب.
+
+511
+00:39:02,550 --> 00:39:07,190
+فالقيمة المطلقة هنا في الـ elements كنت بتقول إنه
+
+512
+00:39:07,190 --> 00:39:11,430
+موجب أو سالب بحطها موجب. صح؟ بتحطوا القيمة الموجبة
+
+513
+00:39:11,430 --> 00:39:15,570
+لها. في الـ set ما فيش حاجة اسمها القيمة الموجبة لأنه
+
+514
+00:39:15,570 --> 00:39:21,250
+أصغر مجموعة هي الـ phi، zero. ما فيش إيش بالسالب. فمعنى
+
+515
+00:39:21,250 --> 00:39:24,870
+ذلك أنه لما أشوف الـ absolute هذه بسميها
+
+516
+00:39:24,870 --> 00:39:29,870
+cardinality of S. cardinality of S ما معناته؟ أجد عدد
+
+517
+00:39:29,870 --> 00:39:36,310
+عناصر داخلها. أجد عدد عناصر S هي معناها. فإذا
+
+518
+00:39:36,310 --> 00:39:42,030
+نقرأها cardinality of S. كويس؟ وهذه بتقول لنا how
+
+519
+00:39:42,030 --> 00:39:46,950
+many different elements in S. كويس؟ يعني لما نقول
+
+520
+00:39:46,950 --> 00:39:51,110
+absolute أو cardinality of five، zero. طيب،
+
+521
+00:39:51,110 --> 00:39:54,890
+cardinality of one، two، three، تلاتة. طيب،
+
+522
+00:39:54,890 --> 00:39:58,770
+cardinality of {a, b}، اتنين. طيب، cardinality of
+
+523
+00:39:58,770 --> 00:40:04,090
+{ {1, 2} }، أكيد اتنين. ليش؟ أنا قاعد بقول الـ cardinality
+
+524
+00:40:04,090 --> 00:40:08,430
+لمين؟ لأول curly braces اللي جابه، اللي هو هذا
+
+525
+00:40:11,560 --> 00:40:18,340
+داخل هذا الكلام فعليًا يوجد عنصرين بس، العنصرين
+
+526
+00:40:18,340 --> 00:40:21,560
+هدول مجموعات، أنا معك، صح مجموعات، بس هم في
+
+527
+00:40:21,560 --> 00:40:25,100
+النهاية للمجموعة اللي أنا عامل عليها الـ
+
+528
+00:40:25,100 --> 00:40:31,070
+cardinality هم عنصرين. إيه جواهم ماليش علاقة؟ لما
+
+529
+00:40:31,070 --> 00:40:35,850
+تيجي أقول لك دي قد إيش عدد الـ levels، المستويات، في كلية
+
+530
+00:40:35,850 --> 00:40:39,030
+الهندسة، هتقول لي خمسة. مش هتقول لي تقعد تفسر لي جوه
+
+531
+00:40:39,030 --> 00:40:41,370
+إيش فيهم مساقات وإيش فيهم مش عارف وإيش فيهم مش
+
+532
+00:40:41,370 --> 00:40:45,010
+عارف. أنا ما ليهم علاقة، اللي جوه، أنا بتكلم عن اللي
+
+533
+00:40:45,010 --> 00:40:53,250
+بره. خلاص. ففعليًا واحد، اتنين بس. خلصت. تمام. الله يوفقك
+
+534
+00:40:53,250 --> 00:40:56,570
+على سنة محمد. طيب، إذا كانت الـ cardinality تنتمي للـ
+
+535
+00:40:56,570 --> 00:41:02,670
+natural number، بمعنى هي عدد صحيح أو عدد طبيعي، هو
+
+536
+00:41:02,670 --> 00:41:06,450
+فعليًا أمرها ما حتكون بالسالب، منطقي يعني، هي عدد
+
+537
+00:41:06,450 --> 00:41:11,270
+موجب وصحيح، natural number، عدد طبيعي، فبنقدر نقول
+
+538
+00:41:11,270 --> 00:41:16,750
+أن الـ S هي finite، بمعنى محدودة، بمعنى محدودة،
+
+539
+00:41:16,750 --> 00:41:20,690
+otherwise بنسميها infinite، لانهائية. طيب، هو في
+
+540
+00:41:20,690 --> 00:41:23,650
+فعلاً في cardinality ممكن تسأل إنها تكون infinite؟
+
+541
+00:41:25,230 --> 00:41:28,970
+أكيد. زي هي نفس الـ natural number، هي نفس الـ
+
+542
+00:41:28,970 --> 00:41:32,630
+integers، هي نفس الـ real اللي اتكلمنا عنهم قبل شوية.
+
+543
+00:41:32,630 --> 00:41:38,370
+نحط لهم cardinality، قد إيش عددهم؟ undefined. طيب،
+
+544
+00:41:38,370 --> 00:41:41,110
+undefined حتى للـ natural number. هي لا تنتمي للـ
+
+545
+00:41:41,110 --> 00:41:46,270
+natural number. يعني أنا ما أقدرش أحددها كعدد، كعدد، مش
+
+546
+00:41:46,270 --> 00:41:49,510
+قادر أحددها. فإذا هي خارج الـ .. الـ natural number.
+
+547
+00:41:49,510 --> 00:41:54,190
+فإذا الـ natural number هي غير محدودة، الـ Z أو الـ
+
+548
+00:41:54,190 --> 00:41:57,450
+integers غير محدودة، و الـ real numbers برضه غير
+
+549
+00:41:57,450 --> 00:42:05,230
+محدودة كمجموعة. تمام. الـ power of sets أو قد إيش نتكلم
+
+550
+00:42:05,230 --> 00:42:09,850
+عن الـ P of S. و الـ P of S هذه، لما أقول الـ power of
+
+551
+00:42:09,850 --> 00:42:14,430
+S، معناته كل المجموعات اللي ممكن تكون جزئية من الـ
+
+552
+00:42:14,430 --> 00:42:21,490
+set. جميع المجموعات الجزئية من الـ set S. فبنسميها P of
+
+553
+00:42:21,490 --> 00:42:27,910
+S. فإذا هنا الـ element للـ function هذه هي set وليست
+
+554
+00:42:27,910 --> 00:42:35,710
+element واحد لحاله. فإذا S لازم تكون set. ليش؟ لأن
+
+555
+00:42:35,710 --> 00:42:41,210
+مفهوم الـ power of set إن كل الـ elements .. كل الـ
+
+556
+00:42:41,210 --> 00:42:45,770
+subsets من الـ set هذه. كل الـ subsets من الـ set هذه.
+
+557
+00:42:45,770 --> 00:42:52,730
+فكل الـ subsets of S. فـ P of S هي عبارة عن .. فتحنا
+
+558
+00:42:52,730 --> 00:42:59,670
+أقواس الـ curly. يعني هي نفسها حتكون set. فالـ power of
+
+559
+00:42:59,670 --> 00:43:04,730
+set هي بحد ذاتها set، هي مجموعة، بس تحتوي على إيش؟
+
+560
+00:43:04,730 --> 00:43:08,890
+على عناصر. طيب، العناصر هذه عبارة عن إيش؟ عبارة عن
+
+561
+00:43:08,890 --> 00:43:16,190
+sets. كيف عرفت؟ في بعضها، الـ subset، الـ subset بتأخذ
+
+562
+00:43:16,190 --> 00:43:20,190
+element قبلها، بتأخذ مجموعة. فإذن هي عبارة عن
+
+563
+00:43:20,190 --> 00:43:29,440
+مجموعات جزئية من S، من S. فلما أقول P of ونحط
+
+564
+00:43:29,440 --> 00:43:34,620
+المجموعة {A, B} حتكون كل المجموعات الجزئية من الـ set
+
+565
+00:43:34,620 --> 00:43:40,240
+{A, B}. ابتدائها من phi، ثم هي نفسها {A, B}، ثم A لحال، و B
+
+566
+00:43:40,240 --> 00:43:45,960
+لحال. صاروا أربعة. وعشان هي أحيانًا كتير بيسموها بدل
+
+567
+00:43:45,960 --> 00:43:51,360
+ما هي P of S، بيسموها 2 to the power S، power
+
+568
+00:43:51,360 --> 00:43:56,220
+على اعتبار أنه أصلًا هي اسمها power. power لها. فمش
+
+569
+00:43:56,220 --> 00:44:00,520
+معنى الاتنين. لأن الـ cardinality بتظهر هنا الـ
+
+570
+00:44:00,520 --> 00:44:05,280
+cardinality للـ power هي عبارة عن الـ cardinality أو
+
+571
+00:44:05,280 --> 00:44:09,500
+2 to the power الـ cardinality للـ S نفسها. الـ S
+
+572
+00:44:09,500 --> 00:44:12,240
+نفسها كانت الـ cardinality بتاعتها 2. فالـ power
+
+573
+00:44:12,240 --> 00:44:16,660
+بتاعتها حتكون 2 to the power الـ 2، حتكون
+
+574
+00:44:16,660 --> 00:44:20,630
+4. واحنا قاعدين بنعدهم 4. عدناهم 4. فإذا
+
+575
+00:44:20,630 --> 00:44:24,430
+بيسموها كتير 2 to the power of S. فهي الـ power
+
+576
+00:44:24,430 --> 00:44:28,750
+S، الـ power S، الـ power S. كويس؟ cardinality بتاعتها
+
+577
+00:44:28,750 --> 00:44:33,030
+برضه 2 to the power الـ cardinality لا الـ S
+
+578
+00:44:33,030 --> 00:44:39,210
+نفسها، الـ S نفسها. طيب، وهذا أكيد بيقودنا إنه الـ
+
+579
+00:44:39,210 --> 00:44:46,760
+cardinality لـ P of natural number حيكون أكبر من الـ
+
+580
+00:44:46,760 --> 00:44:51,800
+cardinality للـ natural number. منطقي. أي عنصر طبيعي
+
+581
+00:44:51,800 --> 00:44:54,780
+.. أي عنصر طبيعي. إذا كان الـ cardinality هنا 2،
+
+582
+00:44:54,780 --> 00:45:00,200
+فالـ power بتاعت set of two elements طلعت 4.
+
+583
+00:45:00,200 --> 00:45:04,860
+أكيد حتكون أكبر. و قياس على ذلك .. و قياس على ذلك حتكون
+
+584
+00:45:04,860 --> 00:45:07,680
+دائمًا أكبر منها.
+
+585
+00:45:10,510 --> 00:45:15,270
+طيب، أكيد برضه يوجد different sizes of infinite
+
+586
+00:45:15,270 --> 00:45:18,690
+sets. واتكلمنا الحالة الشهيرة الـ natural number و
+
+587
+00:45:18,690 --> 00:45:25,410
+الـ real number و الـ integers. okay. الـ ordered، كل
+
+588
+00:45:25,410 --> 00:45:29,830
+اللي فات unordered، صحيح؟ طيب، لما بتقول ordered،
+
+589
+00:45:29,830 --> 00:45:33,330
+أكيد معناه ذلك إن الـ curly braces هدول بدك تشيلهم.
+
+590
+00:45:35,870 --> 00:45:40,010
+تشيلهم وتستخدم الأقواس العادية عشان أفهم منك إنك
+
+591
+00:45:40,010 --> 00:45:45,410
+أنت بتتكلم عن زوج مرتب. وزوج مرتب لما يكون two
+
+592
+00:45:45,410 --> 00:45:52,970
+elements بس. أكتر من هيك بنسميه tuples. بنعطيه كلمة
+
+593
+00:45:52,970 --> 00:45:59,030
+tuples. مش ثنائي، زوج اتنين فقط، لأ، ممكن يكون أكثر، زي
+
+594
+00:45:59,030 --> 00:46:02,690
+النقطة في الفراغ ثلاثية الأبعاد، الفراغ اللي بتشوفه
+
+595
+00:46:02,690 --> 00:46:06,910
+الـ 3D. طب، هذه ثلاثية، ما أقدرش أقول زوج مرتب، مش هيك، هذه
+
+596
+00:46:06,910 --> 00:46:14,750
+بنسميها لاحقًا triples، ثلاثية الأرقام، تمام؟ وهي كدا، قياس
+
+597
+00:46:14,750 --> 00:46:18,730
+على ذلك، فهي بتصير ordered in tuples، in general، in
+
+598
+00:46:18,730 --> 00:46:28,040
+tuples. تكرار إني in point أو in إحداثي ومرتّبين، مرتّب
+
+599
+00:46:28,040 --> 00:46:32,500
+فملتزمين بكلمة مرتب. هي فعلاً زي الـ sets، لكن الـ
+
+600
+00:46:32,500 --> 00:46:36,100
+duplication ممكنة. ليش الـ duplication ممكنة؟ لأن واحد
+
+601
+00:46:36,100 --> 00:46:41,560
+واحد حسب الترتيب مختلف عن set of element {1, 1}.
+
+602
+00:46:41,560 --> 00:46:44,540
+set of element {1, 1}. بأختصرهم بقول هذا set of
+
+603
+00:46:44,540 --> 00:46:48,820
+element {1}. بس لأنه عنصر واحد الموجود في المجموعة.
+
+604
+00:46:51,610 --> 00:46:56,570
+لأ، duplication ممكنة، duplication ممكنة. بالعكس،
+
+605
+00:46:56,570 --> 00:47:01,430
+مهمة أصلًا، مهمة لأنه بتوضح ليه قد إيش كل إحداثي من
+
+606
+00:47:01,430 --> 00:47:05,890
+الإحداثيات بتاعتها. وبناء على ذلك ممكن نقول إن هذا
+
+607
+00:47:05,890 --> 00:47:10,290
+ordered element،
+
+608
+00:47:10,290 --> 00:47:15,550
+كويس؟ فلو الطبيعي عشان تكون and doubles، لازم الـ
+
+609
+00:47:15,550 --> 00:47:19,750
+and هذه تكون ضمن الـ natural number، هي عدد صحيح،
+
+610
+00:47:19,750 --> 00:47:24,270
+وموجب. عشان أقول n tuples، وعبارة عن sequence أو
+
+611
+00:47:24,270 --> 00:47:29,430
+بنسميها sequence of length n، وبنكتبه a1, a2 to an.
+
+612
+00:47:2
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/KAeoVdmcXOE_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/KAeoVdmcXOE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2ffd1bb253f5c97adc6e055424cec4de36b76ce1
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/KAeoVdmcXOE_postprocess.srt
@@ -0,0 +1,2512 @@
+1
+00:00:05,230 --> 00:00:08,630
+السلام عليكم، يا عطيك الله عفو يا شباب، نبدأ اليوم
+
+2
+00:00:08,630 --> 00:00:12,850
+ان شاء الله تعالى في درس جديد اللي هو ال theory of
+
+3
+00:00:12,850 --> 00:00:18,050
+sets أو ال set theory فحنتكلم عن نظرية المجموعات
+
+4
+00:00:18,050 --> 00:00:24,050
+ونتحدث عنها وعن خصائصها على اعتبار ان المجموعات هي
+
+5
+00:00:24,050 --> 00:00:27,310
+الجزء
+
+6
+00:00:27,310 --> 00:00:29,710
+الأهم في ال universe of discourse باعتبار ان هو
+
+7
+00:00:29,710 --> 00:00:35,340
+المدخل لقواعد البياناتفلما نيجي نتكلم عن ال set
+
+8
+00:00:35,340 --> 00:00:40,780
+فهي عبارة عن structure أو بناء بيمثل لنا unordered
+
+9
+00:00:42,020 --> 00:00:47,800
+collection أو group فأي مجموعة أو تجمع من الأرقام
+
+10
+00:00:47,800 --> 00:00:53,900
+أو العناصر بشكل عام objects غير مرتبة فالمجموعة هي
+
+11
+00:00:53,900 --> 00:00:56,720
+بشكل او باخر هي بتكون غير مرتبة فلما نتكلم عن
+
+12
+00:00:56,720 --> 00:00:59,940
+مجموعة طلبة ال discrete فهم مش بالضروري دايما
+
+13
+00:00:59,940 --> 00:01:02,400
+يكونوا بنفس الترتيب ونفس الجاعدة اللي قاعدينها
+
+14
+00:01:02,400 --> 00:01:07,320
+ولكن في النهاية هم نفس المجموعة ونفس ال objects
+
+15
+00:01:07,320 --> 00:01:12,550
+بالنسبة لكشف الحضور والغياب مثلا أو كشفأخر العام
+
+16
+00:01:12,550 --> 00:01:17,390
+أو أخر الفصل اللي بده يعطاه درجات فهيكون نفس العدد
+
+17
+00:01:17,390 --> 00:01:20,870
+أه ولكن الترتيب مش بدروري دائما يكونوا نفس الترتيب
+
+18
+00:01:20,870 --> 00:01:24,870
+مش بدروري يكون نفس الترتيب فهذا ممكن يكون zero
+
+19
+00:01:24,870 --> 00:01:29,530
+objects ممكن يكون nothing اللي هو دائما بتسموها
+
+20
+00:01:29,530 --> 00:01:34,010
+المجموعة الخالية كنتوا أو الفاي فإما zero او more
+
+21
+00:01:34,010 --> 00:01:37,550
+distinct او different objects فبتكون مجموعة
+
+22
+00:01:37,550 --> 00:01:41,350
+objectsو اللي سميناها objects مش بضروري نسميها
+
+23
+00:01:41,350 --> 00:01:44,950
+numbers مش بضروري نسميها numbers لأ لأنه هي أي
+
+24
+00:01:44,950 --> 00:01:48,710
+حاجة في الدنيا ممكن تكون sets ممكن تكون sets و زي
+
+25
+00:01:48,710 --> 00:01:54,250
+ما قلنا هنا اتكلمنا عن المسجلين لمصاق معين هم اصلا
+
+26
+00:01:54,250 --> 00:01:58,730
+ضمن مجموعة المسجلين لهذا المصاق بغض النظر عن
+
+27
+00:01:58,730 --> 00:02:02,320
+ترتيبهمكل ال mathematics من تعريفنا البسيطة ده كل
+
+28
+00:02:02,320 --> 00:02:04,740
+ال mathematics اللي ممكن تختار ع بالكم هي ممكن
+
+29
+00:02:04,740 --> 00:02:09,160
+واضحة ب .. ك sets ليش؟ لأن أي mathematics أنت
+
+30
+00:02:09,160 --> 00:02:13,160
+بتتخيلها في الدنيا أكيد محتاج تعطيها قيم أو القيم
+
+31
+00:02:13,160 --> 00:02:16,240
+هذه مش بالضرورة تكون عددية أو رقمية زي ما قلنا مش
+
+32
+00:02:16,240 --> 00:02:18,980
+بالضرورة تكون رقمية أو عددية زي مثلا ال false true
+
+33
+00:02:18,980 --> 00:02:22,540
+اللي كنا بناخدها من أول الفصل حتى الآن هذه ليست
+
+34
+00:02:22,540 --> 00:02:26,040
+عددية هي إيا true إيا false صح أو خطأ فهذه برضه
+
+35
+00:02:26,040 --> 00:02:30,080
+نفس الجثة ممكن تعمل معاها as a setas a set ال set
+
+36
+00:02:30,080 --> 00:02:35,000
+هذه تحتوي على two elements فانا محتاج اعطي قيمة من
+
+37
+00:02:35,000 --> 00:02:37,680
+ال universe of discourse فمدام في حاجة اسمها
+
+38
+00:02:37,680 --> 00:02:40,440
+universe of discourse وهذه ال predicate برضه
+
+39
+00:02:40,440 --> 00:02:45,140
+اتكلمنا عنها و ال predicate هي نفس فكرة ال
+
+40
+00:02:45,140 --> 00:02:49,940
+function هي بتتعامل مع قيمة لل object او لل
+
+41
+00:02:49,940 --> 00:02:52,820
+subject من universe of discourse طب ال universe of
+
+42
+00:02:52,820 --> 00:02:56,640
+discourse هذا هو عبارة عن collection او group of
+
+43
+00:02:56,640 --> 00:03:00,700
+elementsgroup of elements لما نتكلم عن ال X جد إيش
+
+44
+00:03:00,700 --> 00:03:04,900
+القيم اللي ممكن تاخدها فهي ممكن تاخد أي قيمة من ال
+
+45
+00:03:04,900 --> 00:03:08,300
+X axis طيب ال X axis القيم نفسها اللي موجودة على
+
+46
+00:03:08,300 --> 00:03:11,980
+ال X axis هذه طب ما هي برضه elements هي مجموعة
+
+47
+00:03:11,980 --> 00:03:17,060
+elements فبنقدر نقول إن X ممكن ياخد أي قيمة من ال
+
+48
+00:03:17,060 --> 00:03:21,800
+set هذه من ال set هذه اللي بتحتوي على مجموعة ال
+
+49
+00:03:21,800 --> 00:03:26,670
+elements تمامبعض ال mutations الأساسية كلنا
+
+50
+00:03:26,670 --> 00:03:31,050
+بنتعامل مع ال set كمسمة لل set و ال elements بتاعة
+
+51
+00:03:31,050 --> 00:03:35,730
+ال set بشكل بسيط و صريح و واضح عادة ال set نفسها
+
+52
+00:03:35,730 --> 00:03:40,270
+كمتغير بنحطها capital بنعطيها قيمة capital فممكن
+
+53
+00:03:40,270 --> 00:03:46,810
+أقول ال set ل ال discrete دي هذه بتحتوي على كل ال
+
+54
+00:03:46,810 --> 00:03:52,110
+elements و الآن بنحطها بتعرف بال curly braces أو
+
+55
+00:03:52,110 --> 00:03:56,750
+الأقواص المجاعةاللي بالشكل هذا تعرف ان مدبها
+
+56
+00:03:56,750 --> 00:04:00,470
+بداخله هي ال elements وال elements بناها بتعطى قيم
+
+57
+00:04:00,470 --> 00:04:01,190
+small
+
+58
+00:04:04,520 --> 00:04:09,280
+تمام؟ بتعطى قيم small فإذا capital لإسم ال group
+
+59
+00:04:09,280 --> 00:04:14,280
+كله أو ال set الكبيرة ككل و ال elements داخلها
+
+60
+00:04:14,280 --> 00:04:19,220
+بتعطى small letters ف .. و هي بتكون محصورة داخل ال
+
+61
+00:04:19,220 --> 00:04:22,680
+curly braces فانا بعرف ان ال curly هاد ل ال sets
+
+62
+00:04:22,680 --> 00:04:26,680
+.. لمين؟ لل sets و إذا curly معناته مش بالضروري
+
+63
+00:04:26,680 --> 00:04:31,240
+اللي جوا يكون مرتبمش بالضروري أكون مرتب بخلاف
+
+64
+00:04:31,240 --> 00:04:34,880
+الأقواس اللي كنتوا تاخدوها للأزواج المرتبة كنتوا
+
+65
+00:04:34,880 --> 00:04:38,100
+تاخدوا الأقواس إذا أخذناها بهذا الشكل فهذا قوس
+
+66
+00:04:38,100 --> 00:04:44,900
+مرتب قوس مرتب بغض النظر هو زوج أو أكثر يعني هنا لو
+
+67
+00:04:44,900 --> 00:04:50,100
+تلاتة ممكن نحطهم A وB وC أنا بعرف إن هدول مرتبين
+
+68
+00:04:50,100 --> 00:04:54,740
+بمعنى XY وZ محاول XY وZ فهذا بيعطينا نقطة إحداثية
+
+69
+00:04:54,740 --> 00:05:00,920
+بنفعش نقول B وAبتصير نقطة مختلفة تماما فنقطة تماما
+
+70
+00:05:00,920 --> 00:05:04,780
+مختلفة أما هنا أقول ب ب a c بمشي الحال هي نفس ال
+
+71
+00:05:04,780 --> 00:05:08,560
+group ال group أو ال set هي هي ضلت نفس القيمة نفس
+
+72
+00:05:08,560 --> 00:05:13,490
+ال setطيب الطرق اللي بنوصف فيها ال sets من أهمها
+
+73
+00:05:13,490 --> 00:05:17,690
+إما أني أكتبها كاملة و مش بالضروري أنه دايما هذه
+
+74
+00:05:17,690 --> 00:05:21,550
+تسعفني لأن أحيانا بتكون ال set مجموعة ال element
+
+75
+00:05:21,550 --> 00:05:26,250
+ساعتها عددهم كبير عددهم كبير فما بقدر أكتبهم as a
+
+76
+00:05:26,250 --> 00:05:30,290
+sequence كلهم هيك أحطهم على بعض و أكتبهم و ياخدوا
+
+77
+00:05:30,290 --> 00:05:33,670
+مني الصبورة تلت أربعة مرات مش بالضروري دايما بيصير
+
+78
+00:05:33,670 --> 00:05:36,410
+معاك لأ ممكن أن نستخدم حاجة اسمها set builder
+
+79
+00:05:36,410 --> 00:05:42,370
+notationset builder notation اللي هو اختصارات او
+
+80
+00:05:42,370 --> 00:05:49,030
+علامات او symbols تبع البناء او بناء المجموعة و
+
+81
+00:05:49,030 --> 00:05:52,090
+اللي هي ممكن نكتبها as a function ممكن تكتب as a
+
+82
+00:05:52,090 --> 00:05:56,450
+function نقول والله عندي set او proposition P of X
+
+83
+00:05:56,940 --> 00:05:59,920
+ال P of X هذا بدنا نعرفه على ال universe of
+
+84
+00:05:59,920 --> 00:06:04,060
+discourse فممكن نعرف ال set كأنها هي ال elements
+
+85
+00:06:04,060 --> 00:06:07,540
+اللي هناخد منها ال universe of discourse هناخد
+
+86
+00:06:07,540 --> 00:06:13,380
+أمثلة عليها جايةهي مجموعة أمثلة شوية شوية لعند ما
+
+87
+00:06:13,380 --> 00:06:16,880
+نصل لل builder أو ال set builder اللي حنتكلمنا
+
+88
+00:06:16,880 --> 00:06:21,300
+عنها طيب ال set ان أكد على unordered هي مش مرتبة
+
+89
+00:06:21,300 --> 00:06:27,300
+فمعنى ذلك ABC هي نفسها ACB whatever بدلوا شجلب
+
+90
+00:06:27,300 --> 00:06:29,720
+فيهم زي ما بدك و اعملوا كل ال possibilities
+
+91
+00:06:29,720 --> 00:06:33,720
+الممكنين لترتيبهم مش هيفرج معانا كلهم نفس الاشي
+
+92
+00:06:33,720 --> 00:06:38,160
+بعرف منالـ curly braces إن هدولة مجموعة في النهاية
+
+93
+00:06:38,160 --> 00:06:41,640
+هدول مجموعة ما تقوليش ما أنا عاملهم أقواص مرتب لأ
+
+94
+00:06:41,640 --> 00:06:45,340
+هذا مش قواص مرتب هذا قواص المجموعة قواص المجموعة
+
+95
+00:06:45,340 --> 00:06:49,760
+بفرجش كيف الترتيب جوا بمعنى هذه زي هذه زي هذه كلهم
+
+96
+00:06:49,760 --> 00:06:55,240
+نفس الأشي مش هيفرج معانا طيب شغل تانية unequal
+
+97
+00:06:55,240 --> 00:07:00,800
+بمعنى ما تقوليش ما هيو زي العدد لما نقول مثلا في
+
+98
+00:07:00,800 --> 00:07:05,460
+يانديالزوج المرتب واحد واحد، هذه معناته نقطة واحد
+
+99
+00:07:05,460 --> 00:07:09,920
+واحد، بس لما أقول مجموعة واحد واحد، مافيش حاجة
+
+100
+00:07:09,920 --> 00:07:15,260
+اسمها هيك، هذا اسمها تكرار، تكرار، لأ هذه فعليا
+
+101
+00:07:15,260 --> 00:07:20,080
+الأولى أنها تنكتب مجموعة واحد بس، لأن التكرار لا
+
+102
+00:07:20,080 --> 00:07:25,000
+يعتد فيه، فهي لازم تكون ال order ال set unequal
+
+103
+00:07:25,850 --> 00:07:29,670
+مايكونش فيها elements متساوية ال element يمثل مرة
+
+104
+00:07:29,670 --> 00:07:34,130
+واحدة فقط فمعنى ذلك انه اذا كانت a و b بسوا بعض a
+
+105
+00:07:34,130 --> 00:07:39,870
+,b,c هذه زيادة ع الفاضي هذه زيادة ع الفاضي الصح ان
+
+106
+00:07:39,870 --> 00:07:45,710
+اقول a,c و بس او b و c بس الاعتبار ان a و b هم زي
+
+107
+00:07:45,710 --> 00:07:50,630
+بعض هم زي بعض زي عندما اقول a,a,b,a,b,c,c هذه كلها
+
+108
+00:07:51,450 --> 00:07:55,470
+طويلة عريضة على الفاضي هذه كلها a b c وخلاص او a c
+
+109
+00:07:55,470 --> 00:08:00,070
+مدام a وb بسوا بعض فهذه فعليا لا تمثل بهذا الشكل
+
+110
+00:08:00,070 --> 00:08:03,890
+ما تكتبهاش اي مجموعة بهذا الشكل فيها تكرارات ولو
+
+111
+00:08:03,890 --> 00:08:08,470
+انت عارف ان في two elements بسوا بعض اختصرالست ده
+
+112
+00:08:08,470 --> 00:08:12,170
+مابتكون بأصغر صورة ممكنة بحيث يكون distanced أو
+
+113
+00:08:12,170 --> 00:08:15,390
+different elements زي تعريفنا أول ما بدأنا
+
+114
+00:08:15,390 --> 00:08:18,070
+different elements لازم يكونوا مختلفين عن بعض
+
+115
+00:08:18,070 --> 00:08:24,330
+مابنفع تتعامل معاها كزوج مرتب الموقعه بيفرج حتى لو
+
+116
+00:08:24,330 --> 00:08:27,550
+نفس القيمة هنا واحد و هنا واحد لأ مختلفين عن بعض
+
+117
+00:08:27,550 --> 00:08:31,980
+هدولةالـ two ones هدول مختلفين تماما عن بعض لما
+
+118
+00:08:31,980 --> 00:08:34,620
+بتكلم عن ال curly braces لأ أنا بتكلم عن مجموعة
+
+119
+00:08:34,620 --> 00:08:42,020
+المجموعة لازم تختصر كل المتشابه تمام فإذا لما نيجي
+
+120
+00:08:42,020 --> 00:08:45,740
+نتكلم عن ال equality ال equality ل ال sets أو
+
+121
+00:08:45,740 --> 00:08:51,500
+المساوية للمجموعات بدها تحكمنا نفس المجموعة ال
+
+122
+00:08:51,500 --> 00:08:55,620
+rules اللي أخدناها سابقا ال inequalityللمجموعة ال
+
+123
+00:08:55,620 --> 00:08:58,560
+elements ساعتنا و ال unordered في الحالة بتاعتنا
+
+124
+00:08:58,560 --> 00:09:02,120
+بمعنى إذا كان انت قدر تتعرف مجموعة بطريقة و أنا
+
+125
+00:09:02,120 --> 00:09:05,080
+عرفتها بطريقة تانية حتى لو كان عكسية بس في النهاية
+
+126
+00:09:05,080 --> 00:09:08,960
+نفس ال elements موجودين في المجموعتين فبقول ان ال
+
+127
+00:09:08,960 --> 00:09:12,680
+two elements متساويين بغض النظر كيف ترتيبهم بغض
+
+128
+00:09:12,680 --> 00:09:17,300
+النظر كيف ترتيبهم فإذا بقول ان ال two sets هما
+
+129
+00:09:17,300 --> 00:09:23,230
+equal لبعض if and only ifthey contain exactly the
+
+130
+00:09:23,230 --> 00:09:26,730
+same elements إذا اللهم نفس ال elements ماتكلمتش
+
+131
+00:09:26,730 --> 00:09:29,750
+عن ordered ordered elements لأ مش ordered elements
+
+132
+00:09:29,750 --> 00:09:34,230
+ال elements و بس زي ما قلنا المجموعة بتاعتنا لليوم
+
+133
+00:09:34,230 --> 00:09:37,150
+هي نفس المجموعة تاعت يوم الأربعة لحضرة يوم الأربعة
+
+134
+00:09:37,150 --> 00:09:40,310
+بغض النظر أنتم كيف كنتوا جاعدينبغض النظر عن
+
+135
+00:09:40,310 --> 00:09:46,550
+الترتيب، ماليهاش علاقة الترتيب تمام، فبدون زي ما
+
+136
+00:09:46,550 --> 00:09:50,150
+قلنا نومتر، بدون الاهتمام إلى كيف ال set تم
+
+137
+00:09:50,150 --> 00:09:54,810
+تعريفها أو تم الإشارة إلها، بمعنى هل وقت هنشوف هاي
+
+138
+00:09:54,810 --> 00:09:59,160
+set builderو كل مرة ال builder .. ال builder مختلف
+
+139
+00:09:59,160 --> 00:10:02,800
+عن التاني كل مرة هنحط نفس المجموع ولكن تعريف مختلف
+
+140
+00:10:02,800 --> 00:10:06,320
+عن التاني ف for example لو افترضنا ان ال set واحد
+
+141
+00:10:06,320 --> 00:10:10,960
+اتنين تلاتة اربعة هذا تعريف صريح تعريف صريح لل set
+
+142
+00:10:10,960 --> 00:10:15,240
+كويس لكن ما هي نفس ال set هذه ممكن ان اعرفها set
+
+143
+00:10:15,240 --> 00:10:18,840
+builder بطريقة مختلفة تماما ان اقول هيا بدأنا باش
+
+144
+00:10:18,840 --> 00:10:21,950
+بال curly bracesمعنى ذلك إن أنا عارف إن التعريف
+
+145
+00:10:21,950 --> 00:10:27,470
+الآن داخل الأقواس المجعدة هذه هو ل elements داخل
+
+146
+00:10:27,470 --> 00:10:31,430
+set elements داخل .. ما كتبناش الأقواس العادية
+
+147
+00:10:31,430 --> 00:10:37,490
+الأقواس المجعدة معنى ذلك إن بقول set على طول شوفتم
+
+148
+00:10:37,490 --> 00:10:43,890
+على طول بعرف it's set of elements x such that أو
+
+149
+00:10:43,890 --> 00:10:49,690
+إذا كان x هو عبارة عن انتجر ما بينالصفر أكبر من
+
+150
+00:10:49,690 --> 00:10:53,110
+الصفر وأقل من خمسة طب لم تتمثل هذا الكلام حيطلع
+
+151
+00:10:53,110 --> 00:10:57,010
+برضه واحد اتنين تلاتة أربعة حيختلف اشي لأو مش
+
+152
+00:10:57,010 --> 00:11:00,090
+هيختلف اشي حيجي واحد يقول لك لأ طب انا بدي أعرفها
+
+153
+00:11:00,090 --> 00:11:02,870
+بطريقة مختلفة و برضه يعمل لي braces خلاص معناته هو
+
+154
+00:11:02,870 --> 00:11:07,110
+عرفلي ان هوا دي set افهمت منه انه set مدام حطلي ال
+
+155
+00:11:07,110 --> 00:11:11,810
+braces ال curly braces او الأقواص المجاعة ده بعرف
+
+156
+00:11:11,810 --> 00:11:16,930
+ان هوا دي مجموعة مجموعة ال elements Xبشرط ان X هي
+
+157
+00:11:16,930 --> 00:11:22,610
+عبارة عن ال positive integers و اللي تربيحها بين
+
+158
+00:11:22,610 --> 00:11:28,890
+الصفر و 25 طيب بين الصفر و 25 أكم عنصر ممكن يتربع
+
+159
+00:11:28,890 --> 00:11:33,770
+معاه طب نلاحظ أنه أقل من 25 أربع عناصر اللي هو 1,2
+
+160
+00:11:33,770 --> 00:11:37,670
+,3,4 أو السوال بتاعتهم مش هيك بس هو حدد لمينه
+
+161
+00:11:37,670 --> 00:11:41,970
+positive positive معناته 1,2,3,4 يعني كأنه رجع
+
+162
+00:11:41,970 --> 00:11:46,840
+أعرف لنفس ال 6 هي هيعرف نفس ال set كما هي طيب في
+
+163
+00:11:46,840 --> 00:11:50,500
+الآخر نفس ال elements واحدة رغم ان التعريف اختلفت
+
+164
+00:11:50,500 --> 00:11:53,760
+و ال set builders اختلفت لكن في الحالة هنا بقول ان
+
+165
+00:11:53,760 --> 00:11:58,770
+التلاتة هما equal ل بعض تفرج في نفسكالتان فيهم نفس
+
+166
+00:11:58,770 --> 00:12:01,750
+العناصر يعني التان فيهم عناصر متشابهة لكن واحدة
+
+167
+00:12:01,750 --> 00:12:05,070
+بتحتوى على عناصر أكتر لكن هي .. أه لأ هنا لا يسووا
+
+168
+00:12:05,070 --> 00:12:08,330
+بعض لأ بيسووش بعض هذه إلها علاقة مختلفة هناخدها
+
+169
+00:12:08,330 --> 00:12:13,350
+جدام فيها علاقة أن واحدة تشمل الأخرى set و subset
+
+170
+00:12:13,350 --> 00:12:18,220
+و super set هناخدهم لجدام ان شاء الله تعالىطيب ال
+
+171
+00:12:18,220 --> 00:12:22,240
+infinite وال .. ال .. ال finite sits في infinite
+
+172
+00:12:22,240 --> 00:12:25,660
+اللي هي المجموعات اللانهائية و ال finite sits
+
+173
+00:12:25,660 --> 00:12:29,420
+المجموعات المحددة أو اللي معروف أنها نهاية اللي هي
+
+174
+00:12:29,420 --> 00:12:33,500
+ال ending with ending كويس هنتعلمها أول شغل واضح
+
+175
+00:12:33,500 --> 00:12:36,880
+أنه لما بتكلم عن infinite معناته is ان هي not
+
+176
+00:12:36,880 --> 00:12:41,420
+finite هي غير محددة without end يعني أو unending
+
+177
+00:12:43,530 --> 00:12:47,670
+لانهائية لانهائية زي ال natural number ال natural
+
+178
+00:12:47,670 --> 00:12:52,250
+number هي أرقام من صفر to إيش to infinity هم
+
+179
+00:12:52,250 --> 00:12:56,130
+integers في النهاية عدد حقيقي صحيحة ولكن من صفر
+
+180
+00:12:56,130 --> 00:13:02,650
+بتضل to infinity ال z أو ال integers in general ال
+
+181
+00:13:02,650 --> 00:13:06,110
+integers بصورة كبيرة هي ال natural زائد الجزء
+
+182
+00:13:06,110 --> 00:13:10,520
+السالب كمانفإذا من minus infinity to infinity
+
+183
+00:13:10,520 --> 00:13:15,480
+للأرقام الصحيحة الأرقام الصحيحة كويس فإذا هذه اللي
+
+184
+00:13:15,480 --> 00:13:18,480
+نهائية انت مش عارف هي من وين بدت و امتى هتنتهي و
+
+185
+00:13:18,480 --> 00:13:21,240
+ال natural number انت مش عارف امتى هتنتهي برضه طيب
+
+186
+00:13:21,240 --> 00:13:25,000
+ال real number طبعا اللي هي ملاق تبعهم هذا ال real
+
+187
+00:13:25,000 --> 00:13:31,280
+number هي الأرقام الحقيقيةكسور اه كسور fractions
+
+188
+00:13:31,280 --> 00:13:34,900
+زاد integers كله كاملة على بعض طبعا بتتكلم عن ال
+
+189
+00:13:34,900 --> 00:13:38,140
+fractions هي أصلا بين كل integer و integer في عدد
+
+190
+00:13:38,140 --> 00:13:42,020
+لنهائي من ال fractions فتخيل بين كل رقم و رقم في
+
+191
+00:13:42,020 --> 00:13:45,020
+عدد لنهائي من الأرقام بين كل رقم و رقم عدد لها
+
+192
+00:13:45,020 --> 00:13:50,380
+نهائي من الأرقام ف ال real numbers فهدولة أشهر3
+
+193
+00:13:50,380 --> 00:13:58,680
+infinite sets اللي هي مجموعات لا نهائية طيب نفس
+
+194
+00:13:58,680 --> 00:14:02,820
+الكلام من شكلهم أصلا ال infinite sets ممكن تيجي ب
+
+195
+00:14:02,820 --> 00:14:07,080
+different sizesصحيح أنا مش عارف بالظبط قداش لكن
+
+196
+00:14:07,080 --> 00:14:10,240
+بقدر أحدد على الأقل أنه في واحدة أكبر من التانية
+
+197
+00:14:10,240 --> 00:14:13,560
+الأحجام بتاعتهم مختلفة تماما عن بعض مين أكبرهم
+
+198
+00:14:13,560 --> 00:14:18,240
+حجما؟ ال R ال R أكيد و مين أقلهم حجما؟ ال natural
+
+199
+00:14:18,240 --> 00:14:21,830
+number صحيح؟الـ Neutral المبارض واضحة أنه أقلهم
+
+200
+00:14:21,830 --> 00:14:27,490
+لأنه تقريبا نص تقريبا يعني بزيادة شوية نص ال
+
+201
+00:14:27,490 --> 00:14:30,210
+integers نص ال integers لكن العلاقة بين ال
+
+202
+00:14:30,210 --> 00:14:33,930
+integers و ال real لأ ال real هي infinity من كل
+
+203
+00:14:33,930 --> 00:14:36,010
+رقمين بين كل رقمين من ال integer
+
+204
+00:14:40,450 --> 00:14:44,430
+طيب طريقة تمثيل ال sets الطريقة الأبسط والسهلة هي
+
+205
+00:14:44,430 --> 00:14:49,310
+ال Venn diagrams اللي خدتوها في أيام ثانوي Venn
+
+206
+00:14:49,310 --> 00:14:52,070
+diagram بسيط جدا بتحط الأرقام بطريقة أنك تحطها
+
+207
+00:14:52,070 --> 00:14:57,410
+داخل مجموعة و تتحوت عليهابأشكال معينة بشكل مثلث
+
+208
+00:14:57,410 --> 00:15:01,070
+مربع بحط اللي بدك هي المهم انك انت بتكون حاصر
+
+209
+00:15:01,070 --> 00:15:05,430
+الأرقام تبعتك لتسهيل ال visualization بتاعتها او
+
+210
+00:15:05,430 --> 00:15:08,170
+عملية ال representation المرئي تبعها انك انت
+
+211
+00:15:08,170 --> 00:15:11,750
+حاططها بشكل أشكال جدامك لو افترضنا انه مثلا أرقام
+
+212
+00:15:11,750 --> 00:15:15,830
+بهذا الشكل زي اللي انت شايفها عندك اللي هي من
+
+213
+00:15:15,830 --> 00:15:20,470
+minus one to nine بقدر أسميهم هم كلهم هيك على بعض
+
+214
+00:15:21,310 --> 00:15:30,870
+دمن ال curve الخارجى اللى هو هذا على أساس أن هذا
+
+215
+00:15:30,870 --> 00:15:33,870
+هي ال Venn diagram لمن؟ لكل الأرقام ال integers
+
+216
+00:15:33,870 --> 00:15:38,470
+between minus one to nine minus one to nine طيب
+
+217
+00:15:38,470 --> 00:15:44,910
+نفس الاشي ممكن أروح أعملمجموعة داخلها وبرضه ارسمها
+
+218
+00:15:44,910 --> 00:15:49,130
+بهذا الشكل اقول والله مجموعة subset او مجموعة
+
+219
+00:15:49,130 --> 00:15:52,970
+جزئية منها هي مجموعة الأرقام ال integers و ال
+
+220
+00:15:52,970 --> 00:15:57,170
+positive integers او ال nature's اذا ال nature's
+
+221
+00:15:57,170 --> 00:16:00,490
+معناته بتدخل معاها الصفر لكن بهذا الشكل هي ال
+
+222
+00:16:00,490 --> 00:16:07,140
+positive integers و اللي اقل من عشرةcheck positive
+
+223
+00:16:07,140 --> 00:16:11,420
+integers اقل من عشرة او من واحد لعشرة اقل من عشرة
+
+224
+00:16:11,420 --> 00:16:15,220
+فخلاص بتكلم عن هذه المجموعة ايش في عندي مجموعات
+
+225
+00:16:15,220 --> 00:16:18,400
+تانية؟ ممكن مش عارف حيبدأ هو بال .. بس بقى باينة
+
+226
+00:16:18,400 --> 00:16:22,780
+عندي ان ممكن اخد مثلا مجموعة الأرقام هذه الزوجية
+
+227
+00:16:22,780 --> 00:16:27,880
+.. الفردية .. الزوجية عفوا و هذه الفردية .. هذه
+
+228
+00:16:27,880 --> 00:16:33,730
+هيك الفرديةو نتكلم عن فرد مجموعة ال even integers
+
+229
+00:16:33,730 --> 00:16:37,730
+و مجموعة ال odd integers بالاضافة انه ممكن بترتيب
+
+230
+00:16:37,730 --> 00:16:42,610
+معين نحط هذه الأرقام مع بعض و نقول ال brines اللي
+
+231
+00:16:42,610 --> 00:16:47,740
+اقل من عشرة مثلا اقل من عشرة او اقل من 11مش هيك
+
+232
+00:16:47,740 --> 00:16:51,460
+أقل من عشر أو أقل من أحداشر ممشي الحال تمام فلاحظ
+
+233
+00:16:51,460 --> 00:16:54,600
+أن ال Venn diagram جدرنا ان نرتب مجموعة العناصر
+
+234
+00:16:54,600 --> 00:16:58,060
+بحيث ان هي تشمل اكتر من مجموعة في نفس الوقت و ان
+
+235
+00:16:58,060 --> 00:17:03,000
+نرتبها بأكتر من مجموعة من مجموعة فهذه طريقة ال
+
+236
+00:17:03,000 --> 00:17:06,000
+Venn diagrams ان انا ممكن احط مجموعات مع بعض اعمل
+
+237
+00:17:06,000 --> 00:17:09,340
+تقاطعاتهم مع بعض لان واضح ان هنا صار في تقاطعات
+
+238
+00:17:09,340 --> 00:17:15,330
+تقاطع لما اتكلم عن تقاطع ال even مع ال primeواضح
+
+239
+00:17:15,330 --> 00:17:19,790
+أنه في رقم واحد إجا في كلاهما فهذا بقول عليه رقم
+
+240
+00:17:19,790 --> 00:17:23,350
+متقاطع بين الاتنين يعني هو ينتمي للمجموعة هذه
+
+241
+00:17:23,350 --> 00:17:28,910
+وينتمي للمجموعة هذه ينتمي فإذا من ناحية تمثيل مرئي
+
+242
+00:17:28,910 --> 00:17:32,550
+ال Venn diagram أعطتني إمكانية كتير عالية أن أشوف
+
+243
+00:17:32,550 --> 00:17:37,630
+تمثيل البيانات قدامي لمجموعة ال sets أو للمجموعات
+
+244
+00:17:37,630 --> 00:17:41,290
+بصفة عامةفهذه واحدة من الطرق المستخدمة اللي
+
+245
+00:17:41,290 --> 00:17:44,410
+أخدتوها أكيد طبعا انتوا في الزمان يمكن كمان مش في
+
+246
+00:17:44,410 --> 00:17:49,250
+توجيهي يمكن أخدتوها في إعدادي أظن أعتقد يمكن في
+
+247
+00:17:49,250 --> 00:17:57,550
+إعدادي بقى أذكر أن هذه شغل إعدادي كانت تمامالان
+
+248
+00:17:57,550 --> 00:18:01,390
+بعض ال relations داخل ال sets اللي ممكن نتعامل
+
+249
+00:18:01,390 --> 00:18:06,190
+معاها مع ال sets أهمها و أولها هي ال membership أو
+
+250
+00:18:06,190 --> 00:18:10,870
+العضوية العضوية هذه اللي هي ينتمي إلى إذا كان
+
+251
+00:18:10,870 --> 00:18:14,410
+والله العنصر ينتمي للمجموعة أو هو عضو في المجموعة
+
+252
+00:18:14,410 --> 00:18:17,190
+زي لما توقفت تكلمنا عن الإتنين، الإتنين هو عضو في
+
+253
+00:18:17,190 --> 00:18:21,850
+مجموعة الأرقام الزوجية فإذا هو ينتمي للأرقام
+
+254
+00:18:21,850 --> 00:18:28,990
+الزوجية أو بنسمي elementفبنعطيه حرف ال E كأنه يمثل
+
+255
+00:18:28,990 --> 00:18:33,630
+أو ينتمي إلى فبياخد بهذا الشكل طيب ينتمي إلى
+
+256
+00:18:33,630 --> 00:18:39,690
+معناته أنا بتكلم عن زي ما قلنا element نتكلم عن
+
+257
+00:18:39,690 --> 00:18:44,810
+element يعني بمعنى أن ما قبل هذه العلامة هو عنصر
+
+258
+00:18:44,810 --> 00:18:49,790
+هو إيش؟ عنصر ناخد بالنا من هذا الكلام لأنه بعدين
+
+259
+00:18:49,790 --> 00:18:53,390
+هناخد notations تانية ما قبلها مش بالضروري تكون
+
+260
+00:18:53,390 --> 00:18:57,910
+عنصرما قبلها بيكونش عنصر فالعنصر إذا أنا بدي أشوف
+
+261
+00:18:57,910 --> 00:19:03,370
+علاقة ال ما قبل هذه العلامة بيكون عبارة عن element
+
+262
+00:19:03,370 --> 00:19:07,110
+فردي عنصر هو عنصر داخل المجموعة تمام
+
+263
+00:19:09,890 --> 00:19:13,790
+و بده يكون distinct او مميز هو different عن باجي
+
+264
+00:19:13,790 --> 00:19:17,110
+العناصر عشان نقدر نقول انه عنصر زي ما توي قولنا
+
+265
+00:19:17,110 --> 00:19:19,750
+اذا كان والله متشابه مع غيره معناته لازم يختصر هو
+
+266
+00:19:19,750 --> 00:19:24,090
+وغيره اذا كان بيسووا بيسووا بعض بدنا نختار واحد
+
+267
+00:19:24,090 --> 00:19:29,620
+منهم بحيث انه يظل واحد distinct elementOkay لما
+
+268
+00:19:29,620 --> 00:19:33,780
+اقول تلاتة belong to to N to capital N معناته انه
+
+269
+00:19:33,780 --> 00:19:37,380
+تلاتة هيتنتمي لأعداد الطبيعية مش شايف ال natural
+
+270
+00:19:37,380 --> 00:19:44,360
+number طيب لما اقول a هو ينتمي ل set of X بشرط او
+
+271
+00:19:44,360 --> 00:19:49,860
+اذا كان X هو letter of alphabet اذا كان ال X هذه
+
+272
+00:19:49,860 --> 00:19:54,580
+حرف من حروف الأبجادية معناته صحيح برضه بقول صحيح
+
+273
+00:19:54,580 --> 00:19:57,880
+لانه فعلا ال a هو واحد الحروف الأبجاديةهو احد
+
+274
+00:19:57,880 --> 00:20:02,140
+الحروف فبقدر اقول ان ايه هو يمثل احد ال axis اللي
+
+275
+00:20:02,140 --> 00:20:06,600
+موجودة داخل هذه المجموعة فبهذه الطريقة بمشي الحال
+
+276
+00:20:06,600 --> 00:20:11,280
+بال set builder او بهذه الطريقة المباشرة ان اسميه
+
+277
+00:20:11,280 --> 00:20:16,810
+ينتمي لمجموعة واضحة ومعرفة مسبقاطيب بنقدر نعرف ال
+
+278
+00:20:16,810 --> 00:20:22,330
+equality لان in term of belonging to باستخدام انه
+
+279
+00:20:22,330 --> 00:20:27,370
+لو for all capital هدول صحيح؟ يعني إيش بتكلم؟ Sets
+
+280
+00:20:27,370 --> 00:20:33,370
+باتكلمش عن elements هنا فإذا for all sets S و T
+
+281
+00:20:33,370 --> 00:20:38,810
+two sets يعني عندي لكل المجموعات المجموعة S تساوي
+
+282
+00:20:38,810 --> 00:20:45,890
+المجموعة T if and only iffor all x small لكل
+
+283
+00:20:45,890 --> 00:20:51,730
+العناصر هنا بنتكلم لكل العناصر العنصر x ينتمي ل S
+
+284
+00:20:51,730 --> 00:20:58,070
+إذا و إذا فقط هو ينتمي ل T يعني كأنه بينتمي ل S و
+
+285
+00:20:58,070 --> 00:21:05,420
+ينتمي ل T كويس لكل العناصر و العكس صحيحهو مش فقط
+
+286
+00:21:05,420 --> 00:21:09,780
+إذا بينتمي ل S هو بينتمي ل T لأ و كمان إذا بينتمي
+
+287
+00:21:09,780 --> 00:21:15,480
+ل T ينتمي ل S عشان هيك بال implication بتظبطش لازم
+
+288
+00:21:15,480 --> 00:21:19,740
+if and only if لازم إذا بينتمي للأولى بالضرورة
+
+289
+00:21:19,740 --> 00:21:23,200
+ينتمي للتانية أو إذا بينتمي للتانية بالضرورة يجب
+
+290
+00:21:23,200 --> 00:21:27,440
+أن ينتمي للأولى عشان أقول إن هم متساويتين في عدد
+
+291
+00:21:27,440 --> 00:21:32,730
+ال elements و كلهم يحتووا على ال elements Xfor all
+
+292
+00:21:32,730 --> 00:21:37,710
+x لكل العناصر x ففي الحالة دي بنقول انه في
+
+293
+00:21:37,710 --> 00:21:43,730
+equality واضحة بين ال set S و ال set T تمام فال
+
+294
+00:21:43,730 --> 00:21:48,670
+two sets are equal if and only if they haveAll the
+
+295
+00:21:48,670 --> 00:21:53,930
+same members، كل العناصر المتشابهة هي موجودة هنا
+
+296
+00:21:53,930 --> 00:22:00,850
+وموجودة هنا X not belong to S، هذه ال negation
+
+297
+00:22:00,850 --> 00:22:08,070
+بتاعة belong، معناه انها لا تنتمي للستمعناه ذلك ان
+
+298
+00:22:08,070 --> 00:22:13,730
+X ليست موجودة ضمن ال set X هذه مكافئة ل negation X
+
+299
+00:22:13,730 --> 00:22:18,450
+belong to S إذا والله X هي تنتمي ل S لأ ال false
+
+300
+00:22:18,450 --> 00:22:22,490
+تبعها أنها لا تنتمي ل X واضح جدا فيش فيها مشكلة في
+
+301
+00:22:22,490 --> 00:22:30,030
+X is not in set S okay المجموعات الخاصة بعض
+
+302
+00:22:30,030 --> 00:22:32,750
+المجموعات الخاصة اللي اتعاملنا معاهم و اللي
+
+303
+00:22:32,750 --> 00:22:37,120
+اتعاملتوا معاهم سابقا هي ال Phiأو المجموعة الخالية
+
+304
+00:22:37,120 --> 00:22:40,440
+أو ال empty set أو ال null ال null اللي هي nothing
+
+305
+00:22:40,440 --> 00:22:44,680
+اللي هي zero مصفرة يعني مافيش إلها قيمة فهذه
+
+306
+00:22:44,680 --> 00:22:49,100
+unique set هذه حالة فريدة من حالات المجموعات واللي
+
+307
+00:22:49,100 --> 00:22:54,080
+تحتوي على no elements بغض النظرمهما كان، يعني مهما
+
+308
+00:22:54,080 --> 00:22:57,340
+كانت ال universe of discourse تبعك، هي عناصر، هي
+
+309
+00:22:57,340 --> 00:23:02,660
+أرقام، هي أشخاص، هي أسماء، بغض النظر إيش نوحة، بس
+
+310
+00:23:02,660 --> 00:23:06,400
+هي no elements، no elements بمعنى في هي عبارة عن
+
+311
+00:23:06,400 --> 00:23:11,820
+مجموعة فاضية، عشان انك اسمها مجموعة خالية braces
+
+312
+00:23:11,820 --> 00:23:14,400
+لازم نحط ال braces لأن ال braces هاد اللي بتعطيني
+
+313
+00:23:14,400 --> 00:23:18,500
+التعريف الأساسي اللي هو بقول منه set كلمة set
+
+314
+00:23:18,500 --> 00:23:22,120
+بفهمها على طول من ال braces هدولاللي هو ال curly
+
+315
+00:23:22,120 --> 00:23:25,400
+braces بمجرد ما بشوفهم بقول إن أنا بتكلم عن مجموعة
+
+316
+00:23:25,400 --> 00:23:28,540
+طيب إيش فيه جواها صفر nothing خالية فإذا بقول
+
+317
+00:23:28,540 --> 00:23:32,980
+مجموعة خالية تمام فدا يابد إنك تكتبها بتسيبهاش
+
+318
+00:23:32,980 --> 00:23:36,160
+فاضية ما تسيبهاش فاضية لإنه مش حافظ إن أنت بتتكلم
+
+319
+00:23:36,160 --> 00:23:38,360
+عن element ولا بتتكلم عن function ولا بتتكلم عن
+
+320
+00:23:38,360 --> 00:23:42,100
+إيش بالظبط لما تحطلي ال curly braces بفرن تتكلم عن
+
+321
+00:23:42,100 --> 00:23:49,280
+set لأ هذه مافيش صفر أصلاالصفر element هيقولك
+
+322
+00:23:49,280 --> 00:23:53,180
+الصفر هو element بحد ذاته هنا مالفش الصفر قيمة
+
+323
+00:23:53,180 --> 00:23:56,940
+الصفر نفسه عشان تقول والله بدي احط صفر انت هنا
+
+324
+00:23:56,940 --> 00:24:01,160
+حطيت فعليا قيمة و ال set هنا أصبح تحتوي على one
+
+325
+00:24:01,160 --> 00:24:05,420
+element لأ هي فعليا لا تحتوي حتى على الصفر لا
+
+326
+00:24:05,420 --> 00:24:10,800
+تحتويأيوة الصفر الخوارزمي جالنا انه قيمة ان هو
+
+327
+00:24:10,800 --> 00:24:15,160
+object بحد ذاته الصفر object بحد ذاته ولو لأنه
+
+328
+00:24:15,160 --> 00:24:17,420
+object بحد ذاته كان مااختراعناش كل هالاختراعات
+
+329
+00:24:17,420 --> 00:24:20,880
+اللي أوصلناها الأيام هذه فلو الخوارزمي باختراع ال
+
+330
+00:24:20,880 --> 00:24:25,120
+zero تبعه كان ماوصلنا للي احنا فيه من علوم ايش
+
+331
+00:24:25,120 --> 00:24:28,700
+مديش اقولك الرياضيات من علوم الحاسوب من اختراع
+
+332
+00:24:28,700 --> 00:24:34,860
+الحاسوب نفسه طيب فهي عبارة عن set تحتوي على x و x
+
+333
+00:24:34,860 --> 00:24:41,310
+false يعني مافيش xX false لا يوجد X فإذا no matter
+
+334
+00:24:41,310 --> 00:24:44,690
+the domain of this course بغض النظر إيش ال domain
+
+335
+00:24:44,690 --> 00:24:48,130
+أو إيش المجال اللي أنا بتكلم عنه لفضاء العينة أنا
+
+336
+00:24:48,130 --> 00:24:52,750
+قلتلكوا عناصر العناصر هذه إيش أرقام أسماء أشخاص
+
+337
+00:24:52,750 --> 00:24:59,140
+تفرجش بغض النظر الشيية we have the axiomمسلمة
+
+338
+00:24:59,140 --> 00:25:05,000
+عندنا شيئ بديهي انه there is no exist x, x belong
+
+339
+00:25:05,000 --> 00:25:10,600
+to phi لا يوجد x لا يوجد عنصر ينتمي للمجموعة في
+
+340
+00:25:10,600 --> 00:25:18,080
+ولا الصفر لانه صفر عنصر تمام اه تمام الآن بدأنا في
+
+341
+00:25:18,080 --> 00:25:23,970
+علامة جديدة S واعطاني هال notation هذي قداميو جالي
+
+342
+00:25:23,970 --> 00:25:28,510
+T لاحظ أول شغلة هنا تقري لما كنا بنتكلم عن X
+
+343
+00:25:28,510 --> 00:25:37,310
+belonged to S مثلا هنا كانت small يعني element هنا
+
+344
+00:25:37,310 --> 00:25:41,370
+كانت belonged to تستخدم لل elements فقط هنا كانت
+
+345
+00:25:41,370 --> 00:25:45,630
+capital في هذه معروفة أنها set الآن أنا بتكلم عن
+
+346
+00:25:45,630 --> 00:25:51,510
+capital relation مع capitalset و set الاتنين هم
+
+347
+00:25:51,510 --> 00:25:56,690
+عبارة عن two sets طيب ضالت ال notation اللي بينهم
+
+348
+00:25:56,690 --> 00:26:01,070
+ال notation اللي بينهم فقط لتمييز المجموعات لتمييز
+
+349
+00:26:01,070 --> 00:26:05,850
+المجموعات لكن هي بتخيلها تماما زي أصغر أو يساوي
+
+350
+00:26:05,850 --> 00:26:11,650
+لحظ لو غيرتها شوية هيك صارت ايش كأنه أصغر أو يساوي
+
+351
+00:26:11,650 --> 00:26:15,970
+بس للمجموعات فعشان نميزها للمجموعات لإن نعطيها
+
+352
+00:26:15,970 --> 00:26:20,280
+شوية ال curve بتاعتهابحيث ان انا عارف ان ما قبلها
+
+353
+00:26:20,280 --> 00:26:25,220
+هيكون اصغر او يساوي مابعدها فهي عبارة عن set تحتوي
+
+354
+00:26:25,220 --> 00:26:31,620
+على عناصر كل هذه العناصر موجودة في ال set T و بس و
+
+355
+00:26:31,620 --> 00:26:37,670
+بسكت طب هل العكس صحيح؟ لألأ ليس بضروري، فإذا أصغر
+
+356
+00:26:37,670 --> 00:26:43,810
+منها أو تساويها، فبنسميها subset أو مجموعة جزئية،
+
+357
+00:26:43,810 --> 00:26:48,390
+مجموعة جزئية منها فهذا معناه إنه كل ال elements of
+
+358
+00:26:48,390 --> 00:26:54,730
+S هو عبارة عن elements of T، بنسميها S subset of T
+
+359
+00:26:54,730 --> 00:26:59,110
+تمام؟ كويس، هذا if and only if، for all X، X
+
+360
+00:26:59,110 --> 00:27:04,820
+belong to S، مش if and only ifemployees that
+
+361
+00:27:04,820 --> 00:27:10,460
+بيضمننا ان X هي تنتمي ل T العكس مش بالضروري و ليس
+
+362
+00:27:10,460 --> 00:27:16,640
+صحيحا فاي هي subset من كل المجموعات التانية هي فاي
+
+363
+00:27:16,640 --> 00:27:21,080
+فعليا هي subset من اي مجموعة اخرى اي مجموعة هي
+
+364
+00:27:21,080 --> 00:27:25,340
+subset من نفسها subset ليش لأنه لاحظ في عالم او
+
+365
+00:27:25,340 --> 00:27:31,620
+يساويأو يساوي هنا subset معناته أنها أصغر منها أو
+
+366
+00:27:31,620 --> 00:27:38,660
+تساويها فمعنى ذلك أن كل مجموعة هي تساوي نفسها فهي
+
+367
+00:27:38,660 --> 00:27:44,390
+subset من نفسهاالعكس تبعها super set و لاحظ
+
+368
+00:27:44,390 --> 00:27:47,290
+العلامة كأنها أكبر منه فهي الفتحة تعادت دائما
+
+369
+00:27:47,290 --> 00:27:50,510
+بتروح مع الأكبر مع الأكبر معناته ال S هنا هي
+
+370
+00:27:50,510 --> 00:27:54,770
+الأكبر بتسميها هنا super set اسمها super set of T
+
+371
+00:27:54,770 --> 00:27:58,410
+بمعنى
+
+372
+00:27:58,410 --> 00:28:02,510
+أنه العكس صحيح الآن كل عنصر موجود في T هو موجود في
+
+373
+00:28:02,510 --> 00:28:08,880
+S والعكس مش بالضروري العكسT جزئية من S بالظبط
+
+374
+00:28:08,880 --> 00:28:13,300
+دايما الأصغر هي اللي ماخدة بوز الأصغر من أو الأكبر
+
+375
+00:28:13,300 --> 00:28:16,640
+من زي الأرقام العادية انت تخيلها بالظبط زي الأرقام
+
+376
+00:28:16,640 --> 00:28:20,400
+العادية لكن ماخدة ال curve عشان نميز مجموعات و ليس
+
+377
+00:28:20,400 --> 00:28:24,240
+أرقام عشان نميزها كمجموعات و ليس أرقام فنفس الفكرة
+
+378
+00:28:24,240 --> 00:28:27,520
+اللي كانت في ال elements هي هي نفسها في ال sets
+
+379
+00:28:27,520 --> 00:28:33,380
+طيب هذا بيقودنا لشغلة ان S ممكن اقول ان هي تساوي T
+
+380
+00:28:33,380 --> 00:28:36,520
+if and only if كل واحدة منهم هي subset من التانية
+
+381
+00:28:37,940 --> 00:28:41,980
+هي subset من التانية تمام؟ ليش؟ لأنه بيظل العامل
+
+382
+00:28:41,980 --> 00:28:46,180
+المشترك بين الأكبر من و الأصغر من هي أو يساوي فإذا
+
+383
+00:28:46,180 --> 00:28:49,520
+كانت تحقق الأكبر من أو يساوي و الأصغر من أو يساوي
+
+384
+00:28:49,520 --> 00:28:53,520
+أكيد معناته اللي يساوي هو اللي عمل التحقق هذا لأنه
+
+385
+00:28:53,520 --> 00:28:57,020
+مستحيل يكون أكبر من و أصغر من في نفس الوقت لكن
+
+386
+00:28:57,020 --> 00:28:59,520
+أكبر من أو يساوي و أصغر من أو يساوي تحقق معناته
+
+387
+00:28:59,520 --> 00:29:02,960
+اللي يساوي هي اللي شبكت بينهم فإذا اليساوي وهذا
+
+388
+00:29:02,960 --> 00:29:08,050
+and فإذا هما فعلا بيساووا بعضهذه نقطة مهمة جدا حتى
+
+389
+00:29:08,050 --> 00:29:11,530
+لاحقا نبدنا نكتشف هل ال two sets هذول بيساوي بعض
+
+390
+00:29:11,530 --> 00:29:15,830
+ولا لأ كل اللي بنقدر نعمله كإثبات أن نحاول نثبت أن
+
+391
+00:29:15,830 --> 00:29:19,710
+كل من هما هي subset من التانية إذا كان قدرنا نوصل
+
+392
+00:29:19,710 --> 00:29:24,040
+أن الأولى subset من التانيةوالتانية subset من
+
+393
+00:29:24,040 --> 00:29:28,700
+الأولى فمعنى ذلك انه بيساووا بعض بيساووا بعض طيب
+
+394
+00:29:28,700 --> 00:29:32,180
+نفس اللي قلنا not belong في بقى هندي belong وفي
+
+395
+00:29:32,180 --> 00:29:38,260
+هنا not belong نفس الكلام في not subset لما نقول S
+
+396
+00:29:38,260 --> 00:29:43,520
+is not subset of T معناه انه negation انه S subset
+
+397
+00:29:43,520 --> 00:29:48,840
+of T ايش معناه؟ معناته يوجد عنصر موجود في S و غير
+
+398
+00:29:48,840 --> 00:29:53,760
+موجود في Tو غير موجود في T لأن احنا التعريف تبع ال
+
+399
+00:29:53,760 --> 00:29:58,180
+subset كان ان كل العناصر في S هي موجودة في T
+
+400
+00:29:58,180 --> 00:30:03,420
+معناته لو وجد واحد على الأقل موجود في S و غير
+
+401
+00:30:03,420 --> 00:30:08,140
+موجود في T فهي not subset not subset فإذا there
+
+402
+00:30:08,140 --> 00:30:15,260
+exist X X ينتمي ل S و لا ينتمي ل T يكفي أنصر يكفي
+
+403
+00:30:15,260 --> 00:30:18,700
+أنصر عشان ينفلنا ال subset notation
+
+404
+00:30:22,700 --> 00:30:29,660
+Popare أو Struct إلزامي الإلزام لل subset إلزام
+
+405
+00:30:29,660 --> 00:30:34,060
+المجموعة الجزئية معناته هي ضلت زي بالظبط أصغر من
+
+406
+00:30:34,060 --> 00:30:40,500
+أو يساوي ولا أصغر من بس فلاحظ أخدت الأصغر من بس
+
+407
+00:30:40,500 --> 00:30:47,860
+فهي إلزامامجموعة جزئية و لا تساوي واضحة؟ أيه الفرق
+
+408
+00:30:47,860 --> 00:30:51,460
+الوحيد في علامة أو يساوي اللي تحت كانت موجودة هذه
+
+409
+00:30:51,460 --> 00:30:56,160
+الفرقة الوحيد فهنا S إجبارا هي هتكون أقل من T
+
+410
+00:30:56,160 --> 00:31:06,260
+اختلف
+
+411
+00:31:06,260 --> 00:31:10,100
+مفاهيم تماما هداك علم و احنا في علم تاني اختلاف
+
+412
+00:31:10,100 --> 00:31:14,600
+علوم لما نتكلم في هديك ممكننشرح و نفتح و نحاول
+
+413
+00:31:14,600 --> 00:31:17,140
+نفهم ايش هي ال notation بالظبط دي بس احنا الآن في
+
+414
+00:31:17,140 --> 00:31:19,720
+علم تماما مختلف عن ال probability و عشان هيك من
+
+415
+00:31:19,720 --> 00:31:22,620
+أول ما بدأنا يمكن لو متذكرين في أول محاضرة قلتلكوا
+
+416
+00:31:22,620 --> 00:31:25,420
+احنا مش هنتكلم عن ال probability اطلاقا حتى لو
+
+417
+00:31:25,420 --> 00:31:29,080
+تطرقنا لها فتأكدوا ان هي مش probability هي
+
+418
+00:31:29,080 --> 00:31:34,660
+possibilities هي possibilities هدفي ما يخص منهجنا
+
+419
+00:31:34,660 --> 00:31:40,580
+كلها possibilities إمكانية حدوث و ليس احتمال حدوث
+
+420
+00:31:40,580 --> 00:31:43,840
+أنا ماتكلمش عن احتمالاتلان نتكلم عن احتمالات ..
+
+421
+00:31:43,840 --> 00:31:47,160
+امكانية حدوث مجموعة معينة من مجموعة أكبر وهذا
+
+422
+00:31:47,160 --> 00:31:51,540
+الكلام هتفتح لنا يه ال six علم ال six اللي لاحقا
+
+423
+00:31:51,540 --> 00:31:54,980
+لما نيجي نتكلم بعد هيك على التبديل و التوافق اه
+
+424
+00:31:54,980 --> 00:31:57,940
+موجود معانا لان التبديل و التوافق شوية مفهومة
+
+425
+00:31:57,940 --> 00:32:01,980
+مختلفة عن ال probability فهنتعامل معها .. القصة
+
+426
+00:32:01,980 --> 00:32:04,900
+التانية ممكن نشوفها لاحقا أفهم بس ايش ال notation
+
+427
+00:32:04,900 --> 00:32:07,800
+اللي موجودة في ال probability ممكن خارج المصدق
+
+428
+00:32:07,800 --> 00:32:13,370
+نتعامل معاها نتكلم فيها ان شاء اللهفهنا strictly
+
+429
+00:32:13,370 --> 00:32:22,530
+أو proper subset of T معناها أن S subset of T ولكن
+
+430
+00:32:22,530 --> 00:32:28,810
+T ليست subset of S بيسووش بعض في الآخر يعني في
+
+431
+00:32:28,810 --> 00:32:32,970
+النهاية لا يسووا بعض فنفس الفكرة برضه بقدر أقول أن
+
+432
+00:32:32,970 --> 00:32:40,370
+S proper superset فإذا S هي أكبر أو هي تشمل T ولا
+
+433
+00:32:40,370 --> 00:32:45,020
+تسويهاهي تشمل كل عناصر T و لا تسويها فإذا على
+
+434
+00:32:45,020 --> 00:32:49,620
+الأقل يوجد عنصر ازيادة عندها على الأقل على الأقل
+
+435
+00:32:49,620 --> 00:32:53,260
+زي الحالة اللي نسميها الرسمين ال vein diagram لها
+
+436
+00:32:53,260 --> 00:32:58,860
+لما اقول في عندي واحد و اتنين و ست ست واحد و اتنين
+
+437
+00:32:58,860 --> 00:33:05,360
+هي أكيد prepare أو strictly subset من واحد و اتنين
+
+438
+00:33:05,360 --> 00:33:10,430
+و تلاتة أكيدأكيد فحتى بال Venn diagram واضحة تماما
+
+439
+00:33:10,430 --> 00:33:16,810
+ال S هتكون مشمولة بالكامل داخل ال T مشمولة بالكامل
+
+440
+00:33:16,810 --> 00:33:21,170
+داخل ال T ولا تساويها ولا تساويها هذا ال Venn
+
+441
+00:33:21,170 --> 00:33:25,410
+diagram اللي ممكن يوضح لنا ال Structural أو ال
+
+442
+00:33:25,410 --> 00:33:32,530
+prepare subset تمام الآن ال ال set as a object ال
+
+443
+00:33:32,530 --> 00:33:35,050
+set نفسها هل ممكن تكون object او ممكن تكون object
+
+444
+00:33:35,050 --> 00:33:42,470
+بمعنى لما اقولالست لكلية الهندسة هي بالنسبة لباقي
+
+445
+00:33:42,470 --> 00:33:46,270
+الطلاب لباقي طلاب الجامعة هي مجموعة طلاب كلية
+
+446
+00:33:46,270 --> 00:33:51,480
+الهندسة لكن هي نفسها عبارة عن مجموعات مجسمة جوافكل
+
+447
+00:33:51,480 --> 00:33:55,740
+مجموعة هو element داخل مجموعة كلية الهندسة element
+
+448
+00:33:55,740 --> 00:34:00,040
+داخل مجموعة كلية الهندسة واضحيت؟ فإذا ممكن أقول في
+
+449
+00:34:00,040 --> 00:34:02,440
+الآخر هذه الهندسة .. هذه المجموعة الطلاب الهندسة
+
+450
+00:34:02,440 --> 00:34:05,640
+ال .. الهندسة الحسوب الهندسة المدنية الهندسة
+
+451
+00:34:05,640 --> 00:34:09,330
+المعمارية and so onانكمل كل المجموعات طيب داخل نفس
+
+452
+00:34:09,330 --> 00:34:12,610
+المجموع اجسمهم حسب ال level هذا مازال في ال level
+
+453
+00:34:12,610 --> 00:34:15,310
+الأول هذا في ال level التاني هذا في الخامس و هكذا
+
+454
+00:34:15,310 --> 00:34:20,250
+حسب طبعا عدد الساعات اللي مخلصهم كويس فإذا هو نفسه
+
+455
+00:34:20,250 --> 00:34:25,270
+نفسها كمجموعة ممكن اتعامل معاها as a element فممكن
+
+456
+00:34:25,270 --> 00:34:30,450
+نقول والله S هنا هي نفسها زي ما قلنا S هنا ممكن
+
+457
+00:34:30,450 --> 00:34:38,230
+تكون هي ال 6of x كتبناها small بمعنى element بحيث
+
+458
+00:34:38,230 --> 00:34:43,190
+ان ال element هذا اه شوف ايش كتبناه subset طب انا
+
+459
+00:34:43,190 --> 00:34:47,190
+عارف ان ال subset للمجموعاتمش هيك؟ احنا بنعرف انه
+
+460
+00:34:47,190 --> 00:34:50,850
+ال subset للمجموعات فإذا كأنه بده يقول إن ال
+
+461
+00:34:50,850 --> 00:34:56,490
+element هذا هو بالأساس مجموعة داخل المجموعة S طيب
+
+462
+00:34:56,490 --> 00:35:01,550
+المجموعة هذه عبارة عن إيش؟ عبارة عن subset من واحد
+
+463
+00:35:01,550 --> 00:35:04,650
+اتنين تلاتة معناته الآن بتتخيل أن ال S هذه أي
+
+464
+00:35:04,650 --> 00:35:07,790
+مجموعة قد تصلح ان هي تكون subset من واحد اتنين
+
+465
+00:35:07,790 --> 00:35:12,600
+تلاتة في؟ اه في بمش الحلواحد اه بمشي الحال واحد
+
+466
+00:35:12,600 --> 00:35:15,440
+واحد و اتنين بمشي الحال واحد و تلاتة بمشي الحال
+
+467
+00:35:15,440 --> 00:35:18,440
+اتنين و تلاتة بمشي الحال اتنين لحالها بمشي الحال
+
+468
+00:35:18,440 --> 00:35:20,680
+تلاتة لحالها بمشي الحال واحد و اتنين تلاتة نفسها
+
+469
+00:35:20,680 --> 00:35:26,500
+بمشي الحال لأنه او يساوي لاحظت ف S هنا معناته ممكن
+
+470
+00:35:26,500 --> 00:35:34,640
+تاخد set of مجموعة sets دروها كأنه كل set داخلها
+
+471
+00:35:34,640 --> 00:35:38,680
+هو كأنه element بالنسبة لها صحيح هو مجموعة بالنسبة
+
+472
+00:35:38,680 --> 00:35:44,640
+لل elements تبعتهنفسها زي لما أقول الله هي طلاب
+
+473
+00:35:44,640 --> 00:35:48,820
+هندسة الحسوب طيب في الآخر طلاب هندسة الحسوب ممكن
+
+474
+00:35:48,820 --> 00:35:52,000
+أصنفهم المستوى الأول والتاني والتالت والرابع and
+
+475
+00:35:52,000 --> 00:35:56,260
+so on طيب كل مستوى هحطه داخل مجموعة رغم أنه
+
+476
+00:35:56,260 --> 00:36:02,720
+كمجموعة هي عنصر داخل مجموعة هندسة الحسوب أو طلاب
+
+477
+00:36:02,720 --> 00:36:08,190
+هندسة الحسوب ككلبهذا الشكل ممكن نقول أنه ال set هي
+
+478
+00:36:08,190 --> 00:36:14,510
+sub هي element داخل set أكبر منها لما نقول الآن في
+
+479
+00:36:14,510 --> 00:36:21,010
+الحالة هذه واحد أكيد لا تساوي set تحتوي على العنصر
+
+480
+00:36:21,010 --> 00:36:28,290
+واحد هذه واحد element لحالههنا لأ هذه set تحتوي
+
+481
+00:36:28,290 --> 00:36:33,250
+على العنصر واحد، طيب هنا لاتساوي برضه set تحتوي
+
+482
+00:36:33,250 --> 00:36:38,950
+على set فإذا ال set هذه ليست ال set هذه، هذه set
+
+483
+00:36:38,950 --> 00:36:42,810
+تحتوي على element بس، عنصر، هذه لأ ال set تحتوي
+
+484
+00:36:42,810 --> 00:36:47,560
+على set أخرىتمام؟ بغض النظر إيش اللي جوا ال set
+
+485
+00:36:47,560 --> 00:36:52,100
+الأخرى لإنه هنا صارت كأنه بدي أقول هذه ال set خلاص
+
+486
+00:36:52,100 --> 00:36:55,060
+هي نعرفناها هي ال set هل ال elements اللي جوا
+
+487
+00:36:55,060 --> 00:36:57,780
+بيسووا بعض؟ لأ ما احنا رجعناها إن ال element هو
+
+488
+00:36:57,780 --> 00:37:00,160
+element داخل ال set أما هذه ال set داخل ال set
+
+489
+00:37:00,160 --> 00:37:06,500
+بيسووش بعض كيف؟
+
+490
+00:37:06,500 --> 00:37:15,140
+أه تنتمي لل set الأكبر اللي هي هذه كاملة على بعض
+
+491
+00:37:16,850 --> 00:37:23,070
+بهذا الشكل بس بدها تكون واضحة انه هي subset من اشي
+
+492
+00:37:23,070 --> 00:37:27,490
+تاني طبعا
+
+493
+00:37:27,490 --> 00:37:32,370
+لا تساوي هو مسواش بالعكس هو ما ساوى هو بالعكس
+
+494
+00:37:32,370 --> 00:37:36,670
+بيقولك لا تساوي هو بيقولك يعني الكتاب بيقولك انت
+
+495
+00:37:36,670 --> 00:37:42,450
+لا تساوي answer بمجموعة فلأ هو ما ساوى اطلاقاأي
+
+496
+00:37:42,450 --> 00:37:46,090
+واحد مثلا جزء ات جزء من المجموعة التالتة او اي
+
+497
+00:37:46,090 --> 00:37:51,390
+واحد .. اي واحد الأول هو ولا إله أي علاقة بأي بن
+
+498
+00:37:51,390 --> 00:37:56,050
+اللي باجي ولا إله أي علاقة ولا بأي حالة من الحالات
+
+499
+00:37:56,050 --> 00:38:00,670
+مالوش علاقة علاقته الوحيدة أني أقدر أقول هنا أنه
+
+500
+00:38:00,670 --> 00:38:06,710
+واحد belong to واحد بس هي علاقته أما لا يساوي
+
+501
+00:38:06,710 --> 00:38:11,010
+للتالتة
+
+502
+00:38:11,010 --> 00:38:16,700
+أكيد لأاطلاقا أكيد لأ عارف أنت بنفع في حالة واحدة
+
+503
+00:38:16,700 --> 00:38:23,180
+إذا كانت المجموعة بهذا الشكل و واحد أما هي مش هيك
+
+504
+00:38:23,180 --> 00:38:30,220
+ففكرة أني أقول واحد ينتمي إلى هذه أه صح لكن أشيله
+
+505
+00:38:30,220 --> 00:38:38,660
+لأ not belongلازم تكون equal فعلا هو بيسوي حقيقة
+
+506
+00:38:38,660 --> 00:38:42,480
+distinct element تمام
+
+507
+00:38:48,010 --> 00:38:52,610
+الـ cardinality في حاجة اسمها cardinality والعلامة
+
+508
+00:38:52,610 --> 00:38:54,850
+بتاعتها عاملة زي ال absolute absolute معناته
+
+509
+00:38:54,850 --> 00:39:00,250
+القيمة المطلقة مش هيك لما احطها ل مجموعة احنا
+
+510
+00:39:00,250 --> 00:39:02,550
+عارفين ان المجموعة هذه مافيش مجموعة بالسالب
+
+511
+00:39:02,550 --> 00:39:07,190
+فالقيمة المطلقة هنا في ال elements كنت بتقول انه
+
+512
+00:39:07,190 --> 00:39:11,430
+موجب او سالب بحطها موجب صح بتحطوا القيمة الإيجابية
+
+513
+00:39:11,430 --> 00:39:15,570
+لهافي الـ 6 مافيش حاجة اسمها القيمة الإيجابية لأنه
+
+514
+00:39:15,570 --> 00:39:21,250
+أصغر مجموعة هي الـ Phi Zero مافيش إيش بالسلب فمعنى
+
+515
+00:39:21,250 --> 00:39:24,870
+ذلك أنه لما أشوف الـ Absolute هذه بسميها
+
+516
+00:39:24,870 --> 00:39:29,870
+Cardinality of S Cardinality of S ما معناته S أجدش
+
+517
+00:39:29,870 --> 00:39:36,310
+عدد العناصر داخلها أجدش عدد عناصر S هي معناها فإذا
+
+518
+00:39:36,310 --> 00:39:42,030
+نقرأها Cardinality of Sكويس؟ وهذه بتقص لنا how
+
+519
+00:39:42,030 --> 00:39:46,950
+many different elements in 6S كويس؟ يعني لما نقول
+
+520
+00:39:46,950 --> 00:39:51,110
+absolute او cardinality of five، zero طيب
+
+521
+00:39:51,110 --> 00:39:54,890
+cardinality of one, two, three، تلاتة طيب
+
+522
+00:39:54,890 --> 00:39:58,770
+cardinality of a و b، اتنين طيب cardinality of
+
+523
+00:39:58,770 --> 00:40:04,090
+اتنين اكيد اتنين ليش؟ انا قاعد بقول ال cardinality
+
+524
+00:40:04,090 --> 00:40:08,430
+لمين؟ لأول curly braces هيجابله، اللي هو هذا
+
+525
+00:40:11,560 --> 00:40:18,340
+داخل هذا الكلام فعليا يوجد عنصرين بس، العنصرين
+
+526
+00:40:18,340 --> 00:40:21,560
+هدولأ مجموعات، أنا معاك، صح مجموعات، بس هم في
+
+527
+00:40:21,560 --> 00:40:25,100
+النهاية للمجموعة اللي أنا عامل عليها ال
+
+528
+00:40:25,100 --> 00:40:31,070
+cardinality هم عنصرين، إيه جوا هم ماليش علاقة؟لما
+
+529
+00:40:31,070 --> 00:40:35,850
+تيجي اقولك دي قداش عدد ال levels المستويات في كلية
+
+530
+00:40:35,850 --> 00:40:39,030
+الهندسة هتقوللي خمسة مش هتقوللي تقعد تفسرلي جوه
+
+531
+00:40:39,030 --> 00:40:41,370
+ايش فيهم مساقات و ايش فيهم مش عارفش و ايش فيهم مش
+
+532
+00:40:41,370 --> 00:40:45,010
+عارفش انا ماقلهم علاقة اللي جوه انا بتكلم عن اللي
+
+533
+00:40:45,010 --> 00:40:53,250
+برا خلاص ففعليا واحد اتنين بس خلصت تمام الله مصلح
+
+534
+00:40:53,250 --> 00:40:56,570
+على سنة محمد طيب اذا كانت ال cardinality تنتمي لل
+
+535
+00:40:56,570 --> 00:41:02,670
+natural number بمعنى هي عددصحيح أو عدد طبيعي هو
+
+536
+00:41:02,670 --> 00:41:06,450
+فعليا أمره ماحتكون بالسالب، منطقي يعني، هي عدد
+
+537
+00:41:06,450 --> 00:41:11,270
+موجب وصحيح، natural number، عدد طبيعي، فبنقدر نقول
+
+538
+00:41:11,270 --> 00:41:16,750
+أن الـS هي finite، بمعنى محددة، بمعنى محددة،
+
+539
+00:41:16,750 --> 00:41:20,690
+otherwise بنسميها infinite، لانهائية، طيب، هو في
+
+540
+00:41:20,690 --> 00:41:23,650
+فعلا في cardinality ممكن تسأل إنها تكون infinite؟
+
+541
+00:41:25,230 --> 00:41:28,970
+أكيد زي هي نفس ال natural number هي نفس ال
+
+542
+00:41:28,970 --> 00:41:32,630
+integers هي نفس ال real اللي اتكلمنا عنهم قبل شوية
+
+543
+00:41:32,630 --> 00:41:38,370
+حطلهم cardinality جدش عددهم undefined طيب
+
+544
+00:41:38,370 --> 00:41:41,110
+undefined حتى لل natural number هي لا تنتمي لل
+
+545
+00:41:41,110 --> 00:41:46,270
+natural number يعني أنا ماقدرش أحددها كعدد كعدد مش
+
+546
+00:41:46,270 --> 00:41:49,510
+قادر أحددها فإذا هي خارج ال ..الـ natural number
+
+547
+00:41:49,510 --> 00:41:54,190
+فإذا الـ natural number هي غير محددة ال z أو ال
+
+548
+00:41:54,190 --> 00:41:57,450
+integers غير محددة و ال real numbers برضه غير
+
+549
+00:41:57,450 --> 00:42:05,230
+محددة كمجموعة تمام ال power of sets أو جداش نتكلم
+
+550
+00:42:05,230 --> 00:42:09,850
+عن ال P of S و ال P of S هذه لما أقول ال power of
+
+551
+00:42:09,850 --> 00:42:14,430
+S معناته كل المجموعات اللي ممكن تكون جزئية من ال
+
+552
+00:42:14,430 --> 00:42:21,490
+setجميع المجموعات الجزئية من الست S فبنسميها P of
+
+553
+00:42:21,490 --> 00:42:27,910
+S فإذا هنا ال element لل function هذه هي ست و ليست
+
+554
+00:42:27,910 --> 00:42:35,710
+element واحد لحاله فإذا Sلازم تكون set ليش؟ لأن
+
+555
+00:42:35,710 --> 00:42:41,210
+مفهوم ال power of set ان كل ال elements .. كل ال
+
+556
+00:42:41,210 --> 00:42:45,770
+subsets من ال set هذه كل ال subsets من ال set هذه
+
+557
+00:42:45,770 --> 00:42:52,730
+فكل ال subsets of S ف P of S هي عبارة عن .. فتحنا
+
+558
+00:42:52,730 --> 00:42:59,670
+أقواص ال curly يعني هي نفسها هتكون setفال power of
+
+559
+00:42:59,670 --> 00:43:04,730
+set هي بحد ذاتها set هي مجموعة بس تحتوي على إيش؟
+
+560
+00:43:04,730 --> 00:43:08,890
+على عناصر طيب العناصر هذه عبارة عن إيش؟ عبارة عن
+
+561
+00:43:08,890 --> 00:43:16,190
+sets كيف عرفت؟ في بعضها ال subset ال subset بتاخدش
+
+562
+00:43:16,190 --> 00:43:20,190
+element قبلها بتاخد مجموعة فإذن هي عبارة عن
+
+563
+00:43:20,190 --> 00:43:29,440
+مجموعات جزئية من S من S فلما أقول P ofونحط
+
+564
+00:43:29,440 --> 00:43:34,620
+المجموعة A وB هتكون كل المجموعات الجزئية من ال set
+
+565
+00:43:34,620 --> 00:43:40,240
+A وB ابتدائها من فاي ثم هي نفسها A وB ثم A لحال وB
+
+566
+00:43:40,240 --> 00:43:45,960
+لحال صاروا أربعة وعشان هي أحيانا كتير بيسموها بدل
+
+567
+00:43:45,960 --> 00:43:51,360
+ما هي P of S بيسموها from A to the power Spower
+
+568
+00:43:51,360 --> 00:43:56,220
+على اعتبار انه اصلا هي اسمها power power لالها فمش
+
+569
+00:43:56,220 --> 00:44:00,520
+معنى الاتنين لأن ال cardinality بتظهر هنا ال
+
+570
+00:44:00,520 --> 00:44:05,280
+cardinality لل power هي عبارة عن ال cardinality او
+
+571
+00:44:05,280 --> 00:44:09,500
+اتنين to the power ال cardinality لل S نفسها ال S
+
+572
+00:44:09,500 --> 00:44:12,240
+نفسها كانت ال cardinality بتاعتها اتنين فال power
+
+573
+00:44:12,240 --> 00:44:16,660
+بتاعتها هتكون اتنين to the power ال اتنين هتكون
+
+574
+00:44:16,660 --> 00:44:20,630
+اربعة و احنا قاعدين هيعدنهم اربعةعدناهم أربعة فإذا
+
+575
+00:44:20,630 --> 00:44:24,430
+بيسموها كتير اتنين to the power of S فهي ال power
+
+576
+00:44:24,430 --> 00:44:28,750
+S ال power S ال power 6 كويس cardinality بتاعتها
+
+577
+00:44:28,750 --> 00:44:33,030
+برضه اتنين to the power ال cardinality لا ال 6
+
+578
+00:44:33,030 --> 00:44:39,210
+نفسها ال 6 نفسها طيب وهذا اكيد بيقودنا انه ال
+
+579
+00:44:39,210 --> 00:44:46,760
+cardinality ل P ofnatural number هيكون أكبر من ال
+
+580
+00:44:46,760 --> 00:44:51,800
+cardinality لل natural number منطقي أي عنصر طبيعي
+
+581
+00:44:51,800 --> 00:44:54,780
+.. أي عنصر طبيعي إذا كان ال cardinality هنا اتنين
+
+582
+00:44:54,780 --> 00:45:00,200
+فال power بتاعت set of two elements طلعت أربعة
+
+583
+00:45:00,200 --> 00:45:04,860
+أكيد هتكون أكبر و قص على ذلك .. و قص على ذلك هتكون
+
+584
+00:45:04,860 --> 00:45:07,680
+دايما أكبر منها
+
+585
+00:45:10,510 --> 00:45:15,270
+طيب اكيد برضه يوجد different sizes of infinite
+
+586
+00:45:15,270 --> 00:45:18,690
+sets و اتكلمنا الحالة الشهيرة ال natural number و
+
+587
+00:45:18,690 --> 00:45:25,410
+ال real number و ال integers okay ال ordered كل
+
+588
+00:45:25,410 --> 00:45:29,830
+اللي فات unordered صحيح؟ طيب لما بتقول ordered
+
+589
+00:45:29,830 --> 00:45:33,330
+اكيد معناه ذلك ان ال curly braces هدول بدك تشيلهم
+
+590
+00:45:35,870 --> 00:45:40,010
+تشيلهم و تستخدم الأقواص العادية عشان أفهم منك أن
+
+591
+00:45:40,010 --> 00:45:45,410
+انت بتتكلم عن زوج مرتب و زوج مرتب لما يكون two
+
+592
+00:45:45,410 --> 00:45:52,970
+elements بس أكتر من هيك بنسميه tuples بنعطيه كلمة
+
+593
+00:45:52,970 --> 00:45:59,030
+tuplesمش ثنائي زوج اتنين فقط لأ ممكن يكون اكتر زى
+
+594
+00:45:59,030 --> 00:46:02,690
+النقطة فى الفراغ ثلاثية الأبعاد الفراغ اللى بتشوفه
+
+595
+00:46:02,690 --> 00:46:06,910
+ال 3D طب هدى ثلاثية مقدرش يقول زوج مرتب مش هيك هدى
+
+596
+00:46:06,910 --> 00:46:14,750
+بنسميها لاحقا triples ثلاثية الرقم تمام وهى كدا قص
+
+597
+00:46:14,750 --> 00:46:18,730
+على ذلك فهى بتصير ordered in tuples in general in
+
+598
+00:46:18,730 --> 00:46:28,040
+tuplesتكرار اني in point او in إحداثي ومرتبين مرتب
+
+599
+00:46:28,040 --> 00:46:32,500
+فملتزمين كلمة مرتب هي فعلا زي ال sets بلكن ال
+
+600
+00:46:32,500 --> 00:46:36,100
+duplication ممكن ليش ال duplication ممكن لأن واحد
+
+601
+00:46:36,100 --> 00:46:41,560
+واحد حسب الترتيب مختلف عن set of element واحد واحد
+
+602
+00:46:41,560 --> 00:46:44,540
+set of element واحد واحد بختصرهم بقول هذا set of
+
+603
+00:46:44,540 --> 00:46:48,820
+element واحد بسلأنه عنصر واحد الموجود في المجموعة
+
+604
+00:46:51,610 --> 00:46:56,570
+لأ duplication ممكنة، duplication ممكنة بالعكس،
+
+605
+00:46:56,570 --> 00:47:01,430
+مهمة أصلا، مهمة لأنه بتوضح ليه جداش كل إحداثي من
+
+606
+00:47:01,430 --> 00:47:05,890
+الإحداثيات بتاعتها، وبناء على ذلك ممكن نقول إن هذا
+
+607
+00:47:05,890 --> 00:47:10,290
+ordered element،
+
+608
+00:47:10,290 --> 00:47:15,550
+كويس، فلو الطبيعي عشان تكون and doubles لازم ال
+
+609
+00:47:15,550 --> 00:47:19,750
+and هذه تكون ضمن ال natural number، هي عدد صحيح،
+
+610
+00:47:19,750 --> 00:47:24,270
+ومجبعشان أقول n tuples و عبارة عن sequence أو
+
+611
+00:47:24,270 --> 00:47:29,430
+بنسميها sequence of length n و بنكتبه a12 to an
+
+612
+00:47:29,430 --> 00:47:34,010
+إحداثي صارت إحداثيات و الإحداثيات هذه أكيد حققونا
+
+613
+00:47:34,010 --> 00:47:36,570
+أن واحد و اتنين هي لا تساوي اتنين واحد و ان انتوا
+
+614
+00:47:36,570 --> 00:47:39,730
+عارفينوا الكلام في الإحداثيات واحد اتنين لسه اتنين
+
+615
+00:47:39,730 --> 00:47:44,750
+واحد و لا تساوي اتنين واحدوحد تقول ما هي واحد واحد
+
+616
+00:47:44,750 --> 00:47:47,910
+ما انت مش قولت لأ لما كنا بنحط ال curly braces هنا
+
+617
+00:47:47,910 --> 00:47:52,310
+مش curly braces هدى إحدافي هنا ال empty sequence
+
+618
+00:47:52,310 --> 00:47:56,090
+بتسميه empty sequence بمعنى هو إحداثة nothing للفي
+
+619
+00:47:56,090 --> 00:48:00,670
+مقابل للفي sequence empty sequence وفي singlets
+
+620
+00:48:00,670 --> 00:48:06,140
+إحداثة منمن رقم واحد و في ال pairs اللي هم الثنائي
+
+621
+00:48:06,140 --> 00:48:13,280
+او الثنائي المرتب triples quadruples و quantables
+
+622
+00:48:13,280 --> 00:48:19,260
+و intables خلاص بحسب جدهش العدد ال elements داخل
+
+623
+00:48:19,260 --> 00:48:22,880
+الإحداث اللي موجود عندكم المرة الجاية بدنا نشوف
+
+624
+00:48:22,880 --> 00:48:26,360
+إيش بدنا نستفيد من فكرة الإحداث و إيش علاقتها بال
+
+625
+00:48:26,360 --> 00:48:28,700
+sets اللي احنا كنا بدين فيها أصلا احنا بدأنا
+
+626
+00:48:28,700 --> 00:48:30,780
+كلامنا sets إيش اللي نجلنا مرة واحدة على
+
+627
+00:48:30,780 --> 00:48:34,070
+الإحدافياتالمرة الجاية ان شاء الله بكمل كلامنا عن
+
+628
+00:48:34,070 --> 00:48:34,490
+الموضوع
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/QkhqcRfm9Hs_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/QkhqcRfm9Hs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5474ce39c294ca64312c772324c24853c26d4845
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/QkhqcRfm9Hs_postprocess.srt
@@ -0,0 +1,2420 @@
+1
+00:00:05,030 --> 00:00:07,430
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:07,430 --> 00:00:10,990
+بركاتكم العافية نكمل اليوم ان شاء الله تعالى كان
+
+3
+00:00:10,990 --> 00:00:14,990
+جزئيا ضيلالنا في ال complexity عشان نكون هنا الملف
+
+4
+00:00:14,990 --> 00:00:20,690
+فعليا و نبدأ في شوية أسئلة محلولة طبعا كان في
+
+5
+00:00:20,690 --> 00:00:25,530
+أسئلة محلولة عن الأجزاء السابقة اللي هي ال sets و
+
+6
+00:00:25,530 --> 00:00:31,270
+ال matrices و في أسئلة محلولة عن ال ..الـ
+
+7
+00:00:31,270 --> 00:00:35,850
+pseudocode الأكواد فما بعرف أنية اللي ممكن تكون
+
+8
+00:00:35,850 --> 00:00:40,570
+أولى باعتبار أن أحنا دخليني على امتحان هل نستمر في
+
+9
+00:00:40,570 --> 00:00:44,330
+موضوعنا لليوم أن أحنا نضلنا فيه الأكواد فنكمل
+
+10
+00:00:44,330 --> 00:00:49,330
+الأسئلة المحلولةكأكواد نحلل فيها نشتغل عليها و لا
+
+11
+00:00:49,330 --> 00:00:52,710
+نرجع خطوة لورا لإنه بدك نطلع على امتحان ناخد ال
+
+12
+00:00:52,710 --> 00:00:55,670
+matrices و الأمور فبتهير خلاص خلينا ماشيين اليوم
+
+13
+00:00:55,670 --> 00:00:59,850
+كله أكواد و ن .. و نكمل في الموضوع حدا فناخد أقل
+
+14
+00:00:59,850 --> 00:01:03,250
+أكم من code اللي ضايلين كويس و نعتبرهم كأنه هي
+
+15
+00:01:03,250 --> 00:01:06,870
+عملت مراجعة و ناخد برضه أكم من code من اللي عادة
+
+16
+00:01:06,870 --> 00:01:10,310
+كنا .. يعني أجوا قبل هيك في امتحانات شمال أو يمين
+
+17
+00:01:10,310 --> 00:01:14,450
+طيب أخر حاجة كنا اتكلمنا فيها كان ال linear search
+
+18
+00:01:15,070 --> 00:01:19,350
+إذا متذكرين و كنا بنحسبله ال complexity و إشتغلنا
+
+19
+00:01:19,350 --> 00:01:22,890
+عليه و أخدنا التلت حالات كمان ال worst case و
+
+20
+00:01:22,890 --> 00:01:25,530
+أخدنا في ال best case و أخدنا في ال average case
+
+21
+00:01:25,530 --> 00:01:30,350
+لمجرد بس أنه نشوف التلت حالات عن بعض و اتفقنا بعد
+
+22
+00:01:30,350 --> 00:01:34,250
+هيك على ال worst case خلصنا هنشتغل على ال worst
+
+23
+00:01:34,250 --> 00:01:38,530
+case time complexity مش هيك و اتفقنا أن هذا هي
+
+24
+00:01:38,530 --> 00:01:44,080
+اللي فقط هنثبت عليها تمامفي ال binary ال binary
+
+25
+00:01:44,080 --> 00:01:47,800
+الصراحة شرحناها سابقا جابل هيك احنا خدنا ال binary
+
+26
+00:01:47,800 --> 00:01:51,320
+search واتفقنا على تفاصيله مافيش مشكلة و رسمناها
+
+27
+00:01:51,320 --> 00:01:56,180
+على جنبه شرحناها بشكل موسع دل الان نتعامل مع ال
+
+28
+00:01:56,180 --> 00:01:59,340
+complexity كيف بدنا نحسبها كيف بدنا نحسب ال
+
+29
+00:01:59,340 --> 00:02:02,680
+complexity سبعته ال complexity ببساطة حاجة اقول
+
+30
+00:02:02,680 --> 00:02:10,150
+الجزء الاول هنا اللي هو مجرد اعطاء قيمI بتسوى واحد
+
+31
+00:02:10,150 --> 00:02:14,830
+J بتسوى N فهذه θ of واحد وهي constant ثابت يعني
+
+32
+00:02:14,830 --> 00:02:19,030
+معناه ذلك انه الوقت اللي محتاجه على نفسالجهاز نفس
+
+33
+00:02:19,030 --> 00:02:24,350
+ال processor هيكون ثابت من ملف لملف من code ل code
+
+34
+00:02:24,350 --> 00:02:28,490
+هو هو مش هيتغير فإذن بالنسبالي ثابت هنا نفس الجثة
+
+35
+00:02:28,490 --> 00:02:32,870
+أن أحسب كل مرة ال midpoint حسبة ال midpoint لحالها
+
+36
+00:02:32,870 --> 00:02:37,910
+كعملية لحالها هي ثابتة إلها time محدد و بيظل كما
+
+37
+00:02:37,910 --> 00:02:42,690
+هو و بعدين ال if then نفس الجثة بفحص برضه إلها زمن
+
+38
+00:02:42,690 --> 00:02:47,060
+معين ثابتمش مشكلة فلعندي ال end خلصنا الجزيتين
+
+39
+00:02:47,060 --> 00:02:50,280
+هدول خلصنا الجزيتين اللي جوا ال loop بس ماتكلمتش
+
+40
+00:02:50,280 --> 00:02:54,120
+لسه عن ال loop ال loop لسه ماحكيناش عنه بعدك خلصنا
+
+41
+00:02:54,120 --> 00:03:00,360
+ال end تمام في اخر شغلة ان احنا نفحص اخر عنصر
+
+42
+00:03:00,360 --> 00:03:04,960
+موجود ده العنصر الأخير هل هو بساوي x اللي نبحث
+
+43
+00:03:04,960 --> 00:03:12,310
+عنها ولا لأ فبرضه هذهfixed هدى المفروض انها ثابتة
+
+44
+00:03:12,310 --> 00:03:17,490
+constant time ثابت و بيضل ثابت كما هو طيب فكله
+
+45
+00:03:17,490 --> 00:03:21,170
+ثوابت لكن فى شغل احنا لسه ماخدناش بقالنا منها ال
+
+46
+00:03:21,170 --> 00:03:28,650
+while بمعنى ان ثابت اللى هنا اكم مرة بتكرر وهدى كل
+
+47
+00:03:28,650 --> 00:03:30,570
+ال complexity ده دائما جولنا زى ما جولنا فى ال for
+
+48
+00:03:30,570 --> 00:03:33,010
+loop و في ال while ال complexity كلها فى الجزئية
+
+49
+00:03:33,010 --> 00:03:38,990
+هدى فجزئية جداش بتكرر هناعشان نعرف منها ال
+
+50
+00:03:38,990 --> 00:03:42,550
+complexity الحقيقية فعليا فهذا ثابت مش جالجان منه
+
+51
+00:03:42,550 --> 00:03:45,350
+و اللي تحت هذا ثابت مش جالجان منه لأنه مش جوا ال
+
+52
+00:03:45,350 --> 00:03:48,890
+loop أصلا يعني مش هيتكرر ولا بأي حامل أحوال اللي
+
+53
+00:03:48,890 --> 00:03:53,950
+هيتكرر هو اللي جوا ال loop فإذا ال constant هذا هو
+
+54
+00:03:53,950 --> 00:03:58,230
+متغير بمعنى .. هو هيكون بيعتمد على جدش عدد ال
+
+55
+00:03:58,230 --> 00:04:02,410
+inputs لكن عدد ال inputs مربوطة هنا
+
+56
+00:04:10,350 --> 00:04:14,810
+عشان نفهم الجثة كيف كانت ماشية كنا بنشوف ال
+
+57
+00:04:14,810 --> 00:04:21,320
+midpoint و من خلالهابنختصر نص ال interval و بعدين
+
+58
+00:04:21,320 --> 00:04:25,640
+بنحول مباشرة ال midpoint هذا بغض النظر زائد واحد
+
+59
+00:04:25,640 --> 00:04:28,580
+او هو نفسه المهم انه زائد واحد لكن منه بنبدأ
+
+60
+00:04:28,580 --> 00:04:32,660
+interval جديدة عشان ناخد لها ال midpoint and so on
+
+61
+00:04:32,660 --> 00:04:35,780
+بهذا الشكل و نقول والله خلاص خلصنا هذا بدناه شيء
+
+62
+00:04:35,780 --> 00:04:39,960
+فصرنا في midpoint جديدة الان ال loop بيعطيني جديش
+
+63
+00:04:39,960 --> 00:04:45,340
+عدد مراتالتجسيم هذا يدّيش عدد مرات التجسيم اللي
+
+64
+00:04:45,340 --> 00:04:51,400
+هنجعد .. هنجعد كل شوية نعمله لعند ما نصل في الآخر
+
+65
+00:04:51,400 --> 00:04:59,360
+لعنصر واحد فقط نقارن فيه مرة واحدة فالان عدد
+
+66
+00:04:59,360 --> 00:05:03,760
+المرات هذه هذه عدد مرات معناته هذه اكم مرة ال
+
+67
+00:05:03,760 --> 00:05:09,820
+while هتنفذ لكن في نفس الوقت انا عارف ان ال T of N
+
+68
+00:05:09,820 --> 00:05:16,700
+هي زمنأو function في الزمن الزمن هذا معتمد على
+
+69
+00:05:16,700 --> 00:05:24,820
+مين؟ على ال input ال input هي كل عدد العناصر صح؟
+
+70
+00:05:24,820 --> 00:05:30,480
+هي كل عدد العناصر طيب فمعناه ذلك أنه عشان أشوف إيش
+
+71
+00:05:30,480 --> 00:05:34,180
+اللي بيربط لي ال while بعدد العناصر وهي فعلية
+
+72
+00:05:34,180 --> 00:05:39,010
+المتغير الحقيقي عند هنا لازم أجيب علاقة بينهمأجيب
+
+73
+00:05:39,010 --> 00:05:50,210
+علاقة بين جداش عدد مرات تنفيذ ال while و ال in و
+
+74
+00:05:50,210 --> 00:05:55,450
+ال in لأن معنا ذلك هعرف ان كل ما زادت جداش بدي
+
+75
+00:05:55,450 --> 00:06:01,050
+أضطر أزود كمان stage زيادة كل جداش بدي أضطر أزود
+
+76
+00:06:01,050 --> 00:06:06,290
+stage زيادة صحيح؟ لأن ك execution time هو معتمد
+
+77
+00:06:06,290 --> 00:06:11,820
+على أكم مرة بدي أنفذ ال loopواضحة بدي انافذه اربع
+
+78
+00:06:11,820 --> 00:06:16,200
+مرات خلاص اربع مرات طيب ال input لو زاد كمان اتنين
+
+79
+00:06:16,200 --> 00:06:20,020
+زيادة يمكن يظل اربع مرات برضه مايتغيرش طيب عند
+
+80
+00:06:20,020 --> 00:06:24,640
+قيمة معينة ل in اتزيد حتار انافذه كمان مرة خامسة
+
+81
+00:06:24,640 --> 00:06:30,340
+هنا صار في عند زيادة في ال time حيزيد معايا ال
+
+82
+00:06:30,340 --> 00:06:37,250
+time كمان fixedأو time زيادة في rest order .. zero
+
+83
+00:06:37,250 --> 00:06:42,070
+order اللي هو constant .. constant تمام فبدنا نعرف
+
+84
+00:06:42,070 --> 00:06:46,450
+الآن إيه إنت بقدر أقول إنه هضطر أفتح stage زيادة
+
+85
+00:06:46,450 --> 00:06:52,430
+فصار كإني بدي أجيب علاقة ما بين عدد مرات ال stages
+
+86
+00:06:52,430 --> 00:06:57,010
+اللي هي تمثل عدد مرات تنفيذ ال loop بالنسبالنا
+
+87
+00:06:57,010 --> 00:07:00,810
+عشان أصلها قيمة واحدة في الآخر يعني هنا بيكون واحد
+
+88
+00:07:02,160 --> 00:07:07,340
+لأنه عند الواحد احنا عارفين انه بيجف ال loop عرفنا
+
+89
+00:07:07,340 --> 00:07:11,020
+ليش عند الواحد بدنا نوجف لأنه عنده حسب ال
+
+90
+00:07:11,020 --> 00:07:17,600
+proposition تبع ال while بيجف اذا سوا بعض خلاص هنا
+
+91
+00:07:17,600 --> 00:07:21,520
+بتصير false فبنوجف امتى بيسوا بعض اذا وصلت في
+
+92
+00:07:21,520 --> 00:07:24,600
+الآخر لأنصر واحد اللي دل في ال array كلها على
+
+93
+00:07:24,600 --> 00:07:29,240
+بعضها او في ال list كاملة على بعضها طيب ال list
+
+94
+00:07:29,240 --> 00:07:33,990
+هذه من جدش بادية من انفالان بدنا نجيب علاقة بين
+
+95
+00:07:33,990 --> 00:07:41,110
+المرات هذه و امتى بيوصلنا ل .. ل الواحد في الآخر
+
+96
+00:07:41,110 --> 00:07:45,070
+لإمتى بنصل ل الواحد في الآخر فهذه كلنا عارفين انه
+
+97
+00:07:45,070 --> 00:07:49,070
+مدام binary نتعامل
+
+98
+00:07:49,070 --> 00:07:53,990
+معها binary بمعنى هنا كان واحد هنا كانت اتنين
+
+99
+00:07:53,990 --> 00:07:57,510
+بالظبط
+
+100
+00:07:57,510 --> 00:08:03,350
+بالظبط ويلها علاقة بقداش عدد المرات هناهنا صفر لو
+
+101
+00:08:03,350 --> 00:08:07,610
+عملناها بالشكل عكسي في النهاية عدد المرات بدي اعده
+
+102
+00:08:07,610 --> 00:08:12,310
+a to z زي ما بيقولوا او z to a كعدد حيظل واحد
+
+103
+00:08:12,310 --> 00:08:16,150
+فالان احنا بنعده بالعكس بنعده بالعكس لإن انا فاهم
+
+104
+00:08:16,150 --> 00:08:18,810
+ال binary وعارف اعده ال binary ماعنديش مشكلة في ال
+
+105
+00:08:18,810 --> 00:08:23,810
+binary فحنعده بشكل عكسي واحد اتنين اربعة تمانية
+
+106
+00:08:23,810 --> 00:08:29,170
+اين تبقى اصل لقيمة inهنا بدنا ان .. يعني زي ما
+
+107
+00:08:29,170 --> 00:08:32,510
+بقوله انحدد انه ان في الحالة هذه لازم تكون احد
+
+108
+00:08:32,510 --> 00:08:38,230
+مشتقات تضرب في اتنين هذه بمعنى انه ممكن تصل ل 16
+
+109
+00:08:38,230 --> 00:08:47,630
+32 64 صحيح؟ كويس لو كانت اجل من هيك عشان نتفق على
+
+110
+00:08:47,630 --> 00:08:50,770
+نقطة جابل ما نبدأ عملية حسابتنا يعني لو لجيتها
+
+111
+00:08:50,770 --> 00:08:57,700
+مثلا اربعينمعنى ذلك أنا محتاج هنا واحد اتنين تلاتة
+
+112
+00:08:57,700 --> 00:09:06,940
+أربعة خمسة ستة عند الأربعين أكمله بححتاج ستة كأني
+
+113
+00:09:06,940 --> 00:09:10,980
+بعمل sealing بنا نحتاج الستة ساعتها فماعنديش مشكلة
+
+114
+00:09:10,980 --> 00:09:14,760
+حتى لو قيمة n كانت بين رقمين من الأرقام المتعارف
+
+115
+00:09:14,760 --> 00:09:19,090
+عليهم كمضاعفات للاتنين to the power of nماعنديش
+
+116
+00:09:19,090 --> 00:09:24,590
+مشكلة بعمل sealing و خلصناه فإذا انتهت الجثة كل
+
+117
+00:09:24,590 --> 00:09:32,510
+الموضوع صارت بالنسبالي 2 to the power k تساوي n مش
+
+118
+00:09:32,510 --> 00:09:36,870
+هيك .. هي .. هي الكلام هيك بيقول هيك الكلام بيحكي
+
+119
+00:09:36,870 --> 00:09:42,850
+أنه العدد ال total كله هذا ال 64 مثلا أنا عارف أنه
+
+120
+00:09:42,850 --> 00:09:47,430
+الرقم اربع أو من تلاتة و تلاتين لاربع و ستين نفس
+
+121
+00:09:47,430 --> 00:09:51,160
+الشيءمن تلاتة و تلاتين اللي هي من بعد الاتنين و
+
+122
+00:09:51,160 --> 00:09:54,660
+تلاتين خلاص لأربعة و ستين كلهم نفس الاشي ان
+
+123
+00:09:54,660 --> 00:09:58,860
+بالنسبالي كأنها ثابتة مش هيختلف اشي مش هيختلف شي
+
+124
+00:09:58,860 --> 00:10:05,240
+تمام ال K هذه هي اللي بدنا ياها اللي هم عدد ال
+
+125
+00:10:05,240 --> 00:10:10,860
+loops عدد ال loops فهدول هم فعليا ال order فعليا
+
+126
+00:10:10,860 --> 00:10:15,120
+هذا هو ال order بالنسبة للبرنامج لأن البرنامج هو
+
+127
+00:10:15,120 --> 00:10:19,530
+مش شايف انليش مش shape in؟ لأن هو ماعملش linear
+
+128
+00:10:19,530 --> 00:10:25,230
+فهو مامسكش عناصر in واحدة واحدة واحدة مقابل واحدة
+
+129
+00:10:25,230 --> 00:10:28,970
+مقابل واحدة مقابل واحدة فشعر بجدش عددهم، لأ هو
+
+130
+00:10:28,970 --> 00:10:33,610
+مابيعرفش عددهم، هو أشتغل binary binary معناه ذلك
+
+131
+00:10:33,610 --> 00:10:39,010
+إنه في الآخر اللي بهمني جدش عدد مرات تطبيق ال loop
+
+132
+00:10:39,010 --> 00:10:44,890
+أكم مرة عمل عملية ال looping هذه هذه هي ال
+
+133
+00:10:44,890 --> 00:10:49,640
+complexityلما كانت Linear .. لما كانت Linear كان
+
+134
+00:10:49,640 --> 00:10:54,100
+إيش بيعمل؟ بيفحص الأول، التاني، التالت، الرابع،
+
+135
+00:10:54,100 --> 00:10:57,660
+فأنا عارف إن ال loop هو العدد in نفسه، ما كانش
+
+136
+00:10:57,660 --> 00:11:00,360
+عندنا مشكلة، لأنه هيمشي عليهم كلهم، هيمشي عليهم
+
+137
+00:11:00,360 --> 00:11:03,120
+كلهم، هنا لأ، مش هيمشي عليهم كلهم، فعشان هيك بدنا
+
+138
+00:11:03,120 --> 00:11:07,220
+إيش نتلخبط، إيش ال complexity؟ هي function في in،
+
+139
+00:11:07,220 --> 00:11:14,080
+بس مش هي in، صح؟ هي جداش عدد مرات ال loop بقى اللي
+
+140
+00:11:14,080 --> 00:11:17,840
+إنتوا بتعملوهفمعنى ذلك اللي بربطلنا جديش عدد مرات
+
+141
+00:11:17,840 --> 00:11:25,120
+ال loop مع قيمة n حتى لو اختلفت .. حتى لو اختلفت
+
+142
+00:11:25,120 --> 00:11:28,660
+.. هذه هي اللي بدنا ايها فانا عارف ان قيمة n هي
+
+143
+00:11:28,660 --> 00:11:32,480
+بهذا الشكل .. هذا ال input تبعي بس k هي المطلوبة
+
+144
+00:11:32,480 --> 00:11:36,380
+لان لان k هي ال complexity .. k هي ال complexity
+
+145
+00:11:36,380 --> 00:11:40,480
+فهي ال k ك complexity بدها تنحط هي اللي function
+
+146
+00:11:40,480 --> 00:11:45,430
+في المتغير in وليس العجز زي ما احنا كاتبينهمش
+
+147
+00:11:45,430 --> 00:11:47,370
+العكس زي ما احنا كاتبينه الان هلوا جد احنا
+
+148
+00:11:47,370 --> 00:11:51,670
+كاتبينها بطريقة مختلفة كاتبين ان in هي function في
+
+149
+00:11:51,670 --> 00:11:57,870
+k اللي فعليا بدنا ياه هو العكس لأن ال time معتمد
+
+150
+00:11:57,870 --> 00:12:03,310
+على k عدد مرات تنفيذ ال loop طيب عدد مرات تنفيذ ال
+
+151
+00:12:03,310 --> 00:12:07,510
+loop لازم تكون function في in و ليس فبدنا نعكسها
+
+152
+00:12:07,510 --> 00:12:11,310
+بدنا نجيب ال inverse تبعهابدنا نجيب ال inverse
+
+153
+00:12:11,310 --> 00:12:14,390
+تبعها بكل بساطة أتوقع ماعناش هيكون مشكلة كتير
+
+154
+00:12:14,390 --> 00:12:18,870
+خلصنا من الجزء التوضيحي هذه واضحة عندكم فكرة ال
+
+155
+00:12:18,870 --> 00:12:24,430
+binary ممتاز خلصنا منها ففي
+
+156
+00:12:24,430 --> 00:12:32,090
+الحالة هذه بقول log n للطرفين log 2 to the power k
+
+157
+00:12:32,090 --> 00:12:37,910
+كلنا عارفين في ال log ال أس بيطلع ك multiplier
+
+158
+00:12:40,520 --> 00:12:52,440
+.log 2 وهذه log n طيب الأساس إيش هنا عشرة عشرة
+
+159
+00:12:52,440 --> 00:13:00,480
+بيصير الأساس اتنين بيصير الأساس اتنين خلاص من
+
+160
+00:13:00,480 --> 00:13:03,400
+الأساس بس احنا بنوضحها رياضية عشان ماحدش يقولي كيف
+
+161
+00:13:03,400 --> 00:13:09,350
+هيها هذه بتيجي عن ناحية تانية فأصبحت k تساوي logن
+
+162
+00:13:09,350 --> 00:13:15,070
+على log ثابت اتنين قيمة ثابتة مدام على log قيمة
+
+163
+00:13:15,070 --> 00:13:19,090
+ثابتة خلاص معناه ان هو حيكون له قيمة ثابتة فعليا
+
+164
+00:13:19,090 --> 00:13:25,390
+انتهى اللي هي فاصلة تلاتة صفر و بعده في أرقام يعني
+
+165
+00:13:25,390 --> 00:13:29,490
+تلاتة من عشرة تلاتة من عشرة انتهى الموضوع خلاص
+
+166
+00:13:29,490 --> 00:13:35,490
+فإذا كل هذا بنشطبها و بنقول تساوي log الأساس اتنين
+
+167
+00:13:35,490 --> 00:13:42,430
+ل nهيك كافية؟ كافية جدا لأن نقطة نهائية عدد مرات
+
+168
+00:13:42,430 --> 00:13:49,050
+ال loop ال loop أكم مرة بده ينفذ؟ K مرة طب K هل
+
+169
+00:13:49,050 --> 00:13:53,050
+مرتبطة بال N؟ أه هي function في N logarithmic
+
+170
+00:13:53,050 --> 00:13:59,790
+بدليل أنه هين كنا وضحناها أنه أنا مش كل زيادة في N
+
+171
+00:13:59,790 --> 00:14:03,170
+هزيد ال loop زيادة واحد زي ما عملنا في ال linear
+
+172
+00:14:03,170 --> 00:14:09,140
+لأمن تلاتة و تلاتين لاربعة و ستين اي زيادة بتتم في
+
+173
+00:14:09,140 --> 00:14:14,840
+المساحة هذه مش هتأثر معايا هضل عدد ال loops هي هي
+
+174
+00:14:14,840 --> 00:14:22,760
+فالتغير مش خطي كل فترة لما بتذكر اه هتزودلي كمان
+
+175
+00:14:22,760 --> 00:14:31,800
+loop زيادةطيب من 64 او تحديدا من 65 ل 128 زادت ال
+
+176
+00:14:31,800 --> 00:14:37,600
+gap كل هدولة في Loop واحدة بيختصروا كل هدولة
+
+177
+00:14:37,600 --> 00:14:42,380
+بيختصروا في Loop واحدة كل ما بتزود بتزيد الاختصار
+
+178
+00:14:42,380 --> 00:14:45,200
+ليش بيزيد؟ لأنه التبادي أصلا شايف جداش اللي
+
+179
+00:14:45,200 --> 00:14:48,660
+اختصرته هنا؟ طيب في اللي وراها اللي اختصرته بجل
+
+180
+00:14:50,170 --> 00:14:54,110
+فهذه كانت اللي هي من تلاتة و تلاتين مثلا لاربع و
+
+181
+00:14:54,110 --> 00:14:58,310
+ستين بس هنا صرت نتكلم من خمسة و ستين لمية و تمانية
+
+182
+00:14:58,310 --> 00:15:03,770
+و عشرين فأكيد هنا .. غير هنا كل هدول بالنسبالك
+
+183
+00:15:03,770 --> 00:15:10,090
+loop واحد .. كل هدول loop واحد فكل loop زيادة انت
+
+184
+00:15:10,090 --> 00:15:16,590
+بتقدر تختصر كمية أكبر واضحيت؟ تمام فهذه فكرة ان
+
+185
+00:15:16,590 --> 00:15:21,200
+والله ال binary logarithmicو هذا الأهم عشان أعرف
+
+186
+00:15:21,200 --> 00:15:25,100
+ال complexity معناته أنا بدي أعرف اللو بقى كم مرة
+
+187
+00:15:25,100 --> 00:15:30,760
+نفذته بس الفكرة بسيطة أتوقع يعني فكرة بسيطة وسهلة
+
+188
+00:15:30,760 --> 00:15:34,260
+و في .. كل اللي حكيناها هيه مكتوب بترجعله بسهولة
+
+189
+00:15:34,260 --> 00:15:39,320
+بريحية مدى ما اتكلمت عنه log ف automatic نكتبها
+
+190
+00:15:39,320 --> 00:15:48,140
+بصيغة وين راحت هيها ساعتها
+
+191
+00:15:48,860 --> 00:15:54,380
+برغم ان احنا هنا log اتنين وقلنا الأساس اتنين بس
+
+192
+00:15:54,380 --> 00:15:59,280
+متذكرين اخر محاضرة ال order of growth قلنا بغض
+
+193
+00:15:59,280 --> 00:16:03,260
+النظر عن ايش ال complex ال base اسم هال
+
+194
+00:16:03,260 --> 00:16:09,180
+logarithmكوا بس اتوقع واضح ليش هنا انت بتكسب على
+
+195
+00:16:09,180 --> 00:16:14,370
+ايش؟ على ثابتطب ال function linear و ضربتها في
+
+196
+00:16:14,370 --> 00:16:19,330
+ثابت هتظلها linear فانت مش هيفرج معاك ان هو قسم
+
+197
+00:16:19,330 --> 00:16:23,930
+على ثابت عشان هيك مش هتفرج تقولي اتنين لما اكتبها
+
+198
+00:16:23,930 --> 00:16:30,560
+ك order تقولي theta of log و خلاص اتنينللأساس 2
+
+199
+00:16:30,560 --> 00:16:34,780
+للأساس 10 للأساس 5 للأساس 100 بتفرجش لأن كلنا
+
+200
+00:16:34,780 --> 00:16:37,520
+عارفين إن هي عبارة عن C مضروبة في ال function بس
+
+201
+00:16:37,520 --> 00:16:40,000
+هي constant مضروبة في ال function ال constant هذا
+
+202
+00:16:40,000 --> 00:16:45,280
+هنا قيمته مثلا 1 على log 2 بس قيمته هنا اللي هو
+
+203
+00:16:45,280 --> 00:16:52,420
+log 2 وقسمنا عليه 1 على log 2 تمام تمام جدا طيب
+
+204
+00:16:52,420 --> 00:16:54,820
+كمان code
+
+205
+00:16:59,230 --> 00:17:04,810
+اللي هو ضرب المصفوفات وهذا
+
+206
+00:17:04,810 --> 00:17:08,770
+من الأكواد اللي كتير درجة وبيحتاجها الواحد و
+
+207
+00:17:08,770 --> 00:17:11,550
+تحديدا المهندسين كتير بيحتاجوا ان يضربوا مصفوفتين
+
+208
+00:17:11,550 --> 00:17:15,870
+في بعض يضربوا مصفوفتين في بعض فهيطلب منك اعمللي
+
+209
+00:17:15,870 --> 00:17:19,590
+code يعمللنا code كلنا عارفين ان الأكواد في الحالة
+
+210
+00:17:19,590 --> 00:17:23,070
+هذه بدنا نعمل اتنين for loop مبدئيا بس عشان نحددوا
+
+211
+00:17:23,070 --> 00:17:26,430
+العنصر اللي بدنا نحسبه ليش؟ لأن انا عندي rows
+
+212
+00:17:26,430 --> 00:17:31,200
+وعندي columnsفمحتاج أولا قبل ما أبدأ أي حاجة محتاج
+
+213
+00:17:31,200 --> 00:17:34,860
+اتنين for loop لتحديد العنصر اللي أنا بتكلم عنه
+
+214
+00:17:34,860 --> 00:17:47,760
+بدّي for loop هنا و بدنا loop .. loop هنا فهي
+
+215
+00:17:47,760 --> 00:17:51,080
+أول اتنين for loop هدول مافيش مجال تشتغل في ال
+
+216
+00:17:51,080 --> 00:17:55,750
+matrices و ماتكتبهمشعلى طول انتهى الكلام فهي خلصنا
+
+217
+00:17:55,750 --> 00:17:59,770
+التنتين هدولة فإذا انا عارف انه ال I row ال J
+
+218
+00:17:59,770 --> 00:18:05,370
+column طيب هدول عشان يحدد ايش انا بدي احسب العنصر
+
+219
+00:18:05,370 --> 00:18:10,930
+الأول فلما اكتب I واحد J واحد فانا بتكلم عن العنصر
+
+220
+00:18:10,930 --> 00:18:16,550
+الأول في ال row الأول و ال column الأول طيب
+
+221
+00:18:16,550 --> 00:18:22,630
+عملية حسابهعملية حسابه نفسها جاية من خلال ال inner
+
+222
+00:18:22,630 --> 00:18:27,170
+product بتذكرينه؟ بحسب vector في vector يعني هذا
+
+223
+00:18:27,170 --> 00:18:33,250
+عشان ينحسب هو أصلا جايين عبارة عن صف من الأولى في
+
+224
+00:18:33,250 --> 00:18:41,090
+عمود من التانية طب تمام هذا نفسه متغير ليش؟ لأنه
+
+225
+00:18:41,090 --> 00:18:44,210
+أنا مش عارف جديش عدد الصفوف مبدئيا هنا و اللي لازم
+
+226
+00:18:44,210 --> 00:18:49,100
+يتفق مع عدد الأعمدة هنافإذا محتاج برضه كمان loop
+
+227
+00:18:49,100 --> 00:18:52,200
+عشان
+
+228
+00:18:52,200 --> 00:18:58,840
+نعمل عملية الضرب عشان ساعتها أقول العنصر الأول من
+
+229
+00:18:58,840 --> 00:19:02,940
+المصفوفة الأولى في العنصر الأول من المصفوفة
+
+230
+00:19:02,940 --> 00:19:06,560
+التانية العنصر التانى بعد تانى التالت في التالت
+
+231
+00:19:06,560 --> 00:19:09,700
+الرابع في الرابع ونعمل لهم summation ونعمل لهم
+
+232
+00:19:09,700 --> 00:19:13,360
+عملية summation فلاحظت اتنين في ال loop بس عشان
+
+233
+00:19:13,360 --> 00:19:17,750
+أقول ان هو اللي بده حسبه ال Mو لازم كمان for loop
+
+234
+00:19:17,750 --> 00:19:22,790
+عشان عملية الحساب نفسها اللي هي ال inner product
+
+235
+00:19:22,790 --> 00:19:27,510
+اللي كنتوا تعملوها فهي بالظبط got it for loop أول
+
+236
+00:19:27,510 --> 00:19:32,710
+تاني صفوف أعمدة و بعدين بدنا نعمل عملية summation
+
+237
+00:19:32,710 --> 00:19:39,410
+لان لازم نصفر عشان ارتاح بعدين ان اي if then لو في
+
+238
+00:19:39,410 --> 00:19:42,970
+if then بتكون by conditional متأكد متطمن ان هي by
+
+239
+00:19:42,970 --> 00:19:46,970
+conditionalتمام واضحت من أيامها هيها بالظبط
+
+240
+00:19:46,970 --> 00:19:53,270
+فصفرليها بلاش يكون لها قيمة سابقة صفرناها و بنبدأ
+
+241
+00:19:53,270 --> 00:19:57,530
+ال for loop لمين ل Q ال Q اللي هي إيش عدد أعمدة
+
+242
+00:19:57,530 --> 00:20:02,890
+الأول أو صفوف التاني ما هم متساويين عشان نبدأ الآن
+
+243
+00:20:02,890 --> 00:20:08,590
+ناخدهم واحد واحد نبدأ نمسكهم واحد واحد خلصنا خلصنا
+
+244
+00:20:09,650 --> 00:20:13,630
+فهنا لما نيجي نتطلع على الشكل اللي قدامنا هذا بكل
+
+245
+00:20:13,630 --> 00:20:18,130
+بساطة بنقدر نتخيل أبعاد ال matrices اللي عندي إيش
+
+246
+00:20:18,130 --> 00:20:30,150
+أبعادها؟ هنا M في K صح؟
+
+247
+00:20:30,150 --> 00:20:35,170
+آه أيوة تمام خليها توبح أكتر بالنسبالك و قبل أن
+
+248
+00:20:35,170 --> 00:20:37,010
+نبدأ نكمل هنا صارت K
+
+249
+00:20:39,860 --> 00:20:49,020
+لأ اللي فوق هذه نتيجهم
+
+250
+00:20:49,020 --> 00:20:53,040
+فإذا
+
+251
+00:20:53,040 --> 00:20:56,220
+الأتنين ال for loop هدول بس عشان أحدد داخل ال
+
+252
+00:20:56,220 --> 00:21:01,220
+resultant matrix كل عنصر و بعدين أبدأ في عملية
+
+253
+00:21:01,220 --> 00:21:05,980
+حسابه كإني بقولك بدي أمسك أول عنصر يللا نحسبه طب
+
+254
+00:21:05,980 --> 00:21:10,340
+عشان كلمة نقول يللا نحسبه بدها كمان for loopفهمنا
+
+255
+00:21:10,340 --> 00:21:13,320
+ليش بتاعة كمان for loop اللي هي بعدد ال K هدولة
+
+256
+00:21:13,320 --> 00:21:16,840
+لأن كل عنصر لحاله بده ينضرب مع المقابل له فهي
+
+257
+00:21:16,840 --> 00:21:23,780
+ماسكنها ال C اللي بدناها بصفر هنبدأ متفقين من
+
+258
+00:21:23,780 --> 00:21:30,590
+الأساس أنه عند I و J هدولة ثابتيننشيك حدوله ثابتين
+
+259
+00:21:30,590 --> 00:21:33,830
+اللي هي القيمة اللي احنا هنعمل عليها التشبيع بقى
+
+260
+00:21:33,830 --> 00:21:38,930
+طيب إيش اللي بتغير اللي بتغير I في Q طيب هتشوف هذه
+
+261
+00:21:38,930 --> 00:21:44,950
+اللي هي عبارة عن maximum M Q K فانا باخدها من أول
+
+262
+00:21:44,950 --> 00:21:48,950
+matrix باخدها من ال matrix الأولى و التانية من ال
+
+263
+00:21:48,950 --> 00:21:56,910
+matrix التانية هذه طبعا J بس هاي كله نعمل خلصنا
+
+264
+00:21:56,910 --> 00:22:00,850
+انتهت البرنامجالـ for loops هتظلم كاملة بعد هيك
+
+265
+00:22:00,850 --> 00:22:03,050
+لحالها على اعتبار ان انا مش هعمل الا العملية
+
+266
+00:22:03,050 --> 00:22:06,970
+الإجراء هذا فانا مش محتاج لا begin ولا end لها هو
+
+267
+00:22:06,970 --> 00:22:10,430
+هي الإجراء اللي بنعمله هذه هنحتاجها لمين؟ هنحتاجها
+
+268
+00:22:10,430 --> 00:22:18,350
+هنا ال begin و ال end لأن في كذا عملية هتنعمل في
+
+269
+00:22:18,350 --> 00:22:24,760
+التصفير و المهم جدالازم نصفر ال summation قبل ما
+
+270
+00:22:24,760 --> 00:22:27,940
+نبدأ نشتغل ال accumulator هذا لازم نصفره قبل ما
+
+271
+00:22:27,940 --> 00:22:31,940
+نبدأ نتكلم بمعنى ان انا هقولك بده العنصر الأول حتى
+
+272
+00:22:31,940 --> 00:22:37,080
+اللحظة صفر حتى اللحظة صفر انا حددت اه انه يلا بدنا
+
+273
+00:22:37,080 --> 00:22:41,520
+نحسب اول عنصر بس لسه صفر لما تبدأ تقول ليه هنا
+
+274
+00:22:41,520 --> 00:22:46,940
+خليني اكتبها واحد واحد اتنين اتنين and so on لما
+
+275
+00:22:46,940 --> 00:22:50,800
+تبدأ تقول ليه العنصر اللي متخزن هنا زائد واحد في
+
+276
+00:22:50,800 --> 00:22:59,020
+واحدخلاص هقولك سرة واحد في واحد ماشي زائد اتنين في
+
+277
+00:22:59,020 --> 00:23:09,760
+اتنين زائد تلاتة في تلاتة لما تصل مين ك في ك و
+
+278
+00:23:09,760 --> 00:23:18,920
+بالظبط هذا اللي بنعمله جاعدين لاحظ
+
+279
+00:23:18,920 --> 00:23:22,900
+كيف؟هذا إذا كان زي ما قلتلك ال compiler smart
+
+280
+00:23:22,900 --> 00:23:26,140
+enough إنه والله أنت بدأ ب zeros معناه أنك بتعرفها
+
+281
+00:23:26,140 --> 00:23:30,800
+من الأول إنها مصفرة مافيش مشكلة يعني بدك كأنك
+
+282
+00:23:30,800 --> 00:23:34,300
+اعملت ال code هذا بدل ما هو هنا الرقم هذا اعمله
+
+283
+00:23:34,300 --> 00:23:39,520
+برا إنه ال C بتساوي صفر فانت بتتكلم عن ال matrix
+
+284
+00:23:39,520 --> 00:23:42,560
+ككل بس في الحالة هذه برضه إذا أنت بتتكلم عن Java
+
+285
+00:23:42,560 --> 00:23:47,630
+أو whatever بدك تكون معرف أبعادها في الأولأكيد
+
+286
+00:23:47,630 --> 00:23:51,870
+لازم تعرف أبعادها عشان يفهم ال compiler انك قصدك
+
+287
+00:23:51,870 --> 00:23:57,070
+كل element داخل ال matrix يساوي صفر فانت لازم
+
+288
+00:23:57,070 --> 00:24:00,810
+تعملها الخطوة بس جبل بعد هتعملها بشكل individual
+
+289
+00:24:00,810 --> 00:24:04,530
+لكل أنصر اللي حال بدك تعملها بشكل ال matrix كلها
+
+290
+00:24:04,530 --> 00:24:06,650
+على بعض اعملها بالطريقة اللي بدك إياها بس لازم
+
+291
+00:24:06,650 --> 00:24:13,920
+تصفر لازم تبدأ تصفيرهاتمام عموما احنا كتبناها هنا
+
+292
+00:24:13,920 --> 00:24:18,100
+بس مش هذا قصدنا من الكلام قصدنا الان complexity
+
+293
+00:24:18,100 --> 00:24:25,340
+القصد في ال complexity كل loop بدنا نمسكه و نشوف
+
+294
+00:24:25,340 --> 00:24:30,680
+ايش علاقة عدد مرات ال loop بعدد العناصر اللي
+
+295
+00:24:30,680 --> 00:24:37,780
+موجودين عندى نبدأ بالأول من 1 to M linearlinear
+
+296
+00:24:37,780 --> 00:24:43,520
+لأنه انا همسك واحد واحد الأول التاني التالت مش زي
+
+297
+00:24:43,520 --> 00:24:48,800
+ال binary بعمل jump بعمل قفزات اضطريت قولنا من
+
+298
+00:24:48,800 --> 00:24:51,560
+تلاتة وتلاتين لاربعة وستين وعملتها jump مرة واحدة
+
+299
+00:24:51,560 --> 00:24:54,940
+كاملة هد بكلها بلوب واحد لأ هنا مش هنعمل كلام هذا
+
+300
+00:24:54,940 --> 00:25:00,520
+هنا بنفعش اتقول العنصر الأول في ال raw و بعدين
+
+301
+00:25:00,520 --> 00:25:04,380
+العنصر التالت في ال raw ليش كلهم scan كامل فإذا
+
+302
+00:25:04,380 --> 00:25:09,990
+linearهذه linear فهي هتكون عبارة عن ال loop هذا
+
+303
+00:25:09,990 --> 00:25:17,550
+big theta of M تحديدا جدش عدد عناصره M كويس التاني
+
+304
+00:25:17,550 --> 00:25:23,730
+N فإذا مضربين في بعض ليش مضربين في بعض؟ لأنه M في
+
+305
+00:25:23,730 --> 00:25:29,760
+Nهي فعلا لو هدول خمسة و هدول ستة اكم عنصر؟ الاتنين
+
+306
+00:25:29,760 --> 00:25:32,860
+في بعض تلاتين عنصر هيكون ال matrix عندك فمضربين
+
+307
+00:25:32,860 --> 00:25:38,460
+ضرب في بعض مضربين في بعض بمعنى ان لو لاحظ لو ال
+
+308
+00:25:38,460 --> 00:25:45,820
+loop هنا او عفوا الرز هنا زادت بس رز زيادة هل معنى
+
+309
+00:25:45,820 --> 00:25:52,050
+ذلك انه زاد عندي عنصر واحد؟ لأ حقيقة زاد عنديلفة
+
+310
+00:25:52,050 --> 00:25:56,730
+كاملة فإذا فعليا هم مضربين في بعض عملية ضرب تمام
+
+311
+00:25:56,730 --> 00:26:03,070
+هنا صفر عفوا اه zero order لأنه constant عملية
+
+312
+00:26:03,070 --> 00:26:06,330
+تصفير أي رقم هي مرة واحدة يعني يلها زمن محدد وخالص
+
+313
+00:26:06,330 --> 00:26:17,380
+لكن ال loop هناهيكرر أكم مرة كمرة كمرة كمرة كمرة
+
+314
+00:26:17,380 --> 00:26:17,800
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة
+
+315
+00:26:17,800 --> 00:26:19,780
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة
+
+316
+00:26:19,780 --> 00:26:21,580
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة
+
+317
+00:26:21,580 --> 00:26:21,600
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة
+
+318
+00:26:21,600 --> 00:26:26,300
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة
+
+319
+00:26:26,300 --> 00:26:35,590
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرةأيوة معناته
+
+320
+00:26:35,590 --> 00:26:39,530
+مادام لكل عنصر بتكررها K مرة و احنا توي اتفقنا انه
+
+321
+00:26:39,530 --> 00:26:44,550
+تلاتين لانه صار عندى خمسة في ستة يعني في بعض فإذا
+
+322
+00:26:44,550 --> 00:26:52,230
+K مرة في M مرة في N مرةمرة فإذا ك complexity و ال
+
+323
+00:26:52,230 --> 00:26:55,710
+for loop أسهل بكتير من ال while ال for loop أسهل
+
+324
+00:26:55,710 --> 00:26:58,530
+من ال while لأنه linear في الغالب ال linear على
+
+325
+00:26:58,530 --> 00:27:02,610
+طول for loop انت دايما عنصر و اللي ورا زائد واحد
+
+326
+00:27:02,610 --> 00:27:07,170
+زائد اتنين زائد تلاتة لما تصل لل final value خلاص
+
+327
+00:27:07,170 --> 00:27:13,030
+انتهيها دي فبطلع عندك theta of M في N في K يعني ال
+
+328
+00:27:13,030 --> 00:27:17,090
+order تكعيب يعني فعليا
+
+329
+00:27:22,140 --> 00:27:26,060
+تكعيب فإذا هذه هنا ال function تكعيبية ال function
+
+330
+00:27:26,060 --> 00:27:31,580
+ال complexity طبعا طيب نبدأ الآن نشوف مدام تكعيبية
+
+331
+00:27:31,580 --> 00:27:34,240
+طب هل هي مقبولة بالنسبالنا أنها تكون تكعيبية فعليا
+
+332
+00:27:34,240 --> 00:27:38,480
+ولا مش مقبولة ولا بدنا نفهم طب إيش ال limit اللي
+
+333
+00:27:38,480 --> 00:27:41,500
+اللي بدنا نقول عنه أه كويس أو مش كويس ال limit بكل
+
+334
+00:27:41,500 --> 00:27:45,690
+بساطة هذه نشوف معظمالـ functions اللي ممكن نتعامل
+
+335
+00:27:45,690 --> 00:27:48,730
+معها الأولى ال constant مافيش عندي مشكلة فيها
+
+336
+00:27:48,730 --> 00:27:54,630
+التانية logarithmic ال poly logarithmic اللي هي
+
+337
+00:27:54,630 --> 00:27:59,410
+تربية تكعيب تظابر أربع تظابر خمسة بس logarithmic ف
+
+338
+00:27:59,410 --> 00:28:03,730
+ال C ممكن تكون متغيرة واحد اتنين تلاتة خمسة عشرة ف
+
+339
+00:28:03,730 --> 00:28:08,130
+poly logarithmic كويس متعددة الحدود اللغارثمية
+
+340
+00:28:08,130 --> 00:28:12,130
+بتصير تصير اسمها متعددة الحدود اللغارثمية طيبالـ
+
+341
+00:28:12,130 --> 00:28:15,850
+Linear Linear في logarithmic فسمينا Linearithmic
+
+342
+00:28:15,850 --> 00:28:20,990
+Linear في logarithmic طيب متعدد ال polynomial
+
+343
+00:28:20,990 --> 00:28:27,170
+متعدد الحدود خطية مش logarithmia خطية متعدد حدود
+
+344
+00:28:27,170 --> 00:28:32,390
+خطية طيب بعدك exponential اللي أعلى منها ال
+
+345
+00:28:32,390 --> 00:28:41,250
+factorial اللي أعلى منها ال N في Mكان لها اسم بس
+
+346
+00:28:41,250 --> 00:28:45,230
+مش دارج كتير ال power town بيسموها أحيانا ال power
+
+347
+00:28:45,230 --> 00:28:48,190
+town بس لعندي لقد ماحدش ثابت يعني الناس جلال اللي
+
+348
+00:28:48,190 --> 00:28:52,430
+بيسموها بالاسم هذا فعشان هيك في معظم الكتب بيسموها
+
+349
+00:28:52,430 --> 00:28:56,670
+انت طبارن و بس و بسكته هذه .. هذه مستحيلة أصلا
+
+350
+00:28:56,670 --> 00:29:02,580
+ماحدش يجرب عليها هذه ماحدش يجرب عليهاهذه منتهية ..
+
+351
+00:29:02,580 --> 00:29:07,020
+هذه منتهية الصلاحيات هتخليني نشوف قعدنا هنتكلم
+
+352
+00:29:07,020 --> 00:29:11,160
+عنها الان عشان نحدد وين ال limit تبعنا هنقول ان في
+
+353
+00:29:11,160 --> 00:29:15,500
+عندى خط محدد المفروض ماتجوزش لما تكتب code إذا
+
+354
+00:29:15,500 --> 00:29:19,880
+تجاوز نوع معين على طول لحالك انت ألغي ال code تبعك
+
+355
+00:29:19,880 --> 00:29:23,200
+مافيش داعي على codeك هتعرف ان ال code هذا لسه
+
+356
+00:29:23,200 --> 00:29:27,800
+موصلناش لحلول إله المشاكل اللي عندنا هنقول عليها
+
+357
+00:29:27,800 --> 00:29:33,930
+اما tractableTracking اللي هو ممكن تطبحها أو حلها
+
+358
+00:29:33,930 --> 00:29:39,990
+أو حاجة من السماء visible قابلة للحلممكنة الحل ففي
+
+359
+00:29:39,990 --> 00:29:43,150
+برامج مع بعضهم بتسميهم tractable وبعضهم بتسميهم
+
+360
+00:29:43,150 --> 00:29:47,370
+intractable غير قابل للحل حسب طبعا من ال order تبع
+
+361
+00:29:47,370 --> 00:29:50,810
+ال problem اللي هي ال complexity نفسها فإذا هنقول
+
+362
+00:29:50,810 --> 00:29:57,810
+الان في اندي P P بولب P هذه مشهورة جدا ك set ال
+
+363
+00:29:57,810 --> 00:30:01,790
+set هذه عبارة عن ال set لكل tractable problems في
+
+364
+00:30:01,790 --> 00:30:07,640
+العالمكل مشكلة برمجية الكلام ده برمجي الكلام ده
+
+365
+00:30:07,640 --> 00:30:11,040
+نحكي عن الأمور البرمجية مش المشاكل حتى العادية
+
+366
+00:30:11,040 --> 00:30:13,280
+بتاعة ال calculus مالناس في ال calculus الآن انت
+
+367
+00:30:13,280 --> 00:30:16,980
+بتكلم عن كل البرامج البرمجية المشاكل البرمجية إذا
+
+368
+00:30:16,980 --> 00:30:23,020
+كانت tractable فبنحطها ضمن belong to all capital P
+
+369
+00:30:23,020 --> 00:30:30,020
+تمام المشاكل اللي تتجاوزP يعني لا تنتمي لـ P
+
+370
+00:30:30,020 --> 00:30:36,280
+فبنقول عنها Intractable أو Invisible غير معقولة
+
+371
+00:30:36,280 --> 00:30:41,240
+الحل هذه visible مقبولة أو معقول و هنا يمكن تطبحها
+
+372
+00:30:41,240 --> 00:30:47,560
+أو يمكن حلها هذا الكلام نظري في حالات لكن نادرة
+
+373
+00:30:47,560 --> 00:30:52,780
+كتير ممكن نعد الكلام هذا بدنا نحدد أول شغلة أن
+
+374
+00:30:52,780 --> 00:30:56,400
+الحد الفاصل ال P هنا بتتعامل معاه هو ال polynomial
+
+375
+00:30:57,530 --> 00:31:00,610
+لعند polynomial بنسميها tractable لعند ال
+
+376
+00:31:00,610 --> 00:31:06,690
+polynomial tractable لهنا هدول
+
+377
+00:31:06,690 --> 00:31:12,610
+هيك كلهم tractable مقبولين مبلوعين زي تو ال
+
+378
+00:31:12,610 --> 00:31:17,570
+matrices ال ضرب ال matrices كانت polynomial ال C
+
+379
+00:31:17,570 --> 00:31:22,580
+كانت تلاتةفكانت in to the power تلاتة ماشي مجبولة
+
+380
+00:31:22,580 --> 00:31:26,740
+مجبولة الأجهزة أجهزة الحواسيب بتقدر تعملها هاي
+
+381
+00:31:26,740 --> 00:31:29,760
+معناها أنه أجهزة جهاز الحسوب بقدر يعملها ما بعد
+
+382
+00:31:29,760 --> 00:31:34,740
+ذلك لأ ما بعد ذلك بتصير خلاص في range ال
+
+383
+00:31:34,740 --> 00:31:40,060
+interactable كويس الكلام هذا نظر نسبيا لأنه عمليا
+
+384
+00:31:40,060 --> 00:31:44,060
+هتلاقي في حالات نادرة شوية ممكن يظهر عندك حاجة زي
+
+385
+00:31:44,060 --> 00:31:48,830
+هذه in to the power one millionالمفروض ان هي مصنفة
+
+386
+00:31:48,830 --> 00:31:54,670
+tractable مش هي polynomial tractable بس يعني مش
+
+387
+00:31:54,670 --> 00:31:58,970
+هيشتغلها الجهاز هيجف ان هي الجهاز يعني يجرب يعملها
+
+388
+00:31:58,970 --> 00:32:00,970
+على القالة الحاسبة ما هو القالة الحاسبة هي
+
+389
+00:32:00,970 --> 00:32:04,670
+calculator في الآخر يعني computer calculator ال
+
+390
+00:32:04,670 --> 00:32:08,090
+computer و الكلام ده كله عندنا هنشوف هنتكلم عن
+
+391
+00:32:08,090 --> 00:32:12,350
+واحد شوية عمل فلسفة له لحاله اسمه Turing Alan
+
+392
+00:32:12,350 --> 00:32:15,250
+Turing Alan Turing لأنه هو اول واحد عامل قالة
+
+393
+00:32:15,250 --> 00:32:20,490
+حاسبة في العالمالبريطاني هذا جثته جثة يعني لو بدنا
+
+394
+00:32:20,490 --> 00:32:23,370
+نقعد نحكي جثته لو عندنا مجال انه معناه وجد كنا
+
+395
+00:32:23,370 --> 00:32:26,450
+حكينا جثته هتلاقي انه فيها جثث علمية كتير في مصها
+
+396
+00:32:26,450 --> 00:32:30,970
+هل إله علاقة بال Apple؟ مالوش علاقة بالتفاحة
+
+397
+00:32:30,970 --> 00:32:35,750
+المجروطة هذه ولا إله علاقة؟ طيب إيش .. إله علاقة
+
+398
+00:32:35,750 --> 00:32:38,710
+كان في الحرب العالمية؟ كان له ولا ماكانوش جثث
+
+399
+00:32:38,710 --> 00:32:41,790
+تانية؟ بس مش معرضنا يعني ياريت في وجد كنا نحكيلكم
+
+400
+00:32:41,790 --> 00:32:46,990
+جثث علمية هكذا هتنرجع ل ..لشغل، هل وجد هذه
+
+401
+00:32:46,990 --> 00:32:52,450
+polynomial فعليًا، لكن هل في جهاز حسوب يحسبها؟ مش
+
+402
+00:32:52,450 --> 00:32:56,550
+هتلاقي، مش هتلاقي جهاز حسوب يحسبلك إياها، فإذا هي
+
+403
+00:32:56,550 --> 00:32:58,790
+رغم إن هي تكنيكا اللي بقدر أقول إن هي tractable
+
+404
+00:32:58,790 --> 00:33:03,990
+لكن واضح إن هي impossible to solve، كتير معقدة أو
+
+405
+00:33:03,990 --> 00:33:06,950
+كتير صعبة إنك أنت تحلها، كتير صعبة للحل، اعملها
+
+406
+00:33:06,950 --> 00:33:10,110
+على أي حاسبة؟ أقولك على الحاسبة بتاعة الحسوب نفسه
+
+407
+00:33:11,200 --> 00:33:14,680
+عالقالة الحاسوب بتاعة الحاسوب اكتب لك هنا وين راحت
+
+408
+00:33:14,680 --> 00:33:17,160
+ان هنا بتلاتة و لا باربعة و احنا بنتكلم عن رقم
+
+409
+00:33:17,160 --> 00:33:21,520
+متواضع ك input ك input يعني كإنك بتتكلم عن array
+
+410
+00:33:21,520 --> 00:33:26,480
+فيها تلاتة اربعة elements و to the power one
+
+411
+00:33:26,480 --> 00:33:31,160
+million هتجف مش هتطلعلك شيء طيب بس في المقابل هي
+
+412
+00:33:31,160 --> 00:33:35,320
+مثلا متغير to the power متغير يعني انت دخلت في ال
+
+413
+00:33:35,320 --> 00:33:38,820
+exponential هيك دخلت في exponential دخلت في
+
+414
+00:33:38,820 --> 00:33:46,710
+الفعليااللي هي into the power in صحيح من ناحية
+
+415
+00:33:46,710 --> 00:33:51,130
+التقنية انت دخلت في into the power in اللي قلنا
+
+416
+00:33:51,130 --> 00:33:54,170
+عليها مستحيلة ولكن في حالة زي هذه لأ هي ممكنة
+
+417
+00:33:54,170 --> 00:34:00,500
+لأنها تلاقيش أكبر array ممكن تشتغل عليهاpractical
+
+418
+00:34:00,500 --> 00:34:04,440
+أكبر array ممكن تشتغل عليها احنا المرة اللي فاتت
+
+419
+00:34:04,440 --> 00:34:07,860
+لما كنا بتتكلم عن اتنين log قلنا انه وصلتنا لعشرة
+
+420
+00:34:07,860 --> 00:34:12,420
+to the power عشرة طلعت النتج واحد يعني صارت into
+
+421
+00:34:12,420 --> 00:34:17,240
+the power واحد طب كمان log يعني عشرة to the power
+
+422
+00:34:17,240 --> 00:34:18,260
+عشرة to the power عشرة
+
+423
+00:34:21,280 --> 00:34:25,200
+لاحظت؟ فهذه بتسمحلك إنك هنا يطلع in to the power
+
+424
+00:34:25,200 --> 00:34:29,040
+واحد إذا كانت in هنا عشرة to the power عشرة to the
+
+425
+00:34:29,040 --> 00:34:34,680
+power عشرة في قربي هذا الشكل فعمليا بسيطة، رغم إن
+
+426
+00:34:34,680 --> 00:34:41,260
+هي حسب معيارنا، لأ هي تصنف interactableطبعا
+
+427
+00:34:41,260 --> 00:34:44,380
+الحالات هذه كويس ان هي كتير نادرة .. كتير نادرة
+
+428
+00:34:44,380 --> 00:34:47,580
+انه يظهر معاك حالات زي هيك .. كتير نادرة معظم
+
+429
+00:34:47,580 --> 00:34:50,940
+البرامج لأ هي حسب مفهومنا فعلا عند polynomial اوقف
+
+430
+00:34:50,940 --> 00:34:55,400
+.. عند ال polynomial اوقف مثال ع السريحيكي لو
+
+431
+00:34:55,400 --> 00:35:00,820
+أخدنا بتكلم عن ال N ب 10 N ب 10 يعني عدد ال byte
+
+432
+00:35:00,820 --> 00:35:04,560
+ال bits .. ال bits عشرة معنا ذلك ان ال byte ك
+
+433
+00:35:04,560 --> 00:35:10,560
+bytes واحد وربع اللي هي عشرة bitsمقابل one million
+
+434
+00:35:10,560 --> 00:35:14,980
+bit يعني حوالي 125 كيلو 125 كيلو بالنسبالي حاجة
+
+435
+00:35:14,980 --> 00:35:18,680
+صغيرة لغرفنك
+
+436
+00:35:18,680 --> 00:35:22,620
+مقبولة هذه اذا انا بدي اقول بشتغل على الأجهزة
+
+437
+00:35:22,620 --> 00:35:25,740
+العادية اللي هي بتشتغل على السيليكون السيليكون ال
+
+438
+00:35:25,740 --> 00:35:28,440
+slow rate تبعها و ال response تبع انصر السيليكون
+
+439
+00:35:28,440 --> 00:35:31,820
+هو تقريبا one nanosecondبنانو ساكند one nanosecond
+
+440
+00:35:31,820 --> 00:35:35,440
+كويس اللي هو ال response تبع لل silicon فعشان هيك
+
+441
+00:35:35,440 --> 00:35:40,820
+يكون هو المعيار عادة للشغل في الآخر تمام لو قلنا
+
+442
+00:35:40,820 --> 00:35:44,680
+log فإذا هنا بدي أقول والله كل عملية محتاجة
+
+443
+00:35:45,690 --> 00:35:49,710
+response ال silicon تبعنا اللي هو 1 nano فمعنى ذلك
+
+444
+00:35:49,710 --> 00:35:53,690
+انه هنا بتطلع عندي 3.3 nano ولا اشي يعني مافيش على
+
+445
+00:35:53,690 --> 00:35:57,130
+طول خلصلك المعادلة إذا كان بتكلم عنه one million
+
+446
+00:35:57,130 --> 00:36:02,590
+بتصير تسعتاشر نوع عشرين nanoعشرين نانو ساكند سريعة
+
+447
+00:36:02,590 --> 00:36:06,990
+مش مشكلة طيب linear برضه بتتكلم عن عشرة نانو و هنا
+
+448
+00:36:06,990 --> 00:36:11,870
+مليون نانو فبتتكلم عن بالملي برضه مش هتشعر فيها
+
+449
+00:36:11,870 --> 00:36:16,950
+هتلاقيها على طول خلصتلاقيها ماشية طيب ال linear
+
+450
+00:36:16,950 --> 00:36:22,670
+rhythmic هتضرب اتنين في بعض لواحد من انا؟ اه
+
+451
+00:36:22,670 --> 00:36:28,180
+بالظبط اه جزء من الثانية يعنيملي اللي هي واحد من
+
+452
+00:36:28,180 --> 00:36:31,540
+الف من الثانية واحد من الف من الثانية تمام طيب
+
+453
+00:36:31,540 --> 00:36:35,760
+تربيع اللي هي polynomial هيها لعند polynomial اذا
+
+454
+00:36:35,760 --> 00:36:38,880
+كانت بتعامل مع عشرة فهي عشرة nano مافيش اشي يعني
+
+455
+00:36:38,880 --> 00:36:43,140
+مش هشهر فيها اطلاقا مش هنشهر فيها عشرة مية nano
+
+456
+00:36:43,140 --> 00:36:47,000
+يعني تقريبا فاصلة واحد micro فاصلة واحد micro بس
+
+457
+00:36:47,000 --> 00:36:51,120
+في المقابل هنا بتطلع ستاشر minute لما بتكلم عن one
+
+458
+00:36:51,120 --> 00:36:57,970
+million one million تربيع ستاشر دقيقة16 دقيقة إذا
+
+459
+00:36:57,970 --> 00:37:00,910
+كان والله محرز البرنامج وانت محتاج مثلا بتعمل ال
+
+460
+00:37:00,910 --> 00:37:04,890
+neural network بتعمل تدريب ل AI ماشي ربع الساعة مش
+
+461
+00:37:04,890 --> 00:37:09,150
+مشكلة هتقول مش مشكلة الربع الساعة في الزمنات لما
+
+462
+00:37:09,150 --> 00:37:14,350
+كنا نشتغل ال neural network كنت أستنى 24 ساعة اه
+
+463
+00:37:14,350 --> 00:37:18,770
+يعني أطف الشاشة و أسيب الجهاز يشتغل و خلاص 24 ساعة
+
+464
+00:37:18,770 --> 00:37:21,150
+و بعدين تصحى تاني يوم تتفاجأ ان كان في error في
+
+465
+00:37:21,150 --> 00:37:25,910
+البرنامج فترجع تعيد و تتعدل من جديد كويس؟طبعا
+
+466
+00:37:25,910 --> 00:37:29,710
+لعندنا هه مبلوعة بدليل انهيني انا كنت مبلوعة
+
+467
+00:37:29,710 --> 00:37:32,750
+بالنسبالي حتى الاربع عشرين ساعة كنت اقول ماشي في
+
+468
+00:37:32,750 --> 00:37:35,910
+وجتها طبعا الان الأجهزة كتير صارت أسرع .. كتير
+
+469
+00:37:35,910 --> 00:37:40,450
+صارت أسرع فممكن تاخد منا عشر دجاج اه ممكن تاخد عشر
+
+470
+00:37:40,450 --> 00:37:44,280
+دجاج اللي كانت تاخد مني اربع عشرين ساعةطيب لما
+
+471
+00:37:44,280 --> 00:37:48,660
+أدخل على ال exponential لأ exponential بالنسبة
+
+472
+00:37:48,660 --> 00:37:53,500
+لعشرة okay عدد جليل مقبولة بس هنا مليون اتنين to
+
+473
+00:37:53,500 --> 00:37:57,720
+the power مليون زي ما كنا كتبينها و قولنا ان هي
+
+474
+00:37:57,720 --> 00:38:01,540
+attractable فعليا كانت منظرها عفوا ان كانت بالعكس
+
+475
+00:38:01,540 --> 00:38:04,180
+هنا مليون to the power اتنين to the power مليون
+
+476
+00:38:04,180 --> 00:38:08,380
+مظبوط بس كنا كتبينها عكسية كنا كتبين هنا ال in و
+
+477
+00:38:08,380 --> 00:38:12,060
+كنا كتبين هنا ال one million صحيح فهي ظهرت معانا
+
+478
+00:38:12,940 --> 00:38:19,280
+Ten خد to the power تلاتمية و واحد ألف و أربعة و
+
+479
+00:38:19,280 --> 00:38:25,540
+نص جيجا يير فمتخيل
+
+480
+00:38:25,540 --> 00:38:29,820
+جدش الحجم الزمن يعني عمر الأرض أكتر أكتر من عمر
+
+481
+00:38:29,820 --> 00:38:37,320
+الأرض تمام factorial ماشي لعند هنا فيش جهاز حسبها
+
+482
+00:38:37,320 --> 00:38:44,330
+فيش جهاز حسبهايعني أكبر جهاز في الكورة الأرضية ما
+
+483
+00:38:44,330 --> 00:38:48,330
+حسبهاش حتى الآن اللي هي ال nano factory ما حسبهاش
+
+484
+00:38:48,330 --> 00:38:54,370
+فعشان انا مش عارف ماحدش حسبها أصلا ماحسبها ماوصلش
+
+485
+00:38:54,370 --> 00:38:59,700
+ماحدش وصلها يعني ماحدش جابها تمامطب ال unsolved
+
+486
+00:38:59,700 --> 00:39:03,180
+problem هد برضه زي ما قلنا تورينج اكتشف في
+
+487
+00:39:03,180 --> 00:39:06,660
+الارتسان مية و تلاتين انه في بعض ال problems ممكن
+
+488
+00:39:06,660 --> 00:39:11,020
+اصنف ان هي غير محلولة او غير قابلة للحل و unsolved
+
+489
+00:39:11,020 --> 00:39:17,640
+بأي algorithm بأي algorithm نهائيا هد معناته انه
+
+490
+00:39:19,580 --> 00:39:24,180
+ممكن اقول عنها there are undesirable yes or no
+
+491
+00:39:24,180 --> 00:39:33,080
+question بمعنى انا مش جادر حتى مش هحلها مش جادر
+
+492
+00:39:33,080 --> 00:39:38,260
+اتحقق من حل يعني ممكن يعطيني حل ويقولي بس تحقق انه
+
+493
+00:39:38,260 --> 00:39:42,360
+صح ولا غلط انا مش جادر اتحقق من حلها ففي بعض
+
+494
+00:39:42,360 --> 00:39:45,680
+المشاكل انا مش جادر اتحقق من حلها زي تاعتوى ال
+
+495
+00:39:45,680 --> 00:39:50,760
+arch هذه يعني هذا لو انا كتبتلك اي رقمكتبتلك أي
+
+496
+00:39:50,760 --> 00:39:55,660
+رقم و أقولك و الله اتأكدلي هل الرقم هذا صحيح هو مش
+
+497
+00:39:55,660 --> 00:39:58,660
+مطلوب انك تحل هو مطلوب انك بس تتأكد تعمل tracking
+
+498
+00:39:58,660 --> 00:40:02,460
+هل هو الرقم هذا صح ولا مش صح برضه مش هتقدر برضه مش
+
+499
+00:40:02,460 --> 00:40:05,580
+هتقدر فمعناه ذلك انه هنا لو كان في مجموعة
+
+500
+00:40:05,580 --> 00:40:08,820
+functions هي انا مش جادر اقول yes or no يعني مش
+
+501
+00:40:08,820 --> 00:40:12,900
+جادر اقرر حتىأعملها tracking عند الحل موجود بس
+
+502
+00:40:12,900 --> 00:40:16,000
+اعمله tracking انه صح ولا غلق مظبوط ولا مش مظبوط
+
+503
+00:40:16,000 --> 00:40:21,400
+مش طالب حل مش طالبين حل ففي كتير مشاكل بالشكل هذا
+
+504
+00:40:21,400 --> 00:40:24,700
+في كتير مشاكل وهذه بتصير مع ال halting problem في
+
+505
+00:40:24,700 --> 00:40:28,000
+ال halting problem كل اللي بيصير arbitrarily اي
+
+506
+00:40:28,000 --> 00:40:32,520
+algorithm اتجربه ل ال inputs بتاعتها ل problem هذه
+
+507
+00:40:32,520 --> 00:40:36,520
+بعدد ال inputs ال whatever اش بيطلع ال input لو اي
+
+508
+00:40:36,520 --> 00:40:42,020
+code اي algorithm جربته في الآخربشكل نهائي حيصله
+
+509
+00:40:42,020 --> 00:40:49,660
+hard توقف ال code هيتوقف hard توقف خلاص او يدخل في
+
+510
+00:40:49,660 --> 00:40:56,000
+loop او يدخل في loop فإذا اما يتوقف و عادة بيطلعلك
+
+511
+00:40:56,000 --> 00:40:58,920
+في الحالة هادي الشاشة الزرعية بيقولك ال memory
+
+512
+00:40:58,920 --> 00:41:04,740
+خلاص مش جادر تتحمل اكتر فتوقف كامل او انه زي ما
+
+513
+00:41:04,740 --> 00:41:10,270
+بيقوله بيروح برجعش ال code راح منكلازم مضطر بعد اي
+
+514
+00:41:10,270 --> 00:41:13,950
+جداش بدك تسبور عليه يومين تلاتة اربع بعدين بدك
+
+515
+00:41:13,950 --> 00:41:17,730
+تطفي الجهاز بدك تطفي الجهاز ازهجت فاما انه هيضل
+
+516
+00:41:17,730 --> 00:41:22,350
+forever او ان هو لأ automatic خلاص هيوقف هيوقف
+
+517
+00:41:22,350 --> 00:41:26,390
+بمعنى انه لأ ال space عندك هو متسع لبرنامج هو مش
+
+518
+00:41:26,390 --> 00:41:30,230
+هيفرد كتير في ال space لكن ال time forever فهذه
+
+519
+00:41:30,230 --> 00:41:34,860
+دخلت في loopأو أنه لأ ممكن حالة من الحالات يعملك
+
+520
+00:41:34,860 --> 00:41:37,680
+وقف كامل إذا كان ال space اللي جاها ماكملتش معاه
+
+521
+00:41:37,680 --> 00:41:40,300
+فاطوماتيك إذا بتلاحظوا أحيانا بعض البرامج عندكم
+
+522
+00:41:40,300 --> 00:41:44,780
+بتطلعلكوا شاشة زرجة تطلع شاشة .. إذا مش عارف صدفت
+
+523
+00:41:44,780 --> 00:41:47,000
+معاكوا قبل هيكي الشاشة الزرجة بيقولك من الأول ..
+
+524
+00:41:47,000 --> 00:41:50,060
+من الأخر خلاص الجهاز عندك إمكانيته لا تسمح أني
+
+525
+00:41:50,060 --> 00:41:56,860
+أكمل فوقف بوقف و عادة لو قرأت هتلاقي أنه بيشيرلك
+
+526
+00:41:56,860 --> 00:42:00,540
+هيك للذاكرةبيشرلك من قريب أو من بعيد للذاكره لأنه
+
+527
+00:42:00,540 --> 00:42:04,580
+والله مش لاجي الذاكره يكمل وقف فهذه ال problem ..
+
+528
+00:42:04,580 --> 00:42:08,240
+في كذا problem تعمل كلام هذا في كذا problem عشان
+
+529
+00:42:08,240 --> 00:42:11,940
+نفهم هذا الكلام صار في عندي الآن قصتين قصة
+
+530
+00:42:11,940 --> 00:42:16,960
+tractable وسميناهم كل tractable وسميناها capital P
+
+531
+00:42:16,960 --> 00:42:22,840
+صحيح؟ وفي المقابل في حاجة انا مش جادر اتحقق من
+
+532
+00:42:22,840 --> 00:42:30,120
+الحل صح ولا غلطمظبوط؟ طب العكس أني قادر أتحقق من
+
+533
+00:42:30,120 --> 00:42:36,500
+الحل فبن .. في الحالة هذه بنسميهم NP-SET هذه ال
+
+534
+00:42:36,500 --> 00:42:42,740
+problems اللي بقدر أعملها attractable ل algorithm
+
+535
+00:42:42,740 --> 00:42:51,180
+مش حلها خدوا بالكم مش حلها كمان مرة يتأكد من حل
+
+536
+00:42:51,180 --> 00:42:57,250
+معين given عندكيتأكد من حال معين given عندك زي ..
+
+537
+00:42:57,250 --> 00:43:02,330
+زي لما نقول عندك ست بسيطة جدا زي اللي أنا حاططها
+
+538
+00:43:02,330 --> 00:43:09,530
+مشير إليها هيك عساس أنه أتكلم عنها و
+
+539
+00:43:09,530 --> 00:43:14,950
+سبعة خلاص ضل إش .. أه في كمان سالب عشرة لما أقولك
+
+540
+00:43:14,950 --> 00:43:22,410
+اعملي منهم اعملي منهم أكم sub 6 مجموعة أناصرها
+
+541
+00:43:22,410 --> 00:43:22,970
+تسوء صفر
+
+542
+00:43:26,110 --> 00:43:30,050
+طبعا مضطر تعمل كل ال subsets عونها صح؟ ملاحظ حجم
+
+543
+00:43:30,050 --> 00:43:35,210
+المشكلة؟ حجم كبير طيب هذا عشان تحلها لكن لو قلتلك
+
+544
+00:43:35,210 --> 00:43:40,930
+اعملي check هل .. ايش احنا كررت ال 15 كده مرتين؟
+
+545
+00:43:40,930 --> 00:43:53,540
+بهذا الشكل هل سالب 2 سالب 3 15 و سالب 10 هي حل؟حل
+
+546
+00:43:53,540 --> 00:43:58,680
+فشوفتوا عملتلي check جداش ماخدتش شي هي حل لكن لما
+
+547
+00:43:58,680 --> 00:44:04,440
+أقولك الحل نفسه أنه هتلي كل ال subsets اللي مجموع
+
+548
+00:44:04,440 --> 00:44:09,160
+أنصرها يسووا عشرة لأ هي مش مجرد check هي solve the
+
+549
+00:44:09,160 --> 00:44:14,460
+problem هي بدك تحل المشكلة نفسها فاختلفوا تتنين عن
+
+550
+00:44:14,460 --> 00:44:20,120
+بعض فالجثة بطلت tractable لحلها هي tractable for
+
+551
+00:44:20,120 --> 00:44:25,440
+checkingيعني معناه ذلك أن ال NP هي المشاكل اللي
+
+552
+00:44:25,440 --> 00:44:32,280
+يمكن تشك ل given solution هو صح ولا غلط بينما ال P
+
+553
+00:44:32,280 --> 00:44:37,540
+لحالها هي كل ال tractable problems اللي قابلة للحل
+
+554
+00:44:39,010 --> 00:44:43,570
+فمعنى ذلك أن بقدر أقول أن P هي subset من NP بمعنى
+
+555
+00:44:43,570 --> 00:44:49,930
+كل مشكلة قابلة للحل فهي قابلة أن أعمل check لحل
+
+556
+00:44:49,930 --> 00:44:56,570
+given عندها، صح؟ منطقيا، لكن ليس كل مشكلة بقدر
+
+557
+00:44:56,570 --> 00:45:04,570
+أعمل check لها فهي نفسها قابلة للحلصح؟ طيب طب إيش
+
+558
+00:45:04,570 --> 00:45:09,570
+رأيكوا إنه هذه نفسها هذه هيك كإثبات لعند الآن
+
+559
+00:45:09,570 --> 00:45:13,870
+ماحدش أثبت العلاقة هذه صح ولا غلط واللي بيفبتها
+
+560
+00:45:13,870 --> 00:45:18,850
+إله مليون دولار وفي فعلا في أكاديمية علمية لعند
+
+561
+00:45:18,850 --> 00:45:21,650
+الآن طارحة في الألفية كاملة في الألفية ال .. ال ..
+
+562
+00:45:21,650 --> 00:45:28,010
+ألفية ال .. العشرين طارحين تمن مسائل اللي بحل أي
+
+563
+00:45:28,010 --> 00:45:32,980
+واحدة منهم إله مليون دولار على طولهذه واحدة منهم
+
+564
+00:45:32,980 --> 00:45:41,080
+هذه واحدة منهم كويس فكرة انه هل فعلا هي prepare
+
+565
+00:45:41,080 --> 00:45:49,400
+subset بمعنى انه لأ لأ مستثنى منها اليساوي هنا
+
+566
+00:45:49,400 --> 00:45:53,660
+يقولنا subset صح؟ subset عارفش يعني subset؟ يعني
+
+567
+00:45:53,660 --> 00:45:59,420
+أو يساوي مش شايف؟ الآن يقولك لأ الاعتقاد السائد
+
+568
+00:45:59,420 --> 00:46:05,740
+فهي unprovedconjecture الحدث والغير مثبت انه لأ هي
+
+569
+00:46:05,740 --> 00:46:12,480
+super subset اه عفوا ال prepare subset او strictly
+
+570
+00:46:12,480 --> 00:46:20,300
+subset هي مجموعة جزئية ولا تساوي ولا تساوي طب اثبت
+
+571
+00:46:20,300 --> 00:46:24,820
+الكلام هذا تخيل ان احنا لعندي الآن هنا في ال 2000
+
+572
+00:46:24,820 --> 00:46:30,710
+و 21 ولا حد حلالمسألة هذه لأنها ضالت من المسائل
+
+573
+00:46:30,710 --> 00:46:32,830
+السبعة اللي ما انحلتش، في واحدة بالمناسبة انحلت
+
+574
+00:46:32,830 --> 00:46:37,830
+واحدة بس وصاحبها أخد المليون ووزعه وقال بديش مليون
+
+575
+00:46:37,830 --> 00:46:46,870
+اللي حلها يعني، تمام؟ okay هذه جثة طبعا متذكرين ال
+
+576
+00:46:46,870 --> 00:46:52,900
+primes لما اتكلمنا عن ال primesوقولنا هل عندك code
+
+577
+00:46:52,900 --> 00:46:56,920
+يعمل لك كل primes لكن لو قلتلك ان لا يوجد prime
+
+578
+00:46:56,920 --> 00:47:02,640
+أعلى تعمل check سريع مش هيك و احنا أثبتناها لكن في
+
+579
+00:47:02,640 --> 00:47:06,100
+المقابل انك انت تقعد تحسبلي كل primes عشان تثبتلي
+
+580
+00:47:06,100 --> 00:47:10,240
+ان لا يوجد prime أعلى أكيد مش منطقي فهيها
+
+581
+00:47:10,240 --> 00:47:16,020
+tractable و ال P و ال N انا بقدر اعمل check بس مش
+
+582
+00:47:16,020 --> 00:47:19,580
+معناه ذلك اني بقدر احل المشكلة ان اعمل check اه
+
+583
+00:47:20,420 --> 00:47:25,500
+يعطيني given ل solution بعملك check صح ولا غلط أما
+
+584
+00:47:25,500 --> 00:47:28,200
+تقوللي أنا علور على ال solution ل problem صارت إيش
+
+585
+00:47:28,200 --> 00:47:32,060
+interactable واضح الجزئية هذه؟ انت كمبرمج لازم
+
+586
+00:47:32,060 --> 00:47:35,000
+تكون فاهم النقطة هذه نقطة كتير مهمة في ال
+
+587
+00:47:35,000 --> 00:47:41,900
+complexity تمام كيف؟
+
+588
+00:47:41,900 --> 00:47:45,440
+اعكس
+
+589
+00:47:45,440 --> 00:47:48,300
+و اعمل و شوف اللي بدك إياه ساعتها إذا حلتها
+
+590
+00:47:48,300 --> 00:47:53,130
+ماتجينيش أنادور على ال net و خد المليون حلال عليك
+
+591
+00:47:53,130 --> 00:48:01,110
+اشتغل فيها طيب نكمل طيب
+
+592
+00:48:01,110 --> 00:48:05,510
+بالمرة مدام احنا في الأكواد وجدنا يمكن مناسب انه
+
+593
+00:48:05,510 --> 00:48:09,540
+اليومك في هالوقت اللي ضايل ناخد لنا مثال او اتنين
+
+594
+00:48:09,540 --> 00:48:14,300
+من امثلة على الاكواد بديش ارجع و نفصلكم و نرجع على
+
+595
+00:48:14,300 --> 00:48:19,320
+ال .. على جد مثال ناخدلنا هيك سريع .. كويس أخدتوا
+
+596
+00:48:19,320 --> 00:48:24,580
+قبل هيك ال .. ال palindrome ممتاز .. ممتاز
+
+597
+00:48:24,580 --> 00:48:28,920
+أخدتولها code يعني طيب ممتاز كويس فإذا إلها أمثلة
+
+598
+00:48:28,920 --> 00:48:32,820
+كتيرة ال palindrome و يمكن ال code هيكون بسيط جدا
+
+599
+00:48:32,820 --> 00:48:36,270
+أخدتهوا كتبتهواطيب يعني هاي حاجة من الحاجات اللي
+
+600
+00:48:36,270 --> 00:48:39,810
+احنا عادة بجيبها بالاسئلة هيك وطلعته ماخدينها
+
+601
+00:48:39,810 --> 00:48:44,750
+وماشية معاكم ان شاء الله تعالى خلاص بيكفي على هيك
+
+602
+00:48:44,750 --> 00:48:49,190
+بيكفي على هيك أخدنا كذا مثال ويمكن هيك تعتبره
+
+603
+00:48:49,190 --> 00:48:53,390
+خلصته جزئية ال complexity ان شاء الله تكون يعني
+
+604
+00:48:53,390 --> 00:48:56,510
+تناغمت مع ال data structure يعطيكوا ألف عافية
+
+605
+00:48:56,510 --> 00:48:57,170
+وبركة الله فيكم
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/QkhqcRfm9Hs_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/QkhqcRfm9Hs_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5d9af570b786f7909f08d458ffdde158b19f8fa0
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/QkhqcRfm9Hs_raw.srt
@@ -0,0 +1,2424 @@
+1
+00:00:05,030 --> 00:00:07,430
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:07,430 --> 00:00:10,990
+بركاتكم العافية نكمل اليوم ان شاء الله تعالى كان
+
+3
+00:00:10,990 --> 00:00:14,990
+جزئيا ضيلالنا في ال complexity عشان نكون هنا الملف
+
+4
+00:00:14,990 --> 00:00:20,690
+فعليا و نبدأ في شوية أسئلة محلولة طبعا كان في
+
+5
+00:00:20,690 --> 00:00:25,530
+أسئلة محلولة عن الأجزاء السابقة اللي هي ال sets و
+
+6
+00:00:25,530 --> 00:00:31,270
+ال matrices و في أسئلة محلولة عن ال ..الـ
+
+7
+00:00:31,270 --> 00:00:35,850
+pseudocode الأكواد فما بعرف أنية اللي ممكن تكون
+
+8
+00:00:35,850 --> 00:00:40,570
+أولى باعتبار أن أحنا دخليني على امتحان هل نستمر في
+
+9
+00:00:40,570 --> 00:00:44,330
+موضوعنا لليوم أن أحنا نضلنا فيه الأكواد فنكمل
+
+10
+00:00:44,330 --> 00:00:49,330
+الأسئلة المحلولةكأكواد نحلل فيها نشتغل عليها و لا
+
+11
+00:00:49,330 --> 00:00:52,710
+نرجع خطوة لورا لإنه بدك نطلع على امتحان ناخد ال
+
+12
+00:00:52,710 --> 00:00:55,670
+matrices و الأمور فبتهير خلاص خلينا ماشيين اليوم
+
+13
+00:00:55,670 --> 00:00:59,850
+كله أكواد و ن .. و نكمل في الموضوع حدا فناخد أقل
+
+14
+00:00:59,850 --> 00:01:03,250
+أكم من code اللي ضايلين كويس و نعتبرهم كأنه هي
+
+15
+00:01:03,250 --> 00:01:06,870
+عملت مراجعة و ناخد برضه أكم من code من اللي عادة
+
+16
+00:01:06,870 --> 00:01:10,310
+كنا .. يعني أجوا قبل هيك في امتحانات شمال أو يمين
+
+17
+00:01:10,310 --> 00:01:14,450
+طيب أخر حاجة كنا اتكلمنا فيها كان ال linear search
+
+18
+00:01:15,070 --> 00:01:19,350
+إذا متذكرين و كنا بنحسبله ال complexity و إشتغلنا
+
+19
+00:01:19,350 --> 00:01:22,890
+عليه و أخدنا التلت حالات كمان ال worst case و
+
+20
+00:01:22,890 --> 00:01:25,530
+أخدنا في ال best case و أخدنا في ال average case
+
+21
+00:01:25,530 --> 00:01:30,350
+لمجرد بس أنه نشوف التلت حالات عن بعض و اتفقنا بعد
+
+22
+00:01:30,350 --> 00:01:34,250
+هيك على ال worst case خلصنا هنشتغل على ال worst
+
+23
+00:01:34,250 --> 00:01:38,530
+case time complexity مش هيك و اتفقنا أن هذا هي
+
+24
+00:01:38,530 --> 00:01:44,080
+اللي فقط هنثبت عليها تمامفي ال binary ال binary
+
+25
+00:01:44,080 --> 00:01:47,800
+الصراحة شرحناها سابقا جابل هيك احنا خدنا ال binary
+
+26
+00:01:47,800 --> 00:01:51,320
+search واتفقنا على تفاصيله مافيش مشكلة و رسمناها
+
+27
+00:01:51,320 --> 00:01:56,180
+على جنبه شرحناها بشكل موسع دل الان نتعامل مع ال
+
+28
+00:01:56,180 --> 00:01:59,340
+complexity كيف بدنا نحسبها كيف بدنا نحسب ال
+
+29
+00:01:59,340 --> 00:02:02,680
+complexity سبعته ال complexity ببساطة حاجة اقول
+
+30
+00:02:02,680 --> 00:02:10,150
+الجزء الاول هنا اللي هو مجرد اعطاء قيمI بتسوى واحد
+
+31
+00:02:10,150 --> 00:02:14,830
+J بتسوى N فهذه θ of واحد وهي constant ثابت يعني
+
+32
+00:02:14,830 --> 00:02:19,030
+معناه ذلك انه الوقت اللي محتاجه على نفسالجهاز نفس
+
+33
+00:02:19,030 --> 00:02:24,350
+ال processor هيكون ثابت من ملف لملف من code ل code
+
+34
+00:02:24,350 --> 00:02:28,490
+هو هو مش هيتغير فإذن بالنسبالي ثابت هنا نفس الجثة
+
+35
+00:02:28,490 --> 00:02:32,870
+أن أحسب كل مرة ال midpoint حسبة ال midpoint لحالها
+
+36
+00:02:32,870 --> 00:02:37,910
+كعملية لحالها هي ثابتة إلها time محدد و بيظل كما
+
+37
+00:02:37,910 --> 00:02:42,690
+هو و بعدين ال if then نفس الجثة بفحص برضه إلها زمن
+
+38
+00:02:42,690 --> 00:02:47,060
+معين ثابتمش مشكلة فلعندي ال end خلصنا الجزيتين
+
+39
+00:02:47,060 --> 00:02:50,280
+هدول خلصنا الجزيتين اللي جوا ال loop بس ماتكلمتش
+
+40
+00:02:50,280 --> 00:02:54,120
+لسه عن ال loop ال loop لسه ماحكيناش عنه بعدك خلصنا
+
+41
+00:02:54,120 --> 00:03:00,360
+ال end تمام في اخر شغلة ان احنا نفحص اخر عنصر
+
+42
+00:03:00,360 --> 00:03:04,960
+موجود ده العنصر الأخير هل هو بساوي x اللي نبحث
+
+43
+00:03:04,960 --> 00:03:12,310
+عنها ولا لأ فبرضه هذهfixed هدى المفروض انها ثابتة
+
+44
+00:03:12,310 --> 00:03:17,490
+constant time ثابت و بيضل ثابت كما هو طيب فكله
+
+45
+00:03:17,490 --> 00:03:21,170
+ثوابت لكن فى شغل احنا لسه ماخدناش بقالنا منها ال
+
+46
+00:03:21,170 --> 00:03:28,650
+while بمعنى ان ثابت اللى هنا اكم مرة بتكرر وهدى كل
+
+47
+00:03:28,650 --> 00:03:30,570
+ال complexity ده دائما جولنا زى ما جولنا فى ال for
+
+48
+00:03:30,570 --> 00:03:33,010
+loop و في ال while ال complexity كلها فى الجزئية
+
+49
+00:03:33,010 --> 00:03:38,990
+هدى فجزئية جداش بتكرر هناعشان نعرف منها ال
+
+50
+00:03:38,990 --> 00:03:42,550
+complexity الحقيقية فعليا فهذا ثابت مش جالجان منه
+
+51
+00:03:42,550 --> 00:03:45,350
+و اللي تحت هذا ثابت مش جالجان منه لأنه مش جوا ال
+
+52
+00:03:45,350 --> 00:03:48,890
+loop أصلا يعني مش هيتكرر ولا بأي حامل أحوال اللي
+
+53
+00:03:48,890 --> 00:03:53,950
+هيتكرر هو اللي جوا ال loop فإذا ال constant هذا هو
+
+54
+00:03:53,950 --> 00:03:58,230
+متغير بمعنى .. هو هيكون بيعتمد على جدش عدد ال
+
+55
+00:03:58,230 --> 00:04:02,410
+inputs لكن عدد ال inputs مربوطة هنا
+
+56
+00:04:10,350 --> 00:04:14,810
+عشان نفهم الجثة كيف كانت ماشية كنا بنشوف ال
+
+57
+00:04:14,810 --> 00:04:21,320
+midpoint و من خلالهابنختصر نص ال interval و بعدين
+
+58
+00:04:21,320 --> 00:04:25,640
+بنحول مباشرة ال midpoint هذا بغض النظر زائد واحد
+
+59
+00:04:25,640 --> 00:04:28,580
+او هو نفسه المهم انه زائد واحد لكن منه بنبدأ
+
+60
+00:04:28,580 --> 00:04:32,660
+interval جديدة عشان ناخد لها ال midpoint and so on
+
+61
+00:04:32,660 --> 00:04:35,780
+بهذا الشكل و نقول والله خلاص خلصنا هذا بدناه شيء
+
+62
+00:04:35,780 --> 00:04:39,960
+فصرنا في midpoint جديدة الان ال loop بيعطيني جديش
+
+63
+00:04:39,960 --> 00:04:45,340
+عدد مراتالتجسيم هذا يدّيش عدد مرات التجسيم اللي
+
+64
+00:04:45,340 --> 00:04:51,400
+هنجعد .. هنجعد كل شوية نعمله لعند ما نصل في الآخر
+
+65
+00:04:51,400 --> 00:04:59,360
+لعنصر واحد فقط نقارن فيه مرة واحدة فالان عدد
+
+66
+00:04:59,360 --> 00:05:03,760
+المرات هذه هذه عدد مرات معناته هذه اكم مرة ال
+
+67
+00:05:03,760 --> 00:05:09,820
+while هتنفذ لكن في نفس الوقت انا عارف ان ال T of N
+
+68
+00:05:09,820 --> 00:05:16,700
+هي زمنأو function في الزمن الزمن هذا معتمد على
+
+69
+00:05:16,700 --> 00:05:24,820
+مين؟ على ال input ال input هي كل عدد العناصر صح؟
+
+70
+00:05:24,820 --> 00:05:30,480
+هي كل عدد العناصر طيب فمعناه ذلك أنه عشان أشوف إيش
+
+71
+00:05:30,480 --> 00:05:34,180
+اللي بيربط لي ال while بعدد العناصر وهي فعلية
+
+72
+00:05:34,180 --> 00:05:39,010
+المتغير الحقيقي عند هنا لازم أجيب علاقة بينهمأجيب
+
+73
+00:05:39,010 --> 00:05:50,210
+علاقة بين جداش عدد مرات تنفيذ ال while و ال in و
+
+74
+00:05:50,210 --> 00:05:55,450
+ال in لأن معنا ذلك هعرف ان كل ما زادت جداش بدي
+
+75
+00:05:55,450 --> 00:06:01,050
+أضطر أزود كمان stage زيادة كل جداش بدي أضطر أزود
+
+76
+00:06:01,050 --> 00:06:06,290
+stage زيادة صحيح؟ لأن ك execution time هو معتمد
+
+77
+00:06:06,290 --> 00:06:11,820
+على أكم مرة بدي أنفذ ال loopواضحة بدي انافذه اربع
+
+78
+00:06:11,820 --> 00:06:16,200
+مرات خلاص اربع مرات طيب ال input لو زاد كمان اتنين
+
+79
+00:06:16,200 --> 00:06:20,020
+زيادة يمكن يظل اربع مرات برضه مايتغيرش طيب عند
+
+80
+00:06:20,020 --> 00:06:24,640
+قيمة معينة ل in اتزيد حتار انافذه كمان مرة خامسة
+
+81
+00:06:24,640 --> 00:06:30,340
+هنا صار في عند زيادة في ال time حيزيد معايا ال
+
+82
+00:06:30,340 --> 00:06:37,250
+time كمان fixedأو time زيادة في rest order .. zero
+
+83
+00:06:37,250 --> 00:06:42,070
+order اللي هو constant .. constant تمام فبدنا نعرف
+
+84
+00:06:42,070 --> 00:06:46,450
+الآن إيه إنت بقدر أقول إنه هضطر أفتح stage زيادة
+
+85
+00:06:46,450 --> 00:06:52,430
+فصار كإني بدي أجيب علاقة ما بين عدد مرات ال stages
+
+86
+00:06:52,430 --> 00:06:57,010
+اللي هي تمثل عدد مرات تنفيذ ال loop بالنسبالنا
+
+87
+00:06:57,010 --> 00:07:00,810
+عشان أصلها قيمة واحدة في الآخر يعني هنا بيكون واحد
+
+88
+00:07:02,160 --> 00:07:07,340
+لأنه عند الواحد احنا عارفين انه بيجف ال loop عرفنا
+
+89
+00:07:07,340 --> 00:07:11,020
+ليش عند الواحد بدنا نوجف لأنه عنده حسب ال
+
+90
+00:07:11,020 --> 00:07:17,600
+proposition تبع ال while بيجف اذا سوا بعض خلاص هنا
+
+91
+00:07:17,600 --> 00:07:21,520
+بتصير false فبنوجف امتى بيسوا بعض اذا وصلت في
+
+92
+00:07:21,520 --> 00:07:24,600
+الآخر لأنصر واحد اللي دل في ال array كلها على
+
+93
+00:07:24,600 --> 00:07:29,240
+بعضها او في ال list كاملة على بعضها طيب ال list
+
+94
+00:07:29,240 --> 00:07:33,990
+هذه من جدش بادية من انفالان بدنا نجيب علاقة بين
+
+95
+00:07:33,990 --> 00:07:41,110
+المرات هذه و امتى بيوصلنا ل .. ل الواحد في الآخر
+
+96
+00:07:41,110 --> 00:07:45,070
+لإمتى بنصل ل الواحد في الآخر فهذه كلنا عارفين انه
+
+97
+00:07:45,070 --> 00:07:49,070
+مدام binary نتعامل
+
+98
+00:07:49,070 --> 00:07:53,990
+معها binary بمعنى هنا كان واحد هنا كانت اتنين
+
+99
+00:07:53,990 --> 00:07:57,510
+بالظبط
+
+100
+00:07:57,510 --> 00:08:03,350
+بالظبط ويلها علاقة بقداش عدد المرات هناهنا صفر لو
+
+101
+00:08:03,350 --> 00:08:07,610
+عملناها بالشكل عكسي في النهاية عدد المرات بدي اعده
+
+102
+00:08:07,610 --> 00:08:12,310
+a to z زي ما بيقولوا او z to a كعدد حيظل واحد
+
+103
+00:08:12,310 --> 00:08:16,150
+فالان احنا بنعده بالعكس بنعده بالعكس لإن انا فاهم
+
+104
+00:08:16,150 --> 00:08:18,810
+ال binary وعارف اعده ال binary ماعنديش مشكلة في ال
+
+105
+00:08:18,810 --> 00:08:23,810
+binary فحنعده بشكل عكسي واحد اتنين اربعة تمانية
+
+106
+00:08:23,810 --> 00:08:29,170
+اين تبقى اصل لقيمة inهنا بدنا ان .. يعني زي ما
+
+107
+00:08:29,170 --> 00:08:32,510
+بقوله انحدد انه ان في الحالة هذه لازم تكون احد
+
+108
+00:08:32,510 --> 00:08:38,230
+مشتقات تضرب في اتنين هذه بمعنى انه ممكن تصل ل 16
+
+109
+00:08:38,230 --> 00:08:47,630
+32 64 صحيح؟ كويس لو كانت اجل من هيك عشان نتفق على
+
+110
+00:08:47,630 --> 00:08:50,770
+نقطة جابل ما نبدأ عملية حسابتنا يعني لو لجيتها
+
+111
+00:08:50,770 --> 00:08:57,700
+مثلا اربعينمعنى ذلك أنا محتاج هنا واحد اتنين تلاتة
+
+112
+00:08:57,700 --> 00:09:06,940
+أربعة خمسة ستة عند الأربعين أكمله بححتاج ستة كأني
+
+113
+00:09:06,940 --> 00:09:10,980
+بعمل sealing بنا نحتاج الستة ساعتها فماعنديش مشكلة
+
+114
+00:09:10,980 --> 00:09:14,760
+حتى لو قيمة n كانت بين رقمين من الأرقام المتعارف
+
+115
+00:09:14,760 --> 00:09:19,090
+عليهم كمضاعفات للاتنين to the power of nماعنديش
+
+116
+00:09:19,090 --> 00:09:24,590
+مشكلة بعمل sealing و خلصناه فإذا انتهت الجثة كل
+
+117
+00:09:24,590 --> 00:09:32,510
+الموضوع صارت بالنسبالي 2 to the power k تساوي n مش
+
+118
+00:09:32,510 --> 00:09:36,870
+هيك .. هي .. هي الكلام هيك بيقول هيك الكلام بيحكي
+
+119
+00:09:36,870 --> 00:09:42,850
+أنه العدد ال total كله هذا ال 64 مثلا أنا عارف أنه
+
+120
+00:09:42,850 --> 00:09:47,430
+الرقم اربع أو من تلاتة و تلاتين لاربع و ستين نفس
+
+121
+00:09:47,430 --> 00:09:51,160
+الشيءمن تلاتة و تلاتين اللي هي من بعد الاتنين و
+
+122
+00:09:51,160 --> 00:09:54,660
+تلاتين خلاص لأربعة و ستين كلهم نفس الاشي ان
+
+123
+00:09:54,660 --> 00:09:58,860
+بالنسبالي كأنها ثابتة مش هيختلف اشي مش هيختلف شي
+
+124
+00:09:58,860 --> 00:10:05,240
+تمام ال K هذه هي اللي بدنا ياها اللي هم عدد ال
+
+125
+00:10:05,240 --> 00:10:10,860
+loops عدد ال loops فهدول هم فعليا ال order فعليا
+
+126
+00:10:10,860 --> 00:10:15,120
+هذا هو ال order بالنسبة للبرنامج لأن البرنامج هو
+
+127
+00:10:15,120 --> 00:10:19,530
+مش شايف انليش مش shape in؟ لأن هو ماعملش linear
+
+128
+00:10:19,530 --> 00:10:25,230
+فهو مامسكش عناصر in واحدة واحدة واحدة مقابل واحدة
+
+129
+00:10:25,230 --> 00:10:28,970
+مقابل واحدة مقابل واحدة فشعر بجدش عددهم، لأ هو
+
+130
+00:10:28,970 --> 00:10:33,610
+مابيعرفش عددهم، هو أشتغل binary binary معناه ذلك
+
+131
+00:10:33,610 --> 00:10:39,010
+إنه في الآخر اللي بهمني جدش عدد مرات تطبيق ال loop
+
+132
+00:10:39,010 --> 00:10:44,890
+أكم مرة عمل عملية ال looping هذه هذه هي ال
+
+133
+00:10:44,890 --> 00:10:49,640
+complexityلما كانت Linear .. لما كانت Linear كان
+
+134
+00:10:49,640 --> 00:10:54,100
+إيش بيعمل؟ بيفحص الأول، التاني، التالت، الرابع،
+
+135
+00:10:54,100 --> 00:10:57,660
+فأنا عارف إن ال loop هو العدد in نفسه، ما كانش
+
+136
+00:10:57,660 --> 00:11:00,360
+عندنا مشكلة، لأنه هيمشي عليهم كلهم، هيمشي عليهم
+
+137
+00:11:00,360 --> 00:11:03,120
+كلهم، هنا لأ، مش هيمشي عليهم كلهم، فعشان هيك بدنا
+
+138
+00:11:03,120 --> 00:11:07,220
+إيش نتلخبط، إيش ال complexity؟ هي function في in،
+
+139
+00:11:07,220 --> 00:11:14,080
+بس مش هي in، صح؟ هي جداش عدد مرات ال loop بقى اللي
+
+140
+00:11:14,080 --> 00:11:17,840
+إنتوا بتعملوهفمعنى ذلك اللي بربطلنا جديش عدد مرات
+
+141
+00:11:17,840 --> 00:11:25,120
+ال loop مع قيمة n حتى لو اختلفت .. حتى لو اختلفت
+
+142
+00:11:25,120 --> 00:11:28,660
+.. هذه هي اللي بدنا ايها فانا عارف ان قيمة n هي
+
+143
+00:11:28,660 --> 00:11:32,480
+بهذا الشكل .. هذا ال input تبعي بس k هي المطلوبة
+
+144
+00:11:32,480 --> 00:11:36,380
+لان لان k هي ال complexity .. k هي ال complexity
+
+145
+00:11:36,380 --> 00:11:40,480
+فهي ال k ك complexity بدها تنحط هي اللي function
+
+146
+00:11:40,480 --> 00:11:45,430
+في المتغير in وليس العجز زي ما احنا كاتبينهمش
+
+147
+00:11:45,430 --> 00:11:47,370
+العكس زي ما احنا كاتبينه الان هلوا جد احنا
+
+148
+00:11:47,370 --> 00:11:51,670
+كاتبينها بطريقة مختلفة كاتبين ان in هي function في
+
+149
+00:11:51,670 --> 00:11:57,870
+k اللي فعليا بدنا ياه هو العكس لأن ال time معتمد
+
+150
+00:11:57,870 --> 00:12:03,310
+على k عدد مرات تنفيذ ال loop طيب عدد مرات تنفيذ ال
+
+151
+00:12:03,310 --> 00:12:07,510
+loop لازم تكون function في in و ليس فبدنا نعكسها
+
+152
+00:12:07,510 --> 00:12:11,310
+بدنا نجيب ال inverse تبعهابدنا نجيب ال inverse
+
+153
+00:12:11,310 --> 00:12:14,390
+تبعها بكل بساطة أتوقع ماعناش هيكون مشكلة كتير
+
+154
+00:12:14,390 --> 00:12:18,870
+خلصنا من الجزء التوضيحي هذه واضحة عندكم فكرة ال
+
+155
+00:12:18,870 --> 00:12:24,430
+binary ممتاز خلصنا منها ففي
+
+156
+00:12:24,430 --> 00:12:32,090
+الحالة هذه بقول log n للطرفين log 2 to the power k
+
+157
+00:12:32,090 --> 00:12:37,910
+كلنا عارفين في ال log ال أس بيطلع ك multiplier
+
+158
+00:12:40,520 --> 00:12:52,440
+.log 2 وهذه log n طيب الأساس إيش هنا عشرة عشرة
+
+159
+00:12:52,440 --> 00:13:00,480
+بيصير الأساس اتنين بيصير الأساس اتنين خلاص من
+
+160
+00:13:00,480 --> 00:13:03,400
+الأساس بس احنا بنوضحها رياضية عشان ماحدش يقولي كيف
+
+161
+00:13:03,400 --> 00:13:09,350
+هيها هذه بتيجي عن ناحية تانية فأصبحت k تساوي logن
+
+162
+00:13:09,350 --> 00:13:15,070
+على log ثابت اتنين قيمة ثابتة مدام على log قيمة
+
+163
+00:13:15,070 --> 00:13:19,090
+ثابتة خلاص معناه ان هو حيكون له قيمة ثابتة فعليا
+
+164
+00:13:19,090 --> 00:13:25,390
+انتهى اللي هي فاصلة تلاتة صفر و بعده في أرقام يعني
+
+165
+00:13:25,390 --> 00:13:29,490
+تلاتة من عشرة تلاتة من عشرة انتهى الموضوع خلاص
+
+166
+00:13:29,490 --> 00:13:35,490
+فإذا كل هذا بنشطبها و بنقول تساوي log الأساس اتنين
+
+167
+00:13:35,490 --> 00:13:42,430
+ل nهيك كافية؟ كافية جدا لأن نقطة نهائية عدد مرات
+
+168
+00:13:42,430 --> 00:13:49,050
+ال loop ال loop أكم مرة بده ينفذ؟ K مرة طب K هل
+
+169
+00:13:49,050 --> 00:13:53,050
+مرتبطة بال N؟ أه هي function في N logarithmic
+
+170
+00:13:53,050 --> 00:13:59,790
+بدليل أنه هين كنا وضحناها أنه أنا مش كل زيادة في N
+
+171
+00:13:59,790 --> 00:14:03,170
+هزيد ال loop زيادة واحد زي ما عملنا في ال linear
+
+172
+00:14:03,170 --> 00:14:09,140
+لأمن تلاتة و تلاتين لاربعة و ستين اي زيادة بتتم في
+
+173
+00:14:09,140 --> 00:14:14,840
+المساحة هذه مش هتأثر معايا هضل عدد ال loops هي هي
+
+174
+00:14:14,840 --> 00:14:22,760
+فالتغير مش خطي كل فترة لما بتذكر اه هتزودلي كمان
+
+175
+00:14:22,760 --> 00:14:31,800
+loop زيادةطيب من 64 او تحديدا من 65 ل 128 زادت ال
+
+176
+00:14:31,800 --> 00:14:37,600
+gap كل هدولة في Loop واحدة بيختصروا كل هدولة
+
+177
+00:14:37,600 --> 00:14:42,380
+بيختصروا في Loop واحدة كل ما بتزود بتزيد الاختصار
+
+178
+00:14:42,380 --> 00:14:45,200
+ليش بيزيد؟ لأنه التبادي أصلا شايف جداش اللي
+
+179
+00:14:45,200 --> 00:14:48,660
+اختصرته هنا؟ طيب في اللي وراها اللي اختصرته بجل
+
+180
+00:14:50,170 --> 00:14:54,110
+فهذه كانت اللي هي من تلاتة و تلاتين مثلا لاربع و
+
+181
+00:14:54,110 --> 00:14:58,310
+ستين بس هنا صرت نتكلم من خمسة و ستين لمية و تمانية
+
+182
+00:14:58,310 --> 00:15:03,770
+و عشرين فأكيد هنا .. غير هنا كل هدول بالنسبالك
+
+183
+00:15:03,770 --> 00:15:10,090
+loop واحد .. كل هدول loop واحد فكل loop زيادة انت
+
+184
+00:15:10,090 --> 00:15:16,590
+بتقدر تختصر كمية أكبر واضحيت؟ تمام فهذه فكرة ان
+
+185
+00:15:16,590 --> 00:15:21,200
+والله ال binary logarithmicو هذا الأهم عشان أعرف
+
+186
+00:15:21,200 --> 00:15:25,100
+ال complexity معناته أنا بدي أعرف اللو بقى كم مرة
+
+187
+00:15:25,100 --> 00:15:30,760
+نفذته بس الفكرة بسيطة أتوقع يعني فكرة بسيطة وسهلة
+
+188
+00:15:30,760 --> 00:15:34,260
+و في .. كل اللي حكيناها هيه مكتوب بترجعله بسهولة
+
+189
+00:15:34,260 --> 00:15:39,320
+بريحية مدى ما اتكلمت عنه log ف automatic نكتبها
+
+190
+00:15:39,320 --> 00:15:48,140
+بصيغة وين راحت هيها ساعتها
+
+191
+00:15:48,860 --> 00:15:54,380
+برغم ان احنا هنا log اتنين وقلنا الأساس اتنين بس
+
+192
+00:15:54,380 --> 00:15:59,280
+متذكرين اخر محاضرة ال order of growth قلنا بغض
+
+193
+00:15:59,280 --> 00:16:03,260
+النظر عن ايش ال complex ال base اسم هال
+
+194
+00:16:03,260 --> 00:16:09,180
+logarithmكوا بس اتوقع واضح ليش هنا انت بتكسب على
+
+195
+00:16:09,180 --> 00:16:14,370
+ايش؟ على ثابتطب ال function linear و ضربتها في
+
+196
+00:16:14,370 --> 00:16:19,330
+ثابت هتظلها linear فانت مش هيفرج معاك ان هو قسم
+
+197
+00:16:19,330 --> 00:16:23,930
+على ثابت عشان هيك مش هتفرج تقولي اتنين لما اكتبها
+
+198
+00:16:23,930 --> 00:16:30,560
+ك order تقولي theta of log و خلاص اتنينللأساس 2
+
+199
+00:16:30,560 --> 00:16:34,780
+للأساس 10 للأساس 5 للأساس 100 بتفرجش لأن كلنا
+
+200
+00:16:34,780 --> 00:16:37,520
+عارفين إن هي عبارة عن C مضروبة في ال function بس
+
+201
+00:16:37,520 --> 00:16:40,000
+هي constant مضروبة في ال function ال constant هذا
+
+202
+00:16:40,000 --> 00:16:45,280
+هنا قيمته مثلا 1 على log 2 بس قيمته هنا اللي هو
+
+203
+00:16:45,280 --> 00:16:52,420
+log 2 وقسمنا عليه 1 على log 2 تمام تمام جدا طيب
+
+204
+00:16:52,420 --> 00:16:54,820
+كمان code
+
+205
+00:16:59,230 --> 00:17:04,810
+اللي هو ضرب المصفوفات وهذا
+
+206
+00:17:04,810 --> 00:17:08,770
+من الأكواد اللي كتير درجة وبيحتاجها الواحد و
+
+207
+00:17:08,770 --> 00:17:11,550
+تحديدا المهندسين كتير بيحتاجوا ان يضربوا مصفوفتين
+
+208
+00:17:11,550 --> 00:17:15,870
+في بعض يضربوا مصفوفتين في بعض فهيطلب منك اعمللي
+
+209
+00:17:15,870 --> 00:17:19,590
+code يعمللنا code كلنا عارفين ان الأكواد في الحالة
+
+210
+00:17:19,590 --> 00:17:23,070
+هذه بدنا نعمل اتنين for loop مبدئيا بس عشان نحددوا
+
+211
+00:17:23,070 --> 00:17:26,430
+العنصر اللي بدنا نحسبه ليش؟ لأن انا عندي rows
+
+212
+00:17:26,430 --> 00:17:31,200
+وعندي columnsفمحتاج أولا قبل ما أبدأ أي حاجة محتاج
+
+213
+00:17:31,200 --> 00:17:34,860
+اتنين for loop لتحديد العنصر اللي أنا بتكلم عنه
+
+214
+00:17:34,860 --> 00:17:47,760
+بدّي for loop هنا و بدنا loop .. loop هنا فهي
+
+215
+00:17:47,760 --> 00:17:51,080
+أول اتنين for loop هدول مافيش مجال تشتغل في ال
+
+216
+00:17:51,080 --> 00:17:55,750
+matrices و ماتكتبهمشعلى طول انتهى الكلام فهي خلصنا
+
+217
+00:17:55,750 --> 00:17:59,770
+التنتين هدولة فإذا انا عارف انه ال I row ال J
+
+218
+00:17:59,770 --> 00:18:05,370
+column طيب هدول عشان يحدد ايش انا بدي احسب العنصر
+
+219
+00:18:05,370 --> 00:18:10,930
+الأول فلما اكتب I واحد J واحد فانا بتكلم عن العنصر
+
+220
+00:18:10,930 --> 00:18:16,550
+الأول في ال row الأول و ال column الأول طيب
+
+221
+00:18:16,550 --> 00:18:22,630
+عملية حسابهعملية حسابه نفسها جاية من خلال ال inner
+
+222
+00:18:22,630 --> 00:18:27,170
+product بتذكرينه؟ بحسب vector في vector يعني هذا
+
+223
+00:18:27,170 --> 00:18:33,250
+عشان ينحسب هو أصلا جايين عبارة عن صف من الأولى في
+
+224
+00:18:33,250 --> 00:18:41,090
+عمود من التانية طب تمام هذا نفسه متغير ليش؟ لأنه
+
+225
+00:18:41,090 --> 00:18:44,210
+أنا مش عارف جديش عدد الصفوف مبدئيا هنا و اللي لازم
+
+226
+00:18:44,210 --> 00:18:49,100
+يتفق مع عدد الأعمدة هنافإذا محتاج برضه كمان loop
+
+227
+00:18:49,100 --> 00:18:52,200
+عشان
+
+228
+00:18:52,200 --> 00:18:58,840
+نعمل عملية الضرب عشان ساعتها أقول العنصر الأول من
+
+229
+00:18:58,840 --> 00:19:02,940
+المصفوفة الأولى في العنصر الأول من المصفوفة
+
+230
+00:19:02,940 --> 00:19:06,560
+التانية العنصر التانى بعد تانى التالت في التالت
+
+231
+00:19:06,560 --> 00:19:09,700
+الرابع في الرابع ونعمل لهم summation ونعمل لهم
+
+232
+00:19:09,700 --> 00:19:13,360
+عملية summation فلاحظت اتنين في ال loop بس عشان
+
+233
+00:19:13,360 --> 00:19:17,750
+أقول ان هو اللي بده حسبه ال Mو لازم كمان for loop
+
+234
+00:19:17,750 --> 00:19:22,790
+عشان عملية الحساب نفسها اللي هي ال inner product
+
+235
+00:19:22,790 --> 00:19:27,510
+اللي كنتوا تعملوها فهي بالظبط got it for loop أول
+
+236
+00:19:27,510 --> 00:19:32,710
+تاني صفوف أعمدة و بعدين بدنا نعمل عملية summation
+
+237
+00:19:32,710 --> 00:19:39,410
+لان لازم نصفر عشان ارتاح بعدين ان اي if then لو في
+
+238
+00:19:39,410 --> 00:19:42,970
+if then بتكون by conditional متأكد متطمن ان هي by
+
+239
+00:19:42,970 --> 00:19:46,970
+conditionalتمام واضحت من أيامها هيها بالظبط
+
+240
+00:19:46,970 --> 00:19:53,270
+فصفرليها بلاش يكون لها قيمة سابقة صفرناها و بنبدأ
+
+241
+00:19:53,270 --> 00:19:57,530
+ال for loop لمين ل Q ال Q اللي هي إيش عدد أعمدة
+
+242
+00:19:57,530 --> 00:20:02,890
+الأول أو صفوف التاني ما هم متساويين عشان نبدأ الآن
+
+243
+00:20:02,890 --> 00:20:08,590
+ناخدهم واحد واحد نبدأ نمسكهم واحد واحد خلصنا خلصنا
+
+244
+00:20:09,650 --> 00:20:13,630
+فهنا لما نيجي نتطلع على الشكل اللي قدامنا هذا بكل
+
+245
+00:20:13,630 --> 00:20:18,130
+بساطة بنقدر نتخيل أبعاد ال matrices اللي عندي إيش
+
+246
+00:20:18,130 --> 00:20:30,150
+أبعادها؟ هنا M في K صح؟
+
+247
+00:20:30,150 --> 00:20:35,170
+آه أيوة تمام خليها توبح أكتر بالنسبالك و قبل أن
+
+248
+00:20:35,170 --> 00:20:37,010
+نبدأ نكمل هنا صارت K
+
+249
+00:20:39,860 --> 00:20:49,020
+لأ اللي فوق هذه نتيجهم
+
+250
+00:20:49,020 --> 00:20:53,040
+فإذا
+
+251
+00:20:53,040 --> 00:20:56,220
+الأتنين ال for loop هدول بس عشان أحدد داخل ال
+
+252
+00:20:56,220 --> 00:21:01,220
+resultant matrix كل عنصر و بعدين أبدأ في عملية
+
+253
+00:21:01,220 --> 00:21:05,980
+حسابه كإني بقولك بدي أمسك أول عنصر يللا نحسبه طب
+
+254
+00:21:05,980 --> 00:21:10,340
+عشان كلمة نقول يللا نحسبه بدها كمان for loopفهمنا
+
+255
+00:21:10,340 --> 00:21:13,320
+ليش بتاعة كمان for loop اللي هي بعدد ال K هدولة
+
+256
+00:21:13,320 --> 00:21:16,840
+لأن كل عنصر لحاله بده ينضرب مع المقابل له فهي
+
+257
+00:21:16,840 --> 00:21:23,780
+ماسكنها ال C اللي بدناها بصفر هنبدأ متفقين من
+
+258
+00:21:23,780 --> 00:21:30,590
+الأساس أنه عند I و J هدولة ثابتيننشيك حدوله ثابتين
+
+259
+00:21:30,590 --> 00:21:33,830
+اللي هي القيمة اللي احنا هنعمل عليها التشبيع بقى
+
+260
+00:21:33,830 --> 00:21:38,930
+طيب إيش اللي بتغير اللي بتغير I في Q طيب هتشوف هذه
+
+261
+00:21:38,930 --> 00:21:44,950
+اللي هي عبارة عن maximum M Q K فانا باخدها من أول
+
+262
+00:21:44,950 --> 00:21:48,950
+matrix باخدها من ال matrix الأولى و التانية من ال
+
+263
+00:21:48,950 --> 00:21:56,910
+matrix التانية هذه طبعا J بس هاي كله نعمل خلصنا
+
+264
+00:21:56,910 --> 00:22:00,850
+انتهت البرنامجالـ for loops هتظلم كاملة بعد هيك
+
+265
+00:22:00,850 --> 00:22:03,050
+لحالها على اعتبار ان انا مش هعمل الا العملية
+
+266
+00:22:03,050 --> 00:22:06,970
+الإجراء هذا فانا مش محتاج لا begin ولا end لها هو
+
+267
+00:22:06,970 --> 00:22:10,430
+هي الإجراء اللي بنعمله هذه هنحتاجها لمين؟ هنحتاجها
+
+268
+00:22:10,430 --> 00:22:18,350
+هنا ال begin و ال end لأن في كذا عملية هتنعمل في
+
+269
+00:22:18,350 --> 00:22:24,760
+التصفير و المهم جدالازم نصفر ال summation قبل ما
+
+270
+00:22:24,760 --> 00:22:27,940
+نبدأ نشتغل ال accumulator هذا لازم نصفره قبل ما
+
+271
+00:22:27,940 --> 00:22:31,940
+نبدأ نتكلم بمعنى ان انا هقولك بده العنصر الأول حتى
+
+272
+00:22:31,940 --> 00:22:37,080
+اللحظة صفر حتى اللحظة صفر انا حددت اه انه يلا بدنا
+
+273
+00:22:37,080 --> 00:22:41,520
+نحسب اول عنصر بس لسه صفر لما تبدأ تقول ليه هنا
+
+274
+00:22:41,520 --> 00:22:46,940
+خليني اكتبها واحد واحد اتنين اتنين and so on لما
+
+275
+00:22:46,940 --> 00:22:50,800
+تبدأ تقول ليه العنصر اللي متخزن هنا زائد واحد في
+
+276
+00:22:50,800 --> 00:22:59,020
+واحدخلاص هقولك سرة واحد في واحد ماشي زائد اتنين في
+
+277
+00:22:59,020 --> 00:23:09,760
+اتنين زائد تلاتة في تلاتة لما تصل مين ك في ك و
+
+278
+00:23:09,760 --> 00:23:18,920
+بالظبط هذا اللي بنعمله جاعدين لاحظ
+
+279
+00:23:18,920 --> 00:23:22,900
+كيف؟هذا إذا كان زي ما قلتلك ال compiler smart
+
+280
+00:23:22,900 --> 00:23:26,140
+enough إنه والله أنت بدأ ب zeros معناه أنك بتعرفها
+
+281
+00:23:26,140 --> 00:23:30,800
+من الأول إنها مصفرة مافيش مشكلة يعني بدك كأنك
+
+282
+00:23:30,800 --> 00:23:34,300
+اعملت ال code هذا بدل ما هو هنا الرقم هذا اعمله
+
+283
+00:23:34,300 --> 00:23:39,520
+برا إنه ال C بتساوي صفر فانت بتتكلم عن ال matrix
+
+284
+00:23:39,520 --> 00:23:42,560
+ككل بس في الحالة هذه برضه إذا أنت بتتكلم عن Java
+
+285
+00:23:42,560 --> 00:23:47,630
+أو whatever بدك تكون معرف أبعادها في الأولأكيد
+
+286
+00:23:47,630 --> 00:23:51,870
+لازم تعرف أبعادها عشان يفهم ال compiler انك قصدك
+
+287
+00:23:51,870 --> 00:23:57,070
+كل element داخل ال matrix يساوي صفر فانت لازم
+
+288
+00:23:57,070 --> 00:24:00,810
+تعملها الخطوة بس جبل بعد هتعملها بشكل individual
+
+289
+00:24:00,810 --> 00:24:04,530
+لكل أنصر اللي حال بدك تعملها بشكل ال matrix كلها
+
+290
+00:24:04,530 --> 00:24:06,650
+على بعض اعملها بالطريقة اللي بدك إياها بس لازم
+
+291
+00:24:06,650 --> 00:24:13,920
+تصفر لازم تبدأ تصفيرهاتمام عموما احنا كتبناها هنا
+
+292
+00:24:13,920 --> 00:24:18,100
+بس مش هذا قصدنا من الكلام قصدنا الان complexity
+
+293
+00:24:18,100 --> 00:24:25,340
+القصد في ال complexity كل loop بدنا نمسكه و نشوف
+
+294
+00:24:25,340 --> 00:24:30,680
+ايش علاقة عدد مرات ال loop بعدد العناصر اللي
+
+295
+00:24:30,680 --> 00:24:37,780
+موجودين عندى نبدأ بالأول من 1 to M linearlinear
+
+296
+00:24:37,780 --> 00:24:43,520
+لأنه انا همسك واحد واحد الأول التاني التالت مش زي
+
+297
+00:24:43,520 --> 00:24:48,800
+ال binary بعمل jump بعمل قفزات اضطريت قولنا من
+
+298
+00:24:48,800 --> 00:24:51,560
+تلاتة وتلاتين لاربعة وستين وعملتها jump مرة واحدة
+
+299
+00:24:51,560 --> 00:24:54,940
+كاملة هد بكلها بلوب واحد لأ هنا مش هنعمل كلام هذا
+
+300
+00:24:54,940 --> 00:25:00,520
+هنا بنفعش اتقول العنصر الأول في ال raw و بعدين
+
+301
+00:25:00,520 --> 00:25:04,380
+العنصر التالت في ال raw ليش كلهم scan كامل فإذا
+
+302
+00:25:04,380 --> 00:25:09,990
+linearهذه linear فهي هتكون عبارة عن ال loop هذا
+
+303
+00:25:09,990 --> 00:25:17,550
+big theta of M تحديدا جدش عدد عناصره M كويس التاني
+
+304
+00:25:17,550 --> 00:25:23,730
+N فإذا مضربين في بعض ليش مضربين في بعض؟ لأنه M في
+
+305
+00:25:23,730 --> 00:25:29,760
+Nهي فعلا لو هدول خمسة و هدول ستة اكم عنصر؟ الاتنين
+
+306
+00:25:29,760 --> 00:25:32,860
+في بعض تلاتين عنصر هيكون ال matrix عندك فمضربين
+
+307
+00:25:32,860 --> 00:25:38,460
+ضرب في بعض مضربين في بعض بمعنى ان لو لاحظ لو ال
+
+308
+00:25:38,460 --> 00:25:45,820
+loop هنا او عفوا الرز هنا زادت بس رز زيادة هل معنى
+
+309
+00:25:45,820 --> 00:25:52,050
+ذلك انه زاد عندي عنصر واحد؟ لأ حقيقة زاد عنديلفة
+
+310
+00:25:52,050 --> 00:25:56,730
+كاملة فإذا فعليا هم مضربين في بعض عملية ضرب تمام
+
+311
+00:25:56,730 --> 00:26:03,070
+هنا صفر عفوا اه zero order لأنه constant عملية
+
+312
+00:26:03,070 --> 00:26:06,330
+تصفير أي رقم هي مرة واحدة يعني يلها زمن محدد وخالص
+
+313
+00:26:06,330 --> 00:26:17,380
+لكن ال loop هناهيكرر أكم مرة كمرة كمرة كمرة كمرة
+
+314
+00:26:17,380 --> 00:26:17,380
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة
+
+315
+00:26:17,380 --> 00:26:17,800
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة
+
+316
+00:26:17,800 --> 00:26:19,780
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة
+
+317
+00:26:19,780 --> 00:26:21,580
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة
+
+318
+00:26:21,580 --> 00:26:21,600
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة
+
+319
+00:26:21,600 --> 00:26:26,300
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرة
+
+320
+00:26:26,300 --> 00:26:35,590
+كمرة كمرة كمرة كمرة كمرة كمرة كمرة كمرةأيوة معناته
+
+321
+00:26:35,590 --> 00:26:39,530
+مادام لكل عنصر بتكررها K مرة و احنا توي اتفقنا انه
+
+322
+00:26:39,530 --> 00:26:44,550
+تلاتين لانه صار عندى خمسة في ستة يعني في بعض فإذا
+
+323
+00:26:44,550 --> 00:26:52,230
+K مرة في M مرة في N مرةمرة فإذا ك complexity و ال
+
+324
+00:26:52,230 --> 00:26:55,710
+for loop أسهل بكتير من ال while ال for loop أسهل
+
+325
+00:26:55,710 --> 00:26:58,530
+من ال while لأنه linear في الغالب ال linear على
+
+326
+00:26:58,530 --> 00:27:02,610
+طول for loop انت دايما عنصر و اللي ورا زائد واحد
+
+327
+00:27:02,610 --> 00:27:07,170
+زائد اتنين زائد تلاتة لما تصل لل final value خلاص
+
+328
+00:27:07,170 --> 00:27:13,030
+انتهيها دي فبطلع عندك theta of M في N في K يعني ال
+
+329
+00:27:13,030 --> 00:27:17,090
+order تكعيب يعني فعليا
+
+330
+00:27:22,140 --> 00:27:26,060
+تكعيب فإذا هذه هنا ال function تكعيبية ال function
+
+331
+00:27:26,060 --> 00:27:31,580
+ال complexity طبعا طيب نبدأ الآن نشوف مدام تكعيبية
+
+332
+00:27:31,580 --> 00:27:34,240
+طب هل هي مقبولة بالنسبالنا أنها تكون تكعيبية فعليا
+
+333
+00:27:34,240 --> 00:27:38,480
+ولا مش مقبولة ولا بدنا نفهم طب إيش ال limit اللي
+
+334
+00:27:38,480 --> 00:27:41,500
+اللي بدنا نقول عنه أه كويس أو مش كويس ال limit بكل
+
+335
+00:27:41,500 --> 00:27:45,690
+بساطة هذه نشوف معظمالـ functions اللي ممكن نتعامل
+
+336
+00:27:45,690 --> 00:27:48,730
+معها الأولى ال constant مافيش عندي مشكلة فيها
+
+337
+00:27:48,730 --> 00:27:54,630
+التانية logarithmic ال poly logarithmic اللي هي
+
+338
+00:27:54,630 --> 00:27:59,410
+تربية تكعيب تظابر أربع تظابر خمسة بس logarithmic ف
+
+339
+00:27:59,410 --> 00:28:03,730
+ال C ممكن تكون متغيرة واحد اتنين تلاتة خمسة عشرة ف
+
+340
+00:28:03,730 --> 00:28:08,130
+poly logarithmic كويس متعددة الحدود اللغارثمية
+
+341
+00:28:08,130 --> 00:28:12,130
+بتصير تصير اسمها متعددة الحدود اللغارثمية طيبالـ
+
+342
+00:28:12,130 --> 00:28:15,850
+Linear Linear في logarithmic فسمينا Linearithmic
+
+343
+00:28:15,850 --> 00:28:20,990
+Linear في logarithmic طيب متعدد ال polynomial
+
+344
+00:28:20,990 --> 00:28:27,170
+متعدد الحدود خطية مش logarithmia خطية متعدد حدود
+
+345
+00:28:27,170 --> 00:28:32,390
+خطية طيب بعدك exponential اللي أعلى منها ال
+
+346
+00:28:32,390 --> 00:28:41,250
+factorial اللي أعلى منها ال N في Mكان لها اسم بس
+
+347
+00:28:41,250 --> 00:28:45,230
+مش دارج كتير ال power town بيسموها أحيانا ال power
+
+348
+00:28:45,230 --> 00:28:48,190
+town بس لعندي لقد ماحدش ثابت يعني الناس جلال اللي
+
+349
+00:28:48,190 --> 00:28:52,430
+بيسموها بالاسم هذا فعشان هيك في معظم الكتب بيسموها
+
+350
+00:28:52,430 --> 00:28:56,670
+انت طبارن و بس و بسكته هذه .. هذه مستحيلة أصلا
+
+351
+00:28:56,670 --> 00:29:02,580
+ماحدش يجرب عليها هذه ماحدش يجرب عليهاهذه منتهية ..
+
+352
+00:29:02,580 --> 00:29:07,020
+هذه منتهية الصلاحيات هتخليني نشوف قعدنا هنتكلم
+
+353
+00:29:07,020 --> 00:29:11,160
+عنها الان عشان نحدد وين ال limit تبعنا هنقول ان في
+
+354
+00:29:11,160 --> 00:29:15,500
+عندى خط محدد المفروض ماتجوزش لما تكتب code إذا
+
+355
+00:29:15,500 --> 00:29:19,880
+تجاوز نوع معين على طول لحالك انت ألغي ال code تبعك
+
+356
+00:29:19,880 --> 00:29:23,200
+مافيش داعي على codeك هتعرف ان ال code هذا لسه
+
+357
+00:29:23,200 --> 00:29:27,800
+موصلناش لحلول إله المشاكل اللي عندنا هنقول عليها
+
+358
+00:29:27,800 --> 00:29:33,930
+اما tractableTracking اللي هو ممكن تطبحها أو حلها
+
+359
+00:29:33,930 --> 00:29:39,990
+أو حاجة من السماء visible قابلة للحلممكنة الحل ففي
+
+360
+00:29:39,990 --> 00:29:43,150
+برامج مع بعضهم بتسميهم tractable وبعضهم بتسميهم
+
+361
+00:29:43,150 --> 00:29:47,370
+intractable غير قابل للحل حسب طبعا من ال order تبع
+
+362
+00:29:47,370 --> 00:29:50,810
+ال problem اللي هي ال complexity نفسها فإذا هنقول
+
+363
+00:29:50,810 --> 00:29:57,810
+الان في اندي P P بولب P هذه مشهورة جدا ك set ال
+
+364
+00:29:57,810 --> 00:30:01,790
+set هذه عبارة عن ال set لكل tractable problems في
+
+365
+00:30:01,790 --> 00:30:07,640
+العالمكل مشكلة برمجية الكلام ده برمجي الكلام ده
+
+366
+00:30:07,640 --> 00:30:11,040
+نحكي عن الأمور البرمجية مش المشاكل حتى العادية
+
+367
+00:30:11,040 --> 00:30:13,280
+بتاعة ال calculus مالناس في ال calculus الآن انت
+
+368
+00:30:13,280 --> 00:30:16,980
+بتكلم عن كل البرامج البرمجية المشاكل البرمجية إذا
+
+369
+00:30:16,980 --> 00:30:23,020
+كانت tractable فبنحطها ضمن belong to all capital P
+
+370
+00:30:23,020 --> 00:30:30,020
+تمام المشاكل اللي تتجاوزP يعني لا تنتمي لـ P
+
+371
+00:30:30,020 --> 00:30:36,280
+فبنقول عنها Intractable أو Invisible غير معقولة
+
+372
+00:30:36,280 --> 00:30:41,240
+الحل هذه visible مقبولة أو معقول و هنا يمكن تطبحها
+
+373
+00:30:41,240 --> 00:30:47,560
+أو يمكن حلها هذا الكلام نظري في حالات لكن نادرة
+
+374
+00:30:47,560 --> 00:30:52,780
+كتير ممكن نعد الكلام هذا بدنا نحدد أول شغلة أن
+
+375
+00:30:52,780 --> 00:30:56,400
+الحد الفاصل ال P هنا بتتعامل معاه هو ال polynomial
+
+376
+00:30:57,530 --> 00:31:00,610
+لعند polynomial بنسميها tractable لعند ال
+
+377
+00:31:00,610 --> 00:31:06,690
+polynomial tractable لهنا هدول
+
+378
+00:31:06,690 --> 00:31:12,610
+هيك كلهم tractable مقبولين مبلوعين زي تو ال
+
+379
+00:31:12,610 --> 00:31:17,570
+matrices ال ضرب ال matrices كانت polynomial ال C
+
+380
+00:31:17,570 --> 00:31:22,580
+كانت تلاتةفكانت in to the power تلاتة ماشي مجبولة
+
+381
+00:31:22,580 --> 00:31:26,740
+مجبولة الأجهزة أجهزة الحواسيب بتقدر تعملها هاي
+
+382
+00:31:26,740 --> 00:31:29,760
+معناها أنه أجهزة جهاز الحسوب بقدر يعملها ما بعد
+
+383
+00:31:29,760 --> 00:31:34,740
+ذلك لأ ما بعد ذلك بتصير خلاص في range ال
+
+384
+00:31:34,740 --> 00:31:40,060
+interactable كويس الكلام هذا نظر نسبيا لأنه عمليا
+
+385
+00:31:40,060 --> 00:31:44,060
+هتلاقي في حالات نادرة شوية ممكن يظهر عندك حاجة زي
+
+386
+00:31:44,060 --> 00:31:48,830
+هذه in to the power one millionالمفروض ان هي مصنفة
+
+387
+00:31:48,830 --> 00:31:54,670
+tractable مش هي polynomial tractable بس يعني مش
+
+388
+00:31:54,670 --> 00:31:58,970
+هيشتغلها الجهاز هيجف ان هي الجهاز يعني يجرب يعملها
+
+389
+00:31:58,970 --> 00:32:00,970
+على القالة الحاسبة ما هو القالة الحاسبة هي
+
+390
+00:32:00,970 --> 00:32:04,670
+calculator في الآخر يعني computer calculator ال
+
+391
+00:32:04,670 --> 00:32:08,090
+computer و الكلام ده كله عندنا هنشوف هنتكلم عن
+
+392
+00:32:08,090 --> 00:32:12,350
+واحد شوية عمل فلسفة له لحاله اسمه Turing Alan
+
+393
+00:32:12,350 --> 00:32:15,250
+Turing Alan Turing لأنه هو اول واحد عامل قالة
+
+394
+00:32:15,250 --> 00:32:20,490
+حاسبة في العالمالبريطاني هذا جثته جثة يعني لو بدنا
+
+395
+00:32:20,490 --> 00:32:23,370
+نقعد نحكي جثته لو عندنا مجال انه معناه وجد كنا
+
+396
+00:32:23,370 --> 00:32:26,450
+حكينا جثته هتلاقي انه فيها جثث علمية كتير في مصها
+
+397
+00:32:26,450 --> 00:32:30,970
+هل إله علاقة بال Apple؟ مالوش علاقة بالتفاحة
+
+398
+00:32:30,970 --> 00:32:35,750
+المجروطة هذه ولا إله علاقة؟ طيب إيش .. إله علاقة
+
+399
+00:32:35,750 --> 00:32:38,710
+كان في الحرب العالمية؟ كان له ولا ماكانوش جثث
+
+400
+00:32:38,710 --> 00:32:41,790
+تانية؟ بس مش معرضنا يعني ياريت في وجد كنا نحكيلكم
+
+401
+00:32:41,790 --> 00:32:46,990
+جثث علمية هكذا هتنرجع ل ..لشغل، هل وجد هذه
+
+402
+00:32:46,990 --> 00:32:52,450
+polynomial فعليًا، لكن هل في جهاز حسوب يحسبها؟ مش
+
+403
+00:32:52,450 --> 00:32:56,550
+هتلاقي، مش هتلاقي جهاز حسوب يحسبلك إياها، فإذا هي
+
+404
+00:32:56,550 --> 00:32:58,790
+رغم إن هي تكنيكا اللي بقدر أقول إن هي tractable
+
+405
+00:32:58,790 --> 00:33:03,990
+لكن واضح إن هي impossible to solve، كتير معقدة أو
+
+406
+00:33:03,990 --> 00:33:06,950
+كتير صعبة إنك أنت تحلها، كتير صعبة للحل، اعملها
+
+407
+00:33:06,950 --> 00:33:10,110
+على أي حاسبة؟ أقولك على الحاسبة بتاعة الحسوب نفسه
+
+408
+00:33:11,200 --> 00:33:14,680
+عالقالة الحاسوب بتاعة الحاسوب اكتب لك هنا وين راحت
+
+409
+00:33:14,680 --> 00:33:17,160
+ان هنا بتلاتة و لا باربعة و احنا بنتكلم عن رقم
+
+410
+00:33:17,160 --> 00:33:21,520
+متواضع ك input ك input يعني كإنك بتتكلم عن array
+
+411
+00:33:21,520 --> 00:33:26,480
+فيها تلاتة اربعة elements و to the power one
+
+412
+00:33:26,480 --> 00:33:31,160
+million هتجف مش هتطلعلك شيء طيب بس في المقابل هي
+
+413
+00:33:31,160 --> 00:33:35,320
+مثلا متغير to the power متغير يعني انت دخلت في ال
+
+414
+00:33:35,320 --> 00:33:38,820
+exponential هيك دخلت في exponential دخلت في
+
+415
+00:33:38,820 --> 00:33:46,710
+الفعليااللي هي into the power in صحيح من ناحية
+
+416
+00:33:46,710 --> 00:33:51,130
+التقنية انت دخلت في into the power in اللي قلنا
+
+417
+00:33:51,130 --> 00:33:54,170
+عليها مستحيلة ولكن في حالة زي هذه لأ هي ممكنة
+
+418
+00:33:54,170 --> 00:34:00,500
+لأنها تلاقيش أكبر array ممكن تشتغل عليهاpractical
+
+419
+00:34:00,500 --> 00:34:04,440
+أكبر array ممكن تشتغل عليها احنا المرة اللي فاتت
+
+420
+00:34:04,440 --> 00:34:07,860
+لما كنا بتتكلم عن اتنين log قلنا انه وصلتنا لعشرة
+
+421
+00:34:07,860 --> 00:34:12,420
+to the power عشرة طلعت النتج واحد يعني صارت into
+
+422
+00:34:12,420 --> 00:34:17,240
+the power واحد طب كمان log يعني عشرة to the power
+
+423
+00:34:17,240 --> 00:34:18,260
+عشرة to the power عشرة
+
+424
+00:34:21,280 --> 00:34:25,200
+لاحظت؟ فهذه بتسمحلك إنك هنا يطلع in to the power
+
+425
+00:34:25,200 --> 00:34:29,040
+واحد إذا كانت in هنا عشرة to the power عشرة to the
+
+426
+00:34:29,040 --> 00:34:34,680
+power عشرة في قربي هذا الشكل فعمليا بسيطة، رغم إن
+
+427
+00:34:34,680 --> 00:34:41,260
+هي حسب معيارنا، لأ هي تصنف interactableطبعا
+
+428
+00:34:41,260 --> 00:34:44,380
+الحالات هذه كويس ان هي كتير نادرة .. كتير نادرة
+
+429
+00:34:44,380 --> 00:34:47,580
+انه يظهر معاك حالات زي هيك .. كتير نادرة معظم
+
+430
+00:34:47,580 --> 00:34:50,940
+البرامج لأ هي حسب مفهومنا فعلا عند polynomial اوقف
+
+431
+00:34:50,940 --> 00:34:55,400
+.. عند ال polynomial اوقف مثال ع السريحيكي لو
+
+432
+00:34:55,400 --> 00:35:00,820
+أخدنا بتكلم عن ال N ب 10 N ب 10 يعني عدد ال byte
+
+433
+00:35:00,820 --> 00:35:04,560
+ال bits .. ال bits عشرة معنا ذلك ان ال byte ك
+
+434
+00:35:04,560 --> 00:35:10,560
+bytes واحد وربع اللي هي عشرة bitsمقابل one million
+
+435
+00:35:10,560 --> 00:35:14,980
+bit يعني حوالي 125 كيلو 125 كيلو بالنسبالي حاجة
+
+436
+00:35:14,980 --> 00:35:18,680
+صغيرة لغرفنك
+
+437
+00:35:18,680 --> 00:35:22,620
+مقبولة هذه اذا انا بدي اقول بشتغل على الأجهزة
+
+438
+00:35:22,620 --> 00:35:25,740
+العادية اللي هي بتشتغل على السيليكون السيليكون ال
+
+439
+00:35:25,740 --> 00:35:28,440
+slow rate تبعها و ال response تبع انصر السيليكون
+
+440
+00:35:28,440 --> 00:35:31,820
+هو تقريبا one nanosecondبنانو ساكند one nanosecond
+
+441
+00:35:31,820 --> 00:35:35,440
+كويس اللي هو ال response تبع لل silicon فعشان هيك
+
+442
+00:35:35,440 --> 00:35:40,820
+يكون هو المعيار عادة للشغل في الآخر تمام لو قلنا
+
+443
+00:35:40,820 --> 00:35:44,680
+log فإذا هنا بدي أقول والله كل عملية محتاجة
+
+444
+00:35:45,690 --> 00:35:49,710
+response ال silicon تبعنا اللي هو 1 nano فمعنى ذلك
+
+445
+00:35:49,710 --> 00:35:53,690
+انه هنا بتطلع عندي 3.3 nano ولا اشي يعني مافيش على
+
+446
+00:35:53,690 --> 00:35:57,130
+طول خلصلك المعادلة إذا كان بتكلم عنه one million
+
+447
+00:35:57,130 --> 00:36:02,590
+بتصير تسعتاشر نوع عشرين nanoعشرين نانو ساكند سريعة
+
+448
+00:36:02,590 --> 00:36:06,990
+مش مشكلة طيب linear برضه بتتكلم عن عشرة نانو و هنا
+
+449
+00:36:06,990 --> 00:36:11,870
+مليون نانو فبتتكلم عن بالملي برضه مش هتشعر فيها
+
+450
+00:36:11,870 --> 00:36:16,950
+هتلاقيها على طول خلصتلاقيها ماشية طيب ال linear
+
+451
+00:36:16,950 --> 00:36:22,670
+rhythmic هتضرب اتنين في بعض لواحد من انا؟ اه
+
+452
+00:36:22,670 --> 00:36:28,180
+بالظبط اه جزء من الثانية يعنيملي اللي هي واحد من
+
+453
+00:36:28,180 --> 00:36:31,540
+الف من الثانية واحد من الف من الثانية تمام طيب
+
+454
+00:36:31,540 --> 00:36:35,760
+تربيع اللي هي polynomial هيها لعند polynomial اذا
+
+455
+00:36:35,760 --> 00:36:38,880
+كانت بتعامل مع عشرة فهي عشرة nano مافيش اشي يعني
+
+456
+00:36:38,880 --> 00:36:43,140
+مش هشهر فيها اطلاقا مش هنشهر فيها عشرة مية nano
+
+457
+00:36:43,140 --> 00:36:47,000
+يعني تقريبا فاصلة واحد micro فاصلة واحد micro بس
+
+458
+00:36:47,000 --> 00:36:51,120
+في المقابل هنا بتطلع ستاشر minute لما بتكلم عن one
+
+459
+00:36:51,120 --> 00:36:57,970
+million one million تربيع ستاشر دقيقة16 دقيقة إذا
+
+460
+00:36:57,970 --> 00:37:00,910
+كان والله محرز البرنامج وانت محتاج مثلا بتعمل ال
+
+461
+00:37:00,910 --> 00:37:04,890
+neural network بتعمل تدريب ل AI ماشي ربع الساعة مش
+
+462
+00:37:04,890 --> 00:37:09,150
+مشكلة هتقول مش مشكلة الربع الساعة في الزمنات لما
+
+463
+00:37:09,150 --> 00:37:14,350
+كنا نشتغل ال neural network كنت أستنى 24 ساعة اه
+
+464
+00:37:14,350 --> 00:37:18,770
+يعني أطف الشاشة و أسيب الجهاز يشتغل و خلاص 24 ساعة
+
+465
+00:37:18,770 --> 00:37:21,150
+و بعدين تصحى تاني يوم تتفاجأ ان كان في error في
+
+466
+00:37:21,150 --> 00:37:25,910
+البرنامج فترجع تعيد و تتعدل من جديد كويس؟طبعا
+
+467
+00:37:25,910 --> 00:37:29,710
+لعندنا هه مبلوعة بدليل انهيني انا كنت مبلوعة
+
+468
+00:37:29,710 --> 00:37:32,750
+بالنسبالي حتى الاربع عشرين ساعة كنت اقول ماشي في
+
+469
+00:37:32,750 --> 00:37:35,910
+وجتها طبعا الان الأجهزة كتير صارت أسرع .. كتير
+
+470
+00:37:35,910 --> 00:37:40,450
+صارت أسرع فممكن تاخد منا عشر دجاج اه ممكن تاخد عشر
+
+471
+00:37:40,450 --> 00:37:44,280
+دجاج اللي كانت تاخد مني اربع عشرين ساعةطيب لما
+
+472
+00:37:44,280 --> 00:37:48,660
+أدخل على ال exponential لأ exponential بالنسبة
+
+473
+00:37:48,660 --> 00:37:53,500
+لعشرة okay عدد جليل مقبولة بس هنا مليون اتنين to
+
+474
+00:37:53,500 --> 00:37:57,720
+the power مليون زي ما كنا كتبينها و قولنا ان هي
+
+475
+00:37:57,720 --> 00:38:01,540
+attractable فعليا كانت منظرها عفوا ان كانت بالعكس
+
+476
+00:38:01,540 --> 00:38:04,180
+هنا مليون to the power اتنين to the power مليون
+
+477
+00:38:04,180 --> 00:38:08,380
+مظبوط بس كنا كتبينها عكسية كنا كتبين هنا ال in و
+
+478
+00:38:08,380 --> 00:38:12,060
+كنا كتبين هنا ال one million صحيح فهي ظهرت معانا
+
+479
+00:38:12,940 --> 00:38:19,280
+Ten خد to the power تلاتمية و واحد ألف و أربعة و
+
+480
+00:38:19,280 --> 00:38:25,540
+نص جيجا يير فمتخيل
+
+481
+00:38:25,540 --> 00:38:29,820
+جدش الحجم الزمن يعني عمر الأرض أكتر أكتر من عمر
+
+482
+00:38:29,820 --> 00:38:37,320
+الأرض تمام factorial ماشي لعند هنا فيش جهاز حسبها
+
+483
+00:38:37,320 --> 00:38:44,330
+فيش جهاز حسبهايعني أكبر جهاز في الكورة الأرضية ما
+
+484
+00:38:44,330 --> 00:38:48,330
+حسبهاش حتى الآن اللي هي ال nano factory ما حسبهاش
+
+485
+00:38:48,330 --> 00:38:54,370
+فعشان انا مش عارف ماحدش حسبها أصلا ماحسبها ماوصلش
+
+486
+00:38:54,370 --> 00:38:59,700
+ماحدش وصلها يعني ماحدش جابها تمامطب ال unsolved
+
+487
+00:38:59,700 --> 00:39:03,180
+problem هد برضه زي ما قلنا تورينج اكتشف في
+
+488
+00:39:03,180 --> 00:39:06,660
+الارتسان مية و تلاتين انه في بعض ال problems ممكن
+
+489
+00:39:06,660 --> 00:39:11,020
+اصنف ان هي غير محلولة او غير قابلة للحل و unsolved
+
+490
+00:39:11,020 --> 00:39:17,640
+بأي algorithm بأي algorithm نهائيا هد معناته انه
+
+491
+00:39:19,580 --> 00:39:24,180
+ممكن اقول عنها there are undesirable yes or no
+
+492
+00:39:24,180 --> 00:39:33,080
+question بمعنى انا مش جادر حتى مش هحلها مش جادر
+
+493
+00:39:33,080 --> 00:39:38,260
+اتحقق من حل يعني ممكن يعطيني حل ويقولي بس تحقق انه
+
+494
+00:39:38,260 --> 00:39:42,360
+صح ولا غلط انا مش جادر اتحقق من حلها ففي بعض
+
+495
+00:39:42,360 --> 00:39:45,680
+المشاكل انا مش جادر اتحقق من حلها زي تاعتوى ال
+
+496
+00:39:45,680 --> 00:39:50,760
+arch هذه يعني هذا لو انا كتبتلك اي رقمكتبتلك أي
+
+497
+00:39:50,760 --> 00:39:55,660
+رقم و أقولك و الله اتأكدلي هل الرقم هذا صحيح هو مش
+
+498
+00:39:55,660 --> 00:39:58,660
+مطلوب انك تحل هو مطلوب انك بس تتأكد تعمل tracking
+
+499
+00:39:58,660 --> 00:40:02,460
+هل هو الرقم هذا صح ولا مش صح برضه مش هتقدر برضه مش
+
+500
+00:40:02,460 --> 00:40:05,580
+هتقدر فمعناه ذلك انه هنا لو كان في مجموعة
+
+501
+00:40:05,580 --> 00:40:08,820
+functions هي انا مش جادر اقول yes or no يعني مش
+
+502
+00:40:08,820 --> 00:40:12,900
+جادر اقرر حتىأعملها tracking عند الحل موجود بس
+
+503
+00:40:12,900 --> 00:40:16,000
+اعمله tracking انه صح ولا غلق مظبوط ولا مش مظبوط
+
+504
+00:40:16,000 --> 00:40:21,400
+مش طالب حل مش طالبين حل ففي كتير مشاكل بالشكل هذا
+
+505
+00:40:21,400 --> 00:40:24,700
+في كتير مشاكل وهذه بتصير مع ال halting problem في
+
+506
+00:40:24,700 --> 00:40:28,000
+ال halting problem كل اللي بيصير arbitrarily اي
+
+507
+00:40:28,000 --> 00:40:32,520
+algorithm اتجربه ل ال inputs بتاعتها ل problem هذه
+
+508
+00:40:32,520 --> 00:40:36,520
+بعدد ال inputs ال whatever اش بيطلع ال input لو اي
+
+509
+00:40:36,520 --> 00:40:42,020
+code اي algorithm جربته في الآخربشكل نهائي حيصله
+
+510
+00:40:42,020 --> 00:40:49,660
+hard توقف ال code هيتوقف hard توقف خلاص او يدخل في
+
+511
+00:40:49,660 --> 00:40:56,000
+loop او يدخل في loop فإذا اما يتوقف و عادة بيطلعلك
+
+512
+00:40:56,000 --> 00:40:58,920
+في الحالة هادي الشاشة الزرعية بيقولك ال memory
+
+513
+00:40:58,920 --> 00:41:04,740
+خلاص مش جادر تتحمل اكتر فتوقف كامل او انه زي ما
+
+514
+00:41:04,740 --> 00:41:10,270
+بيقوله بيروح برجعش ال code راح منكلازم مضطر بعد اي
+
+515
+00:41:10,270 --> 00:41:13,950
+جداش بدك تسبور عليه يومين تلاتة اربع بعدين بدك
+
+516
+00:41:13,950 --> 00:41:17,730
+تطفي الجهاز بدك تطفي الجهاز ازهجت فاما انه هيضل
+
+517
+00:41:17,730 --> 00:41:22,350
+forever او ان هو لأ automatic خلاص هيوقف هيوقف
+
+518
+00:41:22,350 --> 00:41:26,390
+بمعنى انه لأ ال space عندك هو متسع لبرنامج هو مش
+
+519
+00:41:26,390 --> 00:41:30,230
+هيفرد كتير في ال space لكن ال time forever فهذه
+
+520
+00:41:30,230 --> 00:41:34,860
+دخلت في loopأو أنه لأ ممكن حالة من الحالات يعملك
+
+521
+00:41:34,860 --> 00:41:37,680
+وقف كامل إذا كان ال space اللي جاها ماكملتش معاه
+
+522
+00:41:37,680 --> 00:41:40,300
+فاطوماتيك إذا بتلاحظوا أحيانا بعض البرامج عندكم
+
+523
+00:41:40,300 --> 00:41:44,780
+بتطلعلكوا شاشة زرجة تطلع شاشة .. إذا مش عارف صدفت
+
+524
+00:41:44,780 --> 00:41:47,000
+معاكوا قبل هيكي الشاشة الزرجة بيقولك من الأول ..
+
+525
+00:41:47,000 --> 00:41:50,060
+من الأخر خلاص الجهاز عندك إمكانيته لا تسمح أني
+
+526
+00:41:50,060 --> 00:41:56,860
+أكمل فوقف بوقف و عادة لو قرأت هتلاقي أنه بيشيرلك
+
+527
+00:41:56,860 --> 00:42:00,540
+هيك للذاكرةبيشرلك من قريب أو من بعيد للذاكره لأنه
+
+528
+00:42:00,540 --> 00:42:04,580
+والله مش لاجي الذاكره يكمل وقف فهذه ال problem ..
+
+529
+00:42:04,580 --> 00:42:08,240
+في كذا problem تعمل كلام هذا في كذا problem عشان
+
+530
+00:42:08,240 --> 00:42:11,940
+نفهم هذا الكلام صار في عندي الآن قصتين قصة
+
+531
+00:42:11,940 --> 00:42:16,960
+tractable وسميناهم كل tractable وسميناها capital P
+
+532
+00:42:16,960 --> 00:42:22,840
+صحيح؟ وفي المقابل في حاجة انا مش جادر اتحقق من
+
+533
+00:42:22,840 --> 00:42:30,120
+الحل صح ولا غلطمظبوط؟ طب العكس أني قادر أتحقق من
+
+534
+00:42:30,120 --> 00:42:36,500
+الحل فبن .. في الحالة هذه بنسميهم NP-SET هذه ال
+
+535
+00:42:36,500 --> 00:42:42,740
+problems اللي بقدر أعملها attractable ل algorithm
+
+536
+00:42:42,740 --> 00:42:51,180
+مش حلها خدوا بالكم مش حلها كمان مرة يتأكد من حل
+
+537
+00:42:51,180 --> 00:42:57,250
+معين given عندكيتأكد من حال معين given عندك زي ..
+
+538
+00:42:57,250 --> 00:43:02,330
+زي لما نقول عندك ست بسيطة جدا زي اللي أنا حاططها
+
+539
+00:43:02,330 --> 00:43:09,530
+مشير إليها هيك عساس أنه أتكلم عنها و
+
+540
+00:43:09,530 --> 00:43:14,950
+سبعة خلاص ضل إش .. أه في كمان سالب عشرة لما أقولك
+
+541
+00:43:14,950 --> 00:43:22,410
+اعملي منهم اعملي منهم أكم sub 6 مجموعة أناصرها
+
+542
+00:43:22,410 --> 00:43:22,970
+تسوء صفر
+
+543
+00:43:26,110 --> 00:43:30,050
+طبعا مضطر تعمل كل ال subsets عونها صح؟ ملاحظ حجم
+
+544
+00:43:30,050 --> 00:43:35,210
+المشكلة؟ حجم كبير طيب هذا عشان تحلها لكن لو قلتلك
+
+545
+00:43:35,210 --> 00:43:40,930
+اعملي check هل .. ايش احنا كررت ال 15 كده مرتين؟
+
+546
+00:43:40,930 --> 00:43:53,540
+بهذا الشكل هل سالب 2 سالب 3 15 و سالب 10 هي حل؟حل
+
+547
+00:43:53,540 --> 00:43:58,680
+فشوفتوا عملتلي check جداش ماخدتش شي هي حل لكن لما
+
+548
+00:43:58,680 --> 00:44:04,440
+أقولك الحل نفسه أنه هتلي كل ال subsets اللي مجموع
+
+549
+00:44:04,440 --> 00:44:09,160
+أنصرها يسووا عشرة لأ هي مش مجرد check هي solve the
+
+550
+00:44:09,160 --> 00:44:14,460
+problem هي بدك تحل المشكلة نفسها فاختلفوا تتنين عن
+
+551
+00:44:14,460 --> 00:44:20,120
+بعض فالجثة بطلت tractable لحلها هي tractable for
+
+552
+00:44:20,120 --> 00:44:25,440
+checkingيعني معناه ذلك أن ال NP هي المشاكل اللي
+
+553
+00:44:25,440 --> 00:44:32,280
+يمكن تشك ل given solution هو صح ولا غلط بينما ال P
+
+554
+00:44:32,280 --> 00:44:37,540
+لحالها هي كل ال tractable problems اللي قابلة للحل
+
+555
+00:44:39,010 --> 00:44:43,570
+فمعنى ذلك أن بقدر أقول أن P هي subset من NP بمعنى
+
+556
+00:44:43,570 --> 00:44:49,930
+كل مشكلة قابلة للحل فهي قابلة أن أعمل check لحل
+
+557
+00:44:49,930 --> 00:44:56,570
+given عندها، صح؟ منطقيا، لكن ليس كل مشكلة بقدر
+
+558
+00:44:56,570 --> 00:45:04,570
+أعمل check لها فهي نفسها قابلة للحلصح؟ طيب طب إيش
+
+559
+00:45:04,570 --> 00:45:09,570
+رأيكوا إنه هذه نفسها هذه هيك كإثبات لعند الآن
+
+560
+00:45:09,570 --> 00:45:13,870
+ماحدش أثبت العلاقة هذه صح ولا غلط واللي بيفبتها
+
+561
+00:45:13,870 --> 00:45:18,850
+إله مليون دولار وفي فعلا في أكاديمية علمية لعند
+
+562
+00:45:18,850 --> 00:45:21,650
+الآن طارحة في الألفية كاملة في الألفية ال .. ال ..
+
+563
+00:45:21,650 --> 00:45:28,010
+ألفية ال .. العشرين طارحين تمن مسائل اللي بحل أي
+
+564
+00:45:28,010 --> 00:45:32,980
+واحدة منهم إله مليون دولار على طولهذه واحدة منهم
+
+565
+00:45:32,980 --> 00:45:41,080
+هذه واحدة منهم كويس فكرة انه هل فعلا هي prepare
+
+566
+00:45:41,080 --> 00:45:49,400
+subset بمعنى انه لأ لأ مستثنى منها اليساوي هنا
+
+567
+00:45:49,400 --> 00:45:53,660
+يقولنا subset صح؟ subset عارفش يعني subset؟ يعني
+
+568
+00:45:53,660 --> 00:45:59,420
+أو يساوي مش شايف؟ الآن يقولك لأ الاعتقاد السائد
+
+569
+00:45:59,420 --> 00:46:05,740
+فهي unprovedconjecture الحدث والغير مثبت انه لأ هي
+
+570
+00:46:05,740 --> 00:46:12,480
+super subset اه عفوا ال prepare subset او strictly
+
+571
+00:46:12,480 --> 00:46:20,300
+subset هي مجموعة جزئية ولا تساوي ولا تساوي طب اثبت
+
+572
+00:46:20,300 --> 00:46:24,820
+الكلام هذا تخيل ان احنا لعندي الآن هنا في ال 2000
+
+573
+00:46:24,820 --> 00:46:30,710
+و 21 ولا حد حلالمسألة هذه لأنها ضالت من المسائل
+
+574
+00:46:30,710 --> 00:46:32,830
+السبعة اللي ما انحلتش، في واحدة بالمناسبة انحلت
+
+575
+00:46:32,830 --> 00:46:37,830
+واحدة بس وصاحبها أخد المليون ووزعه وقال بديش مليون
+
+576
+00:46:37,830 --> 00:46:46,870
+اللي حلها يعني، تمام؟ okay هذه جثة طبعا متذكرين ال
+
+577
+00:46:46,870 --> 00:46:52,900
+primes لما اتكلمنا عن ال primesوقولنا هل عندك code
+
+578
+00:46:52,900 --> 00:46:56,920
+يعمل لك كل primes لكن لو قلتلك ان لا يوجد prime
+
+579
+00:46:56,920 --> 00:47:02,640
+أعلى تعمل check سريع مش هيك و احنا أثبتناها لكن في
+
+580
+00:47:02,640 --> 00:47:06,100
+المقابل انك انت تقعد تحسبلي كل primes عشان تثبتلي
+
+581
+00:47:06,100 --> 00:47:10,240
+ان لا يوجد prime أعلى أكيد مش منطقي فهيها
+
+582
+00:47:10,240 --> 00:47:16,020
+tractable و ال P و ال N انا بقدر اعمل check بس مش
+
+583
+00:47:16,020 --> 00:47:19,580
+معناه ذلك اني بقدر احل المشكلة ان اعمل check اه
+
+584
+00:47:20,420 --> 00:47:25,500
+يعطيني given ل solution بعملك check صح ولا غلط أما
+
+585
+00:47:25,500 --> 00:47:28,200
+تقوللي أنا علور على ال solution ل problem صارت إيش
+
+586
+00:47:28,200 --> 00:47:32,060
+interactable واضح الجزئية هذه؟ انت كمبرمج لازم
+
+587
+00:47:32,060 --> 00:47:35,000
+تكون فاهم النقطة هذه نقطة كتير مهمة في ال
+
+588
+00:47:35,000 --> 00:47:41,900
+complexity تمام كيف؟
+
+589
+00:47:41,900 --> 00:47:45,440
+اعكس
+
+590
+00:47:45,440 --> 00:47:48,300
+و اعمل و شوف اللي بدك إياه ساعتها إذا حلتها
+
+591
+00:47:48,300 --> 00:47:53,130
+ماتجينيش أنادور على ال net و خد المليون حلال عليك
+
+592
+00:47:53,130 --> 00:48:01,110
+اشتغل فيها طيب نكمل طيب
+
+593
+00:48:01,110 --> 00:48:05,510
+بالمرة مدام احنا في الأكواد وجدنا يمكن مناسب انه
+
+594
+00:48:05,510 --> 00:48:09,540
+اليومك في هالوقت اللي ضايل ناخد لنا مثال او اتنين
+
+595
+00:48:09,540 --> 00:48:14,300
+من امثلة على الاكواد بديش ارجع و نفصلكم و نرجع على
+
+596
+00:48:14,300 --> 00:48:19,320
+ال .. على جد مثال ناخدلنا هيك سريع .. كويس أخدتوا
+
+597
+00:48:19,320 --> 00:48:24,580
+قبل هيك ال .. ال palindrome ممتاز .. ممتاز
+
+598
+00:48:24,580 --> 00:48:28,920
+أخدتولها code يعني طيب ممتاز كويس فإذا إلها أمثلة
+
+599
+00:48:28,920 --> 00:48:32,820
+كتيرة ال palindrome و يمكن ال code هيكون بسيط جدا
+
+600
+00:48:32,820 --> 00:48:36,270
+أخدتهوا كتبتهواطيب يعني هاي حاجة من الحاجات اللي
+
+601
+00:48:36,270 --> 00:48:39,810
+احنا عادة بجيبها بالاسئلة هيك وطلعته ماخدينها
+
+602
+00:48:39,810 --> 00:48:44,750
+وماشية معاكم ان شاء الله تعالى خلاص بيكفي على هيك
+
+603
+00:48:44,750 --> 00:48:49,190
+بيكفي على هيك أخدنا كذا مثال ويمكن هيك تعتبره
+
+604
+00:48:49,190 --> 00:48:53,390
+خلصته جزئية ال complexity ان شاء الله تكون يعني
+
+605
+00:48:53,390 --> 00:48:56,510
+تناغمت مع ال data structure يعطيكوا ألف عافية
+
+606
+00:48:56,510 --> 00:48:57,170
+وبركة الله فيكم
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/REG9T5tb2MA_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/REG9T5tb2MA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1992f716bbf46a1ab20a79c668c034e34a38dc67
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/REG9T5tb2MA_postprocess.srt
@@ -0,0 +1,2236 @@
+1
+00:00:04,810 --> 00:00:07,910
+طيب، يا عطيكم العفو يا شباب نبدأ اليوم ان شاء الله
+
+2
+00:00:07,910 --> 00:00:12,750
+تعالى في ال proof methods مهدناها المرة السابقة و
+
+3
+00:00:12,750 --> 00:00:17,350
+أخدنا ال inference و ال rule of inference و بدأنا
+
+4
+00:00:17,350 --> 00:00:21,970
+نتكلم عن بعض قواعد الاستدلال و اليوم هنتوج الموضوع
+
+5
+00:00:21,970 --> 00:00:25,710
+بال strategies اللي هنستخدمها لعملية الإثبات نفسها
+
+6
+00:00:25,710 --> 00:00:29,590
+لعملية الإثبات نفسها هناخد مجموعة من ال methods او
+
+7
+00:00:29,590 --> 00:00:35,520
+ال strategiesهناخد ال direct ال indirect ال
+
+8
+00:00:35,520 --> 00:00:41,200
+vicious proof و ال trivial proof ثم هناخد حالة
+
+9
+00:00:41,200 --> 00:00:45,580
+اسمها ال introduction اللي هي التناقض فخليني نبدأ
+
+10
+00:00:45,580 --> 00:00:49,620
+شوية شوية في strategy واحدة ورا التانية نبدأ في ال
+
+11
+00:00:49,620 --> 00:00:53,180
+direct في ال direct مباشرة كل الأنواع اللي هنتكلم
+
+12
+00:00:53,180 --> 00:00:57,560
+عنها هي تتبع لل implicationإيش يعني؟ يعني ما أنا
+
+13
+00:00:57,560 --> 00:01:00,840
+بتقول قبل ما نبدأ محاضرتنا بدنا نحط جدولنا على جنب
+
+14
+00:01:00,840 --> 00:01:07,160
+لإنه هنبدأ كل شغلنا من خلاله فهنقول P EQ و ال
+
+15
+00:01:07,160 --> 00:01:16,500
+implication تبعتنا if true true if و true true
+
+16
+00:01:16,500 --> 00:01:21,480
+فهتكون هنا true true false و true
+
+17
+00:01:24,630 --> 00:01:28,110
+فال proofs بتاعتنا كلها مبنية على ال F then واللي
+
+18
+00:01:28,110 --> 00:01:31,190
+زي ما قلنا هي الحالة اللي احنا بناخدها .. بناخدها
+
+19
+00:01:31,190 --> 00:01:34,850
+.. بنتكلم عنها أساسا في ال condition في البرمجة
+
+20
+00:01:34,850 --> 00:01:38,150
+اللي هي ال F then فهي الجملة اللي هنتعامل معها
+
+21
+00:01:38,150 --> 00:01:41,470
+أكتر فال implication بهذا الشكل طيب لما بقول
+
+22
+00:01:41,470 --> 00:01:47,430
+direct .. direct كلنا عارفين عنده premises إذا
+
+23
+00:01:47,430 --> 00:01:50,010
+تحققوا إذا ال conclusion
+
+24
+00:01:52,670 --> 00:01:59,490
+بنبدأ بهذا الشكل direct خلاص تمام بفترض بفترض ان P
+
+25
+00:01:59,490 --> 00:02:08,930
+is true و احاول اثبت ان اذا P true ال Q هتروح ل
+
+26
+00:02:08,930 --> 00:02:15,400
+trueإذا أثبتنا حققت الطريقة البسيطة السهلة حققنا
+
+27
+00:02:15,400 --> 00:02:20,380
+ال proof تبعنا هتشوف طبعا عليه أمثلة كتير بس قبل
+
+28
+00:02:20,380 --> 00:02:23,140
+ما ناخد الأمثلة بتاعتنا فيها كم من تعريف محتاجينه
+
+29
+00:02:23,140 --> 00:02:27,120
+لإنه هنحتاجه في الأمثلة اللي هناخدها لليوم أول
+
+30
+00:02:27,120 --> 00:02:30,380
+تعريف طبعا تعريف بسيطة جدا مش الحاجة الكبيرة انه
+
+31
+00:02:30,380 --> 00:02:34,280
+أي integer definition أول any integer n هد أي
+
+32
+00:02:34,280 --> 00:02:40,990
+integer هنسمي oddأو even في حالة تالتة مافيش حالة
+
+33
+00:02:40,990 --> 00:02:45,430
+تالتة ففعليا ال axiom بتاعتنا أو المسلمة بتاعتنا
+
+34
+00:02:45,430 --> 00:02:50,190
+الشي المسلم البديهي ان كل integer هو either odd or
+
+35
+00:02:50,190 --> 00:02:58,010
+even فهيكون odd if and only if ان بقدر احطها بصورة
+
+36
+00:02:58,010 --> 00:03:03,680
+two k plus واحد و k some other integerأي انتجار
+
+37
+00:03:03,680 --> 00:03:08,680
+أخر فإذا قدرنا نحطها بهذه الصورة ال N معناه ذلك أن
+
+38
+00:03:08,680 --> 00:03:14,940
+ال N هذه odd طيب أما إذا قدرنا نحطها بصورة 2K بس
+
+39
+00:03:14,940 --> 00:03:20,400
+مافيش plus واحد فهتصبح even تمام؟ تعريف هذا
+
+40
+00:03:20,400 --> 00:03:24,140
+هنحتاجه كتير عشان نميز الأرقام اللي هتطلع معانا هي
+
+41
+00:03:24,140 --> 00:03:29,660
+odd ولا even و أقدر أعمل عليها حكم لنظرياتنا فبدنا
+
+42
+00:03:29,660 --> 00:03:33,810
+ناخد بالنا من بس التعريفين هدولةالجزء هذا هيو
+
+43
+00:03:33,810 --> 00:03:37,350
+والجزء هذا امتى بتكون odd امتى even لا أكتر ولا
+
+44
+00:03:37,350 --> 00:03:41,590
+أقل وكلنا عارفين انه لا يوجد عنصر تالت يا odd يا
+
+45
+00:03:41,590 --> 00:03:48,710
+even تفضل الشخص الحقيقة اتنين بس اكتر مع ال even
+
+46
+00:03:48,710 --> 00:03:54,690
+هو استخدامه اكتر مع ال even بتقدر تقول ان هو اتنين
+
+47
+00:03:54,690 --> 00:03:58,450
+من نفسه فهو even اكتر تمام
+
+48
+00:04:01,950 --> 00:04:05,770
+لأ مظبوطش على ال word فعشان يقولوا هو أكتر
+
+49
+00:04:05,770 --> 00:04:11,570
+استخداما هو لإنه فعليا محايد لكن إذا بدك تصنفه
+
+50
+00:04:11,570 --> 00:04:12,610
+ضروري تصنفه هو even
+
+51
+00:04:16,080 --> 00:04:18,960
+طيب theorem و بدنا نثبتها نحاول نثبت ال theorem
+
+52
+00:04:18,960 --> 00:04:21,780
+هذه خلصنا هدول بدنا نظل حافظينهم و مفكرينهم و
+
+53
+00:04:21,780 --> 00:04:24,420
+مذكرينهم ال theorem طبعتنا اللي بدنا نثبتها لأنه
+
+54
+00:04:24,420 --> 00:04:29,180
+طالب مني أثبتها أثبت التالي أنه لكل أرقام لكل
+
+55
+00:04:29,180 --> 00:04:37,840
+الأرقام N إذا N is odd إذا N تربية is odd على طول
+
+56
+00:04:37,840 --> 00:04:46,250
+هيه بهذا الشكل مباشرة إذا كانت العنصر Nفردي
+
+57
+00:04:46,250 --> 00:04:51,910
+المفروض انه تربيعه يكون فردي طيب بسيطة خليني امشي
+
+58
+00:04:51,910 --> 00:05:00,630
+مع if n is odd direct لاحظ احنا مشي direct then n
+
+59
+00:05:00,630 --> 00:05:12,030
+تربيع is odd صحيح؟ تمام يعني كأنه n is odd n
+
+60
+00:05:12,030 --> 00:05:19,100
+تربيعis odd خلاص ال direct ايش بيقول اتعامل معاها
+
+61
+00:05:19,100 --> 00:05:26,880
+انه فعلا in is odd فإذا assume that in is odd فعلا
+
+62
+00:05:26,880 --> 00:05:31,520
+طب في الحالة هذه معناته بقدر احط اتنين k plus واحد
+
+63
+00:05:31,520 --> 00:05:40,620
+مدام هنا let in is odd يعني لاحظ انت مشيت direct
+
+64
+00:05:40,620 --> 00:05:45,200
+حسب اتجاه ال implication مشيت صحفربط ان هي ال
+
+65
+00:05:45,200 --> 00:05:48,700
+premises مظبوطة وبناء عليها بدك تحاول تجيب ال N
+
+66
+00:05:48,700 --> 00:05:51,340
+تربيع طيب خليني أجيب ال N تربيع ال N تربيع هتصبح
+
+67
+00:05:51,340 --> 00:05:58,520
+اتنين K plus واحد كل تربيع فكفكها بدنا نفكفكها فهي
+
+68
+00:05:58,520 --> 00:06:02,340
+نفكفكلك اياها عندك هنا كده اش فكها هنا اربعة K
+
+69
+00:06:02,340 --> 00:06:11,710
+تربيع زائد اربعة K زائد واحد تمام ممتازهل بنقدر
+
+70
+00:06:11,710 --> 00:06:15,450
+نحط الصورة اللي ضايلة هدى بصورة 2 some integer
+
+71
+00:06:15,450 --> 00:06:20,430
+حقيقة اه بتقبل القسم ع 2 والواحد بيقبلش فضروري يظل
+
+72
+00:06:20,430 --> 00:06:27,230
+برا مش هتقدر تعمله اشي فهنا هحط أصبح 2 في 2k تربيع
+
+73
+00:06:27,230 --> 00:06:35,170
+plus 2k كله زائد 1 كله زائد 1 طيب ال term هذا
+
+74
+00:06:36,460 --> 00:06:44,080
+مبدأيا كل فرضيتنا قائمة على N و N odd odd ايش يعني
+
+75
+00:06:44,080 --> 00:06:49,900
+اتنين some integer يعني K integer K هي integer طيب
+
+76
+00:06:49,900 --> 00:06:54,960
+integer ال integer تربيه برضه هيدل integer عدد
+
+77
+00:06:54,960 --> 00:06:59,500
+صحيح ربعته حاسيه refraction ولا يمكن هيدل عدد صحيح
+
+78
+00:06:59,500 --> 00:07:03,540
+اضربه في اتنين عدد صحيح زائد اتنين في عدد صحيح
+
+79
+00:07:04,250 --> 00:07:10,950
+المجموع كله عدد صحيح حطله اي جي مثلا كل هذا ال
+
+80
+00:07:10,950 --> 00:07:16,850
+term جي ال جي هذي اكيد عدد صحيح integer فإذا أصبحت
+
+81
+00:07:16,850 --> 00:07:23,650
+بصورة اتنين جي plus واحد طيب
+
+82
+00:07:23,650 --> 00:07:26,970
+الشياء
+
+83
+00:07:26,970 --> 00:07:30,270
+لا اللي بهمنيش هو integer هو صمم integer بس انا
+
+84
+00:07:30,270 --> 00:07:35,670
+اللي بهمني هناإذا إن odd معناته بنقدر نحطها بشكل
+
+85
+00:07:35,670 --> 00:07:41,310
+اتنين في some integer plus واحد تمام، لاحظ if and
+
+86
+00:07:41,310 --> 00:07:44,910
+only if، إيش يعني if and only if؟ يعني هذا تحقق،
+
+87
+00:07:44,910 --> 00:07:48,690
+هذا لازم يتحقق، هذا تحقق، هذا لازم يتحقق، طيب إحنا
+
+88
+00:07:48,690 --> 00:07:56,670
+حققنا هذا، فإذا ال term هذا فعليا odd، طب ال term
+
+89
+00:07:56,670 --> 00:08:03,740
+هذا ما هو if تربية، فإذا if تربية is oddبتقنا من
+
+90
+00:08:03,740 --> 00:08:08,920
+ال premise و روحنا في اتجاه ال conclusion بسيطة و
+
+91
+00:08:08,920 --> 00:08:12,140
+مافيها كتير مشاكل ليش لأن هو السؤال بسيط حتى
+
+92
+00:08:12,140 --> 00:08:16,360
+اللحظة هو السؤال direct و مافي مشكلة طيب كمان سؤال
+
+93
+00:08:16,360 --> 00:08:21,100
+لو في عندي معادلة بهذا الشكل اللي احنا شايفينه 6x
+
+94
+00:08:21,100 --> 00:08:27,940
+plus 9y بتساوي 101طبعا كله في النهاية هذا مشروع في
+
+95
+00:08:27,940 --> 00:08:30,580
+المحاضرة المصورة الموجودة حيكون عندكم فمافيش داعي
+
+96
+00:08:30,580 --> 00:08:35,600
+نطول و احنا نكتبينه على الصبورة ايش بدنا نثبت انه
+
+97
+00:08:35,600 --> 00:08:41,440
+المعادر اللي قدامنا اللي هي 6x زائد 9y بتساوي 101
+
+98
+00:08:41,440 --> 00:08:50,480
+تعني بشكل واضح ان يا x يا y is not an integer يعني
+
+99
+00:08:50,480 --> 00:08:55,020
+بمعنى يا x يا y او كلاهما او كلاهم ممكن يكونوا
+
+100
+00:08:55,020 --> 00:09:00,180
+اتنينnot integer هل الكلمة ده صحيح بدنا نثبته بدنا
+
+101
+00:09:00,180 --> 00:09:04,380
+نثبته فالطبيعي أنه أبدأ ب assume that أن هذا ال
+
+102
+00:09:04,380 --> 00:09:09,060
+term هو صحيح هو فعلا حقيقي خلاص فإذا assume that
+
+103
+00:09:09,060 --> 00:09:14,880
+أن 6x زائد 9y هي فعلا تساوي 101 is it true فعلا
+
+104
+00:09:14,880 --> 00:09:19,400
+تساوي 101 طيب في الحالة هذه مدده تساوي 101 فإذا
+
+105
+00:09:19,400 --> 00:09:25,410
+بكل بساطة ممكن نختصرنحاول نختصر منها هنجد ان هنا
+
+106
+00:09:25,410 --> 00:09:28,470
+اتنين
+
+107
+00:09:28,470 --> 00:09:35,790
+X كله قسمنا على مين على تلاتة اتنين X زائد تلاتة Y
+
+108
+00:09:35,790 --> 00:09:39,170
+هيهم integers المعاملات تبعتنا ال coefficients
+
+109
+00:09:39,170 --> 00:09:44,490
+تبعت ال terms تبعتنا integers لكن قسمنا على ايش
+
+110
+00:09:44,490 --> 00:09:50,880
+على some مش integer some fractionsome fraction 101
+
+111
+00:09:50,880 --> 00:09:55,500
+على 3 لا يمكن بأي حال من الأحوال كقيمة تكون
+
+112
+00:09:55,500 --> 00:10:01,420
+integer هذه فعليا fraction طيب معناه ذلك انه سواء
+
+113
+00:10:01,420 --> 00:10:08,440
+x او y لا يمكن ال two terms هدولة يكونوا integers
+
+114
+00:10:08,440 --> 00:10:12,360
+لأن مجموع two integers المفروض يطلع integer طيب
+
+115
+00:10:12,360 --> 00:10:17,060
+مدام الناتج لمجموع two terms fraction على الأقل
+
+116
+00:10:17,060 --> 00:10:21,410
+واحد منهم fractionلازم على الأقل واحد منهم يطلع
+
+117
+00:10:21,410 --> 00:10:24,570
+fractions و ممكن كلاهما ممكن الأتنين يطلعوا
+
+118
+00:10:24,570 --> 00:10:27,610
+fractions لكن على الأقل في واحد ال fraction و هذا
+
+119
+00:10:27,610 --> 00:10:34,890
+كل اللي أنا بديه أنه or هيها x or y is not an
+
+120
+00:10:34,890 --> 00:10:40,810
+integer خلاص حققنا ال or أن واحد منهم على الأقل و
+
+121
+00:10:40,810 --> 00:10:44,730
+هذا منطق جدا واضح هنا تماما فإذا المية واحد على
+
+122
+00:10:44,730 --> 00:10:50,940
+تلاتة تماما باين أن هي مش integerهذه أرقام تقدر
+
+123
+00:10:50,940 --> 00:10:56,900
+تحسيها مباشرة هذا رقم واضح تماما not integer وهذا
+
+124
+00:10:56,900 --> 00:11:02,460
+معناه إنه حتى لما بدي أجيب اتنين X أو تلاتة Y كل
+
+125
+00:11:02,460 --> 00:11:07,240
+واحد لحال هدول اتنين لو هم integers أصلا نجموحهم
+
+126
+00:11:07,240 --> 00:11:11,320
+لا يمكن يطلع fraction فإذا automatically واحد منهم
+
+127
+00:11:11,320 --> 00:11:15,970
+لازم يحقق ليه ال fraction اللي ظهر في الناتجو زي
+
+128
+00:11:15,970 --> 00:11:20,710
+ما قولنا أو كلاهما أو كلاهما كويس فإذا هذه ال
+
+129
+00:11:20,710 --> 00:11:24,590
+direct هذه اسمها direct على طول بمسك ال premise
+
+130
+00:11:24,590 --> 00:11:28,310
+اللي ميعطيني إياها و منها بشتغل مباشرة بقعدش ألعب
+
+131
+00:11:28,310 --> 00:11:32,910
+فيها كتير بقعدش أغلب حالي كتير بطبق و بحاول أوصل
+
+132
+00:11:32,910 --> 00:11:38,290
+للنتج المطلوب بس في ال indirect لأ الموضوع بيختلف
+
+133
+00:11:38,290 --> 00:11:43,240
+شويةفي ال indirect الأمور شوية بتختلف أحيانا انت
+
+134
+00:11:43,240 --> 00:11:46,900
+ال direct بيكونش واضح معاك بتقدرش تشتغل عليه
+
+135
+00:11:46,900 --> 00:11:52,280
+بسهولة بسلاسة فمضطر يكون تعاملك مع ال conclusion
+
+136
+00:11:52,280 --> 00:11:57,760
+أفضل تعاملك أحيانا انت في عندك two terms ال two
+
+137
+00:11:57,760 --> 00:12:01,720
+terms هدولة مع مين تبدأ واحد اسمه premise واحد
+
+138
+00:12:01,720 --> 00:12:05,320
+اسمه conclusionال premise إذا والله بسيط تقدر
+
+139
+00:12:05,320 --> 00:12:09,820
+تتعامل معاه تقدر تتحلله بحيث أنه تقدر تطلع منه ال
+
+140
+00:12:09,820 --> 00:12:13,260
+conclusion خير و بركة direct لكن إذا وجدت أن ال
+
+141
+00:12:13,260 --> 00:12:20,140
+conclusion أحسن أبسط أسهل معناته الأفضل أنك تبدأ
+
+142
+00:12:20,140 --> 00:12:24,320
+من الآخر و ترجع رجوع للأول بس هذا الكلام بدنا نكون
+
+143
+00:12:24,320 --> 00:12:30,020
+ماخدين و مركزين بالنا من الجدولفي الجدول لما أخدنا
+
+144
+00:12:30,020 --> 00:12:32,640
+ال implication أذكركوا أخدنا حاجة اسمها inverse,
+
+145
+00:12:33,460 --> 00:12:38,200
+converse, contrapositive أو contradiction ال
+
+146
+00:12:38,200 --> 00:12:40,320
+contrapositive هذه هي اللي بدنا إياها ال
+
+147
+00:12:40,320 --> 00:12:46,160
+contrapositive إيش كانت بتقول إذا P implies Q is
+
+148
+00:12:46,160 --> 00:12:50,140
+true إذا
+
+149
+00:12:50,140 --> 00:12:59,160
+negation Q implies negation P is trueتذكرتوها؟ بس
+
+150
+00:12:59,160 --> 00:13:05,480
+هاي ال indirect إن أعكس ال conclusion و أثبت إن
+
+151
+00:13:05,480 --> 00:13:11,280
+عكس ال conclusion هيعطيني عكس ال premise بس إذا
+
+152
+00:13:11,280 --> 00:13:13,700
+قلرنا نوصلها إحنا عارفين إن فيها اسمة
+
+153
+00:13:13,700 --> 00:13:18,740
+contrapositive إذا هذه صح، automatic هذه صح اللي
+
+154
+00:13:18,740 --> 00:13:21,700
+هي النظرية اللي كانت مطلوبة بالأساس اللي هي مطلوبة
+
+155
+00:13:21,700 --> 00:13:26,150
+بالأساس عشانك اسمها indirect لفناها شويةواضحة؟
+
+156
+00:13:26,150 --> 00:13:31,590
+تمام هتشوف المثال اللي عندي if 3n plus 2 is odd
+
+157
+00:13:31,590 --> 00:13:35,790
+premise بدنا نثبت إذا كان هذا الكلام صحيح إذا n
+
+158
+00:13:35,790 --> 00:13:40,630
+لحالها is odd طيب
+
+159
+00:13:40,630 --> 00:13:44,610
+ماحنا توي لما كنا بنعود فكرة أني أعود في term كبير
+
+160
+00:13:44,610 --> 00:13:49,230
+مزعجة لكن لما أعود في term صغير بال 2k plus 1 أسهل
+
+161
+00:13:49,230 --> 00:13:55,160
+ليه؟ كتير أسهلفإذا إني أتعامل مع ال conclusion
+
+162
+00:13:55,160 --> 00:13:58,880
+أسهل من إني أتعامل مع ال premise في الحالة هذه
+
+163
+00:13:58,880 --> 00:14:03,040
+الطبيعي أنك تفكر في ال contrapositive اللي هي إيش
+
+164
+00:14:03,040 --> 00:14:06,640
+ال indirect ال indirect إيش هتقول ليه هتقول لمعنته
+
+165
+00:14:06,640 --> 00:14:15,140
+في هذه الحالة هنعكسها تصبح if n is even negation
+
+166
+00:14:15,140 --> 00:14:16,820
+even
+
+167
+00:14:19,970 --> 00:14:27,930
+تلاتة N plus two is even تمام صارت نفس السؤال اللي
+
+168
+00:14:27,930 --> 00:14:30,250
+جابله اللي جابله كان عن الـodd بتهلجت عن ال even
+
+169
+00:14:30,250 --> 00:14:35,270
+القالية واحدة بتعود مكان ال N بيقاش بتنين K بس
+
+170
+00:14:35,270 --> 00:14:45,250
+بتنين K وخلصت الجثة اتنين K فإذا N is even يعني N
+
+171
+00:14:45,250 --> 00:14:50,830
+تساوي اتنين Kوهذا معناها أن تلاتة in plus two
+
+172
+00:14:50,830 --> 00:14:59,710
+تساوي تلاتة في اتنين K plus two يعني تساوي ستة K
+
+173
+00:14:59,710 --> 00:15:09,690
+plus two يعني تساوي اتنين في تلاتة K plus one طيب
+
+174
+00:15:09,690 --> 00:15:17,390
+K هذه أساسا integerطيب انتجر في ثلاثة مازالت انتجر
+
+175
+00:15:17,390 --> 00:15:21,450
+انتجر زائد واحد انتجر يعني كل هذه بقدر اقول عنها
+
+176
+00:15:21,450 --> 00:15:25,950
+some other integer اسمها j وانا ضامن ان هي انتجر
+
+177
+00:15:25,950 --> 00:15:30,290
+عدد صحيح يعني معناه ذلك حطيتها بصورة two في some
+
+178
+00:15:30,290 --> 00:15:35,310
+integer some other integer عدد صحيح مضروف في اتنين
+
+179
+00:15:35,310 --> 00:15:39,490
+خلاص قولة واحدة مدى مضروف في اتنين ومش مجموعة زائد
+
+180
+00:15:39,490 --> 00:15:46,270
+واحد فإذا هذا evenفإذا ال term هذا هيك بهذا الشكل
+
+181
+00:15:46,270 --> 00:15:54,920
+هنا is even انتهى الأثبات أثبتناالحالة هذه by
+
+182
+00:15:54,920 --> 00:16:00,700
+contradiction او by .. سمنها احنا ايش ال ..
+
+183
+00:16:00,700 --> 00:16:03,520
+contrapositive by contrapositive فإذا P employees
+
+184
+00:16:03,520 --> 00:16:09,700
+Q is true تفضل انك
+
+185
+00:16:09,700 --> 00:16:17,030
+تعمل analysis لل premiseعندك two terms مش هيك بدك
+
+186
+00:16:17,030 --> 00:16:21,890
+تثبت أن الأول حدوثه يؤدي لحدوث التاني طيب الأول
+
+187
+00:16:21,890 --> 00:16:26,570
+صعب تتحلله إيش بدك تسويه تتطلع على التاني ال
+
+188
+00:16:26,570 --> 00:16:29,750
+conclusion الاستنتاج اللي بدك تصله هل من السهل أنك
+
+189
+00:16:29,750 --> 00:16:33,730
+تحليله يكون أسهل إذا أسهل على طول أحولها من الشكل
+
+190
+00:16:33,730 --> 00:16:37,370
+هذا للشكل هذا إذا أثبتت الشكل هذا في الآخر تكتب by
+
+191
+00:16:37,370 --> 00:16:41,770
+contrapositive إذا ال theorem is true اللي هي هذه
+
+192
+00:16:42,910 --> 00:16:47,750
+بس فانت عينك ميزانك زي ما يقولوا، إدماجك هو اللي
+
+193
+00:16:47,750 --> 00:16:52,490
+يقودك هو مين الأسهل؟ أسهل تتعامل مع ال premise ولا
+
+194
+00:16:52,490 --> 00:16:54,010
+أسهل تتعامل مع ال conclusion؟
+
+195
+00:16:58,170 --> 00:17:03,810
+بالظبط ومطلوب منك انك تثبت تثبت مش انك انت تقولي
+
+196
+00:17:03,810 --> 00:17:07,430
+اه ما هي صح لأ انا بقولك اثبتلي ان هي صح طيب ال
+
+197
+00:17:07,430 --> 00:17:11,130
+premise صعب اتحلله او صعب اتعامل معاه يمكن يكون
+
+198
+00:17:11,130 --> 00:17:13,990
+انك اتحلل ال conclusion اسهل فبتصير هنا ال
+
+199
+00:17:13,990 --> 00:17:21,010
+indirect سبيل افضل من ال direct من ال direct okay
+
+200
+00:17:21,010 --> 00:17:23,190
+كمان مثال اذا كانت
+
+201
+00:17:27,820 --> 00:17:32,660
+x plus y greater than one hundred إذا كانت x زائد
+
+202
+00:17:32,660 --> 00:17:41,620
+y أكبر من مية بدنا نثبت إذا x أكبر من خمسين أو y
+
+203
+00:17:41,620 --> 00:17:49,360
+أكبر من خمسين بدك تثبت الكلام هذاإذا كانت X زائد Y
+
+204
+00:17:49,360 --> 00:17:54,700
+أكبر من مية إذا X لحالها أكبر من خمسين أو Y لحالها
+
+205
+00:17:54,700 --> 00:17:58,780
+أكبر من خمسين بحيث أن فعلًا مجموحهم يكون أكبر من
+
+206
+00:17:58,780 --> 00:18:04,900
+مية مش هيك طيب كيف بدك تثبتها direct مثلا من هنا
+
+207
+00:18:04,900 --> 00:18:09,320
+لحالها يعني
+
+208
+00:18:09,320 --> 00:18:13,580
+كيف بدك .. بالظبط كيف بدك تنطلق من هذه الجزء صعب
+
+209
+00:18:13,580 --> 00:18:19,100
+انطلاقتك أنك تبدأ حالك من هنافيش limits هذه الها
+
+210
+00:18:19,100 --> 00:18:22,860
+limits بتقدر تعرف هي إيش أقصى قيمة إلها أو أقل
+
+211
+00:18:22,860 --> 00:18:27,120
+قيمة إلها صحيح من خلال ال indirect اللي مكتوبة هنا
+
+212
+00:18:27,120 --> 00:18:31,120
+بقولك إذا X أكبر من خمسين يعني أنت عارف إنه X أقل
+
+213
+00:18:31,120 --> 00:18:35,760
+إشي إلها خمسين تمام اه frankly مش مشكلة بس أنا
+
+214
+00:18:35,760 --> 00:18:38,880
+أتكلم جداش قيمتها ال limit ال threshold تبعت
+
+215
+00:18:38,880 --> 00:18:42,620
+قيمتها هنا واضحة هنا مافيش إش مش باين عندك مافيش
+
+216
+00:18:42,620 --> 00:18:46,620
+إش باين عندكأنا دلوقتي بقولك ابدالي من X زائد Y
+
+217
+00:18:46,620 --> 00:18:50,920
+بتسيق أكبر من 100 يعني إيش الفرضية اللي بده أفرضها
+
+218
+00:18:50,920 --> 00:18:53,800
+الآن؟ إيش كيف بدي أكتبها؟ ف ال direct هنا كتير
+
+219
+00:18:53,800 --> 00:18:56,720
+صعب، كتير صعب تتعامل مع ال direct واضح إنه بدنا
+
+220
+00:18:56,720 --> 00:19:01,060
+نروح لمين؟ ل ال indirect اللي هو أحولها بصورة
+
+221
+00:19:01,060 --> 00:19:10,620
+negation Q employees negation P بحيث إنها تصبحناخد
+
+222
+00:19:10,620 --> 00:19:16,360
+الجزء بعدين هذا و يصبح هو البداية بس إعكسه إيش
+
+223
+00:19:16,360 --> 00:19:25,700
+يعني إعكسه؟ يعني هتصبح X أصغر أو تساوي خمسين and Y
+
+224
+00:19:25,700 --> 00:19:37,820
+أصغر أو يساوي خمسين إذا X زائد Y أقل أو يساوي مية
+
+225
+00:19:40,270 --> 00:19:43,870
+أقل أو يساوي 100 أصبحت الفرضية أو ال theorem اللي
+
+226
+00:19:43,870 --> 00:19:48,990
+بدك تثبتها بهذا الشكل كتير أسهل إثباتها انت قاعد
+
+227
+00:19:48,990 --> 00:19:53,850
+بتقول كلهم أقل من 50 صح يعني أكبر قيمة ممكنة لل X
+
+228
+00:19:53,850 --> 00:20:07,810
+خمسين and طبعا هذه ل X and أكبر قيمة ممكنة ل Y هذه
+
+229
+00:20:07,810 --> 00:20:13,540
+أكبر قيمة ممكنةففي الحالة هذه كأكبر قيمة هيؤدى ان
+
+230
+00:20:13,540 --> 00:20:21,620
+X زائد Y هتساوي 100 مثبتة
+
+231
+00:20:21,620 --> 00:20:25,510
+لحالها بس في البداية ماكنتش مثبتة لحالهافي الأول
+
+232
+00:20:25,510 --> 00:20:28,330
+كان صعب أنك تتعامل معها، هالواجهة صارت سهلة، ليش؟
+
+233
+00:20:28,330 --> 00:20:31,790
+لأن في عندك limits، بتقدر من ال limits هذه تشوف
+
+234
+00:20:31,790 --> 00:20:35,930
+the worst case، إيش أسوأ حالة ممكنة أنها تكون
+
+235
+00:20:35,930 --> 00:20:40,030
+تساوي خمسين، هذه أكبر قيمة ممكنة، مع أن ذلك هي أجل
+
+236
+00:20:40,030 --> 00:20:42,150
+من الخمسين، يعني معناه ذلك أن المجموع هيكون أجل من
+
+237
+00:20:42,150 --> 00:20:47,670
+مية كمان، واضحة، باينة، سهلة إثباتها، بس أنك تبدأ
+
+238
+00:20:47,670 --> 00:20:54,760
+من هنامالهاش معالم زى ما بيقولوا مالهاش فرضية تبدأ
+
+239
+00:20:54,760 --> 00:21:01,220
+تشتغل منها واضحة امتى بدك تروح لل indirect او ال
+
+240
+00:21:01,220 --> 00:21:05,160
+contrapositive فإذن قدرنا نثبتها و الطريقة السابقة
+
+241
+00:21:05,160 --> 00:21:12,700
+طبعا شرح واضح و باين okay الان ال vacuous proof او
+
+242
+00:21:12,700 --> 00:21:18,980
+الفارغ الاثبات الفارغ بمعنى زى ما نقول هى الكلام
+
+243
+00:21:18,980 --> 00:21:24,910
+فارغإثبات الفارغ هذا إيش زي حالة زي اللي قدامنا
+
+244
+00:21:24,910 --> 00:21:36,330
+هنا for all in if in is both odd and even إذا ولا
+
+245
+00:21:36,330 --> 00:21:41,530
+بتفرج معايا إذا تطلع زي ما تطلع ليش لأنه بدناها من
+
+246
+00:21:41,530 --> 00:21:47,990
+الأول false صح
+
+247
+00:21:47,990 --> 00:21:56,450
+بدناها false فإذافارغ هنا إيش ال Q كلام فارغ ولا
+
+248
+00:21:56,450 --> 00:21:58,770
+بيفرج معايا تطلع ال true و تطلع ال false أنا مش
+
+249
+00:21:58,770 --> 00:22:04,650
+حاجة أغلب حالي الشيعة بدأت ال false فإذا ال
+
+250
+00:22:04,650 --> 00:22:09,470
+implication ال true خلصت النظرية صح ماشي نظرية صح
+
+251
+00:22:09,470 --> 00:22:14,930
+فكرة اللي لما ينور الملح هي هي نفسها دي vicious أو
+
+252
+00:22:14,930 --> 00:22:20,210
+كلام فارغ أنت هنا أصبحت مفرغ من معناهاال
+
+253
+00:22:20,210 --> 00:22:24,610
+conclusion اللي بدك تروحله okay إيش هيفرج معاك إنه
+
+254
+00:22:24,610 --> 00:22:29,590
+يطلع true ولا false؟ فمعنى ذلك إنه الإثبات فارغ
+
+255
+00:22:29,590 --> 00:22:34,130
+انت .. إيش بدك تعمل إثبات؟ يعني إيش بدك تثبت؟ بدك
+
+256
+00:22:34,130 --> 00:22:37,970
+تبدأ تعمل زي توي نبدأ خطوات و نحل و نشتغل لإيش؟
+
+257
+00:22:37,970 --> 00:22:43,990
+يعني بدك تثبت مني صح ولا غلط؟ مش هيفرج صح طيب أنت
+
+258
+00:22:43,990 --> 00:22:46,930
+طلع معاك صح وطلع معاه غلط في الحلتين هتقولوا إنه
+
+259
+00:22:46,930 --> 00:22:50,840
+النظرية صحيحةفي الحالتين هتقول ان دراية صحية فإذا
+
+260
+00:22:50,840 --> 00:22:57,960
+automatically خلاص إذا ال P is false انتهى الإثبات
+
+261
+00:22:57,960 --> 00:23:02,780
+مين اللي جالنا الكلام هذا ال if then ال if then
+
+262
+00:23:02,780 --> 00:23:06,420
+انت في النهاية قاعد بتقول if then
+
+263
+00:23:08,390 --> 00:23:12,890
+يعني implication يعني بدأت ب false مش هيفرج معاك
+
+264
+00:23:12,890 --> 00:23:17,250
+ال Q إش ما تطلع فمدام مش هتفرج ليش بدك تغلب حالك و
+
+265
+00:23:17,250 --> 00:23:21,010
+تروح تثبتها؟ إيش بدك تثبت؟ تثبت إن هي صح ولا تثبت
+
+266
+00:23:21,010 --> 00:23:25,830
+إن هي غلط؟ بفرجشفإذن هذه من الحالات اللي خلاص
+
+267
+00:23:25,830 --> 00:23:33,010
+منتهية من أولها vacously is it true بطريقة مفرغة
+
+268
+00:23:33,010 --> 00:23:37,250
+من المحتوى بمعنى ان انا ليش بدك تجيب حل هو فارغ
+
+269
+00:23:37,250 --> 00:23:42,690
+الحل فارغ اش ما حديهه مالوش معنى حل فارغ فإذن
+
+270
+00:23:42,690 --> 00:23:48,630
+بدايته جاب الحل و خلص تمام واضحة؟هذه طبعا أحيانا
+
+271
+00:23:48,630 --> 00:23:52,410
+بتكون logic بتكون زي مسائل ال logic هيك انك انت
+
+272
+00:23:52,410 --> 00:23:56,810
+بدأت بحالة هي مش هيفرج انت و اين بدك تروح انا ممكن
+
+273
+00:23:56,810 --> 00:24:01,130
+اقولك من هذه اثبتلي و الاثبات اللي طالبه معجز طبعا
+
+274
+00:24:01,130 --> 00:24:04,630
+انت هتضلك تفكر في فكرة ان انت بدك تفضته و رايح جاي
+
+275
+00:24:04,630 --> 00:24:08,250
+رايح جاي و هي الفكرة مش هنا الفكرة في البداية
+
+276
+00:24:08,250 --> 00:24:14,110
+البداية لما ينور الملحالبداية لما ينور الملح،
+
+277
+00:24:14,110 --> 00:24:18,670
+المثل اللي كان بحكي طب إذا كان بنورش الملح مش
+
+278
+00:24:18,670 --> 00:24:23,250
+هيفرج إيش اللي بعده؟ إيش بعده مش هيفرج؟ يعني ممكن
+
+279
+00:24:23,250 --> 00:24:27,330
+okay نور الملح ولا ما نور؟ okay خلاص هنجحكوا ماشي
+
+280
+00:24:27,330 --> 00:24:32,190
+أو أقولكوا لما ينور الملح هنجحكوا، مانجحش حدا، في
+
+281
+00:24:32,190 --> 00:24:37,290
+الحالتين بتظبط، صحيح؟ في الحالتين بتظبطانت
+
+282
+00:24:37,290 --> 00:24:42,310
+مابتشوفوش في مدارس لما ينجح حد مثلا؟ صحيح فالقصد
+
+283
+00:24:42,310 --> 00:24:46,790
+انه الحالتين ك conclusion بظبطه ف the casually is
+
+284
+00:24:46,790 --> 00:24:52,750
+true طيب ال trivial ال trivial اللي هو تافه بمعنى
+
+285
+00:24:52,750 --> 00:25:00,360
+انه تافه او عديم الفائدةهناك فارغ وهنا تافع أو
+
+286
+00:25:00,360 --> 00:25:03,120
+عديم الفائدة عديم الفائدة إمتى بنقول عديم الفائدة
+
+287
+00:25:03,120 --> 00:25:09,200
+إذا كنت أنا بعرف أصلا من الأساس قيمة Q ال
+
+288
+00:25:09,200 --> 00:25:12,480
+conclusion اللي مطلوب أثبته أنا عارفه هو مثبت
+
+289
+00:25:12,480 --> 00:25:17,180
+فمعنى ذلك بفرقش معايا إيش ال premise اللي إنت
+
+290
+00:25:17,180 --> 00:25:22,360
+عطتني إيها إذا كان أنا جادر أثبت Q لحالها بدون
+
+291
+00:25:22,360 --> 00:25:28,650
+معرفة ال PP عديمة الفائدة صارت مش شاك .. trivial
+
+292
+00:25:28,650 --> 00:25:35,030
+عديمة الفائدة P أنا مش محتاجها هي مثبتة ال Q
+
+293
+00:25:35,030 --> 00:25:40,110
+لحالها مثبتة مش محتاجة P مش محتاجة P أبدأ .. أبدأ
+
+294
+00:25:40,110 --> 00:25:44,890
+حالي أنه assume that P is true و أبدأ أنطلق منها
+
+295
+00:25:44,890 --> 00:25:50,160
+لأنه مش محتاج أنطلق منها ال Q مثبتة لحالهامثال if
+
+296
+00:25:50,160 --> 00:25:53,640
+it's raining today then three is an odd number
+
+297
+00:25:53,640 --> 00:25:57,980
+والله تشتي ولا ما تشتي مش فارقة معايا ال premise
+
+298
+00:25:57,980 --> 00:26:00,920
+مالهاش معنى يعني أنا مش محتاج هلوجد أروح الاستارة
+
+299
+00:26:00,920 --> 00:26:04,000
+و أفتح عشان أشوف هي فعلا raining ولا it's not
+
+300
+00:26:04,000 --> 00:26:09,520
+raining مش محتاج لأن اللي بعرفه أن التلاتة is odd
+
+301
+00:26:09,520 --> 00:26:14,440
+even بقدر أحطها بصورة اتنين K زائد واحد خلاص is
+
+302
+00:26:14,440 --> 00:26:22,500
+odd is odd خلاصبغض النظر عن إيش الفرضية اللي بده
+
+303
+00:26:22,500 --> 00:26:27,100
+ياني أنطلق منها الفرضية مالهاش علاقة فيها سواء صح
+
+304
+00:26:27,100 --> 00:26:33,140
+ولا غلط يعني افرض فعلا دنيا بتشتي تلاتة odd number
+
+305
+00:26:33,140 --> 00:26:38,380
+طب لأ مابتشتيش و برضه تلاتة is odd number تقريب
+
+306
+00:26:38,380 --> 00:26:43,400
+واضحة okay فهذه ال trivia ليه بنسميها is true
+
+307
+00:26:43,400 --> 00:26:44,560
+النظرية تاعتنا
+
+308
+00:26:51,290 --> 00:26:55,410
+المثال اللي ماتينيه هنا إذا إيش طالب if n is the
+
+309
+00:26:55,410 --> 00:26:58,690
+sum of two primes number إذا كانت n هي عبارة عن
+
+310
+00:26:58,690 --> 00:27:05,970
+مجموعة two primes n هي عبارة عن P1 plus P2 و ال P
+
+311
+00:27:05,970 --> 00:27:10,510
+هدولة primes
+
+312
+00:27:10,510 --> 00:27:18,190
+كويس إيش طالب then either n is odd or n is even
+
+313
+00:27:20,210 --> 00:27:24,410
+بفرقش معاه هي هالوجة بيقولك معناها إذا كان فعلا إن
+
+314
+00:27:24,410 --> 00:27:34,290
+هي مجموع two primes even if is even or odd طب ما
+
+315
+00:27:34,290 --> 00:27:40,590
+هو صحيح ماهي صحيح بغض النظر إذا كانت in هي فعلا
+
+316
+00:27:40,590 --> 00:27:45,270
+مجموع two primes ولا مش مجموع two primesهي ان اكيد
+
+317
+00:27:45,270 --> 00:27:48,790
+مالهاش حالة تالتة هي either odd or even في حالة
+
+318
+00:27:48,790 --> 00:27:52,130
+تالتة مافيش حالة تالتة اذا هي integer فهي هي تكون
+
+319
+00:27:52,130 --> 00:27:56,850
+either odd or even وهو بادي for all integer لكل
+
+320
+00:27:56,850 --> 00:28:03,650
+قيم القيم الصحيحة ان بدك تثبت ان هي odd or even طب
+
+321
+00:28:03,650 --> 00:28:07,650
+ما هي من الأساس odd او even بغض النظر هي مجموع two
+
+322
+00:28:07,650 --> 00:28:10,920
+primes ولا مش مجموع two primesولا مش مجموع two
+
+323
+00:28:10,920 --> 00:28:14,720
+primes؟ ليش؟ لأن أنت بتتكلم هنا عن حالة أن q هي
+
+324
+00:28:14,720 --> 00:28:28,300
+أصلا true هيها true P الشية بتفرجش يعني P هنا
+
+325
+00:28:28,300 --> 00:28:33,930
+والله ليست مجموعة two primesrelation صحيحة طيب لأ
+
+326
+00:28:33,930 --> 00:28:36,790
+هي فعلا مجموعة of primes برضه ال relation صحيحة
+
+327
+00:28:36,790 --> 00:28:43,210
+ليش بمعرفة أن q أصلا بحيث ذاتها هي true فمعنى ذلك
+
+328
+00:28:43,210 --> 00:28:48,030
+أن ال relation صح خلاص هي صحة trivially ال theorem
+
+329
+00:28:48,030 --> 00:28:52,870
+is true صحيحة مثبتة خلص أثبتناها تمام
+
+330
+00:28:58,550 --> 00:29:03,130
+هذه النظرتين ال .. ال .. ال vicious way ال trivial
+
+331
+00:29:03,130 --> 00:29:08,350
+كتير تستخدم مش في عملية زي هذه الحسابية بتستخدم
+
+332
+00:29:08,350 --> 00:29:13,630
+اكتر في ال tricks في الحياة اللي هو انت ماخد بالك
+
+333
+00:29:13,630 --> 00:29:19,020
+ان اصلا انت رايح تثبت حاجة مثبتةوانت تايع في إيش؟
+
+334
+00:29:19,020 --> 00:29:22,440
+في انطلاقك من ال premise ماسك ال premise و قاعد
+
+335
+00:29:22,440 --> 00:29:26,320
+بتلفه بالدور و بتلفه بالدور طيب إمتى ال .. ال ..
+
+336
+00:29:26,320 --> 00:29:29,960
+ال انها دي بتكون مجموع two primes؟ طيب إمتى بتكونش
+
+337
+00:29:29,960 --> 00:29:32,820
+two primes؟ طيب إمتى .. دخلت حالك في احتمالات و
+
+338
+00:29:32,820 --> 00:29:35,720
+دخلت حالك في possibilities كتيرة هتروح تقول طيب
+
+339
+00:29:35,720 --> 00:29:39,040
+بدي أفرض الأول إذا كان هم فعلا two primes طيب إيش
+
+340
+00:29:39,040 --> 00:29:42,200
+هصير معاك؟ طيب لأ هم إذا كانوش two primes إيش هصير
+
+341
+00:29:42,200 --> 00:29:45,390
+معاك؟هتلاقي حالك بتضيع حالك و بتطوي حالك على
+
+342
+00:29:45,390 --> 00:29:49,670
+الفاضي انت في جميع الأحوال هتصلق الناتج .. الناتج
+
+343
+00:29:49,670 --> 00:29:53,950
+بيقولك انه ان معناته هي يا فردي يا زوجي طب ماهي من
+
+344
+00:29:53,950 --> 00:29:56,610
+الأساس يعني فعلا منطقي يا فردي يا زوجي ليش و في إش
+
+345
+00:29:56,610 --> 00:30:02,990
+تالت؟ مافيش إش تالت تمام الآن ال contradictionالـ
+
+346
+00:30:02,990 --> 00:30:06,570
+Contradiction الـ Contradiction هي أكتر حالة ممكن
+
+347
+00:30:06,570 --> 00:30:11,250
+تيجي فيها إثباتات أكتر حالة اللي هي التناقض ال ..
+
+348
+00:30:11,250 --> 00:30:14,910
+التناقض ال method هذه عشان نعمل فيها proving ل P
+
+349
+00:30:14,910 --> 00:30:20,850
+عندك premise أعطاك إياها و بدك تثبت أن هي صح فهذه
+
+350
+00:30:20,850 --> 00:30:25,250
+عادة حتى طريقة السؤال بتكونش زي ما انت متخيل if
+
+351
+00:30:25,250 --> 00:30:29,910
+then لأ بتكونش if then بيعطيك معطأ و بيقولك هو صح
+
+352
+00:30:29,910 --> 00:30:35,980
+ولا غلط بسإثبت لي إن هذا صح طب إذا إيش مافيش إذا
+
+353
+00:30:35,980 --> 00:30:42,340
+إيش هي هيك مافيش حاجة اسمها إذا إيش حاجة إثبتها مش
+
+354
+00:30:42,340 --> 00:30:45,920
+if then تمام ففي الحالة هذه بدنا نثبت هذا الطريقة
+
+355
+00:30:45,920 --> 00:30:53,280
+اللي أثبت P بنفرض عكسها P نفسها أنا مش عارف وين
+
+356
+00:30:53,280 --> 00:30:58,540
+بتهودينيمش عارف إيش لازم أثبت منها لكن لما يقول
+
+357
+00:30:58,540 --> 00:31:03,320
+أفرض عكسها عكسها هذا بدي أثبت من خلاله إنه صار
+
+358
+00:31:03,320 --> 00:31:08,780
+تناقض في الناتج هناخد الأمثلة اللي هتوضح عكسها
+
+359
+00:31:08,780 --> 00:31:18,480
+المفروض منطقي إنه يعطيني عكس ال P صح P given إن هي
+
+360
+00:31:18,480 --> 00:31:22,880
+تسوي كذا أنت هتقول عكسها المفروض إنها لو تسوي كذا
+
+361
+00:31:23,600 --> 00:31:28,180
+مش هيك؟ هتتفاجأ انه عكس اللي انت مفترض انه يطلع لا
+
+362
+00:31:28,180 --> 00:31:33,420
+يساوي كذا طلع بيساوي كذاطب كيف الناتج تناقض مع
+
+363
+00:31:33,420 --> 00:31:38,000
+نفسه فعملية التناقض هذه اللي هتحدث و اللي هنشتغل
+
+364
+00:31:38,000 --> 00:31:40,740
+على وطرها و هنشوف ايش كيف انا ممكن اعمل هذا الكلام
+
+365
+00:31:40,740 --> 00:31:43,200
+من خلال الأمثل الأمثل اللي هتوضحها بس قاعدين احنا
+
+366
+00:31:43,200 --> 00:31:49,500
+بنفكر بالمنطق الطريقة المنطقية اذا فعلا أثبتنا انه
+
+367
+00:31:49,500 --> 00:31:53,160
+صار تناقض في الناتج انا كنت رايح في اتجاه معين و
+
+368
+00:31:53,160 --> 00:31:58,220
+اتفاجأت انه لا هو عكس هو العكس في تناقض التناقض
+
+369
+00:31:58,220 --> 00:32:03,190
+هذا هيقودني ان هذه صارت falseصح هذه false انتهى
+
+370
+00:32:03,190 --> 00:32:10,130
+الجزء هذا false عارفين ايش يعني ان q false نرجع
+
+371
+00:32:10,130 --> 00:32:17,450
+للحالة تاعتنا للحالة
+
+372
+00:32:17,450 --> 00:32:19,890
+اللي احنا شغالين عليها انه هذه اثبتنا ان هي false
+
+373
+00:32:19,890 --> 00:32:24,950
+طب هي ايش كانت ال premise تاعتهاnegation P مش هذه
+
+374
+00:32:24,950 --> 00:32:27,150
+الفرضية اللي احنا فرضناها انا مابدأتش بالفرضية
+
+375
+00:32:27,150 --> 00:32:31,790
+الصحيحة انا بدي اثبت الصحيحة بس فرضت عكسها فمعنى
+
+376
+00:32:31,790 --> 00:32:36,590
+ذلك انه negation P وهذه الحالة هنا طلع هذه false
+
+377
+00:32:36,590 --> 00:32:43,230
+لأنه طلعت ان Q و negation Q التاني اتحققوا طب كيف
+
+378
+00:32:43,230 --> 00:32:48,550
+Q و negation Q أخدناها سابقا اي
+
+379
+00:32:50,130 --> 00:32:54,710
+proposition and ال negation تبعه false فإذا هذه
+
+380
+00:32:54,710 --> 00:32:58,590
+false هتنفسك ال false هي false وهي false هي الحالة
+
+381
+00:32:58,590 --> 00:33:02,110
+تنتهي من ال false ال Q is false هي واحدة وهي
+
+382
+00:33:02,110 --> 00:33:08,150
+التانية طب إمتى النظرية بتكون صحيحة هنا لأ هي
+
+383
+00:33:08,150 --> 00:33:14,630
+الحالة الوحيدة إمتى هتكون true إذا كانت ب false
+
+384
+00:33:14,630 --> 00:33:19,490
+معناه ذلك إن ال term هذا لازم يكون falseطب إذا
+
+385
+00:33:19,490 --> 00:33:26,250
+كانت negation P false فإذا P is true إذا P is true
+
+386
+00:33:26,250 --> 00:33:30,350
+تمام؟ هيك هذا الكلام المنطقي حتى اللحظة كيف بدي
+
+387
+00:33:30,350 --> 00:33:33,890
+أطبقه عملية تطبيقه هذه اللي هتبين الأن في الأمثلة
+
+388
+00:33:33,890 --> 00:33:38,730
+ونشوف
+
+389
+00:33:38,730 --> 00:33:42,870
+إيش فكرة إنه أنا مفترض إن هي تطلع negation P و
+
+390
+00:33:42,870 --> 00:33:46,670
+اتفاجأت .. negation Q و اتفاجأت إن هي طلعت Q هنشوف
+
+391
+00:33:46,670 --> 00:33:49,800
+هذا الكلاملاحظ ايش بيسألني ايش يعطيك theorem على
+
+392
+00:33:49,800 --> 00:33:56,080
+طول روت او square root of two is a rational اثبت
+
+393
+00:33:56,080 --> 00:34:00,460
+طب اذا ايش عشان اعرف اثبت هي هيك فاش اذا ايش فاش
+
+394
+00:34:00,460 --> 00:34:06,940
+if then هي هيك خلاص تمام بدنا نشوف ايش يعني كلمة
+
+395
+00:34:06,940 --> 00:34:13,380
+اولا rational لما اقول ان الرقم rational يعني بقدر
+
+396
+00:34:13,380 --> 00:34:21,200
+احطه بصيغة a over p over bبدون ما يكون في أي
+
+397
+00:34:21,200 --> 00:34:27,220
+common between them يعني فرضيته من الأساس في حالته
+
+398
+00:34:27,220 --> 00:34:31,660
+الأبسط أنا مبسط ولا أقصى حد بمعنى إنه لا يوجد أي
+
+399
+00:34:31,660 --> 00:34:35,820
+عامل مشترك between them إذا يوجد عامل مشترك صارت
+
+400
+00:34:35,820 --> 00:34:43,440
+irrational وإذا بقدرش أحط الرقم in مثلا in هذه
+
+401
+00:34:43,440 --> 00:34:50,100
+بقدرش أحطها بصيغةكسر عشري أو كسر اتيادي كسر اتيادي
+
+402
+00:34:50,100 --> 00:34:54,160
+بهذا الشكل فإذا هي ال rational معناته أنها ليست
+
+403
+00:34:54,160 --> 00:34:59,460
+rational rational لها تعريف واحد بس بقدر احطه
+
+404
+00:34:59,460 --> 00:35:05,920
+بصيغة numerator على denominator بسط على مقام في
+
+405
+00:35:05,920 --> 00:35:12,170
+أبسط صورةفإذن إذا ماقدرتش أحطها بسط على مقام هي
+
+406
+00:35:12,170 --> 00:35:16,090
+ليست rational إذا قدرت أحطها بسط على مقام ولكن
+
+407
+00:35:16,090 --> 00:35:21,770
+يوجد عامل مشترك فهي برضه ليست rational واضحة؟ تمام
+
+408
+00:35:21,770 --> 00:35:28,130
+فإذا التعريف إنها تكون A على B ولا يوجد عامل مشترك
+
+409
+00:35:28,130 --> 00:35:35,890
+بين A وB ممتاز من هنا هننطلق okayجيد جدا فإذا
+
+410
+00:35:35,890 --> 00:35:42,510
+هنبدأ انه مش in irrational هنبدأ ان جذر اتنين هو
+
+411
+00:35:42,510 --> 00:35:46,350
+اللي rational إيش يعني؟ يعني أنا روحت ل negation P
+
+412
+00:35:46,350 --> 00:35:51,630
+هي كان بدلي أنا أثبت أن هي irrational يعني ماقدرش
+
+413
+00:35:51,630 --> 00:35:58,550
+أحطها بصيغة كسر اعتيادي رقم انتجر على انتجرهو
+
+414
+00:35:58,550 --> 00:36:00,970
+بيقول إن انت بتقدرش تحطها integer على integer، أنا
+
+415
+00:36:00,970 --> 00:36:05,750
+هقوله لأ، هي ممكن يوضحها بشكل integer، فإذا هقول
+
+416
+00:36:05,750 --> 00:36:10,470
+الفرضية كأنها negation P، هاي أول خطوة من ال
+
+417
+00:36:10,470 --> 00:36:13,510
+algorithm تبع تويق، إنه إيش بدنا نعمل؟ إن أفرض
+
+418
+00:36:13,510 --> 00:36:20,310
+negation P، واضحة الآن؟بدنا نتأكد هل لما أفرض إن
+
+419
+00:36:20,310 --> 00:36:24,670
+هي rational هيكون كلامنا منطقي على فكرة إيش يعني
+
+420
+00:36:24,670 --> 00:36:28,050
+rational بس احنا عشانك تقوموا بتبحثيلك إيش يعني
+
+421
+00:36:28,050 --> 00:36:31,670
+rational فبدنا نشوف الكلام هدا هيضل ماشي معانا صح
+
+422
+00:36:31,670 --> 00:36:35,170
+للآخر ولا لأ بس لا أكتر ولا أقل تفضل يعني انا يا
+
+423
+00:36:35,170 --> 00:36:38,390
+دكتور بس حافظ النتيجة احفظ الshot بدون مالهاش
+
+424
+00:36:38,390 --> 00:36:42,730
+نتيجة؟ بالظبط النتيجة هي بحد ذاتها الوصف اللي احنا
+
+425
+00:36:42,730 --> 00:36:48,520
+وصفناه كلمة rational أو irrationalجذر اتنين هذا
+
+426
+00:36:48,520 --> 00:36:52,240
+الرقم اثبتنا انه rational او irrational ال
+
+427
+00:36:52,240 --> 00:36:56,940
+rational اللي هي النتيجة بالظبط فالان احنا فرضيتنا
+
+428
+00:36:56,940 --> 00:37:03,540
+ايش هتصير لاحظ ان النتيجة rational الان هبدأ احلل
+
+429
+00:37:03,540 --> 00:37:07,640
+اذا والله اثناء التحليل طلعت معايا ان انا فرض ان
+
+430
+00:37:07,640 --> 00:37:10,320
+هي rational لكن فعليا التحليل طلعنا اللي هي
+
+431
+00:37:10,320 --> 00:37:15,960
+irrational صرت في عندي Q و negation Qكيف Q نيجشن
+
+432
+00:37:15,960 --> 00:37:21,040
+الـ Q؟ معناته False إنها مش هيطلع معاه False وهذا
+
+433
+00:37:21,040 --> 00:37:26,060
+معناه إن الفرضية من أصلها False يعني معناه ذلك
+
+434
+00:37:26,060 --> 00:37:31,760
+عكسه اللي صح عكسها اللي صح واضحة؟ تمام هاي بدأنا
+
+435
+00:37:31,760 --> 00:37:36,140
+بعكس الفرضية هيها Negation P P كانت Irrational لأ
+
+436
+00:37:36,140 --> 00:37:37,380
+أنا قلت Rational
+
+437
+00:37:40,690 --> 00:37:52,030
+معنى ذلك انه جذر اتنين بقدر احطه بصورة I over J
+
+438
+00:37:52,030 --> 00:37:58,150
+I integer J integer يعني بصورة two integers في كسر
+
+439
+00:37:58,150 --> 00:38:03,010
+اعتيادي تمام اللي انا بدنا نفك هذه هناخد تربيه على
+
+440
+00:38:03,010 --> 00:38:07,780
+الطرفينمش بده افك التربيع الجذري التربيعي صارت
+
+441
+00:38:07,780 --> 00:38:15,860
+اتنين تساوي I تربيع على J تربيع تمام جدا هذا
+
+442
+00:38:15,860 --> 00:38:18,820
+هيقودني لاقاش بدنا عشان نعمل implication نعملها
+
+443
+00:38:18,820 --> 00:38:32,080
+هيك يد إلى ان I تربيع تساوي 2J تربيع to some K ايش
+
+444
+00:38:32,080 --> 00:38:41,740
+يعني؟يعني I تربيع is even إذا I تربيع is even مش
+
+445
+00:38:41,740 --> 00:38:45,720
+هيها؟ احنا من الأساس فرضيتنا إنه two integers على
+
+446
+00:38:45,720 --> 00:38:50,800
+بعض عشان تكون rational فمعنى ذلك إنه ال J integer
+
+447
+00:38:50,800 --> 00:38:55,720
+integer تربيع integer integer some integer صارت
+
+448
+00:38:55,720 --> 00:39:02,310
+كأن هي ال K تحت تعريف ال even مبدأيا هي I evenلما
+
+449
+00:39:02,310 --> 00:39:09,210
+أقول I even يعني بقدر منها أقول هذا معناه أن I is
+
+450
+00:39:09,210 --> 00:39:13,590
+even زي الإثمتين اللي اخدناهم في ال direct و ال
+
+451
+00:39:13,590 --> 00:39:17,370
+indirect في ال direct و ال indirect فإذا I هي even
+
+452
+00:39:17,370 --> 00:39:26,130
+I even و مدام I even بقدر من المعادلة هذه أقول
+
+453
+00:39:26,130 --> 00:39:32,790
+معنى ذلك أن هي اتنين sum K كل تربيع تساوي اتنينج
+
+454
+00:39:32,790 --> 00:39:37,410
+تربيع صح؟
+
+455
+00:39:37,410 --> 00:39:43,110
+مظبوط فيك؟ طيب كويس خليني افك القواص هذا اربعة ك
+
+456
+00:39:43,110 --> 00:39:54,830
+تربيع تساوي اتنين ج تربيع يعني ج تربيع تساوي اتنين
+
+457
+00:39:54,830 --> 00:39:58,630
+ك تربيع اتنين some k
+
+458
+00:40:02,150 --> 00:40:12,950
+even فإذن J تربية is is even يعني
+
+459
+00:40:12,950 --> 00:40:18,710
+J even برضه هترجعوا المثالين اللي احنا لسنا
+
+460
+00:40:18,710 --> 00:40:21,090
+ماخدينهم في الحالة ال direct و ال indirect كانوا
+
+461
+00:40:21,090 --> 00:40:26,610
+بيثبتوا هذا الكلام إذا I even معناته I تربية even
+
+462
+00:40:26,610 --> 00:40:30,590
+و العكس صحيح و إذا كانت odd معناته تربيحها برضه
+
+463
+00:40:30,590 --> 00:40:38,090
+oddتمام هيك صارت معناته جذر اتنين اللي كانت بتساوي
+
+464
+00:40:38,090 --> 00:40:44,370
+I على J أصبحت هي عبارة عن even على even يعني في
+
+465
+00:40:44,370 --> 00:40:48,370
+عامل مشترك صح
+
+466
+00:40:48,370 --> 00:40:54,670
+معناته original هنا
+
+467
+00:40:54,670 --> 00:40:59,670
+خربطت النتائج بالظبط معناته الفرضية تاعتنامتناقضة
+
+468
+00:40:59,670 --> 00:41:03,790
+مع الواقع احنا فرضنا من الأساس ان هي rational بس
+
+469
+00:41:03,790 --> 00:41:06,830
+فعليا النتائج بتقول ان هي لأ مظبطتش مع فكرة ال
+
+470
+00:41:06,830 --> 00:41:10,310
+rational ليش؟ لأنه طلعت even على even يعني فعليا
+
+471
+00:41:10,310 --> 00:41:16,310
+يوجد عامل مشترك هو الاتنين هو الاتنين
+
+472
+00:41:16,310 --> 00:41:20,810
+automatically أصبح كأني أنا هنا فرضت negation EQ
+
+473
+00:41:20,810 --> 00:41:25,110
+فعليا طلع Q عكسها
+
+474
+00:41:27,440 --> 00:41:31,280
+ف automatic by contradiction ستكتب هنا في آخرها
+
+475
+00:41:31,280 --> 00:41:36,440
+اذا ال rational و فرضيتنا rational كانت فإذا by
+
+476
+00:41:36,440 --> 00:41:40,220
+contradiction negation
+
+477
+00:41:40,220 --> 00:41:44,640
+P is true A is false النظرية اللي بدأنا فيها false
+
+478
+00:41:44,640 --> 00:41:48,870
+غلط طب إيش الصح؟ أكيد عكسهاهي يا rational يا
+
+479
+00:41:48,870 --> 00:41:52,190
+irrational مافيش احتمال تالت فإذا مدام ما زبطتش ان
+
+480
+00:41:52,190 --> 00:41:56,890
+هي تكون rational ف by default و by .. و .. و أكيد
+
+481
+00:41:56,890 --> 00:42:02,530
+هتكون ايش irrational irrational بمعنى جذر اتنين لا
+
+482
+00:42:02,530 --> 00:42:08,010
+يمكن وضعه بصورة عددين integers مقسمين على بعض في
+
+483
+00:42:08,010 --> 00:42:13,650
+صورة كسر اعتيادي في صورة الكسر الاعتيادي تمام
+
+484
+00:42:13,650 --> 00:42:21,480
+ممتاز جدا ننهيبال .. هدول خلصناهم خلاص بنكون بمثال
+
+485
+00:42:21,480 --> 00:42:26,840
+أخر سريع هيك اللي هو there is no largest prime
+
+486
+00:42:26,840 --> 00:42:33,420
+number لاحظوا بس كلمة لاوجد رقم prime أكبر اثبت
+
+487
+00:42:33,420 --> 00:42:36,760
+اثبت
+
+488
+00:42:36,760 --> 00:42:40,940
+يالا طبعا لا direct هتصبط و حتى indirect انت مش
+
+489
+00:42:40,940 --> 00:42:48,460
+عارف ايش اللي بدك تروحلهأيوة، هذه اللي هي الحدث،
+
+490
+00:42:48,460 --> 00:42:53,760
+هذه اللي اتكلمنا عنها حدث، لكن بدنا .. احنا مجردش
+
+491
+00:42:53,760 --> 00:42:58,820
+نفسي بتعكسها، مجردش نفسي بتعكسها، لكن القانون اللي
+
+492
+00:42:58,820 --> 00:43:04,960
+هنكتبه الآن و اللي هو اللي يعتبر الحدثهو الحادث
+
+493
+00:43:04,960 --> 00:43:08,420
+بالنسبالنا اللي هنعتمد عليه في الشغل فانا معتمد
+
+494
+00:43:08,420 --> 00:43:11,640
+أنه في حادث موجود فعليا هو اللي حدني عليه شغلي أما
+
+495
+00:43:11,640 --> 00:43:15,460
+مش أن هو نفسه هذا الكلام هو الحادث هتشوف كيف
+
+496
+00:43:15,460 --> 00:43:22,960
+مبدأيا
+
+497
+00:43:22,960 --> 00:43:26,400
+الحل الأمثل أو الأوضح بالنسبالنا أنه نعمل
+
+498
+00:43:26,400 --> 00:43:33,070
+contradiction طيبthere is no largest prime number
+
+499
+00:43:33,070 --> 00:43:39,370
+ايش عكسها انه there is largest prime number تمام؟
+
+500
+00:43:39,370 --> 00:43:49,170
+معناته انه يوجد عدد اكبر prime اكبر ويساوي P هقول
+
+501
+00:43:49,170 --> 00:43:53,110
+انه يوجد طب مدام يوجد بدنا نسميه انا مش عارف كده
+
+502
+00:43:53,110 --> 00:43:57,180
+كرقم لكن بدنا نقول ان هو PP هاد يتطلع كده ما تطلع
+
+503
+00:43:57,180 --> 00:44:02,160
+بس المفروض ان هي موجودة يعني هي موجودة طيب مدان
+
+504
+00:44:02,160 --> 00:44:06,240
+موجودة و انا قلت ان فعلا يوجد معناه ذلك ان R اللي
+
+505
+00:44:06,240 --> 00:44:12,500
+هي مجموعة الأرقام ال Primes هي بتبدأ ب2 3 5 7 and
+
+506
+00:44:12,500 --> 00:44:17,760
+so on لما نصل ال P لما نصل ال P اللي هو الأكبر
+
+507
+00:44:17,760 --> 00:44:24,300
+اللي هو الأكبر مش هيك بعد هيك مفيشلأنه الأكبر حسب
+
+508
+00:44:24,300 --> 00:44:30,920
+فرضيتنا حسب فرضيتنا أكبر طيب الحدث الآن أنه حدثا
+
+509
+00:44:30,920 --> 00:44:35,860
+كل ما بدرب مجموع الأرقام لprimes ومجمع واحد
+
+510
+00:44:35,860 --> 00:44:40,320
+بيعطيني prime جديد صح
+
+511
+00:44:40,320 --> 00:44:48,320
+معناه ذلك أنه هقول اتنين مضروبة في تلاتة زائد واحد
+
+512
+00:44:49,110 --> 00:44:54,370
+سبعة طبما سبعة prime طيب هناخد تلات أرقام من الأول
+
+513
+00:44:54,370 --> 00:44:58,170
+صارت تلاتين زائد واحد واحد و تلاتين الواحد و
+
+514
+00:44:58,170 --> 00:45:01,990
+تلاتين هلاجيها في ال primes اللي هنا عدد أولي طيب
+
+515
+00:45:01,990 --> 00:45:08,710
+تلاتين في سبعة متين و عشرة المتين و احداشر prime
+
+516
+00:45:08,710 --> 00:45:15,650
+طيب معنى ذلك انه حسب المفهوم R اتنين في تلاتة في
+
+517
+00:45:15,650 --> 00:45:23,590
+خمسة في سبعةفي حداشر في
+
+518
+00:45:23,590 --> 00:45:35,490
+في في في لعنك بي زائد واحد هيطلع ال prime مش هيك
+
+519
+00:45:35,490 --> 00:45:38,890
+هو
+
+520
+00:45:38,890 --> 00:45:42,430
+مش بزائد واحد هو تخيل جديش مضلوف في أكم رقم جابله
+
+521
+00:45:43,690 --> 00:45:48,370
+يعني رقم متواخد جد اكبر بكتير من ال B اللي انا فرض
+
+522
+00:45:48,370 --> 00:45:52,990
+اصلا ان هو largest prime number اللي احنا فرضنا ان
+
+523
+00:45:52,990 --> 00:45:56,330
+هو ده اكبر رقم اولى اتفاجأنا ان لا في رقم اكبر منه
+
+524
+00:45:56,330 --> 00:46:01,470
+حسب ايش؟ حسب الحدث اللي انت مش قادر تثبت لعكسه
+
+525
+00:46:01,470 --> 00:46:05,710
+اللي انا قلتلك حدث اثبت انه مش صح عشان اقولك ان
+
+526
+00:46:05,710 --> 00:46:10,460
+هذا الكلام غلطلحظة وين الحدث كان؟ الحدث كان في
+
+527
+00:46:10,460 --> 00:46:13,460
+العلاقة هذه في relation هذه اللي هو اتنين في تلاتة
+
+528
+00:46:13,460 --> 00:46:17,320
+في خمسة في سبعة في احداش في في في two P زائد واحد
+
+529
+00:46:17,320 --> 00:46:21,960
+هو prime جديد ليش؟ لأنه زي ما أنا اسمه اتو واحد
+
+530
+00:46:21,960 --> 00:46:25,540
+منكم بيقولوا طب احنا هنضل نمشي till infinityلأ إلى
+
+531
+00:46:25,540 --> 00:46:28,360
+ما لا نهاية صح مش هنضل مش إلى ما لا نهاية بس حتى
+
+532
+00:46:28,360 --> 00:46:32,480
+الأرقام اللي بنعرفهم بتطلع صح ال relation هذه
+
+533
+00:46:32,480 --> 00:46:38,760
+relation ان ر أضرب sequential primes plus واحد
+
+534
+00:46:38,760 --> 00:46:42,920
+بتطلع prime plus واحد بتطلع prime كل ما بتجمع بس
+
+535
+00:46:43,700 --> 00:46:47,260
+واحد على عملية ال multiplication لل sequential
+
+536
+00:46:47,260 --> 00:46:53,020
+primes من الأول من الأصغر للأكبر حيطلع دائما واحد
+
+537
+00:46:53,020 --> 00:46:56,160
+إذا جمعنا .. حيطلع دائما ال prime إذا جمعنا عليه
+
+538
+00:46:56,160 --> 00:47:03,680
+واحد تمام فلاحظ أنت فرضت فرضية وحسب الحدث انتفت
+
+539
+00:47:03,680 --> 00:47:10,630
+فصرت أنت تتكلم هنا عن negation QNegation of Q لأن
+
+540
+00:47:10,630 --> 00:47:16,190
+انت فرضي تبعت انه لأ هو فيه largest number فنقشن
+
+541
+00:47:16,190 --> 00:47:19,090
+ال Q طلعت انه لأ ال Q
+
+542
+00:47:23,770 --> 00:47:29,430
+وP ليست largest prime number بدليل أنه لو ضربنا P
+
+543
+00:47:29,430 --> 00:47:34,430
+بكل الprimes اللي أقل منه وجمعنا واحد هيطلع prime
+
+544
+00:47:34,430 --> 00:47:41,170
+جديد وحتما هيكون أكبر من P فإذا
+
+545
+00:47:41,170 --> 00:47:46,030
+الفرضية بالأساس غلط طيب الفرضية احنا كانت إيش أنه
+
+546
+00:47:46,030 --> 00:47:52,160
+يوجد prime أكبرمدام هي غلط عكسها، صح، إيش عكسها؟
+
+547
+00:47:52,160 --> 00:47:56,880
+there is no largest prime number، واضحيت؟ لاحظ أنه
+
+548
+00:47:56,880 --> 00:48:00,500
+كيف جاياك الجملة هتقول direct مش هتظبط، indirect
+
+549
+00:48:00,500 --> 00:48:05,200
+مش هتظبط، ولا هي زابطة معاك لا vacuous ولا
+
+550
+00:48:05,200 --> 00:48:09,890
+trivial، فمش هتظبط معاك إلا contradictionفعشان هيك
+
+551
+00:48:09,890 --> 00:48:14,210
+ال contradiction هي أكتر حاجة مستخدمة في ال proofs
+
+552
+00:48:14,210 --> 00:48:18,410
+خلصنا ال direct و ال indirect و ال vacuous و ال
+
+553
+00:48:18,410 --> 00:48:22,750
+trivial و ختمنا بال contradiction و هي الأهم كمان
+
+554
+00:48:22,750 --> 00:48:25,090
+مرة و هي الأهم عشان المرة القادمة ان شاء الله
+
+555
+00:48:25,090 --> 00:48:28,830
+تعالى نجيب مجموعة أسئلة و نحلهم على الأربعة اللي
+
+556
+00:48:28,830 --> 00:48:32,990
+جاي بإذن الله تعالى خلصنا ما يخص الأسبوع هذا مش
+
+557
+00:48:32,990 --> 00:48:37,610
+هنبدأ و نستعجلملتزمين زي ما قلنا يوم الأربعة دايما
+
+558
+00:48:37,610 --> 00:48:39,970
+بيكون لها حلول يلا اعطيكوا العفو يا شباب برك الله
+
+559
+00:48:39,970 --> 00:48:40,290
+فيكم
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/SRvt9SNMbTk.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/SRvt9SNMbTk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..88a99ae884d3f10e834ce75f1cc1f73061c77a8a
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/SRvt9SNMbTk.srt
@@ -0,0 +1,1984 @@
+1
+00:00:04,910 --> 00:00:06,790
+طيب بسم الله الرحمن الرحيم والصلاة والسلام علي
+
+2
+00:00:06,790 --> 00:00:09,430
+أشرف الأنبياء والمرسلين سيدنا محمد، ادخل بعافية يا
+
+3
+00:00:09,430 --> 00:00:13,190
+شباب، اليوم إن شاء الله هنكمل في الـ counting بعد ما
+
+4
+00:00:13,190 --> 00:00:17,010
+خلصنا الـ permutation والـ combination وشوفنا إيش
+
+5
+00:00:17,010 --> 00:00:20,870
+تصنيف كل واحدة منهم في نظرية العد، في عملية نظرية
+
+6
+00:00:20,870 --> 00:00:24,850
+العد، قلنا without replacement وواحدة ordered
+
+7
+00:00:24,850 --> 00:00:27,970
+وواحدة unordered، مش هيك؟ المرة اللي فاتت كنا
+
+8
+00:00:27,970 --> 00:00:32,490
+صنفناهم، يعني عمليات العد، اتكلمنا عن تصنيف الـ
+
+9
+00:00:32,490 --> 00:00:35,070
+permutation اللي بتيجي الـ corner تبعها وين، الـ
+
+10
+00:00:35,070 --> 00:00:39,410
+combination بتيجي، وأخدنا أمثلة على كلاهما. الآن
+
+11
+00:00:39,410 --> 00:00:42,090
+آخر شغل أخدناه هي الـ combination، فمن الـ
+
+12
+00:00:42,090 --> 00:00:44,510
+combination وجدنا أنه فيه إمكانية إن إحنا نحل
+
+13
+00:00:44,510 --> 00:00:47,850
+معادلات، بمعنى إنه نجيب الـ coefficients بتاعة
+
+14
+00:00:47,850 --> 00:00:50,410
+المعادلات، يعني معادلات الـ polynomial، الـ
+
+15
+00:00:50,410 --> 00:00:55,730
+polynomial اللي هي بتكون عبارة عن x زائد y to the
+
+16
+00:00:55,730 --> 00:01:02,090
+power n، فهدا الـ polynomial بتكون عبارة عن الـ order n
+
+17
+00:01:02,090 --> 00:01:05,550
+وأكيد هيكون مجموعة الـ coefficients، الـ coefficients
+
+18
+00:01:05,550 --> 00:01:10,870
+اللي هنفكها، هذي هنلاقي إن هي عبارة عن x y زائد x y
+
+19
+00:01:10,870 --> 00:01:16,230
+زائد لعند x y، لكن بتختلف الـ orders، الـ orders هنا
+
+20
+00:01:16,230 --> 00:01:21,270
+هنبدأ بـ n و 0 هنا، وراها هتكون إيش؟ n ناقص واحد و
+
+21
+00:01:21,270 --> 00:01:25,230
+واحد، بمعنى إن الـ orders كلاهما مجموعهما يساوي الـ n
+
+22
+00:01:26,180 --> 00:01:28,960
+مجموعهما بيساوي N، فعشان هيك بنقولها دي من الـ order الـ
+
+23
+00:01:28,960 --> 00:01:33,060
+order تبعها N، الـ order تبعها كمعادلة بتكون N، تمام؟
+
+24
+00:01:33,060 --> 00:01:37,420
+فإذا لو إنتوا حاولتوا تفكوها مثلاً للتربيع، هتقولوا
+
+25
+00:01:37,420 --> 00:01:42,860
+عبارة عن X تربيع، هي Y to the power 0، زائد اتنين في
+
+26
+00:01:42,860 --> 00:01:48,880
+XY، هي واحد وواحد مجموعهما اتنين، زائد Y تربيع، طبعاً
+
+27
+00:01:48,880 --> 00:01:52,720
+X هنا هتكون صفر، فمجموعهما اتنين، فأنت هيكون بهذا
+
+28
+00:01:52,720 --> 00:01:56,480
+الشكل بتفكها، طيب الجزء اللي في البداية هنا هذا
+
+29
+00:01:56,480 --> 00:02:01,740
+مجموعة الـ coefficients بتاعتنا، واحد اتنين واحد، هذه
+
+30
+00:02:01,740 --> 00:02:05,220
+مجموعة الـ coefficients لـ order اتنين، لـ order
+
+31
+00:02:05,220 --> 00:02:10,520
+two أو second order، لـ in order، هل بقدر أجيب نفس
+
+32
+00:02:10,520 --> 00:02:13,180
+الكلام؟ اه، بتقدر تجيب نفس الكلام بدون ما تضطر
+
+33
+00:02:13,180 --> 00:02:17,980
+تضربهم في بعض، احنا هنا ضربناهم ضرب في بعض لأنه
+
+34
+00:02:17,980 --> 00:02:21,120
+معادلتين في بعض وخلصناه، لكن لما بتتكلم عن الـ in
+
+35
+00:02:21,120 --> 00:02:25,140
+هنا بعشرة، بداك تضربهم عشر مرات، خلاص، اعمل هيك في
+
+36
+00:02:25,140 --> 00:02:28,300
+الامتحان، إنت حر، بس إنت المسؤول عن الوقت، يعني مش
+
+37
+00:02:28,300 --> 00:02:31,300
+الامتحان المسؤول عن الوقت، كويس، بلا بيجي عشر و
+
+38
+00:02:31,300 --> 00:02:35,660
+عشرين وخمسين كمان بالعكس، عشان تطبق النظرية، فالآن
+
+39
+00:02:35,660 --> 00:02:39,310
+عدنا، هناخد مثال على خمسة وعشرين، الـ order خمسة و
+
+40
+00:02:39,310 --> 00:02:42,290
+عشرين، إذا كنت تحل الخمسة والعشرين ضرب في بعضه،
+
+41
+00:02:42,290 --> 00:02:45,470
+مستحيل طبعاً، طيب، فهنا جالنا بكل بساطة الـ
+
+42
+00:02:45,470 --> 00:02:48,710
+combination، جابت لنا حل هذا الموضوع، قالت لنا إذا
+
+43
+00:02:48,710 --> 00:02:52,770
+كان، والله نتعامل مع polynomial X زائد Y من الـ
+
+44
+00:02:52,770 --> 00:02:56,670
+order N، معناه ذلك إن هذه بتساوي فعلياً مجموع الـ
+
+45
+00:02:56,670 --> 00:03:01,650
+terms، الـ terms هدول هم هدول اللي بحكي عنهم، عددهم
+
+46
+00:03:01,650 --> 00:03:07,330
+N، هتكون عددهم من صفر لـ N، فعلياً هي هتبدأ من صفر
+
+47
+00:03:07,330 --> 00:03:13,950
+لما نصل هنا لـ للـ N، وهذا سيكون صفر، فإذا فعلياً N
+
+48
+00:03:13,950 --> 00:03:19,110
+زائد واحد، N زائد واحد، تمام؟ هذول عدد الـ terms اللي
+
+49
+00:03:19,110 --> 00:03:23,190
+هم، عفواً، المتغيرات، الـ parameters أو الـ variables الـ
+
+50
+00:03:23,190 --> 00:03:25,990
+variables بتاعتنا، الـ coefficients بتاعتهم عبارة عن
+
+51
+00:03:25,990 --> 00:03:29,970
+الـ combination، الـ combination لمين؟ لـ N from N to
+
+52
+00:03:29,970 --> 00:03:36,060
+select J، و J هذه، جدّيش ترتيب الـ element، جدّيش ترتيب
+
+53
+00:03:36,060 --> 00:03:39,120
+الـ element بس، فوجدنا إنه هذه بتسهل بالطريقة هذه،
+
+54
+00:03:39,120 --> 00:03:42,000
+حلت لي لمجموعة الـ coefficients اللي هي، أقدر أجيب الـ
+
+55
+00:03:42,000 --> 00:03:44,880
+coefficient هذا أو هذا أو هذا أو هذا، حسب أني بس
+
+56
+00:03:44,880 --> 00:03:49,080
+بدي أعرف أني J اللي أنا بدور عليها، الـ J هذي الـ
+
+57
+00:03:49,080 --> 00:03:53,720
+element، أنه element، أنه عنصر؟ الـ عنصر صفر ولا عنصر
+
+58
+00:03:53,720 --> 00:03:57,000
+واحد ولا اتنين ولا تلاتة، ولا الـ عنصر خمسين مثلاً،
+
+59
+00:03:57,000 --> 00:04:00,390
+إذا كان بتكلم عن الـ order أكبر من خمسين، هو العنصر
+
+60
+00:04:00,390 --> 00:04:04,250
+الخمسين، تمام؟ فهذه بكل بساطة جبتها بحيث أنها
+
+61
+00:04:04,250 --> 00:04:07,690
+تصبح كأنها from N to select zero، إذا كانت
+
+62
+00:04:07,690 --> 00:04:13,250
+بتتكلم عن x in y zero، y zero، فإذا لاحظ أن الـ j
+
+63
+00:04:13,250 --> 00:04:18,820
+اللي علاقتها بـ y، صارت اللي علاقتها بـ y plus، from N to
+
+64
+00:04:18,820 --> 00:04:24,520
+select one لـ X، N ناقص واحد و Y وهكذا، لما نصل في
+
+65
+00:04:24,520 --> 00:04:31,260
+الأخر لـ from N to N، لمين؟
+
+66
+00:04:31,260 --> 00:04:35,620
+to the power N، تمام؟
+
+67
+00:04:35,620 --> 00:04:40,640
+فإذا واضح جداً، الآن لو انطلب منك لأي order ومحتاج
+
+68
+00:04:41,650 --> 00:04:46,090
+ترم معين، ما تروحش تقول اللي بدك تضربهم في بعض، خلاص
+
+69
+00:04:46,090 --> 00:04:48,490
+هاي الـ combination بتجيبلك إياها، وخلصنا الـ
+
+70
+00:04:48,490 --> 00:04:52,290
+combination بتجيبلك إياها، وانتهت القصة، في طبعاً في
+
+71
+00:04:52,290 --> 00:04:56,370
+جميع الأحوال بنتكلم عن N و J أكبر من أو يساوي صفر،
+
+72
+00:04:56,370 --> 00:04:59,850
+لأنه ما بديش أروح للـ inverse، بتناشي نروح للـ inverse الـ
+
+73
+00:04:59,850 --> 00:05:03,970
+power تكون بالـ inverse، فإذا هي من صفر فأكثر من صفر،
+
+74
+00:05:03,970 --> 00:05:07,730
+فأكثر، والـ J طبيعي بتكون أقل من أو يساوي N، مش
+
+75
+00:05:07,730 --> 00:05:11,370
+معقول أقولك والله يبدأ الـ term خمسين، وإنت أصلاً كل
+
+76
+00:05:11,370 --> 00:05:14,870
+المعادلة عندك بتتبارى عشر، ما فيش فيها أصلاً term
+
+77
+00:05:14,870 --> 00:05:18,290
+خمسين، من وين بدك تجيب الـ term الخمسين؟ واضحة، تمام؟
+
+78
+00:05:18,290 --> 00:05:24,690
+اتفضل، الـ combination إجت من عملية الضرب، من عملية
+
+79
+00:05:24,690 --> 00:05:28,880
+اللي هو ضربهم في بعض، إنت كل ما قعدت بتضربهم في بعض،
+
+80
+00:05:28,880 --> 00:05:32,760
+يعني كأنك بتعمل تكرار لنفس العنصر، بتكرر نفس
+
+81
+00:05:32,760 --> 00:05:36,240
+العنصر، طب العنصر هذا، لو إجا، لاحظ، إنت
+
+82
+00:05:36,240 --> 00:05:41,660
+الاتنين هذي من وين إجت؟ تكررت مرتين، فأنت بتتكلم
+
+83
+00:05:41,660 --> 00:05:47,020
+عن عدد التكرارات، عن عدد الـ ways، عدد الـ ways، مش إحنا
+
+84
+00:05:47,020 --> 00:05:50,860
+تعريفها كان عدد الـ ways اللي بدك تحسبهم، عدد الطرق
+
+85
+00:05:50,860 --> 00:05:55,860
+اللي بتستخدمهم لـ task معينة، طب نفس الفكرة إنت في
+
+86
+00:05:55,860 --> 00:05:58,860
+عندك الاتنين هذه إجت مرة من الـ term الأول ومرة
+
+87
+00:05:58,860 --> 00:06:01,520
+من الـ term الثاني، طب لما يكونوا أكثر من هيك، معناته
+
+88
+00:06:01,520 --> 00:06:04,820
+عددهم بده يكون له علاقة بقى كم مرة انضربوا في بعض،
+
+89
+00:06:04,820 --> 00:06:10,870
+لأنه عدد تكراراتهم، صارت كم مرة عشان يتجمع نفس نفس
+
+90
+00:06:10,870 --> 00:06:16,110
+مين؟ نفس الـ term، فأنت فعلياً لو ضربناها XY زي ما هي
+
+91
+00:06:16,110 --> 00:06:24,150
+هيها بالطريقة المطولة بتاعتنا، هي X تربيع زائد XY،
+
+92
+00:06:24,150 --> 00:06:30,890
+هي من العملية الأولى بس، لسه في عملية ثانية، XY زائد
+
+93
+00:06:30,890 --> 00:06:35,270
+Y تربيع، طب هيها، هي واحدة، هيتين، ثانية طرق عد، فأنا
+
+94
+00:06:35,270 --> 00:06:38,690
+عديت الـ term هذا كم مرة؟ الـ term هذا أنا أعد معاك
+
+95
+00:06:38,690 --> 00:06:46,160
+كم مرة؟ لحظة، فهنا لأنه ضربتهم تربيع، انعد معاه مرتين،
+
+96
+00:06:46,160 --> 00:06:49,720
+فنفس الفكرة لما يكون تضروب عشرة، لما بتضرب كم مرة،
+
+97
+00:06:49,720 --> 00:06:53,420
+بنعد معاك نفس الـ term، مين اللي بيجيبلك الـ term
+
+98
+00:06:53,420 --> 00:06:56,800
+الكلام هذا؟ هي الـ combination، هي الـ combination كم
+
+99
+00:06:56,800 --> 00:07:02,320
+مرة ممكن يتألف عندك نفس العنصر، okay، ناخد مثال،
+
+100
+00:07:03,880 --> 00:07:07,560
+المثال هذا، هي مثلاً to the power 25، يعني إنت بتتكلم
+
+101
+00:07:07,560 --> 00:07:15,940
+عن x زائد y to the power 25، وطلب منك إيه؟ مطلوب
+
+102
+00:07:15,940 --> 00:07:22,680
+تجيب لنا الـ coefficient لـ x 12 y 13، هي مجموعة من
+
+103
+00:07:22,680 --> 00:07:28,020
+25 جالك، بس بدي هذا term، إيش هتروح تسويه؟ هتروح
+
+104
+00:07:28,020 --> 00:07:30,780
+تضربهم خمسة وعشرين مرة في بعض؟ أكيد ما .. مش
+
+105
+00:07:30,780 --> 00:07:34,760
+منطقي، تمام؟ فأنت قاعد بدك .. بدك إيش تقول؟ الـ
+
+106
+00:07:34,760 --> 00:07:40,600
+combination لعدد مرات تكرار العنصر .. العنصر هذا،
+
+107
+00:07:40,600 --> 00:07:45,440
+تمام؟ فخلاص، بده .. خلاص بتعملها خمسة وعشرين،
+
+108
+00:07:45,440 --> 00:07:51,200
+جدّيش؟ اتناشر، طب هي نفسها  شكت؟ مش قلنا الكلام هذا
+
+109
+00:07:51,200 --> 00:07:56,160
+نفسه؟ يعني هي نفسها خمسة وعشرين، و N ناقص J اللي هي
+
+110
+00:07:56,160 --> 00:07:58,180
+برضه خمسة وعشرين ناقص اتناشر، يعني تطلع تلتاشر،
+
+111
+00:07:58,180 --> 00:08:01,400
+فكلاهما صح، كلاهما صح، يعني إنت بدك تشتغلها بالنسبة لـ
+
+112
+00:08:01,400 --> 00:08:05,480
+X، ماشي، بالنسبة لـ Y، ماشي، مش هتفرق معاك، لأ، ما هو في
+
+113
+00:08:05,480 --> 00:08:10,620
+النهاية مجموعة الاتنين نفسهم N، تمام؟ تمام، فهذه هي
+
+114
+00:08:10,620 --> 00:08:14,660
+تحسب هذه، تحسب هذه، فيكون هذه أو هذه، بيمشي الحال،
+
+115
+00:08:14,660 --> 00:08:19,260
+خلصناها، خلصت، طب ممتازة، مش دائماً الـ polynomial بيكون
+
+116
+00:08:19,260 --> 00:08:22,600
+بهذه السهولة، ممكن جداً يكون هنا فيه أصلاً
+
+117
+00:08:22,600 --> 00:08:27,020
+coefficients مضروبين من الأساس، وبعدين كله تضربه الـ
+
+118
+00:08:27,020 --> 00:08:31,580
+25 زي الـ
+
+119
+00:08:31,580 --> 00:08:37,260
+term هذا، الـ
+
+120
+00:08:37,260 --> 00:08:44,260
+term هذا اللي هو جدّيش؟ 2x ناقص 3y، كله to the power 25، و
+
+121
+00:08:44,260 --> 00:08:47,830
+طلب نفس الـ coefficient، هو هو، طلب نفس الـ coefficient،
+
+122
+00:08:47,830 --> 00:08:50,450
+هو هو، طبعاً في الحالة دي لأ، هيختلف معانا الكلام،
+
+123
+00:08:50,450 --> 00:08:53,230
+لأنه أنا كل ما جيت أضرب، أنا ما بضربش في x لحالها،
+
+124
+00:08:53,230 --> 00:08:56,010
+بضرب في 2x، وكل ما جيت أضرب في .. ما بضربش في y
+
+125
+00:08:56,010 --> 00:09:00,910
+لحالها، بضرب في ناقص تلاتة y، في minus تلاتة y، فإذا
+
+126
+00:09:00,910 --> 00:09:03,970
+لأ، هدول بدنا ناخد حسابنا فيهم، فإذا مبدئياً بتعامل
+
+127
+00:09:03,970 --> 00:09:06,010
+مع الـ term هذا كإنه a زائد b،
+
+128
+00:09:10,240 --> 00:09:12,320
+وهذا بعطيه الـ combination نفسها، ما فيش أدي أي
+
+129
+00:09:12,320 --> 00:09:17,220
+مشكلة، 25 13، خلّيني أقول خلصناها، طيب بس أنا عارف
+
+130
+00:09:17,220 --> 00:09:25,880
+أن a فعلياً هي 2x، 2x، طيب a هذه بعد ما أفكها وأوصل
+
+131
+00:09:25,880 --> 00:09:32,820
+لمرحلة إنه صارت a to the power 12 و b to the power 13، معناه ذلك
+
+132
+00:09:32,820 --> 00:09:36,940
+أن هذا الـ term فعلياً اللي كان 2x، x خلصتها منها، 2
+
+133
+00:09:36,940 --> 00:09:42,330
+to the power 12، الإفكتر بيكون الـ combination هذا بتتنضرب
+
+134
+00:09:42,330 --> 00:09:48,050
+لسه في اتنين to the power اتناشر، طيب نفس الكلام لـ Y،
+
+135
+00:09:48,050 --> 00:09:52,290
+فعلياً أنا اتكلمت على B، ما اتكلمت على minus تلاتة Y،
+
+136
+00:09:52,290 --> 00:09:55,510
+فالـ minus تلاتة إيش مصيرها؟ لأ، الـ minus تلاتة،
+
+137
+00:09:55,510 --> 00:09:58,810
+معناته بتتحط minus تلاتة to the power التلتاش،
+
+138
+00:10:03,630 --> 00:10:07,710
+وهذا إحنا جايبينه سابقاً، حسبناه من فوق خمسة مليون و
+
+139
+00:10:07,710 --> 00:10:11,690
+ثمانين ألف وثلاثمئة، فإذا بيطلع في الـ total هي خمسة
+
+140
+00:10:11,690 --> 00:10:17,190
+وثلاثين ألف وثلاثمئة، اتنين to the power اتناشر، والـ
+
+141
+00:10:17,190 --> 00:10:20,290
+B اللي هي سالب تلاتة to the power تلتاش، فبيطلع برضه
+
+142
+00:10:20,290 --> 00:10:25,360
+مليار ونص تقريباً، جدّيش بيطلع الرقم؟ بيطلع حاجة
+
+143
+00:10:25,360 --> 00:10:29,900
+مظبوطة، يعني ناقص تلاتة وثلاثين quadrillion، تلاتة
+
+144
+00:10:29,900 --> 00:10:32,480
+وثلاثين quadrillion، لأ بعض الأرقام بتطلعها تلاتة
+
+145
+00:10:32,480 --> 00:10:34,760
+وثلاثين quadrillion، تسعة مئة تسعة وتسعين
+
+146
+00:10:34,760 --> 00:10:39,300
+trillion، سبع مئة ثلاثة وستين billion، وخمس مئة أربع
+
+147
+00:10:39,300 --> 00:10:42,400
+خمسة وأربعين مليون، وسبع مئة واتنين ألف وأربع مئة
+
+148
+00:10:44,740 --> 00:10:50,040
+رقم .. على
+
+149
+00:10:50,040 --> 00:10:52,600
+الكمبيوتر .. هذا على الكمبيوتر .. هذا على
+
+150
+00:10:52,600 --> 00:10:57,420
+الكمبيوتر بتحسبه، طيب .. برضه ناخد مجموعة استنتاجات،
+
+151
+00:10:57,420 --> 00:11:03,100
+ممكن، أو corollary أو استنتاجات للنظرية اللي طلعت
+
+152
+00:11:03,100 --> 00:11:05,640
+لنا هذه، اللي هي تاعة الـ combination، منها مثلاً
+
+153
+00:11:06,600 --> 00:11:11,240
+مضاعفات الاتنين، أو الـ binomial لأساس الاتنين،
+
+154
+00:11:11,240 --> 00:11:17,180
+الاتنين to the power n، بكل بساطة بقدر أقول إن هي
+
+155
+00:11:17,180 --> 00:11:21,220
+الـ summation لفقط
+
+156
+00:11:21,220 --> 00:11:26,940
+قيمة الـ combination، ليش؟ على اعتبار إن الاتنين هي
+
+157
+00:11:26,940 --> 00:11:30,440
+عبارة عن واحد زائد واحد، كل تربيع، فهذه كأنها هي الـ
+
+158
+00:11:30,440 --> 00:11:35,470
+X وهذه كأنها هي الـ Y، فلما بدك تش تعوض بـ x y بـ 1 و 1،
+
+159
+00:11:35,470 --> 00:11:40,110
+خلاص مش هتفرق، power جدّيش، فإذا واحد واحد بيبقى
+
+160
+00:11:40,110 --> 00:11:43,390
+combination بيبقى combination، فهي واحدة من الحالات
+
+161
+00:11:43,390 --> 00:11:45,750
+الخاصة اللي ممكن استخدامها في الـ binary system،
+
+162
+00:11:45,750 --> 00:11:50,830
+مثلاً اللي هو جدّيش قيمة الـ binary system، طيب نفس
+
+163
+00:11:50,830 --> 00:11:56,990
+الكلام لما نقول بدنا نصفر المعادلة، بدك تصفر
+
+164
+00:11:56,990 --> 00:12:00,910
+المعادلة، معناه كأنك بتعمل summation لواحد مع سالب
+
+165
+00:12:00,910 --> 00:12:06,780
+واحد، وإنت عارف إن واحد سالب واحد كله تربيع، كأنك
+
+166
+00:12:06,780 --> 00:12:12
+
+223
+00:16:57,840 --> 00:17:00,680
+التانية أخذناها من واحد واثنين من اللي
+
+224
+00:17:00,680 --> 00:17:04,400
+جابلها نفس الكلام هنا، ها هي J معناته بأخذها من J و
+
+225
+00:17:04,400 --> 00:17:08,240
+J نقص واحد من ال coefficient  بتاعت J، بتاع J نقص
+
+226
+00:17:08,240 --> 00:17:14,370
+واحد. إذا أنا مش محتاج أقعد أضرب كمان في term زيادة
+
+227
+00:17:14,370 --> 00:17:18,070
+و ال term هذا ممكن يكون فعلاً كبير، بدي أضرب في x و
+
+228
+00:17:18,070 --> 00:17:20,490
+y المعادلة زيادة، معناته x بدي أضربها في كامل
+
+229
+00:17:20,490 --> 00:17:24,030
+المعادلة، زائد y في كامل المعادلة، وتقعد تجمعها. طب
+
+230
+00:17:24,030 --> 00:17:27,270
+ليش؟ طب ما هي هذه أسهل؟ هي أسهل لو أنت عندك ال
+
+231
+00:17:27,270 --> 00:17:32,470
+order السابق، مش عارف؟ ممتاز، وهي طبعاً وضح لنا
+
+232
+00:17:32,470 --> 00:17:35,470
+Pascal's triangle بهذا الشكل اللي احنا شايفينه، و
+
+233
+00:17:35,470 --> 00:17:43,340
+لاحظ كيف؟ Symmetric، وجدّ بسيطة، جسمها بتبدأ بالصفر
+
+234
+00:17:43,340 --> 00:17:48,760
+هاي الصفر، صفر order، ثم ال first order هذا ال
+
+235
+00:17:48,760 --> 00:17:53,700
+quadratic التربيع هنا، هاي واحد اثنين واحد، طيب
+
+236
+00:17:53,700 --> 00:18:00,640
+الثلاثة واحد ثلاثة ثلاثة واحد، طيب الأربعة، طيب لك
+
+237
+00:18:00,640 --> 00:18:05,320
+تجيب الخمسة لل coefficient مثلاً الثالث اللي هي تجيب
+
+238
+00:18:05,320 --> 00:18:10,340
+اثنين. معناته الأربعة زائد هاي، ألاحظ، عشان هيك هو
+
+239
+00:18:10,340 --> 00:18:16,660
+رسمها بشكل سداسيات على أساس أنه كل رأس هو ياخد
+
+240
+00:18:16,660 --> 00:18:19,900
+المجموع السابق، الاثنين اللي جابله، فهذه تصير عشرة
+
+241
+00:18:19,900 --> 00:18:23,720
+وهذه حينها خمسة، وتلاحظ أن كله ones ونهايته ones
+
+242
+00:18:23,720 --> 00:18:29,070
+لأن هذه ال X to the power N وال Y to the power N، y
+
+243
+00:18:29,070 --> 00:18:34,110
+to the power n، فبسهولة طلع لنا بال triangle تبعه، و
+
+244
+00:18:34,110 --> 00:18:37,050
+صحيح ومئة بالمئة، ما فيش أي مشكلة فيه، بيظل مستمر
+
+245
+00:18:37,050 --> 00:18:41,870
+مع الجد، ما بدك تصل ل orders في الحالة هذه. طيب، بدي
+
+246
+00:18:41,870 --> 00:18:49,270
+أروح لل order العاشر تمام، وأنا كل اللي عندي في
+
+247
+00:18:49,270 --> 00:18:52,990
+الشاشة يعني هنا، تو على الأقل كان عندنا مثلاً ال
+
+248
+00:18:52,990 --> 00:18:56,970
+order الثالث، فجبت منه الرابع. طب أنا بدي أجيب العاشر، و
+
+249
+00:18:56,970 --> 00:18:57,990
+قلت لك في الشاشة غيره
+
+250
+00:19:02,400 --> 00:19:08,920
+هنا .. هنا  Vandermonde Vandermonde عملوا
+
+251
+00:19:08,920 --> 00:19:12,460
+identity لحاله، قال لك لأ أنا بدي أزبطها لك أكثر من
+
+252
+00:19:12,460 --> 00:19:17,100
+هيك، مش مجرد تكون أنت عارف ال order السابق، لك لا،
+
+253
+00:19:17,100 --> 00:19:21,240
+أجيب أي order، مجموعهم نفس ال order اللي أنت بدك
+
+254
+00:19:21,240 --> 00:19:23,800
+تحكي عنه، اللي أنت بدك تجيب ال coefficients تبعته
+
+255
+00:19:23,800 --> 00:19:29,000
+يعني كأنه هنا مثلاً هي ال order M plus N، بتقدر
+
+256
+00:19:29,000 --> 00:19:32,060
+تجيبها من M لحالها و N لحالها. بمعنى إذا كان أنت بدك
+
+257
+00:19:32,060 --> 00:19:35,540
+ال order العاشر، معناته بقدر أقول ال order
+
+258
+00:19:35,540 --> 00:19:41,940
+هذا ستة مثلاً، وأربعة. من ال order ستة وأربعة، طيب
+
+259
+00:19:41,940 --> 00:19:46,300
+أو ال order خمسة وخمسة، يمكن خمسة وخمسة تكون أسهل
+
+260
+00:19:46,300 --> 00:19:49,020
+على اعتبار أنه خلاص مرة واحدة بأجيبها، ف order واحد
+
+261
+00:19:49,020 --> 00:19:52,620
+فليكن خمسة وخمسة. طيب الخامسة نفسها موجود عندي؟ لأ
+
+262
+00:19:52,620 --> 00:19:54,680
+مش موجود عندي، طب ما هي نفسها بقدر أجيبها اثنين و
+
+263
+00:19:54,680 --> 00:19:59,180
+ثلاثة. واضحة؟
+
+264
+00:19:59,180 --> 00:20:03,360
+فإذن حتكون كتير مناسبة لو اشتغلتها recursion
+
+265
+00:20:05,620 --> 00:20:10,240
+ك code، مش هيك، recursive code بيطلع perfect في حالة
+
+266
+00:20:10,240 --> 00:20:14,140
+زي هذه، بيطلع ممتاز جداً لأي order بدك إياه قدام
+
+267
+00:20:14,140 --> 00:20:19,560
+تجيب كل ال coefficients تبعته، إنك تعمله مجموع two
+
+268
+00:20:19,560 --> 00:20:26,000
+orders ثانين، كل order، إذا لسه ما وصلتش لل bases، و
+
+269
+00:20:26,000 --> 00:20:29,220
+ممكن أنت تفترض من عندك ال bases، أول اثنين ثلاثة من
+
+270
+00:20:29,220 --> 00:20:32,000
+هدول اللي أنت حافظهم على طول، واحد اثنين واحد، واحد
+
+271
+00:20:32,000 --> 00:20:36,270
+ثلاثة ثلاثة واحد، واحد أربعة ستة أربعة واحد. هيلاحظهم
+
+272
+00:20:36,270 --> 00:20:39,750
+هدول حاجات سريعة، يعني صرنا من كثر مفهومنا Pascal
+
+273
+00:20:39,750 --> 00:20:43,690
+صرنا عارفينهم، حافظينهم، يعني مكتوب مع السريع اللي
+
+274
+00:20:43,690 --> 00:20:46,690
+هو ال second و ال third و ال fourth، خلاص متأخذين
+
+275
+00:20:46,690 --> 00:20:49,950
+من بعض، فهدول كافيين إنهم يكونوا basis لأي رقم أو
+
+276
+00:20:49,950 --> 00:20:55,790
+أي order بدك إياه، كبير، أي order كبير، بحيث إنه هي M ال
+
+277
+00:20:55,790 --> 00:21:02,030
+combination ل M plus N، ل selection أو ل order R، ل
+
+278
+00:21:02,030 --> 00:21:10,280
+term R هو يساوي من صفر ل R، لمجموعة الأجزاء منه M و
+
+279
+00:21:10,280 --> 00:21:18,000
+R ناقص J و N للـ J، بس فهي بتقدر تعمل طبعاً، لو إن عكس
+
+280
+00:21:18,000 --> 00:21:18,540
+وبمشي الحال
+
+281
+00:21:24,070 --> 00:21:28,450
+مش حتأثر كثير معك، فزي ما بيقولوا لو هذه خانتك في
+
+282
+00:21:28,450 --> 00:21:31,650
+الحفظ، هذه بدل هذه، وهذه بدل هذه، مش مشكلة كبيرة، مش
+
+283
+00:21:31,650 --> 00:21:35,050
+جثة، بس تكون عارف إنه في واحدة منهم J وفي واحدة R
+
+284
+00:21:35,050 --> 00:21:40,010
+ناقص J، بس واحدة هيك، واحدة هيك، وال summation من صفر ل R
+
+285
+00:21:40,010 --> 00:21:44,470
+هذه من الأمثلة اللي كنت جايبها في امتحان سابق،
+
+286
+00:21:44,470 --> 00:21:47,810
+وحنحلها إن شاء الله على آخر الفصل، لما يكون عندنا
+
+287
+00:21:47,810 --> 00:21:49,990
+.. حيكون عندنا مجموعة إن شاء الله، بلكي يطلع عندنا
+
+288
+00:21:49,990 --> 00:21:53,510
+أسبوع زمن، هيك بناخده كله حلول أسئلة امتحانات، حيكون
+
+289
+00:21:53,510 --> 00:21:59,090
+في سؤال من .. على القانون هذا، مجرد سطر كان، يعني كل
+
+290
+00:21:59,090 --> 00:22:03,670
+الفكرة كانت مجرد سطر، ولو كان سطر، لكن ال order يبدو
+
+291
+00:22:03,670 --> 00:22:07,110
+أنه كأنه كبير، فطبعاً الواحد ما بديش يقعد يضرب لهم و
+
+292
+00:22:07,110 --> 00:22:10,150
+يضيع له الدنيا، ويضيع وقته، ويضيع نصف وقت الامتحان،
+
+293
+00:22:10,150 --> 00:22:14,390
+وهو ما كانش ماخذ أكثر من سطر فعلياً، سطر، فحنحل عليه
+
+294
+00:22:14,390 --> 00:22:23,170
+أمثلة سابقة، تمام. فهي Vandermonde اشتغل وعمل شغل
+
+295
+00:22:23,170 --> 00:22:26,350
+سبق فيه على مين؟ على Pascal اللي كان بيقول لك لازم
+
+296
+00:22:26,350 --> 00:22:28,470
+تكون جايب لل order اللي جابله، لإنه جاك، مش محتاج
+
+297
+00:22:28,470 --> 00:22:32,110
+ال order اللي جابله، مش محتاج order جابله، تمام. هذه
+
+298
+00:22:32,110 --> 00:22:35,390
+هي كيف، بنكون خلصنا الجزئية اللي كانت متبقية لنا في
+
+299
+00:22:35,390 --> 00:22:37,490
+ال counting واللي هي كانت خاصة في ال polynomial
+
+300
+00:22:37,490 --> 00:22:39,430
+coefficients، في جزئية ال polynomial coefficients
+
+301
+00:22:39,430 --> 00:22:42,090
+كيف ممكن نستفيد من ال combination اللي أخذناها
+
+302
+00:22:42,090 --> 00:22:48,250
+سابقا، عشان نبدأ إن شاء الله تعالى في جزئية برضه
+
+303
+00:22:48,250 --> 00:22:54,050
+لها علاقة بنفس شغلنا، هي ال recurrence relations
+
+304
+00:22:54,050 --> 00:22:57,430
+احنا أخذنا recursion، أخذنا recursion، فإيش ال
+
+305
+00:22:57,430 --> 00:23:02,620
+recurrence relation هذه؟ بكل بساطة، جزئية ال
+
+306
+00:23:02,620 --> 00:23:08,960
+recursion أصلاً ممكن نمثلها ب two forms، form أول
+
+307
+00:23:08,960 --> 00:23:13,720
+اتكلمنا عنه، إنه أنا بأجيب المعادلة بدلالة اللي
+
+308
+00:23:13,720 --> 00:23:18,060
+قبلها، مش هيك؟ كأني بأقول احنا كنا بنكتب X ولا N، مش
+
+309
+00:23:18,060 --> 00:23:23,820
+عارف، أخلصنا من ال polynomial، ف A to the power N
+
+310
+00:23:23,820 --> 00:23:32,150
+هذه، أو N بنجبها بدلالة A N ناقص واحد، أو أكثر، أو
+
+311
+00:23:32,150 --> 00:23:39,230
+ممكن A N ناقص اثنين، أو A N ناقص ثلاثة، أو لعند A
+
+312
+00:23:39,230 --> 00:23:45,050
+N ناقص K مثلاً، كويس؟
+
+313
+00:23:45,050 --> 00:23:49,410
+هذه recursion، هذه هي recursion، ال element بأجيبه
+
+314
+00:23:49,410 --> 00:23:55,320
+باللي جابله، باللي جابله، وكانت طبعاً معطينا ال
+
+315
+00:23:55,320 --> 00:23:59,460
+background كويسة، عملية ال inductive أو ال
+
+316
+00:23:59,460 --> 00:24:03,220
+inductive step، وال induction، كان إنما بنقول يعتمد
+
+317
+00:24:03,220 --> 00:24:06,040
+على اللي قبله فقط، فهذه كانت ال first principle
+
+318
+00:24:06,040 --> 00:24:09,460
+تذكرين؟ أو لا، ال second principle، معناته كل اللي
+
+319
+00:24:09,460 --> 00:24:13,990
+جابله، كل اللي جابله، لعند لعند نصل للصفر، ممكن نصل
+
+320
+00:24:13,990 --> 00:24:18,250
+للصفر، لكن هنا في عندك إمكانية إنك من N ناقص واحد، N
+
+321
+00:24:18,250 --> 00:24:23,130
+ناقص اثنين، لعند K مثلاً، K terms محتاج، طيب، فبأخذ
+
+322
+00:24:23,130 --> 00:24:26,940
+جدّاش كانت الكيتنين بالظبط، كنت محتاج اللي جابله، و
+
+323
+00:24:26,940 --> 00:24:30,660
+اللي جابله، فكانت N و N ناقص واحد، مجموعهم بتطلع
+
+324
+00:24:30,660 --> 00:24:34,600
+اثنين، فكانت K بالنسبالي كأنها كأنها اثنين، كأنها
+
+325
+00:24:34,600 --> 00:24:40,420
+الاثنين، كويسة؟ نبدأ نتكلم عن ال recurrence relation
+
+326
+00:24:40,420 --> 00:24:42,360
+recurrence relation، هاي مثال مثلاً
+
+327
+00:24:46,550 --> 00:24:50,350
+مثال بدلالة اثنين جابله، فكأنها ال K عندي هنا
+
+328
+00:24:50,350 --> 00:24:54,010
+اثنين، ومعنى إن ال K باثنين، معناته عشان فعلاً أقدر
+
+329
+00:24:54,010 --> 00:24:57,470
+أجيب ال sequence بعد هيك، لازم يكون على الأقل في
+
+330
+00:24:57,470 --> 00:25:01,230
+عندي ال basis step بتاع T، يكون اثنين، لازم يكون
+
+331
+00:25:01,230 --> 00:25:06,910
+اثنين. طب إذا كانت to K، لازم يكون عندي K elements
+
+332
+00:25:08,250 --> 00:25:12,050
+Given أساساً من الأول، إذا مش موجودين، معناته إنك
+
+333
+00:25:12,050 --> 00:25:17,250
+تجيبيهم من ال bases، لإن أكبر من أو يساوي اثنين،
+
+334
+00:25:17,250 --> 00:25:21,090
+معناته تبدأ من اثنين، ثلاثة، أربعة، لما تخلص ال K
+
+335
+00:25:21,090 --> 00:25:26,250
+elements، بعد هيك خلاص بتجيب الباقي ك relation منهم
+
+336
+00:25:26,250 --> 00:25:30,070
+ك relation بيصيروا منهم المعادلة اللي قدامنا الآن.
+
+337
+00:25:30,070 --> 00:25:33,310
+كيف بقدر أعبر عنها بالصيغة الثانية اللي هي ال
+
+338
+00:25:33,310 --> 00:25:38,410
+closed form، closed form، أنا مش محتاج أجيب كل ال
+
+339
+00:25:38,410 --> 00:25:43,770
+elements اللي جابوا ال AN، أنا بدي AN بدلالة ال index
+
+340
+00:25:43,770 --> 00:25:48,990
+تبعها، بدلالة ال index، كويس؟ فاحنا مفترضين تماماً أن
+
+341
+00:25:48,990 --> 00:25:53,370
+هذه الحالة حتكون أسهل من هذه، عشان أقول لك والله حت
+
+342
+00:25:53,370 --> 00:25:58,820
+للعنصر ال 100، هات عنصر 100، وما تعملش برضه في الامتحان
+
+343
+00:25:58,820 --> 00:26:02,340
+تروح تجيب ليهم من ال .. من ال initial وتبدأ تعملي
+
+344
+00:26:02,340 --> 00:26:05,260
+100 عنصر عشان تصل لعنصر 100 اللي مطلوب في الامتحان
+
+345
+00:26:05,260 --> 00:26:09,500
+مثلاً، أو مطلوب في code معين عندك، أنت بكرا بدك تعمل
+
+346
+00:26:09,500 --> 00:26:14,540
+أكواد. طيب ال code ده ممكن يكون لأمثلة كتيرة، تكون
+
+347
+00:26:14,540 --> 00:26:21,620
+مثلاً معامل الربح في مرابحة معينة للبنك، معامل قروض،
+
+348
+00:26:21,620 --> 00:26:24,340
+معامل، مش عارف، اللي هي بتكون في مركبة، هل بدك
+
+349
+00:26:24,340 --> 00:26:27,520
+تروح تبدأها من أول مبادرة المرابحة، لأن أنت في
+
+350
+00:26:27,520 --> 00:26:33,010
+الحالة دي، ليش ما تعمل معادلة معرفة بال index نفسه؟ و
+
+351
+00:26:33,010 --> 00:26:37,950
+خلاص، خطوة واحدة بتخلصها، يعني بمعنى معادلة واحدة
+
+352
+00:26:37,950 --> 00:26:40,890
+بتحسبها وخلاص، أتجبت الرقم اللي أنت محتاجه، أو
+
+353
+00:26:40,890 --> 00:26:44,610
+الرقم التراكمي اللي أنت بدك إياه. مبدئياً هاي فيها
+
+354
+00:26:44,610 --> 00:26:47,690
+ثلاثة options، نفترض إنه هذا سؤال وبدنا نعرف
+
+355
+00:26:47,690 --> 00:26:52,010
+مين من الثلاث حالات هذول يمثل حالة ال recurrence
+
+356
+00:26:52,010 --> 00:26:58,310
+relation اللي فوق. A هي عبارة عن اثنين من العنصر
+
+357
+00:26:58,310 --> 00:27:03,860
+السابق ناقص اللي جابله، ناقص اللي جابله. ثلاثة in
+
+358
+00:27:03,860 --> 00:27:09,800
+تمثل هذا الكلام، بدك تجرب، بدك تبدأ من من الاثنين،
+
+359
+00:27:09,800 --> 00:27:14,520
+بمعنى إنك أنت حتقول إيه
+
+360
+00:27:14,520 --> 00:27:19,000
+خلينا نسميها اثنين، على أساس إننا نلعب، صور اثنين، و
+
+361
+00:27:19,000 --> 00:27:21,340
+خلاص، ونبدأ باثنين، بلاش نبدأها بصفر، وأنا بأعوض عند
+
+362
+00:27:21,340 --> 00:27:24,900
+الاثنين، وأتلخبطكوا، خليني أقول اثنين بتساوي انظروا
+
+363
+00:27:24,900 --> 00:27:31,740
+في اثنين ستة، طيب ثلاثة اللي هي أكبر منها، جدّاش
+
+364
+00:27:35,830 --> 00:27:41,830
+تسعة، صحيح. احنا هنا جايبين، نجرب اللي هنا، طيب أربعة
+
+365
+00:27:41,830 --> 00:27:46,330
+اثنا عشر، طيب أربعة، هل فعلاً بقدر أجيبها من الاثنين
+
+366
+00:27:46,330 --> 00:27:53,330
+اللي جابها بال recurrence relation اللي فوق، اثنين
+
+367
+00:27:53,330 --> 00:27:59,390
+في تسعة ناقص ستة، اثنا عشر. هي اثنا عشر، طيب اللي وراها
+
+368
+00:28:04,160 --> 00:28:09,680
+هل هي ممكن نقول اثنين في اثنا عشر ناقص تسعة؟ مظبوط.
+
+369
+00:28:09,680 --> 00:28:15,560
+معناته الأولى تمثلها، مظبوطة، yes، طيب الثانية، هاي
+
+370
+00:28:15,560 --> 00:28:20,500
+خلصنا من الأولى بالضبط، اه أنت .. لأنه خلاص ال
+
+371
+00:28:20,500 --> 00:28:23,480
+sequence بصير، أنت أول حدين ثلاثة بتكون ضمن، معناته
+
+372
+00:28:23,480 --> 00:28:26,400
+إن هي مظبوطة ك .. ك .. ك .. بالضبط ك series هي
+
+373
+00:28:26,400 --> 00:28:32,640
+سلسلة ورا بعض، ماشية ورا بعض، طيب الثانية هنا، اثنين
+
+374
+00:28:34,210 --> 00:28:41,070
+أربعة، اثنين، ثلاثة، ثمانية، أربعة، ستة عشر، ستة عشر، ستة
+
+375
+00:28:41,070 --> 00:28:42,270
+عشرة، ستة عشر، ستة عشر، ستة عشر، ستة عشر، ستة عشر،
+
+376
+00:28:42,270 --> 00:28:46,690
+ستة عشر، ستة عشر، ستة عشر، ستة عشر، ستة عشر، ستة
+
+377
+00:28:46,690 --> 00:28:47,790
+عشرة، ستة عشر، ستة عشر، ستة عشر، ستة عشر، ستة عشر،
+
+378
+00:28:47,790 --> 00:28:49,330
+ستة عشر، ستة عشر، ستة عشر، ستة عشر، ستة عشر، ستة
+
+379
+00:28:49,330 --> 00:28:51,670
+عشرة، ستة عشر، ستة عشر، ستة عشر، ستة عشر، ستة عشر،
+
+380
+00:28:51,670 --> 00:29:00,370
+ستة عشر، ستة عشر، ستة عشر، ستة عشر، ستة
+
+381
+00:29:00,370 --> 00:29:06,740
+عشرSignal DC، هتفتح إياها DC صحيحة ولا مستحيلة؟ طب
+
+382
+00:29:06,740 --> 00:29:15,080
+جربها، جربها إياها، خمسة
+
+383
+00:29:15,080 --> 00:29:17,600
+ليش على طول بنفترض إنه على السريع هيك ينجح؟
+
+384
+00:29:17,600 --> 00:29:23,000
+ما تجيبوا بسرعة، هدّوا، احكوا، واعملوا check، مش غلط
+
+385
+00:29:23,000 --> 00:29:25,740
+الواحد يعمل check، اعمل check على السريع، هذا اللي
+
+386
+00:29:25,740 --> 00:29:29,380
+حاله، هي على السريع بالنظر بيّان، اه yes، اه هذا
+
+387
+00:29:29,380 --> 00:29:33,270
+بتعبر عن، عن ال sequence اللي فوق، بتعبر عنه، ما فيش
+
+388
+00:29:33,270 --> 00:29:35,990
+مشكلة، لأن الترتيب اللي مش مهم، إن ناقص واحد وإن ناقص
+
+3
+
+445
+00:33:36,920 --> 00:33:40,820
+طيب، ممتاز، هي لأنه بدأت هكذا، هي بدأت هكذا طيب،
+
+446
+00:33:40,820 --> 00:33:44,060
+كمان مثال، المثال هذا يمكن في البنوك أكثر، في
+
+447
+00:33:44,060 --> 00:33:46,680
+البنوك ممكن نستخدمه أكثر، اللي هي الفائدة، الفائدة
+
+448
+00:33:46,680 --> 00:33:53,180
+المركبة، بالفوائد المركبة عادةً مسكين المستخدم أو
+
+449
+00:33:53,180 --> 00:33:58,040
+صاحب الحساب يروح يأخذ القرض ويبورط بعضه، القرض
+
+450
+00:33:58,040 --> 00:34:03,380
+هذا إذا عجز، بيصير تراكميًا، يصير تراكمي، إيش يعني
+
+451
+00:34:03,380 --> 00:34:07,000
+تراكمي؟ يعني الشهر جديش المبلغ اللي المفروض يدفع
+
+452
+00:34:07,000 --> 00:34:10,340
+الشهر هذا هو يساوي اللي كان لازم يدفع الشهر اللي
+
+453
+00:34:10,340 --> 00:34:13,420
+فات، هذا طبعًا لو عجز وماقدرش يصدر، الشهر اللي فات
+
+454
+00:34:13,420 --> 00:34:18,120
+زائد أرباحه أو زائد فائضه، الفائدة جديش، لو بدي
+
+455
+00:34:18,120 --> 00:34:22,530
+أفترض أن الفائدة هي P في المئة، هي interest معينة، الـ
+
+456
+00:34:22,530 --> 00:34:27,510
+interest هذه لكل one period هي عبارة عن P مثلًا
+
+457
+00:34:27,510 --> 00:34:30,070
+واحد في المئة، خمسة في المئة، عشرة في المئة، جديش ما
+
+458
+00:34:30,070 --> 00:34:34,850
+تكون، تكون. وإذا جديش قيمة المبلغ نفسه زائد الـ repeat
+
+459
+00:34:34,850 --> 00:34:39,930
+تبعته أو زائد الإضافة، الفائدة تبعتها، فالفائدة هي
+
+460
+00:34:39,930 --> 00:34:45,870
+النسبة في مين؟ في قيمة الشهر، في قيمة الشهر الماضي، مش
+
+461
+00:34:45,870 --> 00:34:50,590
+أصل المرابحة أو أصل القرض من الشهر الماضي جديش كان
+
+462
+00:34:50,590 --> 00:34:54,710
+ضايل عليك، النسبة بتنحط عليه، تنحط عليه، تمام. فإذا الـ
+
+463
+00:34:54,710 --> 00:34:59,070
+total هنا لما آخذ الـ M ناقص واحد كعامل مشترك تصبح
+
+464
+00:34:59,070 --> 00:35:03,050
+واحد زائد النسبة مضروبة في الشهر الماضي. فبدأ افترض
+
+465
+00:35:03,050 --> 00:35:06,770
+أن هذه القيمة، الواحد زائد النسبة، بدي أسميها R، بدي
+
+466
+00:35:06,770 --> 00:35:11,590
+أسميها R من القيمة السابقة. طيب ممتاز، و R هي الواحد
+
+467
+00:35:11,590 --> 00:35:17,670
+زائد النسبة. طيب، إن ناقص واحد، هي جاية من وين؟ هو
+
+468
+00:35:17,670 --> 00:35:20,570
+نفس المبلغ هذا، من وين صار عليّ بهذه القيمة؟ هروح
+
+469
+00:35:20,570 --> 00:35:23,750
+طبعًا أحتاج، عشان المحاسب يقول، اه تعال، أهلاً
+
+470
+00:35:23,750 --> 00:35:25,590
+و سهلاً، ما فيش مش مش مشكلة، أنت الشهر اللي فات كان
+
+471
+00:35:25,590 --> 00:35:28,630
+عليك مئة، عامةً أنا ما أخذتش مئة، طب ماشي تعال نشوف،
+
+472
+00:35:28,630 --> 00:35:32,670
+هذه المئة صارت مئة لأن أنت قبلها كنت آخذ خمسين
+
+473
+00:35:32,670 --> 00:35:35,290
+وظهر عليك فيه زيادة، مش عارف جديش، فالشهر اللي فات
+
+474
+00:35:35,290 --> 00:35:38,110
+كان المفروض أنك ليش تدفع مئة، ما دفعتش المئة، فصار
+
+475
+00:35:38,110 --> 00:35:43,150
+المئة زائد أرباح المئة، مش أرباح الخمسين الأولى
+
+476
+00:35:43,150 --> 00:35:48,110
+واضحة. فهنا صار كأنه الـ N ناقص واحد، الشهر السابق هو
+
+477
+00:35:48,110 --> 00:35:52,050
+من الشهر اللي قبله برضه بالنسبة R زائد الـ R بتاعة
+
+478
+00:35:52,050 --> 00:35:56,890
+هذا الشهر، فصارت R تربيع، أصبحت R تربيع، يعني معناه
+
+479
+00:35:56,890 --> 00:36:01,790
+ذلك أنه، قبل كم شهر بتصير R to the power الكم
+
+480
+00:36:01,790 --> 00:36:06,570
+شهر، هدول N ناقص اثنين، بتصير هنا R to the power
+
+481
+00:36:06,570 --> 00:36:12,540
+اثنين. لما نصِل لـ M0 اللي هو الشهر اللي أخذنا فيه
+
+482
+00:36:12,540 --> 00:36:16,440
+المرابحة أو أخذنا فيه، عفواً، القرض هذا، عشان يصبح قرض
+
+483
+00:36:16,440 --> 00:36:23,160
+مركب بهذا الشكل. فإذا بتصير R to the power N صحيح
+
+484
+00:36:23,160 --> 00:36:27,420
+فأنت في الحالة هذه لو النسبة مثلًا 2%، لنقل 2%، و
+
+485
+00:36:27,420 --> 00:36:30,440
+بقوا لخمس سنوات، والمفروض تدفع الأقساط بتاعتها
+
+486
+00:36:30,440 --> 00:36:37,180
+شهريًا 2%، وتدفعهم شهريًا، صار بعد خمس سنوات ستين، ستين
+
+487
+00:36:37,180 --> 00:36:47,940
+اثنين زائد مئة، 100.2 أو 1.02، 1.02 to
+
+488
+00:36:47,940 --> 00:36:53,140
+the power 60 في قيمة المبلغ اللي أنت أخذته هذا،
+
+489
+00:36:53,140 --> 00:36:56,100
+المبلغ اللي بدك توفيه بعد خمس سنوات مثلًا، طبعًا بعد
+
+490
+00:36:56,100 --> 00:36:59,820
+ست سنوات، ست سنوات، بتشوف جديش، لأن هذه المفروض أنها
+
+491
+00:36:59,820 --> 00:37:04,720
+من الرواتب، معناته شهريًا، هتلاقي حالك في كارثة، هتلاقي
+
+492
+00:37:04,720 --> 00:37:08,040
+حالك في كارثة. طيب هذه فعليًا كمثال، recurrence
+
+493
+00:37:08,040 --> 00:37:12,300
+relation، هذه recurrence relation، صحيح؟ أي شهر
+
+494
+00:37:12,300 --> 00:37:17,470
+بدلالة اللي قبله، وقدرت أحطّه بإيش؟ بدلالة الـ index
+
+495
+00:37:17,470 --> 00:37:22,010
+هنا، هدينا نحطّه بدلالة مين؟ index، فصارت كأنه أنت
+
+496
+00:37:22,010 --> 00:37:25,390
+بعد ستين بتحط تضارب ستين، بعد سبعين بتحط تضارب
+
+497
+00:37:25,390 --> 00:37:30,890
+سبعين، بعد جديش؟ خمسين، خمسين شهر لك، مراد، بعد
+
+498
+00:37:30,890 --> 00:37:34,890
+خمسين فبتحط إنه بخمسين مباشرةً بدل ما تحسبها من
+
+499
+00:37:34,890 --> 00:37:38,810
+التسعة والأربعين، الشهر، تسعة وأربعين. طب التسعة
+
+500
+00:37:38,810 --> 00:37:41,030
+و الأربعة والأربعين بتجيبه من التمانين؟ أو أربعين، لأ خلاص
+
+501
+00:37:41,030 --> 00:37:45,420
+مباشرةً في الـ closed form relation. هل كل الـ
+
+502
+00:37:45,420 --> 00:37:49,920
+relations مصبوغ نعملها هيك، أتفادى عنها؟ الأصل هيك
+
+503
+00:37:49,920 --> 00:37:55,880
+هدول، لأنهم مفهومين، صح؟ في حاجات مش مفهومة، مثالنا
+
+504
+00:37:55,880 --> 00:37:59,340
+الآن، أو عفواً، الدرس تبعنا، المحاضرة بتاعتنا، المفروض
+
+505
+00:37:59,340 --> 00:38:03,260
+ما هنخلصها إلا لما نكون أخذنا طريقة لتحويلها لـ
+
+506
+00:38:03,260 --> 00:38:05,910
+closed form. هناخدها إن شاء الله، بس هدول لأنه أنثى
+
+507
+00:38:05,910 --> 00:38:11,270
+واضحة، بنقدر بسهولة نستنتج الـ closed form تبعها، هي
+
+508
+00:38:11,270 --> 00:38:15,330
+مثال من الألعاب المشهورة جدًا، أول ما طلعت الجوالات
+
+509
+00:38:15,330 --> 00:38:19,870
+كانوا بيحطوا لنا الـ Hanoi tower أو tower of Hanoi.
+
+510
+00:38:19,870 --> 00:38:22,690
+هذه الـ Hanoi tower من الحاجات المشهورة جدًا، بدك
+
+511
+00:38:22,690 --> 00:38:29,870
+تنقل الـ disks هدول من الـ big one اللي هي الوتد
+
+512
+00:38:29,870 --> 00:38:33,370
+الأول لـ big two، الوتد الثاني أو للتالت، أنت حر.
+
+513
+00:38:33,370 --> 00:38:38,350
+المهم أنك تنقلهم بنفس الشكل، وكل move تستخدم disk
+
+514
+00:38:38,350 --> 00:38:43,510
+واحد، وممنوع يجيء disk أكبر على disk أصغر، وبيقول لك
+
+515
+00:38:43,510 --> 00:38:48,710
+بكل بساطة، عشان تنقلهم من big one to big two، كم
+
+516
+00:38:48,710 --> 00:38:54,210
+move محتاج؟ كم move محتاج؟ طيب، بكل بساطة، هالوقت بدأ
+
+517
+00:38:54,210 --> 00:38:57,830
+أفترض أنهم في إمكانية لنقلهم، في إمكانية لنقلهم.
+
+518
+00:38:57,830 --> 00:39:02,830
+طيب، عشان أنقل الخمسة، معنى ذلك أنه أنا محتاج أقول
+
+519
+00:39:02,830 --> 00:39:08,390
+جديش عدد اللي أنا محتاجهم كـ moves عشان أنقل أربعة
+
+520
+00:39:08,390 --> 00:39:18,470
+بالضبط، زائد واحد من هنا، زائد الأربعة كمان مرة. فإذا
+
+521
+00:39:18,470 --> 00:39:25,620
+لو قلت Hanoi بـ N disk هو فعليًا يساوي اثنين Hanoi N
+
+522
+00:39:25,620 --> 00:39:30,740
+ناقص واحد، زائد واحد. الأقل
+
+523
+00:39:30,740 --> 00:39:36,180
+بواحد، لأن أنا فعليًا محتاج، عشان أحرك الخمسة، أولًا، لأن
+
+524
+00:39:36,180 --> 00:39:40,990
+لاحظ في شرط أنه ما يجيء disk كبير على disk صغير، صح؟
+
+525
+00:39:40,990 --> 00:39:44,610
+تمام، وفي نفس الوقت الـ disk الأخير لازم يكون فيه
+
+526
+00:39:44,610 --> 00:39:47,370
+مكان فارغ عشان نحط فيه... نحط فيه. بعد ذلك أنا
+
+527
+00:39:47,370 --> 00:39:51,490
+متأكد تمامًا أن الأربعة هدول هيتم نقلهم كما هم بنفس
+
+528
+00:39:51,490 --> 00:39:56,030
+ترتيبهم هنا، عشان يكون فيه مكان فارغ أحط فيه الخامس.
+
+529
+00:39:56,030 --> 00:40:00,790
+طيب، جديش عدد الـ moves اللي أنا محتاجها لنقل أربعة؟
+
+530
+00:40:00,790 --> 00:40:08,240
+يطلع جديش ما يطلع، صحيح، جديش ما يطلع يطلعه، أقول اسمهم H
+
+531
+00:40:08,240 --> 00:40:12,720
+أو Hanoi، النقص واحد، يطلع جديش ما يطلع، تمام، وبعدين
+
+532
+00:40:12,720 --> 00:40:16,700
+في حركة واحدة، move one، عشان آخذ الـ disk الخامس
+
+533
+00:40:16,700 --> 00:40:21,280
+أنقله هنا. الـ answer عند الأربع هدول كمان مرة، بتدر
+
+534
+00:40:21,280 --> 00:40:31,700
+عن كلهم. فوهم واضح لكم حتى اللحظة؟ طيب ممتاز، صحيح.
+
+535
+00:40:31,700 --> 00:40:34,780
+عشان هيك احنا قلنا هدول عدد نقلة، أنا لسه مش
+
+536
+00:40:34,780 --> 00:40:39,910
+عارفهم، لكن أنا قلت عدد النقلات لنقل أربعة discs،
+
+537
+00:40:39,910 --> 00:40:44,230
+أربعة discs، جديش؟ مش عارف. الآن، هالوجهة اللي هتكلمها
+
+538
+00:40:44,230 --> 00:40:47,890
+بجديش، هذه نفسها، طب جديش؟ طب ما هي نفس الفكرة
+
+539
+00:40:47,890 --> 00:40:58,110
+لحالها هتكون اثنين في H ناقص اثنين، زائد واحد، and
+
+540
+00:40:58,110 --> 00:41:04,580
+so on، لما نصل في الآخر لـ 1، جديش بدك عدد moves
+
+541
+00:41:04,580 --> 00:41:10,880
+لنقل disk واحد، move واحدة. كم move محتاجة عشان
+
+542
+00:41:10,880 --> 00:41:13,780
+تنقل one disk؟ هي move واحدة، فهي واضحة، الـ
+
+543
+00:41:13,780 --> 00:41:18,840
+recurrence relation، وواضحة تمامًا، أن كل n معتمد
+
+544
+00:41:18,840 --> 00:41:22,680
+على الـ n ناقص واحد اللي قبله. فعشان في الحالة هذه
+
+545
+00:41:22,680 --> 00:41:26,060
+أقول أن والله الـ H، بدي أفترض أن هي الـ moves لنقل
+
+546
+00:41:26,060 --> 00:41:31,260
+n disks، فالـ strategy الطبيعية أقول أنه جديش محتاج
+
+547
+00:41:31,260 --> 00:41:36,920
+moves لنقل n نقص one، اللي هم كانوا عندي خمسة، بدنا
+
+548
+00:41:36,920 --> 00:41:40,040
+نقول الأربعة اللي فوق، بدنا نقول الأربعة اللي فوق،
+
+549
+00:41:40,040 --> 00:41:45,180
+اللي هي n نقص one disk to spare big، فبتصير H n
+
+550
+00:41:45,180 --> 00:41:50,640
+نقص one، ثم بعدين بحرك الـ disk الأخير، الخامس كان
+
+551
+00:41:50,640 --> 00:41:58,480
+الخامس، ثم بنعيد الـ N نقص واحد من الـ spare هذا لفوق،
+
+552
+00:41:58,480 --> 00:42:03,000
+الـ disk الخامس. ففعلاً بيظهر عندي الـ relation بهذا
+
+553
+00:42:03,000 --> 00:42:07,020
+الشكل، زي اللي احنا كتبناها تمامًا، بشكل recurrence
+
+554
+00:42:07,020 --> 00:42:12,880
+هنجي نعمل المعادلة اللي احنا شايفينها قدامنا بهذا
+
+555
+00:42:12,880 --> 00:42:14,620
+الشكل، فهذه هي، هتنين N
+
+556
+00:42:22,730 --> 00:42:36,330
+حسب حسب حسب حسب حسب حسب حسب
+
+557
+00:42:36,330 --> 00:42:36,390
+حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب
+
+558
+00:42:36,390 --> 00:42:36,450
+حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب
+
+559
+00:42:36,450 --> 00:42:36,690
+حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب
+
+560
+00:42:36,690 --> 00:42:41,530
+حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب
+
+561
+00:42:41,530 --> 00:42:41,570
+حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب حسب
+
+562
+00:42:41,570 --> 00:42:41,650
+حسب حسب حسب حسب حسب حسب حسب حسب حسب
+
+563
+00:42:47,230 --> 00:42:52,930
+زائد واحد. طيب، هي نفسها HN ناقص اثنين برضه بنفس
+
+564
+00:42:52,930 --> 00:42:57,890
+الطريقة، هي اثنين في HN ناقص ثلاثة زائد واحد. طيب
+
+565
+00:42:57,890 --> 00:43:02,230
+اضرب هنا، صارت ثلاثة مع تكعيب مع ثلاثة، طيب.
+
+566
+00:43:02,230 --> 00:43:06,550
+و اثنين مع الواحد بتظل اثنين، تتبارى اثنين واثنين
+
+567
+00:43:06,550 --> 00:43:11,290
+هنا، وواحد هنا، زي ما هم لاحظوا
+
+568
+00:43:11,290 --> 00:43:15,850
+عشان تصل في الآخر لـ H1
+
+569
+00:43:17,060 --> 00:43:23,720
+معناته مضروبة في اثنين n ناقص واحد، هيهم
+
+570
+00:43:23,720 --> 00:43:29,000
+مرتبطين ببعض هنا، زائد اثنين n ناقص اثنين n ناقص
+
+571
+00:43:29,000 --> 00:43:32,300
+ثلاثة، لعندي ما نصل لـ اثنين to the power two، to the
+
+572
+00:43:32,300 --> 00:43:36,060
+power one، to the power zero، يعني أصبحت كأنه
+
+573
+00:43:36,060 --> 00:43:38,560
+الترتيب هذا هو الكامل على بعضه، واحنا كلنا عارفين
+
+574
+00:43:38,560 --> 00:43:41,440
+أنه جديش أنا محتاج الـ Hanoi إذا كان عندي عبارة عن
+
+575
+00:43:41,440 --> 00:43:46,040
+disk واحد، كم move محتاج له؟ move واحدة، خلاص، معناته
+
+576
+00:43:46,040 --> 00:43:51,050
+واحد، مو في واحدة، تمام. هذا الـ term اللي صار عندي ظهر
+
+577
+00:43:51,050 --> 00:43:55,430
+عندي هو عبارة عن summation لـ 2 to the power of I
+
+578
+00:43:55,430 --> 00:44:00,110
+لاحظته كيف؟ كلهم اثنينات، هذا في الآخر 2 to the
+
+579
+00:44:00,110 --> 00:44:06,030
+power of 0 و I to the power واحد، فـ 2 to the power
+
+580
+00:44:06,030 --> 00:44:12,630
+of I، و I بادية من صفر، هي صفر، لأن ناقص one، طب ما هي
+
+581
+00:44:12,630 --> 00:44:17,710
+دي السؤال الامتحاني اللي جاي، هكذا؟ مع هذا طبعًا هيجي لكم
+
+582
+00:44:17,710 --> 00:44:21,430
+لـ closed form، اه، أكيد هذا، بالأسئلة اللي ما فيش مجال
+
+583
+00:44:21,430 --> 00:44:27,110
+يجيء امتحان بدونها، ممتازة. طيب، فهذه مثلًا 2 to the
+
+584
+00:44:27,110 --> 00:44:30,830
+power i، كلكم عارفين إنه لازم لو حليتوها في الامتحان
+
+585
+00:44:30,830 --> 00:44:35,650
+بهذا الشكل كان ماشي حالها، اللي هي الـ form تبع الـ
+
+586
+00:44:35,650 --> 00:44:41,950
+geometric series، تمام، فهتطلع 2 to the power n نقص
+
+587
+00:44:41,950 --> 00:44:46,330
+واحد، على اعتبار أن الـ r هي الاثنين، بتحلوها في
+
+588
+00:44:46,330 --> 00:44:49,350
+الآخر، مدام اثنين، معناته في المقام عندك اثنين ناقص
+
+589
+00:44:49,350 --> 00:44:53,370
+واحد، فكأنها على واحد، بتبقى على واحد، فخلصت هاي الـ
+
+590
+00:44:53,370 --> 00:44:56,530
+closed form تبعنا. جديش عدد الـ disks تبعتك؟ اثنين
+
+591
+00:44:56,530 --> 00:45:00,770
+خمسة عشر، معناته اثنين مضروبة في العشرة ناقص واحد، بيطلع
+
+592
+00:45:00,770 --> 00:45:05,630
+جديش عدد الـ moves، الـ optimal moves، عشان فعليًا تنقل
+
+593
+00:45:05,630 --> 00:45:10,550
+اللي، اللي هو اللعبة كاملة، أو عدد الـ discs كامل، عدد
+
+594
+00:45:10,550 --> 00:45:14,110
+الـ discs كامل، تمام. المرة القادمة إن شاء الله
+
+595
+00:45:14,110 --> 00:45:19,110
+هنتكلم عن... الآن لو عندك form recurrence form، و
+
+596
+00:45:19,110 --> 00:45:22,610
+مش هنقدر نستنتج زي الثلاث أمثلة اللي أخذناهم سابقًا
+
+597
+00:45:22,610 --> 00:45:26,730
+إني أوصلهم هكذا نظريًا، بدي أشوفهم بطريقة حسابية،
+
+598
+00:45:26,730 --> 00:45:35,690
+بمعنى أنه ممكن يكونوا to k، فـ a في الـ order n أو الـ
+
+599
+00:45:35,690 --> 00:45:41,990
+sequence رقم n هذا يساوي بدلالة n نقص واحد، n نقص
+
+600
+00:45:41,990 --> 00:45:46,850
+اثنين، لعند n نقص K، فهو معتمد على K elements قبله.
+
+601
+00:45:46,850 --> 00:45:52,350
+لو فعليًا الصورة هذه موجودة بهذا الشكل، إيش ممكن
+
+602
+00:45:52,350 --> 00:45:56,890
+نعمل؟ محتاج أَحدد بس إيش الـ coefficients اللي موجودة
+
+603
+00:45:56,890 --> 00:45:59,710
+لأن هنا ممكن يكون في مجموعة coefficients إلها برضه
+
+604
+00:45:59,710 --> 00:46:04,350
+دَه، هتكون مهمة جدًا في الشغل بحيث إني أحولها في الآخر
+
+605
+00:46:04,350 --> 00:46:08,090
+لـ closed form، بس عشان أحولها لـ closed form زيها زي
+
+606
+00:46:08,090 --> 00:46:12,350
+أي recurrence ثانية، لازم عندي k initial values
+
+607
+00:46:12,350 --> 00:46:16,990
+موجودين، لازم يكون في k initial values موجودين، مدام
+
+608
+00:46:16,990 --> 00:46:21,930
+أنا
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ddef561462549b9669ee54461a706e62a25f2347
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4.srt
@@ -0,0 +1,1977 @@
+1
+00:00:05,180 --> 00:00:08,780
+بسم الله الرحمن الرحيم يعطيكم العفو يا شباب نكمل
+
+2
+00:00:08,780 --> 00:00:11,500
+اليوم في جزئية الـ algorithm و البداية اللي كانت
+
+3
+00:00:11,500 --> 00:00:15,620
+بسيطة وسهلة، مجرد أن أحنا أخذنا مجموعة statements
+
+4
+00:00:15,620 --> 00:00:20,000
+للغة وصفية على أساس أن نبدأ نتكلم عن مجموعة
+
+5
+00:00:20,000 --> 00:00:23,800
+algorithms، أعتقد أن معظمها مر عليكم سابقا، أن
+
+6
+00:00:23,800 --> 00:00:27,480
+أنتم اللي أنا مخلصين برمجة واحد و اثنين يعني
+
+7
+00:00:27,480 --> 00:00:31,370
+مأخذين two courses في البرمجة، ومأخذين الآن
+
+8
+00:00:31,370 --> 00:00:34,530
+بتأخذوا الـ data structure، يعني المفروض أنه خلال
+
+9
+00:00:34,530 --> 00:00:38,930
+الفترة هذه محاضراتنا يعني بسيطة مرة عليكم، أنا حتى
+
+10
+00:00:38,930 --> 00:00:42,910
+أتوقع أنه أنتم لحالكم على طول بت...اتجاوبوا
+
+11
+00:00:42,910 --> 00:00:48,570
+معنا، طيب من خلال المحاضرة السابقة لهذا الموضوع
+
+12
+00:00:48,570 --> 00:00:52,630
+اللي هو الـ algorithms، كنا اتكلمنا عن مثال ووضحنا
+
+13
+00:00:52,630 --> 00:00:55,550
+فيه مجموعة list statements، واللي هي كان إيجاد الـ
+
+14
+00:00:55,550 --> 00:01:00,070
+maximum value أو الـ maximum element من داخل
+
+15
+00:01:00,070 --> 00:01:05,140
+list معينة، الآن نبدأ في مجموعة تطبيقات ثانية منها
+
+16
+00:01:05,140 --> 00:01:07,860
+وأهمها اللي أنتم أكيد برضه مرت عليكم، اللي هي الـ
+
+17
+00:01:07,860 --> 00:01:11,220
+searching، عملية الـ searching في جزئية الـ searching
+
+18
+00:01:11,220 --> 00:01:15,480
+اللي هي البحث، طبعا في ordered list، هنا بنتكلم عن
+
+19
+00:01:15,480 --> 00:01:21,420
+الـ search في list مرتبة، list مرتبة مرتبة اللي هي
+
+20
+00:01:21,420 --> 00:01:27,040
+بشكل تصاعدي، بشكل تصاعدي، طبعا بشكل تنازلي برضه بيمشي
+
+21
+00:01:27,040 --> 00:01:30,780
+الحال، بس شوية مفاهيم بسيطة بتتغير معاك، فالمفروض
+
+22
+00:01:30,780 --> 00:01:37,540
+الموضوع بيبسط ف... كأكواد، بنفكر بالتالي، given
+
+23
+00:01:37,540 --> 00:01:40,900
+list L، لازم تكون فيها الـ input، الـ input ده و الـ
+
+24
+00:01:40,900 --> 00:01:44,940
+arguments اللي هي الـ list نفسها لمجموعة elements و
+
+25
+00:01:44,940 --> 00:01:50,750
+لازم تكون sorted، بمعنى مصنفة مرتبة مرتبة أو مصنفة
+
+26
+00:01:50,750 --> 00:01:57,450
+تمام، بـ order معين، واحنا قلنا الـ order هذا تساعدي
+
+27
+00:01:57,450 --> 00:02:03,710
+تنازلي، المهم أنه في ترتيب معين واضح، سواء كان أرقام
+
+28
+00:02:03,710 --> 00:02:06,970
+أو حروف، حتى
+
+29
+00:02:26,810 --> 00:02:31,010
+درجة جدا، method درجة جدا في برامج كثيرة، كويس
+
+30
+00:02:31,010 --> 00:02:36,020
+بدنا نحسب من الـ X هذا اللي given عندي، وفي نفس
+
+31
+00:02:36,020 --> 00:02:39,960
+الوقت given عندي list، بدنا نحسب هل الـ X هذا موجود
+
+32
+00:02:39,960 --> 00:02:43,120
+في الـ list ولا لأ، إذا موجود بدي أرجع له بالـ إيش؟
+
+33
+00:02:43,120 --> 00:02:47,220
+بالـ index تبعه، بالـ index تبعه، كافي الـ index؟ كافي
+
+34
+00:02:47,220 --> 00:02:50,760
+ليش؟ لأن أنا بتكلم عن ordered list، يعني معناه ذلك
+
+35
+00:02:50,760 --> 00:02:54,640
+أن الـ index هو ثابت، مكانه مكانه دائما ثابت، أرجع له
+
+36
+00:02:54,640 --> 00:03:00,390
+بالمكان تبع الـ X هذا إذا موجود داخل الـ list L، تمام
+
+37
+00:03:00,390 --> 00:03:04,890
+إذا والله غير موجود، أرجع له أنه غير موجود، أرجعه
+
+38
+00:03:04,890 --> 00:03:09,650
+أنه غير موجود، هذا ببساطة وصف أو بكل بالكلام إيش
+
+39
+00:03:09,650 --> 00:03:13,610
+اللي بدنا نعمله، تمام، الآن عشان نعمل هذا الكلام في
+
+40
+00:03:13,610 --> 00:03:17,350
+عدة algorithms بيشتغلوا في الموضوع هذا، عدة
+
+41
+00:03:17,350 --> 00:03:20,930
+algorithms، ممكن نعمل منهم عملية الـ search، منهم الـ
+
+42
+00:03:20,930 --> 00:03:23,710
+linear، وهذا أبسط نوع، واللي أكيد أخذتموه أكيد مرة
+
+43
+00:03:23,710 --> 00:03:27,290
+عليكم، لأن هذا basic، يعني المفروض أنه شيء مار
+
+44
+00:03:27,290 --> 00:03:33,830
+عليكم سابقا، بتبدأ من a1، a2 to an، هذه الـ list، و
+
+45
+00:03:33,830 --> 00:03:38,810
+عندك قيمة x، بدك تفحص هي موجودة ولا غير موجودة، بمعنى
+
+46
+00:03:38,810 --> 00:03:42,210
+عملية search، إذا موجودة، أرجع لي بالـ index في الـ
+
+47
+00:03:42,210 --> 00:03:44,450
+location الأول، ولا الثاني، ولا الخامس، ولا في الـ
+
+48
+00:03:44,450 --> 00:03:48,910
+location in، أرجع لي بالـ index بس، طيب مش موجودة
+
+49
+00:03:48,910 --> 00:03:52,530
+أعطيني دلالة، أرجع لي بأي حاجة أستدل منها أن أنت
+
+50
+00:03:52,530 --> 00:03:56,930
+مالقيتهاش، غير موجود، أرجع لي بصفر مثلا، أرجع لنا بـ zero
+
+51
+00:03:57,800 --> 00:04:02,800
+طبعا، فإذا procedure، هنبدأ الـ code، طبعا هنسميه
+
+52
+00:04:02,800 --> 00:04:06,180
+باسم معين، التفكير بالنسبالي أنه لازم يكون في
+
+53
+00:04:07,050 --> 00:04:10,170
+arguments، الـ input اللي أنا محتاجها، مستحيل أعرف
+
+54
+00:04:10,170 --> 00:04:13,530
+اشتغل بدونها، هي قيمة الـ X، X اللي أنت بتدور عليها
+
+55
+00:04:13,530 --> 00:04:17,850
+اللي هي الـ integer، كويس، زائد الـ list نفسها، تكتب
+
+56
+00:04:17,850 --> 00:04:24,630
+لها A1، A2 to AN، ماشي، تكتب لها L، كويس، و
+
+57
+00:04:24,630 --> 00:04:29,590
+distinct integers، okay، خلاص فهمنا، بس بدك توضح أن
+
+58
+00:04:29,590 --> 00:04:33,410
+أنت بتكلم عن index بيبدا من واحد، الـ index بيبدا من
+
+59
+00:04:33,410 --> 00:04:36,550
+واحد، لأن أنتم كلكم عارفين أن أحنا في الـ array
+
+60
+00:04:36,550 --> 00:04:40,890
+بنشير للعنصر باستخدام الـ index تبعه، مافيش طريقة
+
+61
+00:04:40,890 --> 00:04:45,190
+ثانية، أنت عشان تعرف الـ index أو element معين
+
+62
+00:04:45,190 --> 00:04:50,090
+بتعرفه من خلال الـ index تبعه، تمام، بنبدأ بواحد
+
+63
+00:04:50,090 --> 00:04:54,040
+معناته كأن أنا بدي أجي عند الـ index الأول، بمعنى بدي
+
+64
+00:04:54,040 --> 00:04:57,520
+أفحص العنصر الأول، الـ element الأول، منطقية جدا
+
+65
+00:04:57,520 --> 00:04:59,920
+مافيش قبل الـ element الأول، فبدي أبدأ أفحص من الـ
+
+66
+00:04:59,920 --> 00:05:05,180
+element الأول، ونبدأ الآن الـ while، أبسط شغلة أن أنت
+
+67
+00:05:05,180 --> 00:05:10,040
+تبقى تعمل for loop، الـ for loop هذا يبقى شغال، يبقى
+
+68
+00:05:10,040 --> 00:05:17,070
+شغال بحيث أنه يعمل scan على الـ list، إمتى هيقف؟ عندك
+
+69
+00:05:17,070 --> 00:05:20,670
+حالتين ممكن يقف فيهم، أما أن يلاقي X أو يخلص الـ
+
+70
+00:05:20,670 --> 00:05:26,190
+list، مش هيك؟ مافيش شيء ثالث، في الحالتين بوقف الـ
+
+71
+00:05:26,190 --> 00:05:31,290
+loop تبعه، والله لاقى الـ X، المفروض يقف، ما لاقاش الـ
+
+72
+00:05:31,290 --> 00:05:38,310
+X؟ بده يكمل لعند ما يخلص الـ n، يعمل n مرة من
+
+73
+00:05:38,310 --> 00:05:41,190
+عمليات الفحص، أكتر من هيك، خلاص وقف، لأنه عارف
+
+74
+00:05:41,190 --> 00:05:44,690
+مسبقا أن الـ list تبعته، الـ length تبعها n، خلصنا
+
+75
+00:05:44,690 --> 00:05:49,990
+فإذن while، طول ما I أقل من أو يساوي n، فهو شغال
+
+76
+00:05:49,990 --> 00:05:54,870
+معناته في عناصر ما شافهاش، طول ما هو أقل من الـ length
+
+77
+00:05:54,870 --> 00:06:00,010
+معناته شغال، and x لا تساوي ai، الـ I اللي أنا موجود
+
+78
+00:06:00,010 --> 00:06:05,290
+عندها حاليا، فإذن لا لاقى X ولا وصل لنهاية الـ list
+
+79
+00:06:05,290 --> 00:06:11,810
+استمر، فإذن استمر، كويس، و I بتساوي I زائد واحد، الـ
+
+80
+00:06:11,810 --> 00:06:16,470
+increment statement اللي موجود عندك، increment، زود
+
+81
+00:06:16,470 --> 00:06:20,570
+كل مرة زود، وارجع افحص، زود، وارجع افحص، زود، وارجع افحص
+
+82
+00:06:20,570 --> 00:06:24,330
+خلاص، مافيش أكثر من هيك، اللي عملنا لا begin ولا end
+
+83
+00:06:24,330 --> 00:06:28,490
+مش هيك، يعني ما فتحتش أقواس الـ curly braces تبعها
+
+84
+00:06:28,490 --> 00:06:32,310
+أنا مش محتاج اللي الشرط هذا، فالجواب هذا بس، لا أكثر
+
+85
+00:06:32,310 --> 00:06:38,130
+ولا أقل، فإذا هاي الـ loop تبعك فقط، بس هاي كل الـ
+
+86
+00:06:38,130 --> 00:06:46,420
+loop، إمتى حقيقة زي ما قلنا يصبح أكبر من n، صحيح؟ طيب
+
+87
+00:06:46,420 --> 00:06:53,820
+إذا وصلت لأكبر من، معناه ذلك إنه ما جابش X، ما جابش
+
+88
+00:06:53,820 --> 00:06:59,400
+X، ليش؟ لأنه إذا وصلت لأكبر من، أنت عديت n، أنت أصبح
+
+89
+00:06:59,400 --> 00:07:05,320
+خلاص، بعدها أنت آخر مرة وصلت لـ I بتساوي n وما حققتش
+
+90
+00:07:05,320 --> 00:07:10,980
+الشرط هذا، وإلا كان وقفت، بس مدام ما وقفتش معناته
+
+91
+00:07:10,980 --> 00:07:16,160
+فعليا ما حققتش أن هي تساوي An، آخر عنصر، ما حققتش، روح
+
+92
+00:07:16,160 --> 00:07:21,480
+اتزودت واحد، فـ automatically صرت n زائد واحد، الآن n
+
+93
+00:07:21,480 --> 00:07:25,780
+زائد واحد، هذا الـ condition هو اللي عطل الـ
+
+94
+00:07:25,780 --> 00:07:29,320
+proposition، هو اللي عطل الـ proposition، فطلعنا عشان
+
+95
+00:07:29,320 --> 00:07:34,100
+تيجي تفحص، أنت أجل من أو يساوي n، طبعا فعليا أنت
+
+96
+00:07:34,100 --> 00:07:39,180
+صرت أكبر من، صحيح، فإذا false، false، إيش يعني أنا
+
+97
+00:07:39,180 --> 00:07:41,240
+هيرجع بصفر، يعني ما لاقيتهاش
+
+98
+00:07:43,570 --> 00:07:47,970
+لكن لو اللي وقف في الـ for loop، مش الـ condition، مش
+
+99
+00:07:47,970 --> 00:07:51,010
+ال...ال...ال...ال...الـ atomic proposition
+
+100
+00:07:51,010 --> 00:07:55,970
+الأول، الـ atomic proposition الثاني، أنت عند I معينة
+
+101
+00:07:55,970 --> 00:08:05,790
+وجدت أن X تساوي AI، تساوت، صار هنا false، طلعت بدون
+
+102
+00:08:05,790 --> 00:08:10,030
+ما تنفذ هذا، صحيح، فأنت ما زلت عند الـ I نفسها اللي
+
+103
+00:08:10,030 --> 00:08:15,760
+كانت هي الـ index للـ X، هي index قيمة X، في الحالة هذه
+
+104
+00:08:15,760 --> 00:08:19,780
+بتطلع هنا، إذا كان أقل من n، هو فعلا هتبقى أقل من n
+
+105
+00:08:19,780 --> 00:08:23,100
+لأنه مش هذا الـ proposition اللي وقفه، هو فعلا الـ
+
+106
+00:08:23,100 --> 00:08:25,240
+proposition هذا اللي وقفه، فهي فعلا هذا ما زال
+
+107
+00:08:25,240 --> 00:08:30,060
+valid، ما زال صحيح حتى اللحظة، مدام صحيح حتى اللحظة
+
+108
+00:08:30,060 --> 00:08:33,840
+أرجع لي بالـ I اللي أنت لاقيتها، فبترجع لي بالـ مين؟ بالـ
+
+109
+00:08:33,840 --> 00:08:41,090
+location اللي وقفت عنده X، فعلا ممثلة بـ Ai، بالـ AI
+
+110
+00:08:41,090 --> 00:08:47,090
+بالـ AI، ممثلة بـ AI، خلاص خلصنا، صار عندك الـ location
+
+111
+00:08:47,090 --> 00:08:53,050
+أما هيطلع صفر أو هيطلع I اللي وقف عندها، تمام، تمال
+
+112
+00:08:53,050 --> 00:08:56,310
+الـ return للـ location، خلصنا أو وقفنا، إذا والله
+
+113
+00:08:56,310 --> 00:09:02,780
+index أو zero، أنت وصلت zero، معناته مش موجود، حلل،
+
+114
+00:09:02,780 --> 00:09:07,680
+index معين، قيمة I، معناته فعليا لاقيت الـ X
+
+115
+00:09:07,680 --> 00:09:12,740
+فعليا، واللي موجودة وين الـ location تبعها، بس، تمام
+
+116
+00:09:12,740 --> 00:09:17,960
+نوع آخر من أنواع الـ search، الـ binary search، برضه
+
+117
+00:09:17,960 --> 00:09:21,610
+by default، أنا متأكد تمام أن أخذتموه، بكل بساطة binary
+
+118
+00:09:21,610 --> 00:09:27,830
+احنا عارفين أنه هو ثنائي، بمعنى كل مرة بتقسم الـ list
+
+119
+00:09:27,830 --> 00:09:33,050
+تبعك لـ two parts متساويتين، two parts، و بدك تعمل
+
+120
+00:09:33,050 --> 00:09:36,550
+elimination لواحد منهم، فهذه العملية بتظهر عملية
+
+121
+00:09:36,550 --> 00:09:40,770
+elimination، كل مرة بتقلل حجم الـ main الـ list تبعك
+
+122
+00:09:40,770 --> 00:09:44,550
+بتقلل حجمها، بتقلل حجمها، بتقلل حجمها، بس دائما الـ
+
+123
+00:09:44,550 --> 00:09:49,390
+target تبعك، أنه المتبقي لو x موجودة لازم يظل فيها
+
+124
+00:09:50,520 --> 00:09:55,230
+لو X موجودة، لابد أن يبقى ضمن الـ interval اللي
+
+125
+00:09:55,230 --> 00:10:00,670
+موجودة ضمن الـ interval اللي موجودة ضمن الـ
+
+126
+00:10:00,670 --> 00:10:07,810
+interval اللي موجودة ضمن الـ interval اللي موجودة
+
+127
+00:10:07,810 --> 00:10:08,910
+ضمن الـ interval اللي موجودة ضمن الـ interval اللي
+
+128
+00:10:08,910 --> 00:10:09,110
+موجودة ضمن الـ interval اللي موجودة ضمن الـ
+
+129
+00:10:09,110 --> 00:10:10,870
+ضمن الـ interval اللي موجودة ضمن الـ interval اللي
+
+130
+00:10:10,870 --> 00:10:12,950
+موجودة ضمن الـ interval اللي موجودة ضمن الـ
+
+131
+00:10:12,950 --> 00:10:19,130
+موجودة ضمن الـ interval اللي موجودة ضمن الـ
+
+132
+00:10:19,130 --> 00:10:23,260
+interval اللي موجودة ضمن الـ interval اللي موجودة
+
+133
+00:10:23,260 --> 00:10:27,620
+اتنين، فأنا جبت العنصر أو الـ index اللي في النص، الـ
+
+134
+00:10:27,620 --> 00:10:30,000
+index اللي في النص، طيب مدام جبت الـ index اللي في
+
+135
+00:10:30,000 --> 00:10:36,120
+النص هنا، الـ a، خلينا نسميه m، أنا فعليا حسبت الـ m
+
+136
+00:10:36,120 --> 00:10:40,480
+على أساس أن هي تساوي I زائد J على اثنين، هذا مش
+
+137
+00:10:40,480 --> 00:10:47,220
+دائما بيطلع صحيح، مش بالضروري يطلع كسر، فـ floor
+
+138
+00:10:47,880 --> 00:10:53,220
+عشان تضمن أن أنت بتتكلم عن index integer، فايش index
+
+139
+00:10:53,220 --> 00:10:55,760
+بدون أن مش integer، يعني أنت بتقول يا الله أنت في الـ
+
+140
+00:10:55,760 --> 00:10:57,380
+location اثنين ونصف، فايش حاجة تسمى الـ location
+
+141
+00:10:57,380 --> 00:11:00,720
+اثنين ونصف، يا في الخانة الأولى يا الثانية، فايش في
+
+142
+00:11:00,720 --> 00:11:05,680
+الخانة اثنين ونصف، تمام، وصلنا هنا إيش بتسوي أنت؟...
+
+143
+00:11:05,680 --> 00:11:10,080
+أجيب أن عندك قيمة x، وهي لازم تكون مرتبة، احنا حتى
+
+144
+00:11:10,080 --> 00:11:14,290
+اللحظة بنتكلم عن ordered list، في الـ linear وفي الـ
+
+145
+00:11:14,290 --> 00:11:21,010
+binary، في الحالتين بتكلم عن ordered، تمام، فإذا كان
+
+146
+00:11:21,010 --> 00:11:28,230
+...بدنا نفترض، إذا كانت X أكبر من An، معناه ذلك
+
+147
+00:11:28,230 --> 00:11:32,290
+بالنسبة لـ list مرتبة، لا يمكن يكون في كل المنطقة
+
+148
+00:11:32,290 --> 00:11:37,650
+الأقل هنا، لأنه أنا ضامن كل الـ As اللي موجودة هنا
+
+149
+00:11:37,650 --> 00:11:44,410
+كلها أقل من Am، مرتبة، الـ sequence تبعك هذا أو الـ
+
+150
+00:11:44,410 --> 00:11:47,590
+list تبعك أو الـ array تبعك مرتبة، معناه ذلك إذا
+
+151
+00:11:47,590 --> 00:11:51,030
+كانت X أكبر من العنصر اللي موجود هنا، فهي بالضرورة
+
+152
+00:11:51,030 --> 00:11:55,370
+أكبر من أي عنصر موجود أقل منها، بالضرورة، ففي الحالة
+
+153
+00:11:55,370 --> 00:11:59,610
+هذه، I جديدة، هنرجع نعيد نفس الكلام، ولكن هتيجي I
+
+154
+00:11:59,610 --> 00:12:08,310
+جديدة، I زائد واحد، على اعتبار أنه عند الـ I اللي هي
+
+155
+00:12:08,310 --> 00:12:13,150
+الـ m هذه، عفوا m زائد واحد، m زائد واحد، عند الـ m
+
+156
+00:12:13,150 --> 00:12:17,490
+نفسها، X أكبر منها، فما بدنا منها، أنا ضامن أن هي
+
+157
+00:12:17,490 --> 00:12:22,630
+خلاص عديناها، احنا عديناها، هي مش هتسويها، معنى ذلك أنه
+
+158
+00:12:22,630 --> 00:12:28,650
+بده من بعدها، فبتصبح I جديدة هي الـ m زائد واحد، m
+
+159
+00:12:28,650 --> 00:12:33,570
+زائد واحد، فصار في عندك interval جديدة تعيد عليها
+
+160
+00:12:33,570 --> 00:12:39,190
+نفس الكلام، من I لـ J، مجموعين على اثنين، فبصير m
+
+161
+00:12:39,190 --> 00:12:43,720
+جديدة هنا، وأرجع أعيد نفس الكلام، لما في الآخر تصل لـ
+
+162
+00:12:43,720 --> 00:12:48,860
+one element فقط، بقارن فيه، يا هو يا مش هو، أو انتهت
+
+163
+00:12:48,860 --> 00:12:56,740
+الجزئية، هاي كل الفكرة، هاي كل فكرة الـ الـ binary، نشوف
+
+164
+00:12:56,740 --> 00:13:02,460
+الـ code نفسه، فشرحنا، اتفقنا، هي بتعمل الـ midpoint
+
+165
+00:13:02,460 --> 00:13:08,160
+جديدة، and so on، لما تصل في الآخر لـ one element، الـ
+
+166
+00:13:08,160 --> 00:13:11,180
+one element هذا بنفحص مباشرة، هو ولا مش هو، إذا هو
+
+167
+00:13:11,180 --> 00:13:13,780
+خير وبركة، أنت فعلا ضالتك، تعمل elimination لما
+
+168
+00:13:13,780 --> 00:13:
+
+223
+00:17:22,000 --> 00:17:28,720
+أقل من العنصر اللي عند النص فبالتالي هو أقل من X ف
+
+224
+00:17:28,720 --> 00:17:32,960
+automatic إيش بسوي بقول I أو الـ ... الـ ... الـ
+
+225
+00:17:32,960 --> 00:17:35,520
+interval الجديدة المفروض تبدأ من إيش؟ من M زائد
+
+226
+00:17:35,520 --> 00:17:40,740
+واحد. من M زائد واحد لأنه فعليًا M نفسها كانت أقل من
+
+227
+00:17:40,740 --> 00:17:45,240
+X فليش أرجع أحطها أبحث عنها كمان مرة؟ خلاص بستغني عنها.
+
+228
+00:17:45,240 --> 00:17:52,380
+بنبدأ من مين؟ M زائد واحد. else إيش else يعني؟ معناها
+
+229
+00:17:52,380 --> 00:17:59,580
+ذلك أنه عكس الشرط. إيش عكس الشرط؟ X أقل أو يساوي أو
+
+230
+00:17:59,580 --> 00:18:06,060
+يساوي. عشان هيك كتبنا M بس ما قلناش نقص واحد يعني
+
+231
+00:18:06,060 --> 00:18:09,280
+ما بننقصش زي ما يقولوا أنت شاطر فيها، يقولوا آه طب ما
+
+232
+00:18:09,280 --> 00:18:13,160
+هي لأ، أنا ما قلتش إن هي ما فحصتش أو يساوي، فممكن
+
+233
+00:18:13,160 --> 00:18:17,400
+تكون تساوي، قد تكون تساوي. فعشان هيك لأ، بتضل موجودة
+
+234
+00:18:17,400 --> 00:18:21,960
+معاك. فـ J تساوي M إذا صار هيك الكلام، و I هتضل زي ما
+
+235
+00:18:21,960 --> 00:18:26,160
+هي. في الحالة هذه I هتظل كما هي. فأنا أخدت الجزء اللي
+
+236
+00:18:26,160 --> 00:18:31,360
+في أول الـ list و سبت اللي في الآخر على اعتبار أنه
+
+237
+00:18:31,360 --> 00:18:37,140
+العكس. إن X أقل. تمام. هنستمر في هذا الـ loop لعند ما
+
+238
+00:18:37,140 --> 00:18:43,760
+كل مرة يتغير I و J، I و J، I و J. يا إما جه هتصير هي
+
+239
+00:18:44,650 --> 00:18:48,730
+الـ mid index أو I هتصير الـ mid index زائد واحد.
+
+240
+00:18:48,730 --> 00:18:51,670
+فمعنى ذلك أن كل مرة أنت الـ interval اللي عندك
+
+241
+00:18:51,670 --> 00:18:55,490
+بتاخد نصها، كل مرة نصها، كل مرة نصها، كل مرة نصها في
+
+242
+00:18:55,490 --> 00:19:01,290
+مرحلة ومرحلة، هتصل لـ element واحد. الـ element
+
+243
+00:19:01,290 --> 00:19:03,970
+الوحيد هذا. تخيل معي سيناريو أنه ظل عندك two
+
+244
+00:19:03,970 --> 00:19:10,210
+elements، I و J. I و J. في الحالة دي لما تحسب الـ M إيش
+
+245
+00:19:10,210 --> 00:19:16,110
+بتساوي نص، صح؟ لما بتاخد الـ floor هتطلع I، هتفحصها
+
+246
+00:19:16,110 --> 00:19:22,650
+لجيت إن الـ X ما زالت أكبر، إيش بتقول؟ I، M زائد
+
+247
+00:19:22,650 --> 00:19:26,150
+واحد، يعني بيصير نفس الـ J. معناه ذلك بيجي في الـ
+
+248
+00:19:26,150 --> 00:19:30,640
+condition واضحات؟ هتجيب الـ condition automatic، صح؟
+
+249
+00:19:30,640 --> 00:19:35,780
+تمام. مدام وجدت الـ condition في الآخر، هتجيب، هتجيب
+
+250
+00:19:35,780 --> 00:19:40,100
+لمجال، طول ما أنت ماشي، بتشغل بالـ loop هذا لعندما تشوف في
+
+251
+00:19:40,100 --> 00:19:43,620
+الآخر، الـ element اللي ضلت في الآخر، اللي هم في الآخر مش
+
+252
+00:19:43,620 --> 00:19:47,140
+ضلوا واحد. وإن ظِلّ واحد، افحص
+
+253
+00:19:47,140 --> 00:19:51,620
+العنصر اللي ضلّ. الـ X تساوي هنا بشكل مباشر. أنت بتفحص
+
+254
+00:19:51,620 --> 00:19:55,280
+عنصر واحد فقط. يا بتساوي، يا بتساويش. إذا بتساوي، أرجع لي
+
+255
+00:19:55,280 --> 00:20:02,140
+بالـ index تبعه، خلصنا. بتساويش، Zero، انتهى الموضوع. طب
+
+256
+00:20:02,140 --> 00:20:04,840
+أنا عارف إن هذا الـ lecture مش عارف رابع خامس مرة
+
+257
+00:20:04,840 --> 00:20:07,440
+بتنشرح لكم الطريقة هذه، لأنه أكيد أخذتوها في البرمجة
+
+258
+00:20:07,440 --> 00:20:11,200
+وأكيد أخذتوها في مقدمات أي حاجة لها algorithms.
+
+259
+00:20:13,560 --> 00:20:19,200
+يعني بهيأ لي هذا الـ code مش كتير هيكون صعب عليكم
+
+260
+00:20:19,200 --> 00:20:24,180
+لمبرمجين زي حالاتكم، الكورس السنة بتاخدوا برمجة
+
+261
+00:20:24,180 --> 00:20:29,220
+فبتتكلم عن algorithm بحيث إنك بدك تجمع عناصر الـ
+
+262
+00:20:29,220 --> 00:20:32,860
+array، بس بدك تجمع عناصر الـ array. مش محتاجك طبعًا
+
+263
+00:20:32,860 --> 00:20:38,020
+for loop، مش هيك أو while. طول ما أنت أقل الـ index
+
+264
+00:20:38,020 --> 00:20:43,720
+أقل من N، اجمعه. فبدك تبدأ بـ sum equal to zero، و تجمع
+
+265
+00:20:43,720 --> 00:20:48,900
+عليه، تبدأ تجمع عليه. فلاحظوا S equal to zero هذه
+
+266
+00:20:48,900 --> 00:20:51,320
+الجزئية اللي خلتني المرة اللي فاتت قلت لكم خذوا
+
+267
+00:20:51,320 --> 00:20:56,680
+بالكم من هل أنا بتكلم عن implication ولا if and
+
+268
+00:20:56,680 --> 00:21:00,140
+only if. إذا والله هذا محدد مسبقًا، فالـ for loop كله
+
+269
+00:21:00,140 --> 00:21:05,340
+صار if and only if. بس إذا أنت محددها مسبقًا، فبتصير
+
+270
+00:21:05,340 --> 00:21:08,840
+زي ما أنتم متخيلين إن هي فعلاً if and only if، خلاص
+
+271
+00:21:08,840 --> 00:21:15,620
+يا yes يا no، انتهى. yes أكيد هتروح لـ then. no أكيد
+
+272
+00:21:15,620 --> 00:21:21,340
+هتروح لـ else. بس يكون هذا، أخذين بالكم إن اتكلمنا
+
+273
+00:21:21,340 --> 00:21:24,540
+عنها. طيب، الـ procedure، و زي ما قلنا summation بده
+
+274
+00:21:24,540 --> 00:21:27,300
+تحدد إيش الـ input تبعك. فالـ input تبعك هي الـ list
+
+275
+00:21:28,150 --> 00:21:31,570
+الشيء بالضبط، هي مجموعة integers، summation equal to
+
+276
+00:21:31,570 --> 00:21:36,110
+zero في البداية. فالعنصر S ده بلاش يكون له قيمة
+
+277
+00:21:36,110 --> 00:21:39,450
+مسبقة، بلاش يكون له قيمة مسبقة. وفي الحالة هذه
+
+278
+00:21:39,450 --> 00:21:43,320
+معناته هبدأ أجمع على قيمة سابقة موجودة. ممكن في
+
+279
+00:21:43,320 --> 00:21:46,880
+الحالة هذه إذا كان الـ compiler تبعك not smart
+
+280
+00:21:46,880 --> 00:21:49,920
+enough، هيشوف إيش الـ equation اللي كان موجود في
+
+281
+00:21:49,920 --> 00:21:54,200
+المكان اللي مخزن على الـ RAM هنا، اللي اتخصص له كقيمة
+
+282
+00:21:54,200 --> 00:22:00,160
+S، ويبدأ يحوش عليه، يبدأ يحوش عليه. كويس. for loop من
+
+283
+00:22:00,160 --> 00:22:03,840
+1 to N وخلصنا. ما هي هي الـ list كاملة، و S بتساوي
+
+284
+00:22:03,840 --> 00:22:08,940
+الـ S زائد A[I]. بترجع لنا في الآخر بمين؟ بقيمة اسمها،
+
+285
+00:22:08,940 --> 00:22:12,420
+طبعًا مش محتاج هنا لا begin ولا end، ليش؟ لأنه
+
+286
+00:22:12,420 --> 00:22:16,420
+statement واحدة، فـ statement واحدة ما فيش داعي تكبر
+
+287
+00:22:16,420 --> 00:22:22,150
+الـ code تبعك، تمام. الآن بنتكلم عن الـ sort
+
+288
+00:22:22,150 --> 00:22:27,030
+algorithms. طب، وأخذنا الـ binary، وأخذنا الـ double، الـ
+
+289
+00:22:27,030 --> 00:22:30,570
+linear على أساس إن هي sorted مسبقًا. sorted الـ list
+
+290
+00:22:30,570 --> 00:22:34,730
+تبعك صحيح؟ طب لأ، هي مش sorted، مع إن أنت بدك تعمل
+
+291
+00:22:34,730 --> 00:22:37,310
+عملية sorting. عملية الـ sorting أنت اللي بدك تعملها.
+
+292
+00:22:37,310 --> 00:22:42,130
+وهذه طبعًا برضه من الأكواد الحيوية جدًا، واللي يكاد
+
+293
+00:22:42,130 --> 00:22:47,700
+يكون ما فيش أي برنامج يخلو منها. أشهر برنامج موجودة
+
+294
+00:22:47,700 --> 00:22:50,720
+فيه هي الـ spreadsheets و الـ databases، قواعد
+
+295
+00:22:50,720 --> 00:22:53,780
+البيانات. أكيد أهم حاجة في قاعدة البيانات إنك أنت
+
+296
+00:22:53,780 --> 00:22:59,320
+تقدر تعمل إعادة ترتيب لقاعدة البيانات حسب الاسم، لأ
+
+297
+00:22:59,320 --> 00:23:04,480
+حسب الرقم الجامعي، ممكن حسب الاسم، ممكن حسب الـ GPA،
+
+298
+00:23:04,480 --> 00:23:09,680
+ممكن. فأنت اللي بتختار ساعتها تعمل sorting حسب إيش.
+
+299
+00:23:09,680 --> 00:23:12,900
+بس في النهاية الـ code لازم يكون بيقدر يفهم إيش
+
+300
+00:23:12,900 --> 00:23:15,730
+يعني عملية sorting. عملية الـ sorting. عشان هيك هي دي
+
+301
+00:23:15,730 --> 00:23:19,150
+من الأكواد المهمة جدًا، واللي محتاج تكون حافظها زي
+
+302
+00:23:19,150 --> 00:23:22,610
+اسمك. مبرمج تكون خلاص أنت في دماغك على طول حافظها،
+
+303
+00:23:22,610 --> 00:23:28,090
+فاهم كيف تشتغل، وفاهم أنواعها. لأنه طبعًا زي ما قلنا
+
+304
+00:23:28,090 --> 00:23:34,190
+في أكواد more efficient عن أكواد تانية، اللي احنا
+
+305
+00:23:34,190 --> 00:23:38,030
+هنشرحهم. بالمناسبة، هم الأفضل. المهم بس نحدد الفكرة.
+
+306
+00:23:38,030 --> 00:23:40,290
+لكن أتوقع إنه في الـ database لأ، أنتم هتاخدوا
+
+307
+00:23:40,290 --> 00:23:44,820
+أنواع غيرها. ولازم تاخدوا حاجة علاقة بالـ sorting...
+
+308
+00:23:44,820 --> 00:23:47,580
+لازم تاخدوا حاجة علاقة بالـ sorting... بس طبعًا
+
+309
+00:23:47,580 --> 00:23:51,040
+الأكواد الحديثة اللي الآن سرعتها أسرع... هذا
+
+310
+00:23:51,040 --> 00:23:54,020
+الكلام اللي عندي هو مش هيبين معنى... هيبين معنى
+
+311
+00:23:54,020 --> 00:23:55,860
+إيه؟ أنت لما نأخذ الـ complexity ونحسب الـ
+
+312
+00:23:55,860 --> 00:23:59,260
+complexity للأكواد، ونشوف إن الـ complexity هذه لأ،
+
+313
+00:23:59,260 --> 00:24:04,260
+هي ضعيفة، ممكن نحسنها، ممكن نحسنها. فزي ما قلنا في الـ
+
+314
+00:24:04,260 --> 00:24:07,940
+Excel، مهم جدًا الـ code. هي ده الـ code، هي ده من الـ
+
+315
+00:24:07,940 --> 00:24:11,920
+code المهم جدًا، واللي أنت فيه أيقونة له فوق عبارة
+
+316
+00:24:11,920 --> 00:24:17,840
+عن اسمها A-Z. هذه معناته إن أنت بتعمل sorting فعليًا.
+
+317
+00:24:17,840 --> 00:24:23,360
+أنت بس بتحدد الـ column وبتعمل بتضغط على الـ icon.
+
+318
+00:24:23,360 --> 00:24:27,220
+هذه بيعملك automatic sorting A to Z ولا Z to A،
+
+319
+00:24:27,220 --> 00:24:31,540
+اللي هي تصاعدي ولا تنازلي بس. فلاحظ إن هي حاجة by
+
+320
+00:24:31,540 --> 00:24:34,760
+default موجودة في البرامج. تمام. هناخد نوعين، هناخد
+
+321
+00:24:34,760 --> 00:24:38,340
+الـ bubble sort، وهناخد فكرة الـ insertion sort.
+
+322
+00:24:40,370 --> 00:24:43,710
+بالنسبة للـ bubble، bubble اللي هي فقاعة، يعني معناته
+
+323
+00:24:43,710 --> 00:24:46,450
+فقاعة. يعني أنا بتكلم عن عملية floating اللي هي
+
+324
+00:24:46,450 --> 00:24:50,870
+تعويم، تعويم الأرقام الصغيرة للأعلى. هي فكرتها. فأنت
+
+325
+00:24:50,870 --> 00:24:56,390
+بيكون عندك الـ array هذا الشكل، من البداية للنهاية مش
+
+326
+00:24:56,390 --> 00:25:01,030
+مرتب. لاحظين مش مرتب. طيب، عشان أرتبه بعمل عملية
+
+327
+00:25:01,030 --> 00:25:07,850
+comparison بين كل عنصرين ورا بعض، بين كل عنصرين ورا
+
+328
+00:25:07,850 --> 00:25:13,140
+بعض. فبمسك الأول والتاني. بهمني إنه دائمًا الأول يكون
+
+329
+00:25:13,140 --> 00:25:18,180
+أصغر من التاني. خلاص تمام. هاي الأول أصغر من التاني،
+
+330
+00:25:18,180 --> 00:25:21,480
+خلاص بتسيبها، وبتنزل اللي وراهم. التاني والتالت.
+
+331
+00:25:21,480 --> 00:25:27,060
+بهمني التاني أو الـ index الأقل يكون قيمته أقل. و
+
+332
+00:25:27,060 --> 00:25:32,720
+وجدنا إنه لأ، طب 3 أكبر... أصغر من 2.
+
+333
+00:25:32,720 --> 00:25:39,540
+بعكسهم. بعمل exchange أو swap زي ما قلنا قبل المرة
+
+334
+00:25:39,540 --> 00:25:44,840
+اللي فاتت، بنعمل swap X و Y. فبعكسهم هنا، صارت هنا الـ
+
+335
+00:25:44,840 --> 00:25:49,580
+31، مش هيك. بعد ما نعكس، وخلاص هذه صارت 31، 31 و 32،
+
+336
+00:25:49,580 --> 00:25:53,000
+لأ، مظبوط ما فيش فيها مشكلة. طيب 32 و 33 برضه ما فيش
+
+337
+00:25:53,000 --> 00:26:00,590
+مشكلة. 2 لازم تحل محل الـ 33، swap أو exchange.
+
+338
+00:26:00,590 --> 00:26:05,770
+عكسنا. تمام. صارت هنا تلاتة وتلاتين، تلاتة وتلاتين،
+
+339
+00:26:05,770 --> 00:26:08,590
+أربعة وتلاتين زي ما هي، ما فيش مشكلة، أسيبها. طيب،
+
+340
+00:26:08,590 --> 00:26:15,450
+أربعة وتلاتين، تلاتة. خلصنا the first stage. stage
+
+341
+00:26:15,450 --> 00:26:19,130
+تانية. بس خد بالك إنه في الـ stage التانية، عدد
+
+342
+00:26:19,130 --> 00:26:28,510
+المقارنات هيقل واحد. عدد المقارنات هيقل واحد. لماذا؟ هنا
+
+343
+00:26:28,510 --> 00:26:35,950
+كنت تعمل هذه مقارنة، هذه 2، هذه 3، هذه 4، هذه 5، 6، 7،
+
+344
+00:26:35,950 --> 00:26:41,810
+سبعة مقارنات. بمعنى أن عدد المقارنات هي N ناقص 1.
+
+345
+00:26:41,810 --> 00:26:49,090
+عندك 8 عناصر، فأنت عشان تعمل أول stage محتاج N ناقص
+
+346
+00:26:49,090 --> 00:26:54,000
+1، سبع عمليات مقارنة. طيب، السبع عمليات مقارنة عن إيش؟
+
+347
+00:26:54,000 --> 00:27:00,240
+نتجت في النهاية، أنتجت لنا حاجة عكسية. بمعنى أنت كنت
+
+348
+00:27:00,240 --> 00:27:03,520
+بتدور على الـ bubble اللي هي فقعات. فقعات ده دائمًا
+
+349
+00:27:03,520 --> 00:27:08,880
+هي الأخف، يعني القيمة الأقل. لأ. لاحظ أن الواحد هي من
+
+350
+00:27:08,880 --> 00:27:14,380
+المرتبة التانية، التالتة للتانية، مشيت بس. لكن لو
+
+351
+00:27:14,380 --> 00:27:18,520
+اتطلعت في الـ code جيدًا هتجد أنه بيعملك ترسيب لأكبر
+
+352
+00:27:18,520 --> 00:27:24,350
+قيمة في كل stage. بالضبط. فالـ 34 هذه اللي صارتها هنا،
+
+353
+00:27:24,350 --> 00:27:29,190
+لو إنها كانت موجودة هنا في أول stage هتنزل في
+
+354
+00:27:29,190 --> 00:27:36,090
+القاع. لاحظ لو هذه 34، 34، 31، أجل صارت هنا الـ 34
+
+355
+00:27:36,090 --> 00:27:41,350
+واحد أجل. فلاحظ إنه رغم إن الـ code هو bubble اسمه،
+
+356
+00:27:41,350 --> 00:27:44,670
+لكن فعليًا في كل stage اللي واضح فيه إنه اتجه
+
+357
+00:27:44,670 --> 00:27:47,870
+العنصر بينزل تحت. فأنت المرة اللي بعدها مش محتاج
+
+358
+00:27:47,870 --> 00:27:53,180
+تقارن فيه. بمعنى مش هعمل المقارنة اللي هنا، لأ، هيكون
+
+359
+00:27:53,180 --> 00:27:57,940
+عندي هاي واحدة، اتنين، تلاتة، أربعة، خمسة، ستة بس مش
+
+360
+00:27:57,940 --> 00:28:06,020
+همشي سبع مقارنات. واضحات؟ تمام. طيب، نفس الفكرة برضه
+
+361
+00:28:06,020 --> 00:28:08,700
+حاجة مهمة جدًا نأخذ بالنا منها، لأنها تسهل علينا في
+
+362
+00:28:08,700 --> 00:28:11,960
+الـ code ده ما يدينيش عدد الـ stages اللي أنا محتاجهم
+
+363
+00:28:11,960 --> 00:28:20,110
+برضه. في أقل واحد، بحيث إن لو الواحد هذا، هذا الواحد
+
+364
+00:28:20,110 --> 00:28:26,810
+كان أقل عنصر تحت في كل stage، أنت هتطلع خطوة. فلو
+
+365
+00:28:26,810 --> 00:28:31,630
+أقل عنصر هذا الـ worst case، الحالة السيئة. وكلّكم
+
+366
+00:28:31,630 --> 00:28:34,050
+عارفين برضه إن إحنا كمبرمجين دائمًا بنشتغل على الـ
+
+367
+00:28:34,050 --> 00:28:38,190
+worst case. في الـ complexity بتشتغل على الـ worst case.
+
+368
+00:28:38,190 --> 00:28:41,870
+هناخد الكلام هذا بس سابق لأوانه، لكن هنا لازم نوضحه
+
+369
+00:28:41,870 --> 00:28:45,420
+على أساس إن الـ worst case إنه بالنسبة للكبير فما فيش
+
+370
+00:28:45,420 --> 00:28:48,440
+مشكلة، الكبير حتى لو كان أول عنصر من أول stage
+
+371
+00:28:48,440 --> 00:28:53,360
+هينزل في القاع. لكن إشكاليتنا في أصغر عنصر لو كان
+
+372
+00:28:53,360 --> 00:28:58,060
+موجود فعلاً في القاع، فهو محتاج إن ناقص واحد stages
+
+373
+00:28:58,060 --> 00:29:06,120
+عشان يوصل لمكانه الصحيح. واضحات؟ تمام، ممتاز. إذا
+
+374
+00:29:06,120 --> 00:29:09,680
+الجزئية هذه واضحة، الـ code الآن هيطلع سهل وبسيط،
+
+375
+00:29:09,680 --> 00:29:15,760
+وما فيهوش مشكلة. كالتالي، هاي الـ code بفسر كل الكلام
+
+376
+00:29:15,760 --> 00:29:19,960
+اللي قلناه. فهنبدأ procedure bubble sort، وهي معطيني
+
+377
+00:29:19,960 --> 00:29:24,440
+list معينة لـ real numbers، with n أكبر من أو يساوي
+
+378
+00:29:24,440 --> 00:29:28,480
+اتنين. بمعنى real numbers حتى لو فيه قصور، خلاص
+
+379
+00:29:28,480 --> 00:29:32,380
+ما عنديش مشكلة، بنحسبها بالقصور. مين اللي أكبر؟ بنزل
+
+380
+00:29:32,380 --> 00:29:35,480
+تحت. مين أكبر؟ بنزل تحته. ومين الـ bubble، أو مين الـ
+
+381
+00:29:35,480 --> 00:29:39,780
+sort، بعمله floating، بعمله تعويم لفوق، بنطلع لفوق.
+
+382
+00:29:39,780 --> 00:29:43,880
+كويس. وطبعًا الـ array لازم تكون تساوي اتنين أو أكثر، لأن
+
+383
+00:29:43,880 --> 00:29:46,660
+إذا واحد، ما لوش معنى إن أنت بتعمل sorting لـ array هو
+
+384
+00:29:46,660 --> 00:29:49,800
+واحد. لازم تكونوا على الأقل اتنين عشان أرتبهم
+
+385
+00:29:49,800 --> 0
+
+445
+00:34:58,310 --> 00:35:03,290
+الأول لحاله طيب العنصر الثاني كأنه X وبيشوف وين
+
+446
+00:35:03,290 --> 00:35:07,640
+الـ location الصحيح تبعه عشان يحقنه في مكانه. طيب إذا
+
+447
+00:35:07,640 --> 00:35:11,260
+كان مكانه هو الـ in الجديدة فليس هناك مشكلة، بيحطه في الـ in
+
+448
+00:35:11,260 --> 00:35:15,920
+الجديدة. أو إذا كان مكانه جبل كل ما بعده بيعملهم
+
+449
+00:35:15,920 --> 00:35:21,260
+shift بواحد وبنحطه في مكانه، بنعمل shift تمام. فهذا
+
+450
+00:35:21,260 --> 00:35:28,560
+ببساطة اللي إحنا كاتبينه، الـ code بسيط جداً وأنتَ
+
+451
+00:35:28,560 --> 00:35:34,330
+عارف أنه سيكون في عندك method أو subroutine اسمه
+
+452
+00:35:34,330 --> 00:35:39,030
+search code، هتستدعيه في كل مرة، هتستدعيه في كل مرة
+
+453
+00:35:39,030 --> 00:35:43,230
+لأنه في كل أو أكثر من مرة هنستدعيه، سنستدعيه مرة واحدة،  ليس
+
+454
+00:35:43,230 --> 00:35:47,590
+هكذا، مرة واحدة، أو نقص واحد، كل مرة بدك تفترض أن
+
+455
+00:35:47,590 --> 00:35:51,330
+هو الـ X وتدور على المكان تبعه، والخطوة الإضافية بس
+
+456
+00:35:51,330 --> 00:35:56,930
+تعمل عملية insert، عملية insertion بس. كويس، الـ code
+
+457
+00:35:56,930 --> 00:36:01,720
+موجود كما قلنا، في الـ...في الكتاب مكتوب
+
+458
+00:36:01,720 --> 00:36:05,600
+واضح جداً، يعني ليس فيه مشكلة، وبسيط جداً، وأتوقع أنه
+
+459
+00:36:05,600 --> 00:36:08,700
+المفروض يكون واضح عليكم، يكون واضح عليكم في أش
+
+460
+00:36:08,700 --> 00:36:09,440
+أشياءٍ، يمين أو يسار
+
+461
+00:36:16,740 --> 00:36:21,420
+الآن قبل ما نروح للـ complexity، بدنا نفهم مقدمة
+
+462
+00:36:21,420 --> 00:36:25,220
+الـ complexity أساساً، المقدمة الأساسية بتاعت الـ
+
+463
+00:36:25,220 --> 00:36:29,820
+complexity، واللي هي لها علاقة بشيء يسمى الـ
+
+464
+00:36:29,820 --> 00:36:34,160
+order of growth. أنت بناءً على ماذا تقول أن هذا الـ
+
+465
+00:36:34,160 --> 00:36:37,640
+code أحسن من هذا؟ أنكَ تجلب الـ order تبع كل code
+
+466
+00:36:37,640 --> 00:36:43,020
+صحيح؟ جلبنا الـ order للـ code، معناها ذلك أنه قبل ما
+
+467
+00:36:43,020 --> 00:36:46,120
+أحكم على الـ order تبع الـ code لازم أكون فاهم إيش
+
+468
+00:36:46,120 --> 00:36:49,780
+يعني الـ orders؟ بدنا نكون فاهمين أساساً أصلاً إيش
+
+469
+00:36:49,780 --> 00:36:54,680
+يعني الـ orders وكيف تُقاس الـ orders هذه؟  الـ orders إيش؟
+
+470
+00:36:54,680 --> 00:36:57,740
+ليس مجرد order، معناته أنه قيمة أكبر من قيمة order
+
+471
+00:36:57,740 --> 00:37:03,900
+ثانيةً، لا، القيم هذه مع الاستمرار، بدها تكون أكبر منه
+
+472
+00:37:03,900 --> 00:37:07,300
+وليس في المرحلة الحالية. فعشان هيك إحنا بنركز على
+
+473
+00:37:07,300 --> 00:37:09,780
+الـ order كـ order، لا، إحنا بنركز على الـ order of
+
+474
+00:37:09,780 --> 00:37:18,960
+growth، بمعنى order نمو الـ function، نمو الـ function
+
+475
+00:37:18,960 --> 00:37:23,980
+نفسها. عندك code أول، الـ order تتبع function معينة، و
+
+476
+00:37:23,980 --> 00:37:27,920
+الـ code الثاني function ثانية. فإذا أنا بأقارن two
+
+477
+00:37:27,920 --> 00:37:32,200
+functions في بعض، two functions في بعض، من نموه
+
+478
+00:37:32,200 --> 00:37:38,660
+أسرع من الثاني؟ من نموه أسرع من الثاني؟  مثلًا، لو
+
+479
+00:37:38,660 --> 00:37:43,040
+قلنا مثلاً الـ function ثلاثين in زائد ثمانية، إحنا
+
+480
+00:37:43,040 --> 00:37:47,100
+عارفين أنه هذا إيش؟ first order أو linear، first
+
+481
+00:37:47,100 --> 00:37:51,060
+order أو linear. لما آجي أقارنها بـ function بهذا
+
+482
+00:37:51,060 --> 00:37:56,400
+الشكل، in تربيع زائد واحد. أنا في النهاية مش هامسك
+
+483
+00:37:56,400 --> 00:38:00,520
+أقول والله يا طيب، ما هي هي الـ first order أعلى
+
+484
+00:38:01,990 --> 00:38:06,690
+إحنا بنتكلم عن الـ growth، معدل نمو الـ function، معدل
+
+485
+00:38:06,690 --> 00:38:10,090
+نمو الـ function، لأنه ضامن إذا معدل نمو الـ function
+
+486
+00:38:10,090 --> 00:38:15,070
+أكبر فهو سيصل إلى نقطة تقاطع، وبعدها ستبقى دائماً
+
+487
+00:38:15,070 --> 00:38:20,370
+أكبر. نقطة التقاطع هي نقطة التقاطع، بعدها بعد K هنا
+
+488
+00:38:20,370 --> 00:38:25,470
+قيمة لك K، دائماً ستجد أن الـ second order أكيد أكبر
+
+489
+00:38:25,470 --> 00:38:30,690
+من first order. لأن في النهاية، ما قبل النقطة المعينة
+
+490
+00:38:30,690 --> 00:38:36,270
+هذه، هو يعتبر حكم خاطئ، يعتبر حكم خاطئ. من الذي
+
+491
+00:38:36,270 --> 00:38:41,130
+يُحكم فيه؟ الـ mail  والـ constant أو الجزء الـ DC في
+
+492
+00:38:41,130 --> 00:38:43,990
+الـ function اللي هي الثمانية مثلاً، أو الـ mail اللي
+
+493
+00:38:43,990 --> 00:38:49,680
+هو الثلاثين هنا، الـ mail عندك واحد فعلياً، ليس هكذا، أنتَ
+
+494
+00:38:49,680 --> 00:38:55,520
+ليس مُعطِيه coefficient معينة لقيمة الـ order نفسه،
+
+495
+00:38:55,520 --> 00:38:59,840
+واحد في int أربعة. هنا أنتَ مُعطِيه ثلاثين، فطبيعي في
+
+496
+00:38:59,840 --> 00:39:04,780
+بدايتها، في بداية الأرقام ستجد أن الـ linear
+
+497
+00:39:04,780 --> 00:39:11,230
+سيكون بشكل خادع، يبدو كأنه أكبر، لكن عند نقطة معينة
+
+498
+00:39:11,230 --> 00:39:16,630
+لا، سيتبين أن الـ second order أعلى. لماذا أعلى؟
+
+499
+00:39:16,630 --> 00:39:22,690
+لأنه من الأساس معدل نموه أكبر، بالضبط السلحفة و
+
+500
+00:39:22,690 --> 00:39:26,550
+الأرنب. السلحفة والأرنب، لكن أنتَ في النهاية السلحفة
+
+501
+00:39:26,550 --> 00:39:31,990
+جعلتها بعيدة كيلومترين، سبقت الأرنب، فمعنى ذلك أنه
+
+502
+00:39:31,990 --> 00:39:36,690
+مسألة وقت، هي مسألة وقت، السلحفة ستظل تمشي، ولكن معدل
+
+503
+00:39:36,690 --> 00:39:41,560
+النمو لديها في المشي بطيء، سيظل بطيئاً، الأرنب أسرع،
+
+504
+00:39:41,560 --> 00:39:46,700
+أنتَ عارف أنه سيأتي لحظة من اللحظات سيتسوق، و
+
+505
+00:39:46,700 --> 00:39:52,390
+سيعديها، الأرنب، صحيح؟ هذا في الحالة الطبيعية، ليست حالة
+
+506
+00:39:52,390 --> 00:39:55,010
+استثنائية، أنه سيذهب تحت الشجرة وينام، ولا أعرف...
+
+507
+00:39:55,010 --> 00:39:59,230
+الحالة الطبيعية، ليس هكذا، عارفين أنه في لحظة معينة
+
+508
+00:39:59,230 --> 00:40:03,390
+إذا مشيا الاثنان بنفس المعدل الطبيعي تبعهم، سيأتيان
+
+509
+00:40:03,390 --> 00:40:05,730
+يتقاربان، يتقاربان، يتقاربان، وبعدين يعديها ويمشي.
+
+510
+00:40:05,730 --> 00:40:10,850
+معنا ذلك الحكم هنا لا يأتي على القيمة اللحظية، يأتي
+
+511
+00:40:10,850 --> 00:40:17,050
+على معدل الحركة، معدل الحركة الذي سنسميه الـ order
+
+512
+00:40:17,050 --> 00:40:23,100
+of growth، واضحة، فتهمنا الـ order of growth، ليس لحظياً،
+
+513
+00:40:23,100 --> 00:40:32,700
+جداً، قيمة كل واحدة منهما، ليس لحظياً، تمام. ففي
+
+514
+00:40:32,700 --> 00:40:35,640
+الحالة هذه نقدر نقول أن الـ function الأولى هي
+
+515
+00:40:35,640 --> 00:40:40,860
+first order، وfirst order أسميها big O of N، وbig
+
+516
+00:40:40,860 --> 00:40:49,070
+O معناته at most، at most، بمعنى أعلى ما يمكن لها، هي
+
+517
+00:40:49,070 --> 00:40:54,950
+linear، ولا في حياتها ستكون أعلى من هكذا.  ممكن تكون DC،
+
+518
+00:40:54,950 --> 00:40:59,730
+ممكن تكون DC، بمعنى أنها تشمل كل اللي تحتها في الـ
+
+519
+00:40:59,730 --> 00:41:06,910
+order، DC أو inverse، أو لماذا يوجد أيضاً logarithmic؟
+
+520
+00:41:06,950 --> 00:41:10,750
+ممكن تكون أقل من الـ first order، okay، بس هنا نسميه
+
+521
+00:41:10,750 --> 00:41:15,390
+at most، at most. فإذا لما أقول function الـ order
+
+522
+00:41:15,390 --> 00:41:19,770
+تبعها big O of N، فهي في أسوأ الأحوال لن تزيد عن
+
+523
+00:41:19,770 --> 00:41:25,210
+الـ linear، الـ order تبعها في أسوأ الأحوال، يعني أعلى
+
+524
+00:41:25,210 --> 00:41:32,810
+order ممكن هو linear، هو الـ linear. بمعنى بالنسبة للـ
+
+525
+00:41:32,810 --> 00:41:39,850
+code، هي أيش المتغير الذي فيه؟ أخذنا big O، تمام. هو
+
+526
+00:41:39,850 --> 00:41:44,150
+أيّش المتغير عندكم في الأكواد؟ الـ input، بس الـ
+
+527
+00:41:44,150 --> 00:41:48,750
+arguments، بمعنى ذلك أنكَ هنا تتكلم عن الـ input،
+
+528
+00:41:48,750 --> 00:41:53,530
+بمعنى أن كل ما تزيد الـ input بواحد، الـ complexity
+
+529
+00:41:53,530 --> 00:41:57,710
+تزيد فقط بـ operation واحدة، هذا معناه لا تزيد
+
+530
+00:41:57,710 --> 00:42:02,110
+تعقيدها بشكل كبير جداً، تعقيدها بواحد فقط، فتزيد بشكل
+
+531
+00:42:02,110 --> 00:42:10,380
+واحدي، فإذا هي ماشية بشكل متناسب أيضاً مع الـ input، الـ
+
+532
+00:42:10,380 --> 00:42:13,860
+input. زِدْ لي كمان input، الزيادة تزيد عملية واحدة فقط
+
+533
+00:42:13,860 --> 00:42:18,980
+في الـ code بهذا الشكل ماشية. فإنا هنا لما آجي أقول
+
+534
+00:42:18,980 --> 00:42:23,680
+والله، عملت لي code، الـ code هذا على عددكم، عددنا
+
+535
+00:42:23,680 --> 00:42:28,280
+دعوني أقول ستين، سبعين طالب، أخذَ ستين ثانية، وجئنا
+
+536
+00:42:28,280 --> 00:42:32,740
+تأملنا، وجئنا أن الـ code هذا فعلاً هو linear، معنى
+
+537
+00:42:32,740 --> 00:42:39,920
+ذلك أن نفس الـ code لما يستخدم مع سكان غزة يصبح
+
+538
+00:42:39,920 --> 00:42:45,540
+الـ 60 مقابل 60 ثانية، يصبح مليوني مقابل مليوني
+
+539
+00:42:45,540 --> 00:42:51,020
+ثانية، فالمتغير هنا هو الـ arguments أو الـ
+
+540
+00:42:51,020 --> 00:42:55,160
+inputs أو الـ inputs، هل هما linear مع بعض أم لا؟
+
+541
+00:42:55,160 --> 00:42:57,760
+لعند linear تظهر مقبولة،  ولكن تخيل لو أنه
+
+542
+00:42:57,760 --> 00:43:02,900
+تربيعي، أو second order، معنى ذلك إذا كان الـ 60
+
+543
+00:43:02,900 --> 00:43:08,200
+كانت 60 ثانية، تربعها، فستشاهد المليوني، كم
+
+544
+00:43:08,200 --> 00:43:12,040
+سيصير مصيره، أكيد سيصبح أكثر من المليوني ثانية
+
+545
+00:43:12,040 --> 00:43:15,300
+التي كنا نحكي عنها، وفي الحالتين هي سيئة، يعني في
+
+546
+00:43:15,300 --> 00:43:17,380
+الحالتين سيئة، عندما لا نتكلم عن مليوني ثانية.
+
+547
+00:43:17,380 --> 00:43:21,340
+تمام، ولكن بدنا نوضح الفكرة، الـ concept تبعنا، تمام.
+
+548
+00:43:21,340 --> 00:43:25,300
+فهنا at most، الـ big O، بمعنى أنه في أسوأ حالتها هي
+
+549
+00:43:26,940 --> 00:43:31,040
+طيب، بالنسبة لـ n تربيع زائد واحد، هي في أسوأ حالتها
+
+550
+00:43:31,040 --> 00:43:37,340
+تربيعية، وطبعاً التربيعية order of growth أكبر من الـ
+
+551
+00:43:37,340 --> 00:43:40,500
+linear، order of growth أكبر من الـ linear، هذا
+
+552
+00:43:40,500 --> 00:43:48,060
+مفهومنا. طيب، بالنسبة للمبرمجين، معناها سيئة، لحظة، كيف؟
+
+553
+00:43:48,060 --> 00:43:52,060
+okay، إحنا هنا جاهدين نتكلم رياضيات بحتة، آه، هي
+
+554
+00:43:52,060 --> 00:43:55,420
+الـ order of growth لديها أعلى، فهي تبدو أن كلمة أعلى
+
+555
+00:43:55,420 --> 00:43:58,860
+دائماً تُوحي لنا أنها أحسن، يعني بالعكس، هنا سيئة.
+
+556
+00:43:58,860 --> 00:44:05,200
+بالنسبة لنا كمبرمجين، كمبرمجين، فهي تتناسب بشكل غير مرضي
+
+557
+00:44:05,200 --> 00:44:09,880
+مع n تربيع، فالمليون، المليونان هذان
+
+558
+00:44:09,880 --> 00:44:14,280
+سيصبحان مليون تربيع، مليون تربيع ثانية.
+
+559
+00:44:15,110 --> 00:44:20,190
+ستصبح في الحالة هذه، تمام. وطبعاً كنا عارفين أن أي
+
+560
+00:44:20,190 --> 00:44:25,630
+big O of N تربيع أكيد سيكون أسرع في الـ growth، كما
+
+561
+00:44:25,630 --> 00:44:29,970
+ما توّ شاهدنا، المعدل كان أسرع من... كما بالضبط
+
+562
+00:44:29,970 --> 00:44:35,490
+الأرنب والسلحفة، تمام. سيكون أكبر من أي big O of N
+
+563
+00:44:35,490 --> 00:44:44,570
+بشكل مطلق، جداً ما تكون الـ N هذه لها mail ثلاثين
+
+564
+00:44:44,570 --> 00:44:48,270
+in، خمسين in، مليون in، ولكن في النهاية في نقطة
+
+565
+00:44:48,270 --> 00:44:53,360
+معينة، التربيع سيتجاوزها ويمضي. النقطة هذه ممكن تبعد،
+
+566
+00:44:53,360 --> 00:44:57,260
+أو ممكن تبعد، ممكن تكون عند K كبيرة، ولكن في النهاية
+
+567
+00:44:57,260 --> 00:45:02,220
+يجب أن تكون موجودة... لها قيمة K، بعدها التربيع
+
+568
+00:45:02,220 --> 00:45:09,240
+سيتجاوز الـ... الـ linear، تمام. فكل ما كان العدد لـ
+
+569
+00:45:09,240 --> 00:45:12,660
+user records، اللي هي الـ inputs، كل ما كانت الـ
+
+570
+00:45:12,660 --> 00:45:16,460
+big O of N تربيع، أكيد كـ function تأخذ more time
+
+571
+00:45:17,350 --> 00:45:22,270
+for إيش؟ في الـ execution، للتنفيذ، لعملية التنفيذ.
+
+572
+00:45:22,270 --> 00:45:26,330
+هذا نفس الفكرة التي نتكلم عنها. إذا أنا بدأت أتحدث عن
+
+573
+00:45:26,330 --> 00:45:28,970
+الـ big O كـ function، فأنا في النهاية أقول إنها
+
+574
+00:45:28,970 --> 00:45:33,390
+function من real to real، أنه يوجد there exist C
+
+575
+00:45:33,390 --> 00:45:36,630
+and K، الـ K هذه النقطة التي نتحدث عنها، التي عند نقطة
+
+576
+00:45:36,630 --> 00:45:42,680
+معينة، الأرنب سيتجاوز السلحفة، عند نقطة معينة... أين
+
+577
+00:45:42,680 --> 00:45:46,900
+النقطة المعينة هذه؟ K... and K، عند نقطة معينة، أكيد
+
+578
+00:45:46,900 --> 00:45:53,000
+سيبين الـ order أو يظهر بشكل واضح، سيتجاوز الـ order
+
+579
+00:45:53,000 --> 00:46:00,320
+الأقل، تمام، بحيث أن for all x أكبر من k، من k فأكبر
+
+580
+00:46:00,320 --> 00:46:08,320
+ستبين أن الـ f of x أقل من c g of x، ستكون، معنى ذلك
+
+581
+00:46:08,320 --> 00:46:14,220
+أن الـ order أقل من الـ big O G، عشان هيك الـ G معناته
+
+582
+00:46:14,220 --> 00:46:18,220
+هي في أسوأ الأحوال هي الـ maximum، هي الأكبر، الـ G هي
+
+583
+00:46:18,220 --> 00:46:23,160
+الأكبر. لما قلنا توّ big O of N تربيع، معنى ذلك أنه
+
+584
+00:46:23,160 --> 00:46:26,960
+هي في جميع الأحوال لن تزيد عن الـ N تربيع، لن تزيد
+
+585
+00:46:26,960 --> 00:46:30,600
+عن الـ N تربيع. فإذا عند قيمة معينة، كما الـ linear
+
+586
+00:46:30,600 --> 00:46:34,820
+بتاع توّ، الثلاثين N زائد ثمانية، في البداية كانت
+
+587
+00:46:34,820 --> 00:46:39,820
+خادعة، كانت أعلى، في البداية كانت أعلى، صحيح؟ هذه
+
+588
+00:46:39,820 --> 00:46:48,160
+خادعة، وK معينة، وK معينة، بعدها ستصبح دائماً
+
+589
+00:46:48,160 --> 00:46:55,990
+أقل من التربيع، أقل من تربيع. فإذا الـ linear مُشمَلة
+
+590
+00:46:55,990 --> 00:46:59,850
+مع الـ big O of N تربيع، ومُشمَلة مع الـ big O of N
+
+591
+00:46:59,850 --> 00:47:06,230
+نفسها، أو تساوي، أو تساوي، تمام. فهنا نتكلم عن النقطة
+
+592
+00:47:06,230 --> 00:47:08,230
+التي تحدثنا عنها، هي ممكن تُؤخَّر، وسيأتي مثال
+
+593
+00:47:08,230 --> 00:47:11,830
+يُبيّنها أكثر، فنقدر نقول، نعبر عنها، طبعاً مصطلحات
+
+594
+00:47:11,830 --> 00:47:15,390
+كثيرة، وممكن نقول أن الـ F هذه is at most order G،
+
+595
+00:47:15,390 --> 00:47:19,730
+نسميها at most order G، فهي أعلى حالتها تساوي الـ
+
+596
+00:47:19,730 --> 00:47:26,970
+order G، كويس، أو نسميها F is big O of G، أو نسميها F
+
+597
+00:47:26,970 --> 00:47:31,930
+تساوي big O of G مباشرةً، نكتب بهذا الشكل مباشرةً، فـ
+
+598
+00:47:31,930 --> 00:47:40,210
+... أو طريقة من الطرق، F belong to big O of G،  إيش
+
+599
+00:47:40,210 --> 00:47:44,150
+يعني؟ يعني معناته أنا افترضت أن الـ F هذه عنصر، ليس
+
+600
+00:47:44,150 --> 00:47:49,740
+الـ belong هذه بتاعة الـ sets، أنها عنصر لـ set، منطق
+
+601
+00:47:49,740 --> 00:47:55,420
+الكلام؟ منطقي. عارفين لماذا؟ لأن الـ big O of G، كل الـ
+
+602
+00:47:55,420 --> 00:47:59,500
+functions التي أقل من G، كل الـ functions التي أقل
+
+603
+00:47:59,500 --> 00:48:06,100
+من G، وF واحدة منها، فـ F تنتمي لمجموعة الـ functions
+
+604
+00:48:06,100 --> 00:48:10,960
+التي أقل من G أو تساوي G. بمعنى لما تقول big O of N
+
+605
+00:48:10,960 --> 00:48:14,940
+تربيع، بكل بساطة أقدر أقول لك أن ثلاثين in
+
+606
+00:48:19,610 --> 00:48:27,110
+ثلاثين N زائد ثمانية، هي belong to big O of N تربيع.
+
+607
+00:48:27,110 --> 00:48:34,110
+بمشي الحال، بمشي الحال، linear أقل من التربيع، تمام.
+
+608
+00:48:34,110 --> 00:48:39,050
+صحيح. طيب
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..058421b3ba249ec2960154a3a65e5686b65ce9e6
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4_postprocess.srt
@@ -0,0 +1,2640 @@
+1
+00:00:05,180 --> 00:00:08,780
+بسم الله الرحمن الرحيم يعطيكوا العفو يا شباب نكمل
+
+2
+00:00:08,780 --> 00:00:11,500
+اليوم في جزئيتي ال algorithm و البداية اللي كانت
+
+3
+00:00:11,500 --> 00:00:15,620
+بسيطة وسهلة مجرد ان احنا أخدنا مجموعة statements
+
+4
+00:00:15,620 --> 00:00:20,000
+للغة وصفية على اساس ان نبدأ نتكلم عن مجموعة
+
+5
+00:00:20,000 --> 00:00:23,800
+algorithms اعتقد ان معظمها مر عليكم السابقة ان
+
+6
+00:00:23,800 --> 00:00:27,480
+انتوا اللي انا مخلصين برمجة واحد و اتنين يعني
+
+7
+00:00:27,480 --> 00:00:31,370
+ماخدين two coursesمن في البرمجة وماخدين الان
+
+8
+00:00:31,370 --> 00:00:34,530
+بتاخدوا ال data structure يعني المفروض انه خلال
+
+9
+00:00:34,530 --> 00:00:38,930
+الفترة هذه محاضراتنا يعني بسيطة مرة عليكمانا حتى
+
+10
+00:00:38,930 --> 00:00:42,910
+اتوقع انه انتوا لحالكوا على طول بت .. اتجاوبوا
+
+11
+00:00:42,910 --> 00:00:48,570
+معانا طيب من خلال المحاضرة السابقة لهذا الموضوع
+
+12
+00:00:48,570 --> 00:00:52,630
+اللي هو ال algorithms كنا اتكلمنا عن مثال وضحنا
+
+13
+00:00:52,630 --> 00:00:55,550
+فيه مجموعة list statements و اللي هي كان إيجاد ال
+
+14
+00:00:55,550 --> 00:01:00,070
+maximum value ل .. او ال maximum element من داخل
+
+15
+00:01:00,070 --> 00:01:05,140
+list معينةالآن نبدأ في مجموعة تطبيقات تانية منها
+
+16
+00:01:05,140 --> 00:01:07,860
+وأهمها اللي انتوا اكيد برضه مرت عليكم اللي هي ال
+
+17
+00:01:07,860 --> 00:01:11,220
+searching عملية ال searching في جزئية ال searching
+
+18
+00:01:11,220 --> 00:01:15,480
+اللي هي البحث طبعا في ordered list هنا بنتكلم عن
+
+19
+00:01:15,480 --> 00:01:21,420
+ال search في list مرتبة list مرتبة مرتبة اللي هي
+
+20
+00:01:21,420 --> 00:01:27,040
+بشكل تسعودي بشكلتصعدي طبعا بشكل تنازلي برضه بيمشي
+
+21
+00:01:27,040 --> 00:01:30,780
+الحال بس شوية مفاهيم بسيطة بتتغير معاك فالمفروض
+
+22
+00:01:30,780 --> 00:01:37,540
+الموضوع بيجلجش ف .. كأكواد بنفكر بالتالي given
+
+23
+00:01:37,540 --> 00:01:40,900
+list L لازم تكون فيها اندل input ال input ده و ال
+
+24
+00:01:40,900 --> 00:01:44,940
+arguments اللي هي ال list نفسها لمجموعة elements و
+
+25
+00:01:44,940 --> 00:01:50,750
+لازم تكون sorted بمعنى مصنفةمرتبة مرتبة أو مصنفة
+
+26
+00:01:50,750 --> 00:01:57,450
+تمام ب order معين و احنا قولنا ال order هذاتساعدة
+
+27
+00:01:57,450 --> 00:02:03,710
+تنازلة المهم أنه في ترتيب معين واضح سواء كان أرقام
+
+28
+00:02:03,710 --> 00:02:06,970
+أو حروف حتى
+
+29
+00:02:26,810 --> 00:02:31,010
+درجة جدا، method درجة جدا في برامج كتيرة، كويس
+
+30
+00:02:31,010 --> 00:02:36,020
+بدنا نحسب من ال X هذا اللي given عنديو في نفس
+
+31
+00:02:36,020 --> 00:02:39,960
+الوقت given عندي list بدنا نحسب هل ال X هذا موجود
+
+32
+00:02:39,960 --> 00:02:43,120
+في ال list ولا لأ إذا موجود بدي أرجعله بال إيش؟
+
+33
+00:02:43,120 --> 00:02:47,220
+بال index تبعه بال index تبعه كافي ال index؟ كافي
+
+34
+00:02:47,220 --> 00:02:50,760
+ليش؟ لأن أنا بتتكلم عن ordered list يعني معناه ذلك
+
+35
+00:02:50,760 --> 00:02:54,640
+إن ال index هو ثابت مكانه مكانه دائما ثابت أرجعله
+
+36
+00:02:54,640 --> 00:03:00,390
+بالمكان تبع ال X هذا إذا موجود داخل ال list Lتمام
+
+37
+00:03:00,390 --> 00:03:04,890
+اذا والله غير موجود ارجع ليه انه غير موجود ارجعه
+
+38
+00:03:04,890 --> 00:03:09,650
+انه غير موجود هذا ببساطة وصف او بكل بالكلام ايش
+
+39
+00:03:09,650 --> 00:03:13,610
+اللي بدنا نعمله تمام الان عشان نعمل هذا الكلام في
+
+40
+00:03:13,610 --> 00:03:17,350
+عدة algorithms بيشتغلوا في الموضوع هذا عدة
+
+41
+00:03:17,350 --> 00:03:20,930
+algorithms ممكن نعمل منهم عملية ال search منهم ال
+
+42
+00:03:20,930 --> 00:03:23,710
+linear وهذا أبسط نوع واللي أكيد أخدتهم أكيد مرة
+
+43
+00:03:23,710 --> 00:03:27,290
+عليكم لأن هذا basic يعني المفروض انهأشي مارر
+
+44
+00:03:27,290 --> 00:03:33,830
+عليكوا سابقا بتبدأ من a1 a2 to an هذه ال list ال و
+
+45
+00:03:33,830 --> 00:03:38,810
+عندك قيمة x بدكتفحص هي موجودة ولا غير موجودة بمعنى
+
+46
+00:03:38,810 --> 00:03:42,210
+عملية search إذا موجودة ارجعلي بال index في ال
+
+47
+00:03:42,210 --> 00:03:44,450
+location الأول ولا التاني ولا الخامس ولا في ال
+
+48
+00:03:44,450 --> 00:03:48,910
+location in ارجعلي بال index بس طيب مش موجودة
+
+49
+00:03:48,910 --> 00:03:52,530
+اعطيني دلالة ارجعلي بأي حاجة أستدل منها أن انت
+
+50
+00:03:52,530 --> 00:03:56,930
+مالجتهش غير موجود ارجعلي بصفر مثلا ارجعلنا ب zero
+
+51
+00:03:57,800 --> 00:04:02,800
+طبعا فإذا procedure هيبدأنا ال code طبعنا هنسميه
+
+52
+00:04:02,800 --> 00:04:06,180
+باسم معين التفكير بالنسبالي أنه لازم يكون في
+
+53
+00:04:07,050 --> 00:04:10,170
+arguments ال input اللي انا محتاجها مستحيل اعرف
+
+54
+00:04:10,170 --> 00:04:13,530
+اشتغل بدونها هي قيمة ال X X اللي انت بتدور عليها
+
+55
+00:04:13,530 --> 00:04:17,850
+اللي هي ال integer كويس زائد ال list نفسها تكتب
+
+56
+00:04:17,850 --> 00:04:24,630
+ليها AB A1 A2 to AN ماشي تكتب ليها L كويس و
+
+57
+00:04:24,630 --> 00:04:29,590
+distinct integers okay خلاص فهمنا بس بدك توضح ان
+
+58
+00:04:29,590 --> 00:04:33,410
+انت بتكلم عن index ببدأ من واحدال index بيبدأ من
+
+59
+00:04:33,410 --> 00:04:36,550
+واحد لان انتوا كلكوا عارفين ان احنا في ال array
+
+60
+00:04:36,550 --> 00:04:40,890
+بنشير للعنصر باستخدام ال index تبعه مافيش طريقة
+
+61
+00:04:40,890 --> 00:04:45,190
+تانية انت عشان تعرف ال index او element معين
+
+62
+00:04:45,190 --> 00:04:50,090
+بتعرفه من خلال ال index تبعه تمام بنبدأ بواحد
+
+63
+00:04:50,090 --> 00:04:54,040
+معناته كأن انا بدي اجف عند ال index الأولبمعنى بدي
+
+64
+00:04:54,040 --> 00:04:57,520
+افحص العنصر الأول ال element الأول منطقية جدا
+
+65
+00:04:57,520 --> 00:04:59,920
+مافيش قبل ال element الأول فبدي أبدأ افحص من ال
+
+66
+00:04:59,920 --> 00:05:05,180
+element الأول ونبدأ الآن ال while أبسط شغله ان انت
+
+67
+00:05:05,180 --> 00:05:10,040
+تبقى تعمل for loop ال for loop هذا يبقى شغال يبقى
+
+68
+00:05:10,040 --> 00:05:17,070
+شغال بحيث انه يعمل scan على ال listامتى هيجف؟ عندك
+
+69
+00:05:17,070 --> 00:05:20,670
+حالتين ممكن يجف فيهم اما ان يلاقي X او يخلص ال
+
+70
+00:05:20,670 --> 00:05:26,190
+list مش هيك؟ مافيش شي تالت في الحالتين بوقف ال
+
+71
+00:05:26,190 --> 00:05:31,290
+loop تبعه والله لاجي ال X المفروض يجف مالاجيش ال
+
+72
+00:05:31,290 --> 00:05:38,310
+X؟بدو يكمل لعند ما يخلص ال in يعمل in مرة من
+
+73
+00:05:38,310 --> 00:05:41,190
+عمليات الفحص أكتر من هيك خلاص وقف لأن هو عارف
+
+74
+00:05:41,190 --> 00:05:44,690
+مسبقا ان ال list تبعته ال length تبعتها in خلصنا
+
+75
+00:05:44,690 --> 00:05:49,990
+فإذن while طول ما I أقل من أو يساوي in فهو شغال
+
+76
+00:05:49,990 --> 00:05:54,870
+معناته في عناصر مش شايف طول ما هو أقل من ال length
+
+77
+00:05:54,870 --> 00:06:00,010
+معناته شغال and x لا تساوي ai ال I اللي أنا موجود
+
+78
+00:06:00,010 --> 00:06:05,290
+عندها حاليافإذن لا لجأ X ولا وصل لنهاية ال list
+
+79
+00:06:05,290 --> 00:06:11,810
+استمر فإذن استمر كويس و I بتساوي I زائد واحد ال
+
+80
+00:06:11,810 --> 00:06:16,470
+incrementstatement اللي موجود عندك increment زود
+
+81
+00:06:16,470 --> 00:06:20,570
+كل مرة زود ورجع افحص زود ورجع افحص زود ورجع افحص
+
+82
+00:06:20,570 --> 00:06:24,330
+خلاص مافيش اكتر من هيك اللي عملنا لا begin ولا end
+
+83
+00:06:24,330 --> 00:06:28,490
+مش هيك يعني مافتحتش اقواس ال curly braces تبعتك
+
+84
+00:06:28,490 --> 00:06:32,310
+انا مش محتاج اللي الشرط هذا فالجواب هذا بس لا اكتر
+
+85
+00:06:32,310 --> 00:06:38,130
+ولا اقل فإذا هاي ال loop تبعك فقط بس هاي كل ال
+
+86
+00:06:38,130 --> 00:06:46,420
+loop امتى حقيقة زي ما قلنا يصبح اكبر منصحيح؟ طيب
+
+87
+00:06:46,420 --> 00:06:53,820
+إذا وصلت لأكبر من معناه ذلك إنه ما جابش X ما جابش
+
+88
+00:06:53,820 --> 00:06:59,400
+X ليش؟ لأنه إذا وصلت لأكبر من أنت عديت N أنت أصبح
+
+89
+00:06:59,400 --> 00:07:05,320
+خلاص بعدها أنت آخر مرة وصلت ل I بتساوي N وماحققتش
+
+90
+00:07:05,320 --> 00:07:10,980
+الشرط هذا وإلا كان وجفت بس مدام ما وجفتش معناته
+
+91
+00:07:10,980 --> 00:07:16,160
+فعليا ماحققتش إن هي تساوي ANاخر عنصر ماتحققش روح
+
+92
+00:07:16,160 --> 00:07:21,480
+اتزودت واحد ف automatically صرت N زائد واحد الان N
+
+93
+00:07:21,480 --> 00:07:25,780
+زائد واحد هذا ال condition هو اللي عطل ال
+
+94
+00:07:25,780 --> 00:07:29,320
+proposition هو اللي عطل ال proposition فطلعنا عشان
+
+95
+00:07:29,320 --> 00:07:34,100
+تيجي تفحص انت أجل من أو يساوي in طبعا فعليا انت
+
+96
+00:07:34,100 --> 00:07:39,180
+صرت أكبر من صحيح فإذا false false إيش يعني انا
+
+97
+00:07:39,180 --> 00:07:41,240
+هيرجع بصفر يعني مالاجتش
+
+98
+00:07:43,570 --> 00:07:47,970
+لكن لو اللي ود في ال for loop مش ال condition مش
+
+99
+00:07:47,970 --> 00:07:51,010
+ال .. ال .. ال .. ال .. ال atomic proposition
+
+100
+00:07:51,010 --> 00:07:55,970
+الأول ال atomic proposition التاني انت عند I معينة
+
+101
+00:07:55,970 --> 00:08:05,790
+وجدت انه X تساوي AI تساوت صار هنا false اطلعت بدون
+
+102
+00:08:05,790 --> 00:08:10,030
+ما تنفذ هذه صحيح فانت ما زلت عند ال I نفسها اللي
+
+103
+00:08:10,030 --> 00:08:15,760
+كانت هي ال index لل Xهي index قيمة X في الحالة هذه
+
+104
+00:08:15,760 --> 00:08:19,780
+بتطلع هنا إذا كان أقل من N هو فعلا هتبقى أقل من N
+
+105
+00:08:19,780 --> 00:08:23,100
+لأنه مش هذا ال proposition اللي وجفها هو فعلا ال
+
+106
+00:08:23,100 --> 00:08:25,240
+proposition هذا اللي وجفها فهي فعلا هذا مازال
+
+107
+00:08:25,240 --> 00:08:30,060
+valid مازال صحيح حتى اللحظة مدام صحيح حتى اللحظة
+
+108
+00:08:30,060 --> 00:08:33,840
+ارجعلي بال I اللي انت لجيتها فبترجعلي بال مين بال
+
+109
+00:08:33,840 --> 00:08:41,090
+location اللي وكفت عنده X فعلا ممثلة ب AMبال AI
+
+110
+00:08:41,090 --> 00:08:47,090
+بال AI ممثلة ب AI خلاص خلصنا صار عندك ال location
+
+111
+00:08:47,090 --> 00:08:53,050
+اما هيطلع صفر او هيطلع I اللي وجف عندها تمام تمال
+
+112
+00:08:53,050 --> 00:08:56,310
+ال return لل location خلصنا او اتجفنا اذا والله
+
+113
+00:08:56,310 --> 00:09:02,780
+index او zero انت وصلتzero معناته مش موجود حلل،
+
+114
+00:09:02,780 --> 00:09:07,680
+index معين قيمة I معناته فعليا تحدى التلة ال X
+
+115
+00:09:07,680 --> 00:09:12,740
+فعليا و اللي موجودة وين ال location تبعها بس تمام
+
+116
+00:09:12,740 --> 00:09:17,960
+نوع أخر من أنواع ال search ال binary search برضه
+
+117
+00:09:17,960 --> 00:09:21,610
+by default أنا متأكد تمام أن أخدتهبكل بساطة binary
+
+118
+00:09:21,610 --> 00:09:27,830
+احنا عارفين ان هو ثنائي بمعنى كل مرة بتجسم ال list
+
+119
+00:09:27,830 --> 00:09:33,050
+تبعك ل two parts متساويتين two parts و بدك تعمل
+
+120
+00:09:33,050 --> 00:09:36,550
+elimination لواحد منهم فهذه العملية بتظهر عملية
+
+121
+00:09:36,550 --> 00:09:40,770
+elimination كل مرة بتجلل حجم ال main ال list تبعتك
+
+122
+00:09:40,770 --> 00:09:44,550
+بتجلل حجمها بتجلل حجمها بتجلل حجمها بس دائما ال
+
+123
+00:09:44,550 --> 00:09:49,390
+target تبعك انه المتبقي لو x موجودة لازم يظل فيها
+
+124
+00:09:50,520 --> 00:09:55,230
+لو X موجودة لابد ان يبقى ضمن الالـ Interval اللي
+
+125
+00:09:55,230 --> 00:10:00,670
+موجودة ضمن الـ Interval اللي موجودة ضمن الـ
+
+126
+00:10:00,670 --> 00:10:07,810
+Interval اللي موجودة ضمن الـ Interval اللي موجودة
+
+127
+00:10:07,810 --> 00:10:08,910
+ضمن الـ Interval اللي موجودة ضمن الـ Interval اللي
+
+128
+00:10:08,910 --> 00:10:09,110
+موجودة ضمن الـ Interval اللي موجودة ضمن الـ
+
+129
+00:10:09,110 --> 00:10:10,870
+ضمن الـ Interval اللي موجودة ضمن الـ Interval اللي
+
+130
+00:10:10,870 --> 00:10:12,950
+موجودة ضمن الـ Interval اللي موجودة ضمن الـ
+
+131
+00:10:12,950 --> 00:10:19,130
+موجودة ضمن الـ Interval اللي موجودة ضمن الـ
+
+132
+00:10:19,130 --> 00:10:23,260
+Interval اللي موجودة ضمن الـ Interval اللي موجعلى
+
+133
+00:10:23,260 --> 00:10:27,620
+اتنين فانا جبت العنصر او ال index اللي في النص ال
+
+134
+00:10:27,620 --> 00:10:30,000
+index اللي في النص طيب مدام جبت ال index اللي في
+
+135
+00:10:30,000 --> 00:10:36,120
+النص هنا ال a خلينا نسميه المد انا فعليا حسبت ال M
+
+136
+00:10:36,120 --> 00:10:40,480
+على اساس ان هي تساوي I زائد J على اتنين هذا مش
+
+137
+00:10:40,480 --> 00:10:47,220
+دايما بيطلع كسر صحيح؟ مش بالضروري يطلع كسر ف floor
+
+138
+00:10:47,880 --> 00:10:53,220
+عشان تضمن ان انت بتتكلم عن index انتجر فاش index
+
+139
+00:10:53,220 --> 00:10:55,760
+بدون ان مش انتجر يعني انت بتقول يا الله انت في ال
+
+140
+00:10:55,760 --> 00:10:57,380
+location اتنين و نص فاش حاجة تسمي ال location
+
+141
+00:10:57,380 --> 00:11:00,720
+اتنين و نص يا في الخانة الأولى يا التانية فاش في
+
+142
+00:11:00,720 --> 00:11:05,680
+الخانة اتنين و نص تمام وصلنا هنا ايش بتسوي انت ..
+
+143
+00:11:05,680 --> 00:11:10,080
+اجيب ان عندك قيمة x و هي لازم تكون مرتبة احنا حتى
+
+144
+00:11:10,080 --> 00:11:14,290
+اللحظة بنتكلم عن ordered listفي ال linear و في ال
+
+145
+00:11:14,290 --> 00:11:21,010
+binary في الحالتين بتكلم عن ordered تمام فإذا كان
+
+146
+00:11:21,010 --> 00:11:28,230
+.. بدنا نفترض إذا كانت X أكبر من AN معناه ذلك
+
+147
+00:11:28,230 --> 00:11:32,290
+بالنسبة ل list مرتبة لا يمكن يكون في كل المنطقة
+
+148
+00:11:32,290 --> 00:11:37,650
+الأقل هنا لأنه أنا ضامن كل ال As اللي موجودة هنا
+
+149
+00:11:37,650 --> 00:11:44,410
+كلها أقل من AM مرتبالـ sequence تبعك هذا أو ال
+
+150
+00:11:44,410 --> 00:11:47,590
+list تبعتك أو ال array تبعتك مرتبة معناه ذلك إذا
+
+151
+00:11:47,590 --> 00:11:51,030
+كانت X أكبر من العنصر اللي موجود هنا فهي بالضرورة
+
+152
+00:11:51,030 --> 00:11:55,370
+أكبر من أي عنصر موجود أقل منها بالضرورة ففي الحالة
+
+153
+00:11:55,370 --> 00:11:59,610
+هذه I لجديدة هنرجع نعيد نفس الكلام ولكن هتيجي I
+
+154
+00:11:59,610 --> 00:12:08,310
+جديدة I زائد واحد على اعتبار أنه عند ال I اللي هي
+
+155
+00:12:08,310 --> 00:12:13,150
+ال M هذه عفوا M زائد واحدم زائد واحد عند ال M
+
+156
+00:12:13,150 --> 00:12:17,490
+نفسها X أكبر منها فمابدهاش منها انا ضامن ان هي
+
+157
+00:12:17,490 --> 00:12:22,630
+خلاص عدناها احنا عدناها هي مش هتسويها معنى ذلك انه
+
+158
+00:12:22,630 --> 00:12:28,650
+بده من بعدها فبتصبح I لجديدة هي ال M زائد واحد M
+
+159
+00:12:28,650 --> 00:12:33,570
+زائد واحد فصار في عندك interval جديدة تعيد عليها
+
+160
+00:12:33,570 --> 00:12:39,190
+نفس الكلام من I ل J مجموعين على اتنين فبصير M
+
+161
+00:12:39,190 --> 00:12:43,720
+جديدةهنا و ارجع ايد نفس الكلام لما في الآخر تصل ل
+
+162
+00:12:43,720 --> 00:12:48,860
+one element فقط بقارن فيه يا هو يا مش هو او انتهت
+
+163
+00:12:48,860 --> 00:12:56,740
+الجثة هاي كل الفكرة هاي كل فكرة ال ال binary نشوف
+
+164
+00:12:56,740 --> 00:13:02,460
+ال code نفسه فشرحنا اتفقنا هي بتعمل ال midpoint
+
+165
+00:13:02,460 --> 00:13:08,160
+لجديدة and so on لما تصل في الآخر ل one elementالـ
+
+166
+00:13:08,160 --> 00:13:11,180
+one element هذا بنفحص مباشرة هو ولا مش هو إذا هو
+
+167
+00:13:11,180 --> 00:13:13,780
+خير وبركة أنت فعلاً ضالتك تعمل elimination لما
+
+168
+00:13:13,780 --> 00:13:18,060
+وصلت ل element واحد يا بيسوي x أو انه بيسويش x
+
+169
+00:13:18,060 --> 00:13:22,640
+معناته x غير موجودة x غير موجودة لأن كل اللي أقل
+
+170
+00:13:22,640 --> 00:13:28,060
+هو أقل من x وكل اللي أكبر هو أكبر من x فإذا x
+
+171
+00:13:28,060 --> 00:13:32,080
+المفروض هي تكون between them لكن مش موجودة هي مش
+
+172
+00:13:32,080 --> 00:13:37,140
+موجودة تمام هتشوف ال codeك .. ك code برضه
+
+173
+00:13:37,140 --> 00:13:40,900
+procedure binary search و بنفتح الأقواص عشان نحدد
+
+174
+00:13:40,900 --> 00:13:43,760
+إيش ال inputs اللي بدنا إياها لل code هذا أول شغل
+
+175
+00:13:43,760 --> 00:13:48,940
+محتاج ال X اللي أنا بدور عليها و أنت بدور عليها
+
+176
+00:13:48,940 --> 00:13:53,900
+خليني أقول في واحدة من الوزارات و بدك خدمة معينة
+
+177
+00:13:53,900 --> 00:13:58,000
+أو أول حاجة بده يفتح ملفك هيقولك هاتلي رقم الهوية
+
+178
+00:13:58,000 --> 00:14:02,660
+هي ال Xصحيح؟ هاتل الرقم الهوية عشان يضرب رقم
+
+179
+00:14:02,660 --> 00:14:06,100
+الهوية افتح .. يفتح ملفك طب هل انت لحالك الوحيد
+
+180
+00:14:06,100 --> 00:14:09,580
+اللي إلك ملف؟ في عندك فوق لتنين مليون بني أدم في
+
+181
+00:14:09,580 --> 00:14:13,020
+غزا اللي هم ملفات مش شيخ إذا بتكلم عن سكان عدد غزا
+
+182
+00:14:13,020 --> 00:14:16,440
+فانت فوق لتنين مليون بدك تعمل search فيهم هدولة
+
+183
+00:14:16,440 --> 00:14:21,810
+listالاتنين مليون هدولة هدولة ال list تبعتك كويس و
+
+184
+00:14:21,810 --> 00:14:24,730
+رقم الهوية هي ال X عشان هيك بقولك هذا من الحاجات
+
+185
+00:14:24,730 --> 00:14:28,330
+الحيوية جدا كأكواد كنوع أكواد اللي هي ال search
+
+186
+00:14:28,330 --> 00:14:32,570
+codes من الحاجات الحيوية جدا اللي بتستخدم في كتير
+
+187
+00:14:32,570 --> 00:14:37,070
+برامج انت عندك رقم و بدك تدور عليه رقم هوية مثلا
+
+188
+00:14:37,070 --> 00:14:43,450
+for example تمام فإذا نبدأ كتالي X لازم تكون موطع
+
+189
+00:14:43,450 --> 00:14:46,530
+انتجر رقم هويتك انتجر فيه عندكوا حد رقم هويته مش
+
+190
+00:14:46,530 --> 00:14:52,100
+انتجرأكيد integer طبعا ال list اللي موجودة مجموعة
+
+191
+00:14:52,100 --> 00:14:57,140
+integers برضه متنوعة مختلفة مش هكونوا مختلف فيهم
+
+192
+00:14:57,140 --> 00:15:01,260
+قصور و بتبدأ زي ما قلنا ال I و ال J ليش؟ لأن أنا
+
+193
+00:15:01,260 --> 00:15:07,080
+بدي أعمم ال interval في أول iteration في أول لفة
+
+194
+00:15:07,080 --> 00:15:10,100
+في البرنامج هي بتكون بادية فعلا من الواحد و راحة
+
+195
+00:15:10,100 --> 00:15:13,940
+to end بس بعد هيك لأ مش هتكون بادية من الواحد عشان
+
+196
+00:15:13,940 --> 00:15:19,770
+هيك مبدأيا بتحط لهابدأوا النهاية I ل J و بنبدأ I
+
+197
+00:15:19,770 --> 00:15:26,770
+بواحد J بال N و نبدأ بعد هيك طول ما I أقل من J فهم
+
+198
+00:15:26,770 --> 00:15:31,270
+ماوصلوش في مرحلة ال elimination التقصير تقصير أو
+
+199
+00:15:31,270 --> 00:15:36,510
+تقليل ال duration أن هم وصلوا لنفس المقطة ما زالوا
+
+200
+00:15:36,510 --> 00:15:40,370
+I أقل من J I أقل من J I أقل من J I أقل من J I أقل
+
+201
+00:15:40,370 --> 00:15:43,210
+من J لما ينطبقوا على بعض بيقولوا اه خلاص وقف أنا
+
+202
+00:15:43,210 --> 00:15:47,960
+وصلت لعنصر واحديا هو يا مش هو .. يا هو يا مش هو
+
+203
+00:15:47,960 --> 00:15:53,340
+فإذا طول ما I أقل من J هنا في شوية statements بدنا
+
+204
+00:15:53,340 --> 00:15:57,720
+نعملهم ف begin و end لإن مش هيكون على جد statement
+
+205
+00:15:57,720 --> 00:16:01,300
+واحدة بدنا نعملها أول شغلة statement واضحة خطوة
+
+206
+00:16:01,300 --> 00:16:06,120
+ضرورية بدها تحسب ال mid point أو ال mid index ال
+
+207
+00:16:06,120 --> 00:16:09,060
+index الوسطي طب هاي لحالها بدون ال begin و ال end
+
+208
+00:16:09,060 --> 00:16:12,920
+معناته هفهم أنه هيبقى بس يحسب Mبالنسبة لل while
+
+209
+00:16:12,920 --> 00:16:17,800
+هذه او جاعت في problem ايش بنسميها ال runtime
+
+210
+00:16:17,800 --> 00:16:21,360
+error هنا صار عندك runtime error اذا ما كتبتش
+
+211
+00:16:21,360 --> 00:16:24,960
+begin بدون ال begin مااخدين بالكم ان الجزية هذه
+
+212
+00:16:24,960 --> 00:16:31,080
+بدون begin و end هيفهم ال while ان هذا فقط جوابها
+
+213
+00:16:31,080 --> 00:16:37,480
+بس ال condition هذا هيجوابه بس هي ال event تبعته
+
+214
+00:16:38,480 --> 00:16:44,080
+الـ F هذه لأ خارجية لكن بدها تكون محسوبة بيجن اند
+
+215
+00:16:44,080 --> 00:16:47,500
+فبفهم ان كل هدول هيك على بعض statement واحدة جواب
+
+216
+00:16:47,500 --> 00:16:51,720
+ل ال condition او ل ال proposition I أقل من J تمام
+
+217
+00:16:51,720 --> 00:16:55,560
+حسبنا ال mid و أخدنا ال floor لإن مش متوقع دائما
+
+218
+00:16:55,560 --> 00:17:00,620
+هتكون integer فبتاخدها ال floor و بتفحص فحصنا هنا
+
+219
+00:17:00,620 --> 00:17:06,200
+العنصر اللي عند ال mid point او ال mid indexالعنصر
+
+220
+00:17:06,200 --> 00:17:11,160
+هذا أقل ولا أكبر من X إذا والله X أكبر X أكبر
+
+221
+00:17:11,160 --> 00:17:16,900
+فمعنى ذلك كل اللي أقل لا يمكن تكون X موجودة فيه X
+
+222
+00:17:16,900 --> 00:17:22,000
+أكبر من العنصر اللي في النص فكل ما فيه قبل النص هو
+
+223
+00:17:22,000 --> 00:17:28,720
+أقل من العنصر اللي عند النص فبالتالي هو أقل منX ف
+
+224
+00:17:28,720 --> 00:17:32,960
+automatic ايش بسوي بقول I او ال .. ال .. ال
+
+225
+00:17:32,960 --> 00:17:35,520
+interval الجديدة المفروض تبدأ من ايش من M زائد
+
+226
+00:17:35,520 --> 00:17:40,740
+واحد من M زائد واحد لأنه فعليا M نفسها كانت اقل من
+
+227
+00:17:40,740 --> 00:17:45,240
+X فليش ارجع احطها ابحث عنها كمان مرة خلاص بستفنيها
+
+228
+00:17:45,240 --> 00:17:52,380
+بنبدأ من مين M زائد واحد else ايش else يعني معنى
+
+229
+00:17:52,380 --> 00:17:59,580
+ذلك انه عكس الشرط ايش عكس الشرطX أقل أو يساوي أو
+
+230
+00:17:59,580 --> 00:18:06,060
+يساوي عشان هيك كتبنا M بس ماقولناش نقص واحد يعني
+
+231
+00:18:06,060 --> 00:18:09,280
+مابتناش زي ما يقولوا انت شاطر فيها يقولوا اه طب ما
+
+232
+00:18:09,280 --> 00:18:13,160
+هي لأ انا ماقولتش ان هي مافحستش أو يساوي فممكن
+
+233
+00:18:13,160 --> 00:18:17,400
+تكون تساوي قد تكون تساوي فعشان هيك لأ بتضل موجودة
+
+234
+00:18:17,400 --> 00:18:21,960
+معاك ف J تساوي M إذا صار هيك الكلام و I هتضل زي ما
+
+235
+00:18:21,960 --> 00:18:26,160
+هيفي الحالة هذه I هتظل كما هي فانا أخدت الجزء اللي
+
+236
+00:18:26,160 --> 00:18:31,360
+في أول ال list و سبت اللي في الآخر على اعتبار انه
+
+237
+00:18:31,360 --> 00:18:37,140
+العكس ان X أقل تمام هنستمر في هذا ال loop لعند ما
+
+238
+00:18:37,140 --> 00:18:43,760
+كل مرة يتجل I و J I و J I و J يا إما جه هتصير هي
+
+239
+00:18:44,650 --> 00:18:48,730
+الـ mid index او I هتصير ال mid index زائد واحد
+
+240
+00:18:48,730 --> 00:18:51,670
+فمعنى ذلك ان كل مرة انت ال interval اللي عندك
+
+241
+00:18:51,670 --> 00:18:55,490
+بتاخد نصها كل مرة نصها كل مرة نصها كل مرة نصها في
+
+242
+00:18:55,490 --> 00:19:01,290
+مرحلة و مرحلة هتصل ل element واحد ال element
+
+243
+00:19:01,290 --> 00:19:03,970
+الوحيد هذا تخيل معي سيناريو انه ضل عندك two
+
+244
+00:19:03,970 --> 00:19:10,210
+elements I و JI و J في الحالة دي لما تحسب ال M إيش
+
+245
+00:19:10,210 --> 00:19:16,110
+بتساوي نص صح لما بتاخد ال floor هتطلع I هتفحصها
+
+246
+00:19:16,110 --> 00:19:22,650
+لجيتها إنه ال X ما زالت أكبر إيش بتقول I M زائد
+
+247
+00:19:22,650 --> 00:19:26,150
+واحد يعني بيصير نفس ال J معناه ذلك بيجي في ال
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+تمام مدام وجف ال condition في الآخر هيجف هيجف
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+لمجال طول ما حضرك تشطل باللوب هذا لعندما تشوف في
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+الآخر الام اللي ضلت في الآخر اللي هم في الآخر مش
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+للانصر اللي ضلهل X تسوي هنا بشكل مباشر انت بتفحص
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+عنصر واحد فقط يا بتسوي يا بتسوهش اذا بتسوي ارجالي
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+255
+00:19:55,280 --> 00:20:02,140
+بال index تبعه خلصنا بتسوهاش Zero انتهى الموضوع طب
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+256
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+انا عارف ان هذا اكلكت مش عارف رابع خمس مرة
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+وأخيرا أخدتوها في مقدمات أي حاجة إلها algorithms
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+يعني بتهيألي هذا يعني code مش كتير هيكون صعب عليكم
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+00:20:19,200 --> 00:20:24,180
+لمبرمجين زي حالاتكم الكوب سنة بتاخدوا برمجة
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+فبتتكلم عن algorithm بحيث انك بدك تجمع عناصر ال
+
+262
+00:20:29,220 --> 00:20:32,860
+array بس بدك تجمع عناصر ال array مش محتاجك طبعا
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+for loop مش هيك او whileطول ما انت اقل ال index
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+اقل من N جمعه فبدك تبدأ ب sum equal to zero و تجمع
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+عليه تبدأ تجمع عليه فلاحظوا S equal to zero هذه
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+الجزئية اللي خلتني المرة اللي فاتت قلتلكوا خدوا
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+بالكم من هل انا بتكلم عن implication ولا if and
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+268
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+only if اذا والله هذا محدد مسبقا فال for loop كله
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+صار if and only ifبس اذا انت محددها مسبقا فبتصير
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+يا yes يا no انتهى yes اكيد هتروح ل Latin نه اكيد
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+هتروح ل else بس يكون هذا ماخدين بالكم انه اتكلمنا
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+عنها طيب ال procedure و زي ما قلنا summation بده
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+تحدد ايش ال input تبعك فال input تبعك هي ال list
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+الشيء بالظبط هي مجموعة integers summation equal to
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+zero في البداية فالعنصر S ده بلاش يكون له قيمة
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+مسبقة بلاش يكون له قيمة مسبقة وفي الحالة هذه
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+الحالة هذه إذا كان ال compiler تبعك not smart
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+280
+00:21:46,880 --> 00:21:49,920
+enough هيشوف إيش ال equation اللي كان موجود في
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+00:21:49,920 --> 00:21:54,200
+المكان اللي مخزن على ال RAM هنا اللي اتخصصله كقيمة
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+S و يبدأ يحوش عليه يبدأ يحوش عليه كويس for loop من
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+283
+00:22:00,160 --> 00:22:03,840
+1 to N و خلصنا ما هي هي ال list كاملة و S بتساوي
+
+284
+00:22:03,840 --> 00:22:08,940
+ال S زائد A Iبترجعنا في الآخر بمين؟ بقيمة اسمة،
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+285
+00:22:08,940 --> 00:22:12,420
+طبعا مش محتاج هنا لا begin ولا end، ليش؟ لأنه
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+286
+00:22:12,420 --> 00:22:16,420
+statement واحدة، ف statement واحدة مافيش داعي تكبر
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+287
+00:22:16,420 --> 00:22:22,150
+ال code تبعك، تمامالان بنتكلم عن ال sort
+
+288
+00:22:22,150 --> 00:22:27,030
+algorithms طب و أخدنا ال binary و أخدنا double ال
+
+289
+00:22:27,030 --> 00:22:30,570
+linear على أساس ان هي sorted مسبقا sorted ال list
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+290
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+تبعتك صحيح؟ طب لأ هي مش sorted مع أن انت بدك تعمل
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+عملية sorting عملية ال sorting انت اللي بدك تعملها
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+وهذه طبعا برضه من الأكواد الحيوية جدا و اللي يكاد
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+يكون مافيش اي برنامج يخلو منهاأشهر برنامج موجودة
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+294
+00:22:47,700 --> 00:22:50,720
+فيه هي ال spreadsheets و ال databases قواعد
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+295
+00:22:50,720 --> 00:22:53,780
+البيانات أكيد أهم حاجة في قاعدة البيانات أنك انت
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+تقدر تعمل إعادة ترتيب لقاعدة البيانات حسب الإسم لأ
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+00:22:59,320 --> 00:23:04,480
+حسب الرقم الجامعي ممكن حسب الإسم ممكن حسب ال GPA
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+298
+00:23:04,480 --> 00:23:09,680
+ممكن فانت اللي بتختار ساعتها تعمل sorting حسب إيش
+
+299
+00:23:09,680 --> 00:23:12,900
+بس في النهاية ال code لازم يكون بيقدر يفهم إيش
+
+300
+00:23:12,900 --> 00:23:15,730
+يعني عمليت sortingعملية ال sorting عشان هيك هي دي
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+301
+00:23:15,730 --> 00:23:19,150
+من الأكواد المهمة جدا و اللي محتاج تكون حافظها زي
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+اسمك مبرمج تكون خلاص انت في دماغك على طول حافظها
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+00:23:22,610 --> 00:23:28,090
+فاهم كيف تشتغل و فاهم أنواعها لأنه طبعا زي ما قلنا
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+00:23:28,090 --> 00:23:34,190
+في أكواد more efficient عن أكواد تانية اللي احنا
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+هنشرحهم بالمناسبة هم الأضعف المهم بس انحدد الفكرة
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+306
+00:23:38,030 --> 00:23:40,290
+لكن اتوقع انه في ال database لأ انتوا هتاخدوا
+
+307
+00:23:40,290 --> 00:23:44,820
+أنواع غيرهاو لازم تاخدوا حاجة علاقة بال sorting ..
+
+308
+00:23:44,820 --> 00:23:47,580
+لازم تاخدوا حاجة علاقة بال sorting .. بس طبعا
+
+309
+00:23:47,580 --> 00:23:51,040
+الأكواد الحديثة اللى الآن سرعتها أسرع .. هذا
+
+310
+00:23:51,040 --> 00:23:54,020
+الكلام اللى عندى هو مش هيبين معنى .. هيبين معنى
+
+311
+00:23:54,020 --> 00:23:55,860
+إيه انت لما ناخد ال complexity و نحسب ال
+
+312
+00:23:55,860 --> 00:23:59,260
+complexity للأكوادو نشوف ان ال complexity هذه لأ
+
+313
+00:23:59,260 --> 00:24:04,260
+هي ضعيفة ممكن نحسنها ممكن نحسنها فزي ما قلنا في ال
+
+314
+00:24:04,260 --> 00:24:07,940
+Excel مهم جدا ال code هي ده ال code هي ده من ال
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+315
+00:24:07,940 --> 00:24:11,920
+code المهم جدا و اللي انت فيه ايقونه له فوق عبارة
+
+316
+00:24:11,920 --> 00:24:17,840
+عن اسمها a-zهذه معناته ان انت بتعمل sorting فعليا
+
+317
+00:24:17,840 --> 00:24:23,360
+انت بس بتحدد ال column و بتعمله بتوص على ال icon
+
+318
+00:24:23,360 --> 00:24:27,220
+هذي بيعملك automatic sorting a to z ولا z to a
+
+319
+00:24:27,220 --> 00:24:31,540
+اللي هي تصعدي ولا تنازلي بس فلاحظ ان هي حاجة by
+
+320
+00:24:31,540 --> 00:24:34,760
+default موجودة في البرامج تمام هناخد نوعين هناخد
+
+321
+00:24:34,760 --> 00:24:38,340
+ال bubble sort و هناخد فكرة ال insertion sort
+
+322
+00:24:40,370 --> 00:24:43,710
+بالنسبة لل bubble بابل اللي هي فقاعة يعني معناته
+
+323
+00:24:43,710 --> 00:24:46,450
+فقاعة يعني انا بتكلم عن عملية floating اللي هي
+
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+00:24:46,450 --> 00:24:50,870
+تعوين تعوين الأرقام الصغيرة للأعلى هي فكرتها فانت
+
+325
+00:24:50,870 --> 00:24:56,390
+بيكون عندك الريب هذا الشكل من البداية للنهاية مش
+
+326
+00:24:56,390 --> 00:25:01,030
+مرتب لاحظين مش مرتب طيب عشان ارتبه بعمل عملية
+
+327
+00:25:01,030 --> 00:25:07,850
+comparison بين كل عنصرين ورا بعض بين كل عنصرين ورا
+
+328
+00:25:07,850 --> 00:25:13,140
+بعض فبمسك الأول والتانيبهمني أنه دائما الأول يكون
+
+329
+00:25:13,140 --> 00:25:18,180
+أصغر من التاني خلاص تمام هاي الأول أصغر من التاني
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+خلاص بتسيبها و بتنزل اللي وراهم التاني و التالت
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+00:25:21,480 --> 00:25:27,060
+بهمني التاني أو ال index الأقل يكون قيمته أقل و
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+00:25:27,060 --> 00:25:32,720
+وجدنا أنه لأ بصبتش تلاتة أكبر .. أصغر من اتنين
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+333
+00:25:32,720 --> 00:25:39,540
+بعكسهمبعمل x exchange او swap زي ما قلنا قبل المرة
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+00:25:39,540 --> 00:25:44,840
+اللي فاتت بنعمل swap x و y فبعكسهم هنا صارت هنا ال
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+335
+00:25:44,840 --> 00:25:49,580
+31 مش هيك بعد ما نعكس و خلاص هذه صارت 31 31 و 32
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+336
+00:25:49,580 --> 00:25:53,000
+لأ مظبوط مافيش فيها مشكلة طيب 32 و 33 برضه مافيش
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+00:25:53,000 --> 00:26:00,590
+مشكلة اتنين لازم تحل محل ال 33 swapأو exchange
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+338
+00:26:00,590 --> 00:26:05,770
+عكسنا تمام صارت هنا تلاتة و تلاتين تلاتة و تلاتين
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+00:26:05,770 --> 00:26:08,590
+اربعة و تلاتين زي ما هي مافيش مشكلة أسيبها طيب
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+00:26:08,590 --> 00:26:15,450
+اربعة و تلاتين تلاتة خلصنا the first stage stage
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+00:26:15,450 --> 00:26:19,130
+تانية بس خد بالك انه في ال stage التانية عدد
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+342
+00:26:19,130 --> 00:26:28,510
+المقارنات هتجل واحدعدد المقارنات ستقل 1 لماذا؟ هنا
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+00:26:28,510 --> 00:26:35,950
+كنت تعمل هذه مقارنة هذه 2 هذه 3 هذه 4 هذه 5 6 7
+
+344
+00:26:35,950 --> 00:26:41,810
+سبعة مقارنات بمعنى أن عدد المقارنات هي N ناقص 1
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+00:26:41,810 --> 00:26:49,090
+عندك 8 عناصر فانت عشان تعمل أول stage محتاج N ناقص
+
+346
+00:26:49,090 --> 00:26:54,000
+1 سبع عمليات مقارنةطيب السبع عمليات مقارنة عن إيش
+
+347
+00:26:54,000 --> 00:27:00,240
+نتجت في النهاية أنتجت لنا حاجة عكسية بمعنى أنت كنت
+
+348
+00:27:00,240 --> 00:27:03,520
+بتدور على ال bubble اللي هي فقعات فقعات ده دايما
+
+349
+00:27:03,520 --> 00:27:08,880
+هي الأخف يعني القيمة الأقل لأ لاحظ أن الواحد هي من
+
+350
+00:27:08,880 --> 00:27:14,380
+المرتبة التانية التالتة للتانية مشيت بس لكن لو
+
+351
+00:27:14,380 --> 00:27:18,520
+اتطلعت في ال code جيدا هتجد أنه بيعملك ترسيب لأكبر
+
+352
+00:27:18,520 --> 00:27:24,350
+قيمة في كل stageبالظبط فال 34 هذه اللي صارتها هنا
+
+353
+00:27:24,350 --> 00:27:29,190
+لو انها كانت موجودة هنا في أول stage هتنزل في
+
+354
+00:27:29,190 --> 00:27:36,090
+القاع لاحظ لو هذه 34 34 31 اجلب صارت هنا ال 34
+
+355
+00:27:36,090 --> 00:27:41,350
+واحد اجلب فلاحظ انه رغم ان ال code هو bubble اسمه
+
+356
+00:27:41,350 --> 00:27:44,670
+لكن فعليا في كل stage اللي واضح فيه انه أتجا
+
+357
+00:27:44,670 --> 00:27:47,870
+العنصر بنزل تحت فانت المرة اللي بعدها مش محتاج
+
+358
+00:27:47,870 --> 00:27:53,180
+تقارن فيهبمعنى مش هعمل المقارنة اللي هنا لأ هيكون
+
+359
+00:27:53,180 --> 00:27:57,940
+عندي هاي واحدة تنتين تلاتة أربع خمسة ستة بس مش
+
+360
+00:27:57,940 --> 00:28:06,020
+همشي سبع مقارنات واضحيت؟ تمام طيب نفس الفكرة برضه
+
+361
+00:28:06,020 --> 00:28:08,700
+حاجة مهمة جدا ناخد بالنا منها لإنها تسهل علينا في
+
+362
+00:28:08,700 --> 00:28:11,960
+ال code ده مديش عدد ال stages اللي انا محتاجهم
+
+363
+00:28:11,960 --> 00:28:20,110
+برضه in عقس واحد بحيث ان لو الواحد هذاهذا الواحد
+
+364
+00:28:20,110 --> 00:28:26,810
+كان أقل عنصر تحت في كل stage انت هتطلع خطوة فلو
+
+365
+00:28:26,810 --> 00:28:31,630
+أقل عنصر هذا ال worst case الحالة السيئة و كلكم
+
+366
+00:28:31,630 --> 00:28:34,050
+عارفين برضه ان احنا كمبرمجين دايما بنشتغل ع ال
+
+367
+00:28:34,050 --> 00:28:38,190
+worst case في ال complexity بتشتغل ع ال worst case
+
+368
+00:28:38,190 --> 00:28:41,870
+هناخد الكلام هذا بس سابق لأوانه لكن هنا لازم نوضحه
+
+369
+00:28:41,870 --> 00:28:45,420
+على أساس ان ال worst case انهبالنسبة للكبير فاش
+
+370
+00:28:45,420 --> 00:28:48,440
+مشكلة، الكبير حتى لو كان أول غنصر من أول stage
+
+371
+00:28:48,440 --> 00:28:53,360
+هينزل في القاع لكن إشكلتنا في أصغر غنصر لو كان
+
+372
+00:28:53,360 --> 00:28:58,060
+موجود فعلا في القاع فهو محتاج ان ناقص واحد stages
+
+373
+00:28:58,060 --> 00:29:06,120
+عشان يقفوا في مكانه الصحيح واضحيت؟ تمام، ممتاز إذا
+
+374
+00:29:06,120 --> 00:29:09,680
+الجزئية هذه واضحة، ال code الآن هيطلع سهل وبسيط
+
+375
+00:29:09,680 --> 00:29:15,760
+وفاش فيه مشكلةكالتالي هاي ال code بفسر كل الكلام
+
+376
+00:29:15,760 --> 00:29:19,960
+اللي قلناه فهنبدأ procedure bubble sort وهي معطيني
+
+377
+00:29:19,960 --> 00:29:24,440
+list معينة ل real numbers with n أكبر من أو يساوي
+
+378
+00:29:24,440 --> 00:29:28,480
+اتنين بمعنى real numbers حتى لو فيه قصور خلاص
+
+379
+00:29:28,480 --> 00:29:32,380
+ماعنديش مشكلة بنحسبها بالقصور مين اللي أكبر بنزل
+
+380
+00:29:32,380 --> 00:29:35,480
+تحت مين أكبر بنزل تحته ومين ال bubble أو مين ال
+
+381
+00:29:35,480 --> 00:29:39,780
+sortبعمله floating بعمله تعويم لفوق بنطلع لفوق
+
+382
+00:29:39,780 --> 00:29:43,880
+كويس وطبعا أكل لازم تكون تساوي اتنين او اكتر لأن
+
+383
+00:29:43,880 --> 00:29:46,660
+اذا واحد مالوش معنى ان انت بتعمل sorting ل meal هو
+
+384
+00:29:46,660 --> 00:29:49,800
+واحد لازم تكونوا على الأقل اتنين عشان اترتبهم
+
+385
+00:29:49,800 --> 00:29:54,360
+بالنسبة لبعضهم طيب هنبدأ for loop ال for loop
+
+386
+00:29:54,360 --> 00:29:59,880
+الأول هذا هذا له ال stage انا في اي stage ولاحظ
+
+387
+00:29:59,880 --> 00:30:02,400
+هنا بدنا من واحد من ال stage الأولى لان ناقص واحد
+
+388
+00:30:02,400 --> 00:30:07,530
+على اعتبار ان انا بداش تطلع ال worst caseانه و هذا
+
+389
+00:30:07,530 --> 00:30:11,830
+وارد انت مش شايف ال list قدامك فبدك تفترض ان ال
+
+390
+00:30:11,830 --> 00:30:16,030
+worst case القيمة الأقل هي جاي في قاع او في آخر
+
+391
+00:30:16,030 --> 00:30:19,730
+عنصر في ال list ففي الحالة دي محتاج عشان يتعومها
+
+392
+00:30:19,730 --> 00:30:27,670
+صح وتوصلها ك bubble اتصل لالخيانة الأولى او العنصر
+
+393
+00:30:27,670 --> 00:30:33,480
+الأول تصبح محتاج ان ناقص واحد stagesتمام هدولة ال
+
+394
+00:30:33,480 --> 00:30:38,400
+stages طيب جوا ال stages المقارنات خلاص أنا في ال
+
+395
+00:30:38,400 --> 00:30:45,320
+stage الأولى أكم مقارنة محتاج؟ محتاجين من 1 ل N
+
+396
+00:30:45,320 --> 00:30:50,890
+نقص Iإذا في أول مرحلة، معناته محتاج سبع مقارنات،
+
+397
+00:30:50,890 --> 00:30:54,890
+زي ما طوي عدناهم، إذا في المرحلة التانية، ستة، لأن
+
+398
+00:30:54,890 --> 00:30:58,610
+مصير هنا المرحلة رقم اتنين، فإن ناقص اتنين، and so
+
+399
+00:30:58,610 --> 00:31:05,170
+on لما تصل لإن ناقص واحد، هيكون إيش؟ محتاج مقارنة
+
+400
+00:31:05,170 --> 00:31:08,700
+واحدة، اللي هي الأنصر الأول والتاني، بسلأن في ال
+
+401
+00:31:08,700 --> 00:31:12,620
+worst case ممكن ساعتها أقل عنصر وصل لمرحلة تانية
+
+402
+00:31:12,620 --> 00:31:17,420
+وصل كعنصر تاني محتاج بس مقارنة بينه وبين الأول يا
+
+403
+00:31:17,420 --> 00:31:20,760
+بت save هم زي ما هم يا بتعكسهم إذا كان بحتاجوا
+
+404
+00:31:20,760 --> 00:31:26,460
+العكس طيب فوضحه إذا وضحت التنتين هدول خلصنا ال
+
+405
+00:31:26,460 --> 00:31:30,060
+code خلاص إذا التنتين هدول ال for loop واضحين
+
+406
+00:31:30,060 --> 00:31:36,720
+انتهى ال code الباقي بس عدل غير إذا أكبر منه تمام؟
+
+407
+00:31:36,720 --> 00:31:42,330
+واضحة؟هدولة هما الحل مافيش داعي نكمل اكتر من ذلك
+
+408
+00:31:42,330 --> 00:31:47,710
+خلاص الباقي مجرد انه اذا كان والله ال J أكبر من ال
+
+409
+00:31:47,710 --> 00:31:52,150
+J اللي وراها او من اللي بعدها معناته لازم تنزل بس
+
+410
+00:31:52,150 --> 00:31:56,070
+خلصنا مع ذلك هي الشطارة هنا في التنتين هدولة اذا
+
+411
+00:31:56,070 --> 00:31:57,490
+فهمت التنتين هدولة خلصت ال code
+
+412
+00:32:00,780 --> 00:32:05,480
+طيب ال insertion sort algorithm طبعا مش هنكتب ال
+
+413
+00:32:05,480 --> 00:32:07,660
+code تبعه اللي بده ال code تبعه مكتوب في الكتاب و
+
+414
+00:32:07,660 --> 00:32:12,040
+برضه بسيط جدا بس هنشرح فكرته الفكرة تبعته ببساطة
+
+415
+00:32:12,040 --> 00:32:16,180
+ان انت بتتعامل معاه كأنك بتعمل search ال insertion
+
+416
+00:32:16,180 --> 00:32:18,960
+هذه كأنك بتعمل search ايش يعني يعني ال list عندي
+
+417
+00:32:18,960 --> 00:32:24,960
+من n element a1
+
+418
+00:32:24,960 --> 00:32:26,940
+a2 ل a n
+
+419
+00:32:30,210 --> 00:32:35,010
+بكل بساطة بتتعامل معاه كالتالي بتفترض ان انت بدك
+
+420
+00:32:35,010 --> 00:32:39,990
+تعمل creation ل list جديدة creation ل list جديدة
+
+421
+00:32:39,990 --> 00:32:47,670
+اول ما هتحط فيها هتحط العنصر الاول A1 و هتفترض ان
+
+422
+00:32:47,670 --> 00:32:55,910
+هذا اسمها list و العنصر التاني X و نرجع لمين لل
+
+423
+00:32:55,910 --> 00:32:59,990
+searchبتشتغل linear؟ okay بتشتغل binary؟ okay مافي
+
+424
+00:32:59,990 --> 00:33:03,990
+مشكلة إيش بتسوي ال X هذه بالنسبة لل list اللي
+
+425
+00:33:03,990 --> 00:33:08,050
+موجودة عشان تحدد هي وين ال location اللي لازم يكون
+
+426
+00:33:08,050 --> 00:33:13,170
+لها وين موجود ال location إذا قرنت لجيت إنه X
+
+427
+00:33:13,170 --> 00:33:16,670
+خليني أفترض linear، linear أسهل و هتتخيلها بشكل
+
+428
+00:33:16,670 --> 00:33:23,850
+أسهل إجيت قرنت لجيت إن X أكبر من AI طيب هنا ال N
+
+429
+00:33:23,850 --> 00:33:28,180
+بالنسبة لك تسوي 1 حتى اللحظةإذا كانت X أكبر
+
+430
+00:33:28,180 --> 00:33:35,160
+فبتحطها في ال location N زائد واحد تمام
+
+431
+00:33:35,160 --> 00:33:39,780
+و خلصنا منها بتاخد A تلاتة بتصير هي ال X اللي بدك
+
+432
+00:33:39,780 --> 00:33:44,700
+تبحث عنها طيب إجينا بحثنا عنها و طبعا صارت هنا
+
+433
+00:33:44,700 --> 00:33:50,500
+بالنسبالي N بتساوي 2 ال list صارت أنصرين كويس
+
+434
+00:33:50,500 --> 00:33:59,610
+إجينا قارننا وجدنا إن X أكبر من Aو أصغر من a2 انا
+
+435
+00:33:59,610 --> 00:34:05,830
+عارف ان in بتساوي 2 فلازم تصير in بتساوي 3 و هنا
+
+436
+00:34:05,830 --> 00:34:08,950
+بده يصير في location تالت اللوكيشن التالت هذا هعمل
+
+437
+00:34:08,950 --> 00:34:18,710
+shift ل a2 ليش؟ لأن a2 أكبر من a3 حسب الفرضيتنا
+
+438
+00:34:18,710 --> 00:34:23,770
+أكبر من a3 ففي الحالة هذه بيروح على الجنب التاني و
+
+439
+00:34:23,770 --> 00:34:29,980
+بيفضّيالـ location تبعه بفضل location تبعه لمين؟ ل
+
+440
+00:34:29,980 --> 00:34:37,960
+X اللي هي A تلاتة and so on بيضل مكمل اللي وراها
+
+441
+00:34:37,960 --> 00:34:43,340
+اللي وراها اللي وراها اللي وراها لما يخلص ال A هاي
+
+442
+00:34:43,340 --> 00:34:50,530
+فكرة الاش ال sorting او ال insertionSorting فبيعمل
+
+443
+00:34:50,530 --> 00:34:54,330
+insertion كل مرة أو بيعمل حقن كل مرة بعنصر من
+
+444
+00:34:54,330 --> 00:34:58,310
+عناصر ال array نفسها بفترض ان ال array هي العنصر
+
+445
+00:34:58,310 --> 00:35:03,290
+الأول لحاله طيب العنصر التاني كأنه X و بيشوف وين
+
+446
+00:35:03,290 --> 00:35:07,640
+ال location الصح تبعه عشان يحقنه في مكانهطيب إذا
+
+447
+00:35:07,640 --> 00:35:11,260
+كان مكانه هو ال in الجديدة فش مشكلة بيحطه في ال in
+
+448
+00:35:11,260 --> 00:35:15,920
+الجديدة أو إذا كان مكانه جبل كل ما بعده بيعملهم
+
+449
+00:35:15,920 --> 00:35:21,260
+shift بواحد و بنحطه في مكانه بنعمل shift تمام فهذا
+
+450
+00:35:21,260 --> 00:35:28,560
+ببساطة اللي احنا كاتبينه ال code بسيط جدا و انت
+
+451
+00:35:28,560 --> 00:35:34,330
+عارف انه هيكون في عندك methodأو subroutine اسمه
+
+452
+00:35:34,330 --> 00:35:39,030
+search code هتستدعيه في كل مرة هتستدعيه في كل مرة
+
+453
+00:35:39,030 --> 00:35:43,230
+لأنه في كل او اكم مرة هنستدعيه هنستدعيه ان مرة مش
+
+454
+00:35:43,230 --> 00:35:47,590
+هيك ان مرة او ان نقص واحد مرة كل مرة بدك تفترض ان
+
+455
+00:35:47,590 --> 00:35:51,330
+هو ال X و تدور على المكان تبعه والخطوة الإضافية بس
+
+456
+00:35:51,330 --> 00:35:56,930
+تعمل عملية insert عملية insertion بس كويس ال code
+
+457
+00:35:56,930 --> 00:36:01,720
+موجود زي ما قولناهعلى في ال .. في الكتاب مكتوب
+
+458
+00:36:01,720 --> 00:36:05,600
+واضح جدا يعني مش فيه مشكلة و بسيط جدا و أتوقع أنه
+
+459
+00:36:05,600 --> 00:36:08,700
+المفروض يكون مرة عليكم يعني يكون مرة عليكم في أش
+
+460
+00:36:08,700 --> 00:36:09,440
+أشمال أو يمين
+
+461
+00:36:16,740 --> 00:36:21,420
+الان جابل ما نروح ل ال complexity بدنا نفهم مقدمة
+
+462
+00:36:21,420 --> 00:36:25,220
+ال complexity بالاساس المقدمة الأساسية بتاعة ال
+
+463
+00:36:25,220 --> 00:36:29,820
+complexity و اللي هي إلها علاقة بحاجة بيسموها ال
+
+464
+00:36:29,820 --> 00:36:34,160
+order of growth انت بناء على إيش بتقول أن هذا ال
+
+465
+00:36:34,160 --> 00:36:37,640
+code أحسن من هذا أن انت بتجيب ال order تبع كل code
+
+466
+00:36:37,640 --> 00:36:43,020
+صحيح؟ جبنا ال order لل code معنا ذلك أنه جابلما
+
+467
+00:36:43,020 --> 00:36:46,120
+أحكم على ال order تاع ال code لازم أكون فاهم إيش
+
+468
+00:36:46,120 --> 00:36:49,780
+يعني ال orders؟ بدنا نكون فاهمين بالأساس أصلا إيش
+
+469
+00:36:49,780 --> 00:36:54,680
+يعني ال orders وكيف تقاس ال orders هذه orders إيش؟
+
+470
+00:36:54,680 --> 00:36:57,740
+مش مجرد order معناته أنه قيمه أكبر من قيم order
+
+471
+00:36:57,740 --> 00:37:03,900
+تاني لأ القيم هذه مع الاستدامة بدها تكون أكبر منه
+
+472
+00:37:03,900 --> 00:37:07,300
+وليس في المرحلة الحالية فعشان هيك احنا بنتركزش على
+
+473
+00:37:07,300 --> 00:37:09,780
+ال order ك order لأ احنا بنركز على ال order of
+
+474
+00:37:09,780 --> 00:37:18,960
+growthبمعنى order نمو ال function نمو ال function
+
+475
+00:37:18,960 --> 00:37:23,980
+نفسها عندك code أول ال order تتبع function معينة و
+
+476
+00:37:23,980 --> 00:37:27,920
+ال code التاني function تانية فإذا أنا بقارن two
+
+477
+00:37:27,920 --> 00:37:32,200
+functions في بعض two functions في بعض مين نموها
+
+478
+00:37:32,200 --> 00:37:38,660
+أسرع من التاني مين نموها أسرع من التاني زي مثللو
+
+479
+00:37:38,660 --> 00:37:43,040
+قلنا مثلا ال function تلاتين in زائد تمانية احنا
+
+480
+00:37:43,040 --> 00:37:47,100
+عارفين انه هاد ايش first order او linear first
+
+481
+00:37:47,100 --> 00:37:51,060
+order او linear لما اجي اقارنها ب function بهذا
+
+482
+00:37:51,060 --> 00:37:56,400
+الشكل in تربيع زائد واحد انا في النهاية مش هامسك
+
+483
+00:37:56,400 --> 00:38:00,520
+اقول والله يا طب ما هيها هي ال first order اعلى
+
+484
+00:38:01,990 --> 00:38:06,690
+أحنا بنتكلم عن ال growth معدل نمو ال function معدل
+
+485
+00:38:06,690 --> 00:38:10,090
+نمو ال function لأنه ضامن إذا معدل نمو ال function
+
+486
+00:38:10,090 --> 00:38:15,070
+أكبر فهو هيجي عند نقطة تقاطع وبعدها هتبقى دائما
+
+487
+00:38:15,070 --> 00:38:20,370
+أكبر فنقطة التقاطع هي نقطة التقاطع بعدها بعد K هنا
+
+488
+00:38:20,370 --> 00:38:25,470
+قيمة ل K دائما هتلاقي أن ال second order أكيد أكبر
+
+489
+00:38:25,470 --> 00:38:30,690
+من first orderلأن في النهاية ما قبل النقطة المعينة
+
+490
+00:38:30,690 --> 00:38:36,270
+هذه هو يعتبر حكم خاطئ يعتبر حكم خاطئ مين اللي
+
+491
+00:38:36,270 --> 00:38:41,130
+بتحكم فيه ال mail و ال constant أو الجزء ال DC في
+
+492
+00:38:41,130 --> 00:38:43,990
+ال function اللي هي التمانية مثلا أو ال mail اللي
+
+493
+00:38:43,990 --> 00:38:49,680
+هو التلاتين هنا ال mail عندك واحد فعلياًمش هيك انت
+
+494
+00:38:49,680 --> 00:38:55,520
+مش ميعطيه coefficient معينة لقيمة ال order نفسه،
+
+495
+00:38:55,520 --> 00:38:59,840
+واحد في int أربعة، هنا انت ميعطيه تلاتين فطبيعي في
+
+496
+00:38:59,840 --> 00:39:04,780
+بدايتها، في بداية ال numbers هتلاقي ان ال linear
+
+497
+00:39:04,780 --> 00:39:11,230
+هيكون بشكل خادع، يبدو كأنه أكبرلكن عند نقطة معينة
+
+498
+00:39:11,230 --> 00:39:16,630
+لأ هترجع تبين انه ال second order أعلى ليش أعلى؟
+
+499
+00:39:16,630 --> 00:39:22,690
+لأنه من الأساس معدل نموه أكبر بالظبط السلحفة و
+
+500
+00:39:22,690 --> 00:39:26,550
+الأرنب السلحفة و الأرنب لكن انت في النهاية السلحفة
+
+501
+00:39:26,550 --> 00:39:31,990
+خلتها بعيدة اتنين كيلو سابج الأرنب فمعنى ذلك انه
+
+502
+00:39:31,990 --> 00:39:36,690
+مسألة وقت هي مسألة وقت السلحفة هتضل تمشي بس معدل
+
+503
+00:39:36,690 --> 00:39:41,560
+النمو بتبحها في المشي بطيءهيضل بطيء الأرنب أسرع
+
+504
+00:39:41,560 --> 00:39:46,700
+انت عارف انه هييجي لحظة من اللحجة اللحظات هيتسوق و
+
+505
+00:39:46,700 --> 00:39:52,390
+هيعديها الأرنبصحيح؟ هذا في الحالة الطبيعية مش حالة
+
+506
+00:39:52,390 --> 00:39:55,010
+الجثث إنه هيروح تحت الشجرة و ينام و مش عارف ..
+
+507
+00:39:55,010 --> 00:39:59,230
+الحالة الطبيعية مش هيك عارفين إنه في لحظة معينة
+
+508
+00:39:59,230 --> 00:40:03,390
+إذا مشيوا الإتنين بنفس ال rate الطبيعي تبعهم هيجوا
+
+509
+00:40:03,390 --> 00:40:05,730
+يتقاربوا يتقاربوا يتقاربوا و بعدين يعديها و يمشي
+
+510
+00:40:05,730 --> 00:40:10,850
+معنا ذلك الحكم هنا بيجيش على القيمة اللحظية بيجي
+
+511
+00:40:10,850 --> 00:40:17,050
+على معدل التحرك معدل التحرك اللي هنسميه ال order
+
+512
+00:40:17,050 --> 00:40:23,100
+of growthواضحة فبهمني ال order of growth مش لحظيا
+
+513
+00:40:23,100 --> 00:40:32,700
+جدش قيمة كل واحدة منهم مش لحظيا تمام ففي
+
+514
+00:40:32,700 --> 00:40:35,640
+الحالة هذه بنقدر نقول ان ال function الأولى هي
+
+515
+00:40:35,640 --> 00:40:40,860
+first order و first order بسميها big O of N و big
+
+516
+00:40:40,860 --> 00:40:49,070
+O معناته at most at most بمعنىأعلى ما يمكن إلها هي
+
+517
+00:40:49,070 --> 00:40:54,950
+linear ولا بحياتها هتكون أعلى من هيك ممكن تكون DC
+
+518
+00:40:54,950 --> 00:40:59,730
+ممكن تكون DC بمعنى إن هي بتشبر كل اللي تحتها في ال
+
+519
+00:40:59,730 --> 00:41:06,910
+order DC أو inverse أو ليش في كمان logarithmic؟
+
+520
+00:41:06,950 --> 00:41:10,750
+ممكن تكون أقل من ال first order okay بس هنا بتسميه
+
+521
+00:41:10,750 --> 00:41:15,390
+at most at most فإذا لما بقول function ال order
+
+522
+00:41:15,390 --> 00:41:19,770
+تبعها big O of N فهي في أسوأ الأحوال مش هتزيد عن
+
+523
+00:41:19,770 --> 00:41:25,210
+ال linear ال order تبعها في أسوأ الأحوال يعني أعلى
+
+524
+00:41:25,210 --> 00:41:32,810
+order ممكن هو linear هو ال linear بمعنى بالنسبة لل
+
+525
+00:41:32,810 --> 00:41:39,850
+code هي إيش المتغير اللي فيه؟أخدته big O تمام هو
+
+526
+00:41:39,850 --> 00:41:44,150
+إيش المتغير عندكوا في الأكواد ال input بس ال
+
+527
+00:41:44,150 --> 00:41:48,750
+arguments بعنى ذلك أن أنت هنا بتتكلم عن in input
+
+528
+00:41:48,750 --> 00:41:53,530
+بمعنى أن كل ما بتزود ال input بواحد ال complexity
+
+529
+00:41:53,530 --> 00:41:57,710
+بتزيد بس على جد operation واحدة هاي معناها بتزيدش
+
+530
+00:41:57,710 --> 00:42:02,110
+تعقيدها بشكل كتير كبير تعقيدها واحد بس فبتزيد بشكل
+
+531
+00:42:02,110 --> 00:42:10,380
+وحدي فإذا هي ماشية بشكلمتناسب برضيا مع ال input ال
+
+532
+00:42:10,380 --> 00:42:13,860
+input زودلي كمان input زيادة بتزيد عملية واحدة فقط
+
+533
+00:42:13,860 --> 00:42:18,980
+في ال code بهذا الشكل ماشية فانا هنا لما أجي أقول
+
+534
+00:42:18,980 --> 00:42:23,680
+والله فعملتلي code ال code هذا على جد عددكم عددنا
+
+535
+00:42:23,680 --> 00:42:28,280
+خلّيني أقول ستين سبعين طالب أخدله ستين ثانية وجينا
+
+536
+00:42:28,280 --> 00:42:32,740
+اتطلعنا وجينا أن ال code هذا فعلا هو linear معنى
+
+537
+00:42:32,740 --> 00:42:39,920
+ذلك أن نفس ال code لما بتستخد معلقسكان غزة بيصير
+
+538
+00:42:39,920 --> 00:42:45,540
+ال 60 مقابل 60 ثانية بيصير 2 مليون مقابل 2 مليون
+
+539
+00:42:45,540 --> 00:42:51,020
+ثانية فبتحسب المتغير هنا هو ال arguments أو ال
+
+540
+00:42:51,020 --> 00:42:55,160
+inputs أو ال inputs هل هم linear مع بعض ولا لأ
+
+541
+00:42:55,160 --> 00:42:57,760
+لعند linear بتظهر مبلوعة مقبولة بس تخيل لو أنه
+
+542
+00:42:57,760 --> 00:43:02,900
+تربيعي أو second order معناه ذلك إذا كان ال 60
+
+543
+00:43:02,900 --> 00:43:08,200
+كانوا 60 ثانيةبتربيع فبدك تشوف الاتنين مليون جديش
+
+544
+00:43:08,200 --> 00:43:12,040
+بده مصيره أكيد هصيره أكتر من الاتنين مليون ثانية
+
+545
+00:43:12,040 --> 00:43:15,300
+اللي كنا نحكي عليها وفي الحالتين هي سيئة يعني في
+
+546
+00:43:15,300 --> 00:43:17,380
+الحالتين سيئة لما ماتش تتكلم عن اتنين مليون ثانية
+
+547
+00:43:17,380 --> 00:43:21,340
+تمام بس بدنا نوضح كل الفكرة ال concept تبعنا تمام
+
+548
+00:43:21,340 --> 00:43:25,300
+فهنا at most ال big O بمعنى انه في أسوأ حالتها هي
+
+549
+00:43:26,940 --> 00:43:31,040
+طيب بالنسبة لإن تربية زائد واحد هي في أسوأ حالتها
+
+550
+00:43:31,040 --> 00:43:37,340
+تربيعية وطبعا التربيعية order of growth أكبر من ال
+
+551
+00:43:37,340 --> 00:43:40,500
+linear order of growth أكبر من ال linear هذا
+
+552
+00:43:40,500 --> 00:43:48,060
+مفهومنا طيب بالنسبة لمبرمجين معناته سيئةلحظته كيف؟
+
+553
+00:43:48,060 --> 00:43:52,060
+okay احنا هنا جاهديني نتكلم كرياضيات بحتها اه هي
+
+554
+00:43:52,060 --> 00:43:55,420
+ال order of growth بحها اعلى فهي تبدو ان كلمة اعلى
+
+555
+00:43:55,420 --> 00:43:58,860
+دايما بتوحينا انه احسن يعني بالعكس هنا سيئ
+
+556
+00:43:58,860 --> 00:44:05,200
+بالنسبالنا كمبرمجين كمبرمجين فهي تتناسب بشكل ترضي
+
+557
+00:44:05,200 --> 00:44:09,880
+مع الان تربيع فالتمانية مليون الاتنين مليون هدول
+
+558
+00:44:09,880 --> 00:44:14,280
+هيصيروا اتنين مليون تربيع اتنين مليون تربيع ثانية
+
+559
+00:44:15,110 --> 00:44:20,190
+هتصبح في الحالة هذه تمام و طبعا كنا عارفين أن أي
+
+560
+00:44:20,190 --> 00:44:25,630
+big O of N تربيع أكيد هيكون أسرع في ال growth زي
+
+561
+00:44:25,630 --> 00:44:29,970
+ما توي شوفنا المعدل كان أسرع من .. زي بالظبط
+
+562
+00:44:29,970 --> 00:44:35,490
+الأرنب والسلحفة تمام هيكون أكبر من أي big O of N
+
+563
+00:44:35,490 --> 00:44:44,570
+بكل بشكل مطلق جد ما تكون ال N هذه لها maleتلاتين
+
+564
+00:44:44,570 --> 00:44:48,270
+in، خمسين in، مليون in، بس في النهاية في نقطة
+
+565
+00:44:48,270 --> 00:44:53,360
+معينة التربيه هيعديها ويمشيالنقطة هذه ممكن تبعد،
+
+566
+00:44:53,360 --> 00:44:57,260
+او ممكن تبعد، ممكن تكون عند K كبيرة، بس في النهاية
+
+567
+00:44:57,260 --> 00:45:02,220
+لازم حتكون فيه موجودة ..يلها قيمة K، بعدها التربيع
+
+568
+00:45:02,220 --> 00:45:09,240
+يعدي ال .. ال linear، تمام فكل ما كان ال number ل
+
+569
+00:45:09,240 --> 00:45:12,660
+ال user records اللي هي ال inputs كل ما كانت ال
+
+570
+00:45:12,660 --> 00:45:16,460
+big O of N تربيع أكيد ك function بتاخد more time
+
+571
+00:45:17,350 --> 00:45:22,270
+for إيش؟ في ال execution للتنفيذ لعملية التنفيذ
+
+572
+00:45:22,270 --> 00:45:26,330
+هذا نفس الفكرة اللي بنتكلمها إذا أنا بدأ أتكلم عن
+
+573
+00:45:26,330 --> 00:45:28,970
+ال big O ك function فأنا في النهاية بقول إن هي
+
+574
+00:45:28,970 --> 00:45:33,390
+function من real to real أنه يوجد there exist C
+
+575
+00:45:33,390 --> 00:45:36,630
+and K، K هذه النقطة اللي بنحكي عنها، اللي عند نقطة
+
+576
+00:45:36,630 --> 00:45:42,680
+معينة الأرنب هيعدل سلحفةعند نقطة معينة .. وين
+
+577
+00:45:42,680 --> 00:45:46,900
+النقطة المعينة دي؟ K .. and K عند نقطة معينة أكيد
+
+578
+00:45:46,900 --> 00:45:53,000
+هيبين ال order أو يظهر بشكل واضح يعدي ال order
+
+579
+00:45:53,000 --> 00:46:00,320
+الأقل تمام بحيث ان for all x أكبر من k من k فأكبر
+
+580
+00:46:00,320 --> 00:46:08,320
+هتبين ان ال f of x أقل من c g of xهتكون معناه ذلك
+
+581
+00:46:08,320 --> 00:46:14,220
+أن ال order أقل من ال big O G عشان هيك ال G معناته
+
+582
+00:46:14,220 --> 00:46:18,220
+هي في أسوأ الأحوال هي ال maximum هي الأكبر ال G هي
+
+583
+00:46:18,220 --> 00:46:23,160
+الأكبر لما قلنا توة big O of N تربيع معناه ذلك أنه
+
+584
+00:46:23,160 --> 00:46:26,960
+هي في جميع الأحوال مش هتزيد عن ال N تربيع مش هتزيد
+
+585
+00:46:26,960 --> 00:46:30,600
+عن ال N تربيع فإذا عند قيمة معينة زي ال linear
+
+586
+00:46:30,600 --> 00:46:34,820
+بتاع التوة التلاتين N زائد تمانية في البداية كانت
+
+587
+00:46:34,820 --> 00:46:39,820
+خدعانة كانت أعلىفي البداية كانت أعلى، صحيح؟ هذه
+
+588
+00:46:39,820 --> 00:46:48,160
+خادعة، and كمعينة، and كمعينة بعدها هتصبح دائما
+
+589
+00:46:48,160 --> 00:46:55,990
+أقل منالتربيع أقل من تربيع فإذا ال linear مشمولة
+
+590
+00:46:55,990 --> 00:46:59,850
+مع ال big O of N تربيع ومشمولة مع ال big O of N
+
+591
+00:46:59,850 --> 00:47:06,230
+نفسها أو تساوي أو تساوي تمام فهنا نتكلم عن النقطة
+
+592
+00:47:06,230 --> 00:47:08,230
+اللي حكينا عنها هي ممكن توي عده و هيجينا مثال
+
+593
+00:47:08,230 --> 00:47:11,830
+يبيّنها أكتر فبنقدر نقول نعبر عنها طبعا مصطلحات
+
+594
+00:47:11,830 --> 00:47:15,390
+كتيرة و ممكن نقول إن ال F هذه is at most order G
+
+595
+00:47:15,390 --> 00:47:19,730
+بنسميها at most order G فهي أعلى حالتها تساوي ال
+
+596
+00:47:19,730 --> 00:47:26,970
+order Gكويس او بسميها F is big O of G او نسميها F
+
+597
+00:47:26,970 --> 00:47:31,930
+تساوي big O of G مباشرة نكتب بهذا الشكل مباشرة ف
+
+598
+00:47:31,930 --> 00:47:40,210
+.. او طريقة من الطرق F belong to big O of G اش
+
+599
+00:47:40,210 --> 00:47:44,150
+يعني؟ يعني معناته انا افترضت ان ال F هذه عنصر مش
+
+600
+00:47:44,150 --> 00:47:49,740
+ال belong هذه بتاعة ال sets ان هي عنصر ل setمنطق
+
+601
+00:47:49,740 --> 00:47:55,420
+الكلام؟ منطقي عارفين ليش؟ لأن ال big O of G كل ال
+
+602
+00:47:55,420 --> 00:47:59,500
+functions اللي أقل من G كل ال functions اللي أقل
+
+603
+00:47:59,500 --> 00:48:06,100
+من G و F واحدة منهم ف F تنتمي لمجموعة ال functions
+
+604
+00:48:06,100 --> 00:48:10,960
+اللي أقل من G أو تسوي G بمعنى لما تقول big O in
+
+605
+00:48:10,960 --> 00:48:14,940
+تربيع بكل بساطة بقدر أقول لك أنه تلاتين in
+
+606
+00:48:19,610 --> 00:48:27,110
+تلاتين N زائد عقمية هي belong to big O of N تربيع
+
+607
+00:48:27,110 --> 00:48:34,110
+بمشي الحال بمشي الحال linear أقل من التربيع تمام
+
+608
+00:48:34,110 --> 00:48:39,050
+صحيح طب ممكن أقول لك برضه تلاتين N تربيع زائد one
+
+609
+00:48:39,050 --> 00:48:47,690
+million برضه big O of N تربيع ما هي تربعية تساوي
+
+610
+00:48:47,690 --> 00:48:52,340
+تربيعهي ال order تبعها تربيع فهي بكل بساطة بتقدر
+
+611
+00:48:52,340 --> 00:48:56,880
+تقول عليها big O of N تربيع ليش؟ لأن ال one
+
+612
+00:48:56,880 --> 00:49:01,860
+million هذا constant constant إيش يعني؟ يعني
+
+613
+00:49:01,860 --> 00:49:06,920
+function of zero ال order تبعه zero طيب ال zero
+
+614
+00:49:06,920 --> 00:49:13,740
+أقل من التربيع فهي مشمولة مع التربيع طيب نفس الجثة
+
+615
+00:49:13,740 --> 00:49:25,750
+تلاتين N تربيع زائد مية Nبرضه big of in تربيع هي
+
+616
+00:49:25,750 --> 00:49:35,870
+هي صحيح فيها جزء linear بس totally هي تربيعية مش
+
+617
+00:49:35,870 --> 00:49:39,870
+هتكون اكتر من تربيع مش هتكون اكتر من تربيع تمام
+
+618
+00:49:39,870 --> 00:49:45,950
+فبنسميها at most at most بمعنى انها ممكن تشمل كل
+
+619
+00:49:45,950 --> 00:49:49,430
+اللي تحتها كل اللي اقل منهاتمام اتكلمنا عن هذا
+
+620
+00:49:49,430 --> 00:49:55,030
+الكلام وهين هنا مثال حددلكم بس حسب التعريف في 30N
+
+621
+00:49:55,030 --> 00:49:59,250
+زائد 8 اقل من أو يساوي CN عشان اضمن ان هي فعلا هل
+
+622
+00:49:59,250 --> 00:50:07,630
+هي big O of N معناه ذلك ان عند mail معين لل order
+
+623
+00:50:07,630 --> 00:50:11,710
+اكيد هيتجاوز ال function اللي موجودة عندكم بعد
+
+624
+00:50:11,710 --> 00:50:16,510
+قيمة K طيب في الحالة هذه ال C اللي هي ال mailالـ
+
+625
+00:50:16,510 --> 00:50:18,810
+mail اللي موجود عندك بتشوف المعادلة اللي عندك جدّي
+
+626
+00:50:18,810 --> 00:50:23,650
+شمالها معناه ذلك أنه عند C زائد واحد تلاتين زائد
+
+627
+00:50:23,650 --> 00:50:27,770
+واحد واحد تلاتين فلو أخدنا أن ال C هنا there exist
+
+628
+00:50:27,770 --> 00:50:32,950
+C and K بتحققلك أنه بعد K تلاتين N زائد تمانية
+
+629
+00:50:32,950 --> 00:50:37,660
+دايما هتكون أقل من أو يساوي ال ordermail ال order
+
+630
+00:50:37,660 --> 00:50:43,300
+تمام فلس C هذه تلاتين واحد تلاتين هنا تمانية and
+
+631
+00:50:43,300 --> 00:50:47,940
+تمانية كي بتساوي تمانية فدائما أبدا لكل قيم N اللي
+
+632
+00:50:47,940 --> 00:50:54,260
+أكبر من تمانية هتتحقق هذه المعادلة فبأضمن أنه ال
+
+633
+00:50:54,260 --> 00:50:58,320
+first order هو شامل التلاتين N زي التمانية
+
+634
+00:50:58,320 --> 00:51:06,040
+فالتلاتين زي التمانية هي أحد عناصر الست big O of N
+
+635
+00:51:07,430 --> 00:51:10,890
+فإذن هو first order فإذن first order نفس الكلام
+
+636
+00:51:10,890 --> 00:51:16,470
+لمين لأ ال second لأ ال second order طبعا هنا هي
+
+637
+00:51:16,470 --> 00:51:21,230
+واضحة بهذا الشكل لأ ال first order لما بتكلم عن n
+
+638
+00:51:21,230 --> 00:51:24,830
+مباشرة فهي بزاوية خمسة وارمين كده مش كتير مظبوطة
+
+639
+00:51:24,830 --> 00:51:30,130
+لو تلاتين n زائد تمانية الميل تبعها بصير أعلى و
+
+640
+00:51:30,130 --> 00:51:34,430
+بعدين ماخدة shift بقيمة التمانية بقيمة التمانية
+
+641
+00:51:34,430 --> 00:51:34,630
+هنا
+
+642
+00:51:38,830 --> 00:51:45,210
+بعد نقطة معينة سين
+
+643
+00:51:45,210 --> 00:51:49,330
+ستتعدي ال function اللي عندك فمعنى ذلك ان ال
+
+644
+00:51:49,330 --> 00:51:54,210
+function هي مشمولة ضمن هذا ال order اللي هو ال
+
+645
+00:51:54,210 --> 00:51:54,490
+linear
+
+646
+00:51:58,250 --> 00:52:01,350
+أنا قلتلك المعادلة نفسها هي اللي هتحددك الثابت
+
+647
+00:52:01,350 --> 00:52:04,590
+بالظبط هتبدأ من الصفر بس بدك تاخد بالك من ال mail
+
+648
+00:52:04,590 --> 00:52:08,270
+ساعتها إذا بتكلم عن تلاتين in ال mail تبعك افرضه
+
+649
+00:52:08,270 --> 00:52:13,170
+واحد تلاتين الواحد تلاتين in linear مش هيك وهي
+
+650
+00:52:13,170 --> 00:52:17,910
+المعادلة دي أقل منها طيب هذا لو كانت صفر هنا لو
+
+651
+00:52:17,910 --> 00:52:22,800
+كانت صفر هنا فمن الصفر هتلاقيها عدتهاأكبر من الصفر
+
+652
+00:52:22,800 --> 00:52:25,940
+لأن انت عارف أن الأرقام هي قبل الصفر أصلا بس احنا
+
+653
+00:52:25,940 --> 00:52:29,120
+تجاوز أن نبدأ من الصفر بس فعلا انا ممكن أبدأ من
+
+654
+00:52:29,120 --> 00:52:32,440
+هنا وهدول ينزلوا من تحت كمان عادي يعني ماكنش فيه
+
+655
+00:52:32,440 --> 00:52:39,850
+مشكلة تمام خليني أقول هيك أخدناتوضيح نكمله المرة
+
+656
+00:52:39,850 --> 00:52:43,590
+القادمة لفكرة ال order of growth عشان ناخد المرة
+
+657
+00:52:43,590 --> 00:52:50,070
+القادمة شوية المجموعة facts عن ال big O و أخواتها
+
+658
+00:52:50,070 --> 00:52:53,090
+لان هنفضل المرة الجاية ناخد باقية أخواتها ال Omega
+
+659
+00:52:53,090 --> 00:52:57,350
+و ال Theta يعطيكوا العافية نشوفكوا المرة القادمة
+
+660
+00:52:57,350 --> 00:52:57,970
+ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..313a914c65bd4748dfb4023e1b98ec4c5b76c026
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4_raw.json
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0.9749348958333334}, {"start": 82.06, "end": 82.62, "word": " تسعودي", "probability": 0.79912109375}, {"start": 82.62, "end": 83.28, "word": " بشكل", "probability": 0.9036458333333334}], "temperature": 1.0}, {"id": 5, "seek": 10778, "start": 84.14, "end": 107.78, "text": "تصعدي طبعا بشكل تنازلي برضه بيمشي الحال بس شوية مفاهيم بسيطة بتتغير معاك فالمفروض الموضوع بيجلجش ف .. كأكواد بنفكر بالتالي given list L لازم تكون فيها اندل input ال input ده و ال arguments اللي هي ال list نفسها لمجموعة elements و لازم تكون sorted بمعنى مصنفة", "tokens": [2655, 9381, 3615, 16254, 23032, 3555, 3615, 995, 4724, 8592, 28820, 6055, 1863, 31377, 20292, 4724, 43042, 3224, 4724, 32640, 8592, 1829, 21542, 6027, 4724, 3794, 13412, 2407, 10632, 3714, 5172, 40294, 32640, 4724, 3794, 1829, 9566, 3660, 39894, 2655, 17082, 13546, 20449, 995, 4117, 6156, 45340, 5172, 32887, 11242, 9673, 2407, 11242, 45367, 4724, 1829, 7435, 1211, 7435, 8592, 6156, 4386, 9122, 10721, 4117, 14407, 3215, 44945, 5172, 37983, 20666, 2655, 6027, 1829, 2212, 1329, 441, 5296, 31377, 2304, 6055, 30544, 8978, 11296, 16472, 3215, 1211, 4846, 2423, 4846, 11778, 3224, 4032, 2423, 12869, 13672, 1829, 39896, 2423, 1329, 8717, 36178, 11296, 32767, 7435, 2304, 2407, 27884, 4959, 4032, 5296, 31377, 2304, 6055, 30544, 25462, 4724, 2304, 3615, 1863, 7578, 3714, 9381, 1863, 5172, 3660], "avg_logprob": -0.16338582442501398, "compression_ratio": 1.6470588235294117, "no_speech_prob": 2.205371856689453e-06, "words": [{"start": 84.14, "end": 84.76, "word": "تصعدي", "probability": 0.712677001953125}, {"start": 84.76, "end": 85.4, "word": " طبعا", "probability": 0.8070068359375}, {"start": 85.4, "end": 86.1, "word": " بشكل", "probability": 0.8580729166666666}, {"start": 86.1, "end": 86.54, "word": " تنازلي", "probability": 0.9019775390625}, {"start": 86.54, "end": 86.78, "word": " برضه", "probability": 0.8592122395833334}, {"start": 86.78, "end": 87.04, "word": " بيمشي", "probability": 0.793212890625}, {"start": 87.04, "end": 87.28, "word": " الحال", "probability": 0.982421875}, {"start": 87.28, "end": 87.84, "word": " بس", "probability": 0.853759765625}, {"start": 87.84, "end": 88.16, "word": " شوية", "probability": 0.9296875}, {"start": 88.16, "end": 88.56, "word": " مفاهيم", "probability": 0.98193359375}, {"start": 88.56, "end": 88.92, "word": " بسيطة", "probability": 0.973046875}, {"start": 88.92, "end": 89.46, "word": " بتتغير", "probability": 0.8641357421875}, {"start": 89.46, "end": 89.72, "word": " معاك", "probability": 0.9632161458333334}, {"start": 89.72, "end": 90.78, "word": " فالمفروض", "probability": 0.86708984375}, {"start": 90.78, "end": 91.08, "word": " الموضوع", "probability": 0.9853515625}, {"start": 91.08, "end": 91.56, "word": " بيجلجش", "probability": 0.8889973958333334}, {"start": 91.56, "end": 92.5, "word": " ف", "probability": 0.77978515625}, {"start": 92.5, "end": 93.06, "word": " ..", "probability": 0.2142333984375}, {"start": 93.06, "end": 95.24, "word": " كأكواد", "probability": 0.93154296875}, {"start": 95.24, "end": 95.96, "word": " بنفكر", "probability": 0.9666341145833334}, {"start": 95.96, "end": 96.88, "word": " بالتالي", "probability": 0.92041015625}, {"start": 96.88, "end": 97.54, "word": " given", "probability": 0.7265625}, {"start": 97.54, "end": 98.3, "word": " list", "probability": 0.90673828125}, {"start": 98.3, "end": 98.54, "word": " L", "probability": 0.62109375}, {"start": 98.54, "end": 98.92, "word": " لازم", "probability": 0.9853515625}, {"start": 98.92, "end": 99.06, "word": " تكون", "probability": 0.76708984375}, {"start": 99.06, "end": 99.3, "word": " فيها", "probability": 0.741455078125}, {"start": 99.3, "end": 99.44, "word": " اندل", "probability": 0.6094563802083334}, {"start": 99.44, "end": 99.88, "word": " input", "probability": 0.9765625}, {"start": 99.88, "end": 100.32, "word": " ال", "probability": 0.9052734375}, {"start": 100.32, "end": 100.58, "word": " input", "probability": 0.9482421875}, {"start": 100.58, "end": 100.76, "word": " ده", "probability": 0.64013671875}, {"start": 100.76, "end": 100.84, "word": " و", "probability": 0.347412109375}, {"start": 100.84, "end": 100.9, "word": " ال", "probability": 0.859375}, {"start": 100.9, "end": 101.46, "word": " arguments", "probability": 0.9013671875}, {"start": 101.46, "end": 101.96, "word": " اللي", "probability": 0.894775390625}, {"start": 101.96, "end": 102.2, "word": " هي", "probability": 0.81103515625}, {"start": 102.2, "end": 102.5, "word": " ال", "probability": 0.908203125}, {"start": 102.5, "end": 102.76, "word": " list", "probability": 0.951171875}, {"start": 102.76, "end": 103.26, "word": " نفسها", "probability": 0.9933268229166666}, {"start": 103.26, "end": 104.06, "word": " لمجموعة", "probability": 0.91220703125}, {"start": 104.06, "end": 104.62, "word": " elements", "probability": 0.9150390625}, {"start": 104.62, "end": 104.94, "word": " و", "probability": 0.86474609375}, {"start": 104.94, "end": 105.14, "word": " لازم", "probability": 0.97802734375}, {"start": 105.14, "end": 105.44, "word": " تكون", "probability": 0.9912109375}, {"start": 105.44, "end": 106.0, "word": " sorted", "probability": 0.96044921875}, {"start": 106.0, "end": 107.02, "word": " بمعنى", "probability": 0.97421875}, {"start": 107.02, "end": 107.78, "word": " مصنفة", "probability": 0.93984375}], "temperature": 1.0}, {"id": 6, "seek": 11593, "start": 108.23, "end": 115.93, "text": "مرتبة مرتبة أو مصنفة تمام ب order معين و احنا قولنا ال order هذا", "tokens": [29973, 2655, 49401, 3714, 43500, 49401, 34051, 3714, 9381, 1863, 5172, 3660, 46811, 10943, 4724, 1668, 20449, 9957, 4032, 1975, 5016, 8315, 12174, 12610, 8315, 2423, 1668, 23758], "avg_logprob": -0.20043103242742605, "compression_ratio": 1.2209302325581395, "no_speech_prob": 2.1696090698242188e-05, "words": [{"start": 108.23, "end": 108.83, "word": "مرتبة", "probability": 0.8517252604166666}, {"start": 108.83, "end": 110.05, "word": " مرتبة", "probability": 0.6947835286458334}, {"start": 110.05, "end": 110.17, "word": " أو", "probability": 0.66552734375}, {"start": 110.17, "end": 110.75, "word": " مصنفة", "probability": 0.95654296875}, {"start": 110.75, "end": 111.39, "word": " تمام", "probability": 0.85498046875}, {"start": 111.39, "end": 112.01, "word": " ب", "probability": 0.60693359375}, {"start": 112.01, "end": 112.61, "word": " order", "probability": 0.822265625}, {"start": 112.61, "end": 113.31, "word": " معين", "probability": 0.96240234375}, {"start": 113.31, "end": 113.87, "word": " و", "probability": 0.71484375}, {"start": 113.87, "end": 114.05, "word": " احنا", "probability": 0.8653971354166666}, {"start": 114.05, "end": 114.43, "word": " قولنا", "probability": 0.8816731770833334}, {"start": 114.43, "end": 115.25, "word": " ال", "probability": 0.9765625}, {"start": 115.25, "end": 115.59, "word": " order", "probability": 0.97607421875}, {"start": 115.59, "end": 115.93, "word": " هذا", "probability": 0.82470703125}], "temperature": 1.0}, {"id": 7, "seek": 12697, "start": 116.77, "end": 126.97, "text": "تساعدة تنازلة المهم أنه في ترتيب معين واضح سواء كان أرقام أو حروف حتى", "tokens": [2655, 3794, 995, 22488, 3660, 6055, 1863, 31377, 37977, 9673, 16095, 14739, 3224, 8978, 6055, 2288, 31371, 3555, 20449, 9957, 4032, 46958, 5016, 8608, 2407, 16606, 25961, 5551, 2288, 4587, 10943, 34051, 11331, 32887, 5172, 11331, 49975], "avg_logprob": -0.3248355176888014, "compression_ratio": 1.3020833333333333, "no_speech_prob": 0.90478515625, "words": [{"start": 116.77, "end": 117.45, "word": "تساعدة", "probability": 0.572412109375}, {"start": 117.45, "end": 118.05, "word": " تنازلة", "probability": 0.75347900390625}, {"start": 118.05, "end": 118.41, "word": " المهم", "probability": 0.916015625}, {"start": 118.41, "end": 118.61, "word": " أنه", "probability": 0.558349609375}, {"start": 118.61, "end": 118.77, "word": " في", "probability": 0.88037109375}, {"start": 118.77, "end": 119.65, "word": " ترتيب", "probability": 0.8773193359375}, {"start": 119.65, "end": 119.99, "word": " معين", "probability": 0.971435546875}, {"start": 119.99, "end": 121.85, "word": " واضح", "probability": 0.7958170572916666}, {"start": 121.85, "end": 122.97, "word": " سواء", "probability": 0.7413736979166666}, {"start": 122.97, "end": 123.21, "word": " كان", "probability": 0.96533203125}, {"start": 123.21, "end": 123.71, "word": " أرقام", "probability": 0.965576171875}, {"start": 123.71, "end": 124.01, "word": " أو", "probability": 0.7861328125}, {"start": 124.01, "end": 126.65, "word": " حروف", "probability": 0.8606770833333334}, {"start": 126.65, "end": 126.97, "word": " حتى", "probability": 0.656005859375}], "temperature": 1.0}, {"id": 8, "seek": 15461, "start": 146.81, "end": 154.61, "text": "درجة جدا، method درجة جدا في برامج كتيرة، كويس بدنا نحسب من ال X هذا اللي given عندي", "tokens": [3215, 47341, 3660, 10874, 28259, 12399, 3170, 11778, 47341, 3660, 10874, 28259, 8978, 4724, 2288, 10943, 7435, 9122, 2655, 48923, 12399, 9122, 45865, 3794, 47525, 8315, 8717, 5016, 35457, 9154, 2423, 1783, 23758, 13672, 1829, 2212, 18871, 16254], "avg_logprob": -0.258012823569469, "compression_ratio": 1.2410714285714286, "no_speech_prob": 4.649162292480469e-06, "words": [{"start": 146.81, "end": 147.25, "word": "درجة", "probability": 0.6834920247395834}, {"start": 147.25, "end": 147.73, "word": " جدا،", "probability": 0.6881917317708334}, {"start": 147.73, "end": 148.13, "word": " method", "probability": 0.90087890625}, {"start": 148.13, "end": 148.63, "word": " درجة", "probability": 0.9749348958333334}, {"start": 148.63, "end": 148.89, "word": " جدا", "probability": 0.984375}, {"start": 148.89, "end": 149.03, "word": " في", "probability": 0.8251953125}, {"start": 149.03, "end": 149.39, "word": " برامج", "probability": 0.9500732421875}, {"start": 149.39, "end": 149.95, "word": " كتيرة،", "probability": 0.744140625}, {"start": 149.95, "end": 151.01, "word": " كويس", "probability": 0.8308919270833334}, {"start": 151.01, "end": 151.35, "word": " بدنا", "probability": 0.829345703125}, {"start": 151.35, "end": 151.73, "word": " نحسب", "probability": 0.9925130208333334}, {"start": 151.73, "end": 152.45, "word": " من", "probability": 0.9755859375}, {"start": 152.45, "end": 152.83, "word": " ال", "probability": 0.966796875}, {"start": 152.83, "end": 153.05, "word": " X", "probability": 0.62255859375}, {"start": 153.05, "end": 153.37, "word": " هذا", "probability": 0.74951171875}, {"start": 153.37, "end": 154.01, "word": " اللي", "probability": 0.858642578125}, {"start": 154.01, "end": 154.23, "word": " given", "probability": 0.9033203125}, {"start": 154.23, "end": 154.61, "word": " عندي", "probability": 0.74951171875}], "temperature": 1.0}, {"id": 9, "seek": 17904, "start": 155.38, "end": 179.04, "text": "و في نفس الوقت given عندي list بدنا نحسب هل ال X هذا موجود في ال list ولا لأ إذا موجود بدي أرجعله بال إيش؟ بال index تبعه بال index تبعه كافي ال index؟ كافي ليش؟ لأن أنا بتتكلم عن ordered list يعني معناه ذلك إن ال index هو ثابت مكانه مكانه دائما ثابت أرجعله بالمكان تبع ال X هذا إذا موجود داخل ال list L", "tokens": [2407, 8978, 8717, 36178, 2423, 30543, 2655, 2212, 18871, 16254, 1329, 47525, 8315, 8717, 5016, 35457, 8032, 1211, 2423, 1783, 23758, 3714, 29245, 23328, 8978, 2423, 1329, 49429, 5296, 10721, 11933, 15730, 3714, 29245, 23328, 4724, 16254, 5551, 47341, 30241, 3224, 20666, 11933, 1829, 8592, 22807, 20666, 8186, 6055, 3555, 3615, 3224, 20666, 8186, 6055, 3555, 3615, 3224, 9122, 31845, 1829, 2423, 8186, 22807, 9122, 31845, 1829, 32239, 8592, 22807, 5296, 33456, 41850, 39894, 2655, 4117, 19528, 18871, 8866, 1329, 37495, 22653, 20449, 8315, 3224, 29910, 23275, 36145, 2423, 8186, 31439, 38637, 16758, 2655, 3714, 41361, 3224, 3714, 41361, 3224, 11778, 16373, 15042, 38637, 16758, 2655, 5551, 47341, 30241, 3224, 20666, 2304, 41361, 6055, 3555, 3615, 2423, 1783, 23758, 11933, 15730, 3714, 29245, 23328, 11778, 47283, 1211, 2423, 1329, 441], "avg_logprob": -0.16114026080561047, "compression_ratio": 2.0081967213114753, "no_speech_prob": 2.682209014892578e-06, "words": [{"start": 155.38, "end": 155.62, "word": "و", "probability": 0.69970703125}, {"start": 155.62, "end": 155.82, "word": " في", "probability": 0.6025390625}, {"start": 155.82, "end": 156.02, "word": " نفس", "probability": 0.99462890625}, {"start": 156.02, "end": 156.32, "word": " الوقت", "probability": 0.9830729166666666}, {"start": 156.32, "end": 156.56, "word": " given", "probability": 0.30322265625}, {"start": 156.56, "end": 156.82, "word": " عندي", "probability": 0.877685546875}, {"start": 156.82, "end": 157.2, "word": " list", "probability": 0.935546875}, {"start": 157.2, "end": 157.64, "word": " بدنا", "probability": 0.87744140625}, {"start": 157.64, "end": 157.98, "word": " نحسب", "probability": 0.9938151041666666}, {"start": 157.98, "end": 158.72, "word": " هل", "probability": 0.9736328125}, {"start": 158.72, "end": 158.94, "word": " ال", "probability": 0.953125}, {"start": 158.94, "end": 159.2, "word": " X", "probability": 0.5361328125}, {"start": 159.2, "end": 159.5, "word": " هذا", "probability": 0.716796875}, {"start": 159.5, "end": 159.96, "word": " موجود", "probability": 0.9928385416666666}, {"start": 159.96, "end": 160.1, "word": " في", "probability": 0.953125}, {"start": 160.1, "end": 160.18, "word": " ال", "probability": 0.92431640625}, {"start": 160.18, "end": 160.38, "word": " list", "probability": 0.96435546875}, {"start": 160.38, "end": 160.54, "word": " ولا", "probability": 0.888671875}, {"start": 160.54, "end": 160.88, "word": " لأ", "probability": 0.97705078125}, {"start": 160.88, "end": 161.66, "word": " إذا", "probability": 0.6727294921875}, {"start": 161.66, "end": 162.04, "word": " موجود", "probability": 0.9912109375}, {"start": 162.04, "end": 162.26, "word": " بدي", "probability": 0.65234375}, {"start": 162.26, "end": 162.64, "word": " أرجعله", "probability": 0.71697998046875}, {"start": 162.64, "end": 162.78, "word": " بال", "probability": 0.83984375}, {"start": 162.78, "end": 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فهمنا بس بدك توضح ان انت بتكلم عن index ببدأ من واحد", "tokens": [33544, 4697, 2423, 4846, 13672, 1829, 1975, 8315, 3714, 33753, 26108, 11296, 3714, 14851, 5016, 26895, 1975, 3615, 28480, 1975, 8592, 2655, 17082, 1211, 47525, 11536, 11296, 39896, 12174, 32640, 3660, 2423, 1783, 1783, 13672, 1829, 16472, 2655, 39894, 3215, 13063, 25894, 11296, 13672, 1829, 39896, 2423, 24922, 9122, 45865, 3794, 30767, 16373, 3215, 2423, 1329, 8717, 36178, 11296, 6055, 4117, 2655, 3555, 32239, 11296, 13838, 316, 16, 316, 17, 281, 5252, 3714, 33599, 1829, 6055, 4117, 2655, 3555, 32239, 11296, 441, 9122, 45865, 3794, 4032, 10644, 41674, 1392, 16490, 1211, 33546, 6156, 16095, 8315, 4724, 3794, 47525, 4117, 33427, 11242, 5016, 16472, 16472, 2655, 39894, 4117, 19528, 18871, 8186, 4724, 44510, 10721, 9154, 36764, 24401], "avg_logprob": -0.17988782306002754, "compression_ratio": 1.6431372549019607, "no_speech_prob": 2.384185791015625e-06, "words": [{"start": 247.05, "end": 247.73, "word": "arguments", 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ماخدين بالكم انه اتكلمنا عنها طيب ال procedure و زي ما قلنا summation بده تحدد ايش ال input تبعك فال input تبعك هي ال list", "tokens": [3555, 3794, 1975, 15730, 16472, 2655, 3714, 24401, 3215, 11296, 3714, 35457, 4587, 995, 6156, 3555, 2655, 9381, 13546, 30767, 1829, 19446, 16472, 39237, 6055, 9778, 26895, 9957, 16472, 39896, 6156, 3615, 15040, 498, 293, 787, 498, 16490, 1211, 33546, 35186, 2086, 35186, 572, 16472, 47395, 7578, 2086, 1975, 4117, 25708, 8032, 2655, 32887, 5016, 5296, 10803, 8717, 3224, 1975, 4117, 25708, 8032, 2655, 32887, 5016, 5296, 1646, 4724, 3794, 7251, 30544, 23758, 3714, 47283, 3215, 9957, 20666, 24793, 16472, 3224, 1975, 2655, 4117, 19528, 8315, 18871, 11296, 23032, 1829, 3555, 2423, 10747, 4032, 30767, 1829, 19446, 12174, 1211, 8315, 28811, 47525, 3224, 6055, 24401, 3215, 1975, 1829, 8592, 2423, 4846, 6055, 3555, 3615, 4117, 6156, 6027, 4846, 6055, 3555, 3615, 4117, 39896, 2423, 1329], "avg_logprob": -0.21081349797665128, "compression_ratio": 1.715415019762846, 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"word": " هي", "probability": 0.7685546875}, {"start": 1266.82, "end": 1267.12, "word": " فعلا", "probability": 0.744140625}, {"start": 1267.12, "end": 1267.34, "word": " if", "probability": 0.475341796875}, {"start": 1267.34, "end": 1267.5, "word": " and", "probability": 0.24951171875}, {"start": 1267.5, "end": 1267.68, "word": " only", "probability": 0.72314453125}, {"start": 1267.68, "end": 1267.98, "word": " if", "probability": 0.970703125}, {"start": 1267.98, "end": 1268.84, "word": " خلاص", "probability": 0.90576171875}, {"start": 1268.84, "end": 1269.5, "word": " يا", "probability": 0.383544921875}, {"start": 1269.5, "end": 1269.78, "word": " yes", "probability": 0.9384765625}, {"start": 1269.78, "end": 1269.94, "word": " يا", "probability": 0.82568359375}, {"start": 1269.94, "end": 1270.14, "word": " no", "probability": 0.86083984375}, {"start": 1270.14, "end": 1271.04, "word": " انتهى", "probability": 0.7853190104166666}, {"start": 1271.04, "end": 1271.82, "word": " yes", "probability": 0.89013671875}, {"start": 1271.82, "end": 1272.98, "word": " اكيد", "probability": 0.8693033854166666}, {"start": 1272.98, "end": 1273.36, "word": " هتروح", "probability": 0.9677734375}, {"start": 1273.36, "end": 1273.56, "word": " ل", "probability": 0.5537109375}, {"start": 1273.56, "end": 1274.34, "word": " Latin", "probability": 0.423095703125}, {"start": 1274.34, "end": 1275.22, "word": " نه", "probability": 0.387939453125}, {"start": 1275.22, "end": 1275.62, "word": " اكيد", "probability": 0.9578450520833334}, {"start": 1275.62, "end": 1276.2, "word": " هتروح", "probability": 0.9896240234375}, {"start": 1276.2, "end": 1276.86, "word": " ل", "probability": 0.90966796875}, {"start": 1276.86, "end": 1277.18, "word": " else", "probability": 0.865234375}, {"start": 1277.18, "end": 1278.18, "word": " بس", "probability": 0.977294921875}, {"start": 1278.18, "end": 1279.66, "word": " يكون", "probability": 0.669921875}, {"start": 1279.66, "end": 1279.92, "word": " هذا", "probability": 0.94970703125}, {"start": 1279.92, "end": 1280.34, "word": " ماخدين", "probability": 0.898681640625}, {"start": 1280.34, "end": 1280.6, "word": " بالكم", "probability": 0.94775390625}, {"start": 1280.6, "end": 1280.84, "word": " انه", "probability": 0.7412109375}, {"start": 1280.84, "end": 1281.34, "word": " اتكلمنا", "probability": 0.9177734375}, {"start": 1281.34, "end": 1281.64, "word": " عنها", "probability": 0.697509765625}, {"start": 1281.64, "end": 1282.08, "word": " طيب", "probability": 0.8855794270833334}, {"start": 1282.08, "end": 1282.52, "word": " ال", "probability": 0.9658203125}, {"start": 1282.52, "end": 1282.92, "word": " procedure", "probability": 0.96826171875}, {"start": 1282.92, "end": 1283.16, "word": " و", "probability": 0.376953125}, {"start": 1283.16, "end": 1283.26, "word": " زي", "probability": 0.80810546875}, {"start": 1283.26, "end": 1283.34, "word": " ما", "probability": 0.9775390625}, {"start": 1283.34, "end": 1283.48, "word": " قلنا", "probability": 0.8933919270833334}, {"start": 1283.48, "end": 1283.96, "word": " summation", "probability": 0.87255859375}, {"start": 1283.96, "end": 1284.54, "word": " بده", "probability": 0.31304931640625}, {"start": 1284.54, "end": 1284.98, "word": " تحدد", "probability": 0.88720703125}, {"start": 1284.98, "end": 1285.16, "word": " ايش", "probability": 0.8644205729166666}, {"start": 1285.16, "end": 1285.3, "word": " ال", "probability": 0.986328125}, {"start": 1285.3, "end": 1285.48, "word": " input", "probability": 0.92333984375}, {"start": 1285.48, "end": 1285.92, "word": " تبعك", "probability": 0.950927734375}, {"start": 1285.92, "end": 1286.18, "word": " فال", "probability": 0.850341796875}, {"start": 1286.18, "end": 1286.32, "word": " input", "probability": 0.9658203125}, {"start": 1286.32, "end": 1286.66, "word": " تبعك", "probability": 0.940185546875}, {"start": 1286.66, "end": 1286.8, "word": " هي", "probability": 0.87744140625}, {"start": 1286.8, "end": 1286.94, "word": " ال", "probability": 0.87890625}, {"start": 1286.94, "end": 1287.3, "word": " list", "probability": 0.48193359375}], "temperature": 1.0}, {"id": 56, "seek": 130157, "start": 1288.15, "end": 1301.57, "text": "الشيء بالظبط هي مجموعة integers summation equal to zero في البداية فالعنصر S ده بلاش يكون له قيمة مسبقة بلاش يكون له قيمة مسبقة وفي الحالة هذه معناته هبدأ أجمع على قيمة سابقة موجودة", "tokens": [6027, 8592, 1829, 38207, 20666, 19913, 3555, 9566, 39896, 3714, 7435, 2304, 2407, 27884, 41674, 28811, 2681, 281, 4018, 8978, 29739, 28259, 10632, 6156, 6027, 3615, 1863, 9381, 2288, 318, 11778, 3224, 4724, 1211, 33599, 7251, 30544, 46740, 12174, 32640, 3660, 3714, 35457, 28671, 4724, 1211, 33599, 7251, 30544, 46740, 12174, 32640, 3660, 3714, 35457, 28671, 4032, 41185, 21542, 6027, 3660, 29538, 20449, 8315, 47395, 8032, 44510, 10721, 5551, 7435, 2304, 3615, 15844, 12174, 32640, 3660, 8608, 16758, 28671, 3714, 29245, 23328, 3660], "avg_logprob": -0.19810268211932408, "compression_ratio": 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{"start": 1292.41, "end": 1294.19, "word": " فالعنصر", "probability": 0.8583170572916666}, {"start": 1294.19, "end": 1294.41, "word": " S", "probability": 0.450927734375}, {"start": 1294.41, "end": 1294.65, "word": " ده", "probability": 0.5941162109375}, {"start": 1294.65, "end": 1295.09, "word": " بلاش", "probability": 0.8499348958333334}, {"start": 1295.09, "end": 1295.57, "word": " يكون", "probability": 0.97802734375}, {"start": 1295.57, "end": 1295.75, "word": " له", "probability": 0.78857421875}, {"start": 1295.75, "end": 1296.11, "word": " قيمة", "probability": 0.9798177083333334}, {"start": 1296.11, "end": 1296.65, "word": " مسبقة", "probability": 0.9464518229166666}, {"start": 1296.65, "end": 1297.69, "word": " بلاش", "probability": 0.7569173177083334}, {"start": 1297.69, "end": 1297.89, "word": " يكون", "probability": 0.967041015625}, {"start": 1297.89, "end": 1298.01, "word": " له", "probability": 0.92333984375}, {"start": 1298.01, "end": 1298.25, "word": " قيمة", 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"seek": 132546, "start": 1302.46, "end": 1325.46, "text": "ممكن في الحالة هذه إذا كان ال compiler تبعك not smart enough هيشوف إيش ال equation اللي كان موجود في المكان اللي مخزن على ال RAM هنا اللي اتخصصله كقيمة S و يبدأ يحوش عليه يبدأ يحوش عليه كويس for loop من 1 to N و خلصنا ما هي هي ال list كاملة و S بتساوي ال S زائد A I", "tokens": [2304, 43020, 8978, 21542, 6027, 3660, 29538, 11933, 15730, 25961, 2423, 31958, 6055, 3555, 3615, 4117, 406, 4069, 1547, 39896, 8592, 38688, 11933, 1829, 8592, 2423, 5367, 13672, 1829, 25961, 3714, 29245, 23328, 8978, 9673, 41361, 13672, 1829, 3714, 9778, 11622, 1863, 15844, 2423, 14561, 34105, 13672, 1829, 1975, 2655, 9778, 9381, 9381, 43761, 9122, 4587, 32640, 3660, 318, 4032, 7251, 44510, 10721, 7251, 5016, 2407, 8592, 47356, 7251, 44510, 10721, 7251, 5016, 2407, 8592, 47356, 9122, 45865, 3794, 337, 6367, 9154, 502, 281, 426, 4032, 16490, 1211, 9381, 8315, 19446, 39896, 39896, 2423, 1329, 9122, 10943, 37977, 4032, 318, 39894, 3794, 995, 45865, 2423, 318, 30767, 16373, 3215, 316, 286], "avg_logprob": -0.1741071424580046, "compression_ratio": 1.603846153846154, "no_speech_prob": 8.821487426757812e-06, "words": [{"start": 1302.46, "end": 1302.96, "word": "ممكن", "probability": 0.807373046875}, {"start": 1302.96, "end": 1303.32, "word": " في", "probability": 0.8076171875}, {"start": 1303.32, "end": 1303.66, "word": " الحالة", "probability": 0.9513346354166666}, {"start": 1303.66, "end": 1303.84, "word": " هذه", "probability": 0.7451171875}, {"start": 1303.84, "end": 1304.02, "word": " إذا", "probability": 0.802734375}, {"start": 1304.02, "end": 1304.28, "word": " كان", "probability": 0.98876953125}, {"start": 1304.28, "end": 1304.72, "word": " ال", "probability": 0.88671875}, {"start": 1304.72, "end": 1305.04, "word": " compiler", "probability": 0.41845703125}, {"start": 1305.04, "end": 1305.6, "word": " تبعك", "probability": 0.92333984375}, {"start": 1305.6, "end": 1306.08, "word": " not", "probability": 0.73828125}, {"start": 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خلصنا", "probability": 0.9356689453125}, {"start": 1321.78, "end": 1321.9, "word": " ما", "probability": 0.90380859375}, {"start": 1321.9, "end": 1321.98, "word": " هي", "probability": 0.87939453125}, {"start": 1321.98, "end": 1322.18, "word": " هي", "probability": 0.68994140625}, {"start": 1322.18, "end": 1322.26, "word": " ال", "probability": 0.86669921875}, {"start": 1322.26, "end": 1322.46, "word": " list", "probability": 0.96875}, {"start": 1322.46, "end": 1322.82, "word": " كاملة", "probability": 0.9788411458333334}, {"start": 1322.82, "end": 1323.32, "word": " و", "probability": 0.8154296875}, {"start": 1323.32, "end": 1323.5, "word": " S", "probability": 0.9248046875}, {"start": 1323.5, "end": 1323.84, "word": " بتساوي", "probability": 0.7225341796875}, {"start": 1323.84, "end": 1323.96, "word": " ال", "probability": 0.724609375}, {"start": 1323.96, "end": 1324.12, "word": " S", "probability": 0.92138671875}, {"start": 1324.12, "end": 1324.48, "word": " زائد", "probability": 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معنى إيه انت لما ناخد ال complexity و نحسب ال complexity للأكواد", "tokens": [2407, 5296, 31377, 2304, 6055, 47283, 3215, 14407, 11331, 26108, 3660, 11203, 995, 28671, 20666, 32411, 4386, 5296, 31377, 2304, 6055, 47283, 3215, 14407, 11331, 26108, 3660, 11203, 995, 28671, 20666, 32411, 4386, 4724, 3794, 23032, 3555, 3615, 995, 16247, 4117, 14407, 3215, 21542, 16254, 12984, 3660, 13672, 7578, 6024, 48506, 8608, 2288, 34268, 11296, 5551, 3794, 2288, 3615, 4386, 23758, 2423, 28820, 10943, 13672, 7578, 43242, 7578, 31439, 37893, 39896, 3555, 9957, 20449, 1863, 7578, 4386, 39896, 3555, 9957, 20449, 1863, 7578, 11933, 1829, 3224, 16472, 2655, 5296, 15042, 8717, 47283, 3215, 2423, 14024, 4032, 8717, 5016, 35457, 2423, 14024, 24976, 10721, 4117, 14407, 3215], "avg_logprob": -0.18326518468767683, "compression_ratio": 2.0051546391752577, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 1422.26, "end": 1422.44, "word": "و", "probability": 0.55859375}, {"start": 1422.44, "end": 1422.7, 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246691, "start": 2447.33, "end": 2466.91, "text": "أعلى ما يمكن إلها هي linear ولا بحياتها هتكون أعلى من هيك ممكن تكون DC ممكن تكون DC بمعنى إن هي بتشبر كل اللي تحتها في ال order DC أو inverse أو ليش في كمان logarithmic؟", "tokens": [10721, 3615, 23942, 19446, 7251, 43020, 11933, 1211, 11296, 39896, 8213, 49429, 4724, 5016, 1829, 9307, 11296, 8032, 2655, 30544, 5551, 3615, 23942, 9154, 39896, 4117, 3714, 43020, 6055, 30544, 9114, 3714, 43020, 6055, 30544, 9114, 4724, 2304, 3615, 1863, 7578, 36145, 39896, 39894, 8592, 3555, 2288, 28242, 13672, 1829, 6055, 33753, 11296, 8978, 2423, 1668, 9114, 34051, 17340, 34051, 32239, 8592, 8978, 9122, 2304, 7649, 41473, 355, 13195, 22807], "avg_logprob": -0.23767606053553836, "compression_ratio": 1.5857988165680474, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2447.33, "end": 2447.71, "word": "أعلى", "probability": 0.8313802083333334}, {"start": 2447.71, "end": 2447.83, "word": " ما", "probability": 0.92919921875}, {"start": 2447.83, 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فبتحسب المتغير هنا هو ال arguments أو ال inputs أو ال inputs هل هم linear مع بعض ولا لأ لعند linear بتظهر مبلوعة مقبولة بس تخيل لو أنه تربيعي أو second order معناه ذلك إذا كان ال 60 كانوا 60 ثانية", "tokens": [3794, 41361, 32771, 11622, 3660, 4724, 1829, 9381, 13546, 2423, 4060, 3714, 4587, 16758, 1211, 4060, 38637, 7649, 10632, 4724, 1829, 9381, 13546, 568, 3714, 20292, 11536, 3714, 4587, 16758, 1211, 568, 3714, 20292, 11536, 38637, 7649, 10632, 6156, 3555, 2655, 5016, 35457, 9673, 2655, 17082, 13546, 34105, 31439, 2423, 12869, 34051, 2423, 15743, 34051, 2423, 15743, 8032, 1211, 8032, 2304, 8213, 20449, 45030, 11242, 49429, 5296, 10721, 5296, 3615, 41260, 8213, 39894, 19913, 3224, 2288, 3714, 36150, 2407, 27884, 3714, 4587, 3555, 12610, 3660, 4724, 3794, 6055, 9778, 26895, 45164, 14739, 3224, 6055, 2288, 21292, 3615, 1829, 34051, 1150, 1668, 20449, 8315, 3224, 29910, 23275, 11933, 15730, 25961, 2423, 4060, 25961, 14407, 4060, 38637, 7649, 10632], "avg_logprob": -0.17597987439672827, 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واحد هي في أسوأ حالتها تربيعية وطبعا التربيعية order of growth أكبر من ال linear order of growth أكبر من ال linear هذا مفهومنا طيب بالنسبة لمبرمجين معناته سيئة", "tokens": [9566, 1829, 3555, 20666, 1863, 35457, 3660, 5296, 28814, 1863, 6055, 25513, 10632, 30767, 16373, 3215, 36764, 24401, 39896, 8978, 5551, 3794, 2407, 10721, 11331, 6027, 2655, 11296, 6055, 2288, 21292, 3615, 10632, 4032, 9566, 3555, 3615, 995, 16712, 2288, 21292, 3615, 10632, 1668, 295, 4599, 5551, 4117, 26890, 9154, 2423, 8213, 1668, 295, 4599, 5551, 4117, 26890, 9154, 2423, 8213, 23758, 3714, 5172, 3224, 20498, 8315, 23032, 1829, 3555, 20666, 1863, 35457, 3660, 32767, 26890, 2304, 7435, 9957, 20449, 8315, 47395, 8608, 1829, 19986, 3660], "avg_logprob": -0.15508262076597104, "compression_ratio": 1.7705882352941176, "no_speech_prob": 0.0002579689025878906, "words": [{"start": 2606.94, "end": 2607.86, "word": "طيب", "probability": 0.6943359375}, {"start": 2607.86, "end": 2608.5, "word": " بالنسبة", "probability": 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"probability": 0.61962890625}, {"start": 2614.1, "end": 2614.34, "word": " of", "probability": 0.9765625}, {"start": 2614.34, "end": 2614.76, "word": " growth", "probability": 0.93505859375}, {"start": 2614.76, "end": 2615.9, "word": " أكبر", "probability": 0.9454752604166666}, {"start": 2615.9, "end": 2616.88, "word": " من", "probability": 0.98486328125}, {"start": 2616.88, "end": 2617.34, "word": " ال", "probability": 0.8349609375}, {"start": 2617.34, "end": 2617.68, "word": " linear", "probability": 0.7392578125}, {"start": 2617.68, "end": 2618.4, "word": " order", "probability": 0.434326171875}, {"start": 2618.4, "end": 2618.6, "word": " of", "probability": 0.94287109375}, {"start": 2618.6, "end": 2618.86, "word": " growth", "probability": 0.9228515625}, {"start": 2618.86, "end": 2619.26, "word": " أكبر", "probability": 0.9602864583333334}, {"start": 2619.26, "end": 2619.42, "word": " من", "probability": 0.99072265625}, {"start": 2619.42, "end": 2619.54, "word": " ال", "probability": 0.9365234375}, {"start": 2619.54, "end": 2619.82, "word": " linear", "probability": 0.869140625}, {"start": 2619.82, "end": 2620.5, "word": " هذا", "probability": 0.5673828125}, {"start": 2620.5, "end": 2621.08, "word": " مفهومنا", "probability": 0.9775390625}, {"start": 2621.08, "end": 2621.72, "word": " طيب", "probability": 0.8497721354166666}, {"start": 2621.72, "end": 2622.38, "word": " بالنسبة", "probability": 0.98779296875}, {"start": 2622.38, "end": 2623.8, "word": " لمبرمجين", "probability": 0.90947265625}, {"start": 2623.8, "end": 2624.34, "word": " معناته", "probability": 0.9606119791666666}, {"start": 2624.34, "end": 2624.78, "word": " سيئة", "probability": 0.9864501953125}], "temperature": 1.0}, {"id": 110, "seek": 265428, "start": 2626.74, "end": 2654.28, "text": "لحظته كيف؟ okay احنا هنا جاهديني نتكلم كرياضيات بحتها اه هي ال order of growth بحها اعلى فهي تبدو ان كلمة اعلى دايما بتوحينا انه احسن يعني بالعكس هنا سيئ بالنسبالنا كمبرمجين كمبرمجين فهي تتناسب بشكل ترضي مع الان تربيع فالتمانية مليون الاتنين مليون هدول هيصيروا اتنين مليون تربيع اتنين مليون تربيع ثانية", "tokens": [1211, 5016, 19913, 47395, 9122, 33911, 22807, 1392, 1975, 5016, 8315, 34105, 10874, 40294, 3215, 9957, 1829, 8717, 2655, 4117, 19528, 9122, 16572, 46958, 1829, 9307, 4724, 33753, 11296, 1975, 3224, 39896, 2423, 1668, 295, 4599, 4724, 5016, 11296, 1975, 3615, 23942, 6156, 3224, 1829, 6055, 44510, 2407, 16472, 9122, 19528, 3660, 1975, 3615, 23942, 11778, 47302, 15042, 39894, 2407, 5016, 1829, 8315, 16472, 3224, 1975, 5016, 3794, 1863, 37495, 22653, 20666, 3615, 4117, 3794, 34105, 8608, 1829, 19986, 20666, 1863, 35457, 6027, 8315, 9122, 2304, 26890, 2304, 7435, 9957, 9122, 2304, 26890, 2304, 7435, 9957, 6156, 3224, 1829, 6055, 2655, 8315, 35457, 4724, 8592, 28820, 6055, 43042, 1829, 20449, 2423, 7649, 6055, 2288, 21292, 3615, 6156, 6027, 39237, 7649, 10632, 3714, 20292, 11536, 2423, 9307, 1863, 9957, 3714, 20292, 11536, 8032, 3215, 12610, 39896, 9381, 13546, 14407, 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{"start": 3167.97, "end": 3168.21, "word": " O", "probability": 0.85595703125}, {"start": 3168.21, "end": 3169.03, "word": " و", "probability": 0.8681640625}, {"start": 3169.03, "end": 3170.07, "word": " أخواتها", "probability": 0.9484375}, {"start": 3170.07, "end": 3170.59, "word": " لان", "probability": 0.612060546875}, {"start": 3170.59, "end": 3170.97, "word": " هنفضل", "probability": 0.6431640625}, {"start": 3170.97, "end": 3171.15, "word": " المرة", "probability": 0.7724609375}, {"start": 3171.15, "end": 3171.31, "word": " الجاية", "probability": 0.77490234375}, {"start": 3171.31, "end": 3171.55, "word": " ناخد", "probability": 0.9869791666666666}, {"start": 3171.55, "end": 3171.75, "word": " باقية", "probability": 0.69683837890625}, {"start": 3171.75, "end": 3172.39, "word": " أخواتها", "probability": 0.976171875}, {"start": 3172.39, "end": 3172.83, "word": " ال", "probability": 0.86279296875}, {"start": 3172.83, "end": 3173.09, "word": " Omega", "probability": 0.4873046875}, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fcd64630527d60271c02f7aa5f7ef9ea1b890db0
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Td82bGClLc4_raw.srt
@@ -0,0 +1,2652 @@
+1
+00:00:05,180 --> 00:00:08,780
+بسم الله الرحمن الرحيم يعطيكوا العفو يا شباب نكمل
+
+2
+00:00:08,780 --> 00:00:11,500
+اليوم في جزئيتي ال algorithm و البداية اللي كانت
+
+3
+00:00:11,500 --> 00:00:15,620
+بسيطة وسهلة مجرد ان احنا أخدنا مجموعة statements
+
+4
+00:00:15,620 --> 00:00:20,000
+للغة وصفية على اساس ان نبدأ نتكلم عن مجموعة
+
+5
+00:00:20,000 --> 00:00:23,800
+algorithms اعتقد ان معظمها مر عليكم السابقة ان
+
+6
+00:00:23,800 --> 00:00:27,480
+انتوا اللي انا مخلصين برمجة واحد و اتنين يعني
+
+7
+00:00:27,480 --> 00:00:31,370
+ماخدين two coursesمن في البرمجة وماخدين الان
+
+8
+00:00:31,370 --> 00:00:34,530
+بتاخدوا ال data structure يعني المفروض انه خلال
+
+9
+00:00:34,530 --> 00:00:38,930
+الفترة هذه محاضراتنا يعني بسيطة مرة عليكمانا حتى
+
+10
+00:00:38,930 --> 00:00:42,910
+اتوقع انه انتوا لحالكوا على طول بت .. اتجاوبوا
+
+11
+00:00:42,910 --> 00:00:48,570
+معانا طيب من خلال المحاضرة السابقة لهذا الموضوع
+
+12
+00:00:48,570 --> 00:00:52,630
+اللي هو ال algorithms كنا اتكلمنا عن مثال وضحنا
+
+13
+00:00:52,630 --> 00:00:55,550
+فيه مجموعة list statements و اللي هي كان إيجاد ال
+
+14
+00:00:55,550 --> 00:01:00,070
+maximum value ل .. او ال maximum element من داخل
+
+15
+00:01:00,070 --> 00:01:05,140
+list معينةالآن نبدأ في مجموعة تطبيقات تانية منها
+
+16
+00:01:05,140 --> 00:01:07,860
+وأهمها اللي انتوا اكيد برضه مرت عليكم اللي هي ال
+
+17
+00:01:07,860 --> 00:01:11,220
+searching عملية ال searching في جزئية ال searching
+
+18
+00:01:11,220 --> 00:01:15,480
+اللي هي البحث طبعا في ordered list هنا بنتكلم عن
+
+19
+00:01:15,480 --> 00:01:21,420
+ال search في list مرتبة list مرتبة مرتبة اللي هي
+
+20
+00:01:21,420 --> 00:01:27,040
+بشكل تسعودي بشكلتصعدي طبعا بشكل تنازلي برضه بيمشي
+
+21
+00:01:27,040 --> 00:01:30,780
+الحال بس شوية مفاهيم بسيطة بتتغير معاك فالمفروض
+
+22
+00:01:30,780 --> 00:01:37,540
+الموضوع بيجلجش ف .. كأكواد بنفكر بالتالي given
+
+23
+00:01:37,540 --> 00:01:40,900
+list L لازم تكون فيها اندل input ال input ده و ال
+
+24
+00:01:40,900 --> 00:01:44,940
+arguments اللي هي ال list نفسها لمجموعة elements و
+
+25
+00:01:44,940 --> 00:01:50,750
+لازم تكون sorted بمعنى مصنفةمرتبة مرتبة أو مصنفة
+
+26
+00:01:50,750 --> 00:01:57,450
+تمام ب order معين و احنا قولنا ال order هذاتساعدة
+
+27
+00:01:57,450 --> 00:02:03,710
+تنازلة المهم أنه في ترتيب معين واضح سواء كان أرقام
+
+28
+00:02:03,710 --> 00:02:06,970
+أو حروف حتى
+
+29
+00:02:26,810 --> 00:02:31,010
+درجة جدا، method درجة جدا في برامج كتيرة، كويس
+
+30
+00:02:31,010 --> 00:02:36,020
+بدنا نحسب من ال X هذا اللي given عنديو في نفس
+
+31
+00:02:36,020 --> 00:02:39,960
+الوقت given عندي list بدنا نحسب هل ال X هذا موجود
+
+32
+00:02:39,960 --> 00:02:43,120
+في ال list ولا لأ إذا موجود بدي أرجعله بال إيش؟
+
+33
+00:02:43,120 --> 00:02:47,220
+بال index تبعه بال index تبعه كافي ال index؟ كافي
+
+34
+00:02:47,220 --> 00:02:50,760
+ليش؟ لأن أنا بتتكلم عن ordered list يعني معناه ذلك
+
+35
+00:02:50,760 --> 00:02:54,640
+إن ال index هو ثابت مكانه مكانه دائما ثابت أرجعله
+
+36
+00:02:54,640 --> 00:03:00,390
+بالمكان تبع ال X هذا إذا موجود داخل ال list Lتمام
+
+37
+00:03:00,390 --> 00:03:04,890
+اذا والله غير موجود ارجع ليه انه غير موجود ارجعه
+
+38
+00:03:04,890 --> 00:03:09,650
+انه غير موجود هذا ببساطة وصف او بكل بالكلام ايش
+
+39
+00:03:09,650 --> 00:03:13,610
+اللي بدنا نعمله تمام الان عشان نعمل هذا الكلام في
+
+40
+00:03:13,610 --> 00:03:17,350
+عدة algorithms بيشتغلوا في الموضوع هذا عدة
+
+41
+00:03:17,350 --> 00:03:20,930
+algorithms ممكن نعمل منهم عملية ال search منهم ال
+
+42
+00:03:20,930 --> 00:03:23,710
+linear وهذا أبسط نوع واللي أكيد أخدتهم أكيد مرة
+
+43
+00:03:23,710 --> 00:03:27,290
+عليكم لأن هذا basic يعني المفروض انهأشي مارر
+
+44
+00:03:27,290 --> 00:03:33,830
+عليكوا سابقا بتبدأ من a1 a2 to an هذه ال list ال و
+
+45
+00:03:33,830 --> 00:03:38,810
+عندك قيمة x بدكتفحص هي موجودة ولا غير موجودة بمعنى
+
+46
+00:03:38,810 --> 00:03:42,210
+عملية search إذا موجودة ارجعلي بال index في ال
+
+47
+00:03:42,210 --> 00:03:44,450
+location الأول ولا التاني ولا الخامس ولا في ال
+
+48
+00:03:44,450 --> 00:03:48,910
+location in ارجعلي بال index بس طيب مش موجودة
+
+49
+00:03:48,910 --> 00:03:52,530
+اعطيني دلالة ارجعلي بأي حاجة أستدل منها أن انت
+
+50
+00:03:52,530 --> 00:03:56,930
+مالجتهش غير موجود ارجعلي بصفر مثلا ارجعلنا ب zero
+
+51
+00:03:57,800 --> 00:04:02,800
+طبعا فإذا procedure هيبدأنا ال code طبعنا هنسميه
+
+52
+00:04:02,800 --> 00:04:06,180
+باسم معين التفكير بالنسبالي أنه لازم يكون في
+
+53
+00:04:07,050 --> 00:04:10,170
+arguments ال input اللي انا محتاجها مستحيل اعرف
+
+54
+00:04:10,170 --> 00:04:13,530
+اشتغل بدونها هي قيمة ال X X اللي انت بتدور عليها
+
+55
+00:04:13,530 --> 00:04:17,850
+اللي هي ال integer كويس زائد ال list نفسها تكتب
+
+56
+00:04:17,850 --> 00:04:24,630
+ليها AB A1 A2 to AN ماشي تكتب ليها L كويس و
+
+57
+00:04:24,630 --> 00:04:29,590
+distinct integers okay خلاص فهمنا بس بدك توضح ان
+
+58
+00:04:29,590 --> 00:04:33,410
+انت بتكلم عن index ببدأ من واحدال index بيبدأ من
+
+59
+00:04:33,410 --> 00:04:36,550
+واحد لان انتوا كلكوا عارفين ان احنا في ال array
+
+60
+00:04:36,550 --> 00:04:40,890
+بنشير للعنصر باستخدام ال index تبعه مافيش طريقة
+
+61
+00:04:40,890 --> 00:04:45,190
+تانية انت عشان تعرف ال index او element معين
+
+62
+00:04:45,190 --> 00:04:50,090
+بتعرفه من خلال ال index تبعه تمام بنبدأ بواحد
+
+63
+00:04:50,090 --> 00:04:54,040
+معناته كأن انا بدي اجف عند ال index الأولبمعنى بدي
+
+64
+00:04:54,040 --> 00:04:57,520
+افحص العنصر الأول ال element الأول منطقية جدا
+
+65
+00:04:57,520 --> 00:04:59,920
+مافيش قبل ال element الأول فبدي أبدأ افحص من ال
+
+66
+00:04:59,920 --> 00:05:05,180
+element الأول ونبدأ الآن ال while أبسط شغله ان انت
+
+67
+00:05:05,180 --> 00:05:10,040
+تبقى تعمل for loop ال for loop هذا يبقى شغال يبقى
+
+68
+00:05:10,040 --> 00:05:17,070
+شغال بحيث انه يعمل scan على ال listامتى هيجف؟ عندك
+
+69
+00:05:17,070 --> 00:05:20,670
+حالتين ممكن يجف فيهم اما ان يلاقي X او يخلص ال
+
+70
+00:05:20,670 --> 00:05:26,190
+list مش هيك؟ مافيش شي تالت في الحالتين بوقف ال
+
+71
+00:05:26,190 --> 00:05:31,290
+loop تبعه والله لاجي ال X المفروض يجف مالاجيش ال
+
+72
+00:05:31,290 --> 00:05:38,310
+X؟بدو يكمل لعند ما يخلص ال in يعمل in مرة من
+
+73
+00:05:38,310 --> 00:05:41,190
+عمليات الفحص أكتر من هيك خلاص وقف لأن هو عارف
+
+74
+00:05:41,190 --> 00:05:44,690
+مسبقا ان ال list تبعته ال length تبعتها in خلصنا
+
+75
+00:05:44,690 --> 00:05:49,990
+فإذن while طول ما I أقل من أو يساوي in فهو شغال
+
+76
+00:05:49,990 --> 00:05:54,870
+معناته في عناصر مش شايف طول ما هو أقل من ال length
+
+77
+00:05:54,870 --> 00:06:00,010
+معناته شغال and x لا تساوي ai ال I اللي أنا موجود
+
+78
+00:06:00,010 --> 00:06:05,290
+عندها حاليافإذن لا لجأ X ولا وصل لنهاية ال list
+
+79
+00:06:05,290 --> 00:06:11,810
+استمر فإذن استمر كويس و I بتساوي I زائد واحد ال
+
+80
+00:06:11,810 --> 00:06:16,470
+incrementstatement اللي موجود عندك increment زود
+
+81
+00:06:16,470 --> 00:06:20,570
+كل مرة زود ورجع افحص زود ورجع افحص زود ورجع افحص
+
+82
+00:06:20,570 --> 00:06:24,330
+خلاص مافيش اكتر من هيك اللي عملنا لا begin ولا end
+
+83
+00:06:24,330 --> 00:06:28,490
+مش هيك يعني مافتحتش اقواس ال curly braces تبعتك
+
+84
+00:06:28,490 --> 00:06:32,310
+انا مش محتاج اللي الشرط هذا فالجواب هذا بس لا اكتر
+
+85
+00:06:32,310 --> 00:06:38,130
+ولا اقل فإذا هاي ال loop تبعك فقط بس هاي كل ال
+
+86
+00:06:38,130 --> 00:06:46,420
+loop امتى حقيقة زي ما قلنا يصبح اكبر منصحيح؟ طيب
+
+87
+00:06:46,420 --> 00:06:53,820
+إذا وصلت لأكبر من معناه ذلك إنه ما جابش X ما جابش
+
+88
+00:06:53,820 --> 00:06:59,400
+X ليش؟ لأنه إذا وصلت لأكبر من أنت عديت N أنت أصبح
+
+89
+00:06:59,400 --> 00:07:05,320
+خلاص بعدها أنت آخر مرة وصلت ل I بتساوي N وماحققتش
+
+90
+00:07:05,320 --> 00:07:10,980
+الشرط هذا وإلا كان وجفت بس مدام ما وجفتش معناته
+
+91
+00:07:10,980 --> 00:07:16,160
+فعليا ماحققتش إن هي تساوي ANاخر عنصر ماتحققش روح
+
+92
+00:07:16,160 --> 00:07:21,480
+اتزودت واحد ف automatically صرت N زائد واحد الان N
+
+93
+00:07:21,480 --> 00:07:25,780
+زائد واحد هذا ال condition هو اللي عطل ال
+
+94
+00:07:25,780 --> 00:07:29,320
+proposition هو اللي عطل ال proposition فطلعنا عشان
+
+95
+00:07:29,320 --> 00:07:34,100
+تيجي تفحص انت أجل من أو يساوي in طبعا فعليا انت
+
+96
+00:07:34,100 --> 00:07:39,180
+صرت أكبر من صحيح فإذا false false إيش يعني انا
+
+97
+00:07:39,180 --> 00:07:41,240
+هيرجع بصفر يعني مالاجتش
+
+98
+00:07:43,570 --> 00:07:47,970
+لكن لو اللي ود في ال for loop مش ال condition مش
+
+99
+00:07:47,970 --> 00:07:51,010
+ال .. ال .. ال .. ال .. ال atomic proposition
+
+100
+00:07:51,010 --> 00:07:55,970
+الأول ال atomic proposition التاني انت عند I معينة
+
+101
+00:07:55,970 --> 00:08:05,790
+وجدت انه X تساوي AI تساوت صار هنا false اطلعت بدون
+
+102
+00:08:05,790 --> 00:08:10,030
+ما تنفذ هذه صحيح فانت ما زلت عند ال I نفسها اللي
+
+103
+00:08:10,030 --> 00:08:15,760
+كانت هي ال index لل Xهي index قيمة X في الحالة هذه
+
+104
+00:08:15,760 --> 00:08:19,780
+بتطلع هنا إذا كان أقل من N هو فعلا هتبقى أقل من N
+
+105
+00:08:19,780 --> 00:08:23,100
+لأنه مش هذا ال proposition اللي وجفها هو فعلا ال
+
+106
+00:08:23,100 --> 00:08:25,240
+proposition هذا اللي وجفها فهي فعلا هذا مازال
+
+107
+00:08:25,240 --> 00:08:30,060
+valid مازال صحيح حتى اللحظة مدام صحيح حتى اللحظة
+
+108
+00:08:30,060 --> 00:08:33,840
+ارجعلي بال I اللي انت لجيتها فبترجعلي بال مين بال
+
+109
+00:08:33,840 --> 00:08:41,090
+location اللي وكفت عنده X فعلا ممثلة ب AMبال AI
+
+110
+00:08:41,090 --> 00:08:47,090
+بال AI ممثلة ب AI خلاص خلصنا صار عندك ال location
+
+111
+00:08:47,090 --> 00:08:53,050
+اما هيطلع صفر او هيطلع I اللي وجف عندها تمام تمال
+
+112
+00:08:53,050 --> 00:08:56,310
+ال return لل location خلصنا او اتجفنا اذا والله
+
+113
+00:08:56,310 --> 00:09:02,780
+index او zero انت وصلتzero معناته مش موجود حلل،
+
+114
+00:09:02,780 --> 00:09:07,680
+index معين قيمة I معناته فعليا تحدى التلة ال X
+
+115
+00:09:07,680 --> 00:09:12,740
+فعليا و اللي موجودة وين ال location تبعها بس تمام
+
+116
+00:09:12,740 --> 00:09:17,960
+نوع أخر من أنواع ال search ال binary search برضه
+
+117
+00:09:17,960 --> 00:09:21,610
+by default أنا متأكد تمام أن أخدتهبكل بساطة binary
+
+118
+00:09:21,610 --> 00:09:27,830
+احنا عارفين ان هو ثنائي بمعنى كل مرة بتجسم ال list
+
+119
+00:09:27,830 --> 00:09:33,050
+تبعك ل two parts متساويتين two parts و بدك تعمل
+
+120
+00:09:33,050 --> 00:09:36,550
+elimination لواحد منهم فهذه العملية بتظهر عملية
+
+121
+00:09:36,550 --> 00:09:40,770
+elimination كل مرة بتجلل حجم ال main ال list تبعتك
+
+122
+00:09:40,770 --> 00:09:44,550
+بتجلل حجمها بتجلل حجمها بتجلل حجمها بس دائما ال
+
+123
+00:09:44,550 --> 00:09:49,390
+target تبعك انه المتبقي لو x موجودة لازم يظل فيها
+
+124
+00:09:50,520 --> 00:09:55,230
+لو X موجودة لابد ان يبقى ضمن الالـ Interval اللي
+
+125
+00:09:55,230 --> 00:10:00,670
+موجودة ضمن الـ Interval اللي موجودة ضمن الـ
+
+126
+00:10:00,670 --> 00:10:07,810
+Interval اللي موجودة ضمن الـ Interval اللي موجودة
+
+127
+00:10:07,810 --> 00:10:08,910
+ضمن الـ Interval اللي موجودة ضمن الـ Interval اللي
+
+128
+00:10:08,910 --> 00:10:09,110
+موجودة ضمن الـ Interval اللي موجودة ضمن الـ
+
+129
+00:10:09,110 --> 00:10:09,110
+Interval اللي موجودة ضمن الـ Interval اللي موجودة
+
+130
+00:10:09,110 --> 00:10:10,870
+ضمن الـ Interval اللي موجودة ضمن الـ Interval اللي
+
+131
+00:10:10,870 --> 00:10:12,950
+موجودة ضمن الـ Interval اللي موجودة ضمن الـ
+
+132
+00:10:12,950 --> 00:10:12,950
+Interval اللي موجودة ضمن الـ Interval اللي موجودة
+
+133
+00:10:12,950 --> 00:10:12,950
+ضمن الـ Interval اللي موجودة ضمن الـ Interval اللي
+
+134
+00:10:12,950 --> 00:10:19,130
+موجودة ضمن الـ Interval اللي موجودة ضمن الـ
+
+135
+00:10:19,130 --> 00:10:23,260
+Interval اللي موجودة ضمن الـ Interval اللي موجعلى
+
+136
+00:10:23,260 --> 00:10:27,620
+اتنين فانا جبت العنصر او ال index اللي في النص ال
+
+137
+00:10:27,620 --> 00:10:30,000
+index اللي في النص طيب مدام جبت ال index اللي في
+
+138
+00:10:30,000 --> 00:10:36,120
+النص هنا ال a خلينا نسميه المد انا فعليا حسبت ال M
+
+139
+00:10:36,120 --> 00:10:40,480
+على اساس ان هي تساوي I زائد J على اتنين هذا مش
+
+140
+00:10:40,480 --> 00:10:47,220
+دايما بيطلع كسر صحيح؟ مش بالضروري يطلع كسر ف floor
+
+141
+00:10:47,880 --> 00:10:53,220
+عشان تضمن ان انت بتتكلم عن index انتجر فاش index
+
+142
+00:10:53,220 --> 00:10:55,760
+بدون ان مش انتجر يعني انت بتقول يا الله انت في ال
+
+143
+00:10:55,760 --> 00:10:57,380
+location اتنين و نص فاش حاجة تسمي ال location
+
+144
+00:10:57,380 --> 00:11:00,720
+اتنين و نص يا في الخانة الأولى يا التانية فاش في
+
+145
+00:11:00,720 --> 00:11:05,680
+الخانة اتنين و نص تمام وصلنا هنا ايش بتسوي انت ..
+
+146
+00:11:05,680 --> 00:11:10,080
+اجيب ان عندك قيمة x و هي لازم تكون مرتبة احنا حتى
+
+147
+00:11:10,080 --> 00:11:14,290
+اللحظة بنتكلم عن ordered listفي ال linear و في ال
+
+148
+00:11:14,290 --> 00:11:21,010
+binary في الحالتين بتكلم عن ordered تمام فإذا كان
+
+149
+00:11:21,010 --> 00:11:28,230
+.. بدنا نفترض إذا كانت X أكبر من AN معناه ذلك
+
+150
+00:11:28,230 --> 00:11:32,290
+بالنسبة ل list مرتبة لا يمكن يكون في كل المنطقة
+
+151
+00:11:32,290 --> 00:11:37,650
+الأقل هنا لأنه أنا ضامن كل ال As اللي موجودة هنا
+
+152
+00:11:37,650 --> 00:11:44,410
+كلها أقل من AM مرتبالـ sequence تبعك هذا أو ال
+
+153
+00:11:44,410 --> 00:11:47,590
+list تبعتك أو ال array تبعتك مرتبة معناه ذلك إذا
+
+154
+00:11:47,590 --> 00:11:51,030
+كانت X أكبر من العنصر اللي موجود هنا فهي بالضرورة
+
+155
+00:11:51,030 --> 00:11:55,370
+أكبر من أي عنصر موجود أقل منها بالضرورة ففي الحالة
+
+156
+00:11:55,370 --> 00:11:59,610
+هذه I لجديدة هنرجع نعيد نفس الكلام ولكن هتيجي I
+
+157
+00:11:59,610 --> 00:12:08,310
+جديدة I زائد واحد على اعتبار أنه عند ال I اللي هي
+
+158
+00:12:08,310 --> 00:12:13,150
+ال M هذه عفوا M زائد واحدم زائد واحد عند ال M
+
+159
+00:12:13,150 --> 00:12:17,490
+نفسها X أكبر منها فمابدهاش منها انا ضامن ان هي
+
+160
+00:12:17,490 --> 00:12:22,630
+خلاص عدناها احنا عدناها هي مش هتسويها معنى ذلك انه
+
+161
+00:12:22,630 --> 00:12:28,650
+بده من بعدها فبتصبح I لجديدة هي ال M زائد واحد M
+
+162
+00:12:28,650 --> 00:12:33,570
+زائد واحد فصار في عندك interval جديدة تعيد عليها
+
+163
+00:12:33,570 --> 00:12:39,190
+نفس الكلام من I ل J مجموعين على اتنين فبصير M
+
+164
+00:12:39,190 --> 00:12:43,720
+جديدةهنا و ارجع ايد نفس الكلام لما في الآخر تصل ل
+
+165
+00:12:43,720 --> 00:12:48,860
+one element فقط بقارن فيه يا هو يا مش هو او انتهت
+
+166
+00:12:48,860 --> 00:12:56,740
+الجثة هاي كل الفكرة هاي كل فكرة ال ال binary نشوف
+
+167
+00:12:56,740 --> 00:13:02,460
+ال code نفسه فشرحنا اتفقنا هي بتعمل ال midpoint
+
+168
+00:13:02,460 --> 00:13:08,160
+لجديدة and so on لما تصل في الآخر ل one elementالـ
+
+169
+00:13:08,160 --> 00:13:11,180
+one element هذا بنفحص مباشرة هو ولا مش هو إذا هو
+
+170
+00:13:11,180 --> 00:13:13,780
+خير وبركة أنت فعلاً ضالتك تعمل elimination لما
+
+171
+00:13:13,780 --> 00:13:18,060
+وصلت ل element واحد يا بيسوي x أو انه بيسويش x
+
+172
+00:13:18,060 --> 00:13:22,640
+معناته x غير موجودة x غير موجودة لأن كل اللي أقل
+
+173
+00:13:22,640 --> 00:13:28,060
+هو أقل من x وكل اللي أكبر هو أكبر من x فإذا x
+
+174
+00:13:28,060 --> 00:13:32,080
+المفروض هي تكون between them لكن مش موجودة هي مش
+
+175
+00:13:32,080 --> 00:13:37,140
+موجودة تمام هتشوف ال codeك .. ك code برضه
+
+176
+00:13:37,140 --> 00:13:40,900
+procedure binary search و بنفتح الأقواص عشان نحدد
+
+177
+00:13:40,900 --> 00:13:43,760
+إيش ال inputs اللي بدنا إياها لل code هذا أول شغل
+
+178
+00:13:43,760 --> 00:13:48,940
+محتاج ال X اللي أنا بدور عليها و أنت بدور عليها
+
+179
+00:13:48,940 --> 00:13:53,900
+خليني أقول في واحدة من الوزارات و بدك خدمة معينة
+
+180
+00:13:53,900 --> 00:13:58,000
+أو أول حاجة بده يفتح ملفك هيقولك هاتلي رقم الهوية
+
+181
+00:13:58,000 --> 00:14:02,660
+هي ال Xصحيح؟ هاتل الرقم الهوية عشان يضرب رقم
+
+182
+00:14:02,660 --> 00:14:06,100
+الهوية افتح .. يفتح ملفك طب هل انت لحالك الوحيد
+
+183
+00:14:06,100 --> 00:14:09,580
+اللي إلك ملف؟ في عندك فوق لتنين مليون بني أدم في
+
+184
+00:14:09,580 --> 00:14:13,020
+غزا اللي هم ملفات مش شيخ إذا بتكلم عن سكان عدد غزا
+
+185
+00:14:13,020 --> 00:14:16,440
+فانت فوق لتنين مليون بدك تعمل search فيهم هدولة
+
+186
+00:14:16,440 --> 00:14:21,810
+listالاتنين مليون هدولة هدولة ال list تبعتك كويس و
+
+187
+00:14:21,810 --> 00:14:24,730
+رقم الهوية هي ال X عشان هيك بقولك هذا من الحاجات
+
+188
+00:14:24,730 --> 00:14:28,330
+الحيوية جدا كأكواد كنوع أكواد اللي هي ال search
+
+189
+00:14:28,330 --> 00:14:32,570
+codes من الحاجات الحيوية جدا اللي بتستخدم في كتير
+
+190
+00:14:32,570 --> 00:14:37,070
+برامج انت عندك رقم و بدك تدور عليه رقم هوية مثلا
+
+191
+00:14:37,070 --> 00:14:43,450
+for example تمام فإذا نبدأ كتالي X لازم تكون موطع
+
+192
+00:14:43,450 --> 00:14:46,530
+انتجر رقم هويتك انتجر فيه عندكوا حد رقم هويته مش
+
+193
+00:14:46,530 --> 00:14:52,100
+انتجرأكيد integer طبعا ال list اللي موجودة مجموعة
+
+194
+00:14:52,100 --> 00:14:57,140
+integers برضه متنوعة مختلفة مش هكونوا مختلف فيهم
+
+195
+00:14:57,140 --> 00:15:01,260
+قصور و بتبدأ زي ما قلنا ال I و ال J ليش؟ لأن أنا
+
+196
+00:15:01,260 --> 00:15:07,080
+بدي أعمم ال interval في أول iteration في أول لفة
+
+197
+00:15:07,080 --> 00:15:10,100
+في البرنامج هي بتكون بادية فعلا من الواحد و راحة
+
+198
+00:15:10,100 --> 00:15:13,940
+to end بس بعد هيك لأ مش هتكون بادية من الواحد عشان
+
+199
+00:15:13,940 --> 00:15:19,770
+هيك مبدأيا بتحط لهابدأوا النهاية I ل J و بنبدأ I
+
+200
+00:15:19,770 --> 00:15:26,770
+بواحد J بال N و نبدأ بعد هيك طول ما I أقل من J فهم
+
+201
+00:15:26,770 --> 00:15:31,270
+ماوصلوش في مرحلة ال elimination التقصير تقصير أو
+
+202
+00:15:31,270 --> 00:15:36,510
+تقليل ال duration أن هم وصلوا لنفس المقطة ما زالوا
+
+203
+00:15:36,510 --> 00:15:40,370
+I أقل من J I أقل من J I أقل من J I أقل من J I أقل
+
+204
+00:15:40,370 --> 00:15:43,210
+من J لما ينطبقوا على بعض بيقولوا اه خلاص وقف أنا
+
+205
+00:15:43,210 --> 00:15:47,960
+وصلت لعنصر واحديا هو يا مش هو .. يا هو يا مش هو
+
+206
+00:15:47,960 --> 00:15:53,340
+فإذا طول ما I أقل من J هنا في شوية statements بدنا
+
+207
+00:15:53,340 --> 00:15:57,720
+نعملهم ف begin و end لإن مش هيكون على جد statement
+
+208
+00:15:57,720 --> 00:16:01,300
+واحدة بدنا نعملها أول شغلة statement واضحة خطوة
+
+209
+00:16:01,300 --> 00:16:06,120
+ضرورية بدها تحسب ال mid point أو ال mid index ال
+
+210
+00:16:06,120 --> 00:16:09,060
+index الوسطي طب هاي لحالها بدون ال begin و ال end
+
+211
+00:16:09,060 --> 00:16:12,920
+معناته هفهم أنه هيبقى بس يحسب Mبالنسبة لل while
+
+212
+00:16:12,920 --> 00:16:17,800
+هذه او جاعت في problem ايش بنسميها ال runtime
+
+213
+00:16:17,800 --> 00:16:21,360
+error هنا صار عندك runtime error اذا ما كتبتش
+
+214
+00:16:21,360 --> 00:16:24,960
+begin بدون ال begin مااخدين بالكم ان الجزية هذه
+
+215
+00:16:24,960 --> 00:16:31,080
+بدون begin و end هيفهم ال while ان هذا فقط جوابها
+
+216
+00:16:31,080 --> 00:16:37,480
+بس ال condition هذا هيجوابه بس هي ال event تبعته
+
+217
+00:16:38,480 --> 00:16:44,080
+الـ F هذه لأ خارجية لكن بدها تكون محسوبة بيجن اند
+
+218
+00:16:44,080 --> 00:16:47,500
+فبفهم ان كل هدول هيك على بعض statement واحدة جواب
+
+219
+00:16:47,500 --> 00:16:51,720
+ل ال condition او ل ال proposition I أقل من J تمام
+
+220
+00:16:51,720 --> 00:16:55,560
+حسبنا ال mid و أخدنا ال floor لإن مش متوقع دائما
+
+221
+00:16:55,560 --> 00:17:00,620
+هتكون integer فبتاخدها ال floor و بتفحص فحصنا هنا
+
+222
+00:17:00,620 --> 00:17:06,200
+العنصر اللي عند ال mid point او ال mid indexالعنصر
+
+223
+00:17:06,200 --> 00:17:11,160
+هذا أقل ولا أكبر من X إذا والله X أكبر X أكبر
+
+224
+00:17:11,160 --> 00:17:16,900
+فمعنى ذلك كل اللي أقل لا يمكن تكون X موجودة فيه X
+
+225
+00:17:16,900 --> 00:17:22,000
+أكبر من العنصر اللي في النص فكل ما فيه قبل النص هو
+
+226
+00:17:22,000 --> 00:17:28,720
+أقل من العنصر اللي عند النص فبالتالي هو أقل منX ف
+
+227
+00:17:28,720 --> 00:17:32,960
+automatic ايش بسوي بقول I او ال .. ال .. ال
+
+228
+00:17:32,960 --> 00:17:35,520
+interval الجديدة المفروض تبدأ من ايش من M زائد
+
+229
+00:17:35,520 --> 00:17:40,740
+واحد من M زائد واحد لأنه فعليا M نفسها كانت اقل من
+
+230
+00:17:40,740 --> 00:17:45,240
+X فليش ارجع احطها ابحث عنها كمان مرة خلاص بستفنيها
+
+231
+00:17:45,240 --> 00:17:52,380
+بنبدأ من مين M زائد واحد else ايش else يعني معنى
+
+232
+00:17:52,380 --> 00:17:59,580
+ذلك انه عكس الشرط ايش عكس الشرطX أقل أو يساوي أو
+
+233
+00:17:59,580 --> 00:18:06,060
+يساوي عشان هيك كتبنا M بس ماقولناش نقص واحد يعني
+
+234
+00:18:06,060 --> 00:18:09,280
+مابتناش زي ما يقولوا انت شاطر فيها يقولوا اه طب ما
+
+235
+00:18:09,280 --> 00:18:13,160
+هي لأ انا ماقولتش ان هي مافحستش أو يساوي فممكن
+
+236
+00:18:13,160 --> 00:18:17,400
+تكون تساوي قد تكون تساوي فعشان هيك لأ بتضل موجودة
+
+237
+00:18:17,400 --> 00:18:21,960
+معاك ف J تساوي M إذا صار هيك الكلام و I هتضل زي ما
+
+238
+00:18:21,960 --> 00:18:26,160
+هيفي الحالة هذه I هتظل كما هي فانا أخدت الجزء اللي
+
+239
+00:18:26,160 --> 00:18:31,360
+في أول ال list و سبت اللي في الآخر على اعتبار انه
+
+240
+00:18:31,360 --> 00:18:37,140
+العكس ان X أقل تمام هنستمر في هذا ال loop لعند ما
+
+241
+00:18:37,140 --> 00:18:43,760
+كل مرة يتجل I و J I و J I و J يا إما جه هتصير هي
+
+242
+00:18:44,650 --> 00:18:48,730
+الـ mid index او I هتصير ال mid index زائد واحد
+
+243
+00:18:48,730 --> 00:18:51,670
+فمعنى ذلك ان كل مرة انت ال interval اللي عندك
+
+244
+00:18:51,670 --> 00:18:55,490
+بتاخد نصها كل مرة نصها كل مرة نصها كل مرة نصها في
+
+245
+00:18:55,490 --> 00:19:01,290
+مرحلة و مرحلة هتصل ل element واحد ال element
+
+246
+00:19:01,290 --> 00:19:03,970
+الوحيد هذا تخيل معي سيناريو انه ضل عندك two
+
+247
+00:19:03,970 --> 00:19:10,210
+elements I و JI و J في الحالة دي لما تحسب ال M إيش
+
+248
+00:19:10,210 --> 00:19:16,110
+بتساوي نص صح لما بتاخد ال floor هتطلع I هتفحصها
+
+249
+00:19:16,110 --> 00:19:22,650
+لجيتها إنه ال X ما زالت أكبر إيش بتقول I M زائد
+
+250
+00:19:22,650 --> 00:19:26,150
+واحد يعني بيصير نفس ال J معناه ذلك بيجي في ال
+
+251
+00:19:26,150 --> 00:19:30,640
+conditionواضحات؟ هيجف ال condition automatic صح
+
+252
+00:19:30,640 --> 00:19:35,780
+تمام مدام وجف ال condition في الآخر هيجف هيجف
+
+253
+00:19:35,780 --> 00:19:40,100
+لمجال طول ما حضرك تشطل باللوب هذا لعندما تشوف في
+
+254
+00:19:40,100 --> 00:19:43,620
+الآخر الام اللي ضلت في الآخر اللي هم في الآخر مش
+
+255
+00:19:43,620 --> 00:19:47,140
+ضلوا واحد و فانصر واحد اتوحدوا فانصر واحد افحص
+
+256
+00:19:47,140 --> 00:19:51,620
+للانصر اللي ضلهل X تسوي هنا بشكل مباشر انت بتفحص
+
+257
+00:19:51,620 --> 00:19:55,280
+عنصر واحد فقط يا بتسوي يا بتسوهش اذا بتسوي ارجالي
+
+258
+00:19:55,280 --> 00:20:02,140
+بال index تبعه خلصنا بتسوهاش Zero انتهى الموضوع طب
+
+259
+00:20:02,140 --> 00:20:04,840
+انا عارف ان هذا اكلكت مش عارف رابع خمس مرة
+
+260
+00:20:04,840 --> 00:20:07,440
+تنشرحلكوا الطريقة هذه لأنه أكيد أخدتوها في البرمجة
+
+261
+00:20:07,440 --> 00:20:11,200
+وأخيرا أخدتوها في مقدمات أي حاجة إلها algorithms
+
+262
+00:20:13,560 --> 00:20:19,200
+يعني بتهيألي هذا يعني code مش كتير هيكون صعب عليكم
+
+263
+00:20:19,200 --> 00:20:24,180
+لمبرمجين زي حالاتكم الكوب سنة بتاخدوا برمجة
+
+264
+00:20:24,180 --> 00:20:29,220
+فبتتكلم عن algorithm بحيث انك بدك تجمع عناصر ال
+
+265
+00:20:29,220 --> 00:20:32,860
+array بس بدك تجمع عناصر ال array مش محتاجك طبعا
+
+266
+00:20:32,860 --> 00:20:38,020
+for loop مش هيك او whileطول ما انت اقل ال index
+
+267
+00:20:38,020 --> 00:20:43,720
+اقل من N جمعه فبدك تبدأ ب sum equal to zero و تجمع
+
+268
+00:20:43,720 --> 00:20:48,900
+عليه تبدأ تجمع عليه فلاحظوا S equal to zero هذه
+
+269
+00:20:48,900 --> 00:20:51,320
+الجزئية اللي خلتني المرة اللي فاتت قلتلكوا خدوا
+
+270
+00:20:51,320 --> 00:20:56,680
+بالكم من هل انا بتكلم عن implication ولا if and
+
+271
+00:20:56,680 --> 00:21:00,140
+only if اذا والله هذا محدد مسبقا فال for loop كله
+
+272
+00:21:00,140 --> 00:21:05,340
+صار if and only ifبس اذا انت محددها مسبقا فبتصير
+
+273
+00:21:05,340 --> 00:21:08,840
+زي ما انتم تخيلين ان هي فعلا if and only if خلاص
+
+274
+00:21:08,840 --> 00:21:15,620
+يا yes يا no انتهى yes اكيد هتروح ل Latin نه اكيد
+
+275
+00:21:15,620 --> 00:21:21,340
+هتروح ل else بس يكون هذا ماخدين بالكم انه اتكلمنا
+
+276
+00:21:21,340 --> 00:21:24,540
+عنها طيب ال procedure و زي ما قلنا summation بده
+
+277
+00:21:24,540 --> 00:21:27,300
+تحدد ايش ال input تبعك فال input تبعك هي ال list
+
+278
+00:21:28,150 --> 00:21:31,570
+الشيء بالظبط هي مجموعة integers summation equal to
+
+279
+00:21:31,570 --> 00:21:36,110
+zero في البداية فالعنصر S ده بلاش يكون له قيمة
+
+280
+00:21:36,110 --> 00:21:39,450
+مسبقة بلاش يكون له قيمة مسبقة وفي الحالة هذه
+
+281
+00:21:39,450 --> 00:21:43,320
+معناته هبدأ أجمع على قيمة سابقة موجودةممكن في
+
+282
+00:21:43,320 --> 00:21:46,880
+الحالة هذه إذا كان ال compiler تبعك not smart
+
+283
+00:21:46,880 --> 00:21:49,920
+enough هيشوف إيش ال equation اللي كان موجود في
+
+284
+00:21:49,920 --> 00:21:54,200
+المكان اللي مخزن على ال RAM هنا اللي اتخصصله كقيمة
+
+285
+00:21:54,200 --> 00:22:00,160
+S و يبدأ يحوش عليه يبدأ يحوش عليه كويس for loop من
+
+286
+00:22:00,160 --> 00:22:03,840
+1 to N و خلصنا ما هي هي ال list كاملة و S بتساوي
+
+287
+00:22:03,840 --> 00:22:08,940
+ال S زائد A Iبترجعنا في الآخر بمين؟ بقيمة اسمة،
+
+288
+00:22:08,940 --> 00:22:12,420
+طبعا مش محتاج هنا لا begin ولا end، ليش؟ لأنه
+
+289
+00:22:12,420 --> 00:22:16,420
+statement واحدة، ف statement واحدة مافيش داعي تكبر
+
+290
+00:22:16,420 --> 00:22:22,150
+ال code تبعك، تمامالان بنتكلم عن ال sort
+
+291
+00:22:22,150 --> 00:22:27,030
+algorithms طب و أخدنا ال binary و أخدنا double ال
+
+292
+00:22:27,030 --> 00:22:30,570
+linear على أساس ان هي sorted مسبقا sorted ال list
+
+293
+00:22:30,570 --> 00:22:34,730
+تبعتك صحيح؟ طب لأ هي مش sorted مع أن انت بدك تعمل
+
+294
+00:22:34,730 --> 00:22:37,310
+عملية sorting عملية ال sorting انت اللي بدك تعملها
+
+295
+00:22:37,310 --> 00:22:42,130
+وهذه طبعا برضه من الأكواد الحيوية جدا و اللي يكاد
+
+296
+00:22:42,130 --> 00:22:47,700
+يكون مافيش اي برنامج يخلو منهاأشهر برنامج موجودة
+
+297
+00:22:47,700 --> 00:22:50,720
+فيه هي ال spreadsheets و ال databases قواعد
+
+298
+00:22:50,720 --> 00:22:53,780
+البيانات أكيد أهم حاجة في قاعدة البيانات أنك انت
+
+299
+00:22:53,780 --> 00:22:59,320
+تقدر تعمل إعادة ترتيب لقاعدة البيانات حسب الإسم لأ
+
+300
+00:22:59,320 --> 00:23:04,480
+حسب الرقم الجامعي ممكن حسب الإسم ممكن حسب ال GPA
+
+301
+00:23:04,480 --> 00:23:09,680
+ممكن فانت اللي بتختار ساعتها تعمل sorting حسب إيش
+
+302
+00:23:09,680 --> 00:23:12,900
+بس في النهاية ال code لازم يكون بيقدر يفهم إيش
+
+303
+00:23:12,900 --> 00:23:15,730
+يعني عمليت sortingعملية ال sorting عشان هيك هي دي
+
+304
+00:23:15,730 --> 00:23:19,150
+من الأكواد المهمة جدا و اللي محتاج تكون حافظها زي
+
+305
+00:23:19,150 --> 00:23:22,610
+اسمك مبرمج تكون خلاص انت في دماغك على طول حافظها
+
+306
+00:23:22,610 --> 00:23:28,090
+فاهم كيف تشتغل و فاهم أنواعها لأنه طبعا زي ما قلنا
+
+307
+00:23:28,090 --> 00:23:34,190
+في أكواد more efficient عن أكواد تانية اللي احنا
+
+308
+00:23:34,190 --> 00:23:38,030
+هنشرحهم بالمناسبة هم الأضعف المهم بس انحدد الفكرة
+
+309
+00:23:38,030 --> 00:23:40,290
+لكن اتوقع انه في ال database لأ انتوا هتاخدوا
+
+310
+00:23:40,290 --> 00:23:44,820
+أنواع غيرهاو لازم تاخدوا حاجة علاقة بال sorting ..
+
+311
+00:23:44,820 --> 00:23:47,580
+لازم تاخدوا حاجة علاقة بال sorting .. بس طبعا
+
+312
+00:23:47,580 --> 00:23:51,040
+الأكواد الحديثة اللى الآن سرعتها أسرع .. هذا
+
+313
+00:23:51,040 --> 00:23:54,020
+الكلام اللى عندى هو مش هيبين معنى .. هيبين معنى
+
+314
+00:23:54,020 --> 00:23:55,860
+إيه انت لما ناخد ال complexity و نحسب ال
+
+315
+00:23:55,860 --> 00:23:59,260
+complexity للأكوادو نشوف ان ال complexity هذه لأ
+
+316
+00:23:59,260 --> 00:24:04,260
+هي ضعيفة ممكن نحسنها ممكن نحسنها فزي ما قلنا في ال
+
+317
+00:24:04,260 --> 00:24:07,940
+Excel مهم جدا ال code هي ده ال code هي ده من ال
+
+318
+00:24:07,940 --> 00:24:11,920
+code المهم جدا و اللي انت فيه ايقونه له فوق عبارة
+
+319
+00:24:11,920 --> 00:24:17,840
+عن اسمها a-zهذه معناته ان انت بتعمل sorting فعليا
+
+320
+00:24:17,840 --> 00:24:23,360
+انت بس بتحدد ال column و بتعمله بتوص على ال icon
+
+321
+00:24:23,360 --> 00:24:27,220
+هذي بيعملك automatic sorting a to z ولا z to a
+
+322
+00:24:27,220 --> 00:24:31,540
+اللي هي تصعدي ولا تنازلي بس فلاحظ ان هي حاجة by
+
+323
+00:24:31,540 --> 00:24:34,760
+default موجودة في البرامج تمام هناخد نوعين هناخد
+
+324
+00:24:34,760 --> 00:24:38,340
+ال bubble sort و هناخد فكرة ال insertion sort
+
+325
+00:24:40,370 --> 00:24:43,710
+بالنسبة لل bubble بابل اللي هي فقاعة يعني معناته
+
+326
+00:24:43,710 --> 00:24:46,450
+فقاعة يعني انا بتكلم عن عملية floating اللي هي
+
+327
+00:24:46,450 --> 00:24:50,870
+تعوين تعوين الأرقام الصغيرة للأعلى هي فكرتها فانت
+
+328
+00:24:50,870 --> 00:24:56,390
+بيكون عندك الريب هذا الشكل من البداية للنهاية مش
+
+329
+00:24:56,390 --> 00:25:01,030
+مرتب لاحظين مش مرتب طيب عشان ارتبه بعمل عملية
+
+330
+00:25:01,030 --> 00:25:07,850
+comparison بين كل عنصرين ورا بعض بين كل عنصرين ورا
+
+331
+00:25:07,850 --> 00:25:13,140
+بعض فبمسك الأول والتانيبهمني أنه دائما الأول يكون
+
+332
+00:25:13,140 --> 00:25:18,180
+أصغر من التاني خلاص تمام هاي الأول أصغر من التاني
+
+333
+00:25:18,180 --> 00:25:21,480
+خلاص بتسيبها و بتنزل اللي وراهم التاني و التالت
+
+334
+00:25:21,480 --> 00:25:27,060
+بهمني التاني أو ال index الأقل يكون قيمته أقل و
+
+335
+00:25:27,060 --> 00:25:32,720
+وجدنا أنه لأ بصبتش تلاتة أكبر .. أصغر من اتنين
+
+336
+00:25:32,720 --> 00:25:39,540
+بعكسهمبعمل x exchange او swap زي ما قلنا قبل المرة
+
+337
+00:25:39,540 --> 00:25:44,840
+اللي فاتت بنعمل swap x و y فبعكسهم هنا صارت هنا ال
+
+338
+00:25:44,840 --> 00:25:49,580
+31 مش هيك بعد ما نعكس و خلاص هذه صارت 31 31 و 32
+
+339
+00:25:49,580 --> 00:25:53,000
+لأ مظبوط مافيش فيها مشكلة طيب 32 و 33 برضه مافيش
+
+340
+00:25:53,000 --> 00:26:00,590
+مشكلة اتنين لازم تحل محل ال 33 swapأو exchange
+
+341
+00:26:00,590 --> 00:26:05,770
+عكسنا تمام صارت هنا تلاتة و تلاتين تلاتة و تلاتين
+
+342
+00:26:05,770 --> 00:26:08,590
+اربعة و تلاتين زي ما هي مافيش مشكلة أسيبها طيب
+
+343
+00:26:08,590 --> 00:26:15,450
+اربعة و تلاتين تلاتة خلصنا the first stage stage
+
+344
+00:26:15,450 --> 00:26:19,130
+تانية بس خد بالك انه في ال stage التانية عدد
+
+345
+00:26:19,130 --> 00:26:28,510
+المقارنات هتجل واحدعدد المقارنات ستقل 1 لماذا؟ هنا
+
+346
+00:26:28,510 --> 00:26:35,950
+كنت تعمل هذه مقارنة هذه 2 هذه 3 هذه 4 هذه 5 6 7
+
+347
+00:26:35,950 --> 00:26:41,810
+سبعة مقارنات بمعنى أن عدد المقارنات هي N ناقص 1
+
+348
+00:26:41,810 --> 00:26:49,090
+عندك 8 عناصر فانت عشان تعمل أول stage محتاج N ناقص
+
+349
+00:26:49,090 --> 00:26:54,000
+1 سبع عمليات مقارنةطيب السبع عمليات مقارنة عن إيش
+
+350
+00:26:54,000 --> 00:27:00,240
+نتجت في النهاية أنتجت لنا حاجة عكسية بمعنى أنت كنت
+
+351
+00:27:00,240 --> 00:27:03,520
+بتدور على ال bubble اللي هي فقعات فقعات ده دايما
+
+352
+00:27:03,520 --> 00:27:08,880
+هي الأخف يعني القيمة الأقل لأ لاحظ أن الواحد هي من
+
+353
+00:27:08,880 --> 00:27:14,380
+المرتبة التانية التالتة للتانية مشيت بس لكن لو
+
+354
+00:27:14,380 --> 00:27:18,520
+اتطلعت في ال code جيدا هتجد أنه بيعملك ترسيب لأكبر
+
+355
+00:27:18,520 --> 00:27:24,350
+قيمة في كل stageبالظبط فال 34 هذه اللي صارتها هنا
+
+356
+00:27:24,350 --> 00:27:29,190
+لو انها كانت موجودة هنا في أول stage هتنزل في
+
+357
+00:27:29,190 --> 00:27:36,090
+القاع لاحظ لو هذه 34 34 31 اجلب صارت هنا ال 34
+
+358
+00:27:36,090 --> 00:27:41,350
+واحد اجلب فلاحظ انه رغم ان ال code هو bubble اسمه
+
+359
+00:27:41,350 --> 00:27:44,670
+لكن فعليا في كل stage اللي واضح فيه انه أتجا
+
+360
+00:27:44,670 --> 00:27:47,870
+العنصر بنزل تحت فانت المرة اللي بعدها مش محتاج
+
+361
+00:27:47,870 --> 00:27:53,180
+تقارن فيهبمعنى مش هعمل المقارنة اللي هنا لأ هيكون
+
+362
+00:27:53,180 --> 00:27:57,940
+عندي هاي واحدة تنتين تلاتة أربع خمسة ستة بس مش
+
+363
+00:27:57,940 --> 00:28:06,020
+همشي سبع مقارنات واضحيت؟ تمام طيب نفس الفكرة برضه
+
+364
+00:28:06,020 --> 00:28:08,700
+حاجة مهمة جدا ناخد بالنا منها لإنها تسهل علينا في
+
+365
+00:28:08,700 --> 00:28:11,960
+ال code ده مديش عدد ال stages اللي انا محتاجهم
+
+366
+00:28:11,960 --> 00:28:20,110
+برضه in عقس واحد بحيث ان لو الواحد هذاهذا الواحد
+
+367
+00:28:20,110 --> 00:28:26,810
+كان أقل عنصر تحت في كل stage انت هتطلع خطوة فلو
+
+368
+00:28:26,810 --> 00:28:31,630
+أقل عنصر هذا ال worst case الحالة السيئة و كلكم
+
+369
+00:28:31,630 --> 00:28:34,050
+عارفين برضه ان احنا كمبرمجين دايما بنشتغل ع ال
+
+370
+00:28:34,050 --> 00:28:38,190
+worst case في ال complexity بتشتغل ع ال worst case
+
+371
+00:28:38,190 --> 00:28:41,870
+هناخد الكلام هذا بس سابق لأوانه لكن هنا لازم نوضحه
+
+372
+00:28:41,870 --> 00:28:45,420
+على أساس ان ال worst case انهبالنسبة للكبير فاش
+
+373
+00:28:45,420 --> 00:28:48,440
+مشكلة، الكبير حتى لو كان أول غنصر من أول stage
+
+374
+00:28:48,440 --> 00:28:53,360
+هينزل في القاع لكن إشكلتنا في أصغر غنصر لو كان
+
+375
+00:28:53,360 --> 00:28:58,060
+موجود فعلا في القاع فهو محتاج ان ناقص واحد stages
+
+376
+00:28:58,060 --> 00:29:06,120
+عشان يقفوا في مكانه الصحيح واضحيت؟ تمام، ممتاز إذا
+
+377
+00:29:06,120 --> 00:29:09,680
+الجزئية هذه واضحة، ال code الآن هيطلع سهل وبسيط
+
+378
+00:29:09,680 --> 00:29:15,760
+وفاش فيه مشكلةكالتالي هاي ال code بفسر كل الكلام
+
+379
+00:29:15,760 --> 00:29:19,960
+اللي قلناه فهنبدأ procedure bubble sort وهي معطيني
+
+380
+00:29:19,960 --> 00:29:24,440
+list معينة ل real numbers with n أكبر من أو يساوي
+
+381
+00:29:24,440 --> 00:29:28,480
+اتنين بمعنى real numbers حتى لو فيه قصور خلاص
+
+382
+00:29:28,480 --> 00:29:32,380
+ماعنديش مشكلة بنحسبها بالقصور مين اللي أكبر بنزل
+
+383
+00:29:32,380 --> 00:29:35,480
+تحت مين أكبر بنزل تحته ومين ال bubble أو مين ال
+
+384
+00:29:35,480 --> 00:29:39,780
+sortبعمله floating بعمله تعويم لفوق بنطلع لفوق
+
+385
+00:29:39,780 --> 00:29:43,880
+كويس وطبعا أكل لازم تكون تساوي اتنين او اكتر لأن
+
+386
+00:29:43,880 --> 00:29:46,660
+اذا واحد مالوش معنى ان انت بتعمل sorting ل meal هو
+
+387
+00:29:46,660 --> 00:29:49,800
+واحد لازم تكونوا على الأقل اتنين عشان اترتبهم
+
+388
+00:29:49,800 --> 00:29:54,360
+بالنسبة لبعضهم طيب هنبدأ for loop ال for loop
+
+389
+00:29:54,360 --> 00:29:59,880
+الأول هذا هذا له ال stage انا في اي stage ولاحظ
+
+390
+00:29:59,880 --> 00:30:02,400
+هنا بدنا من واحد من ال stage الأولى لان ناقص واحد
+
+391
+00:30:02,400 --> 00:30:07,530
+على اعتبار ان انا بداش تطلع ال worst caseانه و هذا
+
+392
+00:30:07,530 --> 00:30:11,830
+وارد انت مش شايف ال list قدامك فبدك تفترض ان ال
+
+393
+00:30:11,830 --> 00:30:16,030
+worst case القيمة الأقل هي جاي في قاع او في آخر
+
+394
+00:30:16,030 --> 00:30:19,730
+عنصر في ال list ففي الحالة دي محتاج عشان يتعومها
+
+395
+00:30:19,730 --> 00:30:27,670
+صح وتوصلها ك bubble اتصل لالخيانة الأولى او العنصر
+
+396
+00:30:27,670 --> 00:30:33,480
+الأول تصبح محتاج ان ناقص واحد stagesتمام هدولة ال
+
+397
+00:30:33,480 --> 00:30:38,400
+stages طيب جوا ال stages المقارنات خلاص أنا في ال
+
+398
+00:30:38,400 --> 00:30:45,320
+stage الأولى أكم مقارنة محتاج؟ محتاجين من 1 ل N
+
+399
+00:30:45,320 --> 00:30:50,890
+نقص Iإذا في أول مرحلة، معناته محتاج سبع مقارنات،
+
+400
+00:30:50,890 --> 00:30:54,890
+زي ما طوي عدناهم، إذا في المرحلة التانية، ستة، لأن
+
+401
+00:30:54,890 --> 00:30:58,610
+مصير هنا المرحلة رقم اتنين، فإن ناقص اتنين، and so
+
+402
+00:30:58,610 --> 00:31:05,170
+on لما تصل لإن ناقص واحد، هيكون إيش؟ محتاج مقارنة
+
+403
+00:31:05,170 --> 00:31:08,700
+واحدة، اللي هي الأنصر الأول والتاني، بسلأن في ال
+
+404
+00:31:08,700 --> 00:31:12,620
+worst case ممكن ساعتها أقل عنصر وصل لمرحلة تانية
+
+405
+00:31:12,620 --> 00:31:17,420
+وصل كعنصر تاني محتاج بس مقارنة بينه وبين الأول يا
+
+406
+00:31:17,420 --> 00:31:20,760
+بت save هم زي ما هم يا بتعكسهم إذا كان بحتاجوا
+
+407
+00:31:20,760 --> 00:31:26,460
+العكس طيب فوضحه إذا وضحت التنتين هدول خلصنا ال
+
+408
+00:31:26,460 --> 00:31:30,060
+code خلاص إذا التنتين هدول ال for loop واضحين
+
+409
+00:31:30,060 --> 00:31:36,720
+انتهى ال code الباقي بس عدل غير إذا أكبر منه تمام؟
+
+410
+00:31:36,720 --> 00:31:42,330
+واضحة؟هدولة هما الحل مافيش داعي نكمل اكتر من ذلك
+
+411
+00:31:42,330 --> 00:31:47,710
+خلاص الباقي مجرد انه اذا كان والله ال J أكبر من ال
+
+412
+00:31:47,710 --> 00:31:52,150
+J اللي وراها او من اللي بعدها معناته لازم تنزل بس
+
+413
+00:31:52,150 --> 00:31:56,070
+خلصنا مع ذلك هي الشطارة هنا في التنتين هدولة اذا
+
+414
+00:31:56,070 --> 00:31:57,490
+فهمت التنتين هدولة خلصت ال code
+
+415
+00:32:00,780 --> 00:32:05,480
+طيب ال insertion sort algorithm طبعا مش هنكتب ال
+
+416
+00:32:05,480 --> 00:32:07,660
+code تبعه اللي بده ال code تبعه مكتوب في الكتاب و
+
+417
+00:32:07,660 --> 00:32:12,040
+برضه بسيط جدا بس هنشرح فكرته الفكرة تبعته ببساطة
+
+418
+00:32:12,040 --> 00:32:16,180
+ان انت بتتعامل معاه كأنك بتعمل search ال insertion
+
+419
+00:32:16,180 --> 00:32:18,960
+هذه كأنك بتعمل search ايش يعني يعني ال list عندي
+
+420
+00:32:18,960 --> 00:32:24,960
+من n element a1
+
+421
+00:32:24,960 --> 00:32:26,940
+a2 ل a n
+
+422
+00:32:30,210 --> 00:32:35,010
+بكل بساطة بتتعامل معاه كالتالي بتفترض ان انت بدك
+
+423
+00:32:35,010 --> 00:32:39,990
+تعمل creation ل list جديدة creation ل list جديدة
+
+424
+00:32:39,990 --> 00:32:47,670
+اول ما هتحط فيها هتحط العنصر الاول A1 و هتفترض ان
+
+425
+00:32:47,670 --> 00:32:55,910
+هذا اسمها list و العنصر التاني X و نرجع لمين لل
+
+426
+00:32:55,910 --> 00:32:59,990
+searchبتشتغل linear؟ okay بتشتغل binary؟ okay مافي
+
+427
+00:32:59,990 --> 00:33:03,990
+مشكلة إيش بتسوي ال X هذه بالنسبة لل list اللي
+
+428
+00:33:03,990 --> 00:33:08,050
+موجودة عشان تحدد هي وين ال location اللي لازم يكون
+
+429
+00:33:08,050 --> 00:33:13,170
+لها وين موجود ال location إذا قرنت لجيت إنه X
+
+430
+00:33:13,170 --> 00:33:16,670
+خليني أفترض linear، linear أسهل و هتتخيلها بشكل
+
+431
+00:33:16,670 --> 00:33:23,850
+أسهل إجيت قرنت لجيت إن X أكبر من AI طيب هنا ال N
+
+432
+00:33:23,850 --> 00:33:28,180
+بالنسبة لك تسوي 1 حتى اللحظةإذا كانت X أكبر
+
+433
+00:33:28,180 --> 00:33:35,160
+فبتحطها في ال location N زائد واحد تمام
+
+434
+00:33:35,160 --> 00:33:39,780
+و خلصنا منها بتاخد A تلاتة بتصير هي ال X اللي بدك
+
+435
+00:33:39,780 --> 00:33:44,700
+تبحث عنها طيب إجينا بحثنا عنها و طبعا صارت هنا
+
+436
+00:33:44,700 --> 00:33:50,500
+بالنسبالي N بتساوي 2 ال list صارت أنصرين كويس
+
+437
+00:33:50,500 --> 00:33:59,610
+إجينا قارننا وجدنا إن X أكبر من Aو أصغر من a2 انا
+
+438
+00:33:59,610 --> 00:34:05,830
+عارف ان in بتساوي 2 فلازم تصير in بتساوي 3 و هنا
+
+439
+00:34:05,830 --> 00:34:08,950
+بده يصير في location تالت اللوكيشن التالت هذا هعمل
+
+440
+00:34:08,950 --> 00:34:18,710
+shift ل a2 ليش؟ لأن a2 أكبر من a3 حسب الفرضيتنا
+
+441
+00:34:18,710 --> 00:34:23,770
+أكبر من a3 ففي الحالة هذه بيروح على الجنب التاني و
+
+442
+00:34:23,770 --> 00:34:29,980
+بيفضّيالـ location تبعه بفضل location تبعه لمين؟ ل
+
+443
+00:34:29,980 --> 00:34:37,960
+X اللي هي A تلاتة and so on بيضل مكمل اللي وراها
+
+444
+00:34:37,960 --> 00:34:43,340
+اللي وراها اللي وراها اللي وراها لما يخلص ال A هاي
+
+445
+00:34:43,340 --> 00:34:50,530
+فكرة الاش ال sorting او ال insertionSorting فبيعمل
+
+446
+00:34:50,530 --> 00:34:54,330
+insertion كل مرة أو بيعمل حقن كل مرة بعنصر من
+
+447
+00:34:54,330 --> 00:34:58,310
+عناصر ال array نفسها بفترض ان ال array هي العنصر
+
+448
+00:34:58,310 --> 00:35:03,290
+الأول لحاله طيب العنصر التاني كأنه X و بيشوف وين
+
+449
+00:35:03,290 --> 00:35:07,640
+ال location الصح تبعه عشان يحقنه في مكانهطيب إذا
+
+450
+00:35:07,640 --> 00:35:11,260
+كان مكانه هو ال in الجديدة فش مشكلة بيحطه في ال in
+
+451
+00:35:11,260 --> 00:35:15,920
+الجديدة أو إذا كان مكانه جبل كل ما بعده بيعملهم
+
+452
+00:35:15,920 --> 00:35:21,260
+shift بواحد و بنحطه في مكانه بنعمل shift تمام فهذا
+
+453
+00:35:21,260 --> 00:35:28,560
+ببساطة اللي احنا كاتبينه ال code بسيط جدا و انت
+
+454
+00:35:28,560 --> 00:35:34,330
+عارف انه هيكون في عندك methodأو subroutine اسمه
+
+455
+00:35:34,330 --> 00:35:39,030
+search code هتستدعيه في كل مرة هتستدعيه في كل مرة
+
+456
+00:35:39,030 --> 00:35:43,230
+لأنه في كل او اكم مرة هنستدعيه هنستدعيه ان مرة مش
+
+457
+00:35:43,230 --> 00:35:47,590
+هيك ان مرة او ان نقص واحد مرة كل مرة بدك تفترض ان
+
+458
+00:35:47,590 --> 00:35:51,330
+هو ال X و تدور على المكان تبعه والخطوة الإضافية بس
+
+459
+00:35:51,330 --> 00:35:56,930
+تعمل عملية insert عملية insertion بس كويس ال code
+
+460
+00:35:56,930 --> 00:36:01,720
+موجود زي ما قولناهعلى في ال .. في الكتاب مكتوب
+
+461
+00:36:01,720 --> 00:36:05,600
+واضح جدا يعني مش فيه مشكلة و بسيط جدا و أتوقع أنه
+
+462
+00:36:05,600 --> 00:36:08,700
+المفروض يكون مرة عليكم يعني يكون مرة عليكم في أش
+
+463
+00:36:08,700 --> 00:36:09,440
+أشمال أو يمين
+
+464
+00:36:16,740 --> 00:36:21,420
+الان جابل ما نروح ل ال complexity بدنا نفهم مقدمة
+
+465
+00:36:21,420 --> 00:36:25,220
+ال complexity بالاساس المقدمة الأساسية بتاعة ال
+
+466
+00:36:25,220 --> 00:36:29,820
+complexity و اللي هي إلها علاقة بحاجة بيسموها ال
+
+467
+00:36:29,820 --> 00:36:34,160
+order of growth انت بناء على إيش بتقول أن هذا ال
+
+468
+00:36:34,160 --> 00:36:37,640
+code أحسن من هذا أن انت بتجيب ال order تبع كل code
+
+469
+00:36:37,640 --> 00:36:43,020
+صحيح؟ جبنا ال order لل code معنا ذلك أنه جابلما
+
+470
+00:36:43,020 --> 00:36:46,120
+أحكم على ال order تاع ال code لازم أكون فاهم إيش
+
+471
+00:36:46,120 --> 00:36:49,780
+يعني ال orders؟ بدنا نكون فاهمين بالأساس أصلا إيش
+
+472
+00:36:49,780 --> 00:36:54,680
+يعني ال orders وكيف تقاس ال orders هذه orders إيش؟
+
+473
+00:36:54,680 --> 00:36:57,740
+مش مجرد order معناته أنه قيمه أكبر من قيم order
+
+474
+00:36:57,740 --> 00:37:03,900
+تاني لأ القيم هذه مع الاستدامة بدها تكون أكبر منه
+
+475
+00:37:03,900 --> 00:37:07,300
+وليس في المرحلة الحالية فعشان هيك احنا بنتركزش على
+
+476
+00:37:07,300 --> 00:37:09,780
+ال order ك order لأ احنا بنركز على ال order of
+
+477
+00:37:09,780 --> 00:37:18,960
+growthبمعنى order نمو ال function نمو ال function
+
+478
+00:37:18,960 --> 00:37:23,980
+نفسها عندك code أول ال order تتبع function معينة و
+
+479
+00:37:23,980 --> 00:37:27,920
+ال code التاني function تانية فإذا أنا بقارن two
+
+480
+00:37:27,920 --> 00:37:32,200
+functions في بعض two functions في بعض مين نموها
+
+481
+00:37:32,200 --> 00:37:38,660
+أسرع من التاني مين نموها أسرع من التاني زي مثللو
+
+482
+00:37:38,660 --> 00:37:43,040
+قلنا مثلا ال function تلاتين in زائد تمانية احنا
+
+483
+00:37:43,040 --> 00:37:47,100
+عارفين انه هاد ايش first order او linear first
+
+484
+00:37:47,100 --> 00:37:51,060
+order او linear لما اجي اقارنها ب function بهذا
+
+485
+00:37:51,060 --> 00:37:56,400
+الشكل in تربيع زائد واحد انا في النهاية مش هامسك
+
+486
+00:37:56,400 --> 00:38:00,520
+اقول والله يا طب ما هيها هي ال first order اعلى
+
+487
+00:38:01,990 --> 00:38:06,690
+أحنا بنتكلم عن ال growth معدل نمو ال function معدل
+
+488
+00:38:06,690 --> 00:38:10,090
+نمو ال function لأنه ضامن إذا معدل نمو ال function
+
+489
+00:38:10,090 --> 00:38:15,070
+أكبر فهو هيجي عند نقطة تقاطع وبعدها هتبقى دائما
+
+490
+00:38:15,070 --> 00:38:20,370
+أكبر فنقطة التقاطع هي نقطة التقاطع بعدها بعد K هنا
+
+491
+00:38:20,370 --> 00:38:25,470
+قيمة ل K دائما هتلاقي أن ال second order أكيد أكبر
+
+492
+00:38:25,470 --> 00:38:30,690
+من first orderلأن في النهاية ما قبل النقطة المعينة
+
+493
+00:38:30,690 --> 00:38:36,270
+هذه هو يعتبر حكم خاطئ يعتبر حكم خاطئ مين اللي
+
+494
+00:38:36,270 --> 00:38:41,130
+بتحكم فيه ال mail و ال constant أو الجزء ال DC في
+
+495
+00:38:41,130 --> 00:38:43,990
+ال function اللي هي التمانية مثلا أو ال mail اللي
+
+496
+00:38:43,990 --> 00:38:49,680
+هو التلاتين هنا ال mail عندك واحد فعلياًمش هيك انت
+
+497
+00:38:49,680 --> 00:38:55,520
+مش ميعطيه coefficient معينة لقيمة ال order نفسه،
+
+498
+00:38:55,520 --> 00:38:59,840
+واحد في int أربعة، هنا انت ميعطيه تلاتين فطبيعي في
+
+499
+00:38:59,840 --> 00:39:04,780
+بدايتها، في بداية ال numbers هتلاقي ان ال linear
+
+500
+00:39:04,780 --> 00:39:11,230
+هيكون بشكل خادع، يبدو كأنه أكبرلكن عند نقطة معينة
+
+501
+00:39:11,230 --> 00:39:16,630
+لأ هترجع تبين انه ال second order أعلى ليش أعلى؟
+
+502
+00:39:16,630 --> 00:39:22,690
+لأنه من الأساس معدل نموه أكبر بالظبط السلحفة و
+
+503
+00:39:22,690 --> 00:39:26,550
+الأرنب السلحفة و الأرنب لكن انت في النهاية السلحفة
+
+504
+00:39:26,550 --> 00:39:31,990
+خلتها بعيدة اتنين كيلو سابج الأرنب فمعنى ذلك انه
+
+505
+00:39:31,990 --> 00:39:36,690
+مسألة وقت هي مسألة وقت السلحفة هتضل تمشي بس معدل
+
+506
+00:39:36,690 --> 00:39:41,560
+النمو بتبحها في المشي بطيءهيضل بطيء الأرنب أسرع
+
+507
+00:39:41,560 --> 00:39:46,700
+انت عارف انه هييجي لحظة من اللحجة اللحظات هيتسوق و
+
+508
+00:39:46,700 --> 00:39:52,390
+هيعديها الأرنبصحيح؟ هذا في الحالة الطبيعية مش حالة
+
+509
+00:39:52,390 --> 00:39:55,010
+الجثث إنه هيروح تحت الشجرة و ينام و مش عارف ..
+
+510
+00:39:55,010 --> 00:39:59,230
+الحالة الطبيعية مش هيك عارفين إنه في لحظة معينة
+
+511
+00:39:59,230 --> 00:40:03,390
+إذا مشيوا الإتنين بنفس ال rate الطبيعي تبعهم هيجوا
+
+512
+00:40:03,390 --> 00:40:05,730
+يتقاربوا يتقاربوا يتقاربوا و بعدين يعديها و يمشي
+
+513
+00:40:05,730 --> 00:40:10,850
+معنا ذلك الحكم هنا بيجيش على القيمة اللحظية بيجي
+
+514
+00:40:10,850 --> 00:40:17,050
+على معدل التحرك معدل التحرك اللي هنسميه ال order
+
+515
+00:40:17,050 --> 00:40:23,100
+of growthواضحة فبهمني ال order of growth مش لحظيا
+
+516
+00:40:23,100 --> 00:40:32,700
+جدش قيمة كل واحدة منهم مش لحظيا تمام ففي
+
+517
+00:40:32,700 --> 00:40:35,640
+الحالة هذه بنقدر نقول ان ال function الأولى هي
+
+518
+00:40:35,640 --> 00:40:40,860
+first order و first order بسميها big O of N و big
+
+519
+00:40:40,860 --> 00:40:49,070
+O معناته at most at most بمعنىأعلى ما يمكن إلها هي
+
+520
+00:40:49,070 --> 00:40:54,950
+linear ولا بحياتها هتكون أعلى من هيك ممكن تكون DC
+
+521
+00:40:54,950 --> 00:40:59,730
+ممكن تكون DC بمعنى إن هي بتشبر كل اللي تحتها في ال
+
+522
+00:40:59,730 --> 00:41:06,910
+order DC أو inverse أو ليش في كمان logarithmic؟
+
+523
+00:41:06,950 --> 00:41:10,750
+ممكن تكون أقل من ال first order okay بس هنا بتسميه
+
+524
+00:41:10,750 --> 00:41:15,390
+at most at most فإذا لما بقول function ال order
+
+525
+00:41:15,390 --> 00:41:19,770
+تبعها big O of N فهي في أسوأ الأحوال مش هتزيد عن
+
+526
+00:41:19,770 --> 00:41:25,210
+ال linear ال order تبعها في أسوأ الأحوال يعني أعلى
+
+527
+00:41:25,210 --> 00:41:32,810
+order ممكن هو linear هو ال linear بمعنى بالنسبة لل
+
+528
+00:41:32,810 --> 00:41:39,850
+code هي إيش المتغير اللي فيه؟أخدته big O تمام هو
+
+529
+00:41:39,850 --> 00:41:44,150
+إيش المتغير عندكوا في الأكواد ال input بس ال
+
+530
+00:41:44,150 --> 00:41:48,750
+arguments بعنى ذلك أن أنت هنا بتتكلم عن in input
+
+531
+00:41:48,750 --> 00:41:53,530
+بمعنى أن كل ما بتزود ال input بواحد ال complexity
+
+532
+00:41:53,530 --> 00:41:57,710
+بتزيد بس على جد operation واحدة هاي معناها بتزيدش
+
+533
+00:41:57,710 --> 00:42:02,110
+تعقيدها بشكل كتير كبير تعقيدها واحد بس فبتزيد بشكل
+
+534
+00:42:02,110 --> 00:42:10,380
+وحدي فإذا هي ماشية بشكلمتناسب برضيا مع ال input ال
+
+535
+00:42:10,380 --> 00:42:13,860
+input زودلي كمان input زيادة بتزيد عملية واحدة فقط
+
+536
+00:42:13,860 --> 00:42:18,980
+في ال code بهذا الشكل ماشية فانا هنا لما أجي أقول
+
+537
+00:42:18,980 --> 00:42:23,680
+والله فعملتلي code ال code هذا على جد عددكم عددنا
+
+538
+00:42:23,680 --> 00:42:28,280
+خلّيني أقول ستين سبعين طالب أخدله ستين ثانية وجينا
+
+539
+00:42:28,280 --> 00:42:32,740
+اتطلعنا وجينا أن ال code هذا فعلا هو linear معنى
+
+540
+00:42:32,740 --> 00:42:39,920
+ذلك أن نفس ال code لما بتستخد معلقسكان غزة بيصير
+
+541
+00:42:39,920 --> 00:42:45,540
+ال 60 مقابل 60 ثانية بيصير 2 مليون مقابل 2 مليون
+
+542
+00:42:45,540 --> 00:42:51,020
+ثانية فبتحسب المتغير هنا هو ال arguments أو ال
+
+543
+00:42:51,020 --> 00:42:55,160
+inputs أو ال inputs هل هم linear مع بعض ولا لأ
+
+544
+00:42:55,160 --> 00:42:57,760
+لعند linear بتظهر مبلوعة مقبولة بس تخيل لو أنه
+
+545
+00:42:57,760 --> 00:43:02,900
+تربيعي أو second order معناه ذلك إذا كان ال 60
+
+546
+00:43:02,900 --> 00:43:08,200
+كانوا 60 ثانيةبتربيع فبدك تشوف الاتنين مليون جديش
+
+547
+00:43:08,200 --> 00:43:12,040
+بده مصيره أكيد هصيره أكتر من الاتنين مليون ثانية
+
+548
+00:43:12,040 --> 00:43:15,300
+اللي كنا نحكي عليها وفي الحالتين هي سيئة يعني في
+
+549
+00:43:15,300 --> 00:43:17,380
+الحالتين سيئة لما ماتش تتكلم عن اتنين مليون ثانية
+
+550
+00:43:17,380 --> 00:43:21,340
+تمام بس بدنا نوضح كل الفكرة ال concept تبعنا تمام
+
+551
+00:43:21,340 --> 00:43:25,300
+فهنا at most ال big O بمعنى انه في أسوأ حالتها هي
+
+552
+00:43:26,940 --> 00:43:31,040
+طيب بالنسبة لإن تربية زائد واحد هي في أسوأ حالتها
+
+553
+00:43:31,040 --> 00:43:37,340
+تربيعية وطبعا التربيعية order of growth أكبر من ال
+
+554
+00:43:37,340 --> 00:43:40,500
+linear order of growth أكبر من ال linear هذا
+
+555
+00:43:40,500 --> 00:43:48,060
+مفهومنا طيب بالنسبة لمبرمجين معناته سيئةلحظته كيف؟
+
+556
+00:43:48,060 --> 00:43:52,060
+okay احنا هنا جاهديني نتكلم كرياضيات بحتها اه هي
+
+557
+00:43:52,060 --> 00:43:55,420
+ال order of growth بحها اعلى فهي تبدو ان كلمة اعلى
+
+558
+00:43:55,420 --> 00:43:58,860
+دايما بتوحينا انه احسن يعني بالعكس هنا سيئ
+
+559
+00:43:58,860 --> 00:44:05,200
+بالنسبالنا كمبرمجين كمبرمجين فهي تتناسب بشكل ترضي
+
+560
+00:44:05,200 --> 00:44:09,880
+مع الان تربيع فالتمانية مليون الاتنين مليون هدول
+
+561
+00:44:09,880 --> 00:44:14,280
+هيصيروا اتنين مليون تربيع اتنين مليون تربيع ثانية
+
+562
+00:44:15,110 --> 00:44:20,190
+هتصبح في الحالة هذه تمام و طبعا كنا عارفين أن أي
+
+563
+00:44:20,190 --> 00:44:25,630
+big O of N تربيع أكيد هيكون أسرع في ال growth زي
+
+564
+00:44:25,630 --> 00:44:29,970
+ما توي شوفنا المعدل كان أسرع من .. زي بالظبط
+
+565
+00:44:29,970 --> 00:44:35,490
+الأرنب والسلحفة تمام هيكون أكبر من أي big O of N
+
+566
+00:44:35,490 --> 00:44:44,570
+بكل بشكل مطلق جد ما تكون ال N هذه لها maleتلاتين
+
+567
+00:44:44,570 --> 00:44:48,270
+in، خمسين in، مليون in، بس في النهاية في نقطة
+
+568
+00:44:48,270 --> 00:44:53,360
+معينة التربيه هيعديها ويمشيالنقطة هذه ممكن تبعد،
+
+569
+00:44:53,360 --> 00:44:57,260
+او ممكن تبعد، ممكن تكون عند K كبيرة، بس في النهاية
+
+570
+00:44:57,260 --> 00:45:02,220
+لازم حتكون فيه موجودة ..يلها قيمة K، بعدها التربيع
+
+571
+00:45:02,220 --> 00:45:09,240
+يعدي ال .. ال linear، تمام فكل ما كان ال number ل
+
+572
+00:45:09,240 --> 00:45:12,660
+ال user records اللي هي ال inputs كل ما كانت ال
+
+573
+00:45:12,660 --> 00:45:16,460
+big O of N تربيع أكيد ك function بتاخد more time
+
+574
+00:45:17,350 --> 00:45:22,270
+for إيش؟ في ال execution للتنفيذ لعملية التنفيذ
+
+575
+00:45:22,270 --> 00:45:26,330
+هذا نفس الفكرة اللي بنتكلمها إذا أنا بدأ أتكلم عن
+
+576
+00:45:26,330 --> 00:45:28,970
+ال big O ك function فأنا في النهاية بقول إن هي
+
+577
+00:45:28,970 --> 00:45:33,390
+function من real to real أنه يوجد there exist C
+
+578
+00:45:33,390 --> 00:45:36,630
+and K، K هذه النقطة اللي بنحكي عنها، اللي عند نقطة
+
+579
+00:45:36,630 --> 00:45:42,680
+معينة الأرنب هيعدل سلحفةعند نقطة معينة .. وين
+
+580
+00:45:42,680 --> 00:45:46,900
+النقطة المعينة دي؟ K .. and K عند نقطة معينة أكيد
+
+581
+00:45:46,900 --> 00:45:53,000
+هيبين ال order أو يظهر بشكل واضح يعدي ال order
+
+582
+00:45:53,000 --> 00:46:00,320
+الأقل تمام بحيث ان for all x أكبر من k من k فأكبر
+
+583
+00:46:00,320 --> 00:46:08,320
+هتبين ان ال f of x أقل من c g of xهتكون معناه ذلك
+
+584
+00:46:08,320 --> 00:46:14,220
+أن ال order أقل من ال big O G عشان هيك ال G معناته
+
+585
+00:46:14,220 --> 00:46:18,220
+هي في أسوأ الأحوال هي ال maximum هي الأكبر ال G هي
+
+586
+00:46:18,220 --> 00:46:23,160
+الأكبر لما قلنا توة big O of N تربيع معناه ذلك أنه
+
+587
+00:46:23,160 --> 00:46:26,960
+هي في جميع الأحوال مش هتزيد عن ال N تربيع مش هتزيد
+
+588
+00:46:26,960 --> 00:46:30,600
+عن ال N تربيع فإذا عند قيمة معينة زي ال linear
+
+589
+00:46:30,600 --> 00:46:34,820
+بتاع التوة التلاتين N زائد تمانية في البداية كانت
+
+590
+00:46:34,820 --> 00:46:39,820
+خدعانة كانت أعلىفي البداية كانت أعلى، صحيح؟ هذه
+
+591
+00:46:39,820 --> 00:46:48,160
+خادعة، and كمعينة، and كمعينة بعدها هتصبح دائما
+
+592
+00:46:48,160 --> 00:46:55,990
+أقل منالتربيع أقل من تربيع فإذا ال linear مشمولة
+
+593
+00:46:55,990 --> 00:46:59,850
+مع ال big O of N تربيع ومشمولة مع ال big O of N
+
+594
+00:46:59,850 --> 00:47:06,230
+نفسها أو تساوي أو تساوي تمام فهنا نتكلم عن النقطة
+
+595
+00:47:06,230 --> 00:47:08,230
+اللي حكينا عنها هي ممكن توي عده و هيجينا مثال
+
+596
+00:47:08,230 --> 00:47:11,830
+يبيّنها أكتر فبنقدر نقول نعبر عنها طبعا مصطلحات
+
+597
+00:47:11,830 --> 00:47:15,390
+كتيرة و ممكن نقول إن ال F هذه is at most order G
+
+598
+00:47:15,390 --> 00:47:19,730
+بنسميها at most order G فهي أعلى حالتها تساوي ال
+
+599
+00:47:19,730 --> 00:47:26,970
+order Gكويس او بسميها F is big O of G او نسميها F
+
+600
+00:47:26,970 --> 00:47:31,930
+تساوي big O of G مباشرة نكتب بهذا الشكل مباشرة ف
+
+601
+00:47:31,930 --> 00:47:40,210
+.. او طريقة من الطرق F belong to big O of G اش
+
+602
+00:47:40,210 --> 00:47:44,150
+يعني؟ يعني معناته انا افترضت ان ال F هذه عنصر مش
+
+603
+00:47:44,150 --> 00:47:49,740
+ال belong هذه بتاعة ال sets ان هي عنصر ل setمنطق
+
+604
+00:47:49,740 --> 00:47:55,420
+الكلام؟ منطقي عارفين ليش؟ لأن ال big O of G كل ال
+
+605
+00:47:55,420 --> 00:47:59,500
+functions اللي أقل من G كل ال functions اللي أقل
+
+606
+00:47:59,500 --> 00:48:06,100
+من G و F واحدة منهم ف F تنتمي لمجموعة ال functions
+
+607
+00:48:06,100 --> 00:48:10,960
+اللي أقل من G أو تسوي G بمعنى لما تقول big O in
+
+608
+00:48:10,960 --> 00:48:14,940
+تربيع بكل بساطة بقدر أقول لك أنه تلاتين in
+
+609
+00:48:19,610 --> 00:48:27,110
+تلاتين N زائد عقمية هي belong to big O of N تربيع
+
+610
+00:48:27,110 --> 00:48:34,110
+بمشي الحال بمشي الحال linear أقل من التربيع تمام
+
+611
+00:48:34,110 --> 00:48:39,050
+صحيح طب ممكن أقول لك برضه تلاتين N تربيع زائد one
+
+612
+00:48:39,050 --> 00:48:47,690
+million برضه big O of N تربيع ما هي تربعية تساوي
+
+613
+00:48:47,690 --> 00:48:52,340
+تربيعهي ال order تبعها تربيع فهي بكل بساطة بتقدر
+
+614
+00:48:52,340 --> 00:48:56,880
+تقول عليها big O of N تربيع ليش؟ لأن ال one
+
+615
+00:48:56,880 --> 00:49:01,860
+million هذا constant constant إيش يعني؟ يعني
+
+616
+00:49:01,860 --> 00:49:06,920
+function of zero ال order تبعه zero طيب ال zero
+
+617
+00:49:06,920 --> 00:49:13,740
+أقل من التربيع فهي مشمولة مع التربيع طيب نفس الجثة
+
+618
+00:49:13,740 --> 00:49:25,750
+تلاتين N تربيع زائد مية Nبرضه big of in تربيع هي
+
+619
+00:49:25,750 --> 00:49:35,870
+هي صحيح فيها جزء linear بس totally هي تربيعية مش
+
+620
+00:49:35,870 --> 00:49:39,870
+هتكون اكتر من تربيع مش هتكون اكتر من تربيع تمام
+
+621
+00:49:39,870 --> 00:49:45,950
+فبنسميها at most at most بمعنى انها ممكن تشمل كل
+
+622
+00:49:45,950 --> 00:49:49,430
+اللي تحتها كل اللي اقل منهاتمام اتكلمنا عن هذا
+
+623
+00:49:49,430 --> 00:49:55,030
+الكلام وهين هنا مثال حددلكم بس حسب التعريف في 30N
+
+624
+00:49:55,030 --> 00:49:59,250
+زائد 8 اقل من أو يساوي CN عشان اضمن ان هي فعلا هل
+
+625
+00:49:59,250 --> 00:50:07,630
+هي big O of N معناه ذلك ان عند mail معين لل order
+
+626
+00:50:07,630 --> 00:50:11,710
+اكيد هيتجاوز ال function اللي موجودة عندكم بعد
+
+627
+00:50:11,710 --> 00:50:16,510
+قيمة K طيب في الحالة هذه ال C اللي هي ال mailالـ
+
+628
+00:50:16,510 --> 00:50:18,810
+mail اللي موجود عندك بتشوف المعادلة اللي عندك جدّي
+
+629
+00:50:18,810 --> 00:50:23,650
+شمالها معناه ذلك أنه عند C زائد واحد تلاتين زائد
+
+630
+00:50:23,650 --> 00:50:27,770
+واحد واحد تلاتين فلو أخدنا أن ال C هنا there exist
+
+631
+00:50:27,770 --> 00:50:32,950
+C and K بتحققلك أنه بعد K تلاتين N زائد تمانية
+
+632
+00:50:32,950 --> 00:50:37,660
+دايما هتكون أقل من أو يساوي ال ordermail ال order
+
+633
+00:50:37,660 --> 00:50:43,300
+تمام فلس C هذه تلاتين واحد تلاتين هنا تمانية and
+
+634
+00:50:43,300 --> 00:50:47,940
+تمانية كي بتساوي تمانية فدائما أبدا لكل قيم N اللي
+
+635
+00:50:47,940 --> 00:50:54,260
+أكبر من تمانية هتتحقق هذه المعادلة فبأضمن أنه ال
+
+636
+00:50:54,260 --> 00:50:58,320
+first order هو شامل التلاتين N زي التمانية
+
+637
+00:50:58,320 --> 00:51:06,040
+فالتلاتين زي التمانية هي أحد عناصر الست big O of N
+
+638
+00:51:07,430 --> 00:51:10,890
+فإذن هو first order فإذن first order نفس الكلام
+
+639
+00:51:10,890 --> 00:51:16,470
+لمين لأ ال second لأ ال second order طبعا هنا هي
+
+640
+00:51:16,470 --> 00:51:21,230
+واضحة بهذا الشكل لأ ال first order لما بتكلم عن n
+
+641
+00:51:21,230 --> 00:51:24,830
+مباشرة فهي بزاوية خمسة وارمين كده مش كتير مظبوطة
+
+642
+00:51:24,830 --> 00:51:30,130
+لو تلاتين n زائد تمانية الميل تبعها بصير أعلى و
+
+643
+00:51:30,130 --> 00:51:34,430
+بعدين ماخدة shift بقيمة التمانية بقيمة التمانية
+
+644
+00:51:34,430 --> 00:51:34,630
+هنا
+
+645
+00:51:38,830 --> 00:51:45,210
+بعد نقطة معينة سين
+
+646
+00:51:45,210 --> 00:51:49,330
+ستتعدي ال function اللي عندك فمعنى ذلك ان ال
+
+647
+00:51:49,330 --> 00:51:54,210
+function هي مشمولة ضمن هذا ال order اللي هو ال
+
+648
+00:51:54,210 --> 00:51:54,490
+linear
+
+649
+00:51:58,250 --> 00:52:01,350
+أنا قلتلك المعادلة نفسها هي اللي هتحددك الثابت
+
+650
+00:52:01,350 --> 00:52:04,590
+بالظبط هتبدأ من الصفر بس بدك تاخد بالك من ال mail
+
+651
+00:52:04,590 --> 00:52:08,270
+ساعتها إذا بتكلم عن تلاتين in ال mail تبعك افرضه
+
+652
+00:52:08,270 --> 00:52:13,170
+واحد تلاتين الواحد تلاتين in linear مش هيك وهي
+
+653
+00:52:13,170 --> 00:52:17,910
+المعادلة دي أقل منها طيب هذا لو كانت صفر هنا لو
+
+654
+00:52:17,910 --> 00:52:22,800
+كانت صفر هنا فمن الصفر هتلاقيها عدتهاأكبر من الصفر
+
+655
+00:52:22,800 --> 00:52:25,940
+لأن انت عارف أن الأرقام هي قبل الصفر أصلا بس احنا
+
+656
+00:52:25,940 --> 00:52:29,120
+تجاوز أن نبدأ من الصفر بس فعلا انا ممكن أبدأ من
+
+657
+00:52:29,120 --> 00:52:32,440
+هنا وهدول ينزلوا من تحت كمان عادي يعني ماكنش فيه
+
+658
+00:52:32,440 --> 00:52:39,850
+مشكلة تمام خليني أقول هيك أخدناتوضيح نكمله المرة
+
+659
+00:52:39,850 --> 00:52:43,590
+القادمة لفكرة ال order of growth عشان ناخد المرة
+
+660
+00:52:43,590 --> 00:52:50,070
+القادمة شوية المجموعة facts عن ال big O و أخواتها
+
+661
+00:52:50,070 --> 00:52:53,090
+لان هنفضل المرة الجاية ناخد باقية أخواتها ال Omega
+
+662
+00:52:53,090 --> 00:52:57,350
+و ال Theta يعطيكوا العافية نشوفكوا المرة القادمة
+
+663
+00:52:57,350 --> 00:52:57,970
+ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/URd9zqvHits_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/URd9zqvHits_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..50f3098257c9eea205a5f1ca312510720ed03e3f
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/URd9zqvHits_postprocess.srt
@@ -0,0 +1,2612 @@
+1
+00:00:05,060 --> 00:00:07,600
+بسم الله الرحمن الرحيم و الصلاة والسلام على أشرف
+
+2
+00:00:07,600 --> 00:00:11,080
+الأنبياء و المرسلين سيدنا محمد اليوم نكمل ان شاء
+
+3
+00:00:11,080 --> 00:00:15,860
+الله ما تبقالنا في ال relationو اتوقع انه صار
+
+4
+00:00:15,860 --> 00:00:18,340
+معانا إمكانية في الوقت بإذن الله تعالى ان احنا
+
+5
+00:00:18,340 --> 00:00:22,180
+يعني الكمان أسبوعين ان شاء الله تعالى نبدأ نعمل
+
+6
+00:00:22,180 --> 00:00:25,320
+معاملة مراجعة فعلى الأقل هيكون معانا أسبوع كامل
+
+7
+00:00:25,320 --> 00:00:29,720
+للمراجعة على الأقل هذا يعني أقل شيء ممكن يطلعنا في
+
+8
+00:00:29,720 --> 00:00:32,160
+الأخر أربع محاضرات بدل تلت محاضرات بتاعة الأسبوع
+
+9
+00:00:32,160 --> 00:00:36,160
+ان شاء الله تعالى كلهم هنستثمرهم في حل أسئلة كلهم
+
+10
+00:00:36,160 --> 00:00:40,510
+هنستثمرهم في حل أسئلة فمعنى ذلك انهأنا مكمل معاكوا
+
+11
+00:00:40,510 --> 00:00:44,690
+لآخر موعد في الفصل الفصل بيخلص في تسعة و عشرين
+
+12
+00:00:44,690 --> 00:00:48,810
+اتناشر فمحاضرة تسعة و عشرين اتناشر أنا موجود فيها
+
+13
+00:00:48,810 --> 00:00:53,370
+كويس و هذا طبيعي .. طبيعي بالأساس فهنضلنا ماشيين
+
+14
+00:00:53,370 --> 00:00:57,190
+إلى آخر نفس انت بنخلص هنبدأ على طول في عملية
+
+15
+00:00:57,190 --> 00:01:00,990
+المراجعة و عملية حل أسئلة من أسئلة امتحانات ان شاء
+
+16
+00:01:00,990 --> 00:01:03,450
+الله تعالى و قلتلكوا ان في .. يعني في أسئلة كويسة
+
+17
+00:01:03,450 --> 00:01:09,390
+ذخيرة منيحة ممكن تشغلنا لأسبوعين تلاتةفنصل لأخر
+
+18
+00:01:09,390 --> 00:01:12,050
+حاجة اتكلمنا عنها المرة الماضية هي closures of
+
+19
+00:01:12,050 --> 00:01:16,150
+relations و اللي حكينا كيف انا ممكن اعمل reflexive
+
+20
+00:01:16,150 --> 00:01:19,430
+closure بمعنى اقربها ال relation ان هي تصبح
+
+21
+00:01:19,430 --> 00:01:22,350
+reflexive فكانت بسيطة جدا نعمل اتحاد مع ال
+
+22
+00:01:22,350 --> 00:01:27,290
+identity ل ال a و خلصناها لل relation identity لل
+
+23
+00:01:27,290 --> 00:01:31,230
+relation معنى ذلك ان a مع a, b مع b, c مع c واحد
+
+24
+00:01:31,230 --> 00:01:33,650
+مع واحد اتنين مع اتنين لازم يكونوا كلهم موجودين
+
+25
+00:01:33,650 --> 00:01:40,400
+فهذه ال identity بمعنى لو بدك اتمثلعناصر ال
+
+26
+00:01:40,400 --> 00:01:48,900
+relation a,b,c,1,2 هيكونوا a,b,c,1,2 بدهم يكونوا
+
+27
+00:01:48,900 --> 00:01:53,040
+بهذا الشكل ال diagonal كله ones معناه ذلك و ال
+
+28
+00:01:53,040 --> 00:01:55,740
+back zeros معناه ذلك ان انت بتتكلم عن identity
+
+29
+00:01:55,740 --> 00:02:00,580
+relation في الحالة هذه اعملها اتحاد مع اي relation
+
+30
+00:02:00,580 --> 00:02:04,740
+هتصبح اكيد حتما ناتج الاتحاد هيصبح reflexive
+
+31
+00:02:04,740 --> 00:02:10,240
+relation اكيدالـ Symmetric closure قلنا إن كل عنصر
+
+32
+00:02:10,240 --> 00:02:13,600
+بدنا نحط له العكس تبعه فهنا العكس لما بتكلم عن ال
+
+33
+00:02:13,600 --> 00:02:17,280
+inverse هو العكس تبع كل عنصر العكس تبع كل عنصر
+
+34
+00:02:17,280 --> 00:02:20,700
+اللي كانت مهمة شوية و بدها شغل هي ال transitive
+
+35
+00:02:23,710 --> 00:02:26,550
+يعني بحقيقة مشكور الباشر المهندس أنه جال يدورلنا
+
+36
+00:02:26,550 --> 00:02:30,090
+على حل تاني يعني كان مشكور فعلا أنه خلانا شوية هيك
+
+37
+00:02:30,090 --> 00:02:34,550
+ننشط حالنا و جيبنالكوا حلول تانية ساعدتنا حتى في
+
+38
+00:02:34,550 --> 00:02:38,310
+حال هالجثة كانت قديما عشان تيجي تحلها كانت شوية
+
+39
+00:02:38,310 --> 00:02:42,070
+بدها التركيز كتير فلو جيت لأ اتفك فكانت مع الطرق
+
+40
+00:02:42,070 --> 00:02:44,710
+اللي أخدناها و جيبتلكوا عليها مثال في ال slide
+
+41
+00:02:44,710 --> 00:02:47,990
+اللي وراها أنه أنا بعمل اتحاد لكل ال art to the
+
+42
+00:02:47,990 --> 00:02:50,090
+power in مع بعض إيش يعني art to the power in يعني
+
+43
+00:02:50,090 --> 00:02:55,360
+معناته ال relationCompose نفس ال relation بتصير
+
+44
+00:02:55,360 --> 00:03:00,120
+اسمها R تربيع فالإن تربيع طيب جبنا ال R تربيع ال R
+
+45
+00:03:00,120 --> 00:03:05,320
+تربيع composition مع R بتصير R تكعيب مع كمان R، R
+
+46
+00:03:05,320 --> 00:03:08,760
+تتطور أربعة كلهم هدول عملهم اتحاد ما تجلجش مش هتظل
+
+47
+00:03:08,760 --> 00:03:12,760
+تو infinity لإن عند مرحلة معينة بعد اتنين تلاتة
+
+48
+00:03:12,760 --> 00:03:18,250
+composition هتجد انه هتثبتهتثبت مدام ثبتت معناته
+
+49
+00:03:18,250 --> 00:03:22,190
+هو خلاص هيك استوفى كل العناصر اللي محتاج يزودها
+
+50
+00:03:22,190 --> 00:03:27,250
+عشان يصبح transitive closure خلاص اعملهم اتجمحهم
+
+51
+00:03:27,250 --> 00:03:31,650
+مع بعض هذه اقل transitive لل matrix عشان يعني
+
+52
+00:03:31,650 --> 00:03:35,210
+عناصر تزودها عشان تصبح transitive ال matrix تبعتك
+
+53
+00:03:35,210 --> 00:03:40,270
+بدل ما كنت مضطر تمسك جميع العناصر وتزودلهم عناصر
+
+54
+00:03:40,270 --> 00:03:44,220
+إضافيةناتج لل Transitive و بعدين العناصر الإضافية
+
+55
+00:03:44,220 --> 00:03:47,440
+تروح تعملها test كمان معاهم كمان مرة عشان تعمل
+
+56
+00:03:47,440 --> 00:03:49,880
+للكل تضمن ان ال relation كامل على بعض هي
+
+57
+00:03:49,880 --> 00:03:53,580
+Transitive relation لأالوضع كان كتير أسهل المرة
+
+58
+00:03:53,580 --> 00:03:56,660
+الماضية لما قلنا إن هى فيه هناك function أو
+
+59
+00:03:56,660 --> 00:04:00,260
+relation بهذا الشكل فأبسط شغل أعملها composition
+
+60
+00:04:00,260 --> 00:04:03,180
+مع نفسها أعملناها composition مع نفسها فصار اسمها
+
+61
+00:04:03,180 --> 00:04:08,160
+R تربيع R تربيع R تربيع automatically أعمل
+
+62
+00:04:08,160 --> 00:04:11,060
+composition جبنا ال composition طلع بهذا الشكل
+
+63
+00:04:11,060 --> 00:04:15,800
+فصار في عنده أنصر زيادة و أتوقع اتكلمنا عنها من
+
+64
+00:04:15,800 --> 00:04:18,820
+المرة الماضية ممكن تسهل على حال نبتش هيك على همش
+
+65
+00:04:18,820 --> 00:04:24,200
+الورقةورقة الأسئلة تبعتك هتحط الواحد و واحد كل
+
+66
+00:04:24,200 --> 00:04:28,640
+عناصر ال relation تبعتك اتنين و واحد هتحط تلاتة و
+
+67
+00:04:28,640 --> 00:04:35,820
+اتنين و اربعة و تلاتة اربعة و تلاتة هذه ال
+
+68
+00:04:35,820 --> 00:04:38,460
+relation وهنا هتعملها برضه مع نفس ال relation بس
+
+69
+00:04:38,460 --> 00:04:41,980
+هنا اللي تتفق معاها فمعنى ذلك بدك تشوف مين ال
+
+70
+00:04:41,980 --> 00:04:45,880
+relation مين اللي بيبدأ بالواحد فالواحد و واحد فقط
+
+71
+00:04:47,820 --> 00:04:50,240
+تمام في غيرها الواحد و واحد فاش الواحد و واحد طيب
+
+72
+00:04:50,240 --> 00:04:56,180
+برضه هنا الواحد برضه واحد و واحد اتنين اتنين و
+
+73
+00:04:56,180 --> 00:05:03,380
+واحد تلاتة تلاتة و اتنين تمام هنا اشطب هادي مع
+
+74
+00:05:03,380 --> 00:05:07,860
+هادي بيضل واحد و واحد و هنا بيضل عندك اتنين و واحد
+
+75
+00:05:07,860 --> 00:05:11,860
+هنا الاتنين مع الاتنين بيضل تلاتة و واحد فهي أنصر
+
+76
+00:05:11,860 --> 00:05:14,460
+جديد وهي اربعة و اتنين هي أنصر جديد
+
+77
+00:05:17,160 --> 00:05:21,220
+تمام، كمان مرة، برضه مع مين؟ مع نفس R، فإذن
+
+78
+00:05:21,220 --> 00:05:27,220
+automatically هذه هنا صارت R تربيع مع ال R اللي هي
+
+79
+00:05:27,220 --> 00:05:32,220
+بدك تجيب واحد، كان في واحد واحد، واحد، كان في برضه
+
+80
+00:05:32,220 --> 00:05:38,340
+واحد واحد، واحد، برضه في واحد واحد، check، اتنين
+
+81
+00:05:39,190 --> 00:05:44,370
+أتنين و واحد فعشان ننتج منها R تلاتة R to the
+
+82
+00:05:44,370 --> 00:05:47,090
+power تلاتة واحد واحد فإذا بيظل عندي الواحد و
+
+83
+00:05:47,090 --> 00:05:54,030
+الواحد اتنين و واحد و تلاتة و واحد و أربعة و واحد
+
+84
+00:05:54,030 --> 00:05:59,890
+لدك تزود خلاص هتجف بعدك هتجف فكل اللي انت محتاجه
+
+85
+00:05:59,890 --> 00:06:07,470
+هادي اتنينتلاتة اتحاد هتجد انه في مشتركات كتير انت
+
+86
+00:06:07,470 --> 00:06:12,630
+ايش اللي ضفته فعليا ال R زي ما هي هيها هذه كانت مع
+
+87
+00:06:12,630 --> 00:06:18,090
+ال R وهذه كانت مع R وهذه جديدة وهذه جديدة هنا هذه
+
+88
+00:06:18,090 --> 00:06:21,850
+الجديدة فقطفإذا تلت عناصر اللي انت محتاجة تضيفهم
+
+89
+00:06:21,850 --> 00:06:24,690
+.. تلت عناصر اللي انت محتاجة تضيفهم .. خلاص
+
+90
+00:06:24,690 --> 00:06:30,490
+بنضيفهم و بنخلص المسألة عشان نقدر نقول والله إيش
+
+91
+00:06:30,490 --> 00:06:33,930
+ال transitive closure .. transitive closure بمعنى
+
+92
+00:06:33,930 --> 00:06:40,090
+أقل super set .. أقل super set محتاجها من ال
+
+93
+00:06:40,090 --> 00:06:45,280
+relation عشان تصبح transitiveتمام، الآن ال path أو
+
+94
+00:06:45,280 --> 00:06:48,880
+ال paths in directed graphs أخدنا طريقة من طرق
+
+95
+00:06:48,880 --> 00:06:52,740
+تمثيل ال relation بال directed graph و قلنا من إلى
+
+96
+00:06:52,740 --> 00:06:56,700
+فإذا كان عندي زوج مرتب فهي من أربعة لتلاتة و
+
+97
+00:06:56,700 --> 00:07:01,580
+عملناها بالشكل graph بكل بساطة بقدر أقول الآن لما
+
+98
+00:07:01,580 --> 00:07:05,140
+صار عندي graph كامل في path لل graph أكيد، ال path
+
+99
+00:07:05,140 --> 00:07:09,580
+هذا ببساطة جدا ما هو هيعطيك ال transitiveلما انت
+
+100
+00:07:09,580 --> 00:07:14,820
+تقول في عندك علاقة بين ا واحد و اتنين طب اتنين و
+
+101
+00:07:14,820 --> 00:07:18,400
+اتلاتة معناته يوجد path بين واحد و تلاتة مش شايف
+
+102
+00:07:18,400 --> 00:07:21,360
+اكيد معناه ذلك انه صار في transitive صار فعليا في
+
+103
+00:07:21,360 --> 00:07:26,380
+transitive ك graph او ك path ال path المسار اللي
+
+104
+00:07:26,380 --> 00:07:32,760
+بينهم تمام بكل بساطة لو قلنا خلصنا هذه لو قلنا
+
+105
+00:07:32,760 --> 00:07:40,440
+مثلا في عندي ال relations من a ل x واحد ومن X1 ل
+
+106
+00:07:40,440 --> 00:07:46,320
+X2، X2 ل X3، X3 ل X4، لعند ما نصل ل XN نقص واحد مع
+
+107
+00:07:46,320 --> 00:07:51,640
+B فبكل بساطة بقول أن يوجد path أو a path of length
+
+108
+00:07:51,640 --> 00:07:53,980
+N from A to B
+
+109
+00:07:57,810 --> 00:08:01,270
+جدش عدد ال relations هاي relation اتنين تلاتة
+
+110
+00:08:01,270 --> 00:08:05,870
+اربعة لعين بنصل ل N N relation فإذا هنا بنقول ال
+
+111
+00:08:05,870 --> 00:08:10,610
+length تبعنا N قيمة ال length هي قيمتها ال N و N
+
+112
+00:08:10,610 --> 00:08:16,270
+ordered pairs in edges لل graph ال edges لل graph
+
+113
+00:08:16,270 --> 00:08:19,830
+أو ال relation لأن هذه كلها relation هنا يوجد
+
+114
+00:08:19,830 --> 00:08:25,070
+relation بين A و X واحد هذه ال relation E edge X
+
+115
+00:08:25,070 --> 00:08:30,230
+واحد و X اتنين edgeX2 و X3 هدى كلها مجموعة الـ
+
+116
+00:08:30,230 --> 00:08:37,650
+edges بتاعة الـ graph طيب empty sequence of edges
+
+117
+00:08:37,650 --> 00:08:41,270
+إذا كان عندي empty sequence الـ sequence طبعاً ال
+
+118
+00:08:41,270 --> 00:08:49,830
+link طبعاً Zero من A ل A فإذا بتكلم عن Zero order
+
+119
+00:08:49,830 --> 00:08:56,240
+من A ل A فهنا ال link طبعاً Zeroالlength zero تمام
+
+120
+00:08:56,240 --> 00:09:00,520
+self loop ال length بتلع عندي كأنه zero فهنا أصبحت
+
+121
+00:09:00,520 --> 00:09:05,220
+من ال length zero from a to a منها لنفسها منها
+
+122
+00:09:05,220 --> 00:09:09,340
+لنفسها طيب أما إذا كان ال path from a to b exists
+
+123
+00:09:09,340 --> 00:09:14,460
+فعليا هو موجود فبقدر أقول أن a is connected to b
+
+124
+00:09:14,460 --> 00:09:23,060
+مدام يوجد بينهم path هناA connected to B كيف؟ زي
+
+125
+00:09:23,060 --> 00:09:25,800
+أنت والله موجود في الشمال في بيت حنون، بدك تنزل من
+
+126
+00:09:25,800 --> 00:09:30,180
+بيت حنون على غزة، high connection من غزة للوسطة،
+
+127
+00:09:30,180 --> 00:09:32,280
+high connection، من الوسطة لخانيونس، high
+
+128
+00:09:32,280 --> 00:09:34,340
+connection، من خانيونس لرفح، high connection،
+
+129
+00:09:34,340 --> 00:09:39,350
+معناته بيت حنون متصلة في من؟ في رفحببساطة، يعني
+
+130
+00:09:39,350 --> 00:09:42,790
+أنتوا بتحنون، بتصلوا في الرفع، بتضل والله جداش ال
+
+131
+00:09:42,790 --> 00:09:45,290
+.. ال edges .. ال edges هي أكم سيارة أنت انتقلت
+
+132
+00:09:45,290 --> 00:09:48,750
+منها، خليني أقول، نفطر أنت بتنتقل من محافظة
+
+133
+00:09:48,750 --> 00:09:52,030
+لمحافظة، كل واحدة سيارة شكل، فجداش عدد السيارات
+
+134
+00:09:52,030 --> 00:09:54,550
+اللي انتقلت فيهمها هي عدد ال relations، هدول عدد
+
+135
+00:09:54,550 --> 00:09:58,770
+ال relations بالنسبالكتمام، إذا كان ال length لل
+
+136
+00:09:58,770 --> 00:10:01,530
+path، ال path اللي موجود عندك، ال length تبعه هو
+
+137
+00:10:01,530 --> 00:10:06,410
+واحد فأكثر، إيه له قيمة أكبر؟ من واحد، من A عفوا،
+
+138
+00:10:06,410 --> 00:10:11,570
+ل A، بس لاحظ أنهم الصفر، هنا كانت صفر، self-loop،
+
+139
+00:10:11,570 --> 00:10:14,070
+self-loop كانت zero، مافيش مشكلة، لكن إذا كانت
+
+140
+00:10:14,070 --> 00:10:19,910
+واحد فأكثر، هنا، معناه ذلك أنه بيصير عندي circuit
+
+141
+00:10:19,910 --> 00:10:26,980
+أو cycleمدهم أكتر معناته فعليا من a لنقطة على
+
+142
+00:10:26,980 --> 00:10:31,500
+الأقل من
+
+143
+00:10:31,500 --> 00:10:38,220
+a ل a طلعت من a و رجعتها ل a فأصبحت ال connection
+
+144
+00:10:38,220 --> 00:10:43,500
+تبعتي هي من a ل a لكن ال length تبعي أكبر من واحد
+
+145
+00:10:43,500 --> 00:10:47,020
+فهذه cycle ممكن تكون أكتر من هيك
+
+146
+00:10:50,380 --> 00:10:54,760
+بهذا الشكل و برضه من a ل a طلعت من a و رجعت ل a
+
+147
+00:10:54,760 --> 00:11:00,320
+برضه cycle او circuit او circuit جيد الان هنلاحظ
+
+148
+00:11:00,320 --> 00:11:04,720
+انه اذا فعلا وجد ال path of length in from a to b
+
+149
+00:11:04,720 --> 00:11:10,420
+in Rحسب ال relation are ال relation are واللي قلنا
+
+150
+00:11:10,420 --> 00:11:14,620
+عليها مواصلة بالسيارة فإذا من بيت حنون لغزة هي
+
+151
+00:11:14,620 --> 00:11:18,500
+مواصلة سيارة طب ما هي نفس الاشي برضه ال relation
+
+152
+00:11:18,500 --> 00:11:23,560
+هي نفسها أني بدي أركب سيارة من غزة لأي مدينة في
+
+153
+00:11:23,560 --> 00:11:26,920
+الوسط مثلا خليني أقول دير البلح okay معناته هي في
+
+154
+00:11:26,920 --> 00:11:32,200
+عندك نفس ال relation نفس ال relation لكن من غزة
+
+155
+00:11:32,200 --> 00:11:36,600
+لدير البلح مثلاكويس فهنا هيكون عندك مجموعة
+
+156
+00:11:36,600 --> 00:11:44,260
+relations if and only if a و b تنتمي ل relation to
+
+157
+00:11:44,260 --> 00:11:47,940
+the power n طب احنا ال relation to the power n دي
+
+158
+00:11:47,940 --> 00:11:51,780
+كانت ايش؟ كنا بنتكلم عنها composition طب ما هي نفس
+
+159
+00:11:51,780 --> 00:11:57,500
+الفكرة انت هيك طلعت من مين؟ ال relation الأولى بيت
+
+160
+00:11:57,500 --> 00:12:02,920
+حنون غزةهي نهايتها ايش؟ غزة، معناه انت بدك
+
+161
+00:12:02,920 --> 00:12:06,600
+relation بدايتها غزة، ماهي مش هيك ال composition
+
+162
+00:12:06,600 --> 00:12:11,320
+اللي شغلناها؟ خلاص غزة دير البلح، هي relation
+
+163
+00:12:11,320 --> 00:12:14,380
+تانية، معناه انت صارت بيت حنون متصلة بدير البلح،
+
+164
+00:12:14,380 --> 00:12:17,180
+طيب دير البلح اللي خلصنا فيها ال relation المفروض
+
+165
+00:12:17,180 --> 00:12:20,020
+الان ندور على ال relation تبدأ منها، دير البلح
+
+166
+00:12:20,020 --> 00:12:24,640
+خانيونسطيب من خانيونس بدك تبدأ منها خانيونس رفح
+
+167
+00:12:24,640 --> 00:12:27,980
+وهي نفس اللي احنا عملناها composition فبقدر ساعتها
+
+168
+00:12:27,980 --> 00:12:32,960
+اقول جدش عددهم R to the power N R to the power to
+
+169
+00:12:32,960 --> 00:12:36,160
+the power N composition فانا عملت ال composition
+
+170
+00:12:36,160 --> 00:12:42,820
+لل R مع نفسها مع يعني عدد سيارات كانتقال N مرة N
+
+171
+00:12:42,820 --> 00:12:45,500
+مرة ففي الحالة دي بقول ان ال length تبع هي N فعلا
+
+172
+00:12:45,500 --> 00:12:52,910
+N مرة N مرة تمامال equivalence relations أمتى بقدر
+
+173
+00:12:52,910 --> 00:12:57,130
+أسمي ال relation تبعتي هي equivalence relation على
+
+174
+00:12:57,130 --> 00:13:01,330
+ال 6A بكل بساطة إذا كانت بتعامل معه binary فإذا
+
+175
+00:13:01,330 --> 00:13:06,370
+كانت والله reflexive، symmetric و transitive فهي
+
+176
+00:13:06,370 --> 00:13:09,650
+equivalence relation فهي إيش؟ بيسموها equivalence
+
+177
+00:13:09,650 --> 00:13:15,900
+relation أو EER زي المساواةالمساوية دي equivalence
+
+178
+00:13:15,900 --> 00:13:19,440
+relation ليش؟ لأنه بكل بساطة انت بتقدر تقول a
+
+179
+00:13:19,440 --> 00:13:24,820
+بتساوي a هاي reflexive هاي ال reflexive طيب تقدر
+
+180
+00:13:24,820 --> 00:13:31,000
+تقول إذا a بتساوي b أكيد b بتساوي a ف symmetric
+
+181
+00:13:31,000 --> 00:13:36,080
+مدام فعلا علمت اللي يساوي صحيحة أكيد صحيح طيب إذا
+
+182
+00:13:36,080 --> 00:13:44,780
+a بتساوي b و b بتساوي c أكيد a هتساوي ctransitive
+
+183
+00:13:44,780 --> 00:13:51,580
+فإذا ال relation يساوي هي فعلا بتحقق التلاتة ال
+
+184
+00:13:51,580 --> 00:13:58,060
+three properties بتتحقق باستخدام هذه ال notation
+
+185
+00:13:58,060 --> 00:14:02,520
+أو المساواة فإذا المساواة هي فعليانقدر بكل بساطة
+
+186
+00:14:02,520 --> 00:14:06,960
+نسميها equivalence relation طيب إذا كان عندك أي
+
+187
+00:14:06,960 --> 00:14:11,440
+function if from A to B بقدر أسميها relation have
+
+188
+00:14:11,440 --> 00:14:16,500
+the same if value إذا كان لهم نفس القيمة .. لهم
+
+189
+00:14:16,500 --> 00:14:22,480
+نفس القيمة أو if هي عبارة عن زوج مرتب A1 و A2 بشرط
+
+190
+00:14:22,480 --> 00:14:27,240
+إنه if ل A1 تساوي if ل A2 فبقدر أقول إن ال two
+
+191
+00:14:27,240 --> 00:14:32,140
+functions هدولةequivalence لبعض بيساووا بعض نقدر
+
+192
+00:14:32,140 --> 00:14:36,840
+نقول عليهم بيساووا بعض أو ال relation have the
+
+193
+00:14:36,840 --> 00:14:40,580
+same value have the same value زي مثل إذا كان
+
+194
+00:14:40,580 --> 00:14:43,280
+والله يقولنا equivalence relation بسميها
+
+195
+00:14:43,280 --> 00:14:45,940
+equivalence relation في الحلقة دي إذا كان مثلا let
+
+196
+00:14:45,940 --> 00:14:54,000
+M brother of يعني قلنا A brother of B معناته بقدر
+
+197
+00:14:54,000 --> 00:15:01,050
+أقول A and B have the same motherK جزئيا بطريقة او
+
+198
+00:15:01,050 --> 00:15:04,430
+باخره ممكن نقول بهذا الشكل فإذا ممكن نقول ان ال M
+
+199
+00:15:04,430 --> 00:15:08,230
+هنا مكافئة لل M، ال M هنا ف equivalence relation
+
+200
+00:15:08,230 --> 00:15:11,210
+لو مسكنا كل واحدة منهم على حدا المفروض انها تحقق
+
+201
+00:15:11,210 --> 00:15:13,330
+ال equivalence relation اللي اتكلمنا او ال three
+
+202
+00:15:13,330 --> 00:15:17,690
+properties اللي حكينا عنهم بمعنى لما تقول A
+
+203
+00:15:17,690 --> 00:15:25,730
+brother of B معناته بي brother of Aصح؟ يعني لو انت
+
+204
+00:15:25,730 --> 00:15:29,550
+صياغة الجملة عكستها، هيتغير إشي؟ مش هيتغير إشي،
+
+205
+00:15:29,550 --> 00:15:34,290
+الكلام صحيح، الكلام صحيح، و لو قلت A brother of B
+
+206
+00:15:34,290 --> 00:15:41,230
+و B brother of C، معناته أكيد A brother of C،
+
+207
+00:15:41,230 --> 00:15:48,870
+صحيح؟ تمامصحيح بشروط لكن .. بشروط لكن ماشية يمكن
+
+208
+00:15:48,870 --> 00:15:51,470
+عندنا في مجتمعاتنا العربية شوية بتصير ال .. بتختلف
+
+209
+00:15:51,470 --> 00:15:56,230
+الشروط بس عالميا لأ مش كتير طيب فنفس الفكرة هنا لو
+
+210
+00:15:56,230 --> 00:16:00,870
+قلت a و b have the same mother و قلت b و a have
+
+211
+00:16:00,870 --> 00:16:05,370
+the same mother نفس الجثة طيب لو قلنا a and b have
+
+212
+00:16:05,370 --> 00:16:08,790
+the same mother, b and c have the same mother أكيد
+
+213
+00:16:08,790 --> 00:16:14,340
+a and c have the same mother أكيدفهي مثال شوية
+
+214
+00:16:14,340 --> 00:16:24,060
+ممكن على ثقافتنا كان بده شروط لكن كفكرة يعني وصلت
+
+215
+00:16:24,060 --> 00:16:30,460
+الفكرة تمام طيب الآن ال equivalent relation او ال
+
+216
+00:16:30,460 --> 00:16:32,660
+equivalent element لما نتكلم عن ال equivalent
+
+217
+00:16:32,660 --> 00:16:36,120
+element بقدر اقول انه كل element المفروض ان هو
+
+218
+00:16:36,120 --> 00:16:40,720
+equivalent to itself فمعنى ذلك ان هو reflexive زي
+
+219
+00:16:40,720 --> 00:16:46,820
+المسواه هذهالعنصر هو مكافئ لنفسه العنصر مكافئ
+
+220
+00:16:46,820 --> 00:16:52,320
+لنفسه تمام طيب we can say that a and b are related
+
+221
+00:16:52,320 --> 00:16:56,460
+are related لاحظ ماقولتش مين related للتاني هما
+
+222
+00:16:56,460 --> 00:17:02,480
+التنتين related يعني معناته a to b أو b to a فهذه
+
+223
+00:17:02,480 --> 00:17:07,220
+مش زي لما نقول a is related to b هذه معناته من a
+
+224
+00:17:07,220 --> 00:17:10,660
+لb بسلأ أنا ماقولتش هيك احنا قولنا are related
+
+225
+00:17:10,660 --> 00:17:14,920
+اتنتين فاتنتين متساويتين اي نعم ليش لأن هذا معناته
+
+226
+00:17:14,920 --> 00:17:21,960
+ان a relation b هي نفسها b relation a زي المساوية
+
+227
+00:17:21,960 --> 00:17:26,000
+ال relation مساوية هنا معناته من a لb ماشي من b لa
+
+228
+00:17:26,000 --> 00:17:30,160
+ماشي فهذه symmetric هذه المساوية كانت symmetric
+
+229
+00:17:30,160 --> 00:17:37,440
+فعليا طيب إذا كانت a and b are equivalent وB and C
+
+230
+00:17:37,440 --> 00:17:41,420
+برضه are equivalent المفروض إنه يطبع ذلك استنتاج
+
+231
+00:17:41,420 --> 00:17:46,460
+واضح إنه A and C are equivalent لازم هذه بتحقق ال
+
+232
+00:17:46,460 --> 00:17:48,940
+Transitive وهذه شفناها هنا إذا كانت A فعلا بتساوي
+
+233
+00:17:48,940 --> 00:17:57,300
+B A R B and B R C محقق ال relation ال equal كويس
+
+234
+00:17:57,300 --> 00:18:02,180
+إذا A relation C تحققت تحققت فإذا هذه تلت شروط
+
+235
+00:18:02,180 --> 00:18:06,040
+اللي بنعملهم ال check عشان نشوف هل فعلافي عندى
+
+236
+00:18:06,040 --> 00:18:09,760
+equivalent elements ومعنى ذلك انه equivalent
+
+237
+00:18:09,760 --> 00:18:12,900
+relation اللى بتكلم عنها اللى هى ال R و اللى هى
+
+238
+00:18:12,900 --> 00:18:15,780
+هنا مساوية مع انها اللى هى عندنا هنا استخدمنا
+
+239
+00:18:15,780 --> 00:18:20,560
+اليساوي طيب مجموعة equivalent equivalence relation
+
+240
+00:18:20,560 --> 00:18:23,280
+examples بعض الأمثل لل equivalence relations زى
+
+241
+00:18:23,280 --> 00:18:28,820
+لما نقول strings A and B are the same length بكل
+
+242
+00:18:28,820 --> 00:18:36,700
+بساطة هقولك ان طول حرف ال A بساوة طول حرف ال Zليش؟
+
+243
+00:18:36,700 --> 00:18:40,740
+لأن كل كلاهما .. كل واحد منهم له strength طوله
+
+244
+00:18:40,740 --> 00:18:48,040
+تمانية ك character صح؟ طيب و بقدر أقولك أن ال A هي
+
+245
+00:18:48,040 --> 00:18:54,580
+مكافئة للعلامة المئويةهتقولي طب انت بناء على إيش
+
+246
+00:18:54,580 --> 00:18:57,460
+المكافئة هنا بتصير ال relation بتعرف إيش ال
+
+247
+00:18:57,460 --> 00:19:01,200
+relation اللي بحكي عنها ال relation هي ال string
+
+248
+00:19:01,200 --> 00:19:06,420
+تبعك جدّيش عدد ال bits الممثلة لكل منهما هتقولي اه
+
+249
+00:19:06,420 --> 00:19:10,280
+هي كلمك صح ما هم كله تمانية شك هي كله تمانية ف ال
+
+250
+00:19:10,280 --> 00:19:14,280
+strings a and b are the same length لو قولنا a
+
+251
+00:19:14,280 --> 00:19:18,190
+have the same length مع a نفسهطيب و في الحالة دي
+
+252
+00:19:18,190 --> 00:19:22,670
+إذا ال strings a and b بيسوا بعض معناته b and a
+
+253
+00:19:22,670 --> 00:19:26,870
+بيسوا بعض طيب إذا a و b بيسوا بعض بي و c بيسوا بعض
+
+254
+00:19:26,870 --> 00:19:32,290
+فأكيد إذا كان أنا هنا قول تهينا هدول a مكافئة ل z
+
+255
+00:19:32,290 --> 00:19:35,750
+و a مكافئة لعلامة المئوية معناته العلم المئو
+
+256
+00:19:35,750 --> 00:19:41,960
+مكافئة ل z صح؟أكيد هيكونوا مكافئين لبعض طيب التاني
+
+257
+00:19:41,960 --> 00:19:45,300
+مثال تاني ال integers a and b have the same
+
+258
+00:19:45,300 --> 00:19:49,820
+absolute value have the same absolute value بمعنى
+
+259
+00:19:49,820 --> 00:19:54,200
+بتقدر تقول إذا كان والله a have the same absolute
+
+260
+00:19:54,200 --> 00:19:58,920
+value مع a نفسها خمسة خمسة خلاص طيب إذا كانت a و
+
+261
+00:19:58,920 --> 00:20:02,620
+سالب a كلا هما له نفس ال absolute معناته برضه سالب
+
+262
+00:20:02,620 --> 00:20:07,600
+a و a اللي هم نفس ال absolute value نفس ال
+
+263
+00:20:07,600 --> 00:20:12,530
+absolute valueطيب A have the same absolute value ل
+
+264
+00:20:12,530 --> 00:20:17,830
+B طيب B have the same absolute value ل C المنطق
+
+265
+00:20:17,830 --> 00:20:21,750
+بيقول معناته A و C لهم نفس ال absolute value نفس
+
+266
+00:20:21,750 --> 00:20:26,410
+ال absolute value تمامالـ real numbers a and b
+
+267
+00:20:26,410 --> 00:20:33,550
+have the same fractional part، عشرة و سبعة و
+
+268
+00:20:33,550 --> 00:20:37,090
+أربعين، خمسين أو تلاتة و خمسين، برضه سبعة و
+
+269
+00:20:37,090 --> 00:20:39,610
+أربعين، اللي هو نفس ال fractional part، معنى ذلك
+
+270
+00:20:39,610 --> 00:20:43,770
+أن ال difference between them أكيد integer، صح؟
+
+271
+00:20:43,770 --> 00:20:48,690
+الفرق بينهم أكيد integerكفرق تمام فإذا في الحالة
+
+272
+00:20:48,690 --> 00:20:52,090
+هذه بقدر أقول إن هما the same في ال fractional
+
+273
+00:20:52,090 --> 00:20:56,270
+part فكأنه a نقص b هي دائما هتكون z دائما هتكون z
+
+274
+00:20:56,270 --> 00:21:02,050
+هذا بالظبط ما هو كله the same هنا اللي بيحدد mean
+
+275
+00:21:02,050 --> 00:21:05,630
+the same هذه هي أني أعرفك ال function فهي الفكرة
+
+276
+00:21:05,630 --> 00:21:10,990
+كلها هنا the same ish the same ish هي ال the same
+
+277
+00:21:10,990 --> 00:21:15,220
+ish fractional أه مش الحالfractional مش الحالة لو
+
+278
+00:21:15,220 --> 00:21:17,680
+fractional حطيتها مع ال absolute لأ بيمشيش الحالة
+
+279
+00:21:17,680 --> 00:21:21,440
+فبتاخد بالك هي ال relation بتدجك في ال relation
+
+280
+00:21:21,440 --> 00:21:24,760
+نفسها عشان تحدد ال relation هي فعلا equivalence
+
+281
+00:21:24,760 --> 00:21:29,700
+relation و لا لأ طيب في المقابل هتلاقي مثلا ال
+
+282
+00:21:29,700 --> 00:21:34,860
+integers a and b have the same residue modulo m
+
+283
+00:21:34,860 --> 00:21:42,680
+تمام ل given m أكبر من واحد أكبر مثلا من واحد زي
+
+284
+00:21:42,680 --> 00:21:48,070
+لما نقولالاتنين equivalent للاربعتاش إذا كانت ال M
+
+285
+00:21:48,070 --> 00:21:53,350
+سوى اتناش للساعة خمسة وعشرين equivalent للواحد طيب
+
+286
+00:21:53,350 --> 00:21:55,630
+معناه ذلك إذا كان الخمسة وعشرين equivalent للواحد
+
+287
+00:21:55,630 --> 00:21:59,590
+والواحد equivalent للتلتاش أكيد التلتاش equivalent
+
+288
+00:21:59,590 --> 00:22:05,030
+للخمسة وعشرين أكيد طيب نفس الكلام الخمسة وعشرين
+
+289
+00:22:05,030 --> 00:22:07,430
+equivalent للواحد فالواحد equivalent للخمسة وعشرين
+
+290
+00:22:08,210 --> 00:22:12,170
+برضه متفرجش مين جاب المين والواحد طبعا اكيد
+
+291
+00:22:12,170 --> 00:22:15,170
+equivalent لنفسه والخمسة وعشرين equivalent لنفسها
+
+292
+00:22:15,170 --> 00:22:19,410
+تمام فإذا برضه بتحقق التلت شروط الأساسية فإذا بقدر
+
+293
+00:22:19,410 --> 00:22:25,190
+أقول عنها equivalence relation check إذا كانت
+
+294
+00:22:25,190 --> 00:22:29,470
+divides relation هل فعلا متحقق نفس الكلام ولا لا
+
+295
+00:22:29,470 --> 00:22:37,870
+هتشوف a divides b لو قلنا a divides aبمشي true ولا
+
+296
+00:22:37,870 --> 00:22:45,530
+false true لأنه الناتج integer خدوا بالكم هنا لما
+
+297
+00:22:45,530 --> 00:22:48,090
+بقول divides معناته الناتج لازم يكون integer
+
+298
+00:22:48,090 --> 00:22:51,750
+الكلام هذه أول حاجة أخدناها في ال numbers أول حاجة
+
+299
+00:22:51,750 --> 00:22:55,250
+بعدين روحنا لل long division أصلا اسمها division
+
+300
+00:22:55,250 --> 00:22:58,170
+أنه يكون فيه متبقي بس مدين بقول divides و بس
+
+301
+00:22:58,170 --> 00:23:02,410
+معناته لأ لازم يطلع integer فمعليش الكلمتين
+
+302
+00:23:02,410 --> 00:23:07,510
+مختلفين عن بعض long division غير dividesOkay فهذه
+
+303
+00:23:07,510 --> 00:23:10,690
+okay بتطلع في نهاية واحد فإذا okay مقبولة مبلوعة
+
+304
+00:23:10,690 --> 00:23:17,310
+طيب لما تكون A divides B and B divides C أكيد هذا
+
+305
+00:23:17,310 --> 00:23:26,230
+equivalent إنه A divides C صح إذا A تقسم B نفترض
+
+306
+00:23:26,230 --> 00:23:33,030
+اتنين و تمانية A تقسم B طيب B تقسم C تمانية مثلا و
+
+307
+00:23:33,030 --> 00:23:39,710
+16فإذن بالضرورة أكيد هتكون A divides C اتنين تقسم
+
+308
+00:23:39,710 --> 00:23:44,690
+ستة عشر صح؟ أكيد تقسم ستة عشر طيب بتظل الشغل
+
+309
+00:23:44,690 --> 00:23:49,750
+الوحيدة هل A divides B equivalent ل B divides A
+
+310
+00:23:49,750 --> 00:23:52,910
+أكيد
+
+311
+00:23:52,910 --> 00:23:54,590
+لأ فهذه
+
+312
+00:23:57,610 --> 00:24:02,150
+لأ، هذه ليست equivalence relation، هذه ليست
+
+313
+00:24:02,150 --> 00:24:04,950
+equivalence relation، رغم أن طول ما أنا قاعد بشرح
+
+314
+00:24:04,950 --> 00:24:08,670
+أنت تخيلت أنها رايحة أن هي تكون equivalence
+
+315
+00:24:08,670 --> 00:24:13,790
+relation، هي لأ مش equivalence relation، لأنه
+
+316
+00:24:13,790 --> 00:24:17,610
+symmetric لأ هي مش symmetric، هي مش symmetric، هي
+
+317
+00:24:17,610 --> 00:24:21,210
+ليست symmetric، هذه إيش بنسميها؟ Asymmetric؟
+
+318
+00:24:28,930 --> 00:24:36,210
+والا انت symmetric انت symmetric بتمشي اه بيطلع
+
+319
+00:24:36,210 --> 00:24:40,350
+بيمشي الحال بيمشي الحال فبتضل مقبولة فإذا في
+
+320
+00:24:40,350 --> 00:24:42,970
+النهاية هي مش symmetric وهذا اللي بيهمنا مدام مش
+
+321
+00:24:42,970 --> 00:24:45,810
+symmetric لأن هو هذا الشرط اللي انا محتاج احققه
+
+322
+00:24:45,810 --> 00:24:49,650
+فخلاص هي مش symmetric بس هي ليست symmetric مدام
+
+323
+00:24:49,650 --> 00:24:52,330
+ليست symmetric فإذا لأ بقدرش أسميها equivalence
+
+324
+00:24:52,330 --> 00:24:57,230
+relation تمام الان equivalence classes ال classes
+
+325
+00:24:57,230 --> 00:25:01,650
+هي ديإن هو تصنيف، تصنيف كامل، بمعنى كإني بقول إن
+
+326
+00:25:01,650 --> 00:25:04,590
+والله إذا تحقق .. عشان أقول إنه تحقق equivalence
+
+327
+00:25:04,590 --> 00:25:09,170
+class of A معنى ذلك إنه يوجد عندي set of
+
+328
+00:25:09,170 --> 00:25:15,930
+equivalent elements of A زي الواحدالواحد
+
+329
+00:25:15,930 --> 00:25:20,810
+equivalent له واحد تلات عشر خمسة اذا بتكلم عن
+
+330
+00:25:20,810 --> 00:25:25,390
+الساعة خمسة و عشرين وجمع اقعد جمع اتناشط جمع
+
+331
+00:25:25,390 --> 00:25:29,710
+اتناشط سبعة و تلاتين ال تسعة و اربعين و اكمل
+
+332
+00:25:29,710 --> 00:25:34,070
+الصحيح اللي هي بتزود اربعة و عشرين جاعد كل هدول
+
+333
+00:25:34,070 --> 00:25:39,230
+equivalent له معناته كل هدوله classكل element فيه
+
+334
+00:25:39,230 --> 00:25:44,670
+هو equivalent لإيه فبحطهم كلهم ك class واحد كوان
+
+335
+00:25:44,670 --> 00:25:52,050
+class فبصير اسمها equivalent class كويس كلهم
+
+336
+00:25:52,050 --> 00:25:57,720
+equivalent لمين لل relation R زي لما نقولبما فيها
+
+337
+00:25:57,720 --> 00:26:04,400
+A نفسها هي نقدر نسميها representative of A under
+
+338
+00:26:04,400 --> 00:26:07,340
+relation R فunder relation R هنا مثلا زي المثال
+
+339
+00:26:07,340 --> 00:26:11,580
+اللي قلناه توي ال relation هي ال modulo أو ال
+
+340
+00:26:11,580 --> 00:26:16,670
+residue of modulo معاشرإذا قلت فعلا الكلام هذا أن
+
+341
+00:26:16,670 --> 00:26:18,890
+هذه هي ال relation اللي هي ال residue of موديول
+
+342
+00:26:18,890 --> 00:26:22,910
+أتناش بقدر أقول ساعتها أن الواحد مع الخمسة و عشرين
+
+343
+00:26:22,910 --> 00:26:28,630
+ماشي مع التلتاش ماشي مع التسعة و أربعين ماشي ستة و
+
+344
+00:26:28,630 --> 00:26:33,530
+تلاتين و واحد سبعة و تلاتين ماشي هدى صارت ستة ولا
+
+345
+00:26:33,530 --> 00:26:38,330
+relation؟ هدى صارت لأ هدى هنا بتتكلم عن ستة مش
+
+346
+00:26:38,330 --> 00:26:43,600
+هتفرج مين جاب المين هدى six of relationsلأ ال
+
+347
+00:26:43,600 --> 00:26:47,660
+relation بمعنى هي تجميعة كل العناصر اللي
+
+348
+00:26:47,660 --> 00:26:51,320
+equivalent او equivalent بالظبط للعنصر A
+
+349
+00:26:51,320 --> 00:26:55,260
+equivalent للعنصر A لما بتتكلم عن طبعا نيجي نقول
+
+350
+00:26:55,260 --> 00:26:59,440
+مثلا مثلا
+
+351
+00:26:59,440 --> 00:27:03,160
+المتبقى ال fractional part the same fractional
+
+352
+00:27:03,160 --> 00:27:07,610
+part معنى ذلك أن Aزائد واحد، زائد اتنين، زائد
+
+353
+00:27:07,610 --> 00:27:10,070
+تلاتة، زائد اربعة، ناقص واحد، ناقص اتنين، ناقص
+
+354
+00:27:10,070 --> 00:27:13,590
+تلاتة، ناقص اربعة، ناقص to infinity من minus
+
+355
+00:27:13,590 --> 00:27:16,250
+infinity to infinity اللي هي بتجمع عليها integer
+
+356
+00:27:16,250 --> 00:27:19,830
+فانت ضامن ان ال fractional part هيظل زي ما هو،
+
+357
+00:27:19,830 --> 00:27:23,510
+هيظل كما هو فهذه معناته انت عندك كائنة ست لا
+
+358
+00:27:23,510 --> 00:27:28,750
+متناهية صارت من ال equivalent elements للعنصر A
+
+359
+00:27:28,750 --> 00:27:36,070
+with the same fractional partمش هيك كلها بتعملوا
+
+360
+00:27:36,070 --> 00:27:39,190
+انك بتجمع عليها integers فانت ضامن ان ال
+
+361
+00:27:39,190 --> 00:27:42,010
+fractional part هو هو ال fractional part كما هو
+
+362
+00:27:42,010 --> 00:27:49,030
+طيب مجموعة examples لل class او ال equivalence
+
+363
+00:27:49,030 --> 00:27:54,910
+class classes strings
+
+364
+00:27:54,910 --> 00:27:58,790
+a and b have the same length لهم نفس ال length ففي
+
+365
+00:27:58,790 --> 00:28:03,270
+الحالة هذه بنقدر نقول انهبراكت a اللي هو
+
+366
+00:28:03,270 --> 00:28:07,530
+representative of a لإن ال relation have the same
+
+367
+00:28:07,530 --> 00:28:12,650
+length، كويس، هي كل الست، هاي ست، مين جاب المين
+
+368
+00:28:12,650 --> 00:28:16,090
+بتفرجش معناه، بس هي في أنها ست، لكل ال strings of
+
+369
+00:28:16,090 --> 00:28:22,280
+the same lengthof a a قدش طولها فكل length نفس
+
+370
+00:28:22,280 --> 00:28:26,520
+الطول هو ضمن هذه ال set ضمن هذه ال set طيب ال
+
+371
+00:28:26,520 --> 00:28:30,460
+integers a and b have the same absolute value فإذا
+
+372
+00:28:30,460 --> 00:28:36,760
+بقدر اقول انه representative of a ل ال relation
+
+373
+00:28:36,760 --> 00:28:40,000
+absolute value have the same absolute value هي a و
+
+374
+00:28:40,000 --> 00:28:45,790
+سالب aفي غيرهم؟ خلاص فهذه الست تبعتنا a and سالب a
+
+375
+00:28:45,790 --> 00:28:49,390
+في الحالة هذه طيب real numbers a and b have the
+
+376
+00:28:49,390 --> 00:28:54,910
+same fractional part هذه معناته أن a ناقص b عبارة
+
+377
+00:28:54,910 --> 00:28:58,630
+عن تنتمي المفروض ل z ففي الآخر بقدر أقول أن ال
+
+378
+00:28:58,630 --> 00:29:04,190
+representative of a هي كل الست a و a ناقص واحد a
+
+379
+00:29:04,190 --> 00:29:10,760
+زائد واحدE نقص اتنين E زائد اتنين جمع integers لما
+
+380
+00:29:10,760 --> 00:29:13,240
+تصل minus infinity to infinity لما تصل minus
+
+381
+00:29:13,240 --> 00:29:17,020
+infinity او infinity فكل هدول العناصر هيكونهم the
+
+382
+00:29:17,020 --> 00:29:23,080
+same fractional part كلهم اكيد ال integers A and B
+
+383
+00:29:23,080 --> 00:29:28,160
+have the same residue modulo M في الحالة هذه كل
+
+384
+00:29:28,160 --> 00:29:30,820
+اللي انت بتعمله بس زي ما توي عملنا جمعنا جداش
+
+385
+00:29:30,820 --> 00:29:36,910
+اتناشاتنفس الفكرة هي ال A نفسها وال A زائد M نخص M
+
+386
+00:29:36,910 --> 00:29:43,940
+زائد اتنين M نخص اتنين Mقلت لك 21 و بعدين اضفت لهم
+
+387
+00:29:43,940 --> 00:29:48,180
+12 قلت لك 13 مش الحال قلت لك مش اتناش اتناش في
+
+388
+00:29:48,180 --> 00:29:51,060
+اتنين اربع و عشرين زاد الواحد هي خمسة و عشرين قلت
+
+389
+00:29:51,060 --> 00:29:53,820
+لك خمسة و عشرين كل equivalent مدام انت بتجمع جاعد
+
+390
+00:29:53,820 --> 00:29:59,020
+مضاعفات ال modulus مضاعفات ال modulus عندك فبمش
+
+391
+00:29:59,020 --> 00:30:03,260
+الحال كلهم هدولة عبارة عن set of elements كل
+
+392
+00:30:03,260 --> 00:30:06,460
+element فيهم هو equivalent ل a هو equivalent ل ال
+
+393
+00:30:06,460 --> 00:30:12,790
+aOkay ال partitions ال partitions هي عبارة عن أنت
+
+394
+00:30:12,790 --> 00:30:14,890
+بقدر أقول أن في عندي partitions فعليا ال
+
+395
+00:30:14,890 --> 00:30:19,750
+partitions هي ال set A ل set A معينة هي كل ال sets
+
+396
+00:30:19,750 --> 00:30:23,450
+اللي بقدر أسميه equivalence classes فإذا كل
+
+397
+00:30:23,450 --> 00:30:28,190
+equivalence class بقول عليه A one هدولة مثلا
+
+398
+00:30:28,190 --> 00:30:32,690
+العناصر اللي .. أقولكوا أبسط شغلة بدي أقول أن ال
+
+399
+00:30:32,690 --> 00:30:37,490
+set تبعتنا هي طلبة هندسة الحسوبطلبة هندسة الحسوب
+
+400
+00:30:37,490 --> 00:30:40,910
+class one هم طلبة هندسة الحسوب في المستوى التاني
+
+401
+00:30:40,910 --> 00:30:47,010
+هدول class one مثلا شك .. ليش؟ لأن كلهم لما أجي
+
+402
+00:30:47,010 --> 00:30:51,650
+أحطهم تحت relation أنه have the same level هنطبق
+
+403
+00:30:51,650 --> 00:30:55,750
+عليهم have the same level معناته level two هدول
+
+404
+00:30:55,750 --> 00:31:00,690
+المستوى التاني في الكلية في القسم فإذا إذا كان a و
+
+405
+00:31:00,690 --> 00:31:04,210
+b have the same level b و c have the same level
+
+406
+00:31:04,210 --> 00:31:08,120
+معناته أكيد a و c have the same levelو A و B have
+
+407
+00:31:08,120 --> 00:31:10,020
+the same level معناته B و A have the same level
+
+408
+00:31:10,020 --> 00:31:14,860
+نفس الجثة A مع نفسه أكيد هي reflexive فإذا هذه
+
+409
+00:31:14,860 --> 00:31:18,500
+equivalent ك equivalent تمام في نفس الوقت في عندي
+
+410
+00:31:18,500 --> 00:31:25,320
+class 2 للمستوى التالت طيب class 3 للمستوى الرابع
+
+411
+00:31:25,320 --> 00:31:28,820
+class 4 للمستوى الخامس طب total كلهم على بعض
+
+412
+00:31:28,820 --> 00:31:35,820
+بكونوا ليه؟كل class تبع هندسة الحاسوب، صح؟ ماحدش
+
+413
+00:31:35,820 --> 00:31:40,100
+هيطلع منهم، ماحدش هيطلع منهم وفي نفس الوجد مافيش
+
+414
+00:31:40,100 --> 00:31:46,200
+intersection between them مافيش تقاطع، معنى ذلك أن
+
+415
+00:31:46,200 --> 00:31:48,740
+التقاطع بينهم في في الحالة دي بقدر أقول إنهم
+
+416
+00:31:48,740 --> 00:31:52,320
+partitions، مافيش تقاطعات بينهم، هذه مهمة جدا
+
+417
+00:31:52,320 --> 00:31:56,650
+الفكرة في ال database بكرةلما تشوف تتكلم عن قواعد
+
+418
+00:31:56,650 --> 00:32:00,150
+البيانات و منفصلة لو هي partitions ولا مش
+
+419
+00:32:00,150 --> 00:32:04,120
+partitions مهم جدا الفكرة هذهتمام، فإذا في الحالة
+
+420
+00:32:04,120 --> 00:32:08,220
+دي بتقدر تقول إنه ال equivalent classes هذه بنحطهم
+
+421
+00:32:08,220 --> 00:32:12,320
+ك partitions داخل equivalent class كبيرة جدا، داخل
+
+422
+00:32:12,320 --> 00:32:15,000
+equivalent class كبيرة بحيث إنه أجسمها جوا لمجموعة
+
+423
+00:32:15,000 --> 00:32:20,220
+classes أو parts أو parts، the same ER، كل واحدة
+
+424
+00:32:20,220 --> 00:32:23,080
+منهم طبعا بتحقق ال ER أو ال equivalence relation
+
+425
+00:32:23,080 --> 00:32:25,120
+لحالها، كل واحدة بتحقق ال equivalence relation
+
+426
+00:32:25,120 --> 00:32:32,080
+لحالهالازم تكون disjoint اكيد a1 مع a2 او ال a مع
+
+427
+00:32:32,080 --> 00:32:36,120
+بعضها لازم تكون disjoint فمثال ال levels مناسب جدا
+
+428
+00:32:36,120 --> 00:32:39,780
+كان لنا مش هتلاقي طالب مكتوب اللي في ال transcript
+
+429
+00:32:39,780 --> 00:32:42,840
+تبعه هو level تلاتة و أربعة في نفس الوجه تصبتش
+
+430
+00:32:42,840 --> 00:32:45,820
+صحيح يا تلاتة يا أربعة يعني مش هتيجي تنتم مع بعض
+
+431
+00:32:45,820 --> 00:32:48,760
+بس ضايقلك ساعة خلاص خلص الساعة فجأة بتلاقي حالك
+
+432
+00:32:48,760 --> 00:32:51,640
+انتقلت لل .. للمستوى الرابع انتهى على حسب عدد
+
+433
+00:32:51,640 --> 00:32:55,320
+الساعات معينة ففيه thresholdكويس فى three short
+
+434
+00:32:55,320 --> 00:33:00,760
+خلصنا بنتى كويس فإذا this joint ال groups هدى مع
+
+435
+00:33:00,760 --> 00:33:03,600
+بعضها أو ال partitions هدى مع بعضها و ال union
+
+436
+00:33:03,600 --> 00:33:07,840
+تبعهم كلهم مع بعض المفروض يعطيني ال a ال total ايه
+
+437
+00:33:07,840 --> 00:33:11,960
+ال total ايه لما أجى أقول والله كل طلبة هندسة
+
+438
+00:33:11,960 --> 00:33:15,000
+الحسوب على اعتبار أنه سنة أولى لسه مش متخصصين
+
+439
+00:33:15,000 --> 00:33:18,020
+فماقدرش نحطهم فبدأت من المستوى التانى التالت
+
+440
+00:33:18,020 --> 00:33:21,960
+الرابع الخامس كل هدولة بيحددولنا من طلبة هندسة
+
+441
+00:33:21,960 --> 00:33:26,490
+الحسوب ك totalبالتالي بسيطة يعني هذه الفكرة كلها
+
+442
+00:33:26,490 --> 00:33:30,970
+هي مجرد مقدمة مجرد مقدمة مش هنخوض كتير فيها يمكن
+
+443
+00:33:30,970 --> 00:33:33,530
+مناسب بكرا لما تاخدوا قواعد بيانات أو تاخدوا اي
+
+444
+00:33:33,530 --> 00:33:36,270
+حاجة اللي هي علاقة بال partition مش غلط الكتاب
+
+445
+00:33:36,270 --> 00:33:39,350
+عندكم بترجعوله هتلاقي انه فعلا في معلومات كتيرة
+
+446
+00:33:39,350 --> 00:33:43,990
+احنا عادة بنعديها لكن لما تيجي تحتاجها هتلاقي لها
+
+447
+00:33:43,990 --> 00:33:47,250
+solid background الحقيقة في الكتاب طبعكم اللي
+
+448
+00:33:47,250 --> 00:33:51,980
+موجود معاكوا صفقوا بيهتمام أمثلة على ال partitions
+
+449
+00:33:51,980 --> 00:33:56,300
+زي لما نقول مثلا افرض انه عندي الست S هنا واحد
+
+450
+00:33:56,300 --> 00:34:00,080
+اتنين تلاتة لعندي الستة و جسمناهم لمجموعة
+
+451
+00:34:00,080 --> 00:34:03,380
+partitions ال partition الأولى اي واحد واحد اتنين
+
+452
+00:34:03,380 --> 00:34:06,620
+تلاتة ال partition التانية أربعة أو خمسة و ال
+
+453
+00:34:06,620 --> 00:34:09,500
+partition الأخيرة هي ستة زي لما نقول والله بدنا
+
+454
+00:34:09,500 --> 00:34:12,580
+نجسم نعمل دوري لكن ديروا بأكوا يا شباب بدنا
+
+455
+00:34:12,580 --> 00:34:17,100
+نجسمكوا بطريقةمعينة ان جول والله بدنا نعمل مصابقة
+
+456
+00:34:17,100 --> 00:34:20,200
+لطلبة سنة أولى أو تانية أو تالتة مع بعض هدولة يعني
+
+457
+00:34:20,200 --> 00:34:23,700
+طريقة تفكيرهم جريبة من بعض هدولة لأ خلص جربوا
+
+458
+00:34:23,700 --> 00:34:26,440
+يصيروا مهندسين رابعة أو خمسة بدنا نحطهم لحالهم
+
+459
+00:34:26,440 --> 00:34:31,360
+نختبرهم بأسئلة لحالهم ثقافة مختلفة الماجستير لحاله
+
+460
+00:34:31,360 --> 00:34:35,200
+ستة بدنا نقول ماجستير لحاله فجسمناهم لمجموعة
+
+461
+00:34:35,200 --> 00:34:38,860
+levels مثلا جسمناهم فرضا لمجموعة levels فالان لما
+
+462
+00:34:38,860 --> 00:34:43,790
+نقول forms a partition of Sفي الحالة هذه هو لازم
+
+463
+00:34:43,790 --> 00:34:47,890
+يكون disjoint لازم يكون disjoint لكن الآن الفكرة
+
+464
+00:34:47,890 --> 00:34:50,790
+مش فى فكرة تقسيمه بس فى فكرة ال operations اللى
+
+465
+00:34:50,790 --> 00:34:54,450
+هتتم بعد ذلك على التقسيم على ال partitions بأبسط
+
+466
+00:34:54,450 --> 00:34:57,970
+شغل لو قلنا list the ordered pairs in the
+
+467
+00:34:57,970 --> 00:35:03,070
+equivalence relation are produced by the partition
+
+468
+00:35:04,340 --> 00:35:07,980
+معنى ذلك ان احنا بدنا نحط الان ordered pairs بدنا
+
+469
+00:35:07,980 --> 00:35:11,660
+نحط أزواج مرتبة كيف بدي أعمل أزواج مرتبة؟ لأنك انت
+
+470
+00:35:11,660 --> 00:35:15,500
+بدك تعمل relation الان لو بدنا نختار .. نفترض من
+
+471
+00:35:15,500 --> 00:35:19,640
+هنا مجموعة التركيبة كيف ممكن تكون؟ ممكن تكون واحد
+
+472
+00:35:19,640 --> 00:35:23,800
+من مستوى أول ومستوى تاني مستوى أول ومستوى تالت
+
+473
+00:35:23,800 --> 00:35:28,020
+مستوى تاني ومستوى تالت بس مش مسموح تدخل partition
+
+474
+00:35:28,020 --> 00:35:35,750
+مع partition مدام هي أصلاby partition by partition
+
+475
+00:35:35,750 --> 00:35:39,130
+معنى ذلك كل partition لحاله هنا بقول واحد واحد
+
+476
+00:35:39,130 --> 00:35:42,170
+واحد اتنين واحد تلتة اتنين واحد اتنين اتنين اتنين
+
+477
+00:35:42,170 --> 00:35:47,110
+تلتة وخلاص و تلتة واحد هذه اللي كان ضايلة تلتة
+
+478
+00:35:47,110 --> 00:35:49,310
+اتنين اه لسه بدنا نبدأ بها ده تلتة اتنين و تلتة
+
+479
+00:35:49,310 --> 00:35:54,830
+اتنين cartesian product و خجفنا خلصنا هيك class A1
+
+480
+00:35:54,830 --> 00:35:59,130
+بنروح ل class A2 اللي هو أربعة مع أربعة أربعة خمسة
+
+481
+00:35:59,130 --> 00:36:05,320
+خمسة أربعة وخمسة خمسةخلصنا class two طيب الأخيرة
+
+482
+00:36:05,320 --> 00:36:10,740
+خلاص هي ستة و ستة هي ستة و ستة تمام فإذا كان
+
+483
+00:36:10,740 --> 00:36:14,200
+السؤال partition تاخدوا بالك إذا كان فعلا عملية
+
+484
+00:36:14,200 --> 00:36:16,580
+على ال partitions تاخدوا بالك أن العملية تتم لكل
+
+485
+00:36:16,580 --> 00:36:20,860
+partition على حده بس totally كله على بعضه كاملين
+
+486
+00:36:20,860 --> 00:36:26,980
+مع بعض لكن مش هضطر أعمل ستة و واحد تمام أو واحد و
+
+487
+00:36:26,980 --> 00:36:30,780
+خمسة لكن كلهم كست اه كلهم بحطهم مع بعض كست واحدة
+
+488
+00:36:31,760 --> 00:36:35,800
+كاسيت واحدة ليش؟ لأنه في النهاية إذا بدنا ناخد
+
+489
+00:36:35,800 --> 00:36:40,400
+المثال تبع اللجنة الثقافية هذه و كله بدها تتجسم
+
+490
+00:36:40,400 --> 00:36:42,860
+بهذا الشكل، معناته كل هدول هو ال combination تبعة
+
+491
+00:36:42,860 --> 00:36:47,360
+كلية الهندسة مثلا، خلاص، كلهم مع بعض بهذا الشكل
+
+492
+00:36:47,360 --> 00:36:52,380
+كنتيجة واحدة، كنتيجة واحدة تمام، هذا الجزء اللي
+
+493
+00:36:52,380 --> 00:36:59,680
+كان متبقيل من جزئية ال relationعشان نبدأ برضه جزء
+
+494
+00:36:59,680 --> 00:37:02,540
+من ال relation على اعتبار ان احنا ديروا بالكونهنا
+
+495
+00:37:02,540 --> 00:37:06,740
+بجزئية ال diagramطوي و قولنا بنتكلم عن ال path ال
+
+496
+00:37:06,740 --> 00:37:09,760
+path و ال diagram و الأنواع هذه يكفي اليوم ان احنا
+
+497
+00:37:09,760 --> 00:37:15,000
+بس على الأقل ناخد ايش أنواع ال path الممكنة اللي
+
+498
+00:37:15,000 --> 00:37:19,700
+ممكن تكون مقدمة ل ال graphs ل مين؟ ل ال graphs ال
+
+499
+00:37:19,700 --> 00:37:23,780
+graphs أخدناها سابقا مع ال relation فإذا اللحظة ان
+
+500
+00:37:23,780 --> 00:37:27,140
+انا بتكلم عن أنواع واحدة من أنواع ال relationقبل
+
+501
+00:37:27,140 --> 00:37:30,400
+ما نخوض كتير فيها و نغوص في تفاصيلها زي ما اتكلمنا
+
+502
+00:37:30,400 --> 00:37:35,120
+ان ال relation هي الكبيرة هي الشاملة لكل شيء و
+
+503
+00:37:35,120 --> 00:37:38,440
+اللي بتشمل جواها ال function ماهي ال function
+
+504
+00:37:38,440 --> 00:37:42,140
+relation relation بين ال F of X اللي هي ال Y و X
+
+505
+00:37:42,140 --> 00:37:44,480
+بين ال input و ال output ال dependent و ال
+
+506
+00:37:44,480 --> 00:37:51,160
+independent صحيح؟وحدة من أنواع الحالات اللي ضمن ال
+
+507
+00:37:51,160 --> 00:37:54,600
+relation هي ال graph ال graph هي relation هي
+
+508
+00:37:54,600 --> 00:38:00,940
+relation بينبداية و نهاية و بعمل بينهم relation
+
+509
+00:38:00,940 --> 00:38:08,100
+فصار كأنه directed graph في علاقة بين a و b graph
+
+510
+00:38:08,100 --> 00:38:11,620
+يمثل ك graph فانت برضه ممكن تفكر بنفس القلية لل
+
+511
+00:38:11,620 --> 00:38:15,060
+graphs كلها in general هي ال graphs ممكن بالشكل
+
+512
+00:38:15,060 --> 00:38:19,320
+رسومات عبارة عن خطوط الخطوط هذه relation بين مين و
+
+513
+00:38:19,320 --> 00:38:23,860
+مين بين البداية و النهاية لكل خطبداية و نهاية كل
+
+514
+00:38:23,860 --> 00:38:27,280
+خط فانت لما تيجي تتكلم عن بداية و نهاية كأنك بتقول
+
+515
+00:38:27,280 --> 00:38:30,980
+إحداثي لبداية الخط و إحداثي لنهاية الخط و ارسم
+
+516
+00:38:30,980 --> 00:38:36,340
+بينهم خط مستقيم فهي خط مش شيك ف graph اه منطق جدا
+
+517
+00:38:36,340 --> 00:38:39,140
+ان اتكلم هنا في الحالة هدا عن ال graphs تمام أول
+
+518
+00:38:39,140 --> 00:38:40,840
+نوع من أنواع ال graphs الحقيقه اللي هو ال simple
+
+519
+00:38:40,840 --> 00:38:46,000
+graphs اللي هو يمثل symmetric فعليا correlation و
+
+520
+00:38:46,000 --> 00:38:52,210
+irreflexiveirreflexive معناته مافيش self loop لأي
+
+521
+00:38:52,210 --> 00:38:55,850
+node من ال nodes تبعته لو يوجد self loop ففي
+
+522
+00:38:55,850 --> 00:38:58,970
+الحالة دي reflexive ل binary relation بس هو
+
+523
+00:38:58,970 --> 00:39:02,070
+symmetric اشي عن symmetric معناته انه كل خط من هنا
+
+524
+00:39:02,070 --> 00:39:06,690
+هو رايح جاي مش محتاج اروح اتجاه و ارجع اتجاه فإذا
+
+525
+00:39:06,690 --> 00:39:11,710
+هو مش متجه هنا هو مابقدرش اقول عليه directed هو مش
+
+526
+00:39:11,710 --> 00:39:19,100
+directed هو خط واحد و خلاص خط واحد و بسفالخط
+
+527
+00:39:19,100 --> 00:39:22,680
+الواحد و بس هذا يمثل ببساطة جدا بال graph اللي هو
+
+528
+00:39:22,680 --> 00:39:27,720
+عبارة عن مجموعة vertices و edges مجموعة قمم اللي
+
+529
+00:39:27,720 --> 00:39:33,860
+هي ال nodes و مجموعة edges او arc هي الخطوطأو ال
+
+530
+00:39:33,860 --> 00:39:37,140
+relation فعليًا ال relation فعليًا فبكل بساطة
+
+531
+00:39:37,140 --> 00:39:42,340
+بنقدر نقول هي عبارة عن ست V of vertices أو nodes
+
+532
+00:39:42,340 --> 00:39:45,500
+بسميها هيك بسميها هيك بس هي في النهاية دي هي ال V
+
+533
+00:39:45,500 --> 00:39:48,500
+و اللي تمثل في النهاية ال universe of discourse
+
+534
+00:39:48,500 --> 00:39:54,060
+تبعكال universe of the scores العناصر تمثل النقاط
+
+535
+00:39:54,060 --> 00:39:58,560
+تمام الآن بعد ذلك بتحط ال relation تبعتك بين
+
+536
+00:39:58,560 --> 00:40:02,200
+النقاط ما بين النقاط عشان تحط relation معناته هده
+
+537
+00:40:02,200 --> 00:40:07,320
+هنا بتصير ال edges او زي ما قلنا ال arc او ال link
+
+538
+00:40:07,320 --> 00:40:10,960
+اللينكات بين في relation ولا مافيش relation في
+
+539
+00:40:10,960 --> 00:40:15,520
+طريق ولا مافيش طريق في path ولا مافيش pathالست إيه
+
+540
+00:40:15,520 --> 00:40:19,840
+هي ال edges ال arc أو ال lengths و اللي نقدر
+
+541
+00:40:19,840 --> 00:40:24,090
+نسميها unordered بدون أن نتكلم عن symbolgraph فهي
+
+542
+00:40:24,090 --> 00:40:27,610
+نوردة peers مين جاب المين مش هتفرج المهم أنه يوجد
+
+543
+00:40:27,610 --> 00:40:31,670
+connection و خلاص يوجد connection و بس ل distinct
+
+544
+00:40:31,670 --> 00:40:37,170
+elements لعناصر متفارقة discrete ببساطة discrete
+
+545
+00:40:37,170 --> 00:40:39,770
+elements ال discrete elements هدول هم ال vertices
+
+546
+00:40:39,770 --> 00:40:42,770
+اللي حاكينا عنه أو ال nodes اللي هم ممكن تمثل U أو
+
+547
+00:40:42,770 --> 00:40:48,670
+V بس كلهم vertices كلهم نقاط أو nodes أو universe
+
+548
+00:40:48,670 --> 00:40:50,510
+of discourse عناصر من ال universe of discourse
+
+549
+00:40:50,510 --> 00:40:56,460
+اللي هي U و Vبحيث أني بقدر امثلها ب U relation V U
+
+550
+00:40:56,460 --> 00:41:01,520
+relation V مدام U relation V وقولنا V هي تمثل ال
+
+551
+00:41:01,520 --> 00:41:05,360
+arc أو ال edges معناه ذلك أنه يوجد خط أو يوجد path
+
+552
+00:41:05,360 --> 00:41:12,020
+أو يوجد link بين U ال .. ال .. ال vertex U و ال
+
+553
+00:41:12,020 --> 00:41:16,620
+vertex V أو ال node U و ال node V بسكأنه خط فهنا
+
+554
+00:41:16,620 --> 00:41:21,320
+مثال واضح لها بهذا الشكل لا فيها self loop ولا
+
+555
+00:41:21,320 --> 00:41:29,060
+فيها directed edges كلها بدون أسهم خلاص هو link و
+
+556
+00:41:29,060 --> 00:41:32,340
+بس link و بس ال link و بس هذا معناته أنه رايح جاي
+
+557
+00:41:32,340 --> 00:41:41,930
+من U ل V أو من V ل U ماشي في الحالتين ماشيمثال
+
+558
+00:41:41,930 --> 00:41:45,750
+عليه هي ال city .. ال cities مثلا cities لو
+
+559
+00:41:45,750 --> 00:41:49,830
+افترضنا انه عندي مجموعة set of cities مدن و بدنا
+
+560
+00:41:49,830 --> 00:41:52,830
+نعمل ال connection between them و بده افترض انه
+
+561
+00:41:52,830 --> 00:42:00,250
+عندي من المدينة C1 ل C8 كل هدول عندى تمانية مدن او
+
+562
+00:42:00,250 --> 00:42:04,450
+تمانية cities محتاجين ان نجيب بينهم edges نمثل ال
+
+563
+00:42:04,450 --> 00:42:09,100
+edges between them على اعتبار ان هي ال cityU مع
+
+564
+00:42:09,100 --> 00:42:15,040
+city V و كلا هما المفروض هما connected لبعض أو
+
+565
+00:42:15,040 --> 00:42:18,080
+متصلين مع بعض متصلين مع بعض عشان نقول انه في
+
+566
+00:42:18,080 --> 00:42:20,460
+relation و إلا معناته مافيش relation يعني ال logic
+
+567
+00:42:20,460 --> 00:42:23,700
+تيجي تقول ليه بين ..لأ والله هدول كلهم connected
+
+568
+00:42:23,700 --> 00:42:27,800
+مع بعض الحقيقة بس تختلف ال R جدش ال order تبعها بس
+
+569
+00:42:27,800 --> 00:42:31,560
+جدش ال order تبعها أو جدش ال dimension تبعها هنا
+
+570
+00:42:31,560 --> 00:42:35,500
+لما نمشي و نرسمها هقول إنه يوجد connection بين C1
+
+571
+00:42:35,500 --> 00:42:43,770
+و C2فهي اول relation اول edges اول relation او
+
+572
+00:42:43,770 --> 00:42:50,560
+edge بعدين واحد تلاتة واحد اربعة واحد خمسةيوجد
+
+573
+00:42:50,560 --> 00:42:54,200
+علاقة فعلا هي يوجد connection بعدين نمسك اتنين
+
+574
+00:42:54,200 --> 00:42:58,260
+اتنين مش حاطه مع اتنين واحد احنا حاطينا اتنين واحد
+
+575
+00:42:58,260 --> 00:43:01,140
+وقولنا ان هي undirected اه اه undirected بالظبط
+
+576
+00:43:01,140 --> 00:43:06,460
+مدام undirected معناته C1 C2 هي نفسها C2 C1 مافيش
+
+577
+00:43:06,460 --> 00:43:09,040
+داعي نرجع نكتبها كمان مرة فإذا ببدأ من C
+
+578
+00:43:13,120 --> 00:43:20,080
+2C3C2C6C2C7 و بتكمل بهذا الشكل لما نستنفذ كل
+
+579
+00:43:20,080 --> 00:43:25,180
+الحالات اللي موجودة عندنا فبنكون خلصنا في الحالة
+
+580
+00:43:25,180 --> 00:43:26,140
+اللي عندنا هذه تمام
+
+581
+00:43:30,260 --> 00:43:33,080
+ال multi-graph في ال multi-graph لأ شويه بتختلف
+
+582
+00:43:33,080 --> 00:43:36,580
+الأمور على اعتبار انه هيكون في عندك شبيهة بال
+
+583
+00:43:36,580 --> 00:43:40,800
+simple graph ولكن ممكن يكون عندك اكتر من one path
+
+584
+00:43:40,800 --> 00:43:44,780
+between ال cities او ال vertices هدول ممكن يكون
+
+585
+00:43:44,780 --> 00:43:48,040
+اكتر من link اكتر من مين؟ من ال link زي لما نقول
+
+586
+00:43:48,040 --> 00:43:52,800
+والله في عندى غزة و خان يونس مثلا طب انت في انك
+
+587
+00:43:52,800 --> 00:43:57,670
+صلاح الدين عندك البحرصح؟ ايه two paths الاتنين ف
+
+588
+00:43:57,670 --> 00:44:00,190
+multi اه multi ممكن يكون في multi في ال graph
+
+589
+00:44:00,190 --> 00:44:03,730
+مافيش مشكلة يعني ان بتش ترسمها كخريطة من فوق هتعمل
+
+590
+00:44:03,730 --> 00:44:07,190
+ال multi واضحة هتكون واضحة في ال graph تبعك جيد
+
+591
+00:44:07,190 --> 00:44:10,950
+ففي الحالة هذه شبيهة ولكن بيكون عندي اكتر من one
+
+592
+00:44:10,950 --> 00:44:16,310
+edge connected to given nodes بيوصل to given nodes
+
+593
+00:44:16,310 --> 00:44:22,670
+فهنا بتصير عندي تمثل ال graph كأنهاNodes, Edges و
+
+594
+00:44:22,670 --> 00:44:26,510
+Function الـ Function هدى اللى اتحدد لنا جداش عدد
+
+595
+00:44:26,510 --> 00:44:30,870
+ال edges between a certain cities أو a certain
+
+596
+00:44:30,870 --> 00:44:35,190
+nodes كويس فهدى بتحتوي على ال set لمجموعة ال
+
+597
+00:44:35,190 --> 00:44:39,710
+vertices تبعتنا ال set E هي ال edges و عندك ال
+
+598
+00:44:39,710 --> 00:44:45,050
+function ال function هنا هتكون هي ببساطة علاقة بين
+
+599
+00:44:45,050 --> 00:44:53,810
+ال edgesعندك edge موجودة بتضمنلك بين U و V و U و V
+
+600
+00:44:53,810 --> 00:44:57,730
+لازم يكونوا ضمن ال vertices ماتيجيش نتكلم عن غزة
+
+601
+00:44:57,730 --> 00:45:01,550
+تحطلي مدينة من خارج قطاع غزة لازم تكون ضمن ال
+
+602
+00:45:01,550 --> 00:45:04,250
+universe of discourse أصلا فهي ضمن ال vertices
+
+603
+00:45:04,250 --> 00:45:11,470
+تبعتنا ولا تساوي ولا يساوي بعض طيب ليش؟ self loop
+
+604
+00:45:11,470 --> 00:45:15,030
+لإن لو بيساوي بعض معناته ستصبح عندك self loopلا
+
+605
+00:45:15,030 --> 00:45:18,630
+يساوي بعض ساعتها بقول ان ال function ها دي بتحدد
+
+606
+00:45:18,630 --> 00:45:25,010
+لجدش عدد ال edgesاللي بين U و V بتحدد قداش عدد ال
+
+607
+00:45:25,010 --> 00:45:29,510
+edges فاني لما بقول غزة و خانيونس اه في طريقين
+
+608
+00:45:29,510 --> 00:45:33,590
+ممكن واحد يحب البحر اذا كان الجو كويس او يبعد عن
+
+609
+00:45:33,590 --> 00:45:36,590
+البحر اذا الدنيا برد في عز الشتاء خلينا في الدفة
+
+610
+00:45:36,590 --> 00:45:40,470
+جوا احسن نمشي من الدفة و اذا كان طبعا الطريق كمان
+
+611
+00:45:40,470 --> 00:45:43,830
+سالكة فإذا لأ انت عندك two options الحقيقة في عندك
+
+612
+00:45:43,830 --> 00:45:48,510
+multi graph multi graph فبتكون الشكل بهذا الشكل في
+
+613
+00:45:48,510 --> 00:45:51,920
+عندك parallel edges هي واحدة هي اتنينممكن يكون
+
+614
+00:45:51,920 --> 00:45:55,500
+تلاتة من اللي بحددها ال function الحقيقة ال
+
+615
+00:45:55,500 --> 00:45:59,700
+function هي اللي اتحددنا جداش عدد الطرق إذا كان
+
+616
+00:45:59,700 --> 00:46:02,420
+فيه زحمة كتير معناته انت مضطر تعمل أكتر من طريق
+
+617
+00:46:02,420 --> 00:46:05,320
+إذا كان لو الله مافيش زحمة المدينة هدى أو ال node
+
+618
+00:46:05,320 --> 00:46:07,620
+هدى و ال node هدى مافيش كتير حركة traffic مافيش
+
+619
+00:46:07,620 --> 00:46:11,040
+كتير عالي بينهم مافيش داعي تعمل طريقين مافيش داعي
+
+620
+00:46:11,040 --> 00:46:14,430
+تعمللهم طريقين مثلاهو يكون كويسة بالنسبالك زي ما
+
+621
+00:46:14,430 --> 00:46:18,150
+قلنا المثال طبعا هي ال nodes are cities و ال edges
+
+622
+00:46:18,150 --> 00:46:22,370
+هي segment of major highways ال highways اللي هي
+
+623
+00:46:22,370 --> 00:46:25,950
+الطرق السريعة احنا لما بتبدأنا نتكلم عن خانيونس
+
+624
+00:46:25,950 --> 00:46:28,970
+معناته بدهروح يا اما صلاح الدنيا يا اما بحر انا
+
+625
+00:46:28,970 --> 00:46:31,910
+بتكلم عن highway بشكل او باخر هو بين المدن يعني
+
+626
+00:46:31,910 --> 00:46:34,570
+بين المدن المتعرف عليه عالميا بين المدن معناته
+
+627
+00:46:34,570 --> 00:46:38,600
+اسمه highwayhighway مش زي المدن عندنا كلها زحمة في
+
+628
+00:46:38,600 --> 00:46:42,360
+زحمة فانت حتى على ال highway مافيش مجال تتحرك كتير
+
+629
+00:46:42,360 --> 00:46:49,020
+يعنى تمام Sodograph Sodograph لأ اختلفت شوية
+
+630
+00:46:49,020 --> 00:46:52,040
+الأمور على اعتبار ان صار في عندك مجال لل self loop
+
+631
+00:46:52,040 --> 00:46:55,320
+هنا اختلفت في جزئية ال self loop عندك multi graph
+
+632
+00:46:55,320 --> 00:46:58,300
+او multi graph مش مشكلة بس زادت معاك ال self loop
+
+633
+00:46:58,300 --> 00:47:01,500
+بمعنى ان والله في غزة صار بإمكانك تنزل على البحر
+
+634
+00:47:01,500 --> 00:47:05,990
+تلف من أول غزة لآخر غزة وترجع لنفس غزةصحيح؟ اه
+
+635
+00:47:05,990 --> 00:47:09,070
+الواحد زهجان بيروح بيعمله هيك لف بس على البحر و
+
+636
+00:47:09,070 --> 00:47:13,450
+بيرجع، صحيح؟ بدأ يمارجع من صلق .. من عمرو المختار
+
+637
+00:47:13,450 --> 00:47:16,510
+من عند رامسيسو مش عارف مين و .. و هودي و .. عند
+
+638
+00:47:16,510 --> 00:47:22,030
+السمك، بيلف تاني من عند ..طل الهوى و خلصناه بعمله
+
+639
+00:47:22,030 --> 00:47:24,930
+كده بس لفه و برجع هو ما طلعش من غزة فعليا ما طلعش
+
+640
+00:47:24,930 --> 00:47:28,710
+من غزة هو فقط علم عمل حاجة زي .. زي self .. زي
+
+641
+00:47:28,710 --> 00:47:33,570
+self loop تمام فإذا نفس الفكرة ل .. ل القديمة بس
+
+642
+00:47:33,570 --> 00:47:38,590
+الفكرة الوحيدة أنه .. وين راحت؟ ممكن يساووا بعض
+
+643
+00:47:38,590 --> 00:47:43,490
+هنا ماكانوش لا يساووا بعضU و V لا تسووا بعض هنا
+
+644
+00:47:43,490 --> 00:47:46,810
+الشرط الوحيد أو خلّيني أقول الإضافة إنه لأ مسموح
+
+645
+00:47:46,810 --> 00:47:50,310
+إنه يساوي بعض من U ل U بمشي الحال زي لما تكون مثلا
+
+646
+00:47:50,310 --> 00:47:54,650
+ال notes هذه هي ال camp sites أو مواقع التقييم في
+
+647
+00:47:54,650 --> 00:47:57,450
+في غابة مثلا و تطلع في الغابة
+
+648
+00:47:57,450 --> 00:48:00,610
+تلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلف
+
+649
+00:48:00,640 --> 00:48:03,840
+الكمب تبعك اكيد هترجع لنفس المخيم انت عملت لفة
+
+650
+00:48:03,840 --> 00:48:08,240
+ورجعت فهذه هي ال self loop self loop كمثال المرة
+
+651
+00:48:08,240 --> 00:48:10,900
+القادمة ان شاء الله بنكمل بال directed لما يصير
+
+652
+00:48:10,900 --> 00:48:13,560
+عندنا directed كيف بنتعامل معاه يعطيكوا العافية
+
+653
+00:48:13,560 --> 00:48:14,320
+برك الله فيك
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/URd9zqvHits_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/URd9zqvHits_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..50f3098257c9eea205a5f1ca312510720ed03e3f
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/URd9zqvHits_raw.srt
@@ -0,0 +1,2612 @@
+1
+00:00:05,060 --> 00:00:07,600
+بسم الله الرحمن الرحيم و الصلاة والسلام على أشرف
+
+2
+00:00:07,600 --> 00:00:11,080
+الأنبياء و المرسلين سيدنا محمد اليوم نكمل ان شاء
+
+3
+00:00:11,080 --> 00:00:15,860
+الله ما تبقالنا في ال relationو اتوقع انه صار
+
+4
+00:00:15,860 --> 00:00:18,340
+معانا إمكانية في الوقت بإذن الله تعالى ان احنا
+
+5
+00:00:18,340 --> 00:00:22,180
+يعني الكمان أسبوعين ان شاء الله تعالى نبدأ نعمل
+
+6
+00:00:22,180 --> 00:00:25,320
+معاملة مراجعة فعلى الأقل هيكون معانا أسبوع كامل
+
+7
+00:00:25,320 --> 00:00:29,720
+للمراجعة على الأقل هذا يعني أقل شيء ممكن يطلعنا في
+
+8
+00:00:29,720 --> 00:00:32,160
+الأخر أربع محاضرات بدل تلت محاضرات بتاعة الأسبوع
+
+9
+00:00:32,160 --> 00:00:36,160
+ان شاء الله تعالى كلهم هنستثمرهم في حل أسئلة كلهم
+
+10
+00:00:36,160 --> 00:00:40,510
+هنستثمرهم في حل أسئلة فمعنى ذلك انهأنا مكمل معاكوا
+
+11
+00:00:40,510 --> 00:00:44,690
+لآخر موعد في الفصل الفصل بيخلص في تسعة و عشرين
+
+12
+00:00:44,690 --> 00:00:48,810
+اتناشر فمحاضرة تسعة و عشرين اتناشر أنا موجود فيها
+
+13
+00:00:48,810 --> 00:00:53,370
+كويس و هذا طبيعي .. طبيعي بالأساس فهنضلنا ماشيين
+
+14
+00:00:53,370 --> 00:00:57,190
+إلى آخر نفس انت بنخلص هنبدأ على طول في عملية
+
+15
+00:00:57,190 --> 00:01:00,990
+المراجعة و عملية حل أسئلة من أسئلة امتحانات ان شاء
+
+16
+00:01:00,990 --> 00:01:03,450
+الله تعالى و قلتلكوا ان في .. يعني في أسئلة كويسة
+
+17
+00:01:03,450 --> 00:01:09,390
+ذخيرة منيحة ممكن تشغلنا لأسبوعين تلاتةفنصل لأخر
+
+18
+00:01:09,390 --> 00:01:12,050
+حاجة اتكلمنا عنها المرة الماضية هي closures of
+
+19
+00:01:12,050 --> 00:01:16,150
+relations و اللي حكينا كيف انا ممكن اعمل reflexive
+
+20
+00:01:16,150 --> 00:01:19,430
+closure بمعنى اقربها ال relation ان هي تصبح
+
+21
+00:01:19,430 --> 00:01:22,350
+reflexive فكانت بسيطة جدا نعمل اتحاد مع ال
+
+22
+00:01:22,350 --> 00:01:27,290
+identity ل ال a و خلصناها لل relation identity لل
+
+23
+00:01:27,290 --> 00:01:31,230
+relation معنى ذلك ان a مع a, b مع b, c مع c واحد
+
+24
+00:01:31,230 --> 00:01:33,650
+مع واحد اتنين مع اتنين لازم يكونوا كلهم موجودين
+
+25
+00:01:33,650 --> 00:01:40,400
+فهذه ال identity بمعنى لو بدك اتمثلعناصر ال
+
+26
+00:01:40,400 --> 00:01:48,900
+relation a,b,c,1,2 هيكونوا a,b,c,1,2 بدهم يكونوا
+
+27
+00:01:48,900 --> 00:01:53,040
+بهذا الشكل ال diagonal كله ones معناه ذلك و ال
+
+28
+00:01:53,040 --> 00:01:55,740
+back zeros معناه ذلك ان انت بتتكلم عن identity
+
+29
+00:01:55,740 --> 00:02:00,580
+relation في الحالة هذه اعملها اتحاد مع اي relation
+
+30
+00:02:00,580 --> 00:02:04,740
+هتصبح اكيد حتما ناتج الاتحاد هيصبح reflexive
+
+31
+00:02:04,740 --> 00:02:10,240
+relation اكيدالـ Symmetric closure قلنا إن كل عنصر
+
+32
+00:02:10,240 --> 00:02:13,600
+بدنا نحط له العكس تبعه فهنا العكس لما بتكلم عن ال
+
+33
+00:02:13,600 --> 00:02:17,280
+inverse هو العكس تبع كل عنصر العكس تبع كل عنصر
+
+34
+00:02:17,280 --> 00:02:20,700
+اللي كانت مهمة شوية و بدها شغل هي ال transitive
+
+35
+00:02:23,710 --> 00:02:26,550
+يعني بحقيقة مشكور الباشر المهندس أنه جال يدورلنا
+
+36
+00:02:26,550 --> 00:02:30,090
+على حل تاني يعني كان مشكور فعلا أنه خلانا شوية هيك
+
+37
+00:02:30,090 --> 00:02:34,550
+ننشط حالنا و جيبنالكوا حلول تانية ساعدتنا حتى في
+
+38
+00:02:34,550 --> 00:02:38,310
+حال هالجثة كانت قديما عشان تيجي تحلها كانت شوية
+
+39
+00:02:38,310 --> 00:02:42,070
+بدها التركيز كتير فلو جيت لأ اتفك فكانت مع الطرق
+
+40
+00:02:42,070 --> 00:02:44,710
+اللي أخدناها و جيبتلكوا عليها مثال في ال slide
+
+41
+00:02:44,710 --> 00:02:47,990
+اللي وراها أنه أنا بعمل اتحاد لكل ال art to the
+
+42
+00:02:47,990 --> 00:02:50,090
+power in مع بعض إيش يعني art to the power in يعني
+
+43
+00:02:50,090 --> 00:02:55,360
+معناته ال relationCompose نفس ال relation بتصير
+
+44
+00:02:55,360 --> 00:03:00,120
+اسمها R تربيع فالإن تربيع طيب جبنا ال R تربيع ال R
+
+45
+00:03:00,120 --> 00:03:05,320
+تربيع composition مع R بتصير R تكعيب مع كمان R، R
+
+46
+00:03:05,320 --> 00:03:08,760
+تتطور أربعة كلهم هدول عملهم اتحاد ما تجلجش مش هتظل
+
+47
+00:03:08,760 --> 00:03:12,760
+تو infinity لإن عند مرحلة معينة بعد اتنين تلاتة
+
+48
+00:03:12,760 --> 00:03:18,250
+composition هتجد انه هتثبتهتثبت مدام ثبتت معناته
+
+49
+00:03:18,250 --> 00:03:22,190
+هو خلاص هيك استوفى كل العناصر اللي محتاج يزودها
+
+50
+00:03:22,190 --> 00:03:27,250
+عشان يصبح transitive closure خلاص اعملهم اتجمحهم
+
+51
+00:03:27,250 --> 00:03:31,650
+مع بعض هذه اقل transitive لل matrix عشان يعني
+
+52
+00:03:31,650 --> 00:03:35,210
+عناصر تزودها عشان تصبح transitive ال matrix تبعتك
+
+53
+00:03:35,210 --> 00:03:40,270
+بدل ما كنت مضطر تمسك جميع العناصر وتزودلهم عناصر
+
+54
+00:03:40,270 --> 00:03:44,220
+إضافيةناتج لل Transitive و بعدين العناصر الإضافية
+
+55
+00:03:44,220 --> 00:03:47,440
+تروح تعملها test كمان معاهم كمان مرة عشان تعمل
+
+56
+00:03:47,440 --> 00:03:49,880
+للكل تضمن ان ال relation كامل على بعض هي
+
+57
+00:03:49,880 --> 00:03:53,580
+Transitive relation لأالوضع كان كتير أسهل المرة
+
+58
+00:03:53,580 --> 00:03:56,660
+الماضية لما قلنا إن هى فيه هناك function أو
+
+59
+00:03:56,660 --> 00:04:00,260
+relation بهذا الشكل فأبسط شغل أعملها composition
+
+60
+00:04:00,260 --> 00:04:03,180
+مع نفسها أعملناها composition مع نفسها فصار اسمها
+
+61
+00:04:03,180 --> 00:04:08,160
+R تربيع R تربيع R تربيع automatically أعمل
+
+62
+00:04:08,160 --> 00:04:11,060
+composition جبنا ال composition طلع بهذا الشكل
+
+63
+00:04:11,060 --> 00:04:15,800
+فصار في عنده أنصر زيادة و أتوقع اتكلمنا عنها من
+
+64
+00:04:15,800 --> 00:04:18,820
+المرة الماضية ممكن تسهل على حال نبتش هيك على همش
+
+65
+00:04:18,820 --> 00:04:24,200
+الورقةورقة الأسئلة تبعتك هتحط الواحد و واحد كل
+
+66
+00:04:24,200 --> 00:04:28,640
+عناصر ال relation تبعتك اتنين و واحد هتحط تلاتة و
+
+67
+00:04:28,640 --> 00:04:35,820
+اتنين و اربعة و تلاتة اربعة و تلاتة هذه ال
+
+68
+00:04:35,820 --> 00:04:38,460
+relation وهنا هتعملها برضه مع نفس ال relation بس
+
+69
+00:04:38,460 --> 00:04:41,980
+هنا اللي تتفق معاها فمعنى ذلك بدك تشوف مين ال
+
+70
+00:04:41,980 --> 00:04:45,880
+relation مين اللي بيبدأ بالواحد فالواحد و واحد فقط
+
+71
+00:04:47,820 --> 00:04:50,240
+تمام في غيرها الواحد و واحد فاش الواحد و واحد طيب
+
+72
+00:04:50,240 --> 00:04:56,180
+برضه هنا الواحد برضه واحد و واحد اتنين اتنين و
+
+73
+00:04:56,180 --> 00:05:03,380
+واحد تلاتة تلاتة و اتنين تمام هنا اشطب هادي مع
+
+74
+00:05:03,380 --> 00:05:07,860
+هادي بيضل واحد و واحد و هنا بيضل عندك اتنين و واحد
+
+75
+00:05:07,860 --> 00:05:11,860
+هنا الاتنين مع الاتنين بيضل تلاتة و واحد فهي أنصر
+
+76
+00:05:11,860 --> 00:05:14,460
+جديد وهي اربعة و اتنين هي أنصر جديد
+
+77
+00:05:17,160 --> 00:05:21,220
+تمام، كمان مرة، برضه مع مين؟ مع نفس R، فإذن
+
+78
+00:05:21,220 --> 00:05:27,220
+automatically هذه هنا صارت R تربيع مع ال R اللي هي
+
+79
+00:05:27,220 --> 00:05:32,220
+بدك تجيب واحد، كان في واحد واحد، واحد، كان في برضه
+
+80
+00:05:32,220 --> 00:05:38,340
+واحد واحد، واحد، برضه في واحد واحد، check، اتنين
+
+81
+00:05:39,190 --> 00:05:44,370
+أتنين و واحد فعشان ننتج منها R تلاتة R to the
+
+82
+00:05:44,370 --> 00:05:47,090
+power تلاتة واحد واحد فإذا بيظل عندي الواحد و
+
+83
+00:05:47,090 --> 00:05:54,030
+الواحد اتنين و واحد و تلاتة و واحد و أربعة و واحد
+
+84
+00:05:54,030 --> 00:05:59,890
+لدك تزود خلاص هتجف بعدك هتجف فكل اللي انت محتاجه
+
+85
+00:05:59,890 --> 00:06:07,470
+هادي اتنينتلاتة اتحاد هتجد انه في مشتركات كتير انت
+
+86
+00:06:07,470 --> 00:06:12,630
+ايش اللي ضفته فعليا ال R زي ما هي هيها هذه كانت مع
+
+87
+00:06:12,630 --> 00:06:18,090
+ال R وهذه كانت مع R وهذه جديدة وهذه جديدة هنا هذه
+
+88
+00:06:18,090 --> 00:06:21,850
+الجديدة فقطفإذا تلت عناصر اللي انت محتاجة تضيفهم
+
+89
+00:06:21,850 --> 00:06:24,690
+.. تلت عناصر اللي انت محتاجة تضيفهم .. خلاص
+
+90
+00:06:24,690 --> 00:06:30,490
+بنضيفهم و بنخلص المسألة عشان نقدر نقول والله إيش
+
+91
+00:06:30,490 --> 00:06:33,930
+ال transitive closure .. transitive closure بمعنى
+
+92
+00:06:33,930 --> 00:06:40,090
+أقل super set .. أقل super set محتاجها من ال
+
+93
+00:06:40,090 --> 00:06:45,280
+relation عشان تصبح transitiveتمام، الآن ال path أو
+
+94
+00:06:45,280 --> 00:06:48,880
+ال paths in directed graphs أخدنا طريقة من طرق
+
+95
+00:06:48,880 --> 00:06:52,740
+تمثيل ال relation بال directed graph و قلنا من إلى
+
+96
+00:06:52,740 --> 00:06:56,700
+فإذا كان عندي زوج مرتب فهي من أربعة لتلاتة و
+
+97
+00:06:56,700 --> 00:07:01,580
+عملناها بالشكل graph بكل بساطة بقدر أقول الآن لما
+
+98
+00:07:01,580 --> 00:07:05,140
+صار عندي graph كامل في path لل graph أكيد، ال path
+
+99
+00:07:05,140 --> 00:07:09,580
+هذا ببساطة جدا ما هو هيعطيك ال transitiveلما انت
+
+100
+00:07:09,580 --> 00:07:14,820
+تقول في عندك علاقة بين ا واحد و اتنين طب اتنين و
+
+101
+00:07:14,820 --> 00:07:18,400
+اتلاتة معناته يوجد path بين واحد و تلاتة مش شايف
+
+102
+00:07:18,400 --> 00:07:21,360
+اكيد معناه ذلك انه صار في transitive صار فعليا في
+
+103
+00:07:21,360 --> 00:07:26,380
+transitive ك graph او ك path ال path المسار اللي
+
+104
+00:07:26,380 --> 00:07:32,760
+بينهم تمام بكل بساطة لو قلنا خلصنا هذه لو قلنا
+
+105
+00:07:32,760 --> 00:07:40,440
+مثلا في عندي ال relations من a ل x واحد ومن X1 ل
+
+106
+00:07:40,440 --> 00:07:46,320
+X2، X2 ل X3، X3 ل X4، لعند ما نصل ل XN نقص واحد مع
+
+107
+00:07:46,320 --> 00:07:51,640
+B فبكل بساطة بقول أن يوجد path أو a path of length
+
+108
+00:07:51,640 --> 00:07:53,980
+N from A to B
+
+109
+00:07:57,810 --> 00:08:01,270
+جدش عدد ال relations هاي relation اتنين تلاتة
+
+110
+00:08:01,270 --> 00:08:05,870
+اربعة لعين بنصل ل N N relation فإذا هنا بنقول ال
+
+111
+00:08:05,870 --> 00:08:10,610
+length تبعنا N قيمة ال length هي قيمتها ال N و N
+
+112
+00:08:10,610 --> 00:08:16,270
+ordered pairs in edges لل graph ال edges لل graph
+
+113
+00:08:16,270 --> 00:08:19,830
+أو ال relation لأن هذه كلها relation هنا يوجد
+
+114
+00:08:19,830 --> 00:08:25,070
+relation بين A و X واحد هذه ال relation E edge X
+
+115
+00:08:25,070 --> 00:08:30,230
+واحد و X اتنين edgeX2 و X3 هدى كلها مجموعة الـ
+
+116
+00:08:30,230 --> 00:08:37,650
+edges بتاعة الـ graph طيب empty sequence of edges
+
+117
+00:08:37,650 --> 00:08:41,270
+إذا كان عندي empty sequence الـ sequence طبعاً ال
+
+118
+00:08:41,270 --> 00:08:49,830
+link طبعاً Zero من A ل A فإذا بتكلم عن Zero order
+
+119
+00:08:49,830 --> 00:08:56,240
+من A ل A فهنا ال link طبعاً Zeroالlength zero تمام
+
+120
+00:08:56,240 --> 00:09:00,520
+self loop ال length بتلع عندي كأنه zero فهنا أصبحت
+
+121
+00:09:00,520 --> 00:09:05,220
+من ال length zero from a to a منها لنفسها منها
+
+122
+00:09:05,220 --> 00:09:09,340
+لنفسها طيب أما إذا كان ال path from a to b exists
+
+123
+00:09:09,340 --> 00:09:14,460
+فعليا هو موجود فبقدر أقول أن a is connected to b
+
+124
+00:09:14,460 --> 00:09:23,060
+مدام يوجد بينهم path هناA connected to B كيف؟ زي
+
+125
+00:09:23,060 --> 00:09:25,800
+أنت والله موجود في الشمال في بيت حنون، بدك تنزل من
+
+126
+00:09:25,800 --> 00:09:30,180
+بيت حنون على غزة، high connection من غزة للوسطة،
+
+127
+00:09:30,180 --> 00:09:32,280
+high connection، من الوسطة لخانيونس، high
+
+128
+00:09:32,280 --> 00:09:34,340
+connection، من خانيونس لرفح، high connection،
+
+129
+00:09:34,340 --> 00:09:39,350
+معناته بيت حنون متصلة في من؟ في رفحببساطة، يعني
+
+130
+00:09:39,350 --> 00:09:42,790
+أنتوا بتحنون، بتصلوا في الرفع، بتضل والله جداش ال
+
+131
+00:09:42,790 --> 00:09:45,290
+.. ال edges .. ال edges هي أكم سيارة أنت انتقلت
+
+132
+00:09:45,290 --> 00:09:48,750
+منها، خليني أقول، نفطر أنت بتنتقل من محافظة
+
+133
+00:09:48,750 --> 00:09:52,030
+لمحافظة، كل واحدة سيارة شكل، فجداش عدد السيارات
+
+134
+00:09:52,030 --> 00:09:54,550
+اللي انتقلت فيهمها هي عدد ال relations، هدول عدد
+
+135
+00:09:54,550 --> 00:09:58,770
+ال relations بالنسبالكتمام، إذا كان ال length لل
+
+136
+00:09:58,770 --> 00:10:01,530
+path، ال path اللي موجود عندك، ال length تبعه هو
+
+137
+00:10:01,530 --> 00:10:06,410
+واحد فأكثر، إيه له قيمة أكبر؟ من واحد، من A عفوا،
+
+138
+00:10:06,410 --> 00:10:11,570
+ل A، بس لاحظ أنهم الصفر، هنا كانت صفر، self-loop،
+
+139
+00:10:11,570 --> 00:10:14,070
+self-loop كانت zero، مافيش مشكلة، لكن إذا كانت
+
+140
+00:10:14,070 --> 00:10:19,910
+واحد فأكثر، هنا، معناه ذلك أنه بيصير عندي circuit
+
+141
+00:10:19,910 --> 00:10:26,980
+أو cycleمدهم أكتر معناته فعليا من a لنقطة على
+
+142
+00:10:26,980 --> 00:10:31,500
+الأقل من
+
+143
+00:10:31,500 --> 00:10:38,220
+a ل a طلعت من a و رجعتها ل a فأصبحت ال connection
+
+144
+00:10:38,220 --> 00:10:43,500
+تبعتي هي من a ل a لكن ال length تبعي أكبر من واحد
+
+145
+00:10:43,500 --> 00:10:47,020
+فهذه cycle ممكن تكون أكتر من هيك
+
+146
+00:10:50,380 --> 00:10:54,760
+بهذا الشكل و برضه من a ل a طلعت من a و رجعت ل a
+
+147
+00:10:54,760 --> 00:11:00,320
+برضه cycle او circuit او circuit جيد الان هنلاحظ
+
+148
+00:11:00,320 --> 00:11:04,720
+انه اذا فعلا وجد ال path of length in from a to b
+
+149
+00:11:04,720 --> 00:11:10,420
+in Rحسب ال relation are ال relation are واللي قلنا
+
+150
+00:11:10,420 --> 00:11:14,620
+عليها مواصلة بالسيارة فإذا من بيت حنون لغزة هي
+
+151
+00:11:14,620 --> 00:11:18,500
+مواصلة سيارة طب ما هي نفس الاشي برضه ال relation
+
+152
+00:11:18,500 --> 00:11:23,560
+هي نفسها أني بدي أركب سيارة من غزة لأي مدينة في
+
+153
+00:11:23,560 --> 00:11:26,920
+الوسط مثلا خليني أقول دير البلح okay معناته هي في
+
+154
+00:11:26,920 --> 00:11:32,200
+عندك نفس ال relation نفس ال relation لكن من غزة
+
+155
+00:11:32,200 --> 00:11:36,600
+لدير البلح مثلاكويس فهنا هيكون عندك مجموعة
+
+156
+00:11:36,600 --> 00:11:44,260
+relations if and only if a و b تنتمي ل relation to
+
+157
+00:11:44,260 --> 00:11:47,940
+the power n طب احنا ال relation to the power n دي
+
+158
+00:11:47,940 --> 00:11:51,780
+كانت ايش؟ كنا بنتكلم عنها composition طب ما هي نفس
+
+159
+00:11:51,780 --> 00:11:57,500
+الفكرة انت هيك طلعت من مين؟ ال relation الأولى بيت
+
+160
+00:11:57,500 --> 00:12:02,920
+حنون غزةهي نهايتها ايش؟ غزة، معناه انت بدك
+
+161
+00:12:02,920 --> 00:12:06,600
+relation بدايتها غزة، ماهي مش هيك ال composition
+
+162
+00:12:06,600 --> 00:12:11,320
+اللي شغلناها؟ خلاص غزة دير البلح، هي relation
+
+163
+00:12:11,320 --> 00:12:14,380
+تانية، معناه انت صارت بيت حنون متصلة بدير البلح،
+
+164
+00:12:14,380 --> 00:12:17,180
+طيب دير البلح اللي خلصنا فيها ال relation المفروض
+
+165
+00:12:17,180 --> 00:12:20,020
+الان ندور على ال relation تبدأ منها، دير البلح
+
+166
+00:12:20,020 --> 00:12:24,640
+خانيونسطيب من خانيونس بدك تبدأ منها خانيونس رفح
+
+167
+00:12:24,640 --> 00:12:27,980
+وهي نفس اللي احنا عملناها composition فبقدر ساعتها
+
+168
+00:12:27,980 --> 00:12:32,960
+اقول جدش عددهم R to the power N R to the power to
+
+169
+00:12:32,960 --> 00:12:36,160
+the power N composition فانا عملت ال composition
+
+170
+00:12:36,160 --> 00:12:42,820
+لل R مع نفسها مع يعني عدد سيارات كانتقال N مرة N
+
+171
+00:12:42,820 --> 00:12:45,500
+مرة ففي الحالة دي بقول ان ال length تبع هي N فعلا
+
+172
+00:12:45,500 --> 00:12:52,910
+N مرة N مرة تمامال equivalence relations أمتى بقدر
+
+173
+00:12:52,910 --> 00:12:57,130
+أسمي ال relation تبعتي هي equivalence relation على
+
+174
+00:12:57,130 --> 00:13:01,330
+ال 6A بكل بساطة إذا كانت بتعامل معه binary فإذا
+
+175
+00:13:01,330 --> 00:13:06,370
+كانت والله reflexive، symmetric و transitive فهي
+
+176
+00:13:06,370 --> 00:13:09,650
+equivalence relation فهي إيش؟ بيسموها equivalence
+
+177
+00:13:09,650 --> 00:13:15,900
+relation أو EER زي المساواةالمساوية دي equivalence
+
+178
+00:13:15,900 --> 00:13:19,440
+relation ليش؟ لأنه بكل بساطة انت بتقدر تقول a
+
+179
+00:13:19,440 --> 00:13:24,820
+بتساوي a هاي reflexive هاي ال reflexive طيب تقدر
+
+180
+00:13:24,820 --> 00:13:31,000
+تقول إذا a بتساوي b أكيد b بتساوي a ف symmetric
+
+181
+00:13:31,000 --> 00:13:36,080
+مدام فعلا علمت اللي يساوي صحيحة أكيد صحيح طيب إذا
+
+182
+00:13:36,080 --> 00:13:44,780
+a بتساوي b و b بتساوي c أكيد a هتساوي ctransitive
+
+183
+00:13:44,780 --> 00:13:51,580
+فإذا ال relation يساوي هي فعلا بتحقق التلاتة ال
+
+184
+00:13:51,580 --> 00:13:58,060
+three properties بتتحقق باستخدام هذه ال notation
+
+185
+00:13:58,060 --> 00:14:02,520
+أو المساواة فإذا المساواة هي فعليانقدر بكل بساطة
+
+186
+00:14:02,520 --> 00:14:06,960
+نسميها equivalence relation طيب إذا كان عندك أي
+
+187
+00:14:06,960 --> 00:14:11,440
+function if from A to B بقدر أسميها relation have
+
+188
+00:14:11,440 --> 00:14:16,500
+the same if value إذا كان لهم نفس القيمة .. لهم
+
+189
+00:14:16,500 --> 00:14:22,480
+نفس القيمة أو if هي عبارة عن زوج مرتب A1 و A2 بشرط
+
+190
+00:14:22,480 --> 00:14:27,240
+إنه if ل A1 تساوي if ل A2 فبقدر أقول إن ال two
+
+191
+00:14:27,240 --> 00:14:32,140
+functions هدولةequivalence لبعض بيساووا بعض نقدر
+
+192
+00:14:32,140 --> 00:14:36,840
+نقول عليهم بيساووا بعض أو ال relation have the
+
+193
+00:14:36,840 --> 00:14:40,580
+same value have the same value زي مثل إذا كان
+
+194
+00:14:40,580 --> 00:14:43,280
+والله يقولنا equivalence relation بسميها
+
+195
+00:14:43,280 --> 00:14:45,940
+equivalence relation في الحلقة دي إذا كان مثلا let
+
+196
+00:14:45,940 --> 00:14:54,000
+M brother of يعني قلنا A brother of B معناته بقدر
+
+197
+00:14:54,000 --> 00:15:01,050
+أقول A and B have the same motherK جزئيا بطريقة او
+
+198
+00:15:01,050 --> 00:15:04,430
+باخره ممكن نقول بهذا الشكل فإذا ممكن نقول ان ال M
+
+199
+00:15:04,430 --> 00:15:08,230
+هنا مكافئة لل M، ال M هنا ف equivalence relation
+
+200
+00:15:08,230 --> 00:15:11,210
+لو مسكنا كل واحدة منهم على حدا المفروض انها تحقق
+
+201
+00:15:11,210 --> 00:15:13,330
+ال equivalence relation اللي اتكلمنا او ال three
+
+202
+00:15:13,330 --> 00:15:17,690
+properties اللي حكينا عنهم بمعنى لما تقول A
+
+203
+00:15:17,690 --> 00:15:25,730
+brother of B معناته بي brother of Aصح؟ يعني لو انت
+
+204
+00:15:25,730 --> 00:15:29,550
+صياغة الجملة عكستها، هيتغير إشي؟ مش هيتغير إشي،
+
+205
+00:15:29,550 --> 00:15:34,290
+الكلام صحيح، الكلام صحيح، و لو قلت A brother of B
+
+206
+00:15:34,290 --> 00:15:41,230
+و B brother of C، معناته أكيد A brother of C،
+
+207
+00:15:41,230 --> 00:15:48,870
+صحيح؟ تمامصحيح بشروط لكن .. بشروط لكن ماشية يمكن
+
+208
+00:15:48,870 --> 00:15:51,470
+عندنا في مجتمعاتنا العربية شوية بتصير ال .. بتختلف
+
+209
+00:15:51,470 --> 00:15:56,230
+الشروط بس عالميا لأ مش كتير طيب فنفس الفكرة هنا لو
+
+210
+00:15:56,230 --> 00:16:00,870
+قلت a و b have the same mother و قلت b و a have
+
+211
+00:16:00,870 --> 00:16:05,370
+the same mother نفس الجثة طيب لو قلنا a and b have
+
+212
+00:16:05,370 --> 00:16:08,790
+the same mother, b and c have the same mother أكيد
+
+213
+00:16:08,790 --> 00:16:14,340
+a and c have the same mother أكيدفهي مثال شوية
+
+214
+00:16:14,340 --> 00:16:24,060
+ممكن على ثقافتنا كان بده شروط لكن كفكرة يعني وصلت
+
+215
+00:16:24,060 --> 00:16:30,460
+الفكرة تمام طيب الآن ال equivalent relation او ال
+
+216
+00:16:30,460 --> 00:16:32,660
+equivalent element لما نتكلم عن ال equivalent
+
+217
+00:16:32,660 --> 00:16:36,120
+element بقدر اقول انه كل element المفروض ان هو
+
+218
+00:16:36,120 --> 00:16:40,720
+equivalent to itself فمعنى ذلك ان هو reflexive زي
+
+219
+00:16:40,720 --> 00:16:46,820
+المسواه هذهالعنصر هو مكافئ لنفسه العنصر مكافئ
+
+220
+00:16:46,820 --> 00:16:52,320
+لنفسه تمام طيب we can say that a and b are related
+
+221
+00:16:52,320 --> 00:16:56,460
+are related لاحظ ماقولتش مين related للتاني هما
+
+222
+00:16:56,460 --> 00:17:02,480
+التنتين related يعني معناته a to b أو b to a فهذه
+
+223
+00:17:02,480 --> 00:17:07,220
+مش زي لما نقول a is related to b هذه معناته من a
+
+224
+00:17:07,220 --> 00:17:10,660
+لb بسلأ أنا ماقولتش هيك احنا قولنا are related
+
+225
+00:17:10,660 --> 00:17:14,920
+اتنتين فاتنتين متساويتين اي نعم ليش لأن هذا معناته
+
+226
+00:17:14,920 --> 00:17:21,960
+ان a relation b هي نفسها b relation a زي المساوية
+
+227
+00:17:21,960 --> 00:17:26,000
+ال relation مساوية هنا معناته من a لb ماشي من b لa
+
+228
+00:17:26,000 --> 00:17:30,160
+ماشي فهذه symmetric هذه المساوية كانت symmetric
+
+229
+00:17:30,160 --> 00:17:37,440
+فعليا طيب إذا كانت a and b are equivalent وB and C
+
+230
+00:17:37,440 --> 00:17:41,420
+برضه are equivalent المفروض إنه يطبع ذلك استنتاج
+
+231
+00:17:41,420 --> 00:17:46,460
+واضح إنه A and C are equivalent لازم هذه بتحقق ال
+
+232
+00:17:46,460 --> 00:17:48,940
+Transitive وهذه شفناها هنا إذا كانت A فعلا بتساوي
+
+233
+00:17:48,940 --> 00:17:57,300
+B A R B and B R C محقق ال relation ال equal كويس
+
+234
+00:17:57,300 --> 00:18:02,180
+إذا A relation C تحققت تحققت فإذا هذه تلت شروط
+
+235
+00:18:02,180 --> 00:18:06,040
+اللي بنعملهم ال check عشان نشوف هل فعلافي عندى
+
+236
+00:18:06,040 --> 00:18:09,760
+equivalent elements ومعنى ذلك انه equivalent
+
+237
+00:18:09,760 --> 00:18:12,900
+relation اللى بتكلم عنها اللى هى ال R و اللى هى
+
+238
+00:18:12,900 --> 00:18:15,780
+هنا مساوية مع انها اللى هى عندنا هنا استخدمنا
+
+239
+00:18:15,780 --> 00:18:20,560
+اليساوي طيب مجموعة equivalent equivalence relation
+
+240
+00:18:20,560 --> 00:18:23,280
+examples بعض الأمثل لل equivalence relations زى
+
+241
+00:18:23,280 --> 00:18:28,820
+لما نقول strings A and B are the same length بكل
+
+242
+00:18:28,820 --> 00:18:36,700
+بساطة هقولك ان طول حرف ال A بساوة طول حرف ال Zليش؟
+
+243
+00:18:36,700 --> 00:18:40,740
+لأن كل كلاهما .. كل واحد منهم له strength طوله
+
+244
+00:18:40,740 --> 00:18:48,040
+تمانية ك character صح؟ طيب و بقدر أقولك أن ال A هي
+
+245
+00:18:48,040 --> 00:18:54,580
+مكافئة للعلامة المئويةهتقولي طب انت بناء على إيش
+
+246
+00:18:54,580 --> 00:18:57,460
+المكافئة هنا بتصير ال relation بتعرف إيش ال
+
+247
+00:18:57,460 --> 00:19:01,200
+relation اللي بحكي عنها ال relation هي ال string
+
+248
+00:19:01,200 --> 00:19:06,420
+تبعك جدّيش عدد ال bits الممثلة لكل منهما هتقولي اه
+
+249
+00:19:06,420 --> 00:19:10,280
+هي كلمك صح ما هم كله تمانية شك هي كله تمانية ف ال
+
+250
+00:19:10,280 --> 00:19:14,280
+strings a and b are the same length لو قولنا a
+
+251
+00:19:14,280 --> 00:19:18,190
+have the same length مع a نفسهطيب و في الحالة دي
+
+252
+00:19:18,190 --> 00:19:22,670
+إذا ال strings a and b بيسوا بعض معناته b and a
+
+253
+00:19:22,670 --> 00:19:26,870
+بيسوا بعض طيب إذا a و b بيسوا بعض بي و c بيسوا بعض
+
+254
+00:19:26,870 --> 00:19:32,290
+فأكيد إذا كان أنا هنا قول تهينا هدول a مكافئة ل z
+
+255
+00:19:32,290 --> 00:19:35,750
+و a مكافئة لعلامة المئوية معناته العلم المئو
+
+256
+00:19:35,750 --> 00:19:41,960
+مكافئة ل z صح؟أكيد هيكونوا مكافئين لبعض طيب التاني
+
+257
+00:19:41,960 --> 00:19:45,300
+مثال تاني ال integers a and b have the same
+
+258
+00:19:45,300 --> 00:19:49,820
+absolute value have the same absolute value بمعنى
+
+259
+00:19:49,820 --> 00:19:54,200
+بتقدر تقول إذا كان والله a have the same absolute
+
+260
+00:19:54,200 --> 00:19:58,920
+value مع a نفسها خمسة خمسة خلاص طيب إذا كانت a و
+
+261
+00:19:58,920 --> 00:20:02,620
+سالب a كلا هما له نفس ال absolute معناته برضه سالب
+
+262
+00:20:02,620 --> 00:20:07,600
+a و a اللي هم نفس ال absolute value نفس ال
+
+263
+00:20:07,600 --> 00:20:12,530
+absolute valueطيب A have the same absolute value ل
+
+264
+00:20:12,530 --> 00:20:17,830
+B طيب B have the same absolute value ل C المنطق
+
+265
+00:20:17,830 --> 00:20:21,750
+بيقول معناته A و C لهم نفس ال absolute value نفس
+
+266
+00:20:21,750 --> 00:20:26,410
+ال absolute value تمامالـ real numbers a and b
+
+267
+00:20:26,410 --> 00:20:33,550
+have the same fractional part، عشرة و سبعة و
+
+268
+00:20:33,550 --> 00:20:37,090
+أربعين، خمسين أو تلاتة و خمسين، برضه سبعة و
+
+269
+00:20:37,090 --> 00:20:39,610
+أربعين، اللي هو نفس ال fractional part، معنى ذلك
+
+270
+00:20:39,610 --> 00:20:43,770
+أن ال difference between them أكيد integer، صح؟
+
+271
+00:20:43,770 --> 00:20:48,690
+الفرق بينهم أكيد integerكفرق تمام فإذا في الحالة
+
+272
+00:20:48,690 --> 00:20:52,090
+هذه بقدر أقول إن هما the same في ال fractional
+
+273
+00:20:52,090 --> 00:20:56,270
+part فكأنه a نقص b هي دائما هتكون z دائما هتكون z
+
+274
+00:20:56,270 --> 00:21:02,050
+هذا بالظبط ما هو كله the same هنا اللي بيحدد mean
+
+275
+00:21:02,050 --> 00:21:05,630
+the same هذه هي أني أعرفك ال function فهي الفكرة
+
+276
+00:21:05,630 --> 00:21:10,990
+كلها هنا the same ish the same ish هي ال the same
+
+277
+00:21:10,990 --> 00:21:15,220
+ish fractional أه مش الحالfractional مش الحالة لو
+
+278
+00:21:15,220 --> 00:21:17,680
+fractional حطيتها مع ال absolute لأ بيمشيش الحالة
+
+279
+00:21:17,680 --> 00:21:21,440
+فبتاخد بالك هي ال relation بتدجك في ال relation
+
+280
+00:21:21,440 --> 00:21:24,760
+نفسها عشان تحدد ال relation هي فعلا equivalence
+
+281
+00:21:24,760 --> 00:21:29,700
+relation و لا لأ طيب في المقابل هتلاقي مثلا ال
+
+282
+00:21:29,700 --> 00:21:34,860
+integers a and b have the same residue modulo m
+
+283
+00:21:34,860 --> 00:21:42,680
+تمام ل given m أكبر من واحد أكبر مثلا من واحد زي
+
+284
+00:21:42,680 --> 00:21:48,070
+لما نقولالاتنين equivalent للاربعتاش إذا كانت ال M
+
+285
+00:21:48,070 --> 00:21:53,350
+سوى اتناش للساعة خمسة وعشرين equivalent للواحد طيب
+
+286
+00:21:53,350 --> 00:21:55,630
+معناه ذلك إذا كان الخمسة وعشرين equivalent للواحد
+
+287
+00:21:55,630 --> 00:21:59,590
+والواحد equivalent للتلتاش أكيد التلتاش equivalent
+
+288
+00:21:59,590 --> 00:22:05,030
+للخمسة وعشرين أكيد طيب نفس الكلام الخمسة وعشرين
+
+289
+00:22:05,030 --> 00:22:07,430
+equivalent للواحد فالواحد equivalent للخمسة وعشرين
+
+290
+00:22:08,210 --> 00:22:12,170
+برضه متفرجش مين جاب المين والواحد طبعا اكيد
+
+291
+00:22:12,170 --> 00:22:15,170
+equivalent لنفسه والخمسة وعشرين equivalent لنفسها
+
+292
+00:22:15,170 --> 00:22:19,410
+تمام فإذا برضه بتحقق التلت شروط الأساسية فإذا بقدر
+
+293
+00:22:19,410 --> 00:22:25,190
+أقول عنها equivalence relation check إذا كانت
+
+294
+00:22:25,190 --> 00:22:29,470
+divides relation هل فعلا متحقق نفس الكلام ولا لا
+
+295
+00:22:29,470 --> 00:22:37,870
+هتشوف a divides b لو قلنا a divides aبمشي true ولا
+
+296
+00:22:37,870 --> 00:22:45,530
+false true لأنه الناتج integer خدوا بالكم هنا لما
+
+297
+00:22:45,530 --> 00:22:48,090
+بقول divides معناته الناتج لازم يكون integer
+
+298
+00:22:48,090 --> 00:22:51,750
+الكلام هذه أول حاجة أخدناها في ال numbers أول حاجة
+
+299
+00:22:51,750 --> 00:22:55,250
+بعدين روحنا لل long division أصلا اسمها division
+
+300
+00:22:55,250 --> 00:22:58,170
+أنه يكون فيه متبقي بس مدين بقول divides و بس
+
+301
+00:22:58,170 --> 00:23:02,410
+معناته لأ لازم يطلع integer فمعليش الكلمتين
+
+302
+00:23:02,410 --> 00:23:07,510
+مختلفين عن بعض long division غير dividesOkay فهذه
+
+303
+00:23:07,510 --> 00:23:10,690
+okay بتطلع في نهاية واحد فإذا okay مقبولة مبلوعة
+
+304
+00:23:10,690 --> 00:23:17,310
+طيب لما تكون A divides B and B divides C أكيد هذا
+
+305
+00:23:17,310 --> 00:23:26,230
+equivalent إنه A divides C صح إذا A تقسم B نفترض
+
+306
+00:23:26,230 --> 00:23:33,030
+اتنين و تمانية A تقسم B طيب B تقسم C تمانية مثلا و
+
+307
+00:23:33,030 --> 00:23:39,710
+16فإذن بالضرورة أكيد هتكون A divides C اتنين تقسم
+
+308
+00:23:39,710 --> 00:23:44,690
+ستة عشر صح؟ أكيد تقسم ستة عشر طيب بتظل الشغل
+
+309
+00:23:44,690 --> 00:23:49,750
+الوحيدة هل A divides B equivalent ل B divides A
+
+310
+00:23:49,750 --> 00:23:52,910
+أكيد
+
+311
+00:23:52,910 --> 00:23:54,590
+لأ فهذه
+
+312
+00:23:57,610 --> 00:24:02,150
+لأ، هذه ليست equivalence relation، هذه ليست
+
+313
+00:24:02,150 --> 00:24:04,950
+equivalence relation، رغم أن طول ما أنا قاعد بشرح
+
+314
+00:24:04,950 --> 00:24:08,670
+أنت تخيلت أنها رايحة أن هي تكون equivalence
+
+315
+00:24:08,670 --> 00:24:13,790
+relation، هي لأ مش equivalence relation، لأنه
+
+316
+00:24:13,790 --> 00:24:17,610
+symmetric لأ هي مش symmetric، هي مش symmetric، هي
+
+317
+00:24:17,610 --> 00:24:21,210
+ليست symmetric، هذه إيش بنسميها؟ Asymmetric؟
+
+318
+00:24:28,930 --> 00:24:36,210
+والا انت symmetric انت symmetric بتمشي اه بيطلع
+
+319
+00:24:36,210 --> 00:24:40,350
+بيمشي الحال بيمشي الحال فبتضل مقبولة فإذا في
+
+320
+00:24:40,350 --> 00:24:42,970
+النهاية هي مش symmetric وهذا اللي بيهمنا مدام مش
+
+321
+00:24:42,970 --> 00:24:45,810
+symmetric لأن هو هذا الشرط اللي انا محتاج احققه
+
+322
+00:24:45,810 --> 00:24:49,650
+فخلاص هي مش symmetric بس هي ليست symmetric مدام
+
+323
+00:24:49,650 --> 00:24:52,330
+ليست symmetric فإذا لأ بقدرش أسميها equivalence
+
+324
+00:24:52,330 --> 00:24:57,230
+relation تمام الان equivalence classes ال classes
+
+325
+00:24:57,230 --> 00:25:01,650
+هي ديإن هو تصنيف، تصنيف كامل، بمعنى كإني بقول إن
+
+326
+00:25:01,650 --> 00:25:04,590
+والله إذا تحقق .. عشان أقول إنه تحقق equivalence
+
+327
+00:25:04,590 --> 00:25:09,170
+class of A معنى ذلك إنه يوجد عندي set of
+
+328
+00:25:09,170 --> 00:25:15,930
+equivalent elements of A زي الواحدالواحد
+
+329
+00:25:15,930 --> 00:25:20,810
+equivalent له واحد تلات عشر خمسة اذا بتكلم عن
+
+330
+00:25:20,810 --> 00:25:25,390
+الساعة خمسة و عشرين وجمع اقعد جمع اتناشط جمع
+
+331
+00:25:25,390 --> 00:25:29,710
+اتناشط سبعة و تلاتين ال تسعة و اربعين و اكمل
+
+332
+00:25:29,710 --> 00:25:34,070
+الصحيح اللي هي بتزود اربعة و عشرين جاعد كل هدول
+
+333
+00:25:34,070 --> 00:25:39,230
+equivalent له معناته كل هدوله classكل element فيه
+
+334
+00:25:39,230 --> 00:25:44,670
+هو equivalent لإيه فبحطهم كلهم ك class واحد كوان
+
+335
+00:25:44,670 --> 00:25:52,050
+class فبصير اسمها equivalent class كويس كلهم
+
+336
+00:25:52,050 --> 00:25:57,720
+equivalent لمين لل relation R زي لما نقولبما فيها
+
+337
+00:25:57,720 --> 00:26:04,400
+A نفسها هي نقدر نسميها representative of A under
+
+338
+00:26:04,400 --> 00:26:07,340
+relation R فunder relation R هنا مثلا زي المثال
+
+339
+00:26:07,340 --> 00:26:11,580
+اللي قلناه توي ال relation هي ال modulo أو ال
+
+340
+00:26:11,580 --> 00:26:16,670
+residue of modulo معاشرإذا قلت فعلا الكلام هذا أن
+
+341
+00:26:16,670 --> 00:26:18,890
+هذه هي ال relation اللي هي ال residue of موديول
+
+342
+00:26:18,890 --> 00:26:22,910
+أتناش بقدر أقول ساعتها أن الواحد مع الخمسة و عشرين
+
+343
+00:26:22,910 --> 00:26:28,630
+ماشي مع التلتاش ماشي مع التسعة و أربعين ماشي ستة و
+
+344
+00:26:28,630 --> 00:26:33,530
+تلاتين و واحد سبعة و تلاتين ماشي هدى صارت ستة ولا
+
+345
+00:26:33,530 --> 00:26:38,330
+relation؟ هدى صارت لأ هدى هنا بتتكلم عن ستة مش
+
+346
+00:26:38,330 --> 00:26:43,600
+هتفرج مين جاب المين هدى six of relationsلأ ال
+
+347
+00:26:43,600 --> 00:26:47,660
+relation بمعنى هي تجميعة كل العناصر اللي
+
+348
+00:26:47,660 --> 00:26:51,320
+equivalent او equivalent بالظبط للعنصر A
+
+349
+00:26:51,320 --> 00:26:55,260
+equivalent للعنصر A لما بتتكلم عن طبعا نيجي نقول
+
+350
+00:26:55,260 --> 00:26:59,440
+مثلا مثلا
+
+351
+00:26:59,440 --> 00:27:03,160
+المتبقى ال fractional part the same fractional
+
+352
+00:27:03,160 --> 00:27:07,610
+part معنى ذلك أن Aزائد واحد، زائد اتنين، زائد
+
+353
+00:27:07,610 --> 00:27:10,070
+تلاتة، زائد اربعة، ناقص واحد، ناقص اتنين، ناقص
+
+354
+00:27:10,070 --> 00:27:13,590
+تلاتة، ناقص اربعة، ناقص to infinity من minus
+
+355
+00:27:13,590 --> 00:27:16,250
+infinity to infinity اللي هي بتجمع عليها integer
+
+356
+00:27:16,250 --> 00:27:19,830
+فانت ضامن ان ال fractional part هيظل زي ما هو،
+
+357
+00:27:19,830 --> 00:27:23,510
+هيظل كما هو فهذه معناته انت عندك كائنة ست لا
+
+358
+00:27:23,510 --> 00:27:28,750
+متناهية صارت من ال equivalent elements للعنصر A
+
+359
+00:27:28,750 --> 00:27:36,070
+with the same fractional partمش هيك كلها بتعملوا
+
+360
+00:27:36,070 --> 00:27:39,190
+انك بتجمع عليها integers فانت ضامن ان ال
+
+361
+00:27:39,190 --> 00:27:42,010
+fractional part هو هو ال fractional part كما هو
+
+362
+00:27:42,010 --> 00:27:49,030
+طيب مجموعة examples لل class او ال equivalence
+
+363
+00:27:49,030 --> 00:27:54,910
+class classes strings
+
+364
+00:27:54,910 --> 00:27:58,790
+a and b have the same length لهم نفس ال length ففي
+
+365
+00:27:58,790 --> 00:28:03,270
+الحالة هذه بنقدر نقول انهبراكت a اللي هو
+
+366
+00:28:03,270 --> 00:28:07,530
+representative of a لإن ال relation have the same
+
+367
+00:28:07,530 --> 00:28:12,650
+length، كويس، هي كل الست، هاي ست، مين جاب المين
+
+368
+00:28:12,650 --> 00:28:16,090
+بتفرجش معناه، بس هي في أنها ست، لكل ال strings of
+
+369
+00:28:16,090 --> 00:28:22,280
+the same lengthof a a قدش طولها فكل length نفس
+
+370
+00:28:22,280 --> 00:28:26,520
+الطول هو ضمن هذه ال set ضمن هذه ال set طيب ال
+
+371
+00:28:26,520 --> 00:28:30,460
+integers a and b have the same absolute value فإذا
+
+372
+00:28:30,460 --> 00:28:36,760
+بقدر اقول انه representative of a ل ال relation
+
+373
+00:28:36,760 --> 00:28:40,000
+absolute value have the same absolute value هي a و
+
+374
+00:28:40,000 --> 00:28:45,790
+سالب aفي غيرهم؟ خلاص فهذه الست تبعتنا a and سالب a
+
+375
+00:28:45,790 --> 00:28:49,390
+في الحالة هذه طيب real numbers a and b have the
+
+376
+00:28:49,390 --> 00:28:54,910
+same fractional part هذه معناته أن a ناقص b عبارة
+
+377
+00:28:54,910 --> 00:28:58,630
+عن تنتمي المفروض ل z ففي الآخر بقدر أقول أن ال
+
+378
+00:28:58,630 --> 00:29:04,190
+representative of a هي كل الست a و a ناقص واحد a
+
+379
+00:29:04,190 --> 00:29:10,760
+زائد واحدE نقص اتنين E زائد اتنين جمع integers لما
+
+380
+00:29:10,760 --> 00:29:13,240
+تصل minus infinity to infinity لما تصل minus
+
+381
+00:29:13,240 --> 00:29:17,020
+infinity او infinity فكل هدول العناصر هيكونهم the
+
+382
+00:29:17,020 --> 00:29:23,080
+same fractional part كلهم اكيد ال integers A and B
+
+383
+00:29:23,080 --> 00:29:28,160
+have the same residue modulo M في الحالة هذه كل
+
+384
+00:29:28,160 --> 00:29:30,820
+اللي انت بتعمله بس زي ما توي عملنا جمعنا جداش
+
+385
+00:29:30,820 --> 00:29:36,910
+اتناشاتنفس الفكرة هي ال A نفسها وال A زائد M نخص M
+
+386
+00:29:36,910 --> 00:29:43,940
+زائد اتنين M نخص اتنين Mقلت لك 21 و بعدين اضفت لهم
+
+387
+00:29:43,940 --> 00:29:48,180
+12 قلت لك 13 مش الحال قلت لك مش اتناش اتناش في
+
+388
+00:29:48,180 --> 00:29:51,060
+اتنين اربع و عشرين زاد الواحد هي خمسة و عشرين قلت
+
+389
+00:29:51,060 --> 00:29:53,820
+لك خمسة و عشرين كل equivalent مدام انت بتجمع جاعد
+
+390
+00:29:53,820 --> 00:29:59,020
+مضاعفات ال modulus مضاعفات ال modulus عندك فبمش
+
+391
+00:29:59,020 --> 00:30:03,260
+الحال كلهم هدولة عبارة عن set of elements كل
+
+392
+00:30:03,260 --> 00:30:06,460
+element فيهم هو equivalent ل a هو equivalent ل ال
+
+393
+00:30:06,460 --> 00:30:12,790
+aOkay ال partitions ال partitions هي عبارة عن أنت
+
+394
+00:30:12,790 --> 00:30:14,890
+بقدر أقول أن في عندي partitions فعليا ال
+
+395
+00:30:14,890 --> 00:30:19,750
+partitions هي ال set A ل set A معينة هي كل ال sets
+
+396
+00:30:19,750 --> 00:30:23,450
+اللي بقدر أسميه equivalence classes فإذا كل
+
+397
+00:30:23,450 --> 00:30:28,190
+equivalence class بقول عليه A one هدولة مثلا
+
+398
+00:30:28,190 --> 00:30:32,690
+العناصر اللي .. أقولكوا أبسط شغلة بدي أقول أن ال
+
+399
+00:30:32,690 --> 00:30:37,490
+set تبعتنا هي طلبة هندسة الحسوبطلبة هندسة الحسوب
+
+400
+00:30:37,490 --> 00:30:40,910
+class one هم طلبة هندسة الحسوب في المستوى التاني
+
+401
+00:30:40,910 --> 00:30:47,010
+هدول class one مثلا شك .. ليش؟ لأن كلهم لما أجي
+
+402
+00:30:47,010 --> 00:30:51,650
+أحطهم تحت relation أنه have the same level هنطبق
+
+403
+00:30:51,650 --> 00:30:55,750
+عليهم have the same level معناته level two هدول
+
+404
+00:30:55,750 --> 00:31:00,690
+المستوى التاني في الكلية في القسم فإذا إذا كان a و
+
+405
+00:31:00,690 --> 00:31:04,210
+b have the same level b و c have the same level
+
+406
+00:31:04,210 --> 00:31:08,120
+معناته أكيد a و c have the same levelو A و B have
+
+407
+00:31:08,120 --> 00:31:10,020
+the same level معناته B و A have the same level
+
+408
+00:31:10,020 --> 00:31:14,860
+نفس الجثة A مع نفسه أكيد هي reflexive فإذا هذه
+
+409
+00:31:14,860 --> 00:31:18,500
+equivalent ك equivalent تمام في نفس الوقت في عندي
+
+410
+00:31:18,500 --> 00:31:25,320
+class 2 للمستوى التالت طيب class 3 للمستوى الرابع
+
+411
+00:31:25,320 --> 00:31:28,820
+class 4 للمستوى الخامس طب total كلهم على بعض
+
+412
+00:31:28,820 --> 00:31:35,820
+بكونوا ليه؟كل class تبع هندسة الحاسوب، صح؟ ماحدش
+
+413
+00:31:35,820 --> 00:31:40,100
+هيطلع منهم، ماحدش هيطلع منهم وفي نفس الوجد مافيش
+
+414
+00:31:40,100 --> 00:31:46,200
+intersection between them مافيش تقاطع، معنى ذلك أن
+
+415
+00:31:46,200 --> 00:31:48,740
+التقاطع بينهم في في الحالة دي بقدر أقول إنهم
+
+416
+00:31:48,740 --> 00:31:52,320
+partitions، مافيش تقاطعات بينهم، هذه مهمة جدا
+
+417
+00:31:52,320 --> 00:31:56,650
+الفكرة في ال database بكرةلما تشوف تتكلم عن قواعد
+
+418
+00:31:56,650 --> 00:32:00,150
+البيانات و منفصلة لو هي partitions ولا مش
+
+419
+00:32:00,150 --> 00:32:04,120
+partitions مهم جدا الفكرة هذهتمام، فإذا في الحالة
+
+420
+00:32:04,120 --> 00:32:08,220
+دي بتقدر تقول إنه ال equivalent classes هذه بنحطهم
+
+421
+00:32:08,220 --> 00:32:12,320
+ك partitions داخل equivalent class كبيرة جدا، داخل
+
+422
+00:32:12,320 --> 00:32:15,000
+equivalent class كبيرة بحيث إنه أجسمها جوا لمجموعة
+
+423
+00:32:15,000 --> 00:32:20,220
+classes أو parts أو parts، the same ER، كل واحدة
+
+424
+00:32:20,220 --> 00:32:23,080
+منهم طبعا بتحقق ال ER أو ال equivalence relation
+
+425
+00:32:23,080 --> 00:32:25,120
+لحالها، كل واحدة بتحقق ال equivalence relation
+
+426
+00:32:25,120 --> 00:32:32,080
+لحالهالازم تكون disjoint اكيد a1 مع a2 او ال a مع
+
+427
+00:32:32,080 --> 00:32:36,120
+بعضها لازم تكون disjoint فمثال ال levels مناسب جدا
+
+428
+00:32:36,120 --> 00:32:39,780
+كان لنا مش هتلاقي طالب مكتوب اللي في ال transcript
+
+429
+00:32:39,780 --> 00:32:42,840
+تبعه هو level تلاتة و أربعة في نفس الوجه تصبتش
+
+430
+00:32:42,840 --> 00:32:45,820
+صحيح يا تلاتة يا أربعة يعني مش هتيجي تنتم مع بعض
+
+431
+00:32:45,820 --> 00:32:48,760
+بس ضايقلك ساعة خلاص خلص الساعة فجأة بتلاقي حالك
+
+432
+00:32:48,760 --> 00:32:51,640
+انتقلت لل .. للمستوى الرابع انتهى على حسب عدد
+
+433
+00:32:51,640 --> 00:32:55,320
+الساعات معينة ففيه thresholdكويس فى three short
+
+434
+00:32:55,320 --> 00:33:00,760
+خلصنا بنتى كويس فإذا this joint ال groups هدى مع
+
+435
+00:33:00,760 --> 00:33:03,600
+بعضها أو ال partitions هدى مع بعضها و ال union
+
+436
+00:33:03,600 --> 00:33:07,840
+تبعهم كلهم مع بعض المفروض يعطيني ال a ال total ايه
+
+437
+00:33:07,840 --> 00:33:11,960
+ال total ايه لما أجى أقول والله كل طلبة هندسة
+
+438
+00:33:11,960 --> 00:33:15,000
+الحسوب على اعتبار أنه سنة أولى لسه مش متخصصين
+
+439
+00:33:15,000 --> 00:33:18,020
+فماقدرش نحطهم فبدأت من المستوى التانى التالت
+
+440
+00:33:18,020 --> 00:33:21,960
+الرابع الخامس كل هدولة بيحددولنا من طلبة هندسة
+
+441
+00:33:21,960 --> 00:33:26,490
+الحسوب ك totalبالتالي بسيطة يعني هذه الفكرة كلها
+
+442
+00:33:26,490 --> 00:33:30,970
+هي مجرد مقدمة مجرد مقدمة مش هنخوض كتير فيها يمكن
+
+443
+00:33:30,970 --> 00:33:33,530
+مناسب بكرا لما تاخدوا قواعد بيانات أو تاخدوا اي
+
+444
+00:33:33,530 --> 00:33:36,270
+حاجة اللي هي علاقة بال partition مش غلط الكتاب
+
+445
+00:33:36,270 --> 00:33:39,350
+عندكم بترجعوله هتلاقي انه فعلا في معلومات كتيرة
+
+446
+00:33:39,350 --> 00:33:43,990
+احنا عادة بنعديها لكن لما تيجي تحتاجها هتلاقي لها
+
+447
+00:33:43,990 --> 00:33:47,250
+solid background الحقيقة في الكتاب طبعكم اللي
+
+448
+00:33:47,250 --> 00:33:51,980
+موجود معاكوا صفقوا بيهتمام أمثلة على ال partitions
+
+449
+00:33:51,980 --> 00:33:56,300
+زي لما نقول مثلا افرض انه عندي الست S هنا واحد
+
+450
+00:33:56,300 --> 00:34:00,080
+اتنين تلاتة لعندي الستة و جسمناهم لمجموعة
+
+451
+00:34:00,080 --> 00:34:03,380
+partitions ال partition الأولى اي واحد واحد اتنين
+
+452
+00:34:03,380 --> 00:34:06,620
+تلاتة ال partition التانية أربعة أو خمسة و ال
+
+453
+00:34:06,620 --> 00:34:09,500
+partition الأخيرة هي ستة زي لما نقول والله بدنا
+
+454
+00:34:09,500 --> 00:34:12,580
+نجسم نعمل دوري لكن ديروا بأكوا يا شباب بدنا
+
+455
+00:34:12,580 --> 00:34:17,100
+نجسمكوا بطريقةمعينة ان جول والله بدنا نعمل مصابقة
+
+456
+00:34:17,100 --> 00:34:20,200
+لطلبة سنة أولى أو تانية أو تالتة مع بعض هدولة يعني
+
+457
+00:34:20,200 --> 00:34:23,700
+طريقة تفكيرهم جريبة من بعض هدولة لأ خلص جربوا
+
+458
+00:34:23,700 --> 00:34:26,440
+يصيروا مهندسين رابعة أو خمسة بدنا نحطهم لحالهم
+
+459
+00:34:26,440 --> 00:34:31,360
+نختبرهم بأسئلة لحالهم ثقافة مختلفة الماجستير لحاله
+
+460
+00:34:31,360 --> 00:34:35,200
+ستة بدنا نقول ماجستير لحاله فجسمناهم لمجموعة
+
+461
+00:34:35,200 --> 00:34:38,860
+levels مثلا جسمناهم فرضا لمجموعة levels فالان لما
+
+462
+00:34:38,860 --> 00:34:43,790
+نقول forms a partition of Sفي الحالة هذه هو لازم
+
+463
+00:34:43,790 --> 00:34:47,890
+يكون disjoint لازم يكون disjoint لكن الآن الفكرة
+
+464
+00:34:47,890 --> 00:34:50,790
+مش فى فكرة تقسيمه بس فى فكرة ال operations اللى
+
+465
+00:34:50,790 --> 00:34:54,450
+هتتم بعد ذلك على التقسيم على ال partitions بأبسط
+
+466
+00:34:54,450 --> 00:34:57,970
+شغل لو قلنا list the ordered pairs in the
+
+467
+00:34:57,970 --> 00:35:03,070
+equivalence relation are produced by the partition
+
+468
+00:35:04,340 --> 00:35:07,980
+معنى ذلك ان احنا بدنا نحط الان ordered pairs بدنا
+
+469
+00:35:07,980 --> 00:35:11,660
+نحط أزواج مرتبة كيف بدي أعمل أزواج مرتبة؟ لأنك انت
+
+470
+00:35:11,660 --> 00:35:15,500
+بدك تعمل relation الان لو بدنا نختار .. نفترض من
+
+471
+00:35:15,500 --> 00:35:19,640
+هنا مجموعة التركيبة كيف ممكن تكون؟ ممكن تكون واحد
+
+472
+00:35:19,640 --> 00:35:23,800
+من مستوى أول ومستوى تاني مستوى أول ومستوى تالت
+
+473
+00:35:23,800 --> 00:35:28,020
+مستوى تاني ومستوى تالت بس مش مسموح تدخل partition
+
+474
+00:35:28,020 --> 00:35:35,750
+مع partition مدام هي أصلاby partition by partition
+
+475
+00:35:35,750 --> 00:35:39,130
+معنى ذلك كل partition لحاله هنا بقول واحد واحد
+
+476
+00:35:39,130 --> 00:35:42,170
+واحد اتنين واحد تلتة اتنين واحد اتنين اتنين اتنين
+
+477
+00:35:42,170 --> 00:35:47,110
+تلتة وخلاص و تلتة واحد هذه اللي كان ضايلة تلتة
+
+478
+00:35:47,110 --> 00:35:49,310
+اتنين اه لسه بدنا نبدأ بها ده تلتة اتنين و تلتة
+
+479
+00:35:49,310 --> 00:35:54,830
+اتنين cartesian product و خجفنا خلصنا هيك class A1
+
+480
+00:35:54,830 --> 00:35:59,130
+بنروح ل class A2 اللي هو أربعة مع أربعة أربعة خمسة
+
+481
+00:35:59,130 --> 00:36:05,320
+خمسة أربعة وخمسة خمسةخلصنا class two طيب الأخيرة
+
+482
+00:36:05,320 --> 00:36:10,740
+خلاص هي ستة و ستة هي ستة و ستة تمام فإذا كان
+
+483
+00:36:10,740 --> 00:36:14,200
+السؤال partition تاخدوا بالك إذا كان فعلا عملية
+
+484
+00:36:14,200 --> 00:36:16,580
+على ال partitions تاخدوا بالك أن العملية تتم لكل
+
+485
+00:36:16,580 --> 00:36:20,860
+partition على حده بس totally كله على بعضه كاملين
+
+486
+00:36:20,860 --> 00:36:26,980
+مع بعض لكن مش هضطر أعمل ستة و واحد تمام أو واحد و
+
+487
+00:36:26,980 --> 00:36:30,780
+خمسة لكن كلهم كست اه كلهم بحطهم مع بعض كست واحدة
+
+488
+00:36:31,760 --> 00:36:35,800
+كاسيت واحدة ليش؟ لأنه في النهاية إذا بدنا ناخد
+
+489
+00:36:35,800 --> 00:36:40,400
+المثال تبع اللجنة الثقافية هذه و كله بدها تتجسم
+
+490
+00:36:40,400 --> 00:36:42,860
+بهذا الشكل، معناته كل هدول هو ال combination تبعة
+
+491
+00:36:42,860 --> 00:36:47,360
+كلية الهندسة مثلا، خلاص، كلهم مع بعض بهذا الشكل
+
+492
+00:36:47,360 --> 00:36:52,380
+كنتيجة واحدة، كنتيجة واحدة تمام، هذا الجزء اللي
+
+493
+00:36:52,380 --> 00:36:59,680
+كان متبقيل من جزئية ال relationعشان نبدأ برضه جزء
+
+494
+00:36:59,680 --> 00:37:02,540
+من ال relation على اعتبار ان احنا ديروا بالكونهنا
+
+495
+00:37:02,540 --> 00:37:06,740
+بجزئية ال diagramطوي و قولنا بنتكلم عن ال path ال
+
+496
+00:37:06,740 --> 00:37:09,760
+path و ال diagram و الأنواع هذه يكفي اليوم ان احنا
+
+497
+00:37:09,760 --> 00:37:15,000
+بس على الأقل ناخد ايش أنواع ال path الممكنة اللي
+
+498
+00:37:15,000 --> 00:37:19,700
+ممكن تكون مقدمة ل ال graphs ل مين؟ ل ال graphs ال
+
+499
+00:37:19,700 --> 00:37:23,780
+graphs أخدناها سابقا مع ال relation فإذا اللحظة ان
+
+500
+00:37:23,780 --> 00:37:27,140
+انا بتكلم عن أنواع واحدة من أنواع ال relationقبل
+
+501
+00:37:27,140 --> 00:37:30,400
+ما نخوض كتير فيها و نغوص في تفاصيلها زي ما اتكلمنا
+
+502
+00:37:30,400 --> 00:37:35,120
+ان ال relation هي الكبيرة هي الشاملة لكل شيء و
+
+503
+00:37:35,120 --> 00:37:38,440
+اللي بتشمل جواها ال function ماهي ال function
+
+504
+00:37:38,440 --> 00:37:42,140
+relation relation بين ال F of X اللي هي ال Y و X
+
+505
+00:37:42,140 --> 00:37:44,480
+بين ال input و ال output ال dependent و ال
+
+506
+00:37:44,480 --> 00:37:51,160
+independent صحيح؟وحدة من أنواع الحالات اللي ضمن ال
+
+507
+00:37:51,160 --> 00:37:54,600
+relation هي ال graph ال graph هي relation هي
+
+508
+00:37:54,600 --> 00:38:00,940
+relation بينبداية و نهاية و بعمل بينهم relation
+
+509
+00:38:00,940 --> 00:38:08,100
+فصار كأنه directed graph في علاقة بين a و b graph
+
+510
+00:38:08,100 --> 00:38:11,620
+يمثل ك graph فانت برضه ممكن تفكر بنفس القلية لل
+
+511
+00:38:11,620 --> 00:38:15,060
+graphs كلها in general هي ال graphs ممكن بالشكل
+
+512
+00:38:15,060 --> 00:38:19,320
+رسومات عبارة عن خطوط الخطوط هذه relation بين مين و
+
+513
+00:38:19,320 --> 00:38:23,860
+مين بين البداية و النهاية لكل خطبداية و نهاية كل
+
+514
+00:38:23,860 --> 00:38:27,280
+خط فانت لما تيجي تتكلم عن بداية و نهاية كأنك بتقول
+
+515
+00:38:27,280 --> 00:38:30,980
+إحداثي لبداية الخط و إحداثي لنهاية الخط و ارسم
+
+516
+00:38:30,980 --> 00:38:36,340
+بينهم خط مستقيم فهي خط مش شيك ف graph اه منطق جدا
+
+517
+00:38:36,340 --> 00:38:39,140
+ان اتكلم هنا في الحالة هدا عن ال graphs تمام أول
+
+518
+00:38:39,140 --> 00:38:40,840
+نوع من أنواع ال graphs الحقيقه اللي هو ال simple
+
+519
+00:38:40,840 --> 00:38:46,000
+graphs اللي هو يمثل symmetric فعليا correlation و
+
+520
+00:38:46,000 --> 00:38:52,210
+irreflexiveirreflexive معناته مافيش self loop لأي
+
+521
+00:38:52,210 --> 00:38:55,850
+node من ال nodes تبعته لو يوجد self loop ففي
+
+522
+00:38:55,850 --> 00:38:58,970
+الحالة دي reflexive ل binary relation بس هو
+
+523
+00:38:58,970 --> 00:39:02,070
+symmetric اشي عن symmetric معناته انه كل خط من هنا
+
+524
+00:39:02,070 --> 00:39:06,690
+هو رايح جاي مش محتاج اروح اتجاه و ارجع اتجاه فإذا
+
+525
+00:39:06,690 --> 00:39:11,710
+هو مش متجه هنا هو مابقدرش اقول عليه directed هو مش
+
+526
+00:39:11,710 --> 00:39:19,100
+directed هو خط واحد و خلاص خط واحد و بسفالخط
+
+527
+00:39:19,100 --> 00:39:22,680
+الواحد و بس هذا يمثل ببساطة جدا بال graph اللي هو
+
+528
+00:39:22,680 --> 00:39:27,720
+عبارة عن مجموعة vertices و edges مجموعة قمم اللي
+
+529
+00:39:27,720 --> 00:39:33,860
+هي ال nodes و مجموعة edges او arc هي الخطوطأو ال
+
+530
+00:39:33,860 --> 00:39:37,140
+relation فعليًا ال relation فعليًا فبكل بساطة
+
+531
+00:39:37,140 --> 00:39:42,340
+بنقدر نقول هي عبارة عن ست V of vertices أو nodes
+
+532
+00:39:42,340 --> 00:39:45,500
+بسميها هيك بسميها هيك بس هي في النهاية دي هي ال V
+
+533
+00:39:45,500 --> 00:39:48,500
+و اللي تمثل في النهاية ال universe of discourse
+
+534
+00:39:48,500 --> 00:39:54,060
+تبعكال universe of the scores العناصر تمثل النقاط
+
+535
+00:39:54,060 --> 00:39:58,560
+تمام الآن بعد ذلك بتحط ال relation تبعتك بين
+
+536
+00:39:58,560 --> 00:40:02,200
+النقاط ما بين النقاط عشان تحط relation معناته هده
+
+537
+00:40:02,200 --> 00:40:07,320
+هنا بتصير ال edges او زي ما قلنا ال arc او ال link
+
+538
+00:40:07,320 --> 00:40:10,960
+اللينكات بين في relation ولا مافيش relation في
+
+539
+00:40:10,960 --> 00:40:15,520
+طريق ولا مافيش طريق في path ولا مافيش pathالست إيه
+
+540
+00:40:15,520 --> 00:40:19,840
+هي ال edges ال arc أو ال lengths و اللي نقدر
+
+541
+00:40:19,840 --> 00:40:24,090
+نسميها unordered بدون أن نتكلم عن symbolgraph فهي
+
+542
+00:40:24,090 --> 00:40:27,610
+نوردة peers مين جاب المين مش هتفرج المهم أنه يوجد
+
+543
+00:40:27,610 --> 00:40:31,670
+connection و خلاص يوجد connection و بس ل distinct
+
+544
+00:40:31,670 --> 00:40:37,170
+elements لعناصر متفارقة discrete ببساطة discrete
+
+545
+00:40:37,170 --> 00:40:39,770
+elements ال discrete elements هدول هم ال vertices
+
+546
+00:40:39,770 --> 00:40:42,770
+اللي حاكينا عنه أو ال nodes اللي هم ممكن تمثل U أو
+
+547
+00:40:42,770 --> 00:40:48,670
+V بس كلهم vertices كلهم نقاط أو nodes أو universe
+
+548
+00:40:48,670 --> 00:40:50,510
+of discourse عناصر من ال universe of discourse
+
+549
+00:40:50,510 --> 00:40:56,460
+اللي هي U و Vبحيث أني بقدر امثلها ب U relation V U
+
+550
+00:40:56,460 --> 00:41:01,520
+relation V مدام U relation V وقولنا V هي تمثل ال
+
+551
+00:41:01,520 --> 00:41:05,360
+arc أو ال edges معناه ذلك أنه يوجد خط أو يوجد path
+
+552
+00:41:05,360 --> 00:41:12,020
+أو يوجد link بين U ال .. ال .. ال vertex U و ال
+
+553
+00:41:12,020 --> 00:41:16,620
+vertex V أو ال node U و ال node V بسكأنه خط فهنا
+
+554
+00:41:16,620 --> 00:41:21,320
+مثال واضح لها بهذا الشكل لا فيها self loop ولا
+
+555
+00:41:21,320 --> 00:41:29,060
+فيها directed edges كلها بدون أسهم خلاص هو link و
+
+556
+00:41:29,060 --> 00:41:32,340
+بس link و بس ال link و بس هذا معناته أنه رايح جاي
+
+557
+00:41:32,340 --> 00:41:41,930
+من U ل V أو من V ل U ماشي في الحالتين ماشيمثال
+
+558
+00:41:41,930 --> 00:41:45,750
+عليه هي ال city .. ال cities مثلا cities لو
+
+559
+00:41:45,750 --> 00:41:49,830
+افترضنا انه عندي مجموعة set of cities مدن و بدنا
+
+560
+00:41:49,830 --> 00:41:52,830
+نعمل ال connection between them و بده افترض انه
+
+561
+00:41:52,830 --> 00:42:00,250
+عندي من المدينة C1 ل C8 كل هدول عندى تمانية مدن او
+
+562
+00:42:00,250 --> 00:42:04,450
+تمانية cities محتاجين ان نجيب بينهم edges نمثل ال
+
+563
+00:42:04,450 --> 00:42:09,100
+edges between them على اعتبار ان هي ال cityU مع
+
+564
+00:42:09,100 --> 00:42:15,040
+city V و كلا هما المفروض هما connected لبعض أو
+
+565
+00:42:15,040 --> 00:42:18,080
+متصلين مع بعض متصلين مع بعض عشان نقول انه في
+
+566
+00:42:18,080 --> 00:42:20,460
+relation و إلا معناته مافيش relation يعني ال logic
+
+567
+00:42:20,460 --> 00:42:23,700
+تيجي تقول ليه بين ..لأ والله هدول كلهم connected
+
+568
+00:42:23,700 --> 00:42:27,800
+مع بعض الحقيقة بس تختلف ال R جدش ال order تبعها بس
+
+569
+00:42:27,800 --> 00:42:31,560
+جدش ال order تبعها أو جدش ال dimension تبعها هنا
+
+570
+00:42:31,560 --> 00:42:35,500
+لما نمشي و نرسمها هقول إنه يوجد connection بين C1
+
+571
+00:42:35,500 --> 00:42:43,770
+و C2فهي اول relation اول edges اول relation او
+
+572
+00:42:43,770 --> 00:42:50,560
+edge بعدين واحد تلاتة واحد اربعة واحد خمسةيوجد
+
+573
+00:42:50,560 --> 00:42:54,200
+علاقة فعلا هي يوجد connection بعدين نمسك اتنين
+
+574
+00:42:54,200 --> 00:42:58,260
+اتنين مش حاطه مع اتنين واحد احنا حاطينا اتنين واحد
+
+575
+00:42:58,260 --> 00:43:01,140
+وقولنا ان هي undirected اه اه undirected بالظبط
+
+576
+00:43:01,140 --> 00:43:06,460
+مدام undirected معناته C1 C2 هي نفسها C2 C1 مافيش
+
+577
+00:43:06,460 --> 00:43:09,040
+داعي نرجع نكتبها كمان مرة فإذا ببدأ من C
+
+578
+00:43:13,120 --> 00:43:20,080
+2C3C2C6C2C7 و بتكمل بهذا الشكل لما نستنفذ كل
+
+579
+00:43:20,080 --> 00:43:25,180
+الحالات اللي موجودة عندنا فبنكون خلصنا في الحالة
+
+580
+00:43:25,180 --> 00:43:26,140
+اللي عندنا هذه تمام
+
+581
+00:43:30,260 --> 00:43:33,080
+ال multi-graph في ال multi-graph لأ شويه بتختلف
+
+582
+00:43:33,080 --> 00:43:36,580
+الأمور على اعتبار انه هيكون في عندك شبيهة بال
+
+583
+00:43:36,580 --> 00:43:40,800
+simple graph ولكن ممكن يكون عندك اكتر من one path
+
+584
+00:43:40,800 --> 00:43:44,780
+between ال cities او ال vertices هدول ممكن يكون
+
+585
+00:43:44,780 --> 00:43:48,040
+اكتر من link اكتر من مين؟ من ال link زي لما نقول
+
+586
+00:43:48,040 --> 00:43:52,800
+والله في عندى غزة و خان يونس مثلا طب انت في انك
+
+587
+00:43:52,800 --> 00:43:57,670
+صلاح الدين عندك البحرصح؟ ايه two paths الاتنين ف
+
+588
+00:43:57,670 --> 00:44:00,190
+multi اه multi ممكن يكون في multi في ال graph
+
+589
+00:44:00,190 --> 00:44:03,730
+مافيش مشكلة يعني ان بتش ترسمها كخريطة من فوق هتعمل
+
+590
+00:44:03,730 --> 00:44:07,190
+ال multi واضحة هتكون واضحة في ال graph تبعك جيد
+
+591
+00:44:07,190 --> 00:44:10,950
+ففي الحالة هذه شبيهة ولكن بيكون عندي اكتر من one
+
+592
+00:44:10,950 --> 00:44:16,310
+edge connected to given nodes بيوصل to given nodes
+
+593
+00:44:16,310 --> 00:44:22,670
+فهنا بتصير عندي تمثل ال graph كأنهاNodes, Edges و
+
+594
+00:44:22,670 --> 00:44:26,510
+Function الـ Function هدى اللى اتحدد لنا جداش عدد
+
+595
+00:44:26,510 --> 00:44:30,870
+ال edges between a certain cities أو a certain
+
+596
+00:44:30,870 --> 00:44:35,190
+nodes كويس فهدى بتحتوي على ال set لمجموعة ال
+
+597
+00:44:35,190 --> 00:44:39,710
+vertices تبعتنا ال set E هي ال edges و عندك ال
+
+598
+00:44:39,710 --> 00:44:45,050
+function ال function هنا هتكون هي ببساطة علاقة بين
+
+599
+00:44:45,050 --> 00:44:53,810
+ال edgesعندك edge موجودة بتضمنلك بين U و V و U و V
+
+600
+00:44:53,810 --> 00:44:57,730
+لازم يكونوا ضمن ال vertices ماتيجيش نتكلم عن غزة
+
+601
+00:44:57,730 --> 00:45:01,550
+تحطلي مدينة من خارج قطاع غزة لازم تكون ضمن ال
+
+602
+00:45:01,550 --> 00:45:04,250
+universe of discourse أصلا فهي ضمن ال vertices
+
+603
+00:45:04,250 --> 00:45:11,470
+تبعتنا ولا تساوي ولا يساوي بعض طيب ليش؟ self loop
+
+604
+00:45:11,470 --> 00:45:15,030
+لإن لو بيساوي بعض معناته ستصبح عندك self loopلا
+
+605
+00:45:15,030 --> 00:45:18,630
+يساوي بعض ساعتها بقول ان ال function ها دي بتحدد
+
+606
+00:45:18,630 --> 00:45:25,010
+لجدش عدد ال edgesاللي بين U و V بتحدد قداش عدد ال
+
+607
+00:45:25,010 --> 00:45:29,510
+edges فاني لما بقول غزة و خانيونس اه في طريقين
+
+608
+00:45:29,510 --> 00:45:33,590
+ممكن واحد يحب البحر اذا كان الجو كويس او يبعد عن
+
+609
+00:45:33,590 --> 00:45:36,590
+البحر اذا الدنيا برد في عز الشتاء خلينا في الدفة
+
+610
+00:45:36,590 --> 00:45:40,470
+جوا احسن نمشي من الدفة و اذا كان طبعا الطريق كمان
+
+611
+00:45:40,470 --> 00:45:43,830
+سالكة فإذا لأ انت عندك two options الحقيقة في عندك
+
+612
+00:45:43,830 --> 00:45:48,510
+multi graph multi graph فبتكون الشكل بهذا الشكل في
+
+613
+00:45:48,510 --> 00:45:51,920
+عندك parallel edges هي واحدة هي اتنينممكن يكون
+
+614
+00:45:51,920 --> 00:45:55,500
+تلاتة من اللي بحددها ال function الحقيقة ال
+
+615
+00:45:55,500 --> 00:45:59,700
+function هي اللي اتحددنا جداش عدد الطرق إذا كان
+
+616
+00:45:59,700 --> 00:46:02,420
+فيه زحمة كتير معناته انت مضطر تعمل أكتر من طريق
+
+617
+00:46:02,420 --> 00:46:05,320
+إذا كان لو الله مافيش زحمة المدينة هدى أو ال node
+
+618
+00:46:05,320 --> 00:46:07,620
+هدى و ال node هدى مافيش كتير حركة traffic مافيش
+
+619
+00:46:07,620 --> 00:46:11,040
+كتير عالي بينهم مافيش داعي تعمل طريقين مافيش داعي
+
+620
+00:46:11,040 --> 00:46:14,430
+تعمللهم طريقين مثلاهو يكون كويسة بالنسبالك زي ما
+
+621
+00:46:14,430 --> 00:46:18,150
+قلنا المثال طبعا هي ال nodes are cities و ال edges
+
+622
+00:46:18,150 --> 00:46:22,370
+هي segment of major highways ال highways اللي هي
+
+623
+00:46:22,370 --> 00:46:25,950
+الطرق السريعة احنا لما بتبدأنا نتكلم عن خانيونس
+
+624
+00:46:25,950 --> 00:46:28,970
+معناته بدهروح يا اما صلاح الدنيا يا اما بحر انا
+
+625
+00:46:28,970 --> 00:46:31,910
+بتكلم عن highway بشكل او باخر هو بين المدن يعني
+
+626
+00:46:31,910 --> 00:46:34,570
+بين المدن المتعرف عليه عالميا بين المدن معناته
+
+627
+00:46:34,570 --> 00:46:38,600
+اسمه highwayhighway مش زي المدن عندنا كلها زحمة في
+
+628
+00:46:38,600 --> 00:46:42,360
+زحمة فانت حتى على ال highway مافيش مجال تتحرك كتير
+
+629
+00:46:42,360 --> 00:46:49,020
+يعنى تمام Sodograph Sodograph لأ اختلفت شوية
+
+630
+00:46:49,020 --> 00:46:52,040
+الأمور على اعتبار ان صار في عندك مجال لل self loop
+
+631
+00:46:52,040 --> 00:46:55,320
+هنا اختلفت في جزئية ال self loop عندك multi graph
+
+632
+00:46:55,320 --> 00:46:58,300
+او multi graph مش مشكلة بس زادت معاك ال self loop
+
+633
+00:46:58,300 --> 00:47:01,500
+بمعنى ان والله في غزة صار بإمكانك تنزل على البحر
+
+634
+00:47:01,500 --> 00:47:05,990
+تلف من أول غزة لآخر غزة وترجع لنفس غزةصحيح؟ اه
+
+635
+00:47:05,990 --> 00:47:09,070
+الواحد زهجان بيروح بيعمله هيك لف بس على البحر و
+
+636
+00:47:09,070 --> 00:47:13,450
+بيرجع، صحيح؟ بدأ يمارجع من صلق .. من عمرو المختار
+
+637
+00:47:13,450 --> 00:47:16,510
+من عند رامسيسو مش عارف مين و .. و هودي و .. عند
+
+638
+00:47:16,510 --> 00:47:22,030
+السمك، بيلف تاني من عند ..طل الهوى و خلصناه بعمله
+
+639
+00:47:22,030 --> 00:47:24,930
+كده بس لفه و برجع هو ما طلعش من غزة فعليا ما طلعش
+
+640
+00:47:24,930 --> 00:47:28,710
+من غزة هو فقط علم عمل حاجة زي .. زي self .. زي
+
+641
+00:47:28,710 --> 00:47:33,570
+self loop تمام فإذا نفس الفكرة ل .. ل القديمة بس
+
+642
+00:47:33,570 --> 00:47:38,590
+الفكرة الوحيدة أنه .. وين راحت؟ ممكن يساووا بعض
+
+643
+00:47:38,590 --> 00:47:43,490
+هنا ماكانوش لا يساووا بعضU و V لا تسووا بعض هنا
+
+644
+00:47:43,490 --> 00:47:46,810
+الشرط الوحيد أو خلّيني أقول الإضافة إنه لأ مسموح
+
+645
+00:47:46,810 --> 00:47:50,310
+إنه يساوي بعض من U ل U بمشي الحال زي لما تكون مثلا
+
+646
+00:47:50,310 --> 00:47:54,650
+ال notes هذه هي ال camp sites أو مواقع التقييم في
+
+647
+00:47:54,650 --> 00:47:57,450
+في غابة مثلا و تطلع في الغابة
+
+648
+00:47:57,450 --> 00:48:00,610
+تلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلفلف
+
+649
+00:48:00,640 --> 00:48:03,840
+الكمب تبعك اكيد هترجع لنفس المخيم انت عملت لفة
+
+650
+00:48:03,840 --> 00:48:08,240
+ورجعت فهذه هي ال self loop self loop كمثال المرة
+
+651
+00:48:08,240 --> 00:48:10,900
+القادمة ان شاء الله بنكمل بال directed لما يصير
+
+652
+00:48:10,900 --> 00:48:13,560
+عندنا directed كيف بنتعامل معاه يعطيكوا العافية
+
+653
+00:48:13,560 --> 00:48:14,320
+برك الله فيك
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Us1h5VYFtm4_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Us1h5VYFtm4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f2588f9634f729b8eebd7755b5feec01af7db1b5
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Us1h5VYFtm4_raw.srt
@@ -0,0 +1,2668 @@
+1
+00:00:05,160 --> 00:00:09,380
+يعطيكوا العفو يا شباب نكمل اليوم في موضوع ال
+
+2
+00:00:09,380 --> 00:00:14,600
+relations تمام؟ فإن شاء الله تعالى نحاول نكمل في
+
+3
+00:00:14,600 --> 00:00:18,520
+موضوعنا و ناخد أمثل أكتر على ال characteristics
+
+4
+00:00:18,520 --> 00:00:20,240
+اللي أخدناها المرة اللي فاتت أو ال properties ..
+
+5
+00:00:20,240 --> 00:00:22,500
+مجموعات ال properties اللي أخدناهم اتكلمنا عن ال
+
+6
+00:00:22,500 --> 00:00:26,180
+reflexive اتكلمنا عن ال symmetry أو ال symmetric
+
+7
+00:00:26,180 --> 00:00:29,820
+relation و transitive .. ال transitivity أو
+
+8
+00:00:29,820 --> 00:00:33,380
+transitive relation و كنا وصلنا عندها و حلنا عليها
+
+9
+00:00:33,380 --> 00:00:37,740
+مثالو بعضكم كان بيسأل في طريقة أسهل من هيك نتعامل
+
+10
+00:00:37,740 --> 00:00:40,960
+فيها فخليني أقول اللي زي ما بيقولوا اطلعنا شمال
+
+11
+00:00:40,960 --> 00:00:43,780
+ويمين ومن هنا ومن هنا أساسا نحاول نلبّي إذا كان في
+
+12
+00:00:43,780 --> 00:00:47,240
+ولا لأ ففعلا لجينا حاجة يمكن أخف شوية نسبيا بنحل
+
+13
+00:00:47,240 --> 00:00:51,440
+فيها اليوم برضه أنفلة ان شاء الله تعالى بلكي وفرت
+
+14
+00:00:51,440 --> 00:00:56,860
+عليكمتمام ناخد مثال تاني على عملية ال combination
+
+15
+00:00:56,860 --> 00:00:59,840
+relation أو ال transitive كيف انا ممكن اركب اكتر
+
+16
+00:00:59,840 --> 00:01:01,760
+من function مع بعض على اعتبار ان ال transitivity
+
+17
+00:01:01,760 --> 00:01:04,720
+في النهاية انا ممكن اتعامل مع انه كان two
+
+18
+00:01:04,720 --> 00:01:08,220
+functions واحدة من a to b واحدة من b ل c هدى
+
+19
+00:01:08,220 --> 00:01:10,500
+function هدى function كيف احنا عملنا combination
+
+20
+00:01:10,500 --> 00:01:14,320
+between themأو combining ال two relations مع بعض
+
+21
+00:01:14,320 --> 00:01:19,260
+بكل بساطة مثل من الأمثلة اللي ببساطة ممكن ييجي في
+
+22
+00:01:19,260 --> 00:01:23,240
+الامتحان أو خليني اقول جبته قبل هيك في امتحان على
+
+23
+00:01:23,240 --> 00:01:27,040
+اعتبار ان احنا كنا متوقعين مثلا انه by default هو
+
+24
+00:01:27,040 --> 00:01:30,720
+مفهوميا معروف يعني لكن مش غلط خليني نشوفه اذا
+
+25
+00:01:30,720 --> 00:01:38,390
+افترضت ان ر واحد هيكل x و y بشرط إنه x أصغر من y
+
+26
+00:01:38,390 --> 00:01:42,210
+فهذه كأنني بتكلم عن إيش عن ال relation أصغر من و
+
+27
+00:01:42,210 --> 00:01:48,750
+R2 هي عبارة عن كل x و y بشرط إنه x أكبر من y وبكل
+
+28
+00:01:48,750 --> 00:01:53,850
+بساطة ممكن أقولك هاتلي R1 union R2 هي relations
+
+29
+00:01:53,850 --> 00:01:59,050
+إيش بتساوي اتحادهم
+
+30
+00:01:59,050 --> 00:02:02,190
+مع بعض إيش بيعطيه كل ال set
+
+31
+00:02:06,020 --> 00:02:13,760
+معناته بكل بساطة بقدر أسميها لا يساوي Sheikh بمعنى
+
+32
+00:02:13,760 --> 00:02:19,660
+أصغر .. أكبر .. أصغر من اتحاد أكبر من كل اللي أصغر
+
+33
+00:02:19,660 --> 00:02:22,580
+و كل اللي أكبر و لا تساوي فإذا بكل بساطة بقدر أقول
+
+34
+00:02:22,580 --> 00:02:29,920
+أنها relation لا يساوي لا يساوي تقطعهم أكيد تمام
+
+35
+00:02:29,920 --> 00:02:34,640
+R1 minus او difference R2 R1
+
+36
+00:02:38,910 --> 00:02:49,630
+R2 ممتاز R1 XOR R2 اللي هي إيش يعني يا الأولى يا
+
+37
+00:02:49,630 --> 00:02:55,090
+التانية وليس كلاهما مش هيك اتحاد هي نفس الاتحاد
+
+38
+00:02:55,090 --> 00:02:59,730
+ايوة هتعطي نفس الاتحاد بس مفهومها انت هتقول يا
+
+39
+00:02:59,730 --> 00:03:03,730
+الأولى يا التانية وليس كلاهما لأن انت كلنا عارفين
+
+40
+00:03:03,730 --> 00:03:05,710
+أيام ما اتكلمنا عن
+
+41
+00:03:12,170 --> 00:03:17,410
+فهذه الواحد واحد بس، فهي يا الأولى، يا التانية،
+
+42
+00:03:17,410 --> 00:03:21,170
+ولا ايه؟ وهذه تقاطؤهما، بمعنى أنه مايكونش موجود في
+
+43
+00:03:21,170 --> 00:03:28,210
+الاتنين، لأنه هات الصفر يعني برضه هيطلع لا يساوي،
+
+44
+00:03:28,210 --> 00:03:32,110
+برضه هيطلع عيش لا يساوي، المفهوم بسيط جدا، بس مع
+
+45
+00:03:32,110 --> 00:03:35,830
+ذلك ماكانش بيجيني إجابات، يعني خليني أقول إجلال
+
+46
+00:03:35,830 --> 00:03:39,690
+اللي كانوا يعرفوا، يتعاملوا معهافهي هذه ال
+
+47
+00:03:39,690 --> 00:03:43,550
+relations بسيطة جدا كيف انت تعمل combination
+
+48
+00:03:43,550 --> 00:03:47,930
+لمجموعة ال relations تبعتك تمام منها هتقودنا لإيش
+
+49
+00:03:47,930 --> 00:03:51,510
+عملية ال combining اللي احنا عملناها او ال
+
+50
+00:03:51,510 --> 00:03:54,670
+combination عادة لل relations هتاخدني لحاجة اسمها
+
+51
+00:03:54,670 --> 00:03:59,010
+composite relation تماما زي ما اتعاملنا مع ال
+
+52
+00:03:59,010 --> 00:04:01,210
+function عندي two functions و بدنا نعمل
+
+53
+00:04:01,210 --> 00:04:04,070
+combination between them اتصير الاتنين مع بعض كان
+
+54
+00:04:04,070 --> 00:04:07,240
+هم فيفانكشن واحدة كأنها فانكشن واحدة هذي أيها
+
+55
+00:04:07,240 --> 00:04:11,300
+مفهوم بال transfer function كأن انت عندك اكتر من
+
+56
+00:04:11,300 --> 00:04:13,080
+فانكشن عملته كله مع بعض صار اسمها transfer
+
+57
+00:04:13,080 --> 00:04:15,780
+function انت لك علاقة ال input ايش بده يطلع جوا
+
+58
+00:04:15,780 --> 00:04:18,120
+ايش اكم ال system فيه مش مشكلة اخدتوها ال transfer
+
+59
+00:04:18,120 --> 00:04:21,080
+function اخدتوا ال signalفي ال signal المفروض
+
+60
+00:04:21,080 --> 00:04:24,500
+أخدته حاجة هيك ان انت بتتعامل معاها ك block input
+
+61
+00:04:24,500 --> 00:04:27,680
+إيش بيطلع output إيش في جوا كام system في جوا كام
+
+62
+00:04:27,680 --> 00:04:30,840
+function في جوا مش إشكال فهنا نفس القصة هقول إن
+
+63
+00:04:30,840 --> 00:04:34,240
+والله أنا كله على بعض و هيك بديها إذا كان ال R
+
+64
+00:04:34,240 --> 00:04:39,420
+from A to B و ال S from B to C أنا بديها من A لC
+
+65
+00:04:39,420 --> 00:04:43,560
+مباشرة ففي الحالة هذه بنقول ال composite أو ال
+
+66
+00:04:43,560 --> 00:04:50,060
+composition اللي هي R and S بقولها S composeR
+
+67
+00:04:50,060 --> 00:04:57,320
+بتساوي كل زوج مرتب من A الأولى هنا ل C التانية هنا
+
+68
+00:04:57,320 --> 00:05:02,080
+تمام بغض النظر ال issue و ال system بغض النظر بيها
+
+69
+00:05:02,080 --> 00:05:07,260
+دي issue فانا بدي أجيبها كأنها علاقة أو كأنها بشرط
+
+70
+00:05:07,260 --> 00:05:14,020
+ان كل A relation مع بي و كل بي relation معC فبتطلع
+
+71
+00:05:14,020 --> 00:05:17,860
+A وC كمحصلة كمجموعة Total للكل هذا مشابه تمام لل
+
+72
+00:05:17,860 --> 00:05:21,180
+function composition لما أخدناها سابق أنا كنت بقول
+
+73
+00:05:21,180 --> 00:05:26,160
+ال function F compose ال function G وحلناها و
+
+74
+00:05:26,160 --> 00:05:28,220
+اعتقد مش عارف ايش جت في الامتحان برضه ايش جت في
+
+75
+00:05:28,220 --> 00:05:30,640
+الامتحان يمكن اهدم الحاجات اللي معظم حلها ماكنش
+
+76
+00:05:30,640 --> 00:05:34,080
+فيها مشكلة فS كيف؟
+
+77
+00:05:36,790 --> 00:05:42,090
+لأ في ناس حلته طيب S compose R ك relation بنفس
+
+78
+00:05:42,090 --> 00:05:45,290
+الفكرة خلاص معناته نرجع نعيد هينا شرحه عشان نثبت
+
+79
+00:05:45,290 --> 00:05:48,890
+أكتر مدام كان في مشكلة على كلامكوا طيب هو عبارة عن
+
+80
+00:05:48,890 --> 00:05:53,690
+construction لإيش باستخدام كل ال ordered pairs of
+
+81
+00:05:53,690 --> 00:05:58,210
+R وكل ال ordered pairs of S باستخدام كل الأزواج
+
+82
+00:05:58,210 --> 00:06:00,630
+المرتبة في ال function الأولى أو في ال relation
+
+83
+00:06:00,630 --> 00:06:02,730
+الأولى وكل ال functions المرتبة في ال relation
+
+84
+00:06:02,730 --> 00:06:08,280
+التانية بشرط أنه whereبشرط إنه ال second element
+
+85
+00:06:08,280 --> 00:06:13,100
+من R يتفق مع ال first element من من من ال S على
+
+86
+00:06:13,100 --> 00:06:17,320
+اعتبار أننا لاحظوا كيف كاتبينها فببدأ بمين؟
+
+87
+00:06:17,320 --> 00:06:21,960
+بالداخلية لأن هذا بالظبط لما يقول F compose G ما
+
+88
+00:06:21,960 --> 00:06:27,200
+أنتوا كلكم كنتوا بتكتبوها G of X check فإذا ببدأ
+
+89
+00:06:27,200 --> 00:06:33,530
+من X ك inputجوة هي فإذا التانية هي تعتبر الداخلية
+
+90
+00:06:33,530 --> 00:06:36,510
+ال internal function أصبحت تقفل فهي برضه ال
+
+91
+00:06:36,510 --> 00:06:41,090
+relation R R ببدأ بال input تبعها هذا اللي هيطلع
+
+92
+00:06:41,090 --> 00:06:44,210
+في ال relation ال total relation اللي هناخدها
+
+93
+00:06:44,210 --> 00:06:48,710
+لاحقا بس ال second term second term تبعها اللي هو
+
+94
+00:06:48,710 --> 00:06:52,330
+مين اللي هو ال G of X اللي هو الناتج ال output
+
+95
+00:06:52,330 --> 00:06:57,650
+فهذا بالظبط بالنسبالنا لو أنت بتكتب A وB بهذا
+
+96
+00:06:57,650 --> 00:06:58,490
+الشكل هذا input
+
+97
+00:07:01,420 --> 00:07:06,380
+وهذا output لل relation هاي input ال relation و
+
+98
+00:07:06,380 --> 00:07:08,860
+output ال relation فانت بتتعامل معها ان هو ده
+
+99
+00:07:08,860 --> 00:07:13,460
+input و output input و output فال output تبع ال
+
+100
+00:07:13,460 --> 00:07:17,320
+function الأولى هيها اللي هو ال g of x هو ال input
+
+101
+00:07:17,320 --> 00:07:21,480
+لمين لل F فلازم يتفقوا مع بعض إذا اتفقوا باخد ال
+
+102
+00:07:21,480 --> 00:07:28,200
+total المحصلة بناخد المحصلة إذا اتفقوا تمام أمثلة
+
+103
+00:07:28,200 --> 00:07:38,480
+على الموضوعهيفي عندك D .. بدنا نعمل S compose D D
+
+104
+00:07:38,480 --> 00:07:43,140
+و S كلا هما هما relation على ال 6 او ال universe
+
+105
+00:07:43,140 --> 00:07:47,700
+of this course واحد اتنين تلاتة اربعة عشان نطلق
+
+106
+00:07:47,700 --> 00:07:51,900
+أرقام واضحة عبارة عن ان D هي كل زوج مرتب A و B
+
+107
+00:07:51,900 --> 00:07:53,920
+بشرط ان B تسوي خمسة ناقص A
+
+108
+00:07:57,850 --> 00:08:02,090
+S هي عبارة عن كل زوج مرتب A وB بشرط أن A أقل من B
+
+109
+00:08:02,090 --> 00:08:06,570
+بدنا نجيب ال composition للاتنين مع بعض طبعا بتقدر
+
+110
+00:08:06,570 --> 00:08:09,010
+من أن انت عارف ال domain تبعك أو عارف ال universal
+
+111
+00:08:09,010 --> 00:08:13,510
+discourse تطلع كل ال relations اللي بتحقق دي عشان
+
+112
+00:08:13,510 --> 00:08:15,970
+نعمل check عندنا عليها يعني نبدأ و نعمل check
+
+113
+00:08:15,970 --> 00:08:20,630
+عليها عندك هاي دي كل الأزواج المرتبة من الأخر اللي
+
+114
+00:08:20,630 --> 00:08:24,110
+مجموحهم بيساوي 5 هذه المعادلة معناته اللي مجموحهم
+
+115
+00:08:24,110 --> 00:08:28,080
+بيساوي 5 مش هيكهي A لو أخدناها على الطرف التاني
+
+116
+00:08:28,080 --> 00:08:32,380
+فهي تصير A زائد B بتساوي خمسة فإذا المجموح بيساوي
+
+117
+00:08:32,380 --> 00:08:36,880
+خمسة هتنشوف هنا عندك واحد وأربعة و أكسها أربعة و
+
+118
+00:08:36,880 --> 00:08:39,760
+واحد عندك اتنين و تلاتة و تلاتة و اتنين هاي
+
+119
+00:08:39,760 --> 00:08:45,580
+الحالات اللي موجودة عندك طيب S الأقل من أخدناها
+
+120
+00:08:45,580 --> 00:08:49,420
+سابقاأخدناها سابقاً جيبناها مش هيك جيبناهم كلهم
+
+121
+00:08:49,420 --> 00:08:52,940
+فعندك واحد واثنين واحد تلاتة واحد واربعة اتنين
+
+122
+00:08:52,940 --> 00:08:56,380
+وتلاتة اتنين واربعة تلاتة واربعة خلصنا هاي جيبناها
+
+123
+00:08:56,380 --> 00:09:00,680
+طيب الآن هنحل بالطريقة اللي جالناها ان هي ال
+
+124
+00:09:00,680 --> 00:09:06,920
+second element من الأولى لازم يكون يتفق مع ال
+
+125
+00:09:06,920 --> 00:09:09,620
+first element من التانية مين الأولى ومين التانية
+
+126
+00:09:09,620 --> 00:09:14,460
+هاي الأولى لأن انت عشان تجيب ال function هذه ككل
+
+127
+00:09:14,460 --> 00:09:19,680
+لازم تطبق هذه الأولالـ G هي اللي تطبق الأول فبتخلص
+
+128
+00:09:19,680 --> 00:09:23,760
+الأولة ثم تاخد منها التانية خلينا نشوف الأولة
+
+129
+00:09:23,760 --> 00:09:30,300
+الأولة هي الأولة وال second في first من التانية
+
+130
+00:09:30,300 --> 00:09:33,760
+اتفق معها فش فإذا هذه خلصناها طب اه احنا قلنالكم
+
+131
+00:09:33,760 --> 00:09:42,660
+بدنا نستخدم طريقة تانية هي
+
+132
+00:09:42,660 --> 00:09:49,080
+عندك الواحد وأربعة الاتنين وتلاتةو عندك تلاتة و
+
+133
+00:09:49,080 --> 00:09:57,420
+اتنين و عندك اربعة و واحد الان بدك تاخد من S كل
+
+134
+00:09:57,420 --> 00:10:07,120
+اللي بيبدأ بالاربعة فش فإذا none من بيبدأ بتلاتة
+
+135
+00:10:11,030 --> 00:10:13,810
+عندك تنتين، اتنين و تلاتة و اتنين و أربعة، check
+
+136
+00:10:13,810 --> 00:10:22,290
+هي اتنين و تلاتة و اتنين و أربعة، لا في واحد و
+
+137
+00:10:22,290 --> 00:10:28,950
+اتنين و في عندك واحد و تلاتة و في عندك واحد و
+
+138
+00:10:28,950 --> 00:10:32,630
+أربعة، فبكل بساطة من هنا، هذه طبعا مش هتجيبلك إشي،
+
+139
+00:10:32,630 --> 00:10:38,140
+هذه هتجيبلك على طول اتنين و أربعةو هنا هيجيك تلاتة
+
+140
+00:10:38,140 --> 00:10:45,400
+و تلاتة و هيجيك تلاتة و أربعة هنا هيطلع لك أربعة و
+
+141
+00:10:45,400 --> 00:10:52,260
+واحد .. أربعة و اتنين و هيطلع أربعة و تلاتة و
+
+142
+00:10:52,260 --> 00:10:55,900
+هيطلع أربعة و أربعة فهي الناتج
+
+143
+00:10:58,680 --> 00:11:01,800
+فهي عندك الناتج خلاص بدل ما تقعد تلخم حالك في
+
+144
+00:11:01,800 --> 00:11:05,820
+التنتين حطهم بشكل جدول واحدة من التانية و خلاص
+
+145
+00:11:05,820 --> 00:11:10,640
+بتريح رأسك بتجيبهم مباشرة تمام هاي أكم عنصر عندك
+
+146
+00:11:10,640 --> 00:11:14,220
+طلع هناك ستة هاي الستة تبعوننا الستة اللي موجودة
+
+147
+00:11:14,220 --> 00:11:17,420
+عندنا طبعا بكل أريحية بتقدرنا عن طريق فكرة ال
+
+148
+00:11:17,420 --> 00:11:20,720
+function تجيبهم ممكن بفكرة ال function نفسها
+
+149
+00:11:20,720 --> 00:11:24,340
+تجيبهم ايش فكرة ال function انه كان عندك S compose
+
+150
+00:11:24,340 --> 00:11:30,280
+R S compose R هذهمعناته ال S هي ال function
+
+151
+00:11:30,280 --> 00:11:38,560
+التانية هي عبارة عن إيش؟ A أقل من B صح؟ هي A أقل
+
+152
+00:11:38,560 --> 00:11:45,560
+من B نكتبها فوق A
+
+153
+00:11:45,560 --> 00:11:49,120
+أقل من B فال input تبعها A طيب ال input تبعها
+
+154
+00:11:49,120 --> 00:11:53,040
+المفروض أن هو output تبع ال D output ال D إيش
+
+155
+00:11:53,040 --> 00:11:53,840
+بالساوي؟
+
+156
+00:11:56,310 --> 00:12:03,610
+خمسة ناقص A فإذا أصبحت هنا كأنه خمسة
+
+157
+00:12:03,610 --> 00:12:06,670
+ناقص
+
+158
+00:12:06,670 --> 00:12:13,930
+A أقل من B صح؟
+
+159
+00:12:13,930 --> 00:12:21,370
+طيب خد على الطرف التاني خمسة أقل من .. فإذا كل زوج
+
+160
+00:12:21,370 --> 00:12:23,630
+مرتب مجموعه أكبر من خمسة
+
+161
+00:12:27,680 --> 00:12:32,780
+يوجد أي زوج مرتب، مجموع أكبر من خمسة، ماذكرناهوش؟
+
+162
+00:12:32,780 --> 00:12:37,840
+طلع عليهم كلهم، فكر فيهم كلهم، هل في إشي انسيناه؟
+
+163
+00:12:37,840 --> 00:12:43,940
+فضل صحيح
+
+164
+00:12:43,940 --> 00:12:52,790
+أه صح، ليش؟لأن هذا كان الناتج اللي هي قيمة B طب
+
+165
+00:12:52,790 --> 00:12:55,930
+أنا عندي A المفروض ا agree with ال input تبع
+
+166
+00:12:55,930 --> 00:13:03,690
+التانية هاي input التانية إيش؟ مش المفروض أنه ناتج
+
+167
+00:13:03,690 --> 00:13:09,590
+الأولى هو input التانية طب input التانية وين في
+
+168
+00:13:09,590 --> 00:13:14,770
+المعادلة هذه؟ هو ال A ولا ال B ال input؟ أه
+
+169
+00:13:18,410 --> 00:13:23,330
+شوف كل زوج مرتب كتبنا توي و رجعنا محيناه أي زوج
+
+170
+00:13:23,330 --> 00:13:34,570
+مرتب a و b correlation input و output ال
+
+171
+00:13:34,570 --> 00:13:43,050
+b ناتج هنا ال b هذه ناتج التانيةتمام؟ هي input
+
+172
+00:13:43,050 --> 00:13:48,530
+التانية و اللي المفروض يحل محله output الأولى ما
+
+173
+00:13:48,530 --> 00:13:54,710
+هي مش .. برضه محيناها هي
+
+174
+00:13:54,710 --> 00:14:03,690
+ناتج الأولى اللي هي G هو input F هو input F عارف
+
+175
+00:14:03,690 --> 00:14:06,930
+أنه هاد بتركز فيها كويس في البكرا في الامتحان مين
+
+176
+00:14:06,930 --> 00:14:10,110
+ال input و مين ال output لازم تركزوا كويس فيها طيب
+
+177
+00:14:11,510 --> 00:14:15,670
+ففي الآخر طلعت total عندى انه مجموع هي كل زوج مرتب
+
+178
+00:14:15,670 --> 00:14:18,350
+الناتج ك total اللى هو تبع ال composition ناتج ال
+
+179
+00:14:18,350 --> 00:14:22,690
+composition هو اى زوج مرتب مجموعه اكبر من خمسة
+
+180
+00:14:22,690 --> 00:14:28,290
+مجموع اكبر من خمسة طيب هى كمان مثال كمان مثال
+
+181
+00:14:42,430 --> 00:14:49,050
+اش ميعطيني؟ ميعطيني برضه بده S compose R و R
+
+182
+00:14:49,050 --> 00:14:58,990
+ميعطيني إياها من 1 2 3 ل 1 2 3 4 تمام؟ يعني واضح
+
+183
+00:14:58,990 --> 00:15:06,130
+إنه هنا ال 6 ل R مختلف عن ال 6 ل S مختلفين عن بعض
+
+184
+00:15:06,130 --> 00:15:13,550
+طيب هذه ال R طيب التانية وميعطيني إياهاهتيجي تطلع
+
+185
+00:15:13,550 --> 00:15:17,770
+هتلاقي واحد اتنين تلاتة فعلا يتفق مع مين مع ال
+
+186
+00:15:17,770 --> 00:15:23,590
+input تبعها طيب النواتج واحد اربعة تلاتة اربعة
+
+187
+00:15:23,590 --> 00:15:27,210
+ماشي ماشي في بعض هم ماخدهمش مش مشكلة المهم انه
+
+188
+00:15:27,210 --> 00:15:32,720
+ماطلعش عنهمالمهم إنه ما طلعش عنهم تمام و S يطنيها
+
+189
+00:15:32,720 --> 00:15:40,520
+من 1,2,3,4 تتفقها مع مين؟ مع ناتج الأولى عشان أقدر
+
+190
+00:15:40,520 --> 00:15:43,660
+أقول أه بمشي الحال بقدر أكمل أعمل composition
+
+191
+00:15:43,660 --> 00:15:49,140
+لإيش؟ لـ 0,1,2 مش نفس هذه مافيش مشكلة تختلف فليكن
+
+192
+00:15:50,480 --> 00:15:54,860
+with و with ثانيها واحد اتنين تلاتة اربعة واحد
+
+193
+00:15:54,860 --> 00:15:58,260
+اتنين تلاتة اربعة مظبوطين هيهم فششه طالع برا ال
+
+194
+00:15:58,260 --> 00:16:02,640
+domain تبعهم طيب ال code domain ك output عبارة عن
+
+195
+00:16:02,640 --> 00:16:06,240
+ال واحد و اتنين صفر اه واحد اتنين صفر خلاص تمام
+
+196
+00:16:06,240 --> 00:16:11,040
+فششه خارج ال code domain فإذا مبدأيا منطق السؤال
+
+197
+00:16:11,040 --> 00:16:15,940
+صح يعني انتوا كم تقدروا تعبلوا عليناتجي ترجحها
+
+198
+00:16:15,940 --> 00:16:20,760
+دكتور استنى انت ميعطيني function ميعطيني ناتج هو
+
+199
+00:16:20,760 --> 00:16:25,080
+خارج ال code من اللي انت ميعطينيه check حقك تمام
+
+200
+00:16:25,080 --> 00:16:29,460
+الان ايش المطلوب بدنا هذه ال relation بدنا هذه ال
+
+201
+00:16:29,460 --> 00:16:36,140
+relation لا أكثر ولا أقل تمام عندي معادلة أولى
+
+202
+00:16:36,140 --> 00:16:39,080
+وعندي معادلة تانية بالطريقة اللي أول كتبناها
+
+203
+00:16:39,080 --> 00:16:44,900
+نستطيع نشتغلها هي عندي واحد واحد هي واحد وأربعةهي
+
+204
+00:16:44,900 --> 00:16:51,440
+اتنين و تلاتة، تلاتة و واحد، وهي عندي تلاتة و
+
+205
+00:16:51,440 --> 00:16:58,080
+أربعة هذه من مين؟ من R من
+
+206
+00:16:58,080 --> 00:17:05,360
+S واحد، مين بيبدأ بواحد؟ في غيره؟ كمان، مين بيبدأ
+
+207
+00:17:05,360 --> 00:17:11,260
+باربعة؟ أربعة و واحد في غيره أربعة و واحد؟ فش،
+
+208
+00:17:11,260 --> 00:17:15,110
+تلاتةفي عندك في الآخر تلاتة و واحد تلاتة و اتنين
+
+209
+00:17:15,110 --> 00:17:20,710
+واحد
+
+210
+00:17:20,710 --> 00:17:26,630
+برضه الواحد و صفر اربعة برضه الاربعة و واحد ماكان
+
+211
+00:17:26,630 --> 00:17:30,650
+فيه اش غيره ماكانش فيه اربعة و واحد خلاص بتهيألي
+
+212
+00:17:30,650 --> 00:17:38,110
+خلصت الجثة فإذا ال composition على طول ينتج واحد و
+
+213
+00:17:38,110 --> 00:17:41,010
+صفر واحد
+
+214
+00:17:42,620 --> 00:17:53,020
+واحد اتنين واحد و اتنين و اتنين تلاتة
+
+215
+00:17:53,020 --> 00:17:57,340
+صفر وهنا
+
+216
+00:17:57,340 --> 00:18:00,940
+في الآخر تلاتة و واحد
+
+217
+00:18:04,640 --> 00:18:08,360
+بعيدا عن لخمة انك تقعد تتبحهم واحدة ورا التانية مش
+
+218
+00:18:08,360 --> 00:18:12,480
+هيك اعملك جدولك على جنب و خلص حالك خلصنا بس بدك
+
+219
+00:18:12,480 --> 00:18:17,480
+تنجل البيانات منقلة عشان تسهل على حالك الشغل خلصنا
+
+220
+00:18:17,480 --> 00:18:20,640
+هيفي عندك واحدة اتنين تلاتة اربعة خمسة ستة هذه
+
+221
+00:18:20,640 --> 00:18:25,380
+طريقة في طريقة تانية او في طريقة تانية مادام في
+
+222
+00:18:25,380 --> 00:18:27,640
+طرق والله الناس بيحلوا فيها ليش ما نحل احنا كمان
+
+223
+00:18:27,640 --> 00:18:30,440
+فيها و نريح على حالنا صح طيب كل اه اتفضل
+
+224
+00:18:35,960 --> 00:18:38,860
+أحنا ولا من أول ال .. القصة .. من أول ال .. زي ما
+
+225
+00:18:38,860 --> 00:18:42,000
+بيقولوا المصاق ولا اتكلمنا في ال continuous نهائي
+
+226
+00:18:42,000 --> 00:18:47,660
+وإلا معناته مصاقنا بيفقد معناه ال function لأ ال
+
+227
+00:18:47,660 --> 00:18:51,120
+function كانت discrete لأن ال domain تبعنا كنا
+
+228
+00:18:51,120 --> 00:18:55,180
+بنتكلم discrete كانت natural number صحيح to
+
+229
+00:18:55,180 --> 00:18:57,840
+infinity from to infinity to infinity ال domain
+
+230
+00:18:57,840 --> 00:19:00,140
+تبعنا كان من صفر to infinity بس أنا بتكلم عن
+
+231
+00:19:00,140 --> 00:19:04,400
+natural number integersعمري ما قولت ال .. يعني حتى
+
+232
+00:19:04,400 --> 00:19:07,620
+لما روحنا لل summation لأنه بتكلم عن discrete انا
+
+233
+00:19:07,620 --> 00:19:10,820
+اطلاقا مش هنقول integration التكامل ال integration
+
+234
+00:19:10,820 --> 00:19:14,280
+ولا جربنا عليه لأنه القيم تبعتك كلها سواء بقول
+
+235
+00:19:14,280 --> 00:19:17,340
+domain أو codomain هي integers هي مجموعة ال
+
+236
+00:19:17,340 --> 00:19:22,700
+integers تمام اللهم صلي على سيدنا محمد okay هايبين
+
+237
+00:19:22,700 --> 00:19:28,140
+يعطيني إيش متذكرين لما مثلنا ال function بال
+
+238
+00:19:28,140 --> 00:19:34,530
+bipartateهي from بالنسبة ل R هي from إيش؟ واحد
+
+239
+00:19:34,530 --> 00:19:42,010
+اتنين تلاتة لإيش؟
+
+240
+00:19:42,010 --> 00:19:49,110
+واحد اتنين تلاتة أربعة تماماً
+
+241
+00:19:49,110 --> 00:19:59,230
+S من صفر واحد اتنين صفر واحد اتنين ال relationهات
+
+242
+00:19:59,230 --> 00:20:03,790
+ال relation اطوني ال relation هنا من واحد لواحد و
+
+243
+00:20:03,790 --> 00:20:14,430
+من واحد لاربعة من اتنين لتلاتة و
+
+244
+00:20:14,430 --> 00:20:20,390
+من تلاتة لوحد و من تلاتة لاربعة هاي خلصنا الأولى
+
+245
+00:20:20,390 --> 00:20:29,700
+التانية من واحد لصفر من واحد لاربعةعفوا من واحد
+
+246
+00:20:29,700 --> 00:20:34,460
+لاربع ايش انا اللي اخبطنا روحنا للتانية من اتنين
+
+247
+00:20:34,460 --> 00:20:39,140
+لصفر تلاتة
+
+248
+00:20:39,140 --> 00:20:50,700
+لواحد تلاتة لاتنين واربعة لواحد الان من المستمر من
+
+249
+00:20:50,700 --> 00:20:55,220
+البداية للنهاية ابدأ
+
+250
+00:20:55,730 --> 00:20:58,270
+خلّيني أخد اللون اللي ضايل، هي اللون اللي ضايل، هي
+
+251
+00:20:58,270 --> 00:21:06,990
+عندك واحدة صحيح؟ طيب، هذي إيش؟ واحد صفر، هي بدية
+
+252
+00:21:06,990 --> 00:21:10,510
+من الواحد ورايحة لمين؟ للصفر، فإذا أنا عندي واحد
+
+253
+00:21:10,510 --> 00:21:14,670
+وصفر طيب، بعد هيك إيه؟ خلص الواحدة دي كاملة، في
+
+254
+00:21:14,670 --> 00:21:19,630
+عندك طريق من هنا لهنا،
+
+255
+00:21:19,630 --> 00:21:25,550
+هي واحد وواحد، خلصنا هدول، خلصناه، اتنينهل فيه
+
+256
+00:21:25,550 --> 00:21:32,190
+طريق كامل للآخر؟ هاي اتنين و واحد متاهة كيف ألعاب
+
+257
+00:21:32,190 --> 00:21:35,050
+المتاهة اللي كنتوا زمان في المجلات في آخر صفحة في
+
+258
+00:21:35,050 --> 00:21:42,510
+المجلة متاهة هايها من اتنين لواحد كويس خلصناهم و
+
+259
+00:21:42,510 --> 00:21:45,810
+من اتنين لاتنين في عندك لسه كمان هاي طريق من اتنين
+
+260
+00:21:45,810 --> 00:21:51,730
+لاتنين طيب من تلاتة لصفر
+
+261
+00:21:54,390 --> 00:22:02,350
+مش كمان من تلاتة لواحد ضال اشي تاني خلصنا الباقى
+
+262
+00:22:02,350 --> 00:22:07,410
+كله مقطع مكملش من
+
+263
+00:22:07,410 --> 00:22:13,070
+تلاتة لواحد تلاتة لاتنين نفس النواتج اللي هناك خلص
+
+264
+00:22:13,070 --> 00:22:16,810
+فهي عندك طريقة جدول شوفوا اللي بتكون إياها
+
+265
+00:22:16,810 --> 00:22:19,990
+استخدموها كيف؟
+
+266
+00:22:20,680 --> 00:22:23,040
+هي .. بس انتوا .. يعني زي ما اقولوا بتتدللوا ..
+
+267
+00:22:23,040 --> 00:22:30,340
+ايش في اشي تاني؟ بندورلك احنا .. كيف؟
+
+268
+00:22:30,340 --> 00:22:33,360
+هي الطريقة الأولى زي ما قلنا الجدول بن .. بنحط
+
+269
+00:22:33,360 --> 00:22:36,960
+الأولى و بنشوف مين مرادفاتها من التانية عشان
+
+270
+00:22:36,960 --> 00:22:40,160
+نجيبها و بعدين هي عندك الطريقة هتنمحى كل هذا خلاص
+
+271
+00:22:40,160 --> 00:22:41,720
+احنا حطنالكوا الحل
+
+272
+00:22:49,220 --> 00:22:52,940
+حلو الان نعمل عملية ال representation كيف نعمل
+
+273
+00:22:52,940 --> 00:22:56,280
+representation لل function لل relation احنا بنتكلم
+
+274
+00:22:56,280 --> 00:22:59,660
+relation ففي عندى طريقتين عشان تمثيل ال relation
+
+275
+00:22:59,660 --> 00:23:03,240
+عشان نمثل اي relation في عندى اما بال .. بال
+
+276
+00:23:03,240 --> 00:23:07,220
+matrices بال matrix وهذا بنسميها 01 matrix بمعنى
+
+277
+00:23:07,220 --> 00:23:10,920
+إذا كان ال relation موجودة فبحطلها one إذا كانت
+
+278
+00:23:10,920 --> 00:23:13,860
+غير موجودة بنحطلها zero طريقة سهلة و بسيطة و مافيش
+
+279
+00:23:13,860 --> 00:23:15,960
+فيها مشكلة قدنا هتشوف في الأمثلة الطريقة التانية
+
+280
+00:23:15,960 --> 00:23:20,020
+هي ال directedGraph او Diagraph هنسميها بعد هيك
+
+281
+00:23:20,020 --> 00:23:23,580
+Direct Graph وهده هتدخلنا على الشبتر اللي بعد هيك
+
+282
+00:23:23,580 --> 00:23:27,220
+اللي هو لما نروح لل Graph فإذا هنجد ان كل ال
+
+283
+00:23:27,220 --> 00:23:30,480
+Relations اللي عبرنا عنها ان أي اشي في ال .. مش بس
+
+284
+00:23:30,480 --> 00:23:33,740
+في الرياضيات في الكون هي Relations معناه ذلك ان
+
+285
+00:23:33,740 --> 00:23:38,100
+تمثيلها ك Graphهتقودنا انه لازم نتعلم ال graph
+
+286
+00:23:38,100 --> 00:23:41,500
+فهنروح لل graph لكن احنا خلّينا الآن في البداية
+
+287
+00:23:41,500 --> 00:23:44,660
+الأول ان نشوف التمثيلات بتاعتنا هذه أول طريقة اللي
+
+288
+00:23:44,660 --> 00:23:48,540
+هي ال matrices ال 01 بكل بساطة بقول ان ال relation
+
+289
+00:23:48,540 --> 00:23:52,740
+عبارة عن matrix ف matrix لل relation R هي عبارة عن
+
+290
+00:23:52,740 --> 00:23:56,580
+bracket معناه ذلك ان هي مجموعة عناصر 2x2 3x3 15
+
+291
+00:23:56,580 --> 00:24:01,300
+6x3 اش ما تطلع تطلع بس في عندي كل عنصر يساوي واحد
+
+292
+00:24:01,300 --> 00:24:09,290
+اذا كانتI و J إذا كانت العنصر AI الإحداث الأول و
+
+293
+00:24:09,290 --> 00:24:13,550
+BJ الإحداث التاني يوجد بينهم علاقة فبحطه واحد ال
+
+294
+00:24:13,550 --> 00:24:16,730
+element هذا يعني automatically بقدر استنتج إيش
+
+295
+00:24:16,730 --> 00:24:21,890
+بقدر استنتج إنه ال input بحطه row وال output بحطه
+
+296
+00:24:21,890 --> 00:24:26,900
+columnتمام else إذا كان غير موجود ال relation هذه
+
+297
+00:24:26,900 --> 00:24:29,880
+يعني هذه لا يتتمي ل r بنحطها مكانها zero نحط
+
+298
+00:24:29,880 --> 00:24:34,760
+مكانها zero مثال ناخد مثلا علي likes الصبح بيجينا
+
+299
+00:24:34,760 --> 00:24:39,960
+علي بفضل أنه يشرب شاي okay مافيش مشكلة and juice
+
+300
+00:24:39,960 --> 00:24:42,780
+مالجه الشاي بياخد juice ممكن يهدي يهدي ويشرب اتنين
+
+301
+00:24:42,780 --> 00:24:45,780
+ويشرب اتنين المهم انه هذه الحاجتين اللي بيشربهم
+
+302
+00:24:45,780 --> 00:24:49,640
+سامي لأ بفضل ال juice لحاله بيجي الصبح على طول
+
+303
+00:24:49,640 --> 00:24:54,310
+ياخدالمشروب العصير و بشربه حسن لأ بفضل ال coffee
+
+304
+00:24:54,310 --> 00:25:00,610
+مزاج كويس بدنا نمثلهم الان ما بين ال people و ال
+
+305
+00:25:00,610 --> 00:25:05,110
+drink الان صارت تصنيف عندي people او مجموعة names
+
+306
+00:25:05,110 --> 00:25:08,950
+أسماء persons و ال output هو ال drink اللي بدهم
+
+307
+00:25:08,950 --> 00:25:15,010
+يشربوا كل واحد منهم فببساطة جدا هنقول في عندي علي
+
+308
+00:25:15,010 --> 00:25:24,610
+في عندي من التاني ساميو في عندى حسن هنا في عندنا
+
+309
+00:25:24,610 --> 00:25:28,870
+فوق هيكون عندنا ترتيبا نكتبها هى عند ال tea عند
+
+310
+00:25:28,870 --> 00:25:38,110
+مين كمان ال juice و ال coffee علي بحب ال tea اه ب
+
+311
+00:25:38,110 --> 00:25:46,090
+like ال tea و ال juice و صفر سامي خلاص
+
+312
+00:25:46,090 --> 00:25:51,580
+مثلناهابنقدر نمثلها، اتمثلناها، خلصناها، فإذا
+
+313
+00:25:51,580 --> 00:25:55,440
+برسمها بهذا الشكل، و بعدين ببدأ أفحصها، و أشوف إيش
+
+314
+00:25:55,440 --> 00:25:58,760
+الشواهد اللي عنده، بنشوف إيش الشواهد اللي عندنا،
+
+315
+00:25:58,760 --> 00:26:02,140
+إذا في إشي بقدر أستنتج منها أو .. أو لأ، إذا في
+
+316
+00:26:02,140 --> 00:26:05,160
+إشي ولا حاجة، تمام، هذه زي ما هي زي ما قلنا هنحلها
+
+317
+00:26:05,160 --> 00:26:08,460
+الآن، بس إحنا كويس إن كنا نفكر فيها مع بعض، فهي ه
+
+318
+00:26:08,460 --> 00:26:13,870
+.. بهذابهذا الشكل، الآن إذا كان بعمل ال relation
+
+319
+00:26:13,870 --> 00:26:16,930
+على نفسها، بمعنى إن ال domain هو نفس ال domain و
+
+320
+00:26:16,930 --> 00:26:20,470
+بدنا نطلع ال matrices، ال matrix هذه، هل بقدر أقرأ
+
+321
+00:26:20,470 --> 00:26:23,890
+منها نتائج أو بقدر أقرأ منها ال properties اللي
+
+322
+00:26:23,890 --> 00:26:26,870
+موجودة لل relation؟ أه بنقدر، بمعنى إن لو لجيت
+
+323
+00:26:26,870 --> 00:26:31,150
+ضياجنا لكله ones، معناته كل عنصر يوجد relation
+
+324
+00:26:31,150 --> 00:26:36,280
+بينه بين نفسه، معناته دي reflexiveصح؟ يعني واحد و
+
+325
+00:26:36,280 --> 00:26:39,700
+واحد او واحد و واحد موجودة اتنين و اتنين موجودة
+
+326
+00:26:39,700 --> 00:26:41,720
+تلاتة و تلاتة موجودة اربعة و اربعة موجودة ال
+
+327
+00:26:41,720 --> 00:26:44,480
+diagonal كله ones otherwise ايش ما يطلع يطلع مش
+
+328
+00:26:44,480 --> 00:26:47,580
+مشكلة بفرجش معناه كتير هنا يطلع فيه ones يطلع فيه
+
+329
+00:26:47,580 --> 00:26:50,860
+zeros فوق و تحت مش اشكال اللي بهمنا مين؟ diagonal
+
+330
+00:26:50,860 --> 00:26:54,040
+طيب في المقابل برضه إذا كان كل ال diagonal zeros
+
+331
+00:26:54,040 --> 00:26:59,380
+ال reflexive طب في هيك و هيك؟not reflexive و not
+
+332
+00:26:59,380 --> 00:27:03,040
+irreflexive لا هيك ولا هيك إذا كان طلع هنا واحد بس
+
+333
+00:27:03,040 --> 00:27:05,940
+خلاص معناته لا هادي ولا هادي لكن كله zeros
+
+334
+00:27:05,940 --> 00:27:08,120
+irreflexive تمام symmetric .. symmetric
+
+335
+00:27:08,120 --> 00:27:11,680
+automatically برضه الدياجونال بترسم خط و بتشوف
+
+336
+00:27:11,680 --> 00:27:15,240
+الخط هذا كأنه mirror بين الأنصر والتاني هل بتشبهه
+
+337
+00:27:15,240 --> 00:27:18,960
+ولا بتشبهوش يعني اتنين واحد هل بيسوي واحد و اتنين
+
+338
+00:27:18,960 --> 00:27:24,560
+خمسة و سبعة بيسوي سبعة و خمسة و هكذا اعكس ال row
+
+339
+00:27:24,560 --> 00:27:29,600
+بال columnأقول لك ببساطة جيب ل Transpose بيطلعوا
+
+340
+00:27:29,600 --> 00:27:33,740
+سوا بعض خلاص معناته symmetric إذا هي و ل Transpose
+
+341
+00:27:33,740 --> 00:27:36,200
+بتاعها بيطلعوا سوا بعض بالمنظر ما هي ما هو عشانك
+
+342
+00:27:36,200 --> 00:27:40,160
+بقولك الرسم على طول بيطلع شكلها من طريق تمثيل ال
+
+343
+00:27:40,160 --> 00:27:44,820
+matrices تبعتنا automatic ال antisymmetric ال
+
+344
+00:27:44,820 --> 00:27:47,840
+antisymmetric مبدأيا بالنسبة لل diagonal بيفرجش
+
+345
+00:27:49,640 --> 00:27:52,880
+بمعنى إن وجد جولنا إذا كان إيه بتسوي بيه بيمشي
+
+346
+00:27:52,880 --> 00:27:57,000
+الحال بتضل .. بتضل اسمها Anti-symmetric صح؟ إذا مش
+
+347
+00:27:57,000 --> 00:28:00,380
+موجودة برضه مش هتفرج معنا كتير أما اللي بهمنا ..
+
+348
+00:28:00,380 --> 00:28:04,440
+اللي بهمنا إنه كل عنصر مع المقابل إله ال symmetric
+
+349
+00:28:04,440 --> 00:28:08,800
+إله مايكونوش متشابهين إذا كان في واحد one بس إذا
+
+350
+00:28:08,800 --> 00:28:13,260
+كانوا zeros مش مشكلةلأن zeros معناته مش موجودة
+
+351
+00:28:13,260 --> 00:28:15,520
+relation أصلا، يعني لا الواحد التلاتة موجودة ولا
+
+352
+00:28:15,520 --> 00:28:18,740
+التلاتة واحد موجودة، خلاص، ليش بدك تغلب حالك فيهم؟
+
+353
+00:28:18,740 --> 00:28:21,620
+هيها، صفر و صفر بمشي الحال، ماشي، مش مشكلة، أما
+
+354
+00:28:21,620 --> 00:28:26,000
+واحد و واحد، لأ، واحد و واحد، لأ، فإذا هنا كأنه
+
+355
+00:28:26,000 --> 00:28:30,060
+أنا بفحص ال ones، هل يقابلها صفر؟ أما الصفر خلاص،
+
+356
+00:28:30,060 --> 00:28:33,710
+ما هي .. مفروض انه مايقابلوش oneبس أما صفر مقابل
+
+357
+00:28:33,710 --> 00:28:36,950
+صفر بمشي بمشي الحال ال relation أصلا مش أو العنصر
+
+358
+00:28:36,950 --> 00:28:41,750
+مش موجود ولا معكوسه موجود فخلصش أغلب حالي فيه مش
+
+359
+00:28:41,750 --> 00:28:46,230
+موجود مالهاش علاقة كيف؟
+
+360
+00:28:46,230 --> 00:28:52,090
+مش
+
+361
+00:28:52,090 --> 00:28:58,810
+بالضرورية ال diagonal ماتنساش ال diagonalإذا انت
+
+362
+00:28:58,810 --> 00:29:03,990
+بتتكلم عن ال other بقولك ماشي صح اللي هو اتجمعها
+
+363
+00:29:03,990 --> 00:29:07,910
+بس انسى ال diagonal كويس بدك تمل ال transpose و
+
+364
+00:29:07,910 --> 00:29:11,870
+اجمع مابيضلنا المشكلة في ال diagonal احنا قلنا ال
+
+365
+00:29:11,870 --> 00:29:16,070
+diagonal ممكن ياخد واحد صح؟ لما تجمع واحد مع واحد
+
+366
+00:29:16,070 --> 00:29:19,630
+ماهي ال transpose بيغيرش ال diagonal هتطلع معاك
+
+367
+00:29:19,630 --> 00:29:23,270
+واحد زاد واحد هيطلع فيه قيمة تطلع ال zeros تطلع ال
+
+368
+00:29:23,270 --> 00:29:26,970
+zeros صح؟ تمام طيب
+
+369
+00:29:29,680 --> 00:29:36,460
+طيب، إيش بتفرج عن الـ Asymmetric؟
+
+370
+00:29:36,460 --> 00:29:40,920
+آه، كيف أعرف إن والله .. معناته الفرق الوحيد إن
+
+371
+00:29:40,920 --> 00:29:46,250
+الـ code الـ diagonal، zerosبس هو الفرق اللي عن ال
+
+372
+00:29:46,250 --> 00:29:48,370
+.. ال .. ال .. ال antisymmetric ال antisymmetric
+
+373
+00:29:48,370 --> 00:29:51,610
+زي ما احنا قلنا ايش ما يطلع يطلع anything لأ ال
+
+374
+00:29:51,610 --> 00:29:55,210
+diagonal أما في ال asymmetric .. asymmetric لأ ال
+
+375
+00:29:55,210 --> 00:29:59,190
+diagonal zeros و يحقق نفس ما قلنا في ال .. في ال
+
+376
+00:29:59,190 --> 00:30:01,990
+antisymmetric ان كل واحد يقابله صفر .. كل واحد
+
+377
+00:30:01,990 --> 00:30:08,610
+يقابله صفر طيب ال directed graph .. directed graph
+
+378
+00:30:09,610 --> 00:30:14,110
+حالة خاصة من ال graphs برضه بإمكاننا انمثل فيها ال
+
+379
+00:30:14,110 --> 00:30:21,090
+relation بحيث انه ال graph يبنى على فكرة انه ال
+
+380
+00:30:21,090 --> 00:30:27,470
+graph مجموعة vertices، vertex، vertex قمم أو nodes
+
+381
+00:30:27,470 --> 00:30:31,010
+ال nodes هذه ال nodes هذه اللي هي كل node تمثل
+
+382
+00:30:31,010 --> 00:30:34,170
+element داخل ال domain تمثل element داخل ال domain
+
+383
+00:30:34,170 --> 00:30:39,150
+و ال edgesE edges ال graph هذه اللي هي ال relation
+
+384
+00:30:39,150 --> 00:30:44,870
+ال edges او ال arc السهم اللي هنستخدمه الأسهم اللي
+
+385
+00:30:44,870 --> 00:30:48,170
+هنستخدمها بحيث انه ال nodes اتفقنا هي ال vertices
+
+386
+00:30:48,170 --> 00:30:55,070
+او ال ال nodes ال E المفروض ان هي هتكون subset من
+
+387
+00:30:55,070 --> 00:31:00,890
+كل ال vertices cartesian product مع كل ال vertices
+
+388
+00:31:00,890 --> 00:31:07,010
+طيب لما يكون عند هنا مجموعة verticesNodes مع nodes
+
+389
+00:31:07,010 --> 00:31:11,690
+هنا و اقول Cartesian product يعني معناته full
+
+390
+00:31:11,690 --> 00:31:17,630
+connection كل ال relations الممكنة يعني هنا الأولى
+
+391
+00:31:17,630 --> 00:31:20,710
+مع الأولى و مع التانية و مع التالتة مع الأولى مع
+
+392
+00:31:20,710 --> 00:31:23,570
+التانية مع التالتة مع الأولى مع التانية مع التالتة
+
+393
+00:31:23,570 --> 00:31:29,040
+full connectionالان ال relation أكيد هي جزء من ال
+
+394
+00:31:29,040 --> 00:31:32,740
+.. من ال .. من ال full connection هذه عشان هيك
+
+395
+00:31:32,740 --> 00:31:37,300
+هتكون subset من .. من .. من ال .. ال vertices
+
+396
+00:31:37,300 --> 00:31:43,040
+كاملة كارتيزيا مع كل ال vertices مع كل ال vertices
+
+397
+00:31:43,040 --> 00:31:47,000
+بحيث أن هي عبارة عن arc أو links فتمثل ال edges
+
+398
+00:31:47,000 --> 00:31:52,810
+ففي الحالة اللي عندنا كل edge من هدولهي تمثل
+
+399
+00:31:52,810 --> 00:31:56,410
+relation يعني معناته علي بالنسبة لها العلاقة هذه
+
+400
+00:31:56,410 --> 00:32:02,030
+علاقة إيش؟ علاقة like علي like أو likes tea وعلي
+
+401
+00:32:02,030 --> 00:32:07,770
+likes juice تمام like الكافي لأ مافيش direction
+
+402
+00:32:07,770 --> 00:32:13,210
+عشان كده سميناها directed graph directed متجه
+
+403
+00:32:13,210 --> 00:32:20,330
+اتجاه واضح من إلى سامي فقط juice وحسن فقط coffee
+
+404
+00:32:21,420 --> 00:32:24,580
+أما بتقالة بسيطة برضه مش .. مش جثة كتير كبيرة نفس
+
+405
+00:32:24,580 --> 00:32:28,060
+فكرة الـ bipartate اللي احنا طوى حلنا فيها .. اللي
+
+406
+00:32:28,060 --> 00:32:34,820
+طوى اشتغلنا فيها ال space .. ال space .. ال space
+
+407
+00:32:34,820 --> 00:32:38,120
+.. ال space
+
+408
+00:32:38,120 --> 00:32:43,420
+.. ال space .. ال space .. ال space .. ال space ..
+
+409
+00:32:43,420 --> 00:32:43,420
+ال space .. ال space .. ال space .. ال space .. ال
+
+410
+00:32:43,420 --> 00:32:43,420
+space .. ال space .. ال space .. ال space .. ال
+
+411
+00:32:43,420 --> 00:32:45,860
+space .. ال space .. ال space .. ال space .. ال
+
+412
+00:32:45,860 --> 00:32:47,640
+space .. ال space .. ال space .. ال space .. ال
+
+413
+00:32:47,640 --> 00:32:47,640
+space .. ال space .. ال space .. ال space .. ال
+
+414
+00:32:47,640 --> 00:32:47,640
+space .. ال space .. ال space .. ال space .. ال
+
+415
+00:32:47,640 --> 00:32:50,400
+space .. ال space .. ال space .. ال space .. ال
+
+416
+00:32:50,400 --> 00:32:50,400
+space .. ال space .. ال space .. ال space .. ال
+
+417
+00:32:50,400 --> 00:32:50,400
+space .. ال space .. ال space .. ال space .. ال
+
+418
+00:32:50,400 --> 00:32:50,400
+space .. ال space .. ال space .. ال space .. ال
+
+419
+00:32:50,400 --> 00:32:50,400
+space .. ال space .. ال space .. ال space .. ال
+
+420
+00:32:50,400 --> 00:32:53,520
+space .. ال space ..الريه دي صارت الريه بس 2D
+
+421
+00:32:53,520 --> 00:32:57,020
+الريه اه بس بدك تخزينها كلها طبعا بدك تخزينها او
+
+422
+00:32:57,020 --> 00:33:01,160
+انك انت تبدأها zero كلها تعرفها ك zero و تخزين فقط
+
+423
+00:33:01,160 --> 00:33:07,130
+ال ones فقطتمام برضه نفس الكلام زي من لما كنا توفي
+
+424
+00:33:07,130 --> 00:33:10,550
+ال matrices و قولنا من ال matrices بقدر يكون فيه
+
+425
+00:33:10,550 --> 00:33:15,270
+indicator معين أفهم منه إيش الخاصية اللي موجودة
+
+426
+00:33:15,270 --> 00:33:18,270
+نفس الكلام برضه في ال graph لو لجيت في self loop
+
+427
+00:33:18,270 --> 00:33:22,950
+لكل ال nodes معناته في علاقة بين كل نقطة و نفسها
+
+428
+00:33:22,950 --> 00:33:26,210
+يعني واحد واحد موجود لو كانت هذه واحد وهذه اتنين
+
+429
+00:33:26,210 --> 00:33:29,470
+وهذه تلاتة هذه أربعة معناته واحد واحد موجودة في
+
+430
+00:33:29,470 --> 00:33:33,770
+علاقة بين واحد واحد يعني تمثل بواحد واحديوجد علاقة
+
+431
+00:33:33,770 --> 00:33:40,950
+من تلاتة لمين لتلاتة و هكذا من أربعة لأربعة فإذا
+
+432
+00:33:40,950 --> 00:33:45,650
+كان هذا self-loop لكل ال nodes بنسميها reflexive
+
+433
+00:33:45,650 --> 00:33:52,650
+طيب ولا loop موجود reflexive طيب طلع loop واحد لا
+
+434
+00:33:52,650 --> 00:33:56,890
+reflexive ولا reflexive لا بتصبط لا هيك ولا هيك
+
+435
+00:33:56,890 --> 00:34:02,170
+طيب في ال symmetric كل سهم رايح لازم يكون فيه سهم
+
+436
+00:34:02,170 --> 00:34:08,870
+جايby directional array check هتصير by directional
+
+437
+00:34:08,870 --> 00:34:14,670
+link بمعنى مدام فيه واحد و تلاتة لازم يكون فيه
+
+438
+00:34:14,670 --> 00:34:19,270
+تلاتة و واحد تلاتة و اتنين لازم يكون في المقابل
+
+439
+00:34:19,270 --> 00:34:23,570
+اتنين و تلاتة and so on and so on فبهذا الشكل
+
+440
+00:34:23,570 --> 00:34:26,310
+بنعرف automatic بجهة بتطل عليه اه هادي symmetric
+
+441
+00:34:26,310 --> 00:34:34,870
+طيب ال antisymmetric السهم رايح برجعشإلا للنقطة مع
+
+442
+00:34:34,870 --> 00:34:37,750
+نفسها، إلا إذا كان في مع النقطة مع نفسها، بمشي
+
+443
+00:34:37,750 --> 00:34:43,110
+الحل، لأن هو يرايح و راجع، لأ اللي بطلع برجعش،
+
+444
+00:34:43,110 --> 00:34:45,690
+اللي بطلع برجعش، فهذه بتسميها Anti-symmetric الـ
+
+445
+00:34:45,690 --> 00:34:50,750
+Asymmetric اللي بطلع برجعش وفيه self-loop، فبتصير
+
+446
+00:34:50,750 --> 00:34:53,870
+Asymmetric، تصبح Asymmetric
+
+447
+00:34:57,080 --> 00:35:00,360
+Closures of relations الان بيكون عندك relation
+
+448
+00:35:00,360 --> 00:35:05,440
+وبنقولك الله كملها او قربها closure اللي هو close
+
+449
+00:35:05,440 --> 00:35:10,120
+يعني من close قربها closures of relations او تقريب
+
+450
+00:35:10,120 --> 00:35:12,980
+ل relation معينة لما يقولك الله فيها عندك relation
+
+451
+00:35:12,980 --> 00:35:19,320
+جرب ليها انها تصبح reflexive معنى ذلك مش تروحزي
+
+452
+00:35:19,320 --> 00:35:22,860
+الناس اللي بدهم يتشاطروا يروح يكتب ليه ال .. ال
+
+453
+00:35:22,860 --> 00:35:26,060
+Cartesian product كلها وقوللي هي صارت .. طب أنا
+
+454
+00:35:26,060 --> 00:35:29,720
+عارف أنه بال Cartesian product بتصير كل شيء لما
+
+455
+00:35:29,720 --> 00:35:32,140
+تعمللي ال Cartesian product لل relation مع نفسهم
+
+456
+00:35:32,140 --> 00:35:34,980
+كلهم على بعض و تقولليها يعني ما هتطلعجيهم كلهم،
+
+457
+00:35:34,980 --> 00:35:38,900
+هذا مش صح فانا هنا بتكلم عن smallest .. smallest
+
+458
+00:35:38,900 --> 00:35:42,560
+number of elements بدك تضيفهم لل relation عشان
+
+459
+00:35:42,560 --> 00:35:47,970
+تصبح بتحققproperty معينة ال reflexive معناته كل
+
+460
+00:35:47,970 --> 00:35:50,290
+اللي انا بدي اعمله بدي اضيفه مع ال identity بس
+
+461
+00:35:50,290 --> 00:35:55,710
+يعني اعمل relation اتحاد مع ال identity بس الشيء
+
+462
+00:35:55,710 --> 00:35:59,930
+ال identity هي ال 1122 اللي هي ال diagonal يعني
+
+463
+00:35:59,930 --> 00:36:02,910
+تلتة و تلتة اربع و اربع انا عارف ان انت لو ضفت
+
+464
+00:36:02,910 --> 00:36:06,610
+بالمرة يعني مع جملة اللي ضفته خمسة و سبعة ماشي
+
+465
+00:36:06,610 --> 00:36:10,570
+بمشي الحال بس مالهاش لزوم فعلامايلها لزوم فلأ بطلت
+
+466
+00:36:10,570 --> 00:36:16,130
+smallest set of elements بدك تعملها اتحاد لأ فهنا
+
+467
+00:36:16,130 --> 00:36:19,350
+في الحالة هذه بدك تجرب لل reflexive فقط اتحاد مع
+
+468
+00:36:19,350 --> 00:36:24,250
+ال identity و بس مع ال identity و بس كويس لما بدك
+
+469
+00:36:24,250 --> 00:36:29,830
+تعمل symmetric closure او تقريب انها تصبح
+
+470
+00:36:29,830 --> 00:36:33,590
+symmetric على طول بعملها ايش اتحاد مع ال inverse
+
+471
+00:36:33,590 --> 00:36:42,430
+تبعها او اتحاد معtranspose بمعنى كل واحد بحطه صفر
+
+472
+00:36:42,430 --> 00:36:47,010
+و كل صفر بحطه واحد هاي ال inverse تبعنا على فكرة
+
+473
+00:36:47,010 --> 00:36:49,690
+بتلاعش نفس ال transpose بتلاعش نفس ال transpose
+
+474
+00:36:49,690 --> 00:36:52,930
+فإذا مع ال inverse الأكتر واقعيا أن أحنا نقول مع
+
+475
+00:36:52,930 --> 00:36:55,790
+ال inverse عشان نكون أكتر دقة ال inverse اللي هي
+
+476
+00:36:55,790 --> 00:36:59,010
+ال .. ال .. ال .. كل واحد بتحطه صفر و كل صفر بتحطه
+
+477
+00:36:59,010 --> 00:37:05,950
+واحد عشان تصبح symmetric كل اه
+
+478
+00:37:06,980 --> 00:37:10,460
+مع ال inverse ال inverse ايش مقصود فيها بمعنى انه
+
+479
+00:37:10,460 --> 00:37:19,380
+لو كان عندك واحد و اتنين هنا
+
+480
+00:37:19,380 --> 00:37:23,960
+واحد و اتنين هذا ال answer موجود المفروض انه برضه
+
+481
+00:37:23,960 --> 00:37:30,860
+اتنين و واحد هذا يصبح موجود فالمفروض هذا ال
+
+482
+00:37:30,860 --> 00:37:37,570
+inverse تبعه ك mirror حوالين ال diagonalكميرور
+
+483
+00:37:37,570 --> 00:37:43,530
+حوالين ال diagonal طيب ال transpose لو حولنا
+
+484
+00:37:43,530 --> 00:37:47,590
+transpose هيكون كل واحد عندك احنا قلنا اتحاد صح اه
+
+485
+00:37:47,590 --> 00:37:53,450
+اتحاد اتحاد بظبط على فكرة transpose لو لفناهم
+
+486
+00:37:53,450 --> 00:38:00,930
+اتحاد كل عنصر هنا هيجي للي مقابله هيجي للي مقابله
+
+487
+00:38:00,930 --> 00:38:03,850
+ال diagonal ايش بده يصير فيه بفرجش معناه
+
+488
+00:38:08,230 --> 00:38:13,810
+مع ال Transpose بيظبط انك تعمل اتحاد مع ال
+
+489
+00:38:13,810 --> 00:38:22,950
+Transpose بتاع ال relation نفسها لأ
+
+490
+00:38:22,950 --> 00:38:25,730
+هنا مش مقصود ال inverse اللي بتعمله احنا هنا متكلم
+
+491
+00:38:25,730 --> 00:38:29,970
+عن binaryمش ال inverse اللي انت متعود عليه ال
+
+492
+00:38:29,970 --> 00:38:32,610
+numerical inverse اللي هو بدك تجيب على المحدد أو
+
+493
+00:38:32,610 --> 00:38:35,910
+بدك تحقق .. لأ لأ لأ مختلف هنا المعنى المعنى هنا
+
+494
+00:38:35,910 --> 00:38:39,390
+تمام مختلف هنا transpose بمعنى كل واحد هتحط صفر و
+
+495
+00:38:39,390 --> 00:38:43,990
+كل صفر هتحط مقابله كويس فهي transpose لأ هنا
+
+496
+00:38:43,990 --> 00:38:48,530
+transpose على أساس تضمن أنه كل relation موجودة لما
+
+497
+00:38:48,530 --> 00:38:50,990
+تعمل ال transpose معناته عكسه أصبح موجود عكس
+
+498
+00:38:50,990 --> 00:38:57,470
+العنصر مش عكس ال matrixكمان مرة عكس الأنصر مش عكس
+
+499
+00:38:57,470 --> 00:39:01,970
+ال matrix لما نقول inverse ال inverse هنا element
+
+500
+00:39:01,970 --> 00:39:06,670
+by element و ليس ال inverse اللي انتوا متخيلونه
+
+501
+00:39:06,670 --> 00:39:09,790
+تبع المصفوفة ال inverse المصفوفة هتطلعلك اشي تاني
+
+502
+00:39:09,790 --> 00:39:14,110
+مختلف تماما انت بتتعامل معاها بطلت ك logic احنا
+
+503
+00:39:14,110 --> 00:39:16,410
+بنتعامل logic ليش؟ لأنه binary معناته انا ايش
+
+504
+00:39:16,410 --> 00:39:20,370
+بتعامل معها logic يا موجود يا غير موجود مش الواحد
+
+505
+00:39:20,370 --> 00:39:28,520
+هذا مش رقمالواحد مش رقم هو دلالة وجود بس ان ال
+
+506
+00:39:28,520 --> 00:39:33,200
+relation موجودة أما ليس رقم واحد اه هي true او
+
+507
+00:39:33,200 --> 00:39:39,120
+false تمام الأهم اللي هي ال transitive closureاللي
+
+508
+00:39:39,120 --> 00:39:42,860
+هي transitive كيف انا ممكن اعملها طبعا هذه هتقودنا
+
+509
+00:39:42,860 --> 00:39:45,180
+هي ال transitive هي اللي هتقودنا اصلا شوية شوية
+
+510
+00:39:45,180 --> 00:39:49,160
+شوية لل graphs اللي هنبدأ من الأسبوع القادم نبدأ
+
+511
+00:39:49,160 --> 00:39:52,880
+نشتغل عليها و نتكلم عنها فشوية شوية هتبدأ تقودنا
+
+512
+00:39:52,880 --> 00:39:56,300
+للموضوع ده بس خليني نبدأ هنا لو يكون عندك لما يكون
+
+513
+00:39:56,300 --> 00:40:05,930
+عندك a و b b و c موجودين بدك aو C بدك A و C مش هيك
+
+514
+00:40:05,930 --> 00:40:10,350
+فهذه الإشكالية كيف بدك تجيبها؟ بنجيبها من خلال أن
+
+515
+00:40:10,350 --> 00:40:13,930
+نقول معناته R Star هذه اللي هي هتظهر ال relation
+
+516
+00:40:13,930 --> 00:40:19,470
+كيف هتصبح عشان أقول إن هي أصبحت Transitive اتحاد
+
+517
+00:40:19,470 --> 00:40:25,830
+ال relation to the power N N
+
+518
+00:40:25,830 --> 00:40:31,740
+تنتمي ل Z أو integer Zهذه بدها جثة عشان نفهمها ..
+
+519
+00:40:31,740 --> 00:40:38,560
+بدها جثة عشان نفهمها R تربية نبدأها شوي شوي عشان
+
+520
+00:40:38,560 --> 00:40:42,380
+بعدين نصلّى ال N تبعته عشان نصلّى ال N تبعته هذه
+
+521
+00:40:42,380 --> 00:40:47,980
+معناته مش R في R و بعدين تروحوا تضربوها صف عمود و
+
+522
+00:40:47,980 --> 00:40:54,620
+صف عمود و تعملولنا ال .. هذه معناها compose
+
+523
+00:40:54,620 --> 00:41:02,390
+R هذه معناها R compose Rطيب لما تصير R compose R
+
+524
+00:41:02,390 --> 00:41:06,370
+يعني معناه ذلك أن هذه علاقة ثنائية فبقدر أقول ر
+
+525
+00:41:06,370 --> 00:41:09,550
+تربيع فإذا تنتمي ل R تربيع ليش لأنه عملت
+
+526
+00:41:09,550 --> 00:41:13,750
+connection أولى connection تانية فال graph هنا لو
+
+527
+00:41:13,750 --> 00:41:17,310
+بتتعامل معاه ك graph ال graph هو أصبح عبارة عن two
+
+528
+00:41:17,310 --> 00:41:22,770
+ways طريقين طريق أول انتهى من حيث بدأت الطريق
+
+529
+00:41:22,770 --> 00:41:27,950
+التاني اللي هي ال node الوسطية زي ما شفناها لما
+
+530
+00:41:27,950 --> 00:41:33,380
+رسمنا الرسم هناشيك مش رسمنا R وصلتني ل ال layer
+
+531
+00:41:33,380 --> 00:41:38,600
+اللي في النص و بعدين S وصلتني لل output فكان عنده
+
+532
+00:41:38,600 --> 00:41:42,240
+طريقين الحقيقة نتيجة two relations نتيجة two
+
+533
+00:41:42,240 --> 00:41:45,060
+relations ال two relations هدول هم نفس ال relation
+
+534
+00:41:45,060 --> 00:41:51,240
+هنقول R و R فبتصبح R تربيع ممتاز الآن لما تعمل
+
+535
+00:41:51,240 --> 00:41:56,680
+اتحاد ل R اتحاد في الآخر
+
+536
+00:41:59,400 --> 00:42:03,240
+مقار تربيع، مقار تكعيب، مقار to the power of 4،
+
+537
+00:42:03,240 --> 00:42:06,020
+مقار to the power of 5، مقار to the power of 6، to
+
+538
+00:42:06,020 --> 00:42:09,140
+infinity، الناتج تبع الارز ال .. ال .. ال
+
+539
+00:42:09,140 --> 00:42:13,840
+composition هدا هيطلع transitive طب هنعمل .. هنضل
+
+540
+00:42:13,840 --> 00:42:19,560
+نعمل هيك كتير؟ لأ، هت .. بالظبط، هتصل لمرحلة، بعد
+
+541
+00:42:19,560 --> 00:42:25,310
+اتنين، تلاتة، ال relation هتبطل تتغير، ابتجفبعد
+
+542
+00:42:25,310 --> 00:42:29,390
+مرحلتين تلاتة هتجي في ال relation خلاص هتلاقي انه
+
+543
+00:42:29,390 --> 00:42:33,610
+كل ما بتعمل composition بتطلع نفسه ليش؟ لأن انت في
+
+544
+00:42:33,610 --> 00:42:36,510
+الآخر طلعت composition ال composition هذا صح طلع
+
+545
+00:42:36,510 --> 00:42:40,750
+معاك فهذا طلعت كأنه R تربيع تساوي مجموعة عناصر
+
+546
+00:42:40,750 --> 00:42:44,370
+خلاص تمام طب هذي إيش بتعملها؟ بتعمل R تربيع
+
+547
+00:42:44,370 --> 00:42:50,310
+compose R طيب هيطلع معاك إشي لما يتساووا الاتنين
+
+548
+00:42:50,310 --> 00:42:55,990
+هتلاقي انه ماتغيرش إزيادة معاك واجفخلاص بتجف و
+
+549
+00:42:55,990 --> 00:43:08,690
+بتعمل إيش اتحاد كل اللي جبته سابق و بس cool فضل صح
+
+550
+00:43:08,690 --> 00:43:12,390
+هي نفس ال function ما أنا قاعد بقولك أنت بتتعامل
+
+551
+00:43:12,390 --> 00:43:16,150
+مع نفس ال domain من ال function لنفسها هل وجد عندك
+
+552
+00:43:16,150 --> 00:43:20,230
+مشكلة أنك تقول x تربيعه مش مضروع x مضروع في y x
+
+553
+00:43:20,230 --> 00:43:25,360
+تربيع هي في نفسها إيش المشكلة عندك يعني فيها؟X في
+
+554
+00:43:25,360 --> 00:43:32,700
+نفسها هذه كأنك انت بتعمل loop انت بتعمل loop جاعد
+
+555
+00:43:32,700 --> 00:43:37,760
+هلوقت انت لما أخدت ال recursion ال recursive code
+
+556
+00:43:37,760 --> 00:43:42,060
+كان عبارة عن إيش؟ انتوا اشرحولي ال recursive code
+
+557
+00:43:42,060 --> 00:43:46,820
+لما كنتوا بتكتبوه هو كان عبارة عن إيش؟ممتاز لما
+
+558
+00:43:46,820 --> 00:43:52,740
+وصلت في الآخر ل ال initial state تمام؟ كويس و رجعت
+
+559
+00:43:52,740 --> 00:43:55,040
+ضربتها في اللي جابلها طب مش هدوا صار مضربين في
+
+560
+00:43:55,040 --> 00:43:58,560
+بعض؟ رجعت ضربتهم في اللي جابلها بواحدة طب ما هي
+
+561
+00:43:58,560 --> 00:44:02,740
+صارت R تربيع في Rطب صارت R تكييب ما انت عملتها
+
+562
+00:44:02,740 --> 00:44:07,640
+كأنك نفذت ال code تلت مرات في الرابعة انت بتمارسوا
+
+563
+00:44:07,640 --> 00:44:11,620
+الكلام هذا بس يمكن شوية مش مربط الدنيا مع بعض فهي
+
+564
+00:44:11,620 --> 00:44:15,200
+نفس الفكرة يعني ليش استغربتها من ال R هنا وماكنتش
+
+565
+00:44:15,200 --> 00:44:18,260
+مستغربها لما كنت بتعملها في الأ code تبعتك هى نفس
+
+566
+00:44:18,260 --> 00:44:23,760
+الفكرة R مع نفسها مع نفسها ايش المشكلة relation
+
+567
+00:44:23,760 --> 00:44:27,220
+لنفسها بمعنى انت بتاخد من نفس ال domain ال input
+
+568
+00:44:27,220 --> 00:44:31,470
+هو نفسهال output تبعك زي ال natural number مثلا زي
+
+569
+00:44:31,470 --> 00:44:34,290
+ال natural number فهنا عشان هيك هتلاقي بعضهم
+
+570
+00:44:34,290 --> 00:44:37,410
+بيقولك infinity بس هذا بيكون وصحة كتير زيادة بس هي
+
+571
+00:44:37,410 --> 00:44:41,590
+الأصح ان هي تنتمي ل integer يعني بمعنى اتنين تلاتة
+
+572
+00:44:41,590 --> 00:44:45,250
+خمسة عشرة هيجف في الآخر هتجف في الآخر بتعمللهم
+
+573
+00:44:45,250 --> 00:44:50,610
+اتحاد مع بعضهم طيب ناخد مثال هي في عندنا مثال كويس
+
+574
+00:44:50,610 --> 00:44:56,030
+المثال اللي موجود عندنا هنا عشان اوضحلكي الجصة
+
+575
+00:44:56,030 --> 00:45:01,500
+الأخيرة هذهأتوقعت أنه هدى هتسألوا فيها فقلنا نجهز
+
+576
+00:45:01,500 --> 00:45:05,180
+حالنا مسبقا نجيب لنا مثال مع بعض بالمرة لو قلت R
+
+577
+00:45:05,180 --> 00:45:08,120
+هي عبارة عن relation على ال set A و ال powers
+
+578
+00:45:08,120 --> 00:45:11,400
+بتاعتنا هي R to the power N و N هنا واحد اتنين
+
+579
+00:45:11,400 --> 00:45:15,480
+تلات اربع جد ما انت محتاج power جد محتاج معاك
+
+580
+00:45:15,480 --> 00:45:21,960
+power بنعرفها recursively by R one بتساوي R ف to
+
+581
+00:45:21,960 --> 00:45:25,060
+the power one معناته هي R لحالها و لاحظ
+
+582
+00:45:25,060 --> 00:45:31,260
+recursivelyتمام و R to the power n plus one هي R
+
+583
+00:45:31,260 --> 00:45:36,580
+to the power n compose مع R compose مع R يعني كأنه
+
+584
+00:45:36,580 --> 00:45:40,220
+ال output تبع حصار input ل ال code اللي جابلها
+
+585
+00:45:40,220 --> 00:45:43,280
+بنتو هيك بتعمله بتروح بتاخد ال output من ال code
+
+586
+00:45:43,280 --> 00:45:46,860
+اللاحق عساس انه ال output تبعه هو ال input للكود
+
+587
+00:45:46,860 --> 00:45:52,180
+السابق لهو هكذا، هحنعمل نفس الفكرة، نفس الجثة طيب
+
+588
+00:45:52,180 --> 00:45:55,740
+ما .. okay ففي الحالة هذه ال relation R on a set A
+
+589
+00:45:55,740 --> 00:46:00,560
+is transitive if and only if لاحظ R to the power N
+
+590
+00:46:00,560 --> 00:46:06,180
+subset of R الأرقام هتقول إنه كل ما بضربها مع
+
+591
+00:46:06,180 --> 00:46:12,620
+نفسها هلاجي إن الناتج هو subset منها إذا كانت
+
+592
+00:46:12,620 --> 00:46:13,860
+transitive
+
+593
+00:46:15,730 --> 00:46:19,230
+طيب إذا ماكنتش transitive، هتظهر عناصر جديدة، فمش
+
+594
+00:46:19,230 --> 00:46:23,750
+هتكون subset أصلت؟
+
+595
+00:46:23,750 --> 00:46:29,290
+إذا كانت transitive، معناته طول ما أنت بتعمل R، R
+
+596
+00:46:29,290 --> 00:46:32,510
+compose, R compose, R compose مش هيطلعلك أي
+
+597
+00:46:32,510 --> 00:46:38,230
+element زيادة، معناته هي من الأساس كانت transitive
+
+598
+00:46:39,070 --> 00:46:44,970
+لكن جبت R2، R تربيع، R تربيع هيطلعلك عناصر متشابهة
+
+599
+00:46:44,970 --> 00:46:48,070
+ويمكن يطلعلك عنصر كمان زيادة أو اتنين، زيادة
+
+600
+00:46:48,070 --> 00:46:54,010
+ماكنوش في R الأصلية طيب، R3 تطابر 3، يمكن يطلعلك
+
+601
+00:46:54,010 --> 00:46:57,450
+كمان عنصر زيادة، طب R4 نفس R3، خلاص معناته مش
+
+602
+00:46:57,450 --> 00:47:01,320
+هتختلف معاك إش لو ضربت أكتر من هيك بعد هيكلأن زي
+
+603
+00:47:01,320 --> 00:47:06,340
+ما كانت R تلاتة اتتك R أربعة وما تغيرش فيها إشي مع
+
+604
+00:47:06,340 --> 00:47:08,900
+R أربعة لو ضربتها برضه في R هترجع هي هي مش هتتغير
+
+605
+00:47:08,900 --> 00:47:12,360
+فيها إشي فهتصل لمرحلة أنه واجف شوف إيش العناصر
+
+606
+00:47:12,360 --> 00:47:15,080
+اللي انضافت إذا إزيادة عندك هدول اللي بدك تضيفهم ل
+
+607
+00:47:15,080 --> 00:47:19,600
+R فبتضمن أن R صارت Transitive لأنه لو رجعت كررت
+
+608
+00:47:19,600 --> 00:47:24,080
+نفس الكلام مش هيطلع ولا عنصر زيادة عن Rالمعنى ذلك
+
+609
+00:47:24,080 --> 00:47:28,440
+أنه هتطلع كل R to the power N subset من R ففي
+
+610
+00:47:28,440 --> 00:47:30,600
+الحالة يبقى الجدول عاملوا عنا transitive أنت
+
+611
+00:47:30,600 --> 00:47:35,440
+المطلوب منك أنه لأ هي مش هتكون subset و لا تساوي
+
+612
+00:47:35,440 --> 00:47:39,300
+ليش؟ لأنه أنا هعطيك سؤال أو هيكون عندك سؤال أصلا
+
+613
+00:47:39,300 --> 00:47:44,680
+أن هي مش transitive فانت المطلوب منك أنت اللي تكمل
+
+614
+00:47:44,680 --> 00:47:47,720
+ال transitivity أنت اللي بدك تكمل ال transitivity
+
+615
+00:47:47,720 --> 00:47:52,020
+أنت اللي لازم تكملهاتمام ففي الحالة هذه بتقول إن
+
+616
+00:47:52,020 --> 00:47:54,260
+هي Transitive ال Transitive معناته إن هي كلها
+
+617
+00:47:54,260 --> 00:47:57,840
+موصولة مع بعض بالظبط زي لما بدنا نروح على ال graph
+
+618
+00:47:57,840 --> 00:48:02,460
+و بدك تعمل model ل مدن و طرق بدك تضمن إن كل ال
+
+619
+00:48:02,460 --> 00:48:05,640
+nodes هذه اللي هي القرى مرتبطة ببعض فبتقدر تحولها
+
+620
+00:48:05,640 --> 00:48:09,240
+في الأخر ل sub problem لمشكلة رياضية و جبلنا
+
+621
+00:48:09,240 --> 00:48:12,940
+Transitive Transitive معناته كل نقطة متصلة بغيرها
+
+622
+00:48:12,940 --> 00:48:20,770
+بتعمل مجموعة طرق و بتكون حل من الحلول تمامالآن أخر
+
+623
+00:48:20,770 --> 00:48:25,490
+إشي ناخد المثال let R وهي معطيني مجموعة عناصر و
+
+624
+00:48:25,490 --> 00:48:29,750
+بدّو يانا نجيب ال powers بتاعتنا نبدأ نجيب مجموعة
+
+625
+00:48:29,750 --> 00:48:33,070
+powers طبعا هنيجي نطلع في الآخر هنشوف كل عنصر جديد
+
+626
+00:48:33,070 --> 00:48:36,030
+هيظهر ماكانش موجود هنا معناته كأنه بيقولي أنا لازم
+
+627
+00:48:36,030 --> 00:48:42,630
+أكون موجود عشان أحولك يا transitive نبدأ ب R2 أو R
+
+628
+00:48:42,630 --> 00:48:47,540
+تربية عبارة عنR Transpose R زي ما قلنا احنا ما
+
+629
+00:48:47,540 --> 00:48:57,800
+احنا خدناها سابق قد نعملها بنفس القالية هذه و
+
+630
+00:48:57,800 --> 00:49:02,020
+برضه هنا هتكون R و
+
+631
+00:49:02,020 --> 00:49:08,000
+ان ارادتنا هي واحد و واحد اتنين و واحد تلاتة و
+
+632
+00:49:08,000 --> 00:49:14,120
+اتنين و اربعة و تلاتة يلا مين بيبدأ بواحد في
+
+633
+00:49:14,120 --> 00:49:19,510
+الشاشةهى نفسها واحد و واحد بس خلاص يالا كويس برضه
+
+634
+00:49:19,510 --> 00:49:22,650
+صح اننا نحطها صح معناها مش هتغير اشي لكن خلّينا
+
+635
+00:49:22,650 --> 00:49:27,450
+نحطها بواحد خلصنا
+
+636
+00:49:27,450 --> 00:49:31,410
+اتنين فى
+
+637
+00:49:31,410 --> 00:49:37,590
+اشي غيرها اتنين لأ طيب ابتلاته تلاته و اتنين بقى
+
+638
+00:49:37,590 --> 00:49:43,090
+اشي تاني خلصنا هتجيب واحد مع واحد اتنين و واحد
+
+639
+00:49:45,270 --> 00:49:53,670
+تلاتة و واحد اربعة و اتنين تمام؟
+
+640
+00:49:53,670 --> 00:50:02,590
+okay خلصنا طيب ايش زاد عند هنا؟ ممتاز معناته الآن
+
+641
+00:50:02,590 --> 00:50:04,070
+لما بدنا ييجي نقول
+
+642
+00:50:07,680 --> 00:50:15,640
+R2 R تربيع اللي هي واحد و واحد اتنين و واحد تلاتة
+
+643
+00:50:15,640 --> 00:50:23,800
+و واحد اربعة و اتنين هدولة مع R R اللي هي مين هيهم
+
+644
+00:50:23,800 --> 00:50:29,600
+هدولة الأصليين مش مع نفسها فإذا خليني واحد أنتي في
+
+645
+00:50:29,600 --> 00:50:37,220
+هنا واحد واحدبرضه واحد نفس الكلام من هنا في الشيء
+
+646
+00:50:37,220 --> 00:50:45,040
+بتنتهي .. بتتبقى واحد إلا الواحد واحد واحد اتنين
+
+647
+00:50:45,040 --> 00:50:51,400
+اتنين وواحد هذا إيش هتعطيني زيادة هتعطيك هذه
+
+648
+00:50:51,400 --> 00:50:58,740
+الواحد واحد مافرقش كتير اتنين وواحد تلاتة واحد
+
+649
+00:51:00,940 --> 00:51:11,160
+وأخيراً أربعة بالظبط بالظبط فإذن هذه R2 R تربيع
+
+650
+00:51:11,160 --> 00:51:18,580
+وهنا R تكعيب R أربعة نفس R تلاتة تمام معناته الآن
+
+651
+00:51:18,580 --> 00:51:24,740
+إيش بنعمل إحنا اتحاد اتحاد R مع R أو خلّيني أحيك
+
+652
+00:51:24,740 --> 00:51:29,780
+بصير كأنها R اتحاد R هذه R واحد R تربيع اتحاد R
+
+653
+00:51:30,580 --> 00:51:34,100
+تكعيب طبعا مافيش داعي أكمل أكتر من هيك لإنه اتكرر
+
+654
+00:51:34,100 --> 00:51:38,140
+و اتوقف التكرار هو in general أنا مش عارف أمتى
+
+655
+00:51:38,140 --> 00:51:43,960
+حاجة عشان هيك سماها توي big U to Z positive لإن هو
+
+656
+00:51:43,960 --> 00:51:45,920
+مش عارف بعد اتنين تلاتة اربعة خمسة بس في نهاية
+
+657
+00:51:45,920 --> 00:51:50,200
+هتجف في نهاية هتجف فالان R هيها موجوه وين راحت R
+
+658
+00:51:50,200 --> 00:51:55,880
+كلها شوية بدها تهم ان هيهاتمام هذه بدنا واحد واحد
+
+659
+00:51:55,880 --> 00:51:58,860
+خلاص اتحاد اتحاد خلاصنا خلاصناها بدها تلاتة واحد
+
+660
+00:51:58,860 --> 00:52:06,620
+طيب خلاصنا من هدول واربعة واثنين و بعدين اربعة و
+
+661
+00:52:06,620 --> 00:52:10,220
+واحد فخلاص هيك صارت transitive
+
+662
+00:52:12,790 --> 00:52:15,850
+أصبحت Transitive هيك ال relation ال relation أصبحت
+
+663
+00:52:15,850 --> 00:52:21,890
+إيش Transitive اهتمام okay بكفي على هيك عشان المرة
+
+664
+00:52:21,890 --> 00:52:24,790
+القادمة نبدأ في مين في ال directed graph نشوف إيش
+
+665
+00:52:24,790 --> 00:52:28,970
+علاقته في ال relation كمقدمات تربطنا في ال chapter
+
+666
+00:52:28,970 --> 00:52:31,930
+اللي بيجي بعده يعطيكم العفو وبركة الله فيكم السلام
+
+667
+00:52:31,930 --> 00:52:32,250
+عليكم
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/VLnEJOyCdIE_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/VLnEJOyCdIE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..36eb0b4914113e39768c8081e9bd1163ff176300
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/VLnEJOyCdIE_raw.srt
@@ -0,0 +1,2524 @@
+1
+00:00:05,330 --> 00:00:07,770
+طيب بسم الله الرحمن الرحيم يعطيكم العفو يا شباب
+
+2
+00:00:07,770 --> 00:00:13,230
+اليوم نكمل في ال .. في ال counting و وصلنا كنا لل
+
+3
+00:00:13,230 --> 00:00:16,890
+vision whole principle و خلينا نشوف باقي أمثلة كنا
+
+4
+00:00:16,890 --> 00:00:19,910
+المرة الماضية بدأنا في الأمثلة في شوية examples
+
+5
+00:00:19,910 --> 00:00:24,430
+فاليوم نكمل مجموعة examples تانيةعلى هذا الموضوع
+
+6
+00:00:24,430 --> 00:00:29,410
+مثال زي لما نقول والله إذا احنا عندنا خمس possible
+
+7
+00:00:29,410 --> 00:00:36,230
+grades لتقييم الطلاب اللي هي A,B,C,D وF اللي هي
+
+8
+00:00:36,230 --> 00:00:42,350
+ممتاز جيد جدا جيد ومقبول ثم الفيل أو الراسب جداش
+
+9
+00:00:42,350 --> 00:00:44,970
+منقدر يكون عندي عدد الطلاب أو جداش لازم يكون عدد
+
+10
+00:00:44,970 --> 00:00:48,150
+الطلاب عشان أضمن أن واحدة من ال grades هذه في ست
+
+11
+00:00:48,150 --> 00:00:53,820
+طلاب حققوهافي ست طلاب حققوها عشان أكون ضامن مئة
+
+12
+00:00:53,820 --> 00:01:01,220
+بالمئة to guarantee that فإذا أنا عندي A B C D و F
+
+13
+00:01:01,220 --> 00:01:06,580
+خمسة كنت بأضمن أن في واحدة من هدول صار فيها ستة
+
+14
+00:01:06,580 --> 00:01:09,820
+ستة students معنى ذلك أنه بدي أعمل distribution أو
+
+15
+00:01:09,820 --> 00:01:12,620
+uniform distribution أنه بدي أفترض أن كلهم يتوزعوا
+
+16
+00:01:12,620 --> 00:01:19,480
+بشكل كامل فبالظبط كلهم بهذا الشكل صاروا خمسات
+
+17
+00:01:24,850 --> 00:01:30,190
+هي خمسة مش هيك سكرت هلوجد الست و عشرين اكيد هيكون
+
+18
+00:01:30,190 --> 00:01:34,390
+في واحدة منهم فهيكون اكيد هنا معناته هي في فعلا في
+
+19
+00:01:34,390 --> 00:01:38,910
+عندي grade حقق ست طلاب فإذا ستة و عشرين فإذا فعلا
+
+20
+00:01:38,910 --> 00:01:45,290
+هيكون عندي ستة و عشرينstudents عشان اضمن ان في
+
+21
+00:01:45,290 --> 00:01:50,990
+واحدة milligrades فعليا ست طلاب حققوها ست طلاب
+
+22
+00:01:50,990 --> 00:01:53,550
+ممكن يكون اكتر من هيك لكن انا بقول to guarantee
+
+23
+00:01:53,550 --> 00:01:57,330
+that عشان تكون ضامن هذا الكلام مائة بالمائة طيب
+
+24
+00:01:57,330 --> 00:02:02,830
+الشغل التاني assume that كمان مثال assume ان ال
+
+25
+00:02:02,830 --> 00:02:09,890
+telephone numberFollowed As Followers AA مجدش عدد
+
+26
+00:02:09,890 --> 00:02:12,630
+ال A هدولة مش عارف كأرقام بس هذا الرقم ممكن يكون
+
+27
+00:02:12,630 --> 00:02:15,690
+من صفر لتسعة أرقام التليفون العادية من صفر لتسعة
+
+28
+00:02:15,690 --> 00:02:19,470
+من صفر لتسعة من صفر لتسعة هدولة مجموعة أرقام في
+
+29
+00:02:19,470 --> 00:02:23,990
+البداية مقدمة هيكونوا لل area مجموعة أرقام لل area
+
+30
+00:02:23,990 --> 00:02:29,790
+بعدين متبعين بخمس أرقام لمين لل user لل user اللي
+
+31
+00:02:29,790 --> 00:02:35,420
+داخل ال area داخل ال area هنقول مثلاالمقسم هذا
+
+32
+00:02:35,420 --> 00:02:40,480
+بيكفي على جد خمس أرقام كل مقسم من المقاسم طيب
+
+33
+00:02:40,480 --> 00:02:44,680
+المقاسم هذه المفروض أنها رقمالرقم هذا جداش عددهم
+
+34
+00:02:44,680 --> 00:02:48,680
+هنمثل ان كل مقسم عبارة عن area فجداش بده يكون
+
+35
+00:02:48,680 --> 00:02:51,940
+عددهم بمعنى جداش بده يكون عدد ال areas خاناتهم
+
+36
+00:02:51,940 --> 00:02:58,560
+نقدر نمثلهم عشان فعلا اكون جادر اغطي جداش اغطي
+
+37
+00:02:58,560 --> 00:03:02,440
+اتنين او خمسة و عشرين مليون خمسة و عشرين مليون
+
+38
+00:03:02,440 --> 00:03:10,050
+user فمعنى ذلك انت عندك بتقدر تجسم areasمقسم عندك
+
+39
+00:03:10,050 --> 00:03:13,410
+مقسم معين بيكفيلك لعند خمس أرقام أو خمسة digits
+
+40
+00:03:13,410 --> 00:03:17,350
+عفوا خمسة digits كل digit من هدولة بياخد من صفر
+
+41
+00:03:17,350 --> 00:03:22,830
+لتسعة كويس فإذا من صفر صفر صفر صفر صفر لعند تسعة
+
+42
+00:03:22,830 --> 00:03:27,130
+تسعة تسعة تسعة تسعة تسعة فممكن يغطيلك أداش مائة
+
+43
+00:03:27,130 --> 00:03:31,250
+ألفلأن دي الآن بيقدر يغطيلك 100 ألف كل مقسم من
+
+44
+00:03:31,250 --> 00:03:34,930
+المقاسم هدول طيب جدش بده يكون عددهم على اعتبار اني
+
+45
+00:03:34,930 --> 00:03:38,310
+بدي امثل ال areas بتاعتهم فلو كل لو قولنا مثلا
+
+46
+00:03:38,310 --> 00:03:42,690
+عددهم بده يكون مية معنى ذلك ان انا محتاج هنا يكون
+
+47
+00:03:42,690 --> 00:03:49,290
+عندي تلت خناط عددهم لأ محتاجه فقط خمسين عددهم
+
+48
+00:03:49,290 --> 00:03:53,170
+معناته محتاج خنتين فقط فجدش عدد الخناط اللي
+
+49
+00:03:53,170 --> 00:03:58,990
+محتاجها في الرقمفي الرقم عشان اقدر totally اكفي
+
+50
+00:03:58,990 --> 00:04:02,630
+خمسة و عشرين مليون user totally بدي اكفي خمسة و
+
+51
+00:04:02,630 --> 00:04:05,450
+عشرين مليون user فبكل بساطة و بنفس الفكرة اللي
+
+52
+00:04:05,450 --> 00:04:09,950
+اخدناها من المرة الماضية بدنا انحدد ان في عندى
+
+53
+00:04:09,950 --> 00:04:15,650
+خمسة و عشرين عفوا خمسة هنا في البداية و في عندى
+
+54
+00:04:15,650 --> 00:04:21,770
+هنا مجموعة انا مش عارف جداش عددهم تمام
+
+55
+00:04:21,770 --> 00:04:25,740
+هدولةممكن يكون عندى عشرة ال possibilities تبعت
+
+56
+00:04:25,740 --> 00:04:31,380
+الرقم هذا عشرة عشرة عشرة عشرة صحيح هدول تعون ال
+
+57
+00:04:31,380 --> 00:04:37,560
+Xات ال users هدول مجموعة ال Xات اللي هنا كويس فإذا
+
+58
+00:04:37,560 --> 00:04:42,900
+هنا في عندي عشرة تغطي باور خمسة هذا إيش في المقسم
+
+59
+00:04:42,900 --> 00:04:45,640
+الواحد أو في ال area الواحدة في ال area الواحدة
+
+60
+00:04:45,640 --> 00:04:49,020
+طيب هالواجهة ال area اللى هتكون موجودة هنا ممكن
+
+61
+00:04:49,020 --> 00:04:53,580
+تكون ال area الأولىأو الارية التانية أو الارية
+
+62
+00:04:53,580 --> 00:04:58,420
+التالتة and so on فإذا هنا بدها تكون totally بنفس
+
+63
+00:04:58,420 --> 00:05:03,280
+الفكرة عشرة to the power of n اللي أنا بدور عليها،
+
+64
+00:05:03,280 --> 00:05:07,380
+بندور عليها، طيب هدول إيش علاقتهم الأتنين ببعض؟
+
+65
+00:05:07,380 --> 00:05:10,600
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+66
+00:05:10,600 --> 00:05:12,640
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+67
+00:05:12,640 --> 00:05:13,400
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+68
+00:05:13,400 --> 00:05:13,900
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+69
+00:05:13,900 --> 00:05:17,730
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،تمام؟
+
+70
+00:05:17,730 --> 00:05:24,270
+هذا المفروض يغطيلي عدد الخمسة و عشرين مليون خمسة و
+
+71
+00:05:24,270 --> 00:05:26,790
+عشرين مليون يعني أنا بتتكلم عن خمسة و عشرين في
+
+72
+00:05:26,790 --> 00:05:31,650
+عشرة to the power سبعة صحيح؟ يعني اتنين فاصلة خمسة
+
+73
+00:05:31,650 --> 00:05:38,410
+في عشرة to the power تمانية مليون
+
+74
+00:05:38,410 --> 00:05:43,590
+اه عفوا انت بتتكلم عن مليون هذه هنا مليون وهنا
+
+75
+00:05:43,590 --> 00:05:48,840
+صارت سبعة مظبوطهنا مليون خمسة وعشرين مليون فهي ستة
+
+76
+00:05:48,840 --> 00:05:55,480
+هنا بتصير سبعة تمام؟ ممتاز الرقم هنا كأنه واحد في
+
+77
+00:05:55,480 --> 00:06:02,380
+عشرة the power صح؟ واحد في عشرة the power خمسة
+
+78
+00:06:02,380 --> 00:06:06,620
+زائد N كويس هذول بدنا نحاول نقارنهم مع بعض بحيث
+
+79
+00:06:06,620 --> 00:06:11,560
+أنه الرقم هنا واضح أنه أكبر من واحد احنا بدنا لأ
+
+80
+00:06:11,560 --> 00:06:17,070
+الرقم اللي هنا يكون أكبرمعنى ذلك تقول تقريبا فاصلة
+
+81
+00:06:17,070 --> 00:06:21,810
+اتنين خمسة في الشيك ten to the power تمانية
+
+82
+00:06:27,500 --> 00:06:31,360
+عدد الأرقام المتاحة عشان تقول والله أنا فعلا غطيت
+
+83
+00:06:31,360 --> 00:06:34,680
+الخمسة وعشرين مليون تكون غطيت الخمسة وعشرين مليون
+
+84
+00:06:34,680 --> 00:06:38,160
+فمعنى ذلك ان هنا هيكون لازم تكون اقل من واحد في
+
+85
+00:06:38,160 --> 00:06:46,020
+عشرة خمسة زائد N بالظبط واضحة لحالها فانت ضامن في
+
+86
+00:06:46,020 --> 00:06:50,340
+الحالة هذه طيب لو قولنا N باتنين هتكون انت بتقارن
+
+87
+00:06:50,340 --> 00:06:57,920
+مع حد فعليا هتطلع اكبر منأكبر من واحد في عشرة
+
+88
+00:06:57,920 --> 00:07:03,840
+تباور سبعة هذي اتنين فاصلة خمسة أكبر من الواحد
+
+89
+00:07:03,840 --> 00:07:08,500
+فمعنى ذلك بدك تتعامل مع التمانية فالبوار هنا لازم
+
+90
+00:07:08,500 --> 00:07:13,260
+تكون مشموحة تمانية انت عندك خمسة لل users فإذا ال
+
+91
+00:07:13,260 --> 00:07:22,140
+N هتساوي تلاتة هنا بسميها K باقين تلاتة هي نفس ال
+
+92
+00:07:22,140 --> 00:07:28,130
+K اللي هنا بستخدمها as a Kتمام فهي مثال برضه اللي
+
+93
+00:07:28,130 --> 00:07:30,990
+علاقة بال telephone system في نفس الموضوع ال
+
+94
+00:07:30,990 --> 00:07:36,730
+vision hall principle طيب generalized vision hall
+
+95
+00:07:36,730 --> 00:07:39,950
+principle in general عشان اقول و الله ان في عندي N
+
+96
+00:07:39,950 --> 00:07:45,310
+object و هدولة بدي احطهم في K places في عدد أماكن
+
+97
+00:07:45,310 --> 00:07:51,710
+K إذا واحد من الأماكن هذه على الأقل بدي يكون في N
+
+98
+00:07:51,710 --> 00:07:59,290
+over K ceilingلما نقول مثلا في عندي خمستاشر بدي
+
+99
+00:07:59,290 --> 00:08:03,350
+أحطهم في عشر أماكن، خمستاشر طالب بدي أحطهم في عشر
+
+100
+00:08:03,350 --> 00:08:08,190
+أماكن، كل مكان بدي يكون فيه at least عشرة على
+
+101
+00:08:08,190 --> 00:08:12,590
+خمستاشر، هاي واحد و نص، ceiling اتنين، يعني بعض
+
+102
+00:08:12,590 --> 00:08:17,740
+الأماكن بدي يكون فيها اتنينمنطق جداً عشرة .. خمساش
+
+103
+00:08:17,740 --> 00:08:20,640
+بدك تحطهم في عشر أماكن أكيد في بعض الأماكن بدوا
+
+104
+00:08:20,640 --> 00:08:25,880
+يكون فيها اتنين at least at least تمام زي لما نقول
+
+105
+00:08:25,880 --> 00:08:28,960
+والله عندي ال N هنا بمتين و تمانين طالب في ال
+
+106
+00:08:28,960 --> 00:08:31,440
+class مثلا لو افترضنا ان ال class من متطلبات
+
+107
+00:08:31,440 --> 00:08:35,400
+الجامعة في متين و تمانين طالبوعدد الأسبوع طبعا في
+
+108
+00:08:35,400 --> 00:08:38,540
+السنة خمسة وعشرين .. اتنين وخمسين أسبوع .. اتنين
+
+109
+00:08:38,540 --> 00:08:42,080
+وخمسين أسبوع فبقى عن ذلك أنه بقدر أقول كل أسبوع
+
+110
+00:08:42,080 --> 00:08:47,360
+جداش عدد الطلبة اللي مولودين في نفس الأسبوع ..
+
+111
+00:08:47,360 --> 00:08:52,700
+متين وخمسين عددهم على الاتنين وخمسين .. على اتنين
+
+112
+00:08:52,700 --> 00:08:56,420
+وخمسين وبيعمللها ceiling .. بيعمللها ceiling ..
+
+113
+00:08:56,420 --> 00:09:01,540
+تمام؟ فبطلع ست طلاب at least .. ممكن يكون أكترممكن
+
+114
+00:09:01,540 --> 00:09:04,460
+يكون أكتر بس 6 طلاب هذا في حالة أنه توزعوا
+
+115
+00:09:04,460 --> 00:09:09,240
+بالتساوي على ال 52 أسبوع بالتساوي فبكون ضامن أنه
+
+116
+00:09:09,240 --> 00:09:13,320
+واحد من هذه الأسبوع فعلا في 6 طلاب انولدوا في نفس
+
+117
+00:09:13,320 --> 00:09:16,580
+الأسبوع في نفس الأسبوع طب هو نفس الكلام لو عملناه
+
+118
+00:09:16,580 --> 00:09:22,460
+للشهور بدل الأسبوع على 12 سنشتغل على 12 في الحالة
+
+119
+00:09:22,460 --> 00:09:26,480
+هذه فسيكون 250 على 12 عشان أقول في عندي 24 طالب at
+
+120
+00:09:26,480 --> 00:09:36,170
+least مولودين في نفسالشهر في نفس الشهر تمام okay
+
+121
+00:09:36,170 --> 00:09:42,630
+الآن عمليات العد اللي احنا بنشتغلها هذه وجدوا انها
+
+122
+00:09:42,630 --> 00:09:48,550
+مجموعة نظريات مجموعة النظريات هذه تتعلق في ترتيبة
+
+123
+00:09:48,550 --> 00:09:51,810
+العد انا ايش بدي اعد و ايش المواصفات بتاعة العد
+
+124
+00:09:51,810 --> 00:09:55,890
+فوجدنا ان في حاجة اسمها permutation تباديل و
+
+125
+00:09:55,890 --> 00:09:59,370
+combination توفيق كنتوا تسموها مش هيك او التراكيب
+
+126
+00:10:00,310 --> 00:10:04,770
+التراكيب فال permutation بكل بساطة هو ل set معينة
+
+127
+00:10:04,770 --> 00:10:10,130
+فيها مجموعة objects هي عبارة عن ال sequence لترتيب
+
+128
+00:10:10,130 --> 00:10:15,210
+اختيار عدد معين من المجموع خلينا نقول عددنا خمسين
+
+129
+00:10:15,210 --> 00:10:20,830
+بدأ اختار منك تلاتة جداش عدد الطرق اللي ممكن نختار
+
+130
+00:10:20,830 --> 00:10:24,310
+فيها تلاتة مع الحفاظ على الترتيب بمعنى بدنا نختار
+
+131
+00:10:24,310 --> 00:10:27,030
+تلت طلاب التلت طلاب هدولة بدنا نشكل فيهم لجنة
+
+132
+00:10:27,030 --> 00:10:31,430
+اللجنة هذه لازم يكون فيها رئيس لجنةنائب رئيس
+
+133
+00:10:31,430 --> 00:10:36,110
+وsecretary لللجنة أو أمين سر لللجنة فإذا هنا
+
+134
+00:10:36,110 --> 00:10:39,510
+الترتيب مهم هنقول والله جديش عدد ال possibilities
+
+135
+00:10:39,510 --> 00:10:44,890
+أختار الأولطيب التاني و ديروا بالك الأول هنا بختلف
+
+136
+00:10:44,890 --> 00:10:48,130
+عن التاني هنا لو التاني اخترته في البداية هيكون عد
+
+137
+00:10:48,130 --> 00:10:52,030
+مختلف ليش؟ لأنه اختلف ال position تبعهم اختلف ال
+
+138
+00:10:52,030 --> 00:10:56,070
+position فهنا كان في رئيس اللجنة نائب الرئيس لأ
+
+139
+00:10:56,070 --> 00:10:59,030
+هيك لما يصير نائب الرئيس هو الرئيس هاد اختلف هاد
+
+140
+00:10:59,030 --> 00:11:03,270
+عد رقم اتنين هاد طريقة تانية صارت لتكوين اللجنة
+
+141
+00:11:03,270 --> 00:11:06,710
+طريقة تانية لتكوين اللجنة فهنا بيكون مهم عندنا
+
+142
+00:11:06,710 --> 00:11:10,700
+الترتيب جدش مين جاب المينفي الحالة الهدفة هذه
+
+143
+00:11:10,700 --> 00:11:15,000
+بيسميها permutation تبديل ومن اسمها باينة انه حتى
+
+144
+00:11:15,000 --> 00:11:20,940
+تبديل الأعضاء داخل الاختيار هو طريقة اصلا هو اصلا
+
+145
+00:11:20,940 --> 00:11:23,800
+طريقة مختلفة بخلاف ال combination زي ما قعدنا
+
+146
+00:11:23,800 --> 00:11:29,140
+هنشوف تمام هذه لما نيجي بدنا نحسبها to select مثلا
+
+147
+00:11:29,140 --> 00:11:37,530
+in او to select our objectR object من N elements
+
+148
+00:11:37,530 --> 00:11:42,990
+عندك الاسهد اللي هي ال set فيها N elements بدنا
+
+149
+00:11:42,990 --> 00:11:50,630
+نختار منهم R عدد R فبنسميها permutation from N to
+
+150
+00:11:50,630 --> 00:11:56,090
+select R من العدد N بدنا نعمل selection لإيش؟لـ R
+
+151
+00:11:56,090 --> 00:12:00,150
+فهذه بكل بساطة لما كنتوا بتعملوها إيش كنتوا تسوق؟
+
+152
+00:12:00,150 --> 00:12:04,090
+زي ما تذكرين لما كنا .. أول ما بدأنا المثال تبعنا
+
+153
+00:12:04,090 --> 00:12:08,410
+و قولنا فيه عنده مائة واحد بدهم يتسابقوا و بدنا
+
+154
+00:12:08,410 --> 00:12:13,150
+أول عشرة إيش عدد ال possibilities لأول عشرة؟ بكل
+
+155
+00:12:13,150 --> 00:12:19,510
+بساطة عندك مية فالأول اختياره هيكون واحد من مية من
+
+156
+00:12:19,510 --> 00:12:24,180
+تسعة وتسعين تمانية وتسعينكويس؟ طيب لعند عشرة
+
+157
+00:12:24,180 --> 00:12:28,920
+معناته بدي اكرر هذه العملية عشر مرات صحيح؟ كررناها
+
+158
+00:12:28,920 --> 00:12:35,160
+عشر مرات كإني بقول ساعتها مية في تسعة وتسعين في
+
+159
+00:12:35,160 --> 00:12:39,180
+خلينا نختار علاجات تلاتة بكفي علاجات تمانية و
+
+160
+00:12:39,180 --> 00:12:42,500
+تسعين، بس، بنوقف، وقفنا، أنا بدي أعمل selection
+
+161
+00:12:42,500 --> 00:12:45,900
+لتلاتة، بس selection لتلاتة فقط، فهذه ال
+
+162
+00:12:45,900 --> 00:12:48,740
+possibilities تبعتنا طيب، لمّا نشي .. نحط الكلام
+
+163
+00:12:48,740 --> 00:12:53,180
+هذا كقانونأنا مش عارف إنه هي مية بالظبط أنا بتكلم
+
+164
+00:12:53,180 --> 00:12:59,760
+عن in نتكلم عن in فقط فهتكون in in ناقص واحد في in
+
+165
+00:12:59,760 --> 00:13:04,300
+ناقص اتنين لعند in ناقص R هذه ال selection اللي
+
+166
+00:13:04,300 --> 00:13:06,960
+انا بدي اختاره احنا لما قلنا تلاتة هنا مثلناهم تلت
+
+167
+00:13:06,960 --> 00:13:11,380
+مرات لما قلنا هنا R معناته هنبدأ من صفر وهنا هتكون
+
+168
+00:13:11,380 --> 00:13:12,540
+فعليا زائد R كمان
+
+169
+00:13:16,650 --> 00:13:22,230
+مش هنا حد يبدأ بصفر؟ واحد اتنين تلاتة لعند R ناقص
+
+170
+00:13:22,230 --> 00:13:27,710
+اه مظبوط R زائد واحد هنا تمام فبطلع عددهم R كعدد
+
+171
+00:13:27,710 --> 00:13:31,530
+طب هدا كيف ممكن نمثله؟ لاحظ انه فعليا هذه ماخدة
+
+172
+00:13:31,530 --> 00:13:37,970
+هيك بداية ال sequence تبعت ال factorial لو كملناها
+
+173
+00:13:37,970 --> 00:13:43,790
+للواحد لو كملناها للواحد فإذا بكل بساطة بتقدر تقول
+
+174
+00:13:43,790 --> 00:13:50,640
+N factorial okayبس دير بالك الجزء اللي هنا هذا مش
+
+175
+00:13:50,640 --> 00:13:55,660
+موجود فبدك تقسم عليه لأن
+
+176
+00:13:55,660 --> 00:13:59,860
+هو فعليا صار موجود هنا في ال numerator فبدك تقسم
+
+177
+00:13:59,860 --> 00:14:03,040
+عليه هنا عشان اللي يظل فقط هو الفارق بين ال N و ال
+
+178
+00:14:03,040 --> 00:14:10,710
+R فهنيجي نقسم على المتبقي اللي هيكون Dial هنااللي
+
+179
+00:14:10,710 --> 00:14:16,550
+هو جداش حطيتنا هنا N ناقص R كله factorial فهو
+
+180
+00:14:16,550 --> 00:14:21,550
+الجزء اللي كان متبقي هنا فانت ضمنت هنا مين فقط
+
+181
+00:14:21,550 --> 00:14:27,210
+العناصر اللي بين ال N و ال R ضمنت فقط العناصر من
+
+182
+00:14:27,210 --> 00:14:32,190
+هذا القانون هو فعلا قانون ال permutation هو فعلا
+
+183
+00:14:32,190 --> 00:14:35,330
+قانون ال permutation ان انت بتعمل ال N factorial
+
+184
+00:14:36,420 --> 00:14:41,720
+على n ناقص r factorial فالقانون مقتنعين اللي انا
+
+185
+00:14:41,720 --> 00:14:45,420
+احنا فيه مش مجرد بتحفظ و خلاص لأ احنا فعلا مقتنعين
+
+186
+00:14:45,420 --> 00:14:49,140
+و هذا فعلا مائة بالمائة صحيح لان انا بدي اشتغل من
+
+187
+00:14:49,140 --> 00:14:56,320
+n ل r زائد واحد ل n ناقص r زائد واحد تمام فإذا
+
+188
+00:14:56,320 --> 00:14:59,840
+بتهيألي واضحة مافيش فيها كتير غلبة و احنا فاهمين
+
+189
+00:14:59,840 --> 00:15:06,760
+هسرنا في شكل هذاطيب الان انعمم شوية كلامنا و نشوف
+
+190
+00:15:06,760 --> 00:15:10,720
+هو ال permutation تنطبق تحت اي category من ال
+
+191
+00:15:10,720 --> 00:15:13,720
+categories بتاعة ال counting بتاعة ال counting فلو
+
+192
+00:15:13,720 --> 00:15:17,040
+افترض انه عندي earn model ال earn model هو model
+
+193
+00:15:17,040 --> 00:15:20,240
+الجرة وهذا من ال models المشهورة جدا للناس اللي
+
+194
+00:15:20,240 --> 00:15:21,860
+بيشتغلوا في ال possibilities و في ال probabilities
+
+195
+00:15:21,860 --> 00:15:25,980
+كمان الاحتماليات او القياس الاحتمال ان والله عندك
+
+196
+00:15:25,980 --> 00:15:28,800
+جرة و فيها مجموعة objects و انت بتمد ايدك بتختار
+
+197
+00:15:28,800 --> 00:15:32,060
+عشوائيبتعمل عملية اختيار عشوائي اخدتوا حاجة اللي
+
+198
+00:15:32,060 --> 00:15:35,120
+علاقة بال probability هتلاقي انه هذا من ال models
+
+199
+00:15:35,120 --> 00:15:39,400
+اللي لازم تظهر فيها سئلة او في أمثلة على الأقل انك
+
+200
+00:15:39,400 --> 00:15:43,000
+لو في earn جرة و مديت ايدك و بدك تختاره فيها
+
+201
+00:15:43,000 --> 00:15:47,360
+مجموعة كور حمره او زرقه و الاخره ايش احتمال يطلع
+
+202
+00:15:47,360 --> 00:15:50,200
+اللون الأزرق؟ هيك كنتوا بتاخدوها اللي احنا بنتكلم
+
+203
+00:15:50,200 --> 00:15:53,860
+ان والله ال earn هذه فيها in object ال in objects
+
+204
+00:15:53,860 --> 00:15:58,060
+هدول عدد عناصر عددهم in او أشياء عددهم in و بدنا
+
+205
+00:15:58,060 --> 00:16:03,440
+نعملpick او select لار objects منهم لار objects
+
+206
+00:16:03,440 --> 00:16:07,560
+منهم فانا بده امد ايدي احرك و اطلع اول تاني تالت
+
+207
+00:16:07,560 --> 00:16:12,580
+لعند R لعند R هذا ال model العموما عموما انه كيف
+
+208
+00:16:12,580 --> 00:16:15,080
+انا ممكن اطلع ال sequence تبعت العناصر اللي
+
+209
+00:16:15,080 --> 00:16:20,460
+هنختارها العناصر اللي هنختارها طيب بعد الاختيار هل
+
+210
+00:16:20,460 --> 00:16:26,060
+لاحظ انا اخترت و طلعت شفته و رجعته تاني ولا شفته و
+
+211
+00:16:26,060 --> 00:16:31,710
+طلعته بالمرةهذه طريقة و هذه طريقة فإذا طريقة العد
+
+212
+00:16:31,710 --> 00:16:38,090
+هل هي selection with replacement مع الإرجاع أن انت
+
+213
+00:16:38,090 --> 00:16:42,170
+عديت الشغل و بعدين رجعتها تاني زي لما نقولك والله
+
+214
+00:16:42,170 --> 00:16:49,470
+من ال decimal شوف ليه أكم عنصر بتقدر تكون منه رقم
+
+215
+00:16:50,250 --> 00:16:54,930
+أحد ومئات وعشرات ومئات من تلت خنات يعني فانت هنا
+
+216
+00:16:54,930 --> 00:17:00,130
+بتعمل selection للأولى وبتعمل replacement لأنه لما
+
+217
+00:17:00,130 --> 00:17:03,530
+يكون تسعة تسعة تسعة هاي هم متكررين بس هو رقم فعلا
+
+218
+00:17:03,530 --> 00:17:07,570
+من التلت خنات فإذا with replacement هنا فهذا مثال
+
+219
+00:17:07,570 --> 00:17:11,990
+واضح ان انت اه بتقدر تختاروتعيد ال object مرة
+
+220
+00:17:11,990 --> 00:17:15,730
+تانية ل ال earn تبعتك لإحتمالات الاختيارات القادمة
+
+221
+00:17:15,730 --> 00:17:19,130
+فهذا with replacement هاي أول selection أو أول
+
+222
+00:17:19,130 --> 00:17:22,090
+طريقة من عملية ال counting التانية without
+
+223
+00:17:22,090 --> 00:17:25,530
+replacement زي مثل إنه والله يابدنا نعمل لجنة
+
+224
+00:17:25,530 --> 00:17:28,330
+بالمثال اللي تقولناه وبدنا تلت أعضاء طب okay انت
+
+225
+00:17:28,330 --> 00:17:32,370
+اخترت الأول مش هتختاره كمان مرة خلاص فإذا طلع من
+
+226
+00:17:32,370 --> 00:17:35,890
+المجموع فالمجموع صار ناقص واحد بتختار منه كمان
+
+227
+00:17:36,800 --> 00:17:40,780
+واضحة فهذه طريقة تانية لها قوانين مختلفة هذه
+
+228
+00:17:40,780 --> 00:17:45,140
+الطريقة و هذه الطريقة واضحة فإذا احنا وين بالظبط
+
+229
+00:17:45,140 --> 00:17:48,420
+في هذا الكلام هنشوف ممكن نكون هنا و ممكن نكون هنا
+
+230
+00:17:48,420 --> 00:17:54,440
+حسب طبيعة السؤال السؤال بالأرقام زي اللي توجلناه و
+
+231
+00:17:54,440 --> 00:17:59,300
+بقولك والله شوف لقداش عدد احتمالات تكوين رقم من
+
+232
+00:17:59,300 --> 00:18:03,800
+تلت خنات طب ما هذا المنطق اه انه ارجع مثلا اما لما
+
+233
+00:18:03,800 --> 00:18:08,950
+بقولك لجنةمن عشرين عضو بدي أختار منهم تلاتة لأ دي
+
+234
+00:18:08,950 --> 00:18:11,910
+without replacement أكيد مش هتختار نفس العضو من
+
+235
+00:18:11,910 --> 00:18:15,590
+منصبين يعني تمام؟ مش هيكون واحد يلو مكتبين يعني
+
+236
+00:18:15,590 --> 00:18:21,210
+كويس؟ how many different possible sequences of R
+
+237
+00:18:21,210 --> 00:18:27,170
+object are there؟ فهنا جدش أنت تختار قيمة R R منهم
+
+238
+00:18:27,170 --> 00:18:30,290
+معناه ذلك أنك تعرف أنه في شيء غلط في الموضوع أنا
+
+239
+00:18:30,290 --> 00:18:34,690
+بقولك في شيء غلط في الموضوعتمام؟ فهنا that's the
+
+240
+00:18:34,690 --> 00:18:38,190
+order أيوة إيجينا لقصة تانية غير replacement
+
+241
+00:18:38,190 --> 00:18:42,030
+without replacement with ولا without هنا لأ في
+
+242
+00:18:42,030 --> 00:18:45,350
+قضية تانية كمان غير الموضوع هذا ترتيب ولا مش
+
+243
+00:18:45,350 --> 00:18:50,590
+ترتيب؟ ترتيب ولا مش ترتيب؟ معنى ذلك أنه صار عندي
+
+244
+00:18:50,590 --> 00:18:53,250
+without replacement مثلا بس هل هو ordered ولا
+
+245
+00:18:53,250 --> 00:18:57,510
+unordered؟ بمعنى التلاتة اللي بدنا نختارهم هل بفرق
+
+246
+00:18:57,510 --> 00:19:01,790
+ترتيبهم؟أجوا قالوا إننا و الله بدنا لجنة من
+
+247
+00:19:01,790 --> 00:19:05,430
+المستوى التالت عشان و الله بنعمل مسابقة ثقافية طب
+
+248
+00:19:05,430 --> 00:19:08,650
+okay بيفرج من ال .. في لا head ولا مالهاش .. لأ
+
+249
+00:19:08,650 --> 00:19:12,110
+جالك لأ بس تلتة و خلاص و دورت ال order يعني
+
+250
+00:19:12,110 --> 00:19:15,930
+unordered هيك .. unordered إجيت إنت اختيارك كالأول
+
+251
+00:19:15,930 --> 00:19:19,010
+ولا تاني ولا تالت مش هتفرج المهم إنك إنت في اللجنة
+
+252
+00:19:19,010 --> 00:19:22,970
+لكن لما يقول لأ أنا بعمل لجنة في رئيس لجنة و في
+
+253
+00:19:22,970 --> 00:19:27,840
+نائب رئيس و في أمين سر لأ بختلفك الترتيبهنا هيك
+
+254
+00:19:27,840 --> 00:19:31,640
+الترتيب بيختلف ويختلف تماما هادي عن هادي عن هادي
+
+255
+00:19:31,640 --> 00:19:35,780
+مختلفين فإذا واضح انه هل هي ordered ولا unordered
+
+256
+00:19:35,780 --> 00:19:38,700
+إذا بتكلم عن ordered فانا بروح ل permutation
+
+257
+00:19:38,700 --> 00:19:42,400
+فعرفنا لوجة احنا وين في ال permutation اللي بتتكلم
+
+258
+00:19:42,400 --> 00:19:49,700
+أول شي without replacement و ordered list فبقول
+
+259
+00:19:49,700 --> 00:19:53,820
+بسميها هنا permutation تباديل أما إذا كانت without
+
+260
+00:19:53,820 --> 00:19:58,850
+replacementو unordered فهذه ال combination اللي
+
+261
+00:19:58,850 --> 00:20:02,270
+هناخدها فإذا إحنا عرفنا الآن ال permutation و ال
+
+262
+00:20:02,270 --> 00:20:05,070
+combination هي وين موقعها على خريطة ال counting
+
+263
+00:20:05,070 --> 00:20:09,650
+without replacement ordered معناته بتكلم عن
+
+264
+00:20:09,650 --> 00:20:16,110
+permutation unordered بتكلم عن combination تمام و
+
+265
+00:20:16,110 --> 00:20:18,610
+ال permutation طوي لسه كنا متكلمين عنها و حكينا
+
+266
+00:20:18,610 --> 00:20:22,830
+على نفس القانون شرحناه الآن ناخد مثال عليه بدك
+
+267
+00:20:22,830 --> 00:20:23,850
+تفترض أنه عندك
+
+268
+00:20:31,670 --> 00:20:37,310
+قنبله planet in your city مزروعة في مدينتك و عليك
+
+269
+00:20:37,310 --> 00:20:42,430
+ال job تبعك ان انت اللي تعمل disable ل .. ايوه
+
+270
+00:20:42,430 --> 00:20:46,070
+disable لل pump هذه بس كيف بدك تعملها disable؟ هي
+
+271
+00:20:46,070 --> 00:20:50,570
+طلعت إلكترونية و فيها عشر أسلاك بدك تعمل disable
+
+272
+00:20:50,570 --> 00:20:56,980
+by cuttingWires of the trigger device كلكوا عارفين
+
+273
+00:20:56,980 --> 00:20:59,640
+ان في trigger device هذا اللي هو المشعل اللي هو
+
+274
+00:20:59,640 --> 00:21:02,100
+بيعطي ال trigger الأولى او ال pulse الأولى عشان
+
+275
+00:21:02,100 --> 00:21:05,320
+تنفجر فانت جيت طلعت ايه يا جماعة الخير طب احنا
+
+276
+00:21:05,320 --> 00:21:08,520
+نتعون حاسوب و أخدنا إلكترونيات الإلكترونيات هي
+
+277
+00:21:08,520 --> 00:21:12,600
+فيها تلت أسلاك هدولة بدهم جاطعة طب وين ال trigger
+
+278
+00:21:12,600 --> 00:21:17,400
+اه هي تلتة طيب حطيلك إياهم في box أسود و ممنوع
+
+279
+00:21:17,400 --> 00:21:20,380
+تفتحه و عشرة أسلاك داخلين فانا مش عارف أنه السلك
+
+280
+00:21:20,380 --> 00:21:25,210
+اللي هو رايح لل triggerكمان كويس فعندك عشر أسلاك
+
+281
+00:21:25,210 --> 00:21:30,150
+الأسلاك هدولة كلهم رايحين لل pump لل pump تبعتك
+
+282
+00:21:30,150 --> 00:21:34,610
+هذه القمبلة لل pump if you cut exactly the right
+
+283
+00:21:34,610 --> 00:21:39,810
+three wires in exactly the right order يعني لو
+
+284
+00:21:39,810 --> 00:21:42,250
+التلت أسلاك هم هدول فعلا اللي بتنقطع لكن إنت قطعت
+
+285
+00:21:42,250 --> 00:21:48,210
+التاني قبل الأول هتنفجر تمام you will disable the
+
+286
+00:21:48,210 --> 00:21:50,670
+pump إذا كان عملتهم بنفس ال order بال right order
+
+287
+00:21:50,670 --> 00:21:51,430
+otherwise
+
+288
+00:21:53,810 --> 00:21:58,670
+Explode هتنفجر، هسير هناك انفجار فالان بكل بساطة
+
+289
+00:21:58,670 --> 00:22:02,650
+من العشرة و افترض ان العشرة look the same يعني
+
+290
+00:22:02,650 --> 00:22:06,130
+كلهم مش هعملك زي مثلا المحقق كونان ومش كونان وعملك
+
+291
+00:22:06,130 --> 00:22:09,990
+سلك أزرج وسلك أحمر وعشان ت .. يعني كلهم هتطلعك
+
+292
+00:22:09,990 --> 00:22:15,570
+إياهم أسود، الآن جدش لتشانس for survival
+
+293
+00:22:18,330 --> 00:22:24,890
+فقداش فرصة انك انت فعلا تفك هذه القنبلة تفكر فيها
+
+294
+00:22:24,890 --> 00:22:33,750
+بشواش .. تفكر فيها بشواش عندك عشر أسلاك طيب
+
+295
+00:22:33,750 --> 00:22:38,570
+.. بدي أفترض انك أنت الأول هتقطعه صح مش shake ..
+
+296
+00:22:38,570 --> 00:22:41,450
+جداش ال possibility تبعته الأولى واحد من عشرة ..
+
+297
+00:22:41,450 --> 00:22:48,900
+واحد من عشرة طيب .. التاني واحد من تسعةالتالت بس
+
+298
+00:22:48,900 --> 00:22:53,540
+هي كل عدد ال possibilities عشان تنجح في المهمة
+
+299
+00:22:53,540 --> 00:23:01,140
+تبعتك ففعليا هتطلع 720 انت فرصتك عاد 1 على 720
+
+300
+00:23:01,140 --> 00:23:04,620
+فرستك
+
+301
+00:23:04,620 --> 00:23:11,000
+1 على 720 1 ما هي لاحظ ال sequence بال order الصح
+
+302
+00:23:11,000 --> 00:23:17,120
+هو حالة واحدة من ال 720 حالةهى حالة واحدة من الـ
+
+303
+00:23:17,120 --> 00:23:23,360
+720 حالة فانت in general عشان يكون بشكل مرتب جداش
+
+304
+00:23:23,360 --> 00:23:26,340
+عدد ال possibility عشان من العشرة هدول تقطع تلاتة
+
+305
+00:23:26,340 --> 00:23:33,020
+720 720 بس واحد منهم هو التلاتة اللى صح و بال
+
+306
+00:23:33,020 --> 00:23:36,420
+order الصح اه لو جدت unordered تلاتة 720 اه بتصير
+
+307
+00:23:36,420 --> 00:23:39,900
+على لأ عفوا لما بتكون unordered لأ مختلف بتصير انت
+
+308
+00:23:39,900 --> 00:23:44,430
+هنا بتصير تتعامل معالـ combination هاد الـ 720
+
+309
+00:23:44,430 --> 00:23:49,470
+هتجل لأنك هتجسمها على رقم تاني هتجسمها على رقم
+
+310
+00:23:49,470 --> 00:23:51,850
+تاني زي ما قعدنا هتشوف في ال combination لكن
+
+311
+00:23:51,850 --> 00:23:55,110
+مبدأيا في ال permutation مدام جل ال order مهم فهي
+
+312
+00:23:55,110 --> 00:24:00,990
+مبدأيا 720 انت لك فرصة واحدة من ال 720 هدول فهي
+
+313
+00:24:00,990 --> 00:24:07,990
+واحد على 720 فعليا ففعليا لل chanceof survival
+
+314
+00:24:07,990 --> 00:24:13,610
+عندك هنا هتكون هي واحد من سبعمائه عشرين حقيقة تمام
+
+315
+00:24:13,610 --> 00:24:21,870
+كمان أمثلة how many different orders can four
+
+316
+00:24:21,870 --> 00:24:27,770
+persons be seated in a row of four chairsعارفين؟
+
+317
+00:24:27,770 --> 00:24:30,650
+بس هنا طبعا هي مش لعبة، تلت كراسي و أربعة أشخاص
+
+318
+00:24:30,650 --> 00:24:34,870
+بيلفوا حواليها، لأ هم أربعة في أربعة، فمنصة الأولى
+
+319
+00:24:34,870 --> 00:24:38,030
+هي أربعة و هم نفس الأربعة اللي عيشوا في الأول،
+
+320
+00:24:38,030 --> 00:24:40,870
+هالولد جدش في possibilities أنه يقعدوا بنفس
+
+321
+00:24:40,870 --> 00:24:45,520
+الترتيب هذاممكن طبعا يغيروا ممكن يبدلوا مع بعض جدش
+
+322
+00:24:45,520 --> 00:24:48,960
+عدد التبديل بينهم جدش عدد التبديل بينهم فهذه بكل
+
+323
+00:24:48,960 --> 00:24:53,420
+بساطة كإني بقول من الأربعة بدهم يقعدوا أربعة خلاص
+
+324
+00:24:53,420 --> 00:24:56,360
+يعني كلهم بدهم يقعدوا أنا هعمل selection للأربعة
+
+325
+00:24:56,360 --> 00:25:01,100
+من الأربعة كويس فانا بتصير كأنها أربعة أربعة
+
+326
+00:25:01,100 --> 00:25:04,800
+factorial أربعة factorial لأنه فعليا كأنها N
+
+327
+00:25:04,800 --> 00:25:12,070
+factorial على N ناقص N factorialR ب N انت بدك
+
+328
+00:25:12,070 --> 00:25:17,010
+تختار أربعة وهو N أربعة فهنا كأنها Zero Factorial
+
+329
+00:25:17,010 --> 00:25:22,250
+هي ب واحد فبتكون ال N Zero Factorial ب واحد فإذا
+
+330
+00:25:22,250 --> 00:25:26,510
+بتصير كأنها ال N Factorial بس فتصبح كأنه عندك
+
+331
+00:25:26,510 --> 00:25:29,670
+أربعة و عشرين possibility طب how many different
+
+332
+00:25:29,670 --> 00:25:33,730
+three digit numbers can be formed using the digits
+
+333
+00:25:33,730 --> 00:25:40,770
+five six seven eight و nine without repetitionجداش
+
+334
+00:25:40,770 --> 00:25:46,030
+عدد الأرقام اللي ممكن تشكلهم بحيث ان يكونوا تلت
+
+335
+00:25:46,030 --> 00:25:51,850
+خنات لكن انت محكوم بالأرقام هذه 4 3 2 كويس هتكون
+
+336
+00:25:51,850 --> 00:25:55,410
+انت محكوم فقط في هذه الجزئية بكل بساطة كأنك بتعمل
+
+337
+00:25:55,410 --> 00:26:07,330
+permutation من جداش 1 2 3 4 5 جداش بتختار 3 ف5 4 3
+
+338
+00:26:09,620 --> 00:26:14,720
+تمام؟ خمسة أربعة تلاتة جدش بتطلع خمسة أربعة تلاتة
+
+339
+00:26:14,720 --> 00:26:20,960
+لإن بتدير بقى بتقسم على اتنين factorial اللي هي
+
+340
+00:26:20,960 --> 00:26:24,420
+خمسة ناقص تلاتة فبتقسم على اتنين فتاخدوا بالك من
+
+341
+00:26:24,420 --> 00:26:29,700
+الموضوع هذا بتطلع ال total ايه ايش ستين اه
+
+342
+00:26:33,320 --> 00:26:38,360
+هي عيدها كمان مرة هلوجد هنا لما بدنا نقول اللي
+
+343
+00:26:38,360 --> 00:26:43,480
+بدنا نختار من الخمس أرقام هدول تلت أرقام بحيث انه
+
+344
+00:26:43,480 --> 00:26:48,320
+يشكلولي رقم من تلت خنات رقم من تلت خنات يعني
+
+345
+00:26:48,320 --> 00:26:53,160
+بتختار تلت أرقام ولكن بالترتيب المحدد فإذا الترتيب
+
+346
+00:26:53,160 --> 00:26:57,220
+مهم هنا ال ordered مهم لأنه تلت مية أربعة و خمسين
+
+347
+00:26:57,220 --> 00:27:00,690
+غير تلت مية خمسة واربعينرغم ان هما نفس الـ three
+
+348
+00:27:00,690 --> 00:27:04,550
+digits فإذا جدّيش العدد اللي انا ممكن اختار منه
+
+349
+00:27:04,550 --> 00:27:09,190
+خمسة هايل واحد اتنين تلاتة اربع خمسة فإذا
+
+350
+00:27:09,190 --> 00:27:14,130
+permutation من خمسة تبديل من خمسة جدّيش بدي اعمل
+
+351
+00:27:14,130 --> 00:27:18,090
+اختار بدي اختار three digit تلاتة فصارت كأنها
+
+352
+00:27:18,090 --> 00:27:21,190
+تلاتة اللي انا بتعود في القانون تبعك عادي خمسة
+
+353
+00:27:21,190 --> 00:27:25,570
+factorial على اتنين factorialأو بالطريقة اللي
+
+354
+00:27:25,570 --> 00:27:29,450
+جالوها زمالك على طول جالوا اللي جالك خمسة في أربعة
+
+355
+00:27:29,450 --> 00:27:34,170
+في تلاتة و ريح راسك و خلصنا هيك تشتغل ماشي هيك
+
+356
+00:27:34,170 --> 00:27:40,530
+تشتغل ماشي فليكن بمشي في الحالتين ال
+
+357
+00:27:40,530 --> 00:27:45,820
+combinationمش مختلفين الحاجة الوحيدة اللي اختلفت
+
+358
+00:27:45,820 --> 00:27:49,020
+ال order بس اما هي without replacement او without
+
+359
+00:27:49,020 --> 00:27:51,960
+replacement دلت زي ما هي لكن اختلف الحاجة الوحيدة
+
+360
+00:27:51,960 --> 00:27:58,200
+اللي اختلفت معنى فقط جزئية ان هنا unordered زي
+
+361
+00:27:58,200 --> 00:28:01,360
+فكرة اللجنة اللي بدنا نختارها فكرة اللجنة بدنا
+
+362
+00:28:01,360 --> 00:28:05,000
+نختارها معنى ذلك ان المتوقع ان العدد هنا يكون اقل
+
+363
+00:28:05,000 --> 00:28:13,260
+صح العدد هنا يكون اقل ليش لأن كل ال ordersبتاعتنا
+
+364
+00:28:13,260 --> 00:28:16,160
+الترتيبات اللي انعملت كلها بتنحسب حاجة واحدة انا
+
+365
+00:28:16,160 --> 00:28:19,400
+في عندى اربع من وند السين جاعدوا على اربع كراسي
+
+366
+00:28:19,400 --> 00:28:23,680
+كيف ترتيبهم بفرقش والله مش وند السين مع مش وند
+
+367
+00:28:23,680 --> 00:28:28,040
+الساي اختلفوا مش هعد زيادة العدد واحد هو نفس الاشي
+
+368
+00:28:28,040 --> 00:28:30,880
+ماختلفش معايا في البرميتيشن قلت لأ بعدها حالة
+
+369
+00:28:30,880 --> 00:28:34,270
+تانيةبتعدك حالة تانية أو تالتة أو رابعة أو خمسة
+
+370
+00:28:34,270 --> 00:28:39,410
+هنا لأ هنا مش هنعدها فإذا أول شغلة متوقع انه عدد
+
+371
+00:28:39,410 --> 00:28:43,190
+او عدد ال elements داخل ال set لل permutation
+
+372
+00:28:43,190 --> 00:28:47,230
+هتكون subset من ال S بتاعة ال permutation يا
+
+373
+00:28:47,230 --> 00:28:54,160
+subset أكيد هتكون أقل مش شايف؟with r members فهنا
+
+374
+00:28:54,160 --> 00:28:57,240
+ال cardinality ل ال T هتكون برضه ال R ان انا بتعمل
+
+375
+00:28:57,240 --> 00:29:02,600
+selection ل R لكن ك set مش ك sequence، sequence
+
+376
+00:29:02,600 --> 00:29:06,220
+معناته الترتيب مهم، set بفرجش معاه، set مش هتفرج
+
+377
+00:29:06,220 --> 00:29:11,920
+معانا ترتيبها، بنحسبها كتالي combination from N to
+
+378
+00:29:11,920 --> 00:29:16,640
+select Rو ممكن نعملها بهذا الشكل ك vector شكل
+
+379
+00:29:16,640 --> 00:29:21,860
+vector from N to R عبارة عن ال permutation لاحظ
+
+380
+00:29:21,860 --> 00:29:26,620
+فهي بدلالة ال permutation permutation to select R
+
+381
+00:29:26,620 --> 00:29:34,620
+from N على ال permutation R to R ليش؟ لأنه R و R
+
+382
+00:29:34,620 --> 00:29:39,600
+طوى احنا لسه كتبناها هنا كانت عبارة عن إيش عبارة
+
+383
+00:29:39,600 --> 00:29:46,440
+عن عدد مرات جلوس أربعأربع أشخاص على أربع كراسي،
+
+384
+00:29:46,440 --> 00:29:50,440
+صحيح؟ هذا بالنسبالي مرة في ال combination، بس هنا
+
+385
+00:29:50,440 --> 00:29:54,200
+لأ مظاهرتش مرة، زهرت أربعة وعشرين مرة، فالأربعة
+
+386
+00:29:54,200 --> 00:29:58,820
+وعشرين هذا بدي أختزلها بواحد، صح؟ لإن مفرجش معايا
+
+387
+00:29:58,820 --> 00:30:02,020
+كيف جاعدوا الأربعة، المهم إنه جاعدوا على نفس عدد
+
+388
+00:30:02,020 --> 00:30:05,900
+الكراسيع نفس عدد الكراسي، معناه ذلك أن الفارق بين
+
+389
+00:30:05,900 --> 00:30:10,420
+التنتين هي الحالة هذه أن هذه بالنسبالي بتجسم عليها
+
+390
+00:30:10,420 --> 00:30:16,580
+اللي هي ال permutation R وR ال permutation R وR
+
+391
+00:30:16,580 --> 00:30:22,340
+لأنه في ال permutation هو كان حسب اختلافهم حالات
+
+392
+00:30:22,340 --> 00:30:26,500
+مختلفة لكن في ال combination اختلافهم شيء واحد
+
+393
+00:30:26,500 --> 00:30:30,480
+فعشان هي كان الطبيعي أنه أجسم على هذا ال termكان
+
+394
+00:30:30,480 --> 00:30:33,800
+الطبيعي أني أجسم على ال permutation اللي موجودة
+
+395
+00:30:33,800 --> 00:30:36,700
+عندنا فإذا ان انا بتتكلم عن أربعة هنا في أربع و
+
+396
+00:30:36,700 --> 00:30:40,860
+عشرين حالة في ال permutation انعدت بس في ال
+
+397
+00:30:40,860 --> 00:30:45,340
+combination هي حالة واحدة يعني لما بقولك شوف ال
+
+398
+00:30:45,340 --> 00:30:49,120
+combination لأربعة بدهم يجدوا على أربع كراسي أي
+
+399
+00:30:49,120 --> 00:30:53,640
+طريقة واحدة كيف الترتيب بيفهمش الترتيب اقعد و ان
+
+400
+00:30:53,640 --> 00:30:56,830
+ما تقعد المهم انك انت جاعد في الصف الأول و خلاصهذه
+
+401
+00:30:56,830 --> 00:30:59,850
+الفكرة المهم إنك جاعد على الصف الأول وانتهى وبس
+
+402
+00:30:59,850 --> 00:31:05,510
+فإذا بنقسم على المعامل المختلف بين الاتنين اللي هي
+
+403
+00:31:05,510 --> 00:31:10,250
+ال permutation R وR فهذه لو عوضنا مكانهابقيمتها
+
+404
+00:31:10,250 --> 00:31:15,590
+اللي طوّد تفقنا عليها وفهمناها كيف ال N factorial
+
+405
+00:31:15,590 --> 00:31:19,410
+على N نقص R factorial على R factorial تقوى ..
+
+406
+00:31:19,410 --> 00:31:22,550
+قاعدين نقول R هي اللي هي الأربعة factorial R
+
+407
+00:31:22,550 --> 00:31:26,630
+factorial فهذه بتنزل تحت لاحظ صارت N factorial على
+
+408
+00:31:26,630 --> 00:31:31,370
+R factorial في N نقص R factorial في N نقص R
+
+409
+00:31:31,370 --> 00:31:35,790
+factorial طيب طب هذا الكلام كتير حلو لأنه بعملك
+
+410
+00:31:35,790 --> 00:31:40,700
+حاجة اسمها symmetricبعملك كأنه صار في عندك
+
+411
+00:31:40,700 --> 00:31:44,820
+symmetric هنا لاحظ
+
+412
+00:31:44,820 --> 00:31:52,260
+هنا R بواحد باتنين تلاتة باربعة طب لما تصل ل N
+
+413
+00:31:52,260 --> 00:32:00,620
+ناقص واحد ن على اتنين N على اتنين هتجلب هتعكس بعد
+
+414
+00:32:00,620 --> 00:32:03,020
+هيك ليش؟ هتصير هذه القيمة مكان هذه وهذه القيمة
+
+415
+00:32:03,020 --> 00:32:08,700
+مكان هذهيعني بمعنى لو بنتكلم مثلا عن ستة ال in
+
+416
+00:32:08,700 --> 00:32:15,500
+okay واحد و هنا ستة ناقص واحد خمسة اتنين اربعة
+
+417
+00:32:15,500 --> 00:32:21,720
+تلاتة تلاتة طب لاحظ بعد اربعة اتنين طب ما هذه
+
+418
+00:32:21,720 --> 00:32:26,040
+القيمة نفس القيمة هذه هنا لو كانت خمسة ت select
+
+419
+00:32:26,040 --> 00:32:29,720
+خمسة من ستة هنا هتكون واحد فإذا هذه نفس قيمة هذه
+
+420
+00:32:32,130 --> 00:32:34,770
+نفس الشيء أنت بتقول واحد factorial في خمسة
+
+421
+00:32:34,770 --> 00:32:37,610
+factorial هي هي لما تقول خمسة factorial في واحد
+
+422
+00:32:37,610 --> 00:32:41,310
+factorial إيش اختلفت يعني بس واحدة جابلة تانية في
+
+423
+00:32:41,310 --> 00:32:44,790
+النهاية عملية ضرب وضرب تبادلية كعملية هي عملية
+
+424
+00:32:44,790 --> 00:32:49,310
+تبادلية تمام فإذا بكل بساطة بتقدر تقول إن ال
+
+425
+00:32:49,310 --> 00:32:54,430
+combination N وR هي نفس ال combination N و N ناقص
+
+426
+00:32:54,430 --> 00:33:00,420
+Rو هذه هتفتح لنا تطبيقات كتيرة جدا الفكرة هذه،
+
+427
+00:33:00,420 --> 00:33:04,500
+هتفتح تطبيقات كتيرة جدا في علم الرياضيات
+
+428
+00:33:08,240 --> 00:33:12,600
+Okay هاي مثال .. المثال هنا بكل بساطة بدنا نختار
+
+429
+00:33:12,600 --> 00:33:17,020
+سبعة card hands .. نختار كروت .. سبعة كروت و نحطهم
+
+430
+00:33:17,020 --> 00:33:19,820
+في إيدنا من الاتنين و خمسين اللي موجودين على ال
+
+431
+00:33:19,820 --> 00:33:23,300
+disk .. موجودين على اللي هو .. على ال disk .. اللي
+
+432
+00:33:23,300 --> 00:33:25,380
+هي من الآخر الاتنين و خمسين هت بتاعون الشدة
+
+433
+00:33:25,380 --> 00:33:29,640
+عارفينها أه الورق هذا محتوطين و مش عارف مفروضين
+
+434
+00:33:29,640 --> 00:33:33,240
+بشكل معين فانت بدك تختار منهم سبعة ال combination
+
+435
+00:33:33,240 --> 00:33:39,160
+أنك تختار سبعةطبعا اكيد هنا الترتيب بيفرجش صح اللي
+
+436
+00:33:39,160 --> 00:33:42,260
+منكوا يعني إيه فيه فكرة اللعب هذه ما هو اختارت
+
+437
+00:33:42,260 --> 00:33:46,460
+الرقم في الأول ولا الأخير خلاص انتصار في إيدك يعني
+
+438
+00:33:46,460 --> 00:33:52,140
+انتهى التركيب مش هيفرج .. هتحطه .. هتحطه في أول
+
+439
+00:33:52,140 --> 00:33:54,880
+إيدك ولا في آخر إيدك مش هيفرج كتير فإذا هنا واضح
+
+440
+00:33:54,880 --> 00:33:57,720
+أن combination ال example هذا جدش عدد ال
+
+441
+00:33:57,720 --> 00:34:01,710
+possibility to select seven cardsعشان تختار seven
+
+442
+00:34:01,710 --> 00:34:05,070
+cards أكيد بالطريقة التقليدية هنقول سبع .. اتنين و
+
+443
+00:34:05,070 --> 00:34:09,770
+خمسين و واحد و خمسين سبع مرات ثم نجسم على السبعة
+
+444
+00:34:09,770 --> 00:34:13,030
+factorial نجسم على سبعة factorial بنفس القانون
+
+445
+00:34:13,030 --> 00:34:17,270
+الرئيسي تبعنا اللي كان ممكن نختاره طبعا هنا رقمية
+
+446
+00:34:17,270 --> 00:34:22,170
+عددية سهلة جدا في الحالة بتقدر تقول تختصر فيهم
+
+447
+00:34:22,170 --> 00:34:27,230
+طبعا لات توضيح في الامتحان لأ بدك تشتغل في
+
+448
+00:34:27,230 --> 00:34:31,370
+القوانينتمام؟ اللي هي بدك تعمل ال factorial .. بده
+
+449
+00:34:31,370 --> 00:34:34,690
+أشوف ال factorial .. اه خلاص اعملها بال factorial
+
+450
+00:34:34,690 --> 00:34:36,810
+.. انت ريح راسك .. ليش تقعد تعمل هيك .. القالة
+
+451
+00:34:36,810 --> 00:34:38,690
+الحاسبة و طالع ليها .. المهم ان افهم انك انت
+
+452
+00:34:38,690 --> 00:34:43,910
+استخدمت القانون هذا و طيب .. اذا كان موجودة ..
+
+453
+00:34:43,910 --> 00:34:46,730
+والله ريحنا .. معناه اننا نبطل نجيبها .. النوع
+
+454
+00:34:46,730 --> 00:34:51,030
+الأسئلة هذا بلا منه ..
+
+455
+00:34:51,030 --> 00:34:55,510
+بالمناسبة احنا معظم امتحانات ناخدها من تمكممعظم
+
+456
+00:34:55,510 --> 00:34:59,370
+امتحاناتها بناخدها من .. من نقاشكم طيب combination
+
+457
+00:34:59,370 --> 00:35:03,710
+كمان مثال how many bit strings of length 4 have
+
+458
+00:35:03,710 --> 00:35:09,610
+exactly two ones or exactly two zeros فإذا أنا
+
+459
+00:35:09,610 --> 00:35:13,290
+محتاج اتنين ones و أكيد هي نفسها لو قلت اتنين
+
+460
+00:35:13,290 --> 00:35:18,510
+zeros هي نفسها لو قلت اتنين zeros بمعنى من الخمسين
+
+461
+00:35:18,510 --> 00:35:24,370
+بدي اعمل selection لعشرين واحدتمام؟ هذه طريقة ان
+
+462
+00:35:24,370 --> 00:35:29,790
+انا بدي اياهم ال 21 اقول في فريق معين او ل 30 اللي
+
+463
+00:35:29,790 --> 00:35:35,130
+بديش اياهم عشان هي كانت المكملة بتاع التو بسوء بعض
+
+464
+00:35:35,130 --> 00:35:38,390
+نفس العدد ال possibilities بتاعتنا فإذا لو قولنا
+
+465
+00:35:38,390 --> 00:35:42,230
+exactly two ones هي نفسها لو قولت exactly two
+
+466
+00:35:42,230 --> 00:35:46,540
+zerosاللي هي المكمل مافيش يا zero يا one مافيش اش
+
+467
+00:35:46,540 --> 00:35:49,840
+تالت يعني بينهم يا zero يا إيش يا one فإذا هدول
+
+468
+00:35:49,840 --> 00:35:53,620
+اتنين مكملين لبعض بيحققوا نفس المعلومة اللي
+
+469
+00:35:53,620 --> 00:35:57,480
+قولناها تولى ال combination مع عكسها فهي عندي
+
+470
+00:35:57,480 --> 00:36:01,160
+أربعة ومحتاجين
+
+471
+00:36:01,160 --> 00:36:06,100
+نعمل تلاتة two ones منهم two إيش؟ two ones منهم
+
+472
+00:36:06,100 --> 00:36:08,380
+طيب two ones إما
+
+473
+00:36:10,800 --> 00:36:15,180
+ال one الأولى بتكون هنا او هنا او هنا او هنا هذا
+
+474
+00:36:15,180 --> 00:36:18,140
+ال one الأولى صحيح فعدد ال possibilities بتاعتها
+
+475
+00:36:18,140 --> 00:36:27,780
+أربعة التانية تلاتة لأ
+
+476
+00:36:27,780 --> 00:36:38,590
+غلط غلط ليش لأن ال two ones حقيقة متشابهينالـ two
+
+477
+00:36:38,590 --> 00:36:43,670
+ones متشابهين بمعنى لو ال one الأول ظهر هنا و ال
+
+478
+00:36:43,670 --> 00:36:49,250
+one التاني ظهر هنا طيب ما هي نفسها لو ال one الأول
+
+479
+00:36:49,250 --> 00:36:54,730
+ظهر هنا و ال one التاني اللي ظهر هنا فإذا
+
+480
+00:36:54,730 --> 00:37:01,090
+هنا لأن صدفت ال two digits متشابهين بختلف الكلام
+
+481
+00:37:01,090 --> 00:37:09,610
+لكن لو قلنا a و b مثلا هنا بختلفبتبين أكثر وضوحا
+
+482
+00:37:09,610 --> 00:37:14,150
+يعني لأنه هيكون في عندك بالطريقة هذه ال A اخترناها
+
+483
+00:37:14,150 --> 00:37:19,950
+هنا و ال B اخترناها هنا طب حالة تانية هتكون ال A
+
+484
+00:37:19,950 --> 00:37:24,770
+بدنا اخترناها هنا و ال B اجت هنا بس فعليا انا
+
+485
+00:37:24,770 --> 00:37:29,470
+عديتها دي مرة و عديتها دي مرة باستخدام 4 على 3 هيك
+
+486
+00:37:29,470 --> 00:37:34,330
+لما استخدمت 4 في 3 و قلنا 12 انا فعليا عديت هذه
+
+487
+00:37:34,330 --> 00:37:36,920
+الحالة و عديت هذه الحالةو هذا مش صح في ال
+
+488
+00:37:36,920 --> 00:37:40,460
+combination هذا صح في ال permutation بس في ال
+
+489
+00:37:40,460 --> 00:37:44,000
+combination المفروض انه لأ انا بهمنيش هدا جاعد في
+
+490
+00:37:44,000 --> 00:37:45,620
+الكرسي اللي هنا و جاعد وهدا جاعد في الكرسي اللي
+
+491
+00:37:45,620 --> 00:37:48,640
+هنا لو بدّروا مع بعض مفرجش فلأ هدولة التنتين
+
+492
+00:37:48,640 --> 00:37:52,580
+المفروض حالة واحدة طيب الحالات هذه جديش بتتكرر انا
+
+493
+00:37:52,580 --> 00:37:55,960
+لاحظ ان انا ماتطبقتش القانون الصح انا فعليا قولت
+
+494
+00:37:55,960 --> 00:38:01,140
+اربعة هنافي تلاتة و سكتت فاتكلمت عن ال permutation
+
+495
+00:38:01,140 --> 00:38:05,300
+المفروض ان لأ اجسم على المتبقي الاتنين انا بدي two
+
+496
+00:38:05,300 --> 00:38:09,060
+ones فالمفروض اجسم على اتنين factorial المفروض
+
+497
+00:38:09,060 --> 00:38:14,200
+اخدنا بالنا من قسمت اتنين factorial فإذا لسه بدنا
+
+498
+00:38:14,200 --> 00:38:16,840
+نجسم على اتنين عشان نطلع عندى فعليا ست حالات فقط
+
+499
+00:38:16,840 --> 00:38:24,620
+عندنا ست حالاتتمام طيب كمان اه و نفس المثال احنا
+
+500
+00:38:24,620 --> 00:38:27,920
+بس وضحنا فيه ال a و ال b عشان يبينوا ال a مكان ال
+
+501
+00:38:27,920 --> 00:38:31,700
+b لأنه ال ones حتى مش هتبين كتير معاك لما تقول one
+
+502
+00:38:31,700 --> 00:38:34,840
+one one one انت ماعرفتش انه one اللي اجى قبل
+
+503
+00:38:34,840 --> 00:38:37,880
+التاني فعشان يقولنا a و b عشان تبين معاك انه ممكن
+
+504
+00:38:37,880 --> 00:38:42,980
+يجوا معاكوا sin عن بعضهم فبطلع فعليا 12 على 2 على
+
+505
+00:38:42,980 --> 00:38:49,850
+2 اخر ال slide okay كمانcombination example هقول
+
+506
+00:38:49,850 --> 00:38:55,410
+انه how many bit string of size ten contain four
+
+507
+00:38:55,410 --> 00:38:59,610
+ones بسيطة مش محتاجة شغل كتير على طول combination
+
+508
+00:38:59,610 --> 00:39:04,230
+عشرة to select أربعة و خلاص طيب we need to form
+
+509
+00:39:04,230 --> 00:39:09,550
+لتشكيل community لجنة من سبعة people السبعة people
+
+510
+00:39:09,550 --> 00:39:13,530
+هدولة three from mathمن الرياضيات تلاتة المفروض ان
+
+511
+00:39:13,530 --> 00:39:16,890
+هم من قسم رياضيات و أربعة من قسم computer science
+
+512
+00:39:16,890 --> 00:39:20,110
+لإيش بدنا يهم دوله لتطوير نفترض مثلا discrete
+
+513
+00:39:20,110 --> 00:39:22,710
+mathematics course بدنا نطوره و نقولنا والله
+
+514
+00:39:22,710 --> 00:39:26,250
+الطلاب مش عاجبهم المساق هتنطور نعدل نظبط طب هاتوا
+
+515
+00:39:26,250 --> 00:39:29,490
+معناته بدنا لجنة من سبع أعضاء السبع أعضاء هدولة
+
+516
+00:39:29,490 --> 00:39:32,850
+تلاتة من ال mathematicsو هتلاك أربعة من ال
+
+517
+00:39:32,850 --> 00:39:35,610
+computer science و هتنشوف يجودوا مع بعض و يشوفوا
+
+518
+00:39:35,610 --> 00:39:38,570
+المساق و ال kid دي كده إيش ممكن نطور فيه الله أستر
+
+519
+00:39:38,570 --> 00:39:44,230
+ما يزودوا مش هيك؟ تمام فعشان أبدأ أعمل selection
+
+520
+00:39:44,230 --> 00:39:47,130
+بدي أشوف طب إيش ال candidates بالنسبالي يعني مين
+
+521
+00:39:47,130 --> 00:39:51,290
+المرشحين يكونوا في اللجنة من ال math و من ال
+
+522
+00:39:51,290 --> 00:39:55,890
+science من هنا و من هنا هتنشوف وجدنا إنه في قسم
+
+523
+00:39:55,890 --> 00:40:02,300
+الرياضيات عددأه عدد ال candidates بتاعنا تسعة ففي
+
+524
+00:40:02,300 --> 00:40:05,680
+عند تسعة أساتذة في الرياضيات ممكن نختار منهم تلاتة
+
+525
+00:40:05,680 --> 00:40:09,580
+لللجنة وفي عند حداشر في الحسوب ممكن نختار منهم
+
+526
+00:40:09,580 --> 00:40:14,440
+أربعة ممكن نختار منهم أربعة فجدش عدد ال ways to
+
+527
+00:40:14,440 --> 00:40:20,740
+select this community أو الاختيار هذهاللجنة اللي
+
+528
+00:40:20,740 --> 00:40:24,660
+احنا بنتكلم عنها طبعا هانيجي نتفصل هذه لحاله وهذه
+
+529
+00:40:24,660 --> 00:40:29,780
+لحاله عشان اعمل selection ل ال math part جزء ال ..
+
+530
+00:40:29,780 --> 00:40:31,700
+ال .. ال .. ال ناس بتاعهم ال mathematics بده اقول
+
+531
+00:40:31,700 --> 00:40:37,260
+من التسعة بده اختار تلاتة خلاص من التسعة بده اختار
+
+532
+00:40:37,260 --> 00:40:41,840
+تلاتة لحالها combination لحالها طيب من ال 11 بدنا
+
+533
+00:40:41,840 --> 00:40:47,640
+نختار اربعة من 11 بده اختار اربعة بس فعليا الاتنين
+
+534
+00:40:47,640 --> 00:40:52,420
+هدول مع بعضالاتنين هدول بدهم كونوا مع بعض بمعنى
+
+535
+00:40:52,420 --> 00:40:55,460
+انه مضروبين مع بعض ليش لأنه هنا هنرجع لأول rule
+
+536
+00:40:55,460 --> 00:40:59,300
+أخدناها في الموضوع هذا اللي هي ال sum و ال product
+
+537
+00:40:59,300 --> 00:41:06,740
+ال sum if كانت or و ال and معناته product طيب هنا
+
+538
+00:41:06,740 --> 00:41:13,100
+انا محتاج تلاتة and أربعة فإذا اللجنة total هي
+
+539
+00:41:13,100 --> 00:41:16,060
+سبعة الاتنين لازم يكونوا موجودين التلاتة اللي
+
+540
+00:41:16,060 --> 00:41:19,790
+هاخدهم من ال math مع الأربعة اللي هاخدهم من مينمن
+
+541
+00:41:19,790 --> 00:41:22,710
+ال computer science الاتنين بدهم ييجوا مع بعض مع
+
+542
+00:41:22,710 --> 00:41:27,350
+بعض فإذا أكيد هيكون ضرب ناتج هذا في ناتج هذا هي مش
+
+543
+00:41:27,350 --> 00:41:33,430
+or يا هدول يا هدول لأ هي الاتنين مع بعض فهنا هيكون
+
+544
+00:41:33,430 --> 00:41:36,270
+مضروب الاتنين مع بعض ففي عندي سبعة و عشرين
+
+545
+00:41:36,270 --> 00:41:40,810
+possibility و سبعة مائة و عشرين ممكنية نعمل فيها
+
+546
+00:41:40,810 --> 00:41:47,690
+تشكيل للجنة تمام طيب كمان مثال بدنا نعمل flipping
+
+547
+00:41:47,690 --> 00:41:51,950
+ل coinال coin اللي هي بدك تعملها flipping اللي هي
+
+548
+00:41:51,950 --> 00:41:55,030
+تطيرها في الهواء هذه ال .. و تشوف جداش ايش بده
+
+549
+00:41:55,030 --> 00:41:58,030
+يطلع معاك طيب لو افترضنا ان في عندك ال coin هذي
+
+550
+00:41:58,030 --> 00:42:03,370
+بدك تعملها in times in مرة واحد اتنين تلاتة in مرة
+
+551
+00:42:03,370 --> 00:42:06,410
+و تشوف ايش النتائج اللي ظهرت في ال in مرة طيب how
+
+552
+00:42:06,410 --> 00:42:12,030
+many different ways can you get no heads عشان فعلا
+
+553
+00:42:12,030 --> 00:42:17,070
+من ال .. من ال in مرة ولا مرة ظهرت معاك head دايما
+
+554
+00:42:17,070 --> 00:42:23,220
+بطلع معاك ال tailاللي هي .. إيش بنسميها احنا ..
+
+555
+00:42:23,220 --> 00:42:26,060
+صورة و كتابة .. مش إذا كانت صورة و كتابة ..
+
+556
+00:42:26,060 --> 00:42:28,460
+الكتابة يعني .. دايما بيطلع كله كتابة .. no hidden
+
+557
+00:42:28,460 --> 00:42:31,540
+.. مولا مرة طلعت صورة فإذا .. لأ combination ..
+
+558
+00:42:31,540 --> 00:42:34,640
+احنا اشتغل combination سيبها زي ما تطلع اشتغل
+
+559
+00:42:34,640 --> 00:42:40,360
+combination .. هينا من .. in .. مرة .. zero
+
+560
+00:42:40,360 --> 00:42:44,080
+selectionzero selection تطلع زي ما تطلع في الآخر
+
+561
+00:42:44,080 --> 00:42:46,940
+حيطلع معاك واحد او حيطلع معاك واحد بس في النهاية
+
+562
+00:42:46,940 --> 00:42:50,720
+خلّيك مع القانون خلّيك مع القانون أفضل بدنا عشان
+
+563
+00:42:50,720 --> 00:42:54,040
+نعمل زيتو هنا نتشطر في اه يالا أربعة افتتح أهم
+
+564
+00:42:54,040 --> 00:42:58,200
+ممكن أبقى سهلة طلع لأ في إشي أنا أخفلته فلأ خلّينا
+
+565
+00:42:58,200 --> 00:43:01,120
+على القانون أحسنلك و بعدين انت أوض في القانون زي
+
+566
+00:43:01,120 --> 00:43:05,660
+ما هو بتضمن عدم وجود أي مفاجئات في النتائج تمام
+
+567
+00:43:05,660 --> 00:43:16,310
+التانية exactly one برضه type twoطب R ماهيش
+
+568
+00:43:16,310 --> 00:43:19,390
+هالسؤال اللي .. ماهيش هالسؤال اللي .. طيب at least
+
+569
+00:43:19,390 --> 00:43:22,810
+two heads واحد ناجس اتنين .. واحد ناجس اتنين ..
+
+570
+00:43:22,810 --> 00:43:24,490
+واحد ناجس اتنين .. واحد ناجس اتنين .. واحد ناجس
+
+571
+00:43:24,490 --> 00:43:24,950
+اتنين .. واحد ناجس اتنين .. واحد ناجس اتنين ..
+
+572
+00:43:24,950 --> 00:43:26,610
+واحد ناجس اتنين .. واحد ناجس اتنين .. واحد ناجس
+
+573
+00:43:26,610 --> 00:43:29,670
+اتنين .. واحد ناجس اتنين .. واحد ناجس اتنين ..
+
+574
+00:43:29,670 --> 00:43:31,670
+واحد ناجس اتنين .. واحد ناجس اتنين .. واحد ناجس
+
+575
+00:43:31,670 --> 00:43:31,810
+اتنين .. واحد ناجس اتنين .. واحد ناجس اتنين ..
+
+576
+00:43:31,810 --> 00:43:34,120
+واحد ناجس اتنين .. واحد ناجس اتنين ..هذه ليست
+
+577
+00:43:34,120 --> 00:43:37,240
+probability عشانك انا حريص ان دائما اقولكم
+
+578
+00:43:37,240 --> 00:43:38,960
+possibilities .. possibilities .. possibilities ..
+
+579
+00:43:38,960 --> 00:43:41,080
+بديش اقول كلمة probability النهائية عشان ما تاخدوش
+
+580
+00:43:41,080 --> 00:43:44,660
+في بالكوا الوحيد احنا ماتكلمش عن one فال total هنا
+
+581
+00:43:44,660 --> 00:43:50,370
+بس انت كلامك صحهي لاحظ هناخد من كلامه هو جال حاجة
+
+582
+00:43:50,370 --> 00:43:53,250
+كويسة بس هو راح في ال probability الواحد في ال
+
+583
+00:43:53,250 --> 00:43:56,490
+probability إيش يعني؟ يعني ال total طيب ال total
+
+584
+00:43:56,490 --> 00:44:00,010
+هنا جديش؟ بمعنى كل ال possibilities الممكنة جديش
+
+585
+00:44:00,010 --> 00:44:03,070
+كل ال possibilities الممكنة عشان نبدأ منها بدل
+
+586
+00:44:03,070 --> 00:44:07,150
+الواحد اللي جالها إيش هي ال possibilities الممكنة؟
+
+587
+00:44:07,150 --> 00:44:12,090
+طيب كمان مرة هاي
+
+588
+00:44:14,030 --> 00:44:18,690
+عدد المرات اللي بناعمل فيهم ال flipping كويس؟
+
+589
+00:44:18,690 --> 00:44:24,210
+المرة الأولى إيش ال possibilities تقونها؟ اتنين مش
+
+590
+00:44:24,210 --> 00:44:30,090
+هيك؟ يا ملك يا كتابة طيب هاي مرتين والتانية أحسنته
+
+591
+00:44:30,090 --> 00:44:34,970
+هاي ال total الواحد تبعنا اللي هي اتنين to the
+
+592
+00:44:34,970 --> 00:44:41,390
+power n الان اطرح منه اللي بدكية هاي بس ال trick
+
+593
+00:44:41,390 --> 00:44:45,650
+في الموضوعواضحت؟ في هذا الواحد تبع ال probability
+
+594
+00:44:45,650 --> 00:44:48,490
+احنا عندنا possibilities فال total لكل ال
+
+595
+00:44:48,490 --> 00:44:53,110
+possibilities الممكنة لاحظ هي اتنين to the power n
+
+596
+00:44:53,110 --> 00:44:56,110
+بيكون يعطاني كل ال possibilities الممكنة بالترتيب
+
+597
+00:44:56,110 --> 00:45:02,350
+تبعها كاملا طيب ناقص الان at least two heads يعني
+
+598
+00:45:02,350 --> 00:45:05,890
+اتنين او تلاتة او اربعة فاذا من المستثنى الصفر
+
+599
+00:45:05,890 --> 00:45:13,140
+والواحد ايه؟هيهم ما احنا سبجنا و جيبناهم فإذا بس
+
+600
+00:45:13,140 --> 00:45:17,060
+القيمتين هدول هنطرحهم من الأثنين to the power بس
+
+601
+00:45:17,060 --> 00:45:20,820
+هي كل الجثة في الموضوع هي ال trick اللي مهدنا لها
+
+602
+00:45:20,820 --> 00:45:24,320
+بالحاجات البسيطة في الأول عشان تاخد بالك من فكرة
+
+603
+00:45:24,320 --> 00:45:28,820
+ممكن تيجي فكرة قد تأتي في الأمثلة بتاعتنا okay
+
+604
+00:45:28,820 --> 00:45:31,980
+بنخلي ال polynomial coefficients ال polynomial
+
+605
+00:45:31,980 --> 00:45:35,880
+coefficients بالمناسبة من كلمة polynomialانتوا
+
+606
+00:45:35,880 --> 00:45:38,700
+عارفين انه binomial اللي هي ايش المعادلات بال
+
+607
+00:45:38,700 --> 00:45:42,520
+order in بال order in فالمرة القادمة هنجد انه جد
+
+608
+00:45:42,520 --> 00:45:45,840
+ما يكون ال order هذا تبعكوا كبير جد ما يكون كبير
+
+609
+00:45:45,840 --> 00:45:48,360
+بتقدروا ال coefficients تبعكوا تجيبوها بكل بساطة
+
+610
+00:45:48,360 --> 00:45:52,120
+من خلال ال combination هناخدها و هناخد ايش
+
+611
+00:45:52,120 --> 00:45:55,260
+الاستفادة ممكن نستفيدها منها و اذا كان في عندك
+
+612
+00:45:56,450 --> 00:45:59,130
+order معين وانت عارف ال coefficients سبعته كيف
+
+613
+00:45:59,130 --> 00:46:02,530
+تجيب ال order اللي وراه بدون ما تضطر تفك المعادلة
+
+614
+00:46:02,530 --> 00:46:06,870
+ايش يعني تفك المعادلة يعني اقولك والله x زائد y to
+
+615
+00:46:06,870 --> 00:46:11,390
+the power 15 هتليها هتلي coefficients سبعتها طبعا
+
+616
+00:46:11,390 --> 00:46:15,190
+مش حد يمكن تضربليها في نفسها خمستاشر مرة كلام فاضي
+
+617
+00:46:15,190 --> 00:46:18,590
+هذا اسمه كلام فاضي تضربها في نفسها خمستاشر مرة طب
+
+618
+00:46:18,590 --> 00:46:22,210
+انا هجيبلكيها في سؤال يلا بدك تضربها خمستاشر مرة و
+
+619
+00:46:22,210 --> 00:46:25,210
+بعدين نقول والله الامتحان طويللأ أنا ما طلبتش
+
+620
+00:46:25,210 --> 00:46:28,470
+تضربها في نفسها 15 مرة أنا بدي من خلال قانون
+
+621
+00:46:28,470 --> 00:46:31,830
+combination فعلا ال جيب اللي تقولي والله هي x و y
+
+622
+00:46:31,830 --> 00:46:35,370
+و تكررهم 15 مرة x و y بصير جديش ال coefficients
+
+623
+00:46:35,370 --> 00:46:38,870
+لكل واحدة منهم على اعتبار انه هنا هتبدأ بإذا كان
+
+624
+00:46:38,870 --> 00:46:46,340
+15 مانا تظابر 15 و 0بعدين اللي وراها 14 و 1 بس طيب
+
+625
+00:46:46,340 --> 00:46:49,260
+بيضل إيش ال coefficients اللي هنا ال combination
+
+626
+00:46:49,260 --> 00:46:52,540
+هيحللك إياها بنشوف المرة الجاية كيف هيحسبلك إياها
+
+627
+00:46:52,540 --> 00:46:55,420
+بدون ما تقعد تضرب في بعضها 15 مرة أنا مش هجيبلك
+
+628
+00:46:55,420 --> 00:47:00,120
+خمسة هجيبلك مية عشان .. عشان أشوف مين .. عشان أشوف
+
+629
+00:47:00,120 --> 00:47:02,040
+مين اللي بيقعد يضرب لي إياها يعمل لي زي ال
+
+630
+00:47:02,040 --> 00:47:04,280
+summation بتاع ال .. ال midterm يعطيكوا العافية
+
+631
+00:47:04,280 --> 00:47:05,460
+بنشوفكوا المرة الجاية ان شاء الله
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/VOPKfsvewqI.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/VOPKfsvewqI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c9c5cff796d0bec80201ccbca98528f60e4c54d4
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/VOPKfsvewqI.srt
@@ -0,0 +1,1955 @@
+1
+00:00:05,130 --> 00:00:07,610
+بسم الله الرحمن الرحيم، يعطيكم العفو يا شباب، اليوم
+
+2
+00:00:07,610 --> 00:00:11,350
+نكمل جزئية الـ applications اللي بدأنا نأخذها على
+
+3
+00:00:11,350 --> 00:00:15,430
+الـ number theory و من المرة الماضية، ممكن اتكلمنا
+
+4
+00:00:15,430 --> 00:00:17,490
+أنّه في حاجة من الحاجات المهمة جداً، اللي هي الـ pseudo
+
+5
+00:00:17,490 --> 00:00:21,710
+random، pseudo random بمعنى أنّه deterministically أو
+
+6
+00:00:21,710 --> 00:00:25,970
+بشكل محسوب، معروف، أيش المعادلات تبعته، بقدر أعمله
+
+7
+00:00:25,970 --> 00:00:30,130
+generation لـ random numbers، رغم أنّه that appear
+
+8
+00:00:30,130 --> 00:00:34,920
+random، يعني هو يظهر كأنه عشوائي، يظهر كأنه عشوائي،
+
+9
+00:00:34,920 --> 00:00:39,650
+فإذا أنت مش عارف الـ .. زي ما بقول الخطة تبعته، أو
+
+10
+00:00:39,650 --> 00:00:43,330
+الجزء الـ deterministic تبعه، okay، أنت تظن أنّه
+
+11
+00:00:43,330 --> 00:00:47,050
+عشوائي، بس هو فعلياً لأ، هو مش عشوائي، هو ليس عشوائي
+
+12
+00:00:47,050 --> 00:00:49,650
+تمام، هذه اتكلمنا عنها المرة الماضية، أيش
+
+13
+00:00:49,650 --> 00:00:52,270
+استخداماتها؟ الاستخدامات كثيرة، منها الـ games، منها
+
+14
+00:00:52,270 --> 00:00:54,490
+الـ graphics، منها الـ simulations اللي بتنعمل كـ
+
+15
+00:00:54,490 --> 00:00:57,930
+simulations، الـ graphics، لما بيكون يعطي أو الـ games
+
+16
+00:00:57,930 --> 00:01:01,350
+لما بيكون يعطيك مجموعة options للحلول، أحياناً بيكون
+
+17
+00:01:01,350 --> 00:01:06,380
+فيها random، randomization، بالموضوع هذا كويس
+
+18
+00:01:06,380 --> 00:01:10,800
+فبتستخدم في حالة زي الحالات هذه في الـ hash
+
+19
+00:01:10,800 --> 00:01:14,280
+functions اللي بيعمل عملية mask للـ data، خصوصاً الـ
+
+20
+00:01:14,280 --> 00:01:17,740
+data الكبيرة، اللي بيعملها عملية security كـ secure
+
+21
+00:01:17,740 --> 00:01:22,520
+code، برضه بيستخدم فيها الـ random، الـ cryptographic
+
+22
+00:01:22,520 --> 00:01:26,630
+algorithm، وهذا اللي حنوصله في آخر المحاضرة في
+
+23
+00:01:26,630 --> 00:01:29,910
+آخر المحاضرة، اللي هو عملية التشفير، تشفير البيانات
+
+24
+00:01:29,910 --> 00:01:34,850
+برضه محتاجة نشتغل على random sequence أو تبدو
+
+25
+00:01:34,850 --> 00:01:37,490
+كأنها random sequence، في الحالة اللي احنا ممكن نحكي
+
+26
+00:01:37,490 --> 00:01:41,190
+عنها، طيب أيش الـ techniques اللي ممكن نستخدمها to
+
+27
+00:01:41,190 --> 00:01:45,450
+generate الـ random numbers هذه؟ هي الـ linear
+
+28
+00:01:45,450 --> 00:01:48,930
+congruential method اللي أخذناها المرة الماضية
+
+29
+00:01:48,930 --> 00:01:52,870
+وقلنا أن هي linear، معناته المعادلة أصلاً هي linear
+
+30
+00:01:52,870 --> 00:01:56,890
+و congruential بمعنى أنّه مش بالضروري هذه تساوي
+
+31
+00:01:56,890 --> 00:02:02,530
+exactly هذه، وإنّما تكافئها حسب الـ modulus M، أخذنا
+
+32
+00:02:02,530 --> 00:02:07,290
+أنّ في فرق بين equal و congruent، مش هيك؟ هذه تكافئ
+
+33
+00:02:07,290 --> 00:02:10,590
+هذه، تساوي، فهم مختلفين تماماً عن بعض في الحالة
+
+34
+00:02:10,590 --> 00:02:13,670
+بتاعتنا، فهي المعادلة linear، اه linear لأن هي
+
+35
+00:02:13,670 --> 00:02:17,610
+معادلة خطية، congruential، okay، مش congruential لأنّ
+
+36
+00:02:17,610 --> 00:02:22,270
+هذه لا تساوي exactly هذه، وإنّما تكافئها حسب الـ
+
+37
+00:02:22,270 --> 00:02:28,070
+modulus اللي احنا شغالين عليه، تمام، وأخذنا مثال
+
+38
+00:02:28,070 --> 00:02:31,870
+تمام، هيعطينا مجموعة الـ parameters اللي محتاجينها
+
+39
+00:02:31,870 --> 00:02:35,230
+to generate a sequence، a certain sequence، وفعلاً
+
+40
+00:02:35,230 --> 00:02:37,710
+شفنا الـ certain sequence اللي اشتغلناه، هي شفناه
+
+41
+00:02:37,710 --> 00:02:41,510
+هنا، وأخذنا شوية ملاحظات، طلعنا بشوية ملاحظات أنّه
+
+42
+00:02:41,510 --> 00:02:46,110
+أنا بقدر أعرف قديش قيمة الـ modulus إذا كان عرفت
+
+43
+00:02:46,110 --> 00:02:50,030
+أنت بتـ ... بتكرر الـ sequence، إذا كان اتكرر الـ
+
+44
+00:02:50,030 --> 00:02:53,490
+sequence، فبنقدر نعرف قديش، وأخذنا مثال اللي هو كان
+
+45
+00:02:53,490 --> 00:02:57,270
+عنده seed بدأناها بثلاثة، فرجعت اتكررت الثلاثة بعد
+
+46
+00:02:57,270 --> 00:03:00,410
+تسعة elements، فأعرف أنّه على طول الـ modulus اللي
+
+47
+00:03:00,410 --> 00:03:02,610
+أنا مستخدمه هو تسعة، هو فعلاً الـ modulus اللي
+
+48
+00:03:02,610 --> 00:03:07,740
+استخدمناه كان تسعة، exactly فعلاً تسعة، طيب هذا الكلام
+
+49
+00:03:07,740 --> 00:03:11,480
+عشان يحاولوا يحسنوا في عملية الـ generation، وجدوا
+
+50
+00:03:11,480 --> 00:03:17,520
+أنّ الـ pure multiplicative generator بـ modulus بدل
+
+51
+00:03:17,520 --> 00:03:21,880
+تسعة، لأ، اثنين أس واحد وثلاثين، واحد وثلاثين، عفواً
+
+52
+00:03:21,880 --> 00:03:26,820
+ناقص واحد، هذا استخدموه كأنّه مين الـ M، فجاؤوا أن
+
+53
+00:03:26,820 --> 00:03:31,480
+هذا أفضل شيء ممكن، لأنّ أنتَ هتحتاج في الحالة هذه لأ
+
+54
+00:03:31,480 --> 00:03:34,940
+حوالي اثنين to the power واحد وثلاثين ناقص اثنين
+
+55
+00:03:34,940 --> 00:03:38,760
+element قبل ما ترجع تتكرر ثانية، فبتكون حتى لو عندك
+
+56
+00:03:38,760 --> 00:03:41,720
+مهمة خلصتها وانتهيت، يعني حتى لو بدك تعمل mask أو
+
+57
+00:03:41,720 --> 00:03:45,860
+شيء، هتكون خلصتها قبل ما تبدأ في عملية التكرار، قبل
+
+58
+00:03:45,860 --> 00:03:48,240
+ما تكون بدأت في عملية التكرار، فأنتم متخيلين قديش
+
+59
+00:03:48,240 --> 00:03:51,330
+اثنين to the power واحد وثلاثين، مش هيك؟ يعني بتتكلم
+
+60
+00:03:51,330 --> 00:03:55,470
+عن اثنين الـ ... الـ ... الـ billion، two billion وكسر، مش
+
+61
+00:03:55,470 --> 00:04:00,750
+هيك، تمام، فبتكون أنسب من أرقام ثانية، طيب الـ
+
+62
+00:04:00,750 --> 00:04:04,330
+multiplier بستخدمه سبعة أس خمسة، اللي هو حوالي
+
+63
+00:04:04,330 --> 00:04:08,830
+ستّة عشر ألف، تماماً، وسبعة كـ parameter أو كقيمة للـ
+
+64
+00:04:08,830 --> 00:04:15,390
+parameter a، كويس، وصلنا هنا، عند هذه المرة الماضية كنا
+
+65
+00:04:15,390 --> 00:04:20,450
+ووقفنا عند النقطة هذه، وقلنا أنّه عشان نشتغل الشغل
+
+66
+00:04:20,450 --> 00:04:26,010
+هذا فعلياً، وفعلاً أبدأ أجيب قيم لـ sequence، أو نفكّ
+
+67
+00:04:26,010 --> 00:04:29,570
+... نفكّ، لاحظ الـ sequence اللي موجود عندك، فأنت بدأت
+
+68
+00:04:29,570 --> 00:04:32,310
+تجيب العكس تبعه، أنتَ عملت encryption، بس طيب الـ
+
+69
+00:04:32,310 --> 00:04:36,350
+decryption أهم من الـ encryption، يعني هو مش شطارة
+
+70
+00:04:36,350 --> 00:04:38,870
+أنّ أنا أشفر بيانات وأرميها وأنا ما أعرفش كمان
+
+71
+00:04:38,870 --> 00:04:43,210
+أرجّعها، ده وش استفدنا منها، طيب عملية أنك ترجعها
+
+72
+00:04:43,210 --> 00:04:48,290
+يعني كأنّك أنت بدأت تجيب قيمة X من المعادلة الخطية
+
+73
+00:04:48,290 --> 00:04:51,750
+فلما يكون عندك a في x، لأنّه على اعتبار أنّ الـ a ده
+
+74
+00:04:51,750 --> 00:04:54,910
+هو الـ mask، فأنت ضربته في الـ data، أيش طلع عندك
+
+75
+00:04:54,910 --> 00:04:59,510
+معلومة معيّنة، تمام، فإذا أنا بدّي أجيب المعلومة
+
+76
+00:04:59,510 --> 00:05:04,290
+بمعلومية الـ mask اللي أنا ضربت فيه، اللي هي ممكن
+
+77
+00:05:04,290 --> 00:05:10,550
+أرجع أعمله إعادة generation والـ data اللي انبعتت
+
+78
+00:05:10,550 --> 00:05:14,880
+أصلاً، اللي هي فعلاً متوفرة ومشفرة أصلاً، مش هيك؟ هي مش
+
+79
+00:05:14,880 --> 00:05:19,140
+مشفرة، طيب كيف بدّي أجيب X منها؟ okay، ببساطة جداً، بجيب
+
+80
+00:05:19,140 --> 00:05:24,380
+الـ inverse لـ A، ممتازة، بس الفكرة أن الـ inverse لـ A
+
+81
+00:05:24,380 --> 00:05:28,840
+هي مش معادلة خطية pure linear، لأ، هي مش pure linear
+
+82
+00:05:28,840 --> 00:05:33,760
+هي congruential، هي linear congruential، ليش؟ لأنّ في
+
+83
+00:05:33,760 --> 00:05:38,210
+عندك الـ modulus M، فأنت ما بتقدر تتعامل معها زي ما
+
+84
+00:05:38,210 --> 00:05:41,090
+كنت تتعامل مع الـ linear، الـ pure linear اللي كنت
+
+85
+00:05:41,090 --> 00:05:44,630
+تشتغلها، لأ، هنا في خصوصية شوية، الخصوصية الشوية هي
+
+86
+00:05:44,630 --> 00:05:51,290
+أنّ الـ inverse للـ A بالـ module M لازم يكون عبارة عن
+
+87
+00:05:51,290 --> 00:05:55,190
+الـ A prime بحيث أنك الـ A prime في الـ A هو
+
+88
+00:05:55,190 --> 00:06:03,310
+equivalent أو congruent للواحد، ولا يساوي الواحد، هي
+
+89
+00:06:03,310 --> 00:06:07,150
+congruent للواحد، عارفين أيش يعني؟ يعني معناه ذلك
+
+90
+00:06:07,150 --> 00:06:10,910
+أنّه ممكن يكون عندك أكثر من inverse، ممكن يكون عندك
+
+91
+00:06:10,910 --> 00:06:15,350
+أكثر من inverse، لكن الفكرة وين؟ الفكرة أنّه أنتَ
+
+92
+00:06:15,350 --> 00:06:18,630
+عشان يكون unique، وتسميته unique، المفروض أنّه في كلّ
+
+93
+00:06:18,630 --> 00:06:24,510
+one loop ما يكون إلا inverse وحيد، okay، إذا الـ
+
+94
+00:06:24,510 --> 00:06:27,010
+inverse الثاني يكون في الـ loop اللي وراها، في الـ
+
+95
+00:06:27,010 --> 00:06:30,390
+loop اللي وراها، بس مش يكون two inverse في نفس الـ
+
+96
+00:06:30,390 --> 00:06:36,090
+loop، في نفس الـ loop، عشان نعمل الكلام هذا، ونضمن أنّه
+
+97
+00:06:36,090 --> 00:06:41,030
+فعلاً مش هيظهر two inverse، أو أنّه يوجد أصلاً inverse
+
+98
+00:06:41,030 --> 00:06:46,920
+كمان داخل الـ one loop، في الحالة هذه، محتاجين نحكم بسّ
+
+99
+00:06:46,920 --> 00:06:49,960
+الـ A مع الـ modulus، الـ A هذا اللي بدنا نجيب له الـ
+
+100
+00:06:49,960 --> 00:06:54,860
+inverse، مع الـ modulus، يكونوا relatively prime أو
+
+101
+00:06:54,860 --> 00:06:58,740
+co-prime، عشان أضمن أنّه الـ greatest common divisor
+
+102
+00:06:58,740 --> 00:07:04,280
+between them واحد، فهم ما فيش تكرار بينهم، فمعنى ذلك
+
+103
+00:07:04,280 --> 00:07:09,310
+أنّه الـ A ما بتظهرش مرتين داخل الـ M، داخل الـ one loop
+
+104
+00:07:09,310 --> 00:07:12,990
+ما تظهرش أكثر من مرة واحدة، فإذا لها inverse
+
+105
+00:07:12,990 --> 00:07:19,250
+بضمن أنّه بتكرر مرة واحدة فقط داخل الـ one loop، تمام
+
+106
+00:07:19,250 --> 00:07:24,470
+فمبدأياً، إذا قدرنا هنا نحقق هذه المعادلة، أنّه فعلاً
+
+107
+00:07:24,470 --> 00:07:28,850
+أي inverse في قيمته في القيمة الأصلية بتساوي واحد
+
+108
+00:07:28,850 --> 00:07:32,730
+بس بدنا نأخذ أنّه نأخذ بأنّها modulo M، هذا معناه إذا
+
+109
+00:07:32,730 --> 00:07:35,610
+كان في الحالة هذه، قدرنا نجيبها، مجرد أنّه بضربها في
+
+110
+00:07:35,610 --> 00:07:41,140
+الطرفين للمعادلة، في الطرفين عشان أقول أن هذا بيساوي
+
+111
+00:07:41,140 --> 00:07:46,940
+واحد حسب المعادلة، واحد، فبتروح الـ X، وبقدر أستخرج قيمة
+
+112
+00:07:46,940 --> 00:07:50,720
+X، نقدر في الحالة هذه نستخرج قيمة الـ X اللي موجودة
+
+113
+00:07:50,720 --> 00:07:57,720
+عندنا، كـ A prime في B، يعني الـ A inverse لـ الـ mask
+
+114
+00:07:57,720 --> 00:08:01,380
+أو لـ الـ random numbers اللي أنت استخدمتها في الـ
+
+115
+00:08:01,380 --> 00:08:04,390
+output اللي وصلك أصلاً، في الـ output اللي وصلك، تضربهم
+
+116
+00:08:04,390 --> 00:08:07,490
+في بعض، وتجيب قيمة A، طيب هذا الكلام عشان يتحقق
+
+117
+00:08:07,490 --> 00:08:10,910
+فعلياً، وأكون ضامن أنّه صحيح، الـ greatest common
+
+118
+00:08:10,910 --> 00:08:13,810
+divisor بين الـ A والـ M لازم يكون بيساوي واحد، عشان
+
+119
+00:08:13,810 --> 00:08:16,930
+أضمن أن هم relatively prime أو co-prime أو co-prime
+
+120
+00:08:16,930 --> 00:08:21,490
+طبعاً الـ M لازم تكون أكبر من واحد، يعني by logic
+
+121
+00:08:21,490 --> 00:08:24,030
+لازم تكون بهذا الشكل، ففي الحالة هذه، إذا اتحقق هذا
+
+122
+00:08:24,030 --> 00:08:28,050
+الكلام، بقدر أقول أن الـ A has a unique inverse
+
+123
+00:08:28,050 --> 00:08:34,930
+فعلياً هي لها unique inverse، A prime، باستخدام الـ modulo
+
+124
+00:08:34,930 --> 00:08:38,890
+M، لأنّ استخدام modulo قيمة ثانية للـ modulus
+
+125
+00:08:38,890 --> 00:08:43,770
+ممكن يختلف الكلام، هيختلف تماماً، تمام؟ فإذا هذه
+
+126
+00:08:43,770 --> 00:08:47,910
+معادلة أساسية ومهمة جداً، okay، خلصنا من المعادلة
+
+127
+00:08:47,910 --> 00:08:50,450
+الأساسية والمهمة جداً كـ concept، الآن كيف بدنا
+
+128
+00:08:50,450 --> 00:08:53,650
+نطبقها؟ جاينالكلام، هيجينا الكلام، بس بدنا نأخذ
+
+129
+00:08:53,650 --> 00:08:58,480
+بالنا أن كيف أجيب الـ inverse بمعادلات بسيطة، عشان
+
+130
+00:08:58,480 --> 00:09:03,320
+لما نكبر المعادلات بتاعتنا، نكون بنفس النهج نشتغل
+
+131
+00:09:03,320 --> 00:09:08,780
+فمبدأياً، مين اللي يحلّ لنا هذا الموضوع؟ Bezout، باللفظ
+
+132
+00:09:08,780 --> 00:09:13,780
+الفرنسي، أو Bezout باللفظ الإنجليزي، فهي Bezout، على
+
+133
+00:09:13,780 --> 00:09:18,880
+أساس أنّه فرنسي، أهو أساساً زي bijou، تكتب  o أو u
+
+134
+00:09:18,880 --> 00:09:26,140
+بس t، بس هي Bezout، كويس، فإذا إذا بدنا نتكلم عن Bezout
+
+135
+00:09:26,140 --> 00:09:34,260
+أو Bezout coefficients لثلاثة modulo سبعة، كأنّه
+
+136
+00:09:34,260 --> 00:09:37,560
+بدّه يجيب أيش الرقمين اللي بدّه يضربهم، رقم في
+
+137
+00:09:37,560 --> 00:09:41,740
+الثلاثة، ورقم في السبعة، بحيث أنّه حاصل ضربهم يساوي
+
+138
+00:09:41,740 --> 00:09:46,820
+بعض، أو inverse لبعض، طيب inverse لبعض، معناته أنّه
+
+139
+00:09:46,820 --> 00:09:50,300
+المفروض بيساوي ... بيساوي، مجموعهم بيساوي واحد، اللي
+
+140
+00:09:50,300 --> 00:09:53,020
+هو الـ inverse، القيمة في الـ inverse تبعها بيساوي
+
+141
+00:09:53,020 --> 00:09:56,980
+واحد، تمام، فهنا بنبحث عنها، أول شغل عشان نعمل هذا
+
+142
+00:09:56,980 --> 00:10:02,780
+الكلام، هل فعلاً الـ ... الـ Bezout coefficient ممكن، ولا
+
+143
+00:10:02,780 --> 00:10:06,710
+لأ؟ هل هو ممكن ولا لأ؟ عشان أقول هو ممكن ولا لأ،
+
+144
+00:10:06,710 --> 00:10:10,490
+بدنا نطبق النظرية اللي كانت آخر نظرية، وشوفناها
+
+145
+00:10:10,490 --> 00:10:17,190
+الـ A والـ M لازم يكونوا co-prime، لازم يكونوا co-
+
+146
+00:10:17,190 --> 00:10:20,510
+prime أو relatively prime، فإذا ثلاثة أو سبعة هما
+
+147
+00:10:20,510 --> 00:10:24,290
+فعلاً co-prime، لأنّ هما أساساً الـ primes، هما أساساً
+
+148
+00:10:24,290 --> 00:10:27,370
+الـ primes كمان، تمام، ففي الحالة هذه بقدر أقول إنّ
+
+149
+00:10:27,370 --> 00:10:33,930
+في قيمة ممكن أضربها في الأول، تمام؟ وأجمعها على
+
+150
+00:10:33,930 --> 00:10:37,930
+الثاني مضروب في K معينة، بحيث أنّه يساوي واحد، بحيث
+
+151
+00:10:37,930 --> 00:10:41,890
+أنّه يساوي واحد، أيش استفدت من الـ ... الـ ... الـ ... الـ
+
+152
+00:10:41,890 --> 00:10:45,470
+Bezout، الـ Bezout أو الـ Bezout coefficient هذه
+
+153
+00:10:45,470 --> 00:10:49,610
+استفدت منها كالتالي، مدام أنا بشتغل على الـ modulus
+
+154
+00:10:49,610 --> 00:10:54,930
+سبعة، معناته السالب اثنين هي فعلياً الـ inverse
+
+155
+00:10:54,930 --> 00:11:01,360
+لثلاثة modulo سبعة، modulo سبعة، هي فعلياً الـ inverse
+
+156
+00:11:01,360 --> 00:11:06,720
+تبعها، الـ inverse تبعها في أي لفة، في اللفة الأولى
+
+157
+00:11:06,720 --> 00:11:12,040
+في اللفة الأولى، طب في اللفة الثانية، معناه أنّنا
+
+158
+00:11:12,040 --> 00:11:16,000
+نضيف سبعة على القيمة هذه، لأنّه خلاص ما حيصير تكرار
+
+159
+00:11:16,000 --> 00:11:20,200
+حيصير تكرارية، باعتبار أنّه السالب اثنين فعلياً هو
+
+160
+00:11:20,200 --> 00:11:24,340
+هيكون congruent لأي رقم زائد أو ناقص سبعة، الـ
+
+161
+00:11:24,340 --> 00:11:28,370
+modulus، موديلوس، زي الساعة، زي الساعة، إذا كان
+
+162
+00:11:28,370 --> 00:11:32,890
+الـ modulus تبعك اثنا عشر، فالواحدة تكافئ مين؟ أجمع اثنا عشر
+
+163
+00:11:32,890 --> 00:11:37,030
+تكافئ ثلاثة عشر، والثلاثة عشر أجمع كمان اثنا عشر، تكافئ الخمسة
+
+164
+00:11:37,030 --> 00:11:41,770
+وعشرين، هي هي، فإذا congruent لبعض، كلهم نفس قيمة
+
+165
+00:11:41,770 --> 00:11:45,310
+الساعة، كساعة، كساعة، فأنتَ حتى الساعة خمسة وعشرين
+
+166
+00:11:45,310 --> 00:11:48,690
+بتقدر تقولها ساعة واحدة، الساعة ثلاثة عشر هي ساعة واحدة
+
+167
+00:11:49,490 --> 00:11:54,610
+تمام، فلكن وين؟ في لفة ثانية، في اللفة الثانية من
+
+168
+00:11:54,610 --> 00:11:59,550
+الساعة، فنفس الفكرة هنا بتقدر تقول أنّه الـ
+
+223
+00:16:05,510 --> 00:16:08,890
+بدنا نعملها كـ analysis، okay. أنت ممكن تكون ضامن
+
+224
+00:16:08,890 --> 00:16:11,950
+exactly أن هي بتساوي واحد، لكن الـ analysis ده هيسهل
+
+225
+00:16:11,950 --> 00:16:16,290
+عليك الآن في إيجاد الـ إيه، في إيجاد الـ إيه، خليني
+
+226
+00:16:16,290 --> 00:16:22,950
+أشوف الـ 4620 بنجسمها على مين؟ على 101، بطلع عندي
+
+227
+00:16:22,950 --> 00:16:24,730
+45، 101
+
+228
+00:16:26,390 --> 00:16:31,610
+زائد خمسة وسبعين، كـ reminder. طيب، المية وواحد كم
+
+229
+00:16:31,610 --> 00:16:36,370
+reminder فيها؟ reminder واحد، وبيزيد ستة وعشرون
+
+230
+00:16:36,370 --> 00:16:43,270
+طيب، برضه الـ خمسة وسبعين، كـ quotient لـ الخط هذا كم
+
+231
+00:16:43,270 --> 00:16:48,350
+reminder فيه؟ الـ two reminders زائد ثلاثة وعشرون
+
+232
+00:16:48,350 --> 00:16:54,000
+نفس الشيء، لما نصل للواحد في الآخر، وصلنا للواحد
+
+233
+00:16:54,000 --> 00:16:56,280
+ضمنّا فعلاً أن الـ greatest common divisor between
+
+234
+00:16:56,280 --> 00:17:01,980
+them بالذات بتساوي واحد، ما صفرتش. احنا قلنا الـ
+
+235
+00:17:01,980 --> 00:17:03,940
+greatest common divisor كنا نجيبها إذا كانت صفرت
+
+236
+00:17:03,940 --> 00:17:07,200
+معناته في الآخر هيكبر القسم على بعض هنا واحد
+
+237
+00:17:07,200 --> 00:17:12,820
+معناته فعلياً relatively prime، هو ما فيش أصلاً عامل
+
+238
+00:17:12,820 --> 00:17:16,060
+مشترك بينهم، ما فيش أصلاً عامل مشترك بينهم. طيب، من هنا
+
+239
+00:17:16,060 --> 00:17:22,000
+بنرجع، نرجع، نلاحظ أنه لو أرجع، نرجع، بحيث إن نصل من
+
+240
+00:17:22,000 --> 00:17:26,900
+الواحد اللي بدأنا فيه هنا، بدي أرجع، أرجع، عشان أصل
+
+241
+00:17:26,900 --> 00:17:31,020
+للرقمين اللي بدي إياهم، أحاول أحقق هذه القيمة. لاحظ، شوف
+
+242
+00:17:31,020 --> 00:17:40,260
+إيش رح نعمل؟ آخر واحد as a remainder، هيها، باخده
+
+243
+00:17:40,260 --> 00:17:44,520
+هنا، وببدأ منها، الواحد بحطه على جنب، لأن أنا محتاج
+
+244
+00:17:44,520 --> 00:17:49,550
+الواحد على جنب هنا، هي لاحظته؟ ممتاز. طيب، مدام حطينا
+
+245
+00:17:49,550 --> 00:17:53,310
+الواحد على جنب، أنا ضامن تماماً، إذا اتزمت بنفس
+
+246
+00:17:53,310 --> 00:17:58,710
+المكونات اللي هنا، في تقييم كل رقم من الأرقام اللي
+
+247
+00:17:58,710 --> 00:18:06,070
+هنا، حصل في الآخر لنفس الرقمين، الـ 4620 والـ 101، لأن
+
+248
+00:18:06,070 --> 00:18:10,130
+أصلاً كلهم مشتقين من بعض، فالواحد هذه إجتني أصلاً من
+
+249
+00:18:11,570 --> 00:18:15,110
+من مرحلة سابقة، وهكذا. طيب، التلاتة كانت موجودة في
+
+250
+00:18:15,110 --> 00:18:17,210
+اللي قبلها، والاتنين كانت موجودة في اللي قبلها، و
+
+251
+00:18:17,210 --> 00:18:21,230
+هكذا. طيب، كيف هنعمل كلام هذا؟ بده بس تركيز، صح، صح، في
+
+252
+00:18:21,230 --> 00:18:25,710
+الامتحان. مشكلته الوحيدة أنك أنت بس تكون مركز، تكون
+
+253
+00:18:25,710 --> 00:18:31,070
+هادئ. تكون هادئ في الامتحان. أسئلة زي هذه بتكون
+
+254
+00:18:31,070 --> 00:18:35,070
+مضمونة. أما إذا اتوترت، رقم بغلط، بغلط مع كل الشغل
+
+255
+00:18:35,070 --> 00:18:40,930
+هتشوف كيف. هنا، من الموضوع اللي هي أخدنا الواحد على
+
+256
+00:18:40,930 --> 00:18:44,810
+طرف لحاله، فبتصير إيش؟ تلاتة ناقص واحد في اتنين، وما
+
+257
+00:18:44,810 --> 00:18:49,930
+تحاولش. أهم شغلة، ما تحاولش تضيع الأرقام. إيش يعني
+
+258
+00:18:49,930 --> 00:18:53,810
+أضيع الأرقام؟ يعني تقول اتنين في واحد، يعني اتنين. لأ،
+
+259
+00:18:53,810 --> 00:18:58,470
+خليه الواحد زي ما هو واحد، لأنه أصلاً جايين من حاجة
+
+260
+00:18:58,470 --> 00:19:02,270
+سابقة، والاتنين جايين من إيش؟ سابق، فما بدناش نخربطهم في
+
+261
+00:19:02,270 --> 00:19:05,690
+بعض. هنشوف، لوجد، كيف الآن. هاي التلاتة زي ما هي،
+
+262
+00:19:05,690 --> 00:19:10,370
+طيب، الاتنين، الاتنين هذه ما هي كانت reminder في
+
+263
+00:19:10,370 --> 00:19:14,550
+اللي جابلها، يعني فعلياً بقدر أقول إن هي تساوي تلاتة
+
+264
+00:19:14,550 --> 00:19:22,120
+وعشرين ناقص سبعة في تلاتة، لأنه أصلاً العملية متسلسلة
+
+265
+00:19:22,120 --> 00:19:25,640
+كانت هنا. هتجد أنه دايماً في رقمين هيتجمعوا مع بعض
+
+266
+00:19:25,640 --> 00:19:32,800
+ما تجمعهم مش totally، اجمعهم coefficient، يعني هتلاقي
+
+267
+00:19:32,800 --> 00:19:38,540
+هي في التلاتة، وهي في تلاتة. هنا التلاتة مضروبة في
+
+268
+00:19:38,540 --> 00:19:42,540
+واحد، يعني مكررة مرة واحدة. هنا مكررة سالب سبعة في
+
+269
+00:19:42,540 --> 00:19:46,640
+سالب بتصير موجبة بسبعة، فبتقول مكررة سبع مرات
+
+270
+00:19:49,450 --> 00:19:52,870
+أما التلاتة حافظ عليها لإيش؟ لأن هذه رأسمالنا، هتوجت
+
+271
+00:19:52,870 --> 00:19:57,030
+في اللي بعدها. أنا بدأ أجيبها من اللي .. من اللي
+
+272
+00:19:57,030 --> 00:20:00,530
+كانت قبلها. تصير في اللي بعدها، هيها، كانت remainder
+
+273
+00:20:00,530 --> 00:20:06,430
+في اللي قبلها. فالآن، كل تلاتة بعوض مكانها بـ 26 ناقص
+
+274
+00:20:06,430 --> 00:20:12,390
+واحد في 23. عرفتوا ليش؟ حتى لو أنت عارف أن الـ greatest
+
+275
+00:20:12,390 --> 00:20:15,210
+common divisor بيساوي 1، بدك تعملها، لأن هذه هي اللي
+
+276
+00:20:15,210 --> 00:20:19,380
+هتساعدك في الرجعة. كويس، هي جبناها بهذا الشكل
+
+277
+00:20:19,380 --> 00:20:23,320
+فهتلاقي أن الـ 23 برضه هتجمع مع ثلاثة وعشرون. تاخد
+
+278
+00:20:23,320 --> 00:20:26,880
+بالك أن هنا في سالب واحد في ثمانية، يعني فعلياً
+
+279
+00:20:26,880 --> 00:20:32,720
+الثلاثة والعشرون اتكررت سالب ثمان مرات. سالب
+
+280
+00:20:32,720 --> 00:20:37,540
+واحد كمان بتصير سالب تسعة. سالب تسعة على طول الرقم
+
+281
+00:20:37,540 --> 00:20:41,340
+هذا من غير ما أكيد هو الـ reminder اللي جابلها، آه
+
+282
+00:20:41,340 --> 00:20:48,520
+صحيح. بدك تعوض بمكانه اللي هو خمسة وسبعين ناقص
+
+283
+00:20:48,520 --> 00:20:53,660
+اتنين في ستة وعشرون، إيه
+
+284
+00:20:53,660 --> 00:20:57,680
+الآن هتلاقي الستة والعشرون مع الستة والعشرون، من
+
+285
+00:20:57,680 --> 00:21:00,580
+الحاجات اللي دايماً في الامتحانات بتخربط معاكم
+
+286
+00:21:00,580 --> 00:21:06,980
+تاخدوا بالكم أن في الأقواس، في رقم خارج القوس، في
+
+287
+00:21:06,980 --> 00:21:11,760
+رقم خارج القوس، ما تنسوش تضربوه في الاتنين. يعني هنا
+
+288
+00:21:11,760 --> 00:21:20,250
+بيصير موجبة بـ 18 زائد ثمانية، ستة وعشرون. طيب،
+
+289
+00:21:20,250 --> 00:21:26,410
+الستة والعشرون، أي نعم، برضه من المعادلة هذه أخدنا
+
+290
+00:21:26,410 --> 00:21:30,790
+الكلام هذا من المعادلة هذه، أخدناها، تمام. فهتلاقي
+
+291
+00:21:30,790 --> 00:21:35,150
+برضه خمسة وسبعين، وهي برضه خمسة وسبعين. خد بالك من
+
+292
+00:21:35,150 --> 00:21:38,570
+الـ 26 اللي برا ده، خارج القوس. 26 في سالب واحد
+
+293
+00:21:38,570 --> 00:21:47,350
+فسالب 26. سالب 26، سالب 9، سالب 35. كويس. هنا الـ 75
+
+294
+00:21:47,350 --> 00:21:53,910
+هنا، وصلناهم، جربنا، صفنّاهم.
+
+295
+00:21:53,910 --> 00:21:57,290
+تعالى، تطلع على الواحد اللي بدأنا فيه، إيش طلع بيساوي؟
+
+296
+00:21:57,290 --> 00:21:59,990
+هاي الـ M، وهي الـ A
+
+297
+00:22:02,950 --> 00:22:07,370
+Automatically، معناته ده هو قيمة الـ inverse، لإنه حقق لك
+
+298
+00:22:07,370 --> 00:22:14,410
+المعادلة، واحنا ضامنين أنه unique، أو الـ greatest
+
+299
+00:22:14,410 --> 00:22:20,790
+common divisor unique بين الـ 101 والـ 4620. طيب، الـ
+
+300
+00:22:20,790 --> 00:22:26,430
+1601 هذه هي inverse لـ 101 في اللفة، جداش؟ في اللفة
+
+301
+00:22:26,430 --> 00:22:31,850
+35، عكس، على جرب الساعة، في اللفة 35 عكس عقارب الساعة
+
+302
+00:22:31,850 --> 00:22:37,850
+الآن أنت مش عاجبك الرقم، تقدر تعدل فيه، تقدر تعدل
+
+303
+00:22:37,850 --> 00:22:40,450
+فيه، إذا لقيته مثلاً بالسالب، okay، أضف له قيمة الـ M
+
+304
+00:22:40,450 --> 00:22:44,710
+بيصير بالموجب. ما احنا قلنا هو congruent لمجموعة
+
+305
+00:22:44,710 --> 00:22:48,250
+أرقام تانية، لمجموعة أرقام تانية. حطه دايماً بأبسط
+
+306
+00:22:48,250 --> 00:22:52,290
+صورة ممكنة. إيش أبسط صورة ممكنة؟ أنه يكون أقل أصلاً
+
+307
+00:22:52,290 --> 00:22:56,300
+من الـ modulus. فمدام جاي هو لحاله، جاي أقل من
+
+308
+00:22:56,300 --> 00:23:02,780
+الـ modulus، فأنت ضامن أن هو ضمن أول لفة، كرقم قيمته أقل
+
+309
+00:23:02,780 --> 00:23:07,140
+من الـ modulus، خلاص. فإذا بقول أن هو هذا الـ inverse لـ
+
+310
+00:23:07,140 --> 00:23:14,960
+101 modulo 4620. هنحتاج الكلام ده في إيش؟ هنحتاجه
+
+311
+00:23:14,960 --> 00:23:19,520
+كتير. هيجينا في الـ encryption، هنشوف في إيش بدنا
+
+312
+00:23:19,520 --> 00:23:24,640
+نستخدمه. الكويس .. الكويس أنه هنزلكم أنا واجبات
+
+313
+00:23:24,640 --> 00:23:26,940
+عليها، ده لأنه لازم تتدربوا عليها، ده إيه؟ تكونوا
+
+314
+00:23:26,940 --> 00:23:29,460
+تاخدوا عليها، إيه؟ تكونوا تاخدوا عليها، وتبقوا
+
+315
+00:23:29,460 --> 00:23:34,240
+مركزين في الشغل تبعها، رغم أن هو نظرياً بسيط، لكن عند
+
+316
+00:23:34,240 --> 00:23:43,400
+التنفيذ، الأرقام كتيرة، بده تركيز. أوه
+
+317
+00:23:43,400 --> 00:23:47,280
+كويس. طيب، الآن، في إيش بستخدم عملية الـ inverse اللي
+
+318
+00:23:47,280 --> 00:23:53,550
+أنا جبتها توي؟ احنا توي قلنا تلاتة modulo سبعة، كان
+
+319
+00:23:53,550 --> 00:23:59,010
+الـ inverse لتلاتة، لا إيش؟ بقد ايش؟ سالب اتنين. كانت بتساوي
+
+320
+00:23:59,010 --> 00:24:01,890
+سالب اتنين. هتيجي تقول، طب ما هم مضروبين في بعض، وطلع
+
+321
+00:24:01,890 --> 00:24:07,750
+سالب ستة. طب ما السالب ستة يعني سبعة، يعني عفواً أن
+
+322
+00:24:07,750 --> 00:24:13,830
+واحد بالسالب، آه، بس اتجاهه بالعكس، اتجاهه عكسي، تمام
+
+323
+00:24:13,830 --> 00:24:17,890
+فسالب واحد، سالب ستة هذه هي فعلياً تكافئ واحد، هي
+
+324
+00:24:17,890 --> 00:24:24,140
+فعلياً تكافئ واحد. طيب، بنضربها في الطرفين لمعادلة
+
+325
+00:24:24,140 --> 00:24:30,280
+بهذا الشكل. تلاتة X تساوي أربعة modulo سبعة، فأنا عارف
+
+326
+00:24:30,280 --> 00:24:32,820
+أنه بدي أجيب الـ inverse لتلاتة modulo سبعة، احنا
+
+327
+00:24:32,820 --> 00:24:37,040
+جايبينها مسبقاً، هي سالب اتنين. فإذا بضرب الطرفين في
+
+328
+00:24:37,040 --> 00:24:42,760
+سالب اتنين، minus two، خلاص، هذه واحد، ضمنّا أنه راح
+
+329
+00:24:42,760 --> 00:24:47,220
+اتخلصنا، فـ X بتساوي سالب تمانية. X في الحالة بتساوي
+
+330
+00:24:47,220 --> 00:24:53,180
+سالب تمانية. ممكن تجمع عليها سبعة، عشان تجيبها قيمة
+
+331
+00:24:53,180 --> 00:24:56,900
+موجبة بقى. إذا مش عاجبك القيم السالبة، المهم أنك تضيف
+
+332
+00:24:56,900 --> 00:25:00,680
+عليهم سبعة، تضيف عليها سبعة. لما يجيلك رقم، إيش؟ أجرب
+
+333
+00:25:00,680 --> 00:25:04,840
+رقم كان، اللي هي أربعة عشر، خليني أقول يعني سبعة و
+
+334
+00:25:04,840 --> 00:25:08,720
+سبعة، مش هيك؟ بطلع ستة على سرد، ستة وثمانية، هيساوي
+
+335
+00:25:08,720 --> 00:25:13,220
+الأربعة عشر. يعني أنت بتعمل لفتين، okay. الستة مناسبة
+
+336
+00:25:13,220 --> 00:25:16,280
+لك، خلاص، أقول أن قيمتها بتساوي ستة. فـ X هنا قيمتها
+
+337
+00:25:16,280 --> 00:25:22,750
+مناسبة أنها تكون بتساوي ستة، عشان تحل السؤال هذا. تمام
+
+338
+00:25:22,750 --> 00:25:29,290
+الآن، الـ pseudo random، هذه الـ، الـ pseudo prime، زي ما
+
+339
+00:25:29,290 --> 00:25:32,030
+أخذنا الـ pseudo random. الآن في الـ pseudo prime، الـ
+
+340
+00:25:32,030 --> 00:25:36,850
+pseudo prime إجت من نظرية صينية قديمة، كانوا
+
+341
+00:25:36,850 --> 00:25:42,650
+بيقولوا، إذا كان الـ n prime، فمعنى ذلك لازم يتحقق أن
+
+342
+00:25:42,650 --> 00:25:46,590
+اتنين to the power لـ prime هذا، ناقص واحد، هي
+
+343
+00:25:46,590 --> 00:25:53,790
+congruent للواحد modulo الـ prime، modulo الـ prime، كويس.
+
+344
+00:25:53,790 --> 00:25:58,390
+وأيامها الصينيين، ادعوا، العلماء الصينيين ادعوا
+
+345
+00:25:58,390 --> 00:26:03,530
+أنه العكس صحيح. إيش يعني العكس الصحيح؟ أنه لو تحقق
+
+346
+00:26:03,530 --> 00:26:07,810
+لأي رقم، أن اتنين to the power الرقم ناقص واحد
+
+347
+00:26:07,810 --> 00:26:14,450
+congruent للواحد، باستخدام الـ modulo للرقم نفسه، معناته
+
+348
+00:26:14,450 --> 00:26:20,030
+ذلك أن الرقم prime. بالظبط، لأ، هي فعلياً طلعت if then
+
+349
+00:26:20,030 --> 00:26:25,190
+مش if and only if. فمع الزمن، ادعائهم هذا أن الـ
+
+350
+00:26:25,190 --> 00:26:30,670
+converse true، طلع مش صحيح، لكن طلعوا بحاجة كويسة
+
+351
+00:26:30,670 --> 00:26:36,670
+جداً، أنه إذا تحقق هذا الكلام فعلياً، فكل الـ n هنا، okay
+
+352
+00:26:36,670 --> 00:26:41,110
+هي مش prime، لكن بقدر أحكم على أنها pseudo prime
+
+353
+00:26:41,110 --> 00:26:46,370
+شبيهة بالـ primes. إيش يعني شبيهة بـ primes؟ يعني هي
+
+354
+00:26:46,370 --> 00:26:53,170
+فعلياً عبارة عن ضرب two primes في بعض، بس، وبدون P to
+
+355
+00:26:53,170 --> 00:26:56,930
+the power كذا، لأ، هي two primes مرة واحدة، هيك الـ
+
+356
+00:26:56,930 --> 00:27:00,210
+prime، وممكن يكونوا كبار، ممكن يكونوا أرقام كبيرة
+
+357
+00:27:00,210 --> 00:27:07,770
+فعبارة عن P في Q بس، والـ two primes، الـ two numbers
+
+358
+00:27:07,770 --> 00:27:12,890
+هدول عبارة عن primes. ففي الحالة هذه، if بقدر أقول
+
+359
+00:27:12,890 --> 00:27:13,330
+عنها
+
+360
+00:27:16,160 --> 00:27:21,660
+pseudoprime، شبيهة بالـ prime، شبيهة بالـ prime، كويس.
+
+361
+00:27:21,660 --> 00:27:25,700
+طيب، الشبيهات بالـ prime هذه، طلعت مش كل الأرقام
+
+362
+00:27:25,700 --> 00:27:30,200
+ممكن تحقق هذا الموضوع. يعني شبيهات الـ primes برضه
+
+363
+00:27:30,200 --> 00:27:35,460
+محكمين، محدودين كعدد، محدودين كعدد، لكن يمكن أيضاً
+
+364
+00:27:35,460 --> 00:27:39,870
+استخدامها في الـ encryption. يعني معنى ذلك أنه حصيلة
+
+365
+00:27:39,870 --> 00:27:43,670
+الـ primes كمان، اللي احنا بالنسبالنا ذخيرة كأرقام
+
+366
+00:27:43,670 --> 00:27:47,090
+نستخدمها في عملية الـ encryption، عشان أضمن أنه الـ
+
+367
+00:27:47,090 --> 00:27:50,190
+code تبعي يكون أطول ما يمكن، قبل ما يتم كسره، وقبل
+
+368
+00:27:50,190 --> 00:27:54,030
+ما يتكرر. لأ، هذا الكلام حتى بيتحقق مع الـ pseudo
+
+369
+00:27:54,030 --> 00:27:54,350
+prime.
+
+370
+00:28:01,970 --> 00:28:07,970
+مثال على هذا الكلام، زي 341، هي عبارة عن 11 في 31،
+
+371
+00:28:07,970 --> 00:28:13,370
+كلاهما primes. هي بحد ذاتها مش prime، لكن مدام حققت
+
+372
+00:28:13,370 --> 00:28:19,340
+المعادلة، أن اتنين to the power تلاتمية وأربعين، هي فعلاً
+
+373
+00:28:19,340 --> 00:28:22,480
+طلعت congruent للواحد، إذا استخدمتها ضمن الـ modulus
+
+374
+00:28:22,480 --> 00:28:29,750
+341، طلعت صحيحة، فبقدر أقول عنها pseudoprime. نقدر نقول
+
+375
+00:28:29,750 --> 00:28:33,290
+عنها pseudoprime. طبعاً، في قائمة من مجموعة الـ
+
+376
+00:28:33,290 --> 00:28:35,690
+pseudoprimes، في قائمة كويسة من مجموعة الـ pseudoprimes
+
+377
+00:28:35,690 --> 00:28:37,990
+اللي العلماء، أو اللي بيخلّوهم يقولوا، اللي بيشتغل في
+
+378
+00:28:37,990 --> 00:28:42,310
+الـ encryption، ممكن يستغلها، واللي بيشتغل في الـ
+
+379
+00:28:42,310 --> 00:28:46,770
+hacking بيفكر فيها، أنه ممكن تكون هي الأرقام اللي
+
+380
+00:28:46,770 --> 00:28:51,310
+ممكن استخدامها. تمام. هذا الكلام مش ينطبق على جدول
+
+381
+00:28:51,310 --> 00:28:57,100
+اتنين بس، كـ primary، كـ binary، لأ، ممكن تكون لأي أساس.
+
+382
+00:28:57,100 --> 00:29:03,340
+لأي أساس، إذا تحققت، فبرضه بنقدر نسميها pseudoprime
+
+383
+00:29:03,340 --> 00:29:08,580
+pseudoprime، تمام؟ كويس. هذه هيك زودت لنا ذخيرة
+
+445
+00:34:02,300 --> 00:34:06,320
+multiplier .. رغم أنك ستستخدم multiplier، تمام؟
+
+446
+00:34:06,320 --> 00:34:09,820
+طبعًا، ببساطة جدًّا، هي مثلًا message بهذا الشكل، وأنت
+
+447
+00:34:09,820 --> 00:34:14,660
+عارف أن هي .. أن عملت باستخدام الـ n plus
+
+448
+00:34:14,660 --> 00:34:20,100
+ثلاثة، أقول لك حتى لو لم تكن عارفًا، ببساطة جدًّا، اللغة ..
+
+449
+00:34:20,100 --> 00:34:23,380
+okay، نحن كاتبينها لأنّ الـ … الفعليّة هي 26، الـ M
+
+450
+00:34:23,380 --> 00:34:28,430
+معروفة فعليًّا في حروف اسمها الـ vowels .. الـ vowels
+
+451
+00:34:28,430 --> 00:34:32,810
+letters، اللي هي الحروف اللينة، واللي كلّنا نعرف
+
+452
+00:34:32,810 --> 00:34:36,950
+أنّ هذه تتكرر أكثر من غيرها، صحيح؟ طيب، عارفين أنّ الـ E
+
+453
+00:34:36,950 --> 00:34:41,450
+أكثر حرف ممكن أن يتكرر، فلما .. لما تأتي إلى message مثل
+
+454
+00:34:41,450 --> 00:34:46,090
+هذه، وتطلع هو أكثر حرف تكرر، بدّك تفترض أنّه
+
+455
+00:34:46,090 --> 00:34:50,950
+يمكن أن يكون الـ E، فبتحاول أن تشفر الـ message لكي يوافق
+
+456
+00:34:50,950 --> 00:34:51,310
+الـ E
+
+457
+00:34:54,180 --> 00:34:59,280
+فَكّكَ التشفير، صحيح؟ لاحظت كيف؟ فأنت عارف أن الـ E
+
+458
+00:34:59,280 --> 00:35:03,340
+أكثر حرف يتكرر، الـ A بعده، الـ I، الـ vowels هذه
+
+459
+00:35:03,340 --> 00:35:07,720
+كلّنا نعلم أنّها حروف لينّة، الحروف اللينة هذه هي
+
+460
+00:35:07,720 --> 00:35:11,850
+أكثر حروف تتكرر في اللغة، منطق أم غير منطق؟  عشانك
+
+461
+00:35:11,850 --> 00:35:16,050
+insecure، عشانك بالطريقة هذه هو insecure، فتقدر
+
+462
+00:35:16,050 --> 00:35:21,430
+ببساطة تقول الـ E، طيب، من أكثر حرفٍ تكرر؟ الـ H، الـ H
+
+463
+00:35:21,430 --> 00:35:26,630
+هَي أربع مرات، فبدّك تفترض أن معناها الـ E، هذا حرف الـ
+
+464
+00:35:26,630 --> 00:35:31,970
+E، فبِهَ انْشَفَتْ، انتهت
+
+465
+00:35:31,970 --> 00:35:37,910
+اشتغل على الثلاثة، وطَلَعَ الـ message، فأنت secure، لستَ
+
+466
+00:35:37,910 --> 00:35:41,210
+بالضرورة أن تكون عارف الـ code نفسه، الطريقة
+
+467
+00:35:41,210 --> 00:35:46,050
+linear، الطريقة حتى لو ضربت في multiplier، هي linear
+
+468
+00:35:46,050 --> 00:35:50,170
+هي linear، والـ linear أسهل ما يمكن، أسهل ما يمكن
+
+469
+00:35:50,170 --> 00:35:53,590
+معادلة linear عبارة عن a مضروبة في x زائد c
+
+470
+00:35:53,590 --> 00:35:59,150
+increment، مثلًا، انتهينا، فهي ليست كثيرة secure، طيب، ننتقل
+
+471
+00:36:00,560 --> 00:36:03,520
+إلى تكنيك أفضل، والذي أستخدمه، والذي أنا أستخدمه من
+
+472
+00:36:03,520 --> 00:36:06,780
+techniques التي تستخدم حتى اللحظة كـ encryptor
+
+473
+00:36:06,780 --> 00:36:11,060
+مناسب، اللي هي الـ RSA، مستخدمة في الـ email حتى
+
+474
+00:36:11,060 --> 00:36:14,940
+اللحظة، مستخدمة في الـ email، مستخدمة في البنوك، في
+
+475
+00:36:14,940 --> 00:36:19,060
+اللي هي تشفير أو تكويدة الأرقام السرية، مثلًا، تاعت
+
+476
+00:36:19,060 --> 00:36:22,080
+الـ visa card، عندك visa card، آه، بس لها رقم سريّ
+
+477
+00:36:22,080 --> 00:36:25,740
+فالرقم السري هذا يُعتبر هو الشفرة تَبَعْتِكَ، اللي من
+
+478
+00:36:25,740 --> 00:36:28,720
+خلالها تُعْمَلُ مجموعة عمليات جُوَّا، بحيث تعرف أن
+
+479
+00:36:28,720 --> 00:36:32,280
+الحساب هذا حسابك أم ليس حسابك، فهي حتى الآن آه، ممكن
+
+480
+00:36:32,280 --> 00:36:37,520
+تستخدم، يُعْمَلُ عليها improvement، بس كـ technique
+
+481
+00:36:37,520 --> 00:36:42,020
+مستخدم حتى اللحظة في بعض التطبيقات، الـ RSA يعتمد
+
+482
+00:36:42,020 --> 00:36:46,290
+على شغلتين: أنّه في عندي مجموعة parameters، بدنا
+
+483
+00:36:46,290 --> 00:36:50,530
+نستخدمها برضه في بناء الـ mask اللي توّ تكلمنا
+
+484
+00:36:50,530 --> 00:36:55,590
+عنه، أنّنا نستخدم مجموعة sequence من الأرقام، تمام
+
+485
+00:36:55,590 --> 00:37:01,670
+أشفر فيها الـ message، تصبح message ثانية مختلفة
+
+486
+00:37:01,670 --> 00:37:06,830
+تمامًا، message أنتَ لن تفهم منها شيء، طيب، في عندي
+
+487
+00:37:06,830 --> 00:37:09,750
+مجموعة parameters، مجموعة الـ parameters سأقسمها إلى
+
+488
+00:37:09,750 --> 00:37:14,180
+private key، private key هذه، من المفترض ألا يعرفها
+
+489
+00:37:14,180 --> 00:37:17,520
+إلاّ
+
+490
+00:37:17,520 --> 00:37:21,340
+الذي عمل الـ code، بس إذا الـ bank، معناته الـ bank فقط
+
+491
+00:37:21,340 --> 00:37:24,920
+فقط، والـ public key، الـ public key، لأ
+
+492
+00:37:24,920 --> 00:37:28,960
+هذه أنتَ في الأصل تحتاجها، أنتَ ممكن ألا تأخذها في يدك، بس
+
+493
+00:37:28,960 --> 00:37:31,540
+ممكن تأخذها من خلال الرقم الذي سيعطيه لك، وأنتَ
+
+494
+00:37:31,540 --> 00:37:36,630
+عارفه، بس الرقم هذا يحتوي على القيم هذه، فهو public
+
+495
+00:37:36,630 --> 00:37:41,390
+في الآخر، هو معطى عندك، أنتَ أخذته، وآخرون ممكن أن يشوفوه
+
+496
+00:37:41,390 --> 00:37:44,890
+منك أيضًا، يعني لو واحد مسك الـ visa card تَبْعَتِكَ، و
+
+497
+00:37:44,890 --> 00:37:49,490
+يطلعها، سيأتي رقم، فليكن سيأخذ الرقم في الـ
+
+498
+00:37:49,490 --> 00:37:52,990
+email، أنتَ تكون كاتب حتى الـ email، لا تفكر فيه
+
+499
+00:37:52,990 --> 00:37:58,170
+أنتَ تُشَفِّرُ الـ email فعليًّا، تُبْعِثُ الـ message
+
+500
+00:37:58,170 --> 00:38:00,870
+تَبْعَتِكَ، الـ message تَبْعَتِكَ، قبل أن تخرج على خط الـ net
+
+501
+00:38:00,870 --> 00:38:07,230
+تُشَفَّرُ، تُشَفَّرُ بالـ … باستخدام الـ RSA، كويس، أُشْفِرَتْ، و
+
+502
+00:38:07,230 --> 00:38:12,890
+ذهبت إلى الـ email الشخص المكتوب في الـ email، فهو
+
+503
+00:38:12,890 --> 00:38:16,770
+الوحيد الذي يقدر أن يقرأها، هو الوحيد الذي يقدر
+
+504
+00:38:16,770 --> 00:38:19,950
+أن يقرأها، لأنّك أصلاً خصيصًا بَعَثْتَها له، فهو هذا الذي
+
+505
+00:38:19,950 --> 00:38:24,250
+يصله الـ public key على ايميله، فآليًّا تفتح عنده
+
+506
+00:38:24,250 --> 00:38:27,130
+فقط، لمّا… لن تفتح لو واحد ثانٍ، لن تفتح لو واحد
+
+507
+00:38:27,130 --> 00:38:31,670
+ثانٍ، مجرد أنّه ماشي… ماشي على الخط، نفترض عمل قرصنة، و
+
+508
+00:38:31,670 --> 00:38:35,230
+أخذ مجموعة بيانات، لن يفهم منها شيء، لن يفهم منها
+
+509
+00:38:35,230 --> 00:38:38,190
+شيء، سترى أي شيء بالضبط، الـ private key، الـ private
+
+510
+00:38:38,190 --> 00:38:46,530
+key هي عبارة عن P و Q و Random Prime Numbers، فهي
+
+511
+00:38:46,530 --> 00:38:51,030
+دخلنا في أنّها بدأت يا Prime و Random، عشان هيك كنا يجب
+
+512
+00:38:51,030 --> 00:38:53,830
+أن نتعلم ما معنى prime وما معنى co-prime وما
+
+513
+00:38:53,830 --> 00:38:58,050
+معنى random، كويس، فبدنا الرقمين اللي هي الـ P والـ
+
+514
+00:38:58,050 --> 00:39:05,850
+Q، يكونا عبارة عن prime number، فهي الـ P والـ
+
+515
+00:39:05,850 --> 00:39:14,470
+Q، ومحتاج الـ E، شيء اسمه الـ exponent E أو دليل،
+
+516
+00:39:14,470 --> 00:39:18,250
+شيء يُسمَّى الدليل، exponent اللي هي الـ E، هذه
+
+517
+00:39:18,250 --> 00:39:22,750
+private، هذه لا أحد يعرفها، هذه من المفترض أصلاً أن
+
+518
+00:39:22,750 --> 00:39:28,610
+لا أحد يكون يعرفها كـ private، تمام، في المقابل، في
+
+519
+00:39:28,610 --> 00:39:32,010
+عندك الـ public، الـ public، ماذا يعطيك؟ يعطيك قيمة in
+
+520
+00:39:32,010 --> 00:39:41,170
+قيمة in، هذه عبارة عن P مضروبة في Q، هذه التي تكون
+
+521
+00:39:41,170 --> 00:39:44,890
+معطاة على الـ message، عشان تساهم أو تساعد في فك الـ
+
+522
+00:39:44,890 --> 00:39:49,330
+message، عشان تساعد في فك الـ message، لماذا؟ بعد هيك
+
+523
+00:39:49,330 --> 00:39:57,930
+محتاج قيمة D، بس D هذه عشان تُحْسَبُ كأنّها الـ inverse
+
+524
+00:39:57,930 --> 00:40:09,990
+للـ E، بس مدول P ناقص واحد في Q ناقص واحد، وليست E
+
+525
+00:40:09,990 --> 00:40:15,830
+نفسها، يعني لا تعطي E نفسها، لا نعطي الـ E نفسها، نحن
+
+526
+00:40:15,830 --> 00:40:21,690
+نعطي D، واللي هي الـ inverse بتاعة E، فإذا public، أنتَ
+
+527
+00:40:21,690 --> 00:40:25,970
+تعرف الـ D، لكن الـ E أنتَ لا تعرفها، أنا فقط الذي
+
+528
+00:40:25,970 --> 00:40:29,010
+أعرفها، أنا الذي عملت الـ code، أنا فقط الذي أعرفها
+
+529
+00:40:29,010 --> 00:40:34,290
+أنتَ أُعْطِيَتَ الـ D، بس عشان تفك الـ call، الـ message التي
+
+530
+00:40:34,290 --> 00:40:36,970
+أعطيتك إياها، بس أنتَ لم تعرف النظام تبعي، أنتَ
+
+531
+00:40:36,970 --> 00:40:40,310
+لم تعرف قواعد التشفير نفسها التي أستخدمها
+
+532
+00:40:40,310 --> 00:40:48,010
+واضحة، فإذا E تَبْعَتِي، وأنا من عندي عملت لك generation
+
+533
+00:40:48,010 --> 00:40:52,570
+لـ D، وأنتَ تتأكد من D، بس على اعتبار أنّ الـ D هذه هي الـ
+
+534
+00:40:52,570 --> 00:40:58,570
+inverse للـ E التي عندي، بس بمَنْ؟ بـ modulus أو modulo
+
+535
+00:40:58,570 --> 00:41:03,750
+P ناقص واحد في Q ناقص واحد، وليه؟ set P في Q التي
+
+536
+00:41:03,750 --> 00:41:11,140
+أنتَ أصلاً given عندك، فإذا إنّكَ تفكّ الشفرة، تفكّها بالـ
+
+537
+00:41:11,140 --> 00:41:18,280
+modulus N، كويس، اللي هي P في Q، لكن لما أنا أعطيك D
+
+538
+00:41:18,280 --> 00:41:21,780
+اللي هي الـ inverse بتاعة E، أعطيك إياها على modulus
+
+539
+00:41:21,780 --> 00:41:27,940
+ثاني، أنتَ لا تعرف قيمة الـ modulus الثاني، أنتَ لا
+
+540
+00:41:27,940 --> 00:41:33,050
+تعرفها، اللي هي P ناقص واحد في Q ناقص واحد، بدّك تفكّه
+
+541
+00:41:33,050 --> 00:41:37,530
+أوكي، اجلس تدور في كل الـ primes، واضربها في بعض، وشوف
+
+542
+00:41:37,530 --> 00:41:42,930
+إيه، وأنتَ وحظّك، متى يخرج معك، تمام، هكذا، ثلاثة
+
+543
+00:41:42,930 --> 00:41:45,150
+كلام، بدنا نطبّقه، بس بدنا نعرف مجموعة الـ parameters
+
+544
+00:41:45,150 --> 00:41:48,390
+هذه، كيف أستخدمها، أول عملٍ، عشان نستخدمها، بدنا نحسب
+
+545
+00:41:48,390 --> 00:41:53,210
+الـ … الـ coded message، الـ coded message، اللي هي
+
+546
+00:41:53,210 --> 00:41:57,650
+ستُشَفَّرُ، تساوي الـ message نفسها، الـ message نفسها، الـ
+
+547
+00:41:57,650 --> 00:42:02,690
+characters نفسها التي كتبتها، to the power E، هي
+
+548
+00:42:02,690 --> 00:42:07,910
+الـ exponent، to the power E modulo N، فمعنى ذلك أنّ
+
+549
+00:42:07,910 --> 00:42:12,830
+سيخرج الـ C، هذه ستُبْعَثُ، طيب، ماذا ستُبْعَثُ معها؟ ستُبْعَثُ
+
+550
+00:42:12,830 --> 00:42:15,610
+معها N و D
+
+551
+00:42:17,730 --> 00:42:21,510
+كيف اُعْمِلَتْ، لك علاقة، هي هذه عشان تفكّ الشفرة
+
+552
+00:42:21,510 --> 00:42:25,290
+تَبْعَتِكَ، بس أنتَ كاتب أنا الـ email تَبْعَكَ، فمعنى ذلك أنّ
+
+553
+00:42:25,290 --> 00:42:28,170
+هذه تُحْمَلُ معي الـ email تَبْعَكَ، بحيث أنّها لـ email فقط
+
+554
+00:42:28,170 --> 00:42:31,450
+تُعْرَفُ قيمة هذه، فـ email آليًّا يُفكّ الشفرة
+
+555
+00:42:31,450 --> 00:42:35,470
+تَبْعَتِكَ، الرسالة التي وصلتك، تُفكَّ، ليست الحالة، بحيث أنّكَ
+
+556
+00:42:35,470 --> 00:42:40,880
+ترجع إلى الـ message التي تساوي الـ coded message to
+
+557
+00:42:40,880 --> 00:42:44,120
+the power D، على نفس الموضوع الأصلي، طيب… بتنّا…
+
+558
+00:42:44,120 --> 00:42:47,220
+رقم… بتنّا… كما أقول مثالًا رقميًّا، يعني الكلام
+
+559
+00:42:47,220 --> 00:42:52,500
+هكذا، قليلًا جافًّا، سترى مثلًا Message
+
+560
+00:42:54,360 --> 00:42:58,820
+عبارة عن كلمة، ماذا سنبعث؟ أين سيقف؟ كلمة
+
+561
+00:42:58,820 --> 00:43:04,240
+stop، مثلًا، كلمة stop وحدها، فقط كلمة stop، هنا كيف
+
+562
+00:43:04,240 --> 00:43:09,240
+نعملها؟ وبدنا نشفّرها، القانون واضح، الـ coded تساوي
+
+563
+00:43:09,240 --> 00:43:12,720
+الـ message to the power e، الـ exponent، في الـ
+
+564
+00:43:12,720 --> 00:43:21,220
+modulus أو modulo n، أول عملٍ سنستخدم الـ P 43، الـ Q
+
+565
+00:43:21,220 --> 00:43:22,080
+59
+
+566
+00:43:24,270 --> 00:43:28,750
+هذه مهمتان جدًا، عشان نحسب منهما قيمة N، مضروبهما في
+
+567
+00:43:28,750 --> 00:43:34,210
+بعض، فسيخرج عندي الـ modulus الذي نستخدمه، okay، الـ E
+
+568
+00:43:34,210 --> 00:43:38,390
+13، طيب، أنا ألاحظ شيء، الـ E والـ P والـ Q كلهم
+
+569
+00:43:38,390 --> 00:43:44,970
+Primes، صحيح؟ لا، ونحن نستخدم Primes متواضعة
+
+570
+00:43:44,970 --> 00:43:49,190
+كذلك هنا، لمجرد أنّ الأرقام تسير معنا، يعني نفهمها
+
+571
+00:43:49,190 --> 00:43:53,290
+بالعادة لا، تُستَخْدَمُ أرقام أكبر بكثير من هذا، يعني الـ E
+
+572
+00:43:53,290 --> 00:43:57,350
+هذه ممكن أن تكون بسعُميات، سبعُميات، خمسُميات، Primes،
+
+573
+00:43:57,350 --> 00:44:02,950
+Primes، كذلك، أول شيء بدنا نضمنه، مادام أنا بدي
+
+574
+00:44:02,950 --> 00:44:08,820
+أعمل على الـ E، ولاحظ الـ E هذه، أنا سأعطيكَ الـ
+
+575
+00:44:08,820 --> 00:44:13,160
+inverse تبعها، أما لن أعطيك الـ E، صحيح؟ ممتاز، فإذا
+
+576
+00:44:13,160 --> 00:44:16,260
+أول شيء بدي أضمنه أنّي أخرج لقيمة الـ inverse، توا
+
+577
+00:44:16,260 --> 00:44:19,960
+أخذناها لتوّ، عشان إيه؟ توا أخذنا كيف نجيب الـ inverse
+
+578
+00:44:19,960 --> 00:44:22,660
+عشان لا تقول لي كيف سأجيبها، هيّا، توّ جبناها
+
+579
+00:44:22,660 --> 00:44:25,200
+فَتَأْتِي، وتنظر فقط إلى الـ greatest common denominator بين
+
+580
+00:44:25,200 --> 00:44:28,480
+الـ E التي تريد أن تجلب لها الـ inverse، ومَنْ؟ ليس الـ
+
+581
+00:44:28,480 --> 00:44:34,850
+modulus، modulus جديد، الـ modulus الجديد هذا ليس P في N
+
+582
+00:44:34,850 --> 00:44:42,010
+في Q، هي P ناقص واحد في Q ناقص واحد، عكس
+
+583
+00:44:42,010 --> 00:44:44,730
+نحن نريد أن نترك الـ hacker يعمل براحته، ليس لازم
+
+584
+00:44:44,730 --> 00:44:49,770
+نُعْجِبَهُ الدنيا، فَتَشْفِرُ، عفوا، الكلام هذا ليس أنتَ
+
+585
+00:44:49,770 --> 00:44:52,370
+الموّجّه، أيّ شيء، بس أنتَ، أنتَ الآن صاحب العلم الذي تريد
+
+586
+00:44:52,370 --> 00:44:57,030
+أن تُكْمِلَ عليه، طوِّره لنا غدًا، أنتَ الآن المهندس
+
+587
+00:44:57,030 --> 00:44:59,050
+المستقبل، أنتَ الذي تريد أن تعمل تشفيره غدًا، أنتَ الذي
+
+588
+00:44:59,050 --> 00:45:02,880
+تريد أن تعمل، أو أن تصبح hacker، أنتَ
+
+589
+00:45:02,880 --> 00:45:07,260
+حر، يعني تمام، ففعليًّا يخرج الـ greatest common
+
+590
+00:45:07,260 --> 00:45:10,440
+divisor equal to one، عشان تجيب منها الـ inverse
+
+591
+00:45:10,440 --> 00:45:14,020
+لاحقًا، تجيب منها الـ inverse، طيب، سنرى كيف
+
+592
+00:45:14,020 --> 00:45:19,420
+يدوسير، الكلام مختلف في الموضوع هذا، أن كيف أعمل
+
+593
+00:45:19,420 --> 00:45:26,380
+عملية الـ representation، لأ، الحروف هذه، عمليّة تمثيلها
+
+594
+00:45:26,380 --> 00:45:30,620
+في ناس مثلّوها كما عمل سيزر، وهذا الذي سنعمل عليه
+
+595
+00:45:30,620 --> 00:45:34,400
+عشان أبسط، عشان أنتَ ممكن أن تفهمه أسرع، أن أقول الـ S
+
+596
+00:45:34,400 --> 00:45:38,720
+هذه، ما هو ترتيبها في الحروف؟ رقم 18، الـ T وراءها على
+
+597
+00:45:38,720 --> 00:45:45,140
+طول 19، لاحظ؟ طيب، الـ O تأتي 14، طيب، الـ O وراءها
+
+598
+00:45:45,140 --> 00:45:48,560
+على طول مباشرة تأتي 15، فممكن أن أضعها في الـ location
+
+599
+00:45:48,560 --> 00:45:52,580
+تَبَعَها في ترتيب الحروف، في طرق ثانية تقول لك لا، أجلب
+
+600
+00:45:52,580 --> 00:45:58,240
+قيمتها بالـ ASCII code، وساعتها سيظهر معانا الـ small
+
+601
+00:45:58,240 --> 00:46:03,410
+عن الـ capital، ليس هكذا، الـ ASCII code يظهر من الـ
+
+602
+00:46:03,410 --> 00:46:06,530
+small والـ capital، هنا لن نُظهِرَ، هنا مجرد أنّكَ
+
+603
+00:46:06,530 --> 00:46:09,690
+تعطيكَ الـ concept أنّكَ تفهم فقط الطريقة كيف تسير، خلاص
+
+604
+00:46:09,690 --> 00:46:12,850
+أ
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/VOPKfsvewqI_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/VOPKfsvewqI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..57ca1ec45d30ecf9552cd4051e40bdfdba5e10a0
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/VOPKfsvewqI_postprocess.srt
@@ -0,0 +1,2644 @@
+1
+00:00:05,130 --> 00:00:07,610
+بسم الله الرحمن الرحيم يعطيكوا العفو يا شباب اليوم
+
+2
+00:00:07,610 --> 00:00:11,350
+نكمل جزئية ال applications اللي بدأنا ناخدها على
+
+3
+00:00:11,350 --> 00:00:15,430
+ال number theory و من المرة الماضية ممكن اتكلمنا
+
+4
+00:00:15,430 --> 00:00:17,490
+انه في حاجة من الحاجات المهمة جدا اللي هي solo
+
+5
+00:00:17,490 --> 00:00:21,710
+random solo random بمعنى انه deterministically او
+
+6
+00:00:21,710 --> 00:00:25,970
+بشكل محسوب معروف ايش المعادلات تبعته بقدر اعمله
+
+7
+00:00:25,970 --> 00:00:30,130
+generation ل random numbers رغم ان هو that appear
+
+8
+00:00:30,130 --> 00:00:34,920
+randomيعني هو يظهر كأنه عشوائي، يظهر كأنه عشوائي،
+
+9
+00:00:34,920 --> 00:00:39,650
+فإذا أنت مش عارف ال ..زي ما بقول الخطة طبعته أو
+
+10
+00:00:39,650 --> 00:00:43,330
+الجزء ال deterministic طبعه okay انت تظن ان هو
+
+11
+00:00:43,330 --> 00:00:47,050
+عشوائي بس هو فعليا لأ هو مش عشوائي هو ليس عشوائي
+
+12
+00:00:47,050 --> 00:00:49,650
+تمام هذه اتكلمنا عنها المرة الماضية ايش
+
+13
+00:00:49,650 --> 00:00:52,270
+استخداماتها الاستخدامات كتيرة منها ال games منها
+
+14
+00:00:52,270 --> 00:00:54,490
+ال graphics منها ال simulations اللي بتنعمل ك
+
+15
+00:00:54,490 --> 00:00:57,930
+simulations ال graphics لما بيكون يعطي او ال games
+
+16
+00:00:57,930 --> 00:01:01,350
+لما بيكون يعطيك مجموعة options للحلول أحيانا بيكون
+
+17
+00:01:01,350 --> 00:01:06,380
+فيها random .. randomization بلا الموضوع هذاكويس
+
+18
+00:01:06,380 --> 00:01:10,800
+فبتستخدم في حالة زي الحالات هذه في ال hash
+
+19
+00:01:10,800 --> 00:01:14,280
+functions اللي بيعمل عملية mask لل data خصوصا ال
+
+20
+00:01:14,280 --> 00:01:17,740
+data الكبيرة اللي بيعملها عملية security ك secure
+
+21
+00:01:17,740 --> 00:01:22,520
+code برضه بيستخدم فيها ال random ال cryptographic
+
+22
+00:01:22,520 --> 00:01:26,630
+algorithm وهذا اللي حققهنصلوا في آخر المحاضرة في
+
+23
+00:01:26,630 --> 00:01:29,910
+آخر المحاضرة اللي هو عملية التشفير تشفير البيانات
+
+24
+00:01:29,910 --> 00:01:34,850
+برضه محتاجة نشتغل على random sequence أو تبدو
+
+25
+00:01:34,850 --> 00:01:37,490
+كأنها random sequenceفي الحالة اللي احنا ممكن نحكي
+
+26
+00:01:37,490 --> 00:01:41,190
+عنها طيب إيش ال techniques اللي ممكن نستخدمها to
+
+27
+00:01:41,190 --> 00:01:45,450
+generate ال random numbers هذه؟ هي ال linear
+
+28
+00:01:45,450 --> 00:01:48,930
+congruential method اللي أخدناها المرة الماضية
+
+29
+00:01:48,930 --> 00:01:52,870
+وقولنا إن هي linear معناته المعادلة أصلا هي linear
+
+30
+00:01:52,870 --> 00:01:56,890
+و congruential بمعنى إنه مش بالضروري هذه تسوي
+
+31
+00:01:56,890 --> 00:02:02,530
+exactly هذه وانما تكافئها حسب ال modulus Mواخدنا
+
+32
+00:02:02,530 --> 00:02:07,290
+ان في فرق بين equal وcongruent مش هيك هذه تكافئ
+
+33
+00:02:07,290 --> 00:02:10,590
+هذه تساوي فهم مختلفين تماما عن بعض في الحالة
+
+34
+00:02:10,590 --> 00:02:13,670
+بتاعتنا فهي المعادلة linear اه linear لان هي
+
+35
+00:02:13,670 --> 00:02:17,610
+معادلة خطية congruential okay مش congruential لان
+
+36
+00:02:17,610 --> 00:02:22,270
+هذه لاتساوي exactly هذه وانما تكافئها حسبالـ
+
+37
+00:02:22,270 --> 00:02:28,070
+modulus اللي احنا شغالين عليه تمام واخدنا مثال
+
+38
+00:02:28,070 --> 00:02:31,870
+تمام هيعطينا مجموعة ال parameters اللي محتاجينها
+
+39
+00:02:31,870 --> 00:02:35,230
+to generate a sequence .. a certain sequence وفعلا
+
+40
+00:02:35,230 --> 00:02:37,710
+شفنا ال certain sequence اللي اشتغلناه هي شفناه
+
+41
+00:02:37,710 --> 00:02:41,510
+هنا واخدنا شوية ملاحظات طلعنا بشوية ملاحظات انه
+
+42
+00:02:41,510 --> 00:02:46,110
+انا بقدر اعرف جداش قيمة ال modulus اذا كان عرفت
+
+43
+00:02:46,110 --> 00:02:50,030
+انت بت ..بتكرر ال sequence إذا كان اتكرر ال
+
+44
+00:02:50,030 --> 00:02:53,490
+sequence فبنقدر نعرف جدش واخدنا مثال اللي هو كان
+
+45
+00:02:53,490 --> 00:02:57,270
+عنده seed بدأناها بتلاتة فرجعت اتكررت التلاتة بعد
+
+46
+00:02:57,270 --> 00:03:00,410
+تسعة elements فبعرف أنه على طول ال modulus اللي
+
+47
+00:03:00,410 --> 00:03:02,610
+أنا مستخدم هو تسعة هو فعلا ال modulus اللي
+
+48
+00:03:02,610 --> 00:03:07,740
+استخدمناهكان تسعة exactly فعلا تسعة طيب هذا الكلام
+
+49
+00:03:07,740 --> 00:03:11,480
+عشان يحاولوا يحسنوا في عملية ال generation وجدوا
+
+50
+00:03:11,480 --> 00:03:17,520
+انه ال pure multiplicative generator ب modulus بدل
+
+51
+00:03:17,520 --> 00:03:21,880
+تسعة لأ اتنين تضابر واحد وعشرين واحد تلاتين عفوا
+
+52
+00:03:21,880 --> 00:03:26,820
+ناقص واحد هذا استخدموه كأن هو مين ال M فجالوا ان
+
+53
+00:03:26,820 --> 00:03:31,480
+هذا افضل شيء ممكن لان انت هتحتاج في الحالة هذهلأ
+
+54
+00:03:31,480 --> 00:03:34,940
+حوالي اتنين to the power واحد تلاتين ناقص اتنين
+
+55
+00:03:34,940 --> 00:03:38,760
+element قبل ما ترجع يتكرر تاني فبتكون حتى لو عندك
+
+56
+00:03:38,760 --> 00:03:41,720
+مهمة خلصتها وانتهيت يعني حتى لو بدك تعمل mask او
+
+57
+00:03:41,720 --> 00:03:45,860
+اشي هتكون خلصته قبل ما تبدأ في عملية التكرار قبل
+
+58
+00:03:45,860 --> 00:03:48,240
+ما تكون بدأت في عملية التكرار فانتوا متخيلين قداش
+
+59
+00:03:48,240 --> 00:03:51,330
+اتنين to the power واحد تلاتينمش هيك يعني بتتكلم
+
+60
+00:03:51,330 --> 00:03:55,470
+عن تنت ال .. ال .. ال billion two billion و كسر مش
+
+61
+00:03:55,470 --> 00:04:00,750
+هيك تمام ف بتكون أنسب من أرقام تانية طيب ال
+
+62
+00:04:00,750 --> 00:04:04,330
+multiplier بستخدمه سبعة تتبار خمسة اللي هو حوالي
+
+63
+00:04:04,330 --> 00:04:08,830
+ستاشر ألف تمامية و سبعة ك parameter أو كقيمة لل
+
+64
+00:04:08,830 --> 00:04:15,390
+parameter a كويس وصلنا هنا ع ده المرة الماضية كنا
+
+65
+00:04:15,390 --> 00:04:20,450
+وجفنا عند النقطة هذه و قلنا انهعشان نشتغل الشغل
+
+66
+00:04:20,450 --> 00:04:26,010
+هذا فعليا و فعلا أبدأ أجيب قيم ل sequence أو نفك
+
+67
+00:04:26,010 --> 00:04:29,570
+.. نفك لاحظ ال sequence اللي موجود عندك فانت بدأت
+
+68
+00:04:29,570 --> 00:04:32,310
+تجيب العكس تبعه انت عملت encryption بس طيب ال
+
+69
+00:04:32,310 --> 00:04:36,350
+decryption أهم من ال encryption يعني هو مش شطارة
+
+70
+00:04:36,350 --> 00:04:38,870
+أن أنا أشفر بيانات و أرميها و أنا ماعرفش كمان
+
+71
+00:04:38,870 --> 00:04:43,210
+أرجحها ده وش استفدنا منها طيب عملية انك ترجحها
+
+72
+00:04:43,210 --> 00:04:48,290
+يعني كأنك انت بدأت تجيب قيمة Xمن المعادلة الخطية
+
+73
+00:04:48,290 --> 00:04:51,750
+فلما يكون عندك a في x لأنه على اعتبار ان ال a ده
+
+74
+00:04:51,750 --> 00:04:54,910
+هو ال mask فانت ضربته في ال data ايه طلع عندك
+
+75
+00:04:54,910 --> 00:04:59,510
+معلومة معينة تشير تمام فإذا انا بدي اجيب المعلومة
+
+76
+00:04:59,510 --> 00:05:04,290
+بمعلومية ال mask اللي انا ضربت فيه اللي هي ممكن
+
+77
+00:05:04,290 --> 00:05:10,550
+ارجع اعمله اعادة generation وال data اللي انبعتت
+
+78
+00:05:10,550 --> 00:05:14,880
+اصلا اللي هي فعلا متوفرة ومشفرة اصلامش هيك هي مش
+
+79
+00:05:14,880 --> 00:05:19,140
+شفرة طيب كيف بدي أجيب X منها؟ okay ببساطة جدا بجيب
+
+80
+00:05:19,140 --> 00:05:24,380
+ال inverse ل A أمتازة بس الفكرة أن ال inverse ل A
+
+81
+00:05:24,380 --> 00:05:28,840
+هي مش معادلة خطية pure linear لأ هي مش pure linear
+
+82
+00:05:28,840 --> 00:05:33,760
+هي congruential هي linear congruential ليش؟ لأن في
+
+83
+00:05:33,760 --> 00:05:38,210
+عندك ال modulus Mفانت ما بتقدر تتعامل معها زي ما
+
+84
+00:05:38,210 --> 00:05:41,090
+كنت تتعامل مع ال linear ال pure linear اللي كنت
+
+85
+00:05:41,090 --> 00:05:44,630
+تشتغلها لأ هنا في خصوصية شوية الخصوصية الشوية هي
+
+86
+00:05:44,630 --> 00:05:51,290
+ان ال inverse لل A بال module M لازم يكون عبارة عن
+
+87
+00:05:51,290 --> 00:05:55,190
+ال A prime بحيث انك ال A prime في ال A هو
+
+88
+00:05:55,190 --> 00:06:03,310
+equivalent او congruent للواحد ولا يساوي الواحد هي
+
+89
+00:06:03,310 --> 00:06:07,150
+congruent للواحدعارفين إيش يعني؟ يعني معناه دالك
+
+90
+00:06:07,150 --> 00:06:10,910
+إنه ممكن يكون عندك أكتر من inverse ممكن يكون عندك
+
+91
+00:06:10,910 --> 00:06:15,350
+أكتر من inverse لكن الفكرة وين؟ الفكرة إنه أنت
+
+92
+00:06:15,350 --> 00:06:18,630
+عشان يكون unique و تسميه unique المفروض إنه في كل
+
+93
+00:06:18,630 --> 00:06:24,510
+one loop مايكونش إلا inverse وحيد okay إذا ال
+
+94
+00:06:24,510 --> 00:06:27,010
+inverse التاني يكون في ال loop اللي وراها في ال
+
+95
+00:06:27,010 --> 00:06:30,390
+loop اللي وراها بس مش يكون two inverse في نفس ال
+
+96
+00:06:30,390 --> 00:06:36,090
+loopفي نفس ال loop عشان نعمل الكلام هذا و نضمن انه
+
+97
+00:06:36,090 --> 00:06:41,030
+فعلا مش هيظهر two inverse او انه يوجد اصلا inverse
+
+98
+00:06:41,030 --> 00:06:46,920
+كمانداخل ال one loop في الحالة هذه محتاجين نحكم بس
+
+99
+00:06:46,920 --> 00:06:49,960
+ال A مع ال modulus ال A هذا اللي بدنا نجيبله ال
+
+100
+00:06:49,960 --> 00:06:54,860
+inverse مع ال modulus يكونوا relatively prime أو
+
+101
+00:06:54,860 --> 00:06:58,740
+co-prime عشان أضمن أنه ال greatest common divisor
+
+102
+00:06:58,740 --> 00:07:04,280
+between them واحد فهم مافيش تكرار بينهم فمعنى ذلك
+
+103
+00:07:04,280 --> 00:07:09,310
+أنه ال A بتظهرش مرتين داخل ال Mداخل ال one loop
+
+104
+00:07:09,310 --> 00:07:12,990
+ماتظهرش أكتر من مرة واحدة فإذا لو إلها inverse
+
+105
+00:07:12,990 --> 00:07:19,250
+بضمن أنه بتكرر مرة واحدة فقط داخل ال one loop تمام
+
+106
+00:07:19,250 --> 00:07:24,470
+فمبدأيا إذا كدرنا هنا انحقق هذه المعادلة أنه فعلا
+
+107
+00:07:24,470 --> 00:07:28,850
+أي inverse في قيمته في القيمة الأصلية بتساوي واحد
+
+108
+00:07:28,850 --> 00:07:32,730
+بس بدنا ناخد أنه ناخد بأنها modulo M هذا معناه إذا
+
+109
+00:07:32,730 --> 00:07:35,610
+كان في الحالة هذه كدرنا نجيبها مجرد أنه بضربها في
+
+110
+00:07:35,610 --> 00:07:41,140
+الطرفين للمعادلةفي الطرفين عشان اقول ان هذا بيساوي
+
+111
+00:07:41,140 --> 00:07:46,940
+واحد حسب المعادلة واحد فبتضال X و بقدر استخرج قيمة
+
+112
+00:07:46,940 --> 00:07:50,720
+X نقدر في الحالة هتستخرج قيمة ال X اللي موجودة
+
+113
+00:07:50,720 --> 00:07:57,720
+عندنا ك A prime في B يعني ال A inverse ل ال mask
+
+114
+00:07:57,720 --> 00:08:01,380
+او ل ال random numbers اللي انت استخدمتها في ال
+
+115
+00:08:01,380 --> 00:08:04,390
+output اللي وصلك اصلافي ال output اللي وصلك تضربهم
+
+116
+00:08:04,390 --> 00:08:07,490
+في بعض و تجيب قيمة A طيب هذا الكلام عشان يتحقق
+
+117
+00:08:07,490 --> 00:08:10,910
+فعليا و أكون ضامن انه صحيح ال greatest common
+
+118
+00:08:10,910 --> 00:08:13,810
+divisor بين ال A و ال M لازم يكون بساوي واحد عشان
+
+119
+00:08:13,810 --> 00:08:16,930
+أضمن ان هم relatively prime او coprime او coprime
+
+120
+00:08:16,930 --> 00:08:21,490
+طبعا ال M لازم تكون اكبر من واحد يعني by logic
+
+121
+00:08:21,490 --> 00:08:24,030
+لازم تكون بهذا الشكل ففي الحالة دي اذا اتحقق هذا
+
+122
+00:08:24,030 --> 00:08:28,050
+الكلام بقدر اقول ان ال A has a unique inverse
+
+123
+00:08:28,050 --> 00:08:34,930
+فعليا هي لها unique inverse A primeباستخدام المدلو
+
+124
+00:08:34,930 --> 00:08:38,890
+M لأن استخدام مدلو تاني قيمة تانية ل ال modulus
+
+125
+00:08:38,890 --> 00:08:43,770
+ممكن يختلف الكلام، هيختلف تماما، تمام؟ فإذا هذه
+
+126
+00:08:43,770 --> 00:08:47,910
+معادلة أساسية ومهمة جدا، okay خلصنا من المعادلة
+
+127
+00:08:47,910 --> 00:08:50,450
+الأساسية والمهمة جدا ك concept، الآن كيف بدنا
+
+128
+00:08:50,450 --> 00:08:53,650
+نطبقها؟ جاينا الكلام، هيجينا الكلام، بس بدنا ناخد
+
+129
+00:08:53,650 --> 00:08:58,480
+بالنا أن كيف أجيب ال inverseبمعادلات بسيطة عشان
+
+130
+00:08:58,480 --> 00:09:03,320
+لما نكبر المعادلات بتاعتنا نكون بنفس النهج نشتغل
+
+131
+00:09:03,320 --> 00:09:08,780
+فمبدأيا مين اللي يحللنا هذا الموضوع بزوعلى باللفظ
+
+132
+00:09:08,780 --> 00:09:13,780
+الفرنسي أو بزاوت باللفظ الإنجليزي فهي بزاو على
+
+133
+00:09:13,780 --> 00:09:18,880
+أساس أنه فرنسي أهو أساسا زي bijou تنكتب ا او او U2
+
+134
+00:09:18,880 --> 00:09:26,140
+بس T بس هي بزاو كويس فإذا إذا بدنا نتكلم عن بزاوت
+
+135
+00:09:26,140 --> 00:09:34,260
+او بزاو coefficients لالتلاتة modulo seven كأنه
+
+136
+00:09:34,260 --> 00:09:37,560
+بده اجيب ايش الرقمين اللي بده اضربهم رقم فى
+
+137
+00:09:37,560 --> 00:09:41,740
+التلاتة ورقم فى السبعة بحيث انه حاصل الضربين بسوء
+
+138
+00:09:41,740 --> 00:09:46,820
+بعضاو inverse لبعض طيب inverse لبعض معناته انه
+
+139
+00:09:46,820 --> 00:09:50,300
+المفروض بيساوي .. بيساوي مجموحهم بيساوي واحد اللي
+
+140
+00:09:50,300 --> 00:09:53,020
+هو ال inverse القيمة في ال inverse تبعها بيساوي
+
+141
+00:09:53,020 --> 00:09:56,980
+واحد تمام فهنا بنبحث عنها اول شغل عشان نعمل هذا
+
+142
+00:09:56,980 --> 00:10:02,780
+الكلام هل فعلا ال .. ال bizot coefficient ممكن ولا
+
+143
+00:10:02,780 --> 00:10:06,710
+لأ؟هل هو ممكن ولا لأ؟ عشان أقول هو ممكن ولا لأ،
+
+144
+00:10:06,710 --> 00:10:10,490
+بدنا نطبق النظرية اللي كانت أخر نظرية وشوفناها
+
+145
+00:10:10,490 --> 00:10:17,190
+الـA والـM لازم يكونوا co-prime لازم يكونوا co
+
+146
+00:10:17,190 --> 00:10:20,510
+-prime أو relatively prime، فإذا تلاتة أو سبعة هما
+
+147
+00:10:20,510 --> 00:10:24,290
+فعلا co-prime، لأن هما أساسا الـprimes هما أساسا
+
+148
+00:10:24,290 --> 00:10:27,370
+الـprimes كمان، تمام، ففي الحالة دي بقدر أقول إن
+
+149
+00:10:27,370 --> 00:10:33,930
+في قيمة ممكن أضربها في الأولتمام؟ و أجمعها على
+
+150
+00:10:33,930 --> 00:10:37,930
+التاني مضروب في K معينة بحيث انه يساوي واحد بحيث
+
+151
+00:10:37,930 --> 00:10:41,890
+انه يساوي واحد ايش استفدت من ال .. ال .. ال .. ال
+
+152
+00:10:41,890 --> 00:10:45,470
+biz out ال biz out او ال bizo coefficient هذه
+
+153
+00:10:45,470 --> 00:10:49,610
+استفدت منها كالتالي مدام انا بشتغل على ال modulus
+
+154
+00:10:49,610 --> 00:10:54,930
+سبعة معناته السالب اتنين هي فعليا ال inverse
+
+155
+00:10:54,930 --> 00:11:01,360
+للتلاتة modulo سبعة modulo سبعةهي فعليا ال inverse
+
+156
+00:11:01,360 --> 00:11:06,720
+تبعها ال inverse تبعها في أي لفة في اللفة الأولى
+
+157
+00:11:06,720 --> 00:11:12,040
+في اللفة الأولى طب في اللفة التانية معناه أننا
+
+158
+00:11:12,040 --> 00:11:16,000
+نضيف سبعة على القيمة هذه لأنه خلاص ما هيحصير تكرر
+
+159
+00:11:16,000 --> 00:11:20,200
+حصير تكررية باعتبار أنه السالب اتنين فعليا هو
+
+160
+00:11:20,200 --> 00:11:24,340
+هيكون congruent لأي رقم زائد أو ناقص سبعة ال
+
+161
+00:11:24,340 --> 00:11:28,370
+modulusموديلوس زي الساعة زي الساعة إذا كان
+
+162
+00:11:28,370 --> 00:11:32,890
+الموديلوس تبعك اتناش فالواحدة تكافئ مين اجمع اتناش
+
+163
+00:11:32,890 --> 00:11:37,030
+تكافئ تلتاش والتلتاش اجمع كمان اتناش تكافئ الخمسة
+
+164
+00:11:37,030 --> 00:11:41,770
+وعشرين هي هي فإذا congruent لبعض كلهم نفس قيمة
+
+165
+00:11:41,770 --> 00:11:45,310
+الساعة كساعة كساعة فانت حتى الساعة خمسة وعشرين
+
+166
+00:11:45,310 --> 00:11:48,690
+بتقدر تقولها ساعة واحدة الساعة تلتاش هي ساعة واحدة
+
+167
+00:11:49,490 --> 00:11:54,610
+تمام فلكن وين؟ في لفة تانية في اللفة التانية من
+
+168
+00:11:54,610 --> 00:11:59,550
+الساعة فنفس الفكرة هنا بتقدر تقول انه ال Bizot
+
+169
+00:11:59,550 --> 00:12:03,670
+coefficient هو بيضمنلك انه القيمة اللي مضروبة في
+
+170
+00:12:03,670 --> 00:12:11,290
+ال A وين ال modulus كاتبينه احنا؟ في ال Aحيكون هو
+
+171
+00:12:11,290 --> 00:12:15,930
+ال inverse ل L و ل A في اللفة اللي مضروبة في مين
+
+172
+00:12:15,930 --> 00:12:19,670
+في ال modulus بحيث انه الاتنين مع بعض بساوي بساوي
+
+173
+00:12:19,670 --> 00:12:24,410
+واحد طيب الان هذه مش على جد سالب اتنين فقط اجمع
+
+174
+00:12:24,410 --> 00:12:30,010
+سبعة معناته حتى الخمسة هي inverse ل Lالتلاتة
+
+175
+00:12:30,010 --> 00:12:33,250
+السالب تسعة برضه inverse للتلاتة الاطنعش inverse
+
+176
+00:12:33,250 --> 00:12:37,610
+للتلاتة و هكذا خلاص لأنه زي ما قلنا الواحدة هي
+
+177
+00:12:37,610 --> 00:12:41,430
+نفسها تلت عشر هي نفسها خمسة و عشرين و بدك تجمع
+
+178
+00:12:41,430 --> 00:12:45,850
+أكتر كمل مش مشكلة كلهم في النهاية مدام تحت ال
+
+179
+00:12:45,850 --> 00:12:49,850
+module operation كلهم متكافئين كلهم congruent لمن؟
+
+180
+00:12:49,850 --> 00:12:55,470
+لبعض كلهم congruent لبعض السالب تسعة هتكون اه كأنك
+
+181
+00:12:55,470 --> 00:12:58,710
+عكسيما تديري بالك انت اللفات الان يا اما مع اقارب
+
+182
+00:12:58,710 --> 00:13:01,050
+الساعة يا اما عكس اقارب الساعة انت عندك حرية
+
+183
+00:13:01,050 --> 00:13:05,290
+بتتحرك بسهولة جدا هنا سالب اتنين هذه معناته انت
+
+184
+00:13:05,290 --> 00:13:10,390
+بتتحرك عكس اقارب الساعة هيها وهي مكافئة هي للخمسة
+
+185
+00:13:10,390 --> 00:13:14,970
+مع اقارب الساعة هي مكافئة للخمسة مع اقارب الساعة
+
+186
+00:13:14,970 --> 00:13:21,380
+تمام هالواجهة لما تيجي تضربهم هنا في بعضهمتضرب في
+
+187
+00:13:21,380 --> 00:13:25,320
+بعض المفروض انه ضمن ال modulus يساوي واحد المفروض
+
+188
+00:13:25,320 --> 00:13:31,660
+ضمن ال modulus يكون بساوي الواحد طيب الكلام ده كيف
+
+189
+00:13:31,660 --> 00:13:36,350
+ممكن انطبقه على معادلة أكبر؟على معادلة أكبر،
+
+190
+00:13:36,350 --> 00:13:39,390
+لاحظوا، أنلخص اللي قلناها قبل شوية، كان في عندي
+
+191
+00:13:39,390 --> 00:13:44,350
+theorem مهم جدا أنه أضمن أول شغلة أنه القيمة اللي
+
+192
+00:13:44,350 --> 00:13:49,470
+بده أجيب لها ال inverse هي co-prime مع ال modulus
+
+193
+00:13:49,470 --> 00:13:55,630
+عشان نضمن أنه أول شغلة في inverse و unique inverse
+
+194
+00:13:56,660 --> 00:13:59,100
+نضمن انه unique inverse امتى بقدر اضمن انه unique
+
+195
+00:13:59,100 --> 00:14:01,980
+inverse اذا كان relatively prime بمعنى انه مش
+
+196
+00:14:01,980 --> 00:14:07,870
+هيكون فيه اكتر من inverse في نفس اللفةطيب نفس
+
+197
+00:14:07,870 --> 00:14:10,770
+اللفة هو مين اللي بيمثل اللفة؟ ال modulus هو اللي
+
+198
+00:14:10,770 --> 00:14:14,690
+بيمثل إيش يعني لفة؟ يعني الأتناش هي اللي تمثل إيش
+
+199
+00:14:14,690 --> 00:14:17,730
+معناه .. إيش مفهوم كلمة لفة؟ ال one loop هذا إيش
+
+200
+00:14:17,730 --> 00:14:20,990
+معناه؟ إتناش إذا أنا بتكلم عن الساعة طيب لما بدي
+
+201
+00:14:20,990 --> 00:14:23,690
+أجيب in أي inverse أو أي رقم ال inverse تبعه
+
+202
+00:14:23,690 --> 00:14:27,410
+معناته بدي أجيب ال relation بينه بين ال modulus هل
+
+203
+00:14:27,410 --> 00:14:33,340
+هم بتكرروش أكتر من مرة؟ بهذا الشكلفأول operation
+
+204
+00:14:33,340 --> 00:14:37,560
+لما نقول والله بدي اجيب ال inverse ل 101 موديوله
+
+205
+00:14:37,560 --> 00:14:44,560
+4620 مثلا اول شغلة بده اضمنها ان ال inverse او ال
+
+206
+00:14:44,560 --> 00:14:52,440
+101 هذه هيكون في كل لفة لها one unique inverse فقط
+
+207
+00:14:52,440 --> 00:14:57,180
+one unique inverse اكتر من هيك هضيع الأمور هيكون
+
+208
+00:14:57,180 --> 00:15:02,000
+من السهل كسر الكود اصلا لانه هيصير التكراراتجريبة
+
+209
+00:15:02,000 --> 00:15:08,660
+اكتير اقل من قيمة المجلس اللى انت متوقعه انت متوقع
+
+210
+00:15:08,660 --> 00:15:15,980
+انه بعد 4619 يرجع يتكرر مش هيك فعليا مابيصرش هتجد
+
+211
+00:15:15,980 --> 00:15:18,540
+انه لأ هم فعليا ماتصرش بهذا الشكل ليش لأنه
+
+212
+00:15:18,540 --> 00:15:23,960
+relatively prime ماتحققتش ففعليا بتكرر بمسافات اقل
+
+213
+00:15:23,960 --> 00:15:29,750
+بصير طيب نشوف الانحسابيا كيف بدنا نعمل هذا الكلام؟
+
+214
+00:15:29,750 --> 00:15:32,770
+أول شغلة حسابيا عشان ننفذ الكلام اللي احنا بنقوله
+
+215
+00:15:32,770 --> 00:15:35,570
+عشان أجيب ال inverse ل 101 كأني بده أقول إيش
+
+216
+00:15:35,570 --> 00:15:40,210
+القيمة؟ قيمة ال inverse هي اللي بده أضربها في 101
+
+217
+00:15:40,210 --> 00:15:45,410
+بحيث أنه لو جمعناها على ال modulus في B واحنا
+
+218
+00:15:45,410 --> 00:15:49,590
+عارفين بيها دي هيمثل في الآخر عدد لفات عدد لفات
+
+219
+00:15:49,590 --> 00:15:54,950
+مجموعه بيساوي واحد مجموعه يساوي الواحد طيب أول
+
+220
+00:15:54,950 --> 00:15:59,270
+شغلة لازم ناخد بالنا منهاالـ Theorem اللي حكيناها
+
+221
+00:15:59,270 --> 00:16:01,430
+ان الـ greatest common divisor between them لازم
+
+222
+00:16:01,430 --> 00:16:05,510
+يكون بيساوي واحد okay عشان نقول والله بيساوي واحد
+
+223
+00:16:05,510 --> 00:16:08,890
+بدنا نعملها ك analysis okay انت ممكن تكون ضامن
+
+224
+00:16:08,890 --> 00:16:11,950
+exactly ان هي بتساوي واحد لكن ال analysis ده هيسهل
+
+225
+00:16:11,950 --> 00:16:16,290
+عليك الآن في إيجاد ال إيه في إيجاد ال إيه خليني
+
+226
+00:16:16,290 --> 00:16:22,950
+أشوف ال 4620 بنجسمها على مين؟ على 101 بطلع عندي
+
+227
+00:16:22,950 --> 00:16:24,730
+45101
+
+228
+00:16:26,390 --> 00:16:31,610
+زائد خمسة وسبعين ك reminder طيب المية و واحد اكم
+
+229
+00:16:31,610 --> 00:16:36,370
+reminder فيها؟ reminder واحد و بيزيد ستة و عشرين
+
+230
+00:16:36,370 --> 00:16:43,270
+طيب برضه ال خمسة و سبعين ك quotient ل الخط هذا اكم
+
+231
+00:16:43,270 --> 00:16:48,350
+reminder فيه؟ ال two reminders زائد تلتة و عشرين
+
+232
+00:16:48,350 --> 00:16:54,000
+نفس الجثةلما نصل للواحد في الآخر وصلنا للواحد
+
+233
+00:16:54,000 --> 00:16:56,280
+ضمننا فعلا ان ال greatest common divisor between
+
+234
+00:16:56,280 --> 00:17:01,980
+them بالذات بتساوي واحد ماصفرتش احنا قلنا ال
+
+235
+00:17:01,980 --> 00:17:03,940
+greatest common divisor كنا نجيبها اذا كانت صفرت
+
+236
+00:17:03,940 --> 00:17:07,200
+معناته في الآخر هيكبر القسم على بعض هنا واحد
+
+237
+00:17:07,200 --> 00:17:12,820
+معناته فعليا relatively prime هو مافيش اصلا عامل
+
+238
+00:17:12,820 --> 00:17:16,060
+مشترك بينهم مافيش اصلا عامل مشترك بينهم طيب من هنا
+
+239
+00:17:16,060 --> 00:17:22,000
+بنرجع ارجوعلاحظ إنه لو أرجع نرجوع بحيث إن أصل من
+
+240
+00:17:22,000 --> 00:17:26,900
+الواحد اللي بدأنا فيه هنا بدي أرجع أرجوع عشان أصل
+
+241
+00:17:26,900 --> 00:17:31,020
+للرقمين اللي بديهم أحاول أحقق هذه القيمة لاحظ شوف
+
+242
+00:17:31,020 --> 00:17:40,260
+إيش رح نعمله آخر واحد as a remainder هيها باخدها
+
+243
+00:17:40,260 --> 00:17:44,520
+هنا و ببدأ منها الواحد بحطه على جنب لإن أنا محتاج
+
+244
+00:17:44,520 --> 00:17:49,550
+الواحد على جنب هنا هي لاحظته؟ممتاز طيب مدام حطينا
+
+245
+00:17:49,550 --> 00:17:53,310
+الواحد على جانب انا ضامن تماما اذا اتزمت بنفس
+
+246
+00:17:53,310 --> 00:17:58,710
+المكونات اللي هنا في تقييم كل رقم من الأرقام اللي
+
+247
+00:17:58,710 --> 00:18:06,070
+هنا حصل في الآخر لنفس الرقامين ال 4620 وال 101 لأن
+
+248
+00:18:06,070 --> 00:18:10,130
+أصلا كلهم مشتقين من بعض فالواحد هذه إيجتني أصلا من
+
+249
+00:18:11,570 --> 00:18:15,110
+من مرحلة سابقة و هكذا طيب التلاتة كانت موجودة في
+
+250
+00:18:15,110 --> 00:18:17,210
+اللي قبلها والاتنين كانت موجودة في اللي قبلها و
+
+251
+00:18:17,210 --> 00:18:21,230
+هكذا طيب كيف هنعمل كلام هذا بده بس صح صح في
+
+252
+00:18:21,230 --> 00:18:25,710
+الامتحان مشكلته الوحيدة أنك انت بس تكون مركز تكون
+
+253
+00:18:25,710 --> 00:18:31,070
+هادي تكون رايك في الامتحان أسئلة زي هذه بتكون
+
+254
+00:18:31,070 --> 00:18:35,070
+مضمونة أما إذا اتوترت رقم بغلط بغلط مع كل الشغل
+
+255
+00:18:35,070 --> 00:18:40,930
+هتنشوف كيفهنا من الموضوع اللي هي أخدنا الواحد على
+
+256
+00:18:40,930 --> 00:18:44,810
+طرف لحاله فبتصير اش تلاتة ناقص واحد في اتنين وما
+
+257
+00:18:44,810 --> 00:18:49,930
+تحاولش اهم شغلة ما تحاولش تضيع الأرقام اش يعني
+
+258
+00:18:49,930 --> 00:18:53,810
+اضيع الأرقام يعني تقول اتنين في واحد يعني اتنين لأ
+
+259
+00:18:53,810 --> 00:18:58,470
+خليه الواحد زي ما هو واحدلأنه أصلا جايين من حاجة
+
+260
+00:18:58,470 --> 00:19:02,270
+سابقة والاتنين جايان من إش سابق فبدناش نخربطهم في
+
+261
+00:19:02,270 --> 00:19:05,690
+بعض، هنشوف لوجد كيف الأن، هاي التلاتة زي ما هي،
+
+262
+00:19:05,690 --> 00:19:10,370
+طيب، الاتنين، الاتنين هذه ما هي كانت remainder في
+
+263
+00:19:10,370 --> 00:19:14,550
+اللي جابلها، يعني فعليا بقدر أقول إن هي تسوى تلاتة
+
+264
+00:19:14,550 --> 00:19:22,120
+وعشرين ناقص سبعة في تلاتةلأنه أصلا العملية متسلسلة
+
+265
+00:19:22,120 --> 00:19:25,640
+كانت هنا هتجد أنه دايما في رقمين هيتجمعوا مع بعض
+
+266
+00:19:25,640 --> 00:19:32,800
+ماتجمعهم مش totally اجمعهم coefficient يعني هتلاقي
+
+267
+00:19:32,800 --> 00:19:38,540
+هي في التلاتة وهي في تلاتة هنا التلاتة مضروبة في
+
+268
+00:19:38,540 --> 00:19:42,540
+واحد يعني مكررة مرة واحدة هنا مكررة سالب سبعة في
+
+269
+00:19:42,540 --> 00:19:46,640
+سالب بتصير موجة بسبعة فبتقول مكررة تمن مرات
+
+270
+00:19:49,450 --> 00:19:52,870
+أما التلاتة حافظ عليها لإيش؟ لأن هذه رسمالنا هلوجت
+
+271
+00:19:52,870 --> 00:19:57,030
+في اللي بعدها أنا بدأ أجيبها من اللي .. من اللي
+
+272
+00:19:57,030 --> 00:20:00,530
+كانت قبلها تصير في اللي بعدها هيها كانت remainder
+
+273
+00:20:00,530 --> 00:20:06,430
+في اللي قبلها فالآن كل تلاتة بعوض مكانها ب 26 ناقص
+
+274
+00:20:06,430 --> 00:20:12,390
+1 في 23 عرفتوا ليش؟ حتى لو أنت عارف أن ال greatest
+
+275
+00:20:12,390 --> 00:20:15,210
+common divisor بيسوي 1 بدك تعملها لأن هذه هي اللي
+
+276
+00:20:15,210 --> 00:20:19,380
+هتساعدك في الرجعةكويس هي جيبناها بهذا الشكل
+
+277
+00:20:19,380 --> 00:20:23,320
+فهتلاقي ان ال 23 برضه هتجمع مع تلاتة و عشرين تاخد
+
+278
+00:20:23,320 --> 00:20:26,880
+بالك ان هنا في سلب واحد في تمانية يعني فعليا
+
+279
+00:20:26,880 --> 00:20:32,720
+التلاتة و عشرين اتكررت تمن سالب تمان مرات سالب
+
+280
+00:20:32,720 --> 00:20:37,540
+واحد كمان بتصير سالب تسعة سالب تسعة على طول الرقم
+
+281
+00:20:37,540 --> 00:20:41,340
+هذا من غير ما اكيد هو ال reminder اللي جابلها اه
+
+282
+00:20:41,340 --> 00:20:48,520
+صحيحبدك تعوض بمكانه اللي هو خمسة و سبعين ناقص
+
+283
+00:20:48,520 --> 00:20:53,660
+اتنين في ستة و عشرين ايه
+
+284
+00:20:53,660 --> 00:20:57,680
+الان هتلاقي الستة و عشرين مع الستة و عشرين من
+
+285
+00:20:57,680 --> 00:21:00,580
+الحاجات اللي دايما في الامتحانات بتخربط معاكم
+
+286
+00:21:00,580 --> 00:21:06,980
+تاخدوا بالكم ان في الأقواص في رقم خارج القوس في
+
+287
+00:21:06,980 --> 00:21:11,760
+رقم خارج القوس ما تنسوش تضربوه في الاتنين يعني هنا
+
+288
+00:21:11,760 --> 00:21:20,250
+بيصير موجة ب18زائد تمانية ستة و أشرين طيب
+
+289
+00:21:20,250 --> 00:21:26,410
+الستة و أشرين أي نعم برضه من المعادلة هذه أخدنا
+
+290
+00:21:26,410 --> 00:21:30,790
+الكلام هذا من المعادلة هذه أخدناها تمام فهتلاقي
+
+291
+00:21:30,790 --> 00:21:35,150
+برضه خمسة و سبعين وهي برضه خمسة و سبعينخد بالك من
+
+292
+00:21:35,150 --> 00:21:38,570
+الـ 26 اللي برا ده خارج القوس 26 في سالب واحد
+
+293
+00:21:38,570 --> 00:21:47,350
+فسالب 26 سالب 26 سالب 9 سالب 35 كويس هنا الـ 75
+
+294
+00:21:47,350 --> 00:21:53,910
+هين أوصلناهم جربنا صفناهم
+
+295
+00:21:53,910 --> 00:21:57,290
+تعالى تطلع على الواحد اللي بدأنا فيه إيش طلع بساوي
+
+296
+00:21:57,290 --> 00:21:59,990
+هاي ال M وهي ال A
+
+297
+00:22:02,950 --> 00:22:07,370
+Automatically معناته ده هو قيمة الانفرس لإنه حققلك
+
+298
+00:22:07,370 --> 00:22:14,410
+المعادلة و احنا ضمنين انه unique او ال greatest
+
+299
+00:22:14,410 --> 00:22:20,790
+common divisor unique بين ال 101 وال 4620 طيب ال
+
+300
+00:22:20,790 --> 00:22:26,430
+1601 هذه هي inverse ل 101 في اللفة جداش؟ في اللفة
+
+301
+00:22:26,430 --> 00:22:31,850
+35 عكس على جرب الساعةفي اللفة 35 عكس عقار بالساعة
+
+302
+00:22:31,850 --> 00:22:37,850
+الان انت مش عاجبك الرقم تقدر تعدل فيه تقدر تعدل
+
+303
+00:22:37,850 --> 00:22:40,450
+فيه اذا لاجيته مثلا بالسالب اوكي اضفله قيمة ال M
+
+304
+00:22:40,450 --> 00:22:44,710
+بصير بالموجة ما احنا قلناه هو congruent لمجموعة
+
+305
+00:22:44,710 --> 00:22:48,250
+ارقام تانية لمجموعة ارقام تانية حطه دايما بأبسط
+
+306
+00:22:48,250 --> 00:22:52,290
+صورة ممكنة ايش أبسط صورة ممكنة انه يكون اقل اصلا
+
+307
+00:22:52,290 --> 00:22:56,300
+من ال modulusفمدام جاينا هو لحاله جاي أقل من
+
+308
+00:22:56,300 --> 00:23:02,780
+المدلص فانت ضامن ان هو ضمن أول لفة كرقم قيمته أقل
+
+309
+00:23:02,780 --> 00:23:07,140
+من المدلص خلاص فإذا بقول ان هو هذا ال inverse ل
+
+310
+00:23:07,140 --> 00:23:14,960
+101 modulo 4620 هنحتاج الكلام ده في إيش؟ هنحتاجه
+
+311
+00:23:14,960 --> 00:23:19,520
+كتير هيجينا ال encryption هنشوف في إيش بدنا
+
+312
+00:23:19,520 --> 00:23:24,640
+نستخدمهالكويس .. الكويس انه هنزلكوا أنا واجبات
+
+313
+00:23:24,640 --> 00:23:26,940
+عليها ده لأنه لازم تتدربوا عليها ده ايه تكونوا
+
+314
+00:23:26,940 --> 00:23:29,460
+تاخدوا عليها ايه تكونوا تاخدوا عليها و تبقوا
+
+315
+00:23:29,460 --> 00:23:34,240
+مركزين في الشغل تبعها رغم ان هو نظريا بسيط لكن عند
+
+316
+00:23:34,240 --> 00:23:43,400
+التنفيذ الأرقام كتيرة بده تركيز اوه
+
+317
+00:23:43,400 --> 00:23:47,280
+كويس طيب الان في ايش بستخدم عملية ال inverse اللي
+
+318
+00:23:47,280 --> 00:23:53,550
+انا جبتها زي توي احنا توي قولنا تلاتةمدله سبعة كان
+
+319
+00:23:53,550 --> 00:23:59,010
+ال inverse لتة لا تائش بقداش سالب اتنين كانت بتسوي
+
+320
+00:23:59,010 --> 00:24:01,890
+سالب اتنين هتيجي تقول طب ما هم مضرومين في بعض وطلع
+
+321
+00:24:01,890 --> 00:24:07,750
+سالب ستة طب ما السالب ستة يعني سبعة يعني عفوا ان
+
+322
+00:24:07,750 --> 00:24:13,830
+واحد بالسالب اه بس اتجاهه بالعكس اتجاهه عكسي تمام
+
+323
+00:24:13,830 --> 00:24:17,890
+فسالب واحد سالب ستة هذه هي فعليا تكافئ واحد هي
+
+324
+00:24:17,890 --> 00:24:24,140
+فعليا تكافئ واحد طيببنضربها في الطرفين لمعادلة
+
+325
+00:24:24,140 --> 00:24:30,280
+بهذا الشكل تلاتة X تساوي أربعة مدله سبعة فانا عارف
+
+326
+00:24:30,280 --> 00:24:32,820
+انه بدي أجيب ال inverse لتلاتة مدله سبعة احنا
+
+327
+00:24:32,820 --> 00:24:37,040
+جايبينها مسبقا هي سالب اتنين فاذا بضرب الطرفين في
+
+328
+00:24:37,040 --> 00:24:42,760
+سالب اتنين minus two خلاص هذه واحد ضمننا انه راح
+
+329
+00:24:42,760 --> 00:24:47,220
+اتخلصنا ف X بتساوي سالب تمانية X في الحالة بتساوي
+
+330
+00:24:47,220 --> 00:24:53,180
+سالب تمانية ممكن تجمع عليها سبعةعشان تجيبها قيمة
+
+331
+00:24:53,180 --> 00:24:56,900
+موجة بقى إذا مش عاجبك القيم السالبة المهم أنك تضيف
+
+332
+00:24:56,900 --> 00:25:00,680
+عليهم سبعت تضيف عليها سبعة لما يجيلك رقم ايش أجرب
+
+333
+00:25:00,680 --> 00:25:04,840
+رقم كان اللي هي أربعة عشر خليني أقول يعني سبعة و
+
+334
+00:25:04,840 --> 00:25:08,720
+سبعة مش هيك بطلع ستة على سرد ستة و تمانية هيس
+
+335
+00:25:08,720 --> 00:25:13,220
+الاربعة عشر يعني انت بتعمل لفتين okay الستة مناسبة
+
+336
+00:25:13,220 --> 00:25:16,280
+لك خلاص أقول إن قيمتها بتسوي ستة ف X هنا قيمتها
+
+337
+00:25:16,280 --> 00:25:22,750
+مناسبة أنها تكون بتسوي ستة عشان تحل السؤال هذاتمام
+
+338
+00:25:22,750 --> 00:25:29,290
+الآن ال pseudo random هذه ال ال pseudo prime زي ما
+
+339
+00:25:29,290 --> 00:25:32,030
+أخدنا ال pseudo random الآن في ال pseudo prime ال
+
+340
+00:25:32,030 --> 00:25:36,850
+pseudo prime إجت من نظرية صينية قديمة كانوا
+
+341
+00:25:36,850 --> 00:25:42,650
+بيقولوا إذا كان ال n prime فمعنى ذلك لازم يتحقق أن
+
+342
+00:25:42,650 --> 00:25:46,590
+اتنين to the power ل prime هذا ناقص واحدهي
+
+343
+00:25:46,590 --> 00:25:53,790
+congruent للواحد مدله ال prime مدله ال prime كويس
+
+344
+00:25:53,790 --> 00:25:58,390
+و أيامها الصينيين اتدعوا العلماء الصينيين اتدعوا
+
+345
+00:25:58,390 --> 00:26:03,530
+انه العكس صحيح ايش يعني العكس الصحيح انه لو تحقق
+
+346
+00:26:03,530 --> 00:26:07,810
+لأي رقم انه اتنين to the power الرقم ناقص واحد
+
+347
+00:26:07,810 --> 00:26:14,450
+congruent للواحد باستخدام المدله للرقم نفسه معناه
+
+348
+00:26:14,450 --> 00:26:20,030
+ذلك ان الرقم primeبالظبط لأ هي فعليا طلعت if then
+
+349
+00:26:20,030 --> 00:26:25,190
+مش if and only if فمع الزمن ادعائهم هذا ان ال
+
+350
+00:26:25,190 --> 00:26:30,670
+converse true طلع مش صحيح لكن طلعوا بحاجة كويسة
+
+351
+00:26:30,670 --> 00:26:36,670
+جدا انه اذا تحقق هذا الكلام فعليا فكل in هنا okay
+
+352
+00:26:36,670 --> 00:26:41,110
+هي مش prime لكن بقدر احكم على ان هي pseudo prime
+
+353
+00:26:41,110 --> 00:26:46,370
+شبيهة بالprimesإيش يعني شبيهة بـprimes؟ يعني هي
+
+354
+00:26:46,370 --> 00:26:53,170
+فعليًا عبارة عن ضرب two primes فبعض بس و بدون P to
+
+355
+00:26:53,170 --> 00:26:56,930
+the power كذا لأ هي two primes مرة واحدة هيكي ال
+
+356
+00:26:56,930 --> 00:27:00,210
+prime و ممكن يكونوا كبار ممكن يكونوا أرقام كبيرة
+
+357
+00:27:00,210 --> 00:27:07,770
+فعبارة عن P في Q بس و ال two primes ال two numbers
+
+358
+00:27:07,770 --> 00:27:12,890
+هدول عبارة عن primes ففي الحالة هذه if بقدر أقول
+
+359
+00:27:12,890 --> 00:27:13,330
+عنها
+
+360
+00:27:16,160 --> 00:27:21,660
+pseudoprime شبيهة بالـ prime شبيهة بالـ prime كويس
+
+361
+00:27:21,660 --> 00:27:25,700
+طيب الشبيهات بالـ prime هذه طلعت مش كل الأرقام
+
+362
+00:27:25,700 --> 00:27:30,200
+ممكن تحقق هذا الموضوع يعني شبيهات الـ primes برضه
+
+363
+00:27:30,200 --> 00:27:35,460
+محكمين محدودين كعدد محدودين كعدد لكن يمكن أيضا
+
+364
+00:27:35,460 --> 00:27:39,870
+استخدامها في ال encryptionيعني معنى ذلك أنه حصيلة
+
+365
+00:27:39,870 --> 00:27:43,670
+ال primes كمان اللي احنا بالنسبالنا ذخيرة كأرقام
+
+366
+00:27:43,670 --> 00:27:47,090
+استخدمها في عملية ال encryption عشان أضمن أنه ال
+
+367
+00:27:47,090 --> 00:27:50,190
+code تبعي يكون أطول مايمكن قبل ما يتم كسره و قبل
+
+368
+00:27:50,190 --> 00:27:54,030
+ما يتكرر، لأ هذا الكلام حتى بيتحقق مع ال pseudo
+
+369
+00:27:54,030 --> 00:27:54,350
+prime
+
+370
+00:28:01,970 --> 00:28:07,970
+مثال على هذا الكلام زي 341 هي عبارة عن 11 في 31
+
+371
+00:28:07,970 --> 00:28:13,370
+كلا هما primes هي بحد ذاتها مش prime لكن مدام حققت
+
+372
+00:28:13,370 --> 00:28:19,340
+المعادلة ان يتنين تظبر تلاتمية وأربعينهي فعلاً
+
+373
+00:28:19,340 --> 00:28:22,480
+طلعت congruent للواحد إذا استخدمتها ضمن ال modulus
+
+374
+00:28:22,480 --> 00:28:29,750
+341 طلعت صحيحة فبقدر أقول عنهاSodoprime نقدر نقول
+
+375
+00:28:29,750 --> 00:28:33,290
+عنها Sodoprime طبعا في قائمة من مجموعة ال
+
+376
+00:28:33,290 --> 00:28:35,690
+Sodoprimes في قائمة كويسة من مجموعة ال Sodoprimes
+
+377
+00:28:35,690 --> 00:28:37,990
+اللي العلماء أو اللي يخلونهم يقولوا اللي بيشتغل في
+
+378
+00:28:37,990 --> 00:28:42,310
+ال encryption ممكن يستغلها واللي بيشتغل في ال
+
+379
+00:28:42,310 --> 00:28:46,770
+hacking بيفكر فيها انه ممكن تكون هي الأرقام اللي
+
+380
+00:28:46,770 --> 00:28:51,310
+ممكن استخدامها تمام هذا الكلام مش ينطبق على جدل
+
+381
+00:28:51,310 --> 00:28:57,100
+اتنين بس ك primary ك binary لأ ممكن تكون لأيباس
+
+382
+00:28:57,100 --> 00:29:03,340
+لأي أساس إذا تحققت فبرضه بنقدر نسميها Sodoprime
+
+383
+00:29:03,340 --> 00:29:08,580
+Sodoprime تمام؟ كويس هذه هيك زودت لنا ذخيرة مين
+
+384
+00:29:08,580 --> 00:29:13,220
+الأرقام اللي ممكن استخدامها في ال encryption زودت
+
+385
+00:29:13,220 --> 00:29:16,340
+لنا إياها إن والله ممكن يكون في عندك options أكتر
+
+386
+00:29:16,340 --> 00:29:19,560
+بحيث إن ال hackers هنا بتلخبط أكتر لإنه بيصير عنده
+
+387
+00:29:19,560 --> 00:29:22,280
+ذخيرة أكبر أنت ممكن تستخدمها عبل ما يقعد يدور و
+
+388
+00:29:22,280 --> 00:29:27,030
+يخلص و ياخد وجه أطول معاهتمام نبدأ الآن في جزئية
+
+389
+00:29:27,030 --> 00:29:30,010
+ال encryption جزئية ال encryption هناخد طريقتين
+
+390
+00:29:30,010 --> 00:29:35,350
+طريقة linear و بسيطة و عملية ال decryption برضه مش
+
+391
+00:29:35,350 --> 00:29:39,450
+كتير عالية لكن بدنا نفهم منه كلها كعلم ال
+
+392
+00:29:39,450 --> 00:29:42,390
+cryptography هذا كان في حاجة سمى cryptography و
+
+393
+00:29:42,390 --> 00:29:46,270
+هذه كعلم هو الطرق اللي بنستخدمها to encrypt and
+
+394
+00:29:46,270 --> 00:29:51,610
+decrypt secret بحيث ان هي بعمل فيها تشفير للرسائل
+
+395
+00:29:51,610 --> 00:29:58,490
+و فك التشفيرهذه بيسموها Cryptography لكن في Crypto
+
+396
+00:29:58,490 --> 00:30:03,550
+Analysis اللي هي Crypto Analysis هذه لأ الطريقة
+
+397
+00:30:03,550 --> 00:30:08,190
+العكسية هذه الناس اللي بدهم يكسروا الأكواد فبتصير
+
+398
+00:30:08,190 --> 00:30:12,150
+العلم تبعهم هو Crypto Analysis اللي هو تحليل
+
+399
+00:30:12,150 --> 00:30:16,310
+الشفرة تحليل الشفرة فممكن استخدام هذا الطرق
+
+400
+00:30:16,310 --> 00:30:23,580
+بتستخدم for breaking او ال code breakingجيد ناخد
+
+401
+00:30:23,580 --> 00:30:26,560
+أول نوع من الأنواع والنوع البسيط وخلّيني أقولكوا
+
+402
+00:30:26,560 --> 00:30:28,740
+هذا أول نوع أصلا يخترعوه في الدنيا أو أول نوع
+
+403
+00:30:28,740 --> 00:30:34,660
+فكروه فيه في الدنيا هو scissors cypher بتاعة رسالة
+
+404
+00:30:34,660 --> 00:30:38,860
+القيصر أو شفرة القيصر بسيطة جدا وسلسة وماكنش فيها
+
+405
+00:30:38,860 --> 00:30:47,080
+كتير إشكاليات كل اللي عمله أنه عمل ترتيب لمجموعة
+
+406
+00:30:47,080 --> 00:30:47,680
+الحروف
+
+407
+00:30:53,820 --> 00:31:02,060
+فببدأ a b c d e و بكمل عند z بحطهم في جدول بهذا
+
+408
+00:31:02,060 --> 00:31:07,520
+الشكل و بعدين بقولك ببعت رسالة الرسالة هذه مشفة
+
+409
+00:31:07,520 --> 00:31:13,120
+تلت او اربع حروف تلت او اربع حروف زي انه يقول لأ
+
+410
+00:31:13,120 --> 00:31:14,960
+بدي الآن احط تحتها
+
+411
+00:31:18,640 --> 00:31:27,120
+A B C D and so on وهنا نفس الكلام يرجع اللي خلص
+
+412
+00:31:27,120 --> 00:31:33,600
+عنده هنا يرجع يبدأ من هنا بحيث انه تيجي زد هنا طيب
+
+413
+00:31:33,600 --> 00:31:41,760
+بده نفترض كلمة نفترض سل هنا يمكن مكتوبة سل بهذا
+
+414
+00:31:41,760 --> 00:31:48,260
+الشكل ببدأ ب C فبروح بدل ما يبعت C يبعت زدالـ E
+
+415
+00:31:48,260 --> 00:31:52,040
+بيبعتها B and so on بشوف ال L هنا ايش وافقت و
+
+416
+00:31:52,040 --> 00:31:57,580
+بكتبها بالشكل هذا و خلاص فانت لو انت قطعت الرسالة
+
+417
+00:31:57,580 --> 00:32:01,540
+في نص الطريق و اللي بعتها للقوات تبعونه في الحروب
+
+418
+00:32:01,540 --> 00:32:07,120
+تبعته القيصر بيجي بلاقي Z بي .. ايش يعني؟مافهمش
+
+419
+00:32:07,120 --> 00:32:10,620
+الرسالة لو وجعت مافهمش الرسالة بس في نفس الوقت
+
+420
+00:32:10,620 --> 00:32:14,900
+التكويدة نفسها ان انت اعمل shift بقيمة كذا القوات
+
+421
+00:32:14,900 --> 00:32:18,580
+تبعونه قبل ما يطلع الحروب كل واحد عارف هو جدش لازم
+
+422
+00:32:18,580 --> 00:32:21,620
+يتحرك انت والله كقائد من القوات بقولك انت shift
+
+423
+00:32:21,620 --> 00:32:25,580
+تبعك تلاتة انت shift تبعك خمسة انت shift تبعك سبعة
+
+424
+00:32:25,580 --> 00:32:29,320
+وخلاص و بتحركوا بتدبع طلبه السبعة خلاص بكون انا
+
+425
+00:32:29,320 --> 00:32:32,900
+مشفت عند الرسالة ب shift سبعة و بعطيله اياه هو
+
+426
+00:32:32,900 --> 00:32:38,270
+الوقت اللي مابدورجحها برجع سالب سبعةفهنا نفس الجصة
+
+427
+00:32:38,270 --> 00:32:44,010
+بيجي بيقدمها بنفس القيمة اللي أنا كنت شفتها لجدام
+
+428
+00:32:44,010 --> 00:32:48,530
+عنها بيجيبها لجدام فهذه بيقولك لأ بدل ما كانت واحد
+
+429
+00:32:48,530 --> 00:32:53,990
+اتنين تلاتة بدي ارجع واحد اتنين تلاتةبرجع ال code
+
+430
+00:32:53,990 --> 00:32:59,430
+اللي عنده و خلاص بس برجع بشوف الرسالة تاني طبعا
+
+431
+00:32:59,430 --> 00:33:03,890
+هذه very modest جدا very modest و مش منطقية في
+
+432
+00:33:03,890 --> 00:33:06,150
+الوقت الحالي يعني في وقتنا الحالي ولا يمكن تكون
+
+433
+00:33:06,150 --> 00:33:11,210
+منطقية حاولوا يزودوها اكتر بحيث انه يكون في
+
+434
+00:33:11,210 --> 00:33:15,260
+multiplier فيهايعني هي مش مجرد shift لأ يضربوها
+
+435
+00:33:15,260 --> 00:33:19,280
+كمان في قيمة تصير بدل ما هي مجرد shift بتلاتة لأ
+
+436
+00:33:19,280 --> 00:33:24,120
+سبعة في n plus تلاتة طبعا أكيد modulo ستة وعشرين
+
+437
+00:33:24,120 --> 00:33:27,020
+عدد الحروف لإن احنا هنا فعلا هنا استخدمنا modulo
+
+438
+00:33:27,020 --> 00:33:33,200
+ستة وعشرين هي بعد ال sub بعد ال z رجعنا بدأنا من
+
+439
+00:33:33,200 --> 00:33:38,320
+الصفررجعنا بدينا صفر من جديد فهنا بتبدأ صفر واحد
+
+440
+00:33:38,320 --> 00:33:41,980
+اتنين تلاتة اربعة على عندك الخمسة وعشرين فستة
+
+441
+00:33:41,980 --> 00:33:46,700
+وعشرين هي صفر ستة وعشرين هترجع للصفر تاني هترجع
+
+442
+00:33:46,700 --> 00:33:51,100
+للصفر تاني فازن تبدأ ال index تبعك من zero لخمسة
+
+443
+00:33:51,100 --> 00:33:55,980
+وعشرين بسيطة الطريقة و بتقدر تقول ان هي very
+
+444
+00:33:55,980 --> 00:34:02,300
+insecure very insecureرغم حتى انك انت هتستخدم
+
+445
+00:34:02,300 --> 00:34:06,320
+multiplier .. رغم ان انت هتستخدم multiplier تمام؟
+
+446
+00:34:06,320 --> 00:34:09,820
+طبعا ببساطة جدا هي مثلا message بهذا الشكل وانت
+
+447
+00:34:09,820 --> 00:34:14,660
+عارف ان هي .. ان عملت باستخدام ال .. ال n plus
+
+448
+00:34:14,660 --> 00:34:20,100
+تلاتة اقولك حتى لو مش عارف ببساطة جدا اللغة ..
+
+449
+00:34:20,100 --> 00:34:23,380
+okay احنا كاتبينها لان بس ال .. الفعليا هي 26 ال M
+
+450
+00:34:23,380 --> 00:34:28,430
+معروفةفعليا في حروف اسمها ال vowels .. ال vowels
+
+451
+00:34:28,430 --> 00:34:32,810
+letters اللي هي الحروف اللينة و اللي كلنا عارفين
+
+452
+00:34:32,810 --> 00:34:36,950
+أن هدي بتتكرر أكتر من غيرها صح؟ طيب عارفين أن ال E
+
+453
+00:34:36,950 --> 00:34:41,450
+أكتر حرف ممكن يتكرر فلما .. لما تيجي ل message زي
+
+454
+00:34:41,450 --> 00:34:46,090
+هدي و تطلع هو أنه أكتر حرف اتكرر بدك تفترض أنه
+
+455
+00:34:46,090 --> 00:34:50,950
+يمكن يكون ال E فبتحاول اتشفة ال message أنه يوافق
+
+456
+00:34:50,950 --> 00:34:51,310
+ال E
+
+457
+00:34:54,180 --> 00:34:59,280
+فكت التشفير، صحيح؟ لاحظت كيف؟ فانت عارف ان ال E
+
+458
+00:34:59,280 --> 00:35:03,340
+أكتر حرف بتتكرر، ال A بعده، ال I، ال vowels هذه
+
+459
+00:35:03,340 --> 00:35:07,720
+كلنا نعلم أن هي حروف اللينة، الحروف اللينة هذه هي
+
+460
+00:35:07,720 --> 00:35:11,850
+أكتر حروف بتتكرر في اللغةمنطق ولا مش منطق؟ عشانك
+
+461
+00:35:11,850 --> 00:35:16,050
+insecure عشانك بالطريقة هذه هو insecure فبتقدر
+
+462
+00:35:16,050 --> 00:35:21,430
+ببساطة تقول ال E طيب مين أكتر حرفنا اتكرر H ال H
+
+463
+00:35:21,430 --> 00:35:26,630
+هاي أربع مرات فبدك تفترض أن معناته ال E هذا حرف ال
+
+464
+00:35:26,630 --> 00:35:31,970
+E فبهت انشفت خلصت
+
+465
+00:35:31,970 --> 00:35:37,910
+اشتغل على التلاتة و طلع ال messageفانت secure مش
+
+466
+00:35:37,910 --> 00:35:41,210
+بالضروري انك انت تكون عارف ال code نفسه الطريقة
+
+467
+00:35:41,210 --> 00:35:46,050
+linear الطريقة حتى لو ضربت في multiplier هي linear
+
+468
+00:35:46,050 --> 00:35:50,170
+هي linear و ال linear أسهل ما يمكن أسهل ما يمكن
+
+469
+00:35:50,170 --> 00:35:53,590
+معادلة linear عبارة عن a مضروبة في x زائد c
+
+470
+00:35:53,590 --> 00:35:59,150
+increment مثلا خلصنا فهي مش كتير secure طيب نجلى
+
+471
+00:36:00,560 --> 00:36:03,520
+تكنيك أحسن و اللي عندي اللي أنا بيستخدم من ال
+
+472
+00:36:03,520 --> 00:36:06,780
+techniques اللي بتستخدم حتى اللحظة ك encryptor
+
+473
+00:36:06,780 --> 00:36:11,060
+مناسب اللي هي ال RSA مستخدمة في ال email حتى
+
+474
+00:36:11,060 --> 00:36:14,940
+اللحظة مستخدمة في ال email مستخدمة في البنوك في
+
+475
+00:36:14,940 --> 00:36:19,060
+اللي هي تشفير أو تكويدة الأرقام السرية مثلا تاعة
+
+476
+00:36:19,060 --> 00:36:22,080
+ال visa cardعندك visa card أه بس إلها رقم سري
+
+477
+00:36:22,080 --> 00:36:25,740
+فالرقم السري هذا يعتبر هو الشفرة تبعتك اللي من
+
+478
+00:36:25,740 --> 00:36:28,720
+خلالها بتنعمل مجموعة عمليات جوا بحيث أنه تعرف أن
+
+479
+00:36:28,720 --> 00:36:32,280
+الحساب هذا حسابك أو مش حسابك فهي حتى الآن أه ممكن
+
+480
+00:36:32,280 --> 00:36:37,520
+تستخدم بيعملوا عليها improvement بس ك technique
+
+481
+00:36:37,520 --> 00:36:42,020
+مستخدم حتى اللحظة في بعض التطبيقات ال RSA بيعتمد
+
+482
+00:36:42,020 --> 00:36:46,290
+علىشغلتين انه في عندى مجموعة parameters بدنا
+
+483
+00:36:46,290 --> 00:36:50,530
+نستخدمها برضه في بناء ال mask اللى تاوى اتكلمنا
+
+484
+00:36:50,530 --> 00:36:55,590
+عنه اننا بنستخدم مجموعة sequence من الأرقام تمام
+
+485
+00:36:55,590 --> 00:37:01,670
+أشفر فيها ال message تصبح message تانية مختلفة
+
+486
+00:37:01,670 --> 00:37:06,830
+تماما message انت مش هتفهم منها حاجة طيب في عندى
+
+487
+00:37:06,830 --> 00:37:09,750
+مجموعة parameters مجموعة ال parameters هتنقسمها لأ
+
+488
+00:37:09,750 --> 00:37:14,180
+private keyprivate key هذه المفروض ان ماحدش يعرفها
+
+489
+00:37:14,180 --> 00:37:17,520
+الا
+
+490
+00:37:17,520 --> 00:37:21,340
+اللي عمل ال code بس اذا ال bank معناته ال bank بس
+
+491
+00:37:21,340 --> 00:37:24,920
+فقط ال bank و في ال public key ال public key لأ
+
+492
+00:37:24,920 --> 00:37:28,960
+هذه انت اصلا محتاجها انت ممكن ماتاخدهاش في ايدك بس
+
+493
+00:37:28,960 --> 00:37:31,540
+ممكن تاخدها من خلال الرقم اللي هيعطيهلك و انت
+
+494
+00:37:31,540 --> 00:37:36,630
+عارفهبس الرقم هذا بيحتوي على القيم هذه فهو public
+
+495
+00:37:36,630 --> 00:37:41,390
+في الآخر هو معطو عندك انت ماخده و غيرك ممكن يشوفه
+
+496
+00:37:41,390 --> 00:37:44,890
+منك كمان يعني لو واحد مسك ال visa card تبعتك و
+
+497
+00:37:44,890 --> 00:37:49,490
+بتطلع هيلاجي رقم ماشي فليكن هيأخذ الرقم في ال
+
+498
+00:37:49,490 --> 00:37:52,990
+email انت بتكون كاتب حتى ال email ماتش تفكر فيه
+
+499
+00:37:52,990 --> 00:37:58,170
+انت بتعملتشفير لل email فعليا بتبعت ال message
+
+500
+00:37:58,170 --> 00:38:00,870
+تبعتك ال message تبعتك قبل ما تطلع على خط ال net
+
+501
+00:38:00,870 --> 00:38:07,230
+بتتشفر بتتشفر بال .. باستخدام ال RSA كويس اتشفرت و
+
+502
+00:38:07,230 --> 00:38:12,890
+راحت ل ال email الشخص اللي مكتوب في ال email فهو
+
+503
+00:38:12,890 --> 00:38:16,770
+الوحيد اللي بيقدر يقرأها هو الوحيد اللي بيقدر
+
+504
+00:38:16,770 --> 00:38:19,950
+يقرأها لإنك أصلا مخصوص بعتله إياها فهو هذا اللي
+
+505
+00:38:19,950 --> 00:38:24,250
+بيصله ال public keyعلى ايميله فاطوماتك بتفتح عنده
+
+506
+00:38:24,250 --> 00:38:27,130
+فقط لما مش هتفتح لو واحد تاني مش هتفتح لو واحد
+
+507
+00:38:27,130 --> 00:38:31,670
+تاني مجرد هو ماشي .. ماشي الخط نفترض عمل قرصانة و
+
+508
+00:38:31,670 --> 00:38:35,230
+أخد مجموعة بيانات مش هيفه منها حاجة مش هيفه منها
+
+509
+00:38:35,230 --> 00:38:38,190
+ايش هتنشوف ايش بالظبط ال private key ال private
+
+510
+00:38:38,190 --> 00:38:46,530
+key هي عبارة عن P و Q و Random Prime Numbers فهي
+
+511
+00:38:46,530 --> 00:38:51,030
+دخلنا في انه بدى يا Prime و Randomعشان هيك كنا توب
+
+512
+00:38:51,030 --> 00:38:53,830
+نتعلم إيش يعني prime و إيش يعني co-prime و إيش
+
+513
+00:38:53,830 --> 00:38:58,050
+يعني random، كويس فبدنا الرقمين اللي هي ال P و ال
+
+514
+00:38:58,050 --> 00:39:05,850
+Q يكونوا عبارة عن ال prime و number، فهي ال P و ال
+
+515
+00:39:05,850 --> 00:39:14,470
+Q و محتاج ال E، حاجة اسمها ال exponent E أو دليل،
+
+516
+00:39:14,470 --> 00:39:18,250
+حاجة بيسموها الدليل، exponent اللي هي ال Eهدولة
+
+517
+00:39:18,250 --> 00:39:22,750
+private هدولة ماحدش بعرفهم هدول المفروض الأصل أنه
+
+518
+00:39:22,750 --> 00:39:28,610
+ماحدش يكون بعرفهم ك private تمام في المقابل في
+
+519
+00:39:28,610 --> 00:39:32,010
+عندك ال public ال public إيش بيعطيك بيعطيه قيمة in
+
+520
+00:39:32,010 --> 00:39:41,170
+قيمة in هد عبارة عن P مضروبة في Q فهد اللي بتكون
+
+521
+00:39:41,170 --> 00:39:44,890
+معطام على ال message عشان تساهم أو تساعد في فك ال
+
+522
+00:39:44,890 --> 00:39:49,330
+message عشان تساعد في فك ال messageليش؟ بعد هيك
+
+523
+00:39:49,330 --> 00:39:57,930
+محتاج قيمة D بس D هذه عشان تنحسب كأنها ال inverse
+
+524
+00:39:57,930 --> 00:40:09,990
+لل E بس مدله P ناقص واحد في Q ناقص واحد وليست E
+
+525
+00:40:09,990 --> 00:40:15,830
+نفسها يعني لا تعطي E نفسها بنعطيش ال E نفسها احنا
+
+526
+00:40:15,830 --> 00:40:21,690
+بنعطيD واللي هي ال inverse بتاعة E فإذا public أنت
+
+527
+00:40:21,690 --> 00:40:25,970
+بتعرف ال D لكن ال E أنت مش عارفها أنا فقط اللي
+
+528
+00:40:25,970 --> 00:40:29,010
+عارفها أنا اللي عملت ال code أنا فقط اللي بعرفها
+
+529
+00:40:29,010 --> 00:40:34,290
+أنت أعطتك ال D بس عشان تفك ال call ال message اللي
+
+530
+00:40:34,290 --> 00:40:36,970
+أعطتك إياها بس أنت ماعرفتش ال system تبعي أنت
+
+531
+00:40:36,970 --> 00:40:40,310
+ماعرفتش قالية التشفير نفسها اللي أنا مستخدمها
+
+532
+00:40:40,310 --> 00:40:48,010
+واضحت فإذاE تبعتى وانا من عندى اعملتلك generation
+
+533
+00:40:48,010 --> 00:40:52,570
+ل D وانت تتاكد D بس على اعتبار ان ال D هدى هى ال
+
+534
+00:40:52,570 --> 00:40:58,570
+inverse لل E اللى عندى بس بمين ب modulus او modulo
+
+535
+00:40:58,570 --> 00:41:03,750
+P ناقص واحد في Q ناقص واحد وليه set P في Q اللى
+
+536
+00:41:03,750 --> 00:41:11,140
+انت اصلا given عندكفإذا إنك تفك الشفرة بتفكها بال
+
+537
+00:41:11,140 --> 00:41:18,280
+modulus N كويس اللي هي P في Q لكن لما أنا بعطيك D
+
+538
+00:41:18,280 --> 00:41:21,780
+اللي هي ال inverse بتاعة E بعطيك إياها على modulus
+
+539
+00:41:21,780 --> 00:41:27,940
+تاني أنت مش عارفه قيمة ال modulus التاني أنت مش
+
+540
+00:41:27,940 --> 00:41:33,050
+عارفه اللي هي P ناقص واحد في Q ناقص واحدبدك تفكه
+
+541
+00:41:33,050 --> 00:41:37,530
+اوكي اقعد تدور في كل ال primes و ضرب في بعض و شوف
+
+542
+00:41:37,530 --> 00:41:42,930
+ايه و انت و نصيبك امتى تطلع معاك تمام هلوك تلاتة
+
+543
+00:41:42,930 --> 00:41:45,150
+كلام بدنا نطبقه بس بدنا نعرف مجموعة ال parameters
+
+544
+00:41:45,150 --> 00:41:48,390
+هذه كيف هستخدمها اول شغل عشان نستخدمها بدنا نحسب
+
+545
+00:41:48,390 --> 00:41:53,210
+ال ال ال coded message ال coded message اللي هي
+
+546
+00:41:53,210 --> 00:41:57,650
+هتتشفر بتساوي ال message نفسها ال message نفسها ال
+
+547
+00:41:57,650 --> 00:42:02,690
+characters نفسها اللي انت كاتبها to the power Eهي
+
+548
+00:42:02,690 --> 00:42:07,910
+ال exponent to the power E modulo N فمعنى ذلك أنه
+
+549
+00:42:07,910 --> 00:42:12,830
+هيطلع ال C هذي هتبعتها طيب إيش هتبعت معها؟ هتبعت
+
+550
+00:42:12,830 --> 00:42:15,610
+معها N وD
+
+551
+00:42:17,730 --> 00:42:21,510
+كيف انعملت دي مالكاش علاقة هي دي عشان تفك الشفرة
+
+552
+00:42:21,510 --> 00:42:25,290
+تبعتي بس فانت كاتب انا ال email تبعك فمعنى ذلك ان
+
+553
+00:42:25,290 --> 00:42:28,170
+هد بتتحمل معي ال email تبعك بحيث ان هي ل email بس
+
+554
+00:42:28,170 --> 00:42:31,450
+تنعرف قيمة دي ف email اك اوتوماتيك بيفك الشفرة
+
+555
+00:42:31,450 --> 00:42:35,470
+تبعتي الرسالة اللي وصلتك تنفكه مش الحال بحيث انك
+
+556
+00:42:35,470 --> 00:42:40,880
+ترجع ل ال message اللي بتساويالـ Coded Message to
+
+557
+00:42:40,880 --> 00:42:44,120
+the power D على نفس الموضوع الاصلي طيب .. بتنا ..
+
+558
+00:42:44,120 --> 00:42:47,220
+رقم .. بتنا .. زي ما بقوله مثال رقمي يعني الكلام
+
+559
+00:42:47,220 --> 00:42:52,500
+هيك شوية بيظل ناشف هتنشوف مثلا Message
+
+560
+00:42:54,360 --> 00:42:58,820
+عبارة عن كلمة ايش بدنا نبعت وين راح ت stop كلمة
+
+561
+00:42:58,820 --> 00:43:04,240
+stop مثلا كلمة stop لحالها فقط كلمة stop هنا كيف
+
+562
+00:43:04,240 --> 00:43:09,240
+نعملها و بدنا نشفرها القانون واضح ال coded بتساوي
+
+563
+00:43:09,240 --> 00:43:12,720
+ال message to the power e ال exponent في ال
+
+564
+00:43:12,720 --> 00:43:21,220
+modulus او modulo n اول شغل هنستخدم ال P 43 ال Q
+
+565
+00:43:21,220 --> 00:43:22,080
+59
+
+566
+00:43:24,270 --> 00:43:28,750
+هدولة مهمين جدا عشان نحسب منهم قيمة N مضروبهم في
+
+567
+00:43:28,750 --> 00:43:34,210
+بعض فهيطلع عندى ال modulus اللى بنستخدمه okay ال E
+
+568
+00:43:34,210 --> 00:43:38,390
+13 طب انا ملاحظ شغلة ال E و ال P و ال Q كلهم
+
+569
+00:43:38,390 --> 00:43:44,970
+Primes صحيح؟ لأ و احنا مستخدمين Primes متواضعة
+
+570
+00:43:44,970 --> 00:43:49,190
+كمان هنا لمجرد بس الأرقام بتمشي معنا يعني نفهمها
+
+571
+00:43:49,190 --> 00:43:53,290
+بالعادة لأ بتستخدم أرقام كتير أكبر من هيكيعني ال E
+
+572
+00:43:53,290 --> 00:43:57,350
+ده ممكن تكون بتسعميات، سبعميات، خمسميات، Primes،
+
+573
+00:43:57,350 --> 00:44:02,950
+Primes كمان تمام أول شغلة بدنا نضمنها مدام أنا بدي
+
+574
+00:44:02,950 --> 00:44:08,820
+أشتغل على ال E و لاحظ ال E هادي أنا هعطيكال
+
+575
+00:44:08,820 --> 00:44:13,160
+inverse تبعها أما مش هتعطيك ال E صح؟ ممتاز فإذا
+
+576
+00:44:13,160 --> 00:44:16,260
+أول شغلة بدي أضمنها أني أطلع لقيمة ال inverse توا
+
+577
+00:44:16,260 --> 00:44:19,960
+أخدناها لسه عشان ايه توا أخدنا كيف بجيب ال inverse
+
+578
+00:44:19,960 --> 00:44:22,660
+عشان ما تقوليش كيف بده أجيبها هيا توا جبناها
+
+579
+00:44:22,660 --> 00:44:25,200
+فبتيجي بتشوف بس ال greatest common denominator بين
+
+580
+00:44:25,200 --> 00:44:28,480
+ال E اللي بدك تجيبلها ال inverse ومين مش ال
+
+581
+00:44:28,480 --> 00:44:34,850
+modulusموديلس جديد الموديلس الجديد هذا مش P في N
+
+582
+00:44:34,850 --> 00:44:42,010
+بي في Q هي P ناقص واحد في Q ناقص واحد عاكب
+
+583
+00:44:42,010 --> 00:44:44,730
+احنا بدنا نسيب ال hacker يشتغل براحته مش لازم
+
+584
+00:44:44,730 --> 00:44:49,770
+نعجبله الدنيا فبدك تشفر لأ عفوا الكلام هذا مش انت
+
+585
+00:44:49,770 --> 00:44:52,370
+الموجه ايه بس انت انت الآن صاحب العلم اللي بدك
+
+586
+00:44:52,370 --> 00:44:57,030
+تكمل عليه طوره لنا ياه بكرا انت الآن المهندس
+
+587
+00:44:57,030 --> 00:44:59,050
+المستقبل انت اللي بدك تعمل تشفيره بكرا انت اللي
+
+588
+00:44:59,050 --> 00:45:02,880
+بدك تشتغلانت اللي بدك تعمل او انك تصير hacker انت
+
+589
+00:45:02,880 --> 00:45:07,260
+حر يعني تمام ففعليا بطلع ال greatest common
+
+590
+00:45:07,260 --> 00:45:10,440
+diverse equal to one عشان تجيب منها ال inverse
+
+591
+00:45:10,440 --> 00:45:14,020
+لاحقا تجيب منها ال inverse طيب هتنشوف نفسه كيف
+
+592
+00:45:14,020 --> 00:45:19,420
+يدوسير الكلام في اختلفه في الموضوع هذا ان كيف اعمل
+
+593
+00:45:19,420 --> 00:45:26,380
+عملية ال representationلأ الحروف هذه عمليت تمثيلها
+
+594
+00:45:26,380 --> 00:45:30,620
+في ناس مثلوها زي ما عمل سيزر وهذا اللي هنشتغل عليه
+
+595
+00:45:30,620 --> 00:45:34,400
+عشان أبسط عشان انت ممكن تفهمه أسرع اني أقول ال S
+
+596
+00:45:34,400 --> 00:45:38,720
+هذه جدش ترتيبها في الحروف رقم 18 ال T وراها على
+
+597
+00:45:38,720 --> 00:45:45,140
+طول 19 لاحظ؟ طيب ال O بتيجي 14 طب ال O بيه وراها
+
+598
+00:45:45,140 --> 00:45:48,560
+على طول مباشرة تيجي 15 فممكن أحطها بال location
+
+599
+00:45:48,560 --> 00:45:52,580
+تبعها في ترتيب الحروففي طرق تانية بتقولك لأ بجيب
+
+600
+00:45:52,580 --> 00:45:58,240
+قيمتها بال ask code و ساعتها بفرج معانا ال small
+
+601
+00:45:58,240 --> 00:46:03,410
+عن ال capital مش هيكالـ ASCII code بيفرج من ال
+
+602
+00:46:03,410 --> 00:46:06,530
+small و ال capital هنا لح نفرجناش هنا بس مجرد انك
+
+603
+00:46:06,530 --> 00:46:09,690
+بتعطيك ال concept انك تفهم بس طريقة كيف ماشية خلاص
+
+604
+00:46:09,690 --> 00:46:12,850
+أخدناها ترتيبها ضمن الحروف فطلع عندي ان ال code
+
+605
+00:46:12,850 --> 00:46:16,390
+اللي بدنا نبعته بهذا الشكل شفرلنايا عشان نقرف
+
+606
+00:46:16,390 --> 00:46:19,650
+نبعته طيب بنجسمه ل groups مين اللي بحكمني في ال
+
+607
+00:46:19,650 --> 00:46:23,710
+groups عادة ان ال term اللي بدي ابعته هذا لازم
+
+608
+00:46:23,710 --> 00:46:28,530
+يكون ضمن ال modulusفالمدرس اللي أنا بستخد مجدش
+
+609
+00:46:28,530 --> 00:46:35,450
+2400 يعني أربع خنات بكفي فكل أربع خنات يعني كل
+
+610
+00:46:35,450 --> 00:46:40,890
+حرفين بقاش بسويلهم بعملهم encryption مع بعض كل
+
+611
+00:46:40,890 --> 00:46:43,690
+حرفين بعملهم encryption مع بعض و توه بالمرة توه ال
+
+612
+00:46:43,690 --> 00:46:47,670
+.. ال hacker أكتر اه بلاش تعملهم حرف حرف اعملهم
+
+613
+00:46:47,670 --> 00:46:51,370
+حرفين اذا والله فيهم .. اعمل تلتة و خربته مش غلط
+
+614
+00:46:51,370 --> 00:46:58,340
+هنا حرفينفبتصير كأنها .. كأنها .. ها 1819 كأنها
+
+615
+00:46:58,340 --> 00:47:02,420
+1819 على طول ال 1819 بتحطها كأنها M to the power
+
+616
+00:47:02,420 --> 00:47:07,920
+13 فأضرب 1819 to the power 13 هيطلع طبعا رقم ضخم
+
+617
+00:47:07,920 --> 00:47:13,400
+جدا لكن modulus 2537
+
+618
+00:47:13,400 --> 00:47:20,190
+أكيد هيطلع أقل من ال 2537 فبطلع لكوين راح؟ بطلع
+
+619
+00:47:20,190 --> 00:47:23,650
+عشرين واحد تمانين طبعا حتى لو بدكتيش ترتبها مافيش
+
+620
+00:47:23,650 --> 00:47:28,670
+في الترتيب الرقم واحد تمانين في الحروف فهنا واضح
+
+621
+00:47:28,670 --> 00:47:31,670
+ان ال message اختلفت تماما نفس الكلام بتعيده لمن؟
+
+622
+00:47:31,670 --> 00:47:33,910
+للألف واربعمية وخمستاش ألف واربعمية وخمستاش
+
+623
+00:47:33,910 --> 00:47:37,210
+هتطلعلك ألفين ومية واتنين وتمانين هذا اللي هتبعته
+
+624
+00:47:37,210 --> 00:47:42,150
+فانت هتبعت الرقم بهذا الشكل انت هتبعت بهذا الرقم
+
+625
+00:47:42,150 --> 00:47:46,780
+بهذا الشكل هتفهم منه أي شيءمش هتفهم منه حاجة
+
+626
+00:47:46,780 --> 00:47:51,300
+إطلاقا مش حد يقدر تفهم منه إشي طلع كأرقام حتى طيب
+
+627
+00:47:51,300 --> 00:47:55,640
+الأرقام هذه كيف نرجع نفكها كيف نرجع نفكها عشان
+
+628
+00:47:55,640 --> 00:48:00,800
+ترجع تفكها هناخد أرقام تانية و هسيبلك طبعا فكرة
+
+629
+00:48:00,800 --> 00:48:04,340
+أنك أنت إذا هو نفس الأرقام ترجع تفكها لحالك بس
+
+630
+00:48:04,340 --> 00:48:08,820
+الآن هفترض أنه يجيك رقم بهذا الشكل القالية هي هي و
+
+631
+00:48:08,820 --> 00:48:12,640
+بدي أستخدم نفس ال P و نفس ال Q و نفس ال E ال E نفس
+
+632
+00:48:12,640 --> 00:48:18,360
+ال E نفس ال Eهيهم هما هما بتستخدمهم ف
+
+633
+00:48:18,360 --> 00:48:23,060
+automatically بدك تجيب ال inverse لمين لتلتاش مدله
+
+634
+00:48:23,060 --> 00:48:28,860
+P ناقص واحد في Q ناقص واحد واللي هي أكيد مش هتساوي
+
+635
+00:48:28,860 --> 00:48:34,780
+نفس قيمة ال N وإنما هتساوي اتنين واربعين في تمانية
+
+636
+00:48:34,780 --> 00:48:37,240
+وخمسين فالفين واربعمين مش الفين وخمسمية سبعة
+
+637
+00:48:37,240 --> 00:48:40,160
+وتلاتين زي طوي لأ الفين واربعمين ستة وتلاتين
+
+638
+00:48:40,160 --> 00:48:45,620
+فاختلفت تماما بتجيب ال inverseللـ 13 ضمن المدرس
+
+639
+00:48:45,620 --> 00:48:51,480
+هذا بيطلع 937 937 هي اللي هتستخدمها لل power
+
+640
+00:48:54,700 --> 00:48:59,320
+فبدك كمبيوتر يشتغلك عشان هيك فعلا الطرق هذه كانت
+
+641
+00:48:59,320 --> 00:49:03,720
+كلها انشرت بعد الكمبيوتر يعني الطريقة هذه ال RSA
+
+642
+00:49:03,720 --> 00:49:07,920
+هذه كفكرة ك concept بدأت في السابعة وسبعين طبعا
+
+643
+00:49:07,920 --> 00:49:11,420
+ازدادت واتطبقت لما صار الكمبيوتر منتشر وواضح
+
+644
+00:49:11,420 --> 00:49:15,040
+وموجود فعلا فعلا موجود انه يحسب كل الجثث هذه وكل
+
+645
+00:49:15,040 --> 00:49:20,420
+قيمها دي فالان ال message اللي هي كانت صفر تسعة
+
+646
+00:49:20,420 --> 00:49:25,130
+تمانية واحد صفر أربع ستة واحدC to the power الرقم
+
+647
+00:49:25,130 --> 00:49:29,750
+الكبير هذا Modulus لألفين و خمسمية لاحظ حتى هنا
+
+648
+00:49:29,750 --> 00:49:34,230
+رغم أن أنا هذا جبته Modulus مختلف بس ال Modulus
+
+649
+00:49:34,230 --> 00:49:39,650
+هنا لأ رجعنا لل in رجعنا ل مين لل in رجعناها عشان
+
+650
+00:49:39,650 --> 00:49:44,510
+نرجع ل صفر سبعة صفر أربعة ال message التاني صلت 11
+
+651
+00:49:44,510 --> 00:49:47,930
+15 فهذا بيعطيني ال sequence بهذا الشكل تعال جيب
+
+652
+00:49:47,930 --> 00:49:49,290
+ترتيب هون بطلع كلمة help
+
+653
+00:49:55,940 --> 00:50:00,740
+كمان؟ بس عشان help عشان لما تبعت لازميلك حاجة
+
+654
+00:50:00,740 --> 00:50:03,800
+ماحدش يخترقها و ماحدش يعرفش اللي بتبعته لما تبعت
+
+655
+00:50:03,800 --> 00:50:09,360
+message ماحدش يعرفش اللي بتبعته بيبعتلك أرقام أحسن
+
+656
+00:50:09,360 --> 00:50:13,520
+بيبعت أرقام الأرقام هذه الآن هل هي ترتيب الحرف
+
+657
+00:50:13,520 --> 00:50:16,580
+داخل ال sequence تبع الحروف أو هو ال ASCII code
+
+658
+00:50:16,580 --> 00:50:17,000
+تبعه
+
+659
+00:50:19,760 --> 00:50:22,860
+خلّي هو يدور ال hacker بس انت بتكون عارف انت بتكون
+
+660
+00:50:22,860 --> 00:50:25,600
+عارف اش اللي باعته تمام يعطي كل عافية احنا بيكون
+
+661
+00:50:25,600 --> 00:50:26,280
+خلاصنا
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Wt6C7l1t9pk_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Wt6C7l1t9pk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e9892b8da9adfb9dcfd5c2c9535af235ca7b26ef
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Wt6C7l1t9pk_postprocess.srt
@@ -0,0 +1,2600 @@
+1
+00:00:05,080 --> 00:00:10,040
+طيب، يعطيكوا العفو يا شباب، نكمل اليوم في موضوع ال
+
+2
+00:00:10,040 --> 00:00:13,280
+recurrence relation، المرة الماضية كنا اتكلمنا عن
+
+3
+00:00:13,280 --> 00:00:18,400
+ال recurrence relation و شفنا مجموعة أمثلة اللي
+
+4
+00:00:18,400 --> 00:00:22,990
+احنا بنقدر نقول بتاخد شكل ال relation بتاعتهابين
+
+5
+00:00:22,990 --> 00:00:27,770
+كل قيمة و القيمة السابقة لها بتاخد شكل recurrence
+
+6
+00:00:27,770 --> 00:00:31,470
+relation بمعنى ان كل قيمة هي معتمدة بشكل او باخر
+
+7
+00:00:31,470 --> 00:00:37,270
+ضمن معادلة معينة على القيمة السابقة لها و أخدنا
+
+8
+00:00:37,270 --> 00:00:41,590
+مجموعة أنفلة منها كانت تربيات الأرانب زي ما
+
+9
+00:00:41,590 --> 00:00:46,030
+بتذكرين و إيش علاقتها بين كل شهر و الشهر اللي ورا
+
+10
+00:00:46,030 --> 00:00:48,970
+جدش ممكن يكون العدد او ال couples تبع ال rabbits
+
+11
+00:00:48,970 --> 00:00:54,710
+دولةكويس و بعدين اتكلمنا عن الفائدة
+
+12
+00:00:54,710 --> 00:00:59,530
+المركبة صحيح و وجدنا ان هي فعليا فعلا فائدة على
+
+13
+00:00:59,530 --> 00:01:01,970
+الشهر اللي جابلها طب الشهر اللي جابلها جدش كانت
+
+14
+00:01:01,970 --> 00:01:05,850
+قيمته؟ قيمته اللي جابله مع الفائدة تبعته و اللي
+
+15
+00:01:05,850 --> 00:01:12,390
+جابله و هكذا فبشكل تراكمي هي معادلة او علاقة
+
+16
+00:01:12,390 --> 00:01:19,210
+تكرارية ف recurrence relationاتكلمنا عن ال Hanoi
+
+17
+00:01:19,210 --> 00:01:22,930
+أو ال tower of Hanoi إذا متذكرين و برضه وجدنا إنه
+
+18
+00:01:22,930 --> 00:01:26,990
+عشان نحله بنقدر نعمله بشكل recurrence relation
+
+19
+00:01:26,990 --> 00:01:32,290
+تمام فكانت الفكرة كلها إنه أي recurrence relation
+
+20
+00:01:32,290 --> 00:01:40,520
+هي معتمدة على الحالة السابقة لها سواءعلى الحالة
+
+21
+00:01:40,520 --> 00:01:44,660
+السابقة فقط او اتنين تلاتة من الحالات السابقة حسب
+
+22
+00:01:44,660 --> 00:01:47,880
+فاتنين تلاتة معناه انك تقول ان ناقص واحد ان ناقص
+
+23
+00:01:47,880 --> 00:01:53,500
+اتنين ان ناقص تلاتة جدش عددهم هسميهم in general K
+
+24
+00:01:53,500 --> 00:02:00,850
+فهي معتمدة على K previous terms خليني نسميهافمعتمد
+
+25
+00:02:00,850 --> 00:02:06,350
+على مجموعة قيم سابقة عددهم K مثلا تمام، ضالت الآن
+
+26
+00:02:06,350 --> 00:02:11,450
+الفكرة أنه عشان أعرف قداش قيمة الان هذه في زمن
+
+27
+00:02:11,450 --> 00:02:17,850
+معين أو في N عند ال N مش مضطر أجيب أجيب N ناقص
+
+28
+00:02:17,850 --> 00:02:20,390
+واحد و N ناقص اتنين و N ناقص تلاتة و خصوصا إذا
+
+29
+00:02:20,390 --> 00:02:25,630
+كانت قيمة N أساساهي قيمة كبيرة فمعنى ذلك انه هيكون
+
+30
+00:02:25,630 --> 00:02:30,130
+مضي على الوقت اني اقعد اشتغل كل term باللي قبله
+
+31
+00:02:30,130 --> 00:02:34,770
+لعند ما نصل لمين لل term A naught اللي هو ال
+
+32
+00:02:34,770 --> 00:02:38,470
+initial value تبعتنا هتكون كتير صعبة الجثة بهذا
+
+33
+00:02:38,470 --> 00:02:42,070
+الشكل فكان ضروري جدا ان نروح ل closed form ل
+
+34
+00:02:42,070 --> 00:02:48,080
+relation هي علاقة بال locationو ليست بال term اللي
+
+35
+00:02:48,080 --> 00:02:51,040
+قبله .. و ليست بال term اللي قبله فمعنى ذلك ان ال
+
+36
+00:02:51,040 --> 00:02:54,620
+an هذه لازم تكون هي function في حاجة اللي هي علاقة
+
+37
+00:02:54,620 --> 00:02:59,920
+بال n نفسها ب n مباشرة مش ب n ناقص واحد ليس ب n
+
+38
+00:02:59,920 --> 00:03:05,340
+ناقص واحد جدش هيكون شكلها كيف شكلهامش عارفين مش
+
+39
+00:03:05,340 --> 00:03:09,340
+عارفين لكن هذا هو ال closed form اللي بندور عليه
+
+40
+00:03:09,340 --> 00:03:11,600
+هذا ال closed form اللي بندور عليه ممكن تكون في
+
+41
+00:03:11,600 --> 00:03:15,880
+النهاية متغير او constant اذا بدناها تكون constant
+
+42
+00:03:15,880 --> 00:03:21,400
+to the power قيمة n هذه مثلا فبضل ان انا اعرف جداش
+
+43
+00:03:21,400 --> 00:03:25,120
+ال term هذا بالضبط على اساس انه اجيب form بهذا
+
+44
+00:03:25,120 --> 00:03:29,340
+الشكل قيمة a n اجيبها مباشرة مش محتاج اجيبها من ان
+
+45
+00:03:29,340 --> 00:03:33,060
+ناقص واحد لكن السؤال كيف بده اجيب هذا ال form اصلا
+
+46
+00:03:34,140 --> 00:03:37,700
+الفكرة ان و الله اه هذا ما انتمنى نفعلها نجيبها
+
+47
+00:03:37,700 --> 00:03:43,480
+بهذا الشكل فهي closed form ل a n مباشرة أحسبها و
+
+48
+00:03:43,480 --> 00:03:49,460
+خلصنا لكن كيف نجيب هذا الكلام من علاقة أساسا جياني
+
+49
+00:03:49,460 --> 00:03:54,200
+بال terms السابقة فهذا اللي هنتكلم عنه ابتداء
+
+50
+00:03:54,200 --> 00:03:59,060
+اليوم فاللي هو solving the recurrences و بنستخدم
+
+51
+00:03:59,060 --> 00:04:04,350
+ال linear homogeneous recurrence of degree kK اللي
+
+52
+00:04:04,350 --> 00:04:08,470
+هو كام term سابق انا محتاج عشان احسب ال term
+
+53
+00:04:08,470 --> 00:04:13,010
+اللاحق كام term سابق فبنسميها degree K فهنا عددهم
+
+54
+00:04:13,010 --> 00:04:16,690
+مثلا K فبنسميها degree تبعت الاش تاعة ال
+
+55
+00:04:16,690 --> 00:04:20,250
+recurrence relation with constant coefficient
+
+56
+00:04:20,250 --> 00:04:23,830
+فهنقول انه بدي افترض ان constant ارها دي constant
+
+57
+00:04:25,170 --> 00:04:28,370
+constant خلاص coefficient و بدنا نشوف إيش ال
+
+58
+00:04:28,370 --> 00:04:31,950
+constant المناسب بحيث إنه فعلا a n هدا يكون
+
+59
+00:04:31,950 --> 00:04:35,570
+function في n نفسها في ال location مش في ال terms
+
+60
+00:04:35,570 --> 00:04:39,090
+اللي قبلها مش في ال terms اللي قبلها فإجت الإسم
+
+61
+00:04:39,090 --> 00:04:42,690
+تبعت الطريقة بتاعتنا linear لإن أنا بتعامل معه
+
+62
+00:04:42,690 --> 00:04:43,410
+linear
+
+63
+00:04:46,250 --> 00:04:50,450
+ان بتساوي الناقص واحد الناقص اتنين مش الناقص واحد
+
+64
+00:04:50,450 --> 00:04:54,910
+تربيه الناقص اتنين التكعيب لأ هي linear هي سبب
+
+65
+00:04:54,910 --> 00:05:00,270
+التسميع homogeneous بمعنى انه ان معتمد على ال K
+
+66
+00:05:00,270 --> 00:05:05,970
+اللي جرب منها مش والله افترض ان هنا an ناقص واحد
+
+67
+00:05:05,970 --> 00:05:13,040
+ناقص en ناقص سبعة زائد en ناقص اربعتاشفلأ هي
+
+68
+00:05:13,040 --> 00:05:17,300
+homogeneous هي متجانسة هي متجانسة عشان نقدر نحلها
+
+69
+00:05:17,300 --> 00:05:21,980
+تمام with constant coefficients زي ما قلنا فيندي
+
+70
+00:05:21,980 --> 00:05:26,160
+constant coefficients هنا هذه إلها ثابت ال
+
+71
+00:05:26,160 --> 00:05:29,160
+constants بتاعتها كلها ثابتة وكل ال constants هذه
+
+72
+00:05:29,160 --> 00:05:35,600
+لا تساوي صفر لإن لو واحدة منهم صارت صفرhome genius
+
+73
+00:05:35,600 --> 00:05:39,500
+بطلت home genius بطلت home genius أو متجانسة
+
+74
+00:05:39,500 --> 00:05:42,580
+فمعناه ذلك أن ال term تبعنا به هذا الشكل in
+
+75
+00:05:42,580 --> 00:05:48,480
+general الآن صحيح هي ال a n هي constant في a n نقص
+
+76
+00:05:48,480 --> 00:05:52,600
+واحد constant في a n نقص اتنين لعند c k ال
+
+77
+00:05:52,600 --> 00:05:57,130
+constant رقم k على اعتبار أنه صار عندي k termفي a
+
+78
+00:05:57,130 --> 00:06:03,270
+n ناقص k فهي k بتاعة ال degree بتاعتنا لعندي الان
+
+79
+00:06:03,270 --> 00:06:08,110
+هذا الشكل اللي بدنا نشتغل عليه الشكل الشغلة المهمة
+
+80
+00:06:08,110 --> 00:06:11,370
+ان ال coefficients هدولة لاتوا سوا صفر عشان احقق
+
+81
+00:06:11,370 --> 00:06:15,710
+كلمة homogeneous عشان نحقق كلمة homogeneous تمام
+
+82
+00:06:16,450 --> 00:06:20,650
+معلومة مهمة جدا سواء بدي اشتغل بهذا الشكل او حتى
+
+83
+00:06:20,650 --> 00:06:25,210
+لو حولتها ل closed form ايش هو انه عشان اجيب AN
+
+84
+00:06:25,210 --> 00:06:32,570
+انا محتاج K initial values شك بقول مش هنعرف نحلها
+
+85
+00:06:32,570 --> 00:06:35,930
+يعني اكيد مش هتعرف تحلها انت الان كأنه عندك عدد
+
+86
+00:06:35,930 --> 00:06:41,130
+معادلات بدك إلها عدد مش ههي تكون عارفهم بعدد
+
+87
+00:06:41,130 --> 00:06:45,270
+المعادلات تبعتك كويس واحد اتنين تلاتة فعندي K
+
+88
+00:06:46,340 --> 00:06:48,880
+constants بدنا نجيبهم دول لازم يتجسدوا هنا لازم
+
+89
+00:06:48,880 --> 00:06:54,640
+يكونوا بينين هناطيب معناته بدهم قيم مسبقة معروفة
+
+90
+00:06:54,640 --> 00:06:58,320
+عشان هيك هنكون نفس الشرط هو هو سواء بتشتغل في ال
+
+91
+00:06:58,320 --> 00:07:01,000
+recurrence relation أو في ال closed form انت محتاج
+
+92
+00:07:01,000 --> 00:07:05,580
+k terms ك initial values as a initial values فهم
+
+93
+00:07:05,580 --> 00:07:07,600
+هدول مش همتوا ال conditions ال initial conditions
+
+94
+00:07:07,600 --> 00:07:13,280
+اللي هي من a node to k ناقص واحد فعددهم k عددهم k
+
+95
+00:07:13,280 --> 00:07:19,540
+حسب ال degree اللي بنشتغل عليها تمامفإذن الآن
+
+96
+00:07:19,540 --> 00:07:24,380
+الفرضية اللى بنفرضها أن a n هذا المفروض أنه يكون
+
+97
+00:07:24,380 --> 00:07:31,280
+constant to the power n جداش لازم يكون ال constant
+
+98
+00:07:31,280 --> 00:07:35,100
+هذا أنا مش عارف هل هينضرب برا في constant تاني
+
+99
+00:07:35,100 --> 00:07:38,260
+مثلا يكون والله هنا برضه في عندى طبعا لاحقا
+
+100
+00:07:38,260 --> 00:07:42,360
+هنسميها Alpha Alpha و R معناه اتصل عندى مجهولين
+
+101
+00:07:42,360 --> 00:07:46,020
+هدول لازم أعرفهم لأن هدول ممكن يغيروا ويبدلوا في
+
+102
+00:07:46,020 --> 00:07:51,860
+قيمالـ A N حسب ما يتوافق مع المعادلة الـ
+
+103
+00:07:51,860 --> 00:07:54,840
+Recurrence Relation الحقيقية فعليا فلازم نكون
+
+104
+00:07:54,840 --> 00:07:58,820
+مربطين في بعض بمعنى أن هذه المعادلة هي لازم تيجي
+
+105
+00:07:58,820 --> 00:08:02,580
+من هنا لأن هذا ال given عندي أنا عندي هذه لكن بدا
+
+106
+00:08:02,580 --> 00:08:08,340
+نجيبها بشكل closed form تمام فإذا لو مسكنا هذا ال
+
+107
+00:08:08,340 --> 00:08:13,100
+term هلاجي النهيه بالنسبة لي مكانه بإيش ب R to the
+
+108
+00:08:13,100 --> 00:08:18,530
+power Nتمام الناقص واحد ال C بتاعتها زي ما هي ما
+
+109
+00:08:18,530 --> 00:08:21,130
+هي كانت مضروبة في ال coefficient في C واحد سميناها
+
+110
+00:08:21,130 --> 00:08:25,450
+بس هنا هتصير R to the power الناقص واحد على اعتبار
+
+111
+00:08:25,450 --> 00:08:28,550
+ان ال R هذه زي ما هي ظابطة ل N المفروض انها بتصبط
+
+112
+00:08:28,550 --> 00:08:32,930
+ل الناقص واحد ماهي ده closed form بمعنى انا هقولك
+
+113
+00:08:32,930 --> 00:08:37,620
+جبلنا A عشرةطب إيش يعني لو قلتلك GA تسعة مش هتظبط
+
+114
+00:08:37,620 --> 00:08:41,080
+ال closed form؟ الاصل أنها تظبط الاصبط أن هو
+
+115
+00:08:41,080 --> 00:08:45,320
+المفروض أن هذا general form general form فمعنى ذلك
+
+116
+00:08:45,320 --> 00:08:49,480
+أنه بقدر أقول R to the power الناقص واحد C2 في R
+
+117
+00:08:49,480 --> 00:08:54,300
+to the power الناقص اتنين لما نصل لCK R to the
+
+118
+00:08:54,300 --> 00:08:59,180
+power الناقص Kهكي استعادنا عن المعادلة هذه بال
+
+119
+00:08:59,180 --> 00:09:02,340
+coefficients أو بال roots بتاعتها خلينا نسميها بال
+
+120
+00:09:02,340 --> 00:09:05,680
+Rs بتاعتها اللي المفروض تمثلها لكن أنا مش عارف جدش
+
+121
+00:09:05,680 --> 00:09:10,200
+قيمها فعاليا جدش قيمها حتى اللحظة طيب ال term ده
+
+122
+00:09:10,200 --> 00:09:16,360
+شوية بايخ أو تجيل أو بده تظبط بده تظبط أبسط شغلة
+
+123
+00:09:16,360 --> 00:09:20,920
+أنا صرت أتعامل مع roots مع ال Rs هدولة طيب ال Rs
+
+124
+00:09:20,920 --> 00:09:26,970
+هدولة محتاج أخفف ال weight تبعهمبس relatively ال
+
+125
+00:09:26,970 --> 00:09:30,910
+terms بتظهر زي بعضها بدي أجسم عفوا أجسم على أصغر
+
+126
+00:09:30,910 --> 00:09:34,810
+واحد فيهم انت بتقسم المعادلة كلها على نفس ال term
+
+127
+00:09:34,810 --> 00:09:39,950
+خلاص يمين و شمال مش هتفرج معاك فإذا أصغر term هو
+
+128
+00:09:39,950 --> 00:09:40,870
+هذا ال term
+
+129
+00:09:48,870 --> 00:09:52,050
+وانجلوا كله على ناحية التانية فصار كله بيسوا صفر
+
+130
+00:09:52,050 --> 00:09:55,490
+فمعنى ذلك لما بتقسم مش هتفرج معاك لما انت بتقسم
+
+131
+00:09:55,490 --> 00:09:59,170
+صفر على ال term هذا صفر على هذا ال term خد كل
+
+132
+00:09:59,170 --> 00:10:05,970
+هدولة على ناحية التانية بالسالب صار أيش؟ بيسوا
+
+133
+00:10:05,970 --> 00:10:13,190
+zero بيسوا zero لما نقسم على أصغر term ل Rفانت في
+
+134
+00:10:13,190 --> 00:10:15,950
+الطرف التاني zero هي هي مش هتفرج معاك كتير خدوا
+
+135
+00:10:15,950 --> 00:10:23,110
+common و أشطبه تمام فهنا R to the power N على R to
+
+136
+00:10:23,110 --> 00:10:27,210
+the power N ناقص K فبتصير R to the power K ناقص
+
+137
+00:10:27,210 --> 00:10:31,430
+فهنا برضه K ناقص واحد هنا بتصير K ناقص اتنين لعند
+
+138
+00:10:31,430 --> 00:10:34,930
+اخر term انت قسمت على كل ال term اللي معه فبتضل ال
+
+139
+00:10:34,930 --> 00:10:40,470
+constant لحالها يساوي صفر فصارت معادلة من الدرجة K
+
+140
+00:10:41,430 --> 00:10:44,430
+بينوميال من الدرجة من الدرجة K بدك تجيب ال roots
+
+141
+00:10:44,430 --> 00:10:50,230
+بتاعتها فحولناها لمعادلة جذرية بدك تجيب مجموعة ال
+
+142
+00:10:50,230 --> 00:10:55,730
+roots بتاعتها فقط جداش ال K هي اللي بتفرق معاك هل
+
+143
+00:10:55,730 --> 00:11:00,210
+تربيع تكعيب تتبارخمسة طب مين اللي بيحددها عدد ال
+
+144
+00:11:00,210 --> 00:11:04,710
+terms اللي انا محتاجها عشان اجيب كل قيمةالقيمة هنا
+
+145
+00:11:04,710 --> 00:11:08,670
+محتاجة K مع أنها توحدت درجة K فإذا من ال order K
+
+146
+00:11:08,670 --> 00:11:13,150
+طبعا هتكون صعبة شوية وهذا بتسميه في الآخر كمعادلة
+
+147
+00:11:13,150 --> 00:11:15,170
+أصبحت اسمها characteristic roots
+
+148
+00:11:18,290 --> 00:11:21,590
+كويس عشان نشتغل الكلام هذا و نقدر نحله بيدويا
+
+149
+00:11:21,590 --> 00:11:25,430
+بشغلنا طب انت في الآخر بتقدر تعمم هذا الكلام إذا
+
+150
+00:11:25,430 --> 00:11:28,210
+بتقدر تشتغل لدرجة K بس هيكون عن طريق الحسوب مش
+
+151
+00:11:28,210 --> 00:11:32,870
+هتقدر تشتغل على إيدك يدوي عشان أننا نحل نقدر نشتغل
+
+152
+00:11:32,870 --> 00:11:37,170
+بإيدنا و يدوي فهنحولها لاتنين بكافة و ناخد أمثلتنا
+
+153
+00:11:37,170 --> 00:11:40,550
+كلها علىالاتنين اللي هي بتصير اسمها quadratic form
+
+154
+00:11:40,550 --> 00:11:43,810
+.. quadratic form فتربيعية كلنا بنعرف نحل
+
+155
+00:11:43,810 --> 00:11:47,150
+التربيعية صح كلكوا بتقدروا تجيب ال roots لتربيعية
+
+156
+00:11:47,150 --> 00:11:50,850
+فبتكون سهل الأمور مافيش أي مشكلة otherwise طبعا
+
+157
+00:11:50,850 --> 00:11:53,030
+هتصير على الكمبيوتر بدك تجيبه عن طريق الكمبيوتر
+
+158
+00:11:53,030 --> 00:11:55,450
+تجيب ال code اللي هو يجيب ال roots ال k roots
+
+159
+00:11:55,450 --> 00:11:58,330
+هدولة إذا كان انت اضطرتش في ال k تمام
+
+160
+00:12:01,960 --> 00:12:05,480
+فإذا إذا كان الآل حولنا بدل ما كانت K linear
+
+161
+00:12:05,480 --> 00:12:08,460
+homogeneous recurrence with constant coefficients
+
+162
+00:12:08,460 --> 00:12:12,720
+لأ مش K2 بدنا نقول إن هي من الدرجة التانية من
+
+163
+00:12:12,720 --> 00:12:18,880
+الدرجة التانية معناته أصبحت An زي مين في بناتشي زي
+
+164
+00:12:18,880 --> 00:12:23,860
+في بناتشي مثلا C1 في A N نقص واحد زائد C2 في A نقص
+
+165
+00:12:23,860 --> 00:12:28,100
+اتنينكويس و طبعا في بناتش كانت هنا واحد و واحد
+
+166
+00:12:28,100 --> 00:12:31,360
+صحيح ال C هدولة C واحد و C اتنين كانوا واحد و واحد
+
+167
+00:12:31,360 --> 00:12:34,640
+اللي هي مجموع القيمتين السابقين هدول نفس الكلام
+
+168
+00:12:34,640 --> 00:12:39,780
+اعمل نفس الفكرة عوض بدل كل A ب R to the power ال
+
+169
+00:12:39,780 --> 00:12:42,320
+order تبعها ال N هنا او N ناقص واحد او ناقص اتنين
+
+170
+00:12:42,320 --> 00:12:50,380
+كويس و اقسم على R N ناقص اتنينفبيظل عندك R² ناقص
+
+171
+00:12:50,380 --> 00:12:54,680
+هده هتاخد على ناحية التانية C1 في R ناقص هده هتاخد
+
+172
+00:12:54,680 --> 00:12:58,100
+على ناحية التانية C2 معادلة من ال quadratic form
+
+173
+00:12:58,100 --> 00:13:02,860
+بنقدر نجيب بكل بساطة قيم R وأكيد هيطلع كم قيمة
+
+174
+00:13:02,860 --> 00:13:08,870
+لـR؟ two values فعندي R1 وعندي R2على اعتبار ان هي
+
+175
+00:13:08,870 --> 00:13:11,590
+quadratic form فمعنى ذلك انه هيطلع عندك two roots
+
+176
+00:13:11,590 --> 00:13:16,290
+ال two roots هدولة كيف بقدر امثلهم في ال closed
+
+177
+00:13:16,290 --> 00:13:19,770
+form عشان احطهم في closed form واضح معنى ذلك اذا
+
+178
+00:13:19,770 --> 00:13:23,030
+كانت هنا بتعامل مع قيمة واحدة تطلع بهذا الشكل بس
+
+179
+00:13:23,030 --> 00:13:26,210
+واضح ان انا محتاج قيمتين سابقتين فمعنى ذلك انه
+
+180
+00:13:26,210 --> 00:13:30,310
+برضه هتكون زائد R to the power N تانية بس كل واحدة
+
+181
+00:13:30,310 --> 00:13:36,310
+ب coefficient مختلففحيقولك إيش ال a n closed form
+
+182
+00:13:36,310 --> 00:13:40,490
+اللي هتساوي alpha واحد في ال root الأول to the
+
+183
+00:13:40,490 --> 00:13:43,350
+power n زائد alpha اتنين في ال root التاني to the
+
+184
+00:13:43,350 --> 00:13:45,870
+power n لأنه الآن بدك تحط أنه root من ال two roots
+
+185
+00:13:45,870 --> 00:13:50,450
+هدول احنا قلنا بدنا root okay ماشي هاي R طب أنه
+
+186
+00:13:50,450 --> 00:13:53,950
+واحد هستخدم لأنك هتستخدم الاتنين فعليا هتستخدم
+
+187
+00:13:53,950 --> 00:13:58,570
+الاتنين كويس وكل واحد هتفترض أنه إله constant خاص
+
+188
+00:13:58,570 --> 00:14:02,740
+فيه أو معامل خاص فيه coefficient خاص فيهالـ
+
+189
+00:14:02,740 --> 00:14:05,600
+coefficient الخاص بي فهي الـ root الأول to the
+
+190
+00:14:05,600 --> 00:14:08,560
+power n بالـ root الخاص بي بالـ coefficient الخاص
+
+191
+00:14:08,560 --> 00:14:11,420
+بي زائد الـ root التاني بالـ coefficient الخاص بي
+
+192
+00:14:11,420 --> 00:14:16,520
+و طبعا كلنا بنتكلم عن n من صفر فأكتر عشان أقدر
+
+193
+00:14:16,520 --> 00:14:21,140
+أعبر عنها طيب و بيظل عندنا الشغل المهم بعد ما نحل
+
+194
+00:14:21,140 --> 00:14:25,760
+ال characteristic roots بدك تجيب قيمة ألف واحد و
+
+195
+00:14:25,760 --> 00:14:29,940
+ألف اتنين من وين؟ من ال two initials اللي لازم
+
+196
+00:14:29,940 --> 00:14:33,160
+يكونوا عندكمن ال two initials اللي لازم يكونوا
+
+197
+00:14:33,160 --> 00:14:37,660
+عندك، ما احنا اتفقنا من الأول، عشان تحلل هذه، انت
+
+198
+00:14:37,660 --> 00:14:42,640
+محتاج two values، مدام ال K ب2، معناته انت محتاج
+
+199
+00:14:42,640 --> 00:14:45,960
+قيمتين مسبقتين، هل هي بتقدر تجيب Fibonacci بدون ما
+
+200
+00:14:45,960 --> 00:14:50,310
+تكون عارف القيمتين السابقتين؟ أبداًإطلاقا فمعنى
+
+201
+00:14:50,310 --> 00:14:53,690
+ذلك ان انت محتاج قيمتين سابقتين على الأقل two
+
+202
+00:14:53,690 --> 00:14:56,890
+values حسب ال degree اللي بتشتغل عليها والله لو ال
+
+203
+00:14:56,890 --> 00:15:00,570
+degree تلاتة معناته محتاج تلت قيم initial values و
+
+204
+00:15:00,570 --> 00:15:03,990
+هكذا فإذا ان انا محتاج اتنين محتاج اتنين الاتنين
+
+205
+00:15:03,990 --> 00:15:07,670
+هدولة بتعوض فيهم في المعادلة بيظل عندك الف واحد و
+
+206
+00:15:07,670 --> 00:15:11,890
+الف اتنين المجاهيل تبعتك في معادلتين لما عوضت في
+
+207
+00:15:11,890 --> 00:15:16,650
+القيمتين ال given عندك خلص انحلت الموضوع ناخد مثل
+
+208
+00:15:16,650 --> 00:15:22,820
+انحدد الأموربهذا الشكل طب بدنا نحدد بس شغلة هنا
+
+209
+00:15:22,820 --> 00:15:27,380
+انه هذا الكلام منطقي جدا انه نفصل R1 وR2 على
+
+210
+00:15:27,380 --> 00:15:35,260
+اعتبار انهم مختلفين فبقدرش اقول والله R هذه هي
+
+211
+00:15:35,260 --> 00:15:39,120
+واحد او هي اتنين فانا مضطر اجمعهم الاتنين مع بعض
+
+212
+00:15:39,120 --> 00:15:43,700
+فإذا هذا الكلام النظرية theorem one هذه في حال انه
+
+213
+00:15:43,700 --> 00:15:48,130
+كانوا لايسوا بعض فاحط كل واحد لحاله في termكل واحد
+
+214
+00:15:48,130 --> 00:15:54,090
+هنحط لحاله في term خاص فيه تمام هنشوف مثالنا هاي
+
+215
+00:15:54,090 --> 00:15:59,590
+عندك an بتساوي an نقص واحد زائد اتنين an نقص اتنين
+
+216
+00:15:59,590 --> 00:16:04,310
+فإذن معتمد على القيمة السابقة زائد ضعف القيمة ما
+
+217
+00:16:04,310 --> 00:16:09,490
+قبل السابقة كويس و ال initial conditions بدونها
+
+218
+00:16:09,490 --> 00:16:12,690
+انسى لإنك تحلي حاجة مش هتعرف تحلي حاجة a node
+
+219
+00:16:12,690 --> 00:16:20,110
+بتنين a واحد بسبعة و قلتلك هاتلي aمية انا مش
+
+220
+00:16:20,110 --> 00:16:22,590
+هجيبلك في الامتحان هتلي تلاتة تروح تجمعلي اياهم و
+
+221
+00:16:22,590 --> 00:16:28,750
+تخلص مش هيك اكيد يعني اكيد فمش هتروح تضطر تعملي زي
+
+222
+00:16:28,750 --> 00:16:32,890
+ال summation اللي خدناها سابقا تقعد تعملي terms مش
+
+223
+00:16:32,890 --> 00:16:38,270
+هتعملي terms بدك تعمل terms لمن مية لصفر واحد خلاص
+
+224
+00:16:38,270 --> 00:16:41,350
+ضيع وقتك وراحتك في الحالة هذه فبتصير انت ضيعت وقت
+
+225
+00:16:41,350 --> 00:16:44,530
+على الفاضي لأ بنحولها ل closed form عشان مباشرة
+
+226
+00:16:44,530 --> 00:16:49,990
+تنعوض ب N بمية و خلاصخلصنا هوية واحدة وانتهى طيب
+
+227
+00:16:49,990 --> 00:16:52,750
+هذا الكلام مناسب جدا في بعض الأمثلة حتى جوا في
+
+228
+00:16:52,750 --> 00:16:55,170
+الكتاب اللي هي علاقة بين ال bacteria ال bacteria
+
+229
+00:16:55,170 --> 00:16:59,450
+بشكل بكل ساعة في كل ساعة بتتضعف لتلت أبعاف لما
+
+230
+00:16:59,450 --> 00:17:03,070
+أقولك والله في يوم كامل كام ضعف صارت مش هتقل
+
+231
+00:17:03,070 --> 00:17:07,350
+تتحلليها بإيدك مش هتقل تتحلها بإيدك كويس فبدك تضطر
+
+232
+00:17:07,350 --> 00:17:13,010
+تجيب ال closed form ك term في in و in هنا هتكون
+
+233
+00:17:13,010 --> 00:17:16,590
+عدد الساعات اللي هي بتتضعف فيها لتلت أربع أضعاف
+
+234
+00:17:17,270 --> 00:17:22,430
+عشان في الآخر اتعود بقيمة ال N بس تمام هتنشوف كلام
+
+235
+00:17:22,430 --> 00:17:26,590
+ليه صار معناه بكل بساطة هنا مدام أنا عارف فاهم من
+
+236
+00:17:26,590 --> 00:17:29,410
+الأساس كيف اجت ال characteristic equation فانا
+
+237
+00:17:29,410 --> 00:17:31,990
+عارف مسبقا ان هدولة هوديهم عن ناحية التانية
+
+238
+00:17:31,990 --> 00:17:38,510
+بالسوالب سوالبها كويس و هدى هتروح ل R تربيع ناقص
+
+239
+00:17:38,510 --> 00:17:43,570
+هنا R مافيش اي coefficient معاها و هنا هتصير ناقص
+
+240
+00:17:43,570 --> 00:17:44,250
+اتنين
+
+241
+00:17:48,240 --> 00:17:52,800
+بداك تعمل الطريقة المطولة و تستعود مكان كل N ب R
+
+242
+00:17:52,800 --> 00:17:56,320
+to the power N و بعدين تقسم على ال N الأصغر خلاص
+
+243
+00:17:56,320 --> 00:18:00,960
+ماذا هي؟ ماهي كلها جام كلها تمام خلصنا فهي صارت
+
+244
+00:18:00,960 --> 00:18:02,920
+عندك المعادلة بهذا الشكل اللي هي ال characteristic
+
+245
+00:18:03,960 --> 00:18:07,980
+characteristic equation كويس كلكوا حافظين ال
+
+246
+00:18:07,980 --> 00:18:12,660
+quadratic form ال quadratic form اللي هو سالب ب
+
+247
+00:18:12,660 --> 00:18:16,580
+زائد ناقص الجذر تبع المحدد و اللي هو ب تربية ناقص
+
+248
+00:18:16,580 --> 00:18:21,560
+أربعة a c على اتنين a هذا كلنا حافظينه فعشان هي
+
+249
+00:18:21,560 --> 00:18:23,880
+كان مناسب ان احنا نشتغل على ال degree اتنين بس
+
+250
+00:18:23,880 --> 00:18:28,650
+اكتر من هيك بصير بدك تحلها بطرق تانيةتمام ف R هنا
+
+251
+00:18:28,650 --> 00:18:33,310
+إيش هتسوي في الحالة دي لو عوضنا ب C1 و C2 اللي هي
+
+252
+00:18:33,310 --> 00:18:36,830
+ال coefficients تبعتك هيها عندك ال A بواحد ال B
+
+253
+00:18:36,830 --> 00:18:41,970
+سالب واحد و C سالب اتنين بنعوض عشان يطلع عندك two
+
+254
+00:18:41,970 --> 00:18:46,610
+roots اتنين و سالب واحد فتنين سالب واحد اللي طلعوا
+
+255
+00:18:46,610 --> 00:18:51,010
+عندك هنا بدأك تحطهم في شكل المعادلة تبعتك كل واحدة
+
+256
+00:18:51,010 --> 00:18:54,010
+كان هي ال root فعلا to the power N ال root to the
+
+257
+00:18:54,010 --> 00:18:56,940
+power N وكل واحدة مضروبة في إيش؟في الـ coefficient
+
+258
+00:18:56,940 --> 00:19:02,680
+تبعها خلصنا كل ما مطلوب منك اتعود بالقيمتين هدول ف
+
+259
+00:19:02,680 --> 00:19:08,120
+a zero تساوي اتنين يعني معنى ذلك تساوي alpha واحد
+
+260
+00:19:08,120 --> 00:19:13,860
+و هنا zero انت بتعود عند n ب zero فإذا هذه بواحد و
+
+261
+00:19:13,860 --> 00:19:17,680
+هنا نفس الكلام alpha اتنين و هنا برضه بواحد خلصنا
+
+262
+00:19:17,680 --> 00:19:20,340
+فاتنين تساوي alpha واحد زي ال alpha اتنين هي
+
+263
+00:19:20,340 --> 00:19:25,980
+معادلة أولى بعدين بنعود عند مين عند n بتساوي بواحد
+
+264
+00:19:26,600 --> 00:19:31,260
+and n ساوي واحد فا ايه واحد تساوي سبعة وهذه تساوي
+
+265
+00:19:31,260 --> 00:19:37,440
+اتنين هتصير واحد اتنين Alpha واحد زائد بتصير ناقص
+
+266
+00:19:37,440 --> 00:19:43,680
+واحد مظبوط هنا to the power واحد بتصير اتنين مظبوط
+
+267
+00:19:43,680 --> 00:19:48,300
+و هنا Alpha نزلت زي ما هي بس بالسالب سالب Alpha
+
+268
+00:19:48,300 --> 00:19:55,560
+اتنين مظبوطك احنا عوضنا في واحد اه to the power
+
+269
+00:19:55,560 --> 00:20:01,780
+oneبتبار one اه سالب واحد كويس فهذا كله المفروض
+
+270
+00:20:01,780 --> 00:20:07,180
+انه بيساوي سبعة وهذا بيساوي اتنين بتالي أبسط شغلة
+
+271
+00:20:07,180 --> 00:20:11,420
+ممكن مثلا تجمعهم ضيعت هدولة مثلا هي سبعة فالف واحد
+
+272
+00:20:11,420 --> 00:20:14,640
+بتلاتة هي بيانت لحالها على اعتبار انه تسعة وهدول
+
+273
+00:20:14,640 --> 00:20:19,180
+مجموحهم تلاتة خلصت يعني بتالي مش الحاجة اللي ضخمة
+
+274
+00:20:19,180 --> 00:20:26,380
+صحيح بسيطة جدا الفكرة تمام فخلصنا هى و جابها و
+
+275
+00:20:26,380 --> 00:20:29,880
+اشتغل عليها و فعلا طلع معانا الف و واحد بتلاتة
+
+276
+00:20:29,880 --> 00:20:33,120
+مظبوط الف و واحد بتلاتة و الف و اتنين اب واحد
+
+277
+00:20:33,120 --> 00:20:37,080
+فارجع عوض فيهم في المعادلة تلاتة و واحد هذا closed
+
+278
+00:20:37,080 --> 00:20:42,960
+form خلاص هذا لان لما نطلب منك مية كل ما هتعمله بس
+
+279
+00:20:42,960 --> 00:20:46,880
+تعود هنا بمية و هنا بمية و انتهى و بتجيب القيمة
+
+280
+00:20:46,880 --> 00:20:50,640
+مباشرة طب مابتقدر تعمل check عليها عند الصفر هيطلع
+
+281
+00:20:50,640 --> 00:20:56,040
+لتنين مظبوطةاللي احنا اصلا عوضنا فيها عند الواحد
+
+282
+00:20:56,040 --> 00:20:59,320
+المفروض يطلع السبعة مظبوطة وبعدين بتقدر تكمل ال
+
+283
+00:20:59,320 --> 00:21:03,440
+series تبعتك بتقدر تكمل ال series لو محتاج هتزول
+
+284
+00:21:03,440 --> 00:21:08,000
+.. اتفضل ماكانتش
+
+285
+00:21:08,000 --> 00:21:13,980
+ال quadratic؟
+
+286
+00:21:13,980 --> 00:21:21,140
+معناته ان هي مش ممكنةلأنه complex .. اي عفوًا ..
+
+287
+00:21:21,140 --> 00:21:23,920
+imaginary part هتكون imaginary part في الحالة هذه
+
+288
+00:21:23,920 --> 00:21:26,920
+معناه ذلك أنه .. معناه ذلك أنه المعادلة هذه فيها
+
+289
+00:21:26,920 --> 00:21:32,840
+مشكلة من الأساس في عندك مشكلة فبناتش بتطلع لحل ..
+
+290
+00:21:32,840 --> 00:21:38,420
+لأ فبناتش بتطلع لحل و إجا في امتحان كان واحدة من
+
+291
+00:21:38,420 --> 00:21:41,860
+أسئلة امتحان سابق أنه جبتلهم معادلة فبناتش نفسها و
+
+292
+00:21:41,860 --> 00:21:45,140
+قلتلهم هتقول ال closed form تبعتها و كان فيها أربع
+
+293
+00:21:45,940 --> 00:21:48,180
+متذكر أنه لعندي الآن كان ألف و واحد و ألف اتنين
+
+294
+00:21:48,180 --> 00:21:54,240
+هدول و ربعه حسب ما أذكر لأ لأ جربها جربها ماتحكمش
+
+295
+00:21:54,240 --> 00:21:57,280
+على حاجة بدون ماتجربها الرياضيات بدها التجريب و
+
+296
+00:21:57,280 --> 00:22:00,340
+عشان هيك بيسموه exercise عشان هيك بيسموه دايما في
+
+297
+00:22:00,340 --> 00:22:02,300
+نهاية ال chapters .. ال chapters تبع ال
+
+298
+00:22:02,300 --> 00:22:05,600
+mathematics بيسموهاش problems بيسموه exercise
+
+299
+00:22:05,600 --> 00:22:11,480
+تدريب تدرب حالك تمام لأ لأ بيطلع لحلو ما هي محلولة
+
+300
+00:22:11,480 --> 00:22:13,900
+يعني حلناها بقولك جابل هيك و جيبناها انتحان أصلا
+
+301
+00:22:14,660 --> 00:22:20,800
+طيب الآن السؤال لو ال roots هذه ال roots هي ما
+
+302
+00:22:20,800 --> 00:22:24,820
+طلعتش مختلفة طلعت متشابهة طلعت ال roots متشابهة
+
+303
+00:22:24,820 --> 00:22:29,380
+ففي الحالة هذه إذا طلعت متشابهة يعني one rule ..
+
+304
+00:22:29,380 --> 00:22:34,040
+one root فقط اللي هي R node واحدة مش R واحد وR
+
+305
+00:22:34,040 --> 00:22:39,020
+اتنين فبنقدر نقول أن نفس ال terms لاحظ لنفس ال R
+
+306
+00:22:39,020 --> 00:22:43,420
+بس واحد منهم اضربه في N واحد من ال two terms اضربه
+
+307
+00:22:43,420 --> 00:22:48,140
+في Nالأول التاني بيفرجش بيفرجش كتير يعني ما تقعدش
+
+308
+00:22:48,140 --> 00:22:51,520
+تحفظليها أنه لازم في التاني خلاص هي نفس المعادلة
+
+309
+00:22:51,520 --> 00:22:56,720
+هي .. هي R وقعينا R واحدة .. واحدة متشابهة فR to
+
+310
+00:22:56,720 --> 00:22:58,880
+the power N وR to the power N كل واحدة مضربها في
+
+311
+00:22:58,880 --> 00:23:01,240
+ال coefficient تبعتها Alpha 1 و Alpha 2 واحدة منهم
+
+312
+00:23:01,240 --> 00:23:05,460
+مضربها في N خلاص في النهاية هيثبتلك إياها مين
+
+313
+00:23:05,460 --> 00:23:08,200
+Alpha 1 لما بتعوض فيها و جيب ال .. جيب ال roots مش
+
+314
+00:23:08,200 --> 00:23:11,800
+هتفرج معاك كتير فانت لاجوش من الجثة اضرب أي واحدة
+
+315
+00:23:11,800 --> 00:23:20,080
+منهم في N تمامOkay نجرب مثال على هذا الموضوع هي
+
+316
+00:23:20,080 --> 00:23:27,000
+عندك a n بتساوي ستة a n ناقص واحد ناقص تسعة a n
+
+317
+00:23:27,000 --> 00:23:32,600
+ناقص اتنين و اعطاك two initial values واحد و صفر
+
+318
+00:23:32,600 --> 00:23:35,680
+عند واحد و ست عفوا عند الصفر و الواحد ال
+
+319
+00:23:35,680 --> 00:23:40,380
+characteristic roots بهذا الشكل هذه مباشرة المحددة
+
+320
+00:23:40,380 --> 00:23:46,050
+بتاعتها او اللي تحت الجذر هتساوي zeroما دام بتساوي
+
+321
+00:23:46,050 --> 00:23:50,790
+zero معناته هو root واحد هو root واحد اللي هو سالب
+
+322
+00:23:50,790 --> 00:23:54,230
+بي على المقام اللي هو اتنين ايه فسالب بي على مقام
+
+323
+00:23:54,230 --> 00:23:58,870
+اتنين كلا هما تلاتة خلاص هنعملها زي ما هي هي سيبك
+
+324
+00:23:58,870 --> 00:24:02,430
+من ال N لو جيتها هي تلاتة وهي تلاتة نفس السابق
+
+325
+00:24:02,430 --> 00:24:07,470
+واحدة منهم ضربها في Nواحدة منهم وضربها في N خلاص
+
+326
+00:24:07,470 --> 00:24:12,110
+ضربناها في N في الآخر جابل طبعا منصل ان والله هذه
+
+327
+00:24:12,110 --> 00:24:16,890
+واحد وهذه واحد فعليا هذه اتت من خلال ايش تعويض من
+
+328
+00:24:16,890 --> 00:24:21,130
+خلال تعويض اللي هنا وكانت بسيطة أعتقد مش مش الشغل
+
+329
+00:24:21,130 --> 00:24:29,370
+الصعب كتير A node بتساوي واحد فهنعود هنا صفرو صفر
+
+330
+00:24:29,370 --> 00:24:33,230
+طبعا ترمد كله راح مع الصفر فبتضل هنا صفر يعني
+
+331
+00:24:33,230 --> 00:24:36,710
+بتساوي Alpha واحد فخلصنا هاي Alpha واحد لحالها
+
+332
+00:24:36,710 --> 00:24:42,950
+طلعت خلصت Alpha واحد لحالها A واحد بتساوي ستة وهد
+
+333
+00:24:42,950 --> 00:24:47,390
+بتساوي خلاص هد بواحد انتهى و هنا بضل تلاتة فبتساوي
+
+334
+00:24:47,390 --> 00:24:52,230
+تلاتة زائد Alpha اتنين اللي لسه بدنا نجيبها و هنا
+
+335
+00:24:52,230 --> 00:24:59,120
+واحد في تلاتة يعني تلاتة لأ يعني واحدهذه هتروح
+
+336
+00:24:59,120 --> 00:25:03,680
+الطرف التاني فبصير تلاتة تساوي تلاتة ألف اتنين
+
+337
+00:25:03,680 --> 00:25:09,420
+برضه واحد فإذا برضه تساوي ألف اتنين فهي واحد واحد
+
+338
+00:25:09,420 --> 00:25:13,260
+فصارت هنا كأنه هنا في واحد و هنا في واحد خلصنا جيب
+
+339
+00:25:13,260 --> 00:25:16,080
+كل ال terms اللي بدك هيها بدك ال term رقم مية جيب
+
+340
+00:25:16,080 --> 00:25:20,920
+مية اضرب بس مكان n بمية جيبنا ال term رقم مية
+
+341
+00:25:20,920 --> 00:25:26,240
+فبناتش بتقدر تجيبها و أي series بعد هيك بتقدر
+
+342
+00:25:26,240 --> 00:25:30,060
+تتعامل معاهاتمام هذا كان الجزء اللي ضايلة عندنا في
+
+343
+00:25:30,060 --> 00:25:33,740
+ال linear أو ال solving recurrences في ال solving
+
+344
+00:25:33,740 --> 00:25:37,720
+recurrences طيب ال recurrence هذه احنا ايش كنا
+
+345
+00:25:37,720 --> 00:25:41,860
+نسميها recurrence relation صحيح ال function ال
+
+346
+00:25:41,860 --> 00:25:46,520
+function ايش هي relationصحيح؟ فإذا واضح ان احنا
+
+347
+00:25:46,520 --> 00:25:50,640
+لما متخيلين ان ال function هي أكبر حاجة خدناها و
+
+348
+00:25:50,640 --> 00:25:53,200
+ان الدنيا كلها functions لأ هي في حاجة أكبر من ال
+
+349
+00:25:53,200 --> 00:25:56,300
+function و هي اللي بتشمل ال function ال relation
+
+350
+00:25:56,300 --> 00:26:01,940
+العلاقات ال relation و عشان هيك طبيعي جدا ان احنا
+
+351
+00:26:01,940 --> 00:26:07,060
+نروح لحاجة اسمها relation اللي هي relation ال
+
+352
+00:26:07,060 --> 00:26:10,520
+function هي relation ليش؟ لأنك انت بتجيب بالنسبة
+
+353
+00:26:10,520 --> 00:26:15,190
+لل function العلاقة بين ال input و ال outputفهي
+
+354
+00:26:15,190 --> 00:26:21,090
+relation كأنها function طيب ال .. ال set هي
+
+355
+00:26:21,090 --> 00:26:25,450
+relation لأن أنت بتعمل relation بين العنصر و
+
+356
+00:26:25,450 --> 00:26:28,430
+انتماءه لل set ينتمي أو لا ينتمي فهنا بتصير
+
+357
+00:26:28,430 --> 00:26:32,290
+relation binary relation يعني يا on يا off يا
+
+358
+00:26:32,290 --> 00:26:36,210
+موجود يا غير موجود مثلا كويس؟ طيب في ال series
+
+359
+00:26:36,210 --> 00:26:40,670
+برضه relation relation بين مين و مين بين العنصر
+
+360
+00:26:40,670 --> 00:26:46,140
+نفسه و ال locationفي علاقة ولا مافيش علاقة، واحنا
+
+361
+00:26:46,140 --> 00:26:49,340
+هنا لسه كنا بنشتغل عليها، هيها، high relation بين
+
+362
+00:26:49,340 --> 00:26:54,960
+العنصر وال location تبعه، هي عنصر و location، احنا
+
+363
+00:26:54,960 --> 00:26:56,760
+إيش اللي كنا نعمله هنا؟ ليش قلتلك هاتلي ال
+
+364
+00:26:56,760 --> 00:26:59,620
+location مية، بدي العنصر في ال location مية،
+
+365
+00:26:59,620 --> 00:27:03,460
+معناته المفروض أنه بدلالة المية تعرف قيمة العنصر،
+
+366
+00:27:03,460 --> 00:27:09,520
+فأصبح العنصر معرف بال location تبعهتمام فأول شغلة
+
+367
+00:27:09,520 --> 00:27:13,560
+ال binary relation اللي هي يوجد أو لا يوجد هذه
+
+368
+00:27:13,560 --> 00:27:17,540
+أبسط أنواع ال relations الممكنة كبداية لل
+
+369
+00:27:17,540 --> 00:27:21,760
+relations و اللي زي ما قلنا هي هتشمل كل العلوم
+
+370
+00:27:21,760 --> 00:27:25,280
+هتتفاجأ انها بتشمل كل علوم الرياضيات بتشمل كل
+
+371
+00:27:25,280 --> 00:27:29,920
+المواضيع اللي أخدناها في الرياضيات لإنه ممكن
+
+372
+00:27:29,920 --> 00:27:34,900
+تمثيلها بشكل relation فلما نقولك binary relation
+
+373
+00:27:34,900 --> 00:27:40,760
+بين ال set A و B عندي two sets domain و codomain
+
+374
+00:27:40,760 --> 00:27:43,820
+مش هاي two sets بتاعونك domain و codomain بتجيب
+
+375
+00:27:43,820 --> 00:27:47,340
+منهم function فبقدر أقول ان ال binary relation R
+
+376
+00:27:47,340 --> 00:27:52,260
+from A to B بنكتبها كتالة كأنها function هي
+
+377
+00:27:52,260 --> 00:27:57,320
+لاحظتوا كده ال R أو ال relation أو كأنها ال F مثلا
+
+378
+00:27:57,320 --> 00:28:03,200
+ال R from Ato B هي subset لإيش؟ لل A Cartesian
+
+379
+00:28:03,200 --> 00:28:06,380
+product B ليش Cartesian product B؟ لأنه عارفين إن
+
+380
+00:28:06,380 --> 00:28:09,180
+إحنا في ال Cartesian product B و اللي جيبناها في
+
+381
+00:28:09,180 --> 00:28:13,120
+الامتحان برضه و عملتولنا شوية مشاكل فيها هي معناته
+
+382
+00:28:13,120 --> 00:28:17,520
+أن أنا بجيب أي عنصر من A و سمناها X و أي عنصر من B
+
+383
+00:28:17,520 --> 00:28:21,890
+و سمناها Y، ماينفعش أقول X هنا و هناماكنش بظبط
+
+384
+00:28:21,890 --> 00:28:24,650
+نقول x هنا و هنا لأن معناته أنا بتكلم من ال set
+
+385
+00:28:24,650 --> 00:28:29,110
+لنفسه و هذا ماكنش صحيح ف Cartesian x و y فإذا كل
+
+386
+00:28:29,110 --> 00:28:33,470
+عنصر كزوج مرتب الجزء الأول من الزوج المرتب هو
+
+387
+00:28:33,470 --> 00:28:38,510
+المفروض يكون جاي ينتمي ل a والجزء الثاني ينتمي ل b
+
+388
+00:28:39,580 --> 00:28:43,580
+و بتعمل كل ال possibilities الممكنة فإذا بتاخد
+
+389
+00:28:43,580 --> 00:28:50,000
+عنصر من a بتحطه في البداية ك x axis في ال x axis
+
+390
+00:28:50,000 --> 00:28:57,800
+كويس و كل عناصر بي بتحطه عنصر الأول في هاي حالة مع
+
+391
+00:28:57,800 --> 00:29:01,640
+عنصر التاني هاي حالة مع عنصر التالت حالة خلصتهم
+
+392
+00:29:01,640 --> 00:29:06,000
+بتاخد عنصر التاني من a و بتكرر و بتكرر فمعنى ذلك
+
+393
+00:29:06,000 --> 00:29:11,290
+بطلع عندكالـ cardinality لـ Cartesian product كأنه
+
+394
+00:29:11,290 --> 00:29:16,230
+ضرب ال two cardinalities ال two cardinalities ل A
+
+395
+00:29:16,230 --> 00:29:20,430
+و B اللي هو عدد عناصر A مضروب في عدد عناصر B طيب
+
+396
+00:29:20,430 --> 00:29:25,840
+لما أقول في relation بين عناصر A و Bبين عناصر a و
+
+397
+00:29:25,840 --> 00:29:29,200
+b بمسككم العنصر الأول هل يوجد relation بين العنصر
+
+398
+00:29:29,200 --> 00:29:33,960
+الأول هنا والعنصر الأول في الناحية هذه لأ لا يوجد
+
+399
+00:29:33,960 --> 00:29:38,400
+relation أو يوجد relation بناء على إيش على إيش ال
+
+400
+00:29:38,400 --> 00:29:42,160
+relation اللي أنا بتتكلم عنها بناء على إيش هي ال
+
+401
+00:29:42,160 --> 00:29:45,660
+relation اللي بحكي عنها نتكلم عن relation طيب لما
+
+402
+00:29:45,660 --> 00:29:50,240
+نقول مثلا هي عندنا مستوى التالتكلنا في المستوى
+
+403
+00:29:50,240 --> 00:29:53,240
+التالت طيب هاتنشوف طلبة مستوى أول طب هل يوجد
+
+404
+00:29:53,240 --> 00:29:57,520
+relation ايش نوع ال relation ان حد أخه التاني مثلا
+
+405
+00:29:57,520 --> 00:30:01,740
+relation relation يمكن يطلع five في النهاية يطلع
+
+406
+00:30:01,740 --> 00:30:03,980
+من المستوى التالت مافيش ولا واحد أخوه في المستوى
+
+407
+00:30:03,980 --> 00:30:06,960
+الأول صح في النهاية ممكن تطلع five ماعنديش مشكلة
+
+408
+00:30:06,960 --> 00:30:12,140
+بس تخيل انه كلكوا يطلعلكم في يعني أخه هناك معنى
+
+409
+00:30:12,140 --> 00:30:16,360
+ذلك ان انتوا في الآخر هتكونوا حددتوا بحد أقصىبحد
+
+410
+00:30:16,360 --> 00:30:20,560
+أقصى لا يمكن ال relations الممكنة تزيد عن ال
+
+411
+00:30:20,560 --> 00:30:22,980
+Cartesian product ليش؟ لأن ال Cartesian product
+
+412
+00:30:22,980 --> 00:30:25,960
+انا حطيت كل الاحتمالات ال possibilities الممكنة
+
+413
+00:30:25,960 --> 00:30:30,240
+حطينا كل ال possibilities الممكنة الأول هل أخو
+
+414
+00:30:30,240 --> 00:30:33,520
+الأول هنا؟ طب الأول أخو التاني هنا؟ الأول أخو
+
+415
+00:30:33,520 --> 00:30:36,660
+التالت هنا؟ خلصنا من الأول التاني أخو الأول هنا؟
+
+416
+00:30:36,660 --> 00:30:39,440
+حطيت كل ال possibilities أنت بال Cartesian product
+
+417
+00:30:40,420 --> 00:30:44,400
+فمعنى ذلك لما اقول subset اه انا متأكد تماما ان ال
+
+418
+00:30:44,400 --> 00:30:46,720
+relation هتكون هي subset من ال Cartesian لان ال
+
+419
+00:30:46,720 --> 00:30:50,180
+Cartesian اعطتك كل ال possibilities الممكنة طيب
+
+420
+00:30:50,180 --> 00:30:54,040
+subset ممكن تكون في اجي امسككم واحد واحد و نشوف
+
+421
+00:30:54,040 --> 00:30:59,080
+سنة أولى ولا واحد أخد تاني خلاص معناته في relation
+
+422
+00:30:59,080 --> 00:31:02,880
+لو يوجد relationrelation لا يوجد relation واضحت
+
+423
+00:31:02,880 --> 00:31:07,380
+فكلمة relation انا بالعمدة نقطتي المثال هذا عشان
+
+424
+00:31:07,380 --> 00:31:10,360
+اوضحلك انه مش بالضرورة ال relation تكون ايش رياضي
+
+425
+00:31:10,360 --> 00:31:16,260
+أرقام علاقات الناس في بعض relation عارفت ليش كلمة
+
+426
+00:31:16,260 --> 00:31:19,660
+relation هل وجد موضوع ال relation أكثر عمومية من
+
+427
+00:31:19,660 --> 00:31:23,640
+ال function لأنه انت بتتكلم حتى في الحالات الشخصية
+
+428
+00:31:23,640 --> 00:31:30,480
+relations تقدر تحطها ضغط اه اللغات relationفواضح
+
+429
+00:31:30,480 --> 00:31:34,920
+ان انت الآن احنا بنتكلم عن موضوع شامل كل اللي انت
+
+430
+00:31:34,920 --> 00:31:40,040
+أخدته سابقا كويس هاي subset من ال Cartesian مثال
+
+431
+00:31:40,040 --> 00:31:42,900
+عشان نوضح اللي الموضوع لو أخدنا ال relation أصغر
+
+432
+00:31:42,900 --> 00:31:46,920
+من هاي relation مش أصغر من relation from natural
+
+433
+00:31:46,920 --> 00:31:50,420
+number to natural number معنى ذلك انه set لكل
+
+434
+00:31:53,520 --> 00:31:58,240
+الأزواج المرتبة N و M بشرط أو such that أن N
+
+435
+00:31:58,240 --> 00:32:02,720
+الأولى تكون فعلا تحقق ال relation بالنسبة للتانية
+
+436
+00:32:02,720 --> 00:32:09,600
+فهي N و M معناته أن N أقل من M فمعناه ذلك أن هذا
+
+437
+00:32:09,600 --> 00:32:12,680
+ال relation أقل من هذا ال relation أقل من في
+
+438
+00:32:12,680 --> 00:32:17,180
+الحالة ده بنقدر نقول ال relation A بنقولها A
+
+439
+00:32:17,180 --> 00:32:23,030
+relation Bكأنه A أصغر لأن استعبنا عن ال relation
+
+440
+00:32:23,030 --> 00:32:27,770
+هنا ال relation كانت أصغر منه فحنحط أصغر منه A
+
+441
+00:32:27,770 --> 00:32:33,130
+أصغر من B هاي ال relation طيب فإذا A relation B أو
+
+442
+00:32:33,130 --> 00:32:39,150
+بنكتبها ARB مباشرة أو بمعنى أن A وB ينتموا لل
+
+443
+00:32:39,150 --> 00:32:43,560
+relation Rينتموا لل relation أصغر من .. إذا فعلا
+
+444
+00:32:43,560 --> 00:32:48,200
+حققوا هذا الشرط أن N فعلا أصغر من M فإذا N و M هم
+
+445
+00:32:48,200 --> 00:32:51,860
+ينتموا لأصغر من .. ال relation أصغر من .. كويس
+
+446
+00:32:51,860 --> 00:32:56,360
+فإذا A أصغر من B معناها أن A و B هم ينتموا لل
+
+447
+00:32:56,360 --> 00:33:00,460
+relation أصغر من .. إذا كانت A و B هذه معناها ..
+
+448
+00:33:00,460 --> 00:33:04,880
+بهذا الشكل تحققت فبقدر أقول أن A is related to B
+
+449
+00:33:04,880 --> 00:33:11,850
+by relation Rفهي related ل B تحت ال relation R
+
+450
+00:33:11,850 --> 00:33:17,850
+محقق ال relation R أو A relates to B under
+
+451
+00:33:17,850 --> 00:33:22,850
+relation R relates B فإذا A related أو A relates
+
+452
+00:33:22,850 --> 00:33:28,590
+to Bكلها مصطلحات ننطقها احنا مانشر كتير في النطاق
+
+453
+00:33:28,590 --> 00:33:33,250
+المهم ان نفهم الموضوع فانا بتكلم عن موضوع اشمل من
+
+454
+00:33:33,250 --> 00:33:36,330
+ال function اكثر شمولية شوية من ال function طيب ال
+
+455
+00:33:36,330 --> 00:33:40,830
+complementary ال relation لو فعلا عندك ال relation
+
+456
+00:33:40,830 --> 00:33:47,110
+a from a to b خلصنا منها معنى ذلك انه R complement
+
+457
+00:33:47,110 --> 00:33:53,930
+عملنا شرطة على ال R معناته انهA هو بيلا تحقق أو لا
+
+458
+00:33:53,930 --> 00:33:57,410
+تنتمي لل relation، معناه أنه لا تنتمي لل relation،
+
+459
+00:33:57,410 --> 00:34:01,630
+فإذا لمّانيش نقول مين من مستوى تالت أخو لمستوى
+
+460
+00:34:01,630 --> 00:34:03,810
+أول، يمكن نطلع في النهاية ال compliment كل
+
+461
+00:34:03,810 --> 00:34:08,930
+العلاقات، ليش؟ لأنه مافيش R أصلا، فال compliment
+
+462
+00:34:08,930 --> 00:34:13,290
+هو المكمل تبعها، المكمل تبعها، بالنسبة لمين؟ كلنا
+
+463
+00:34:13,290 --> 00:34:17,290
+عرفنا أنه لما بتكلم عن مكمل في ال 6، معناه ذلك أنه
+
+464
+00:34:17,290 --> 00:34:20,050
+لازم يكون في عند ال universe of discourse، فمين ال
+
+465
+00:34:20,050 --> 00:34:24,690
+universe of discourse تبعنا؟الـ Cartesian product
+
+466
+00:34:24,690 --> 00:34:29,690
+.. ال Cartesian product هي اللي أعطتك كل ال
+
+467
+00:34:29,690 --> 00:34:33,200
+possibilities الممكنةمنها مين بيحقق ال relation
+
+468
+00:34:33,200 --> 00:34:36,660
+ومين بيحققش ال relation إذا بيحققش معناته ال
+
+469
+00:34:36,660 --> 00:34:40,960
+complement المكمل لل relation المكمل لل relation
+
+470
+00:34:40,960 --> 00:34:45,480
+فإذا كأني بقول هيها ال complement لل relation هو
+
+471
+00:34:45,480 --> 00:34:51,100
+كل زوج مرتب لا ينتمي لل relation بمعنى أن هو ال
+
+472
+00:34:51,100 --> 00:34:55,080
+Cartesian product ناقص ال relation فإذا هو موجود
+
+473
+00:34:55,080 --> 00:34:58,480
+في ال Cartesian وغير موجود في ال relation حسب
+
+474
+00:34:58,480 --> 00:35:03,220
+فهمنا لها ال differenceفي ال sets مش هيك تمام و
+
+475
+00:35:03,220 --> 00:35:08,640
+بنقدر نكتبها اما بهذا الشكل خط مائل slash على ال R
+
+476
+00:35:08,640 --> 00:35:12,180
+مباشرة او بكتبها ال bar اللي انتوا عارفينها اللي
+
+477
+00:35:12,180 --> 00:35:15,220
+معناها ال inverse اللي كنا بنفهمها inverse فإذا
+
+478
+00:35:15,220 --> 00:35:18,200
+compliment في الحالة دي و كلنا فهمنا انه ليش ال
+
+479
+00:35:18,200 --> 00:35:19,820
+universive discourse بده يكون هو ال Cartesian
+
+480
+00:35:19,820 --> 00:35:25,300
+product بحيث نقدر نسمي منه ال compliment نقدر نسمي
+
+481
+00:35:25,300 --> 00:35:28,000
+لأن compliment معناته لازم يكون فيه بالنسبة لإيش
+
+482
+00:35:28,000 --> 00:35:32,140
+complimentهذا مكمل لل relation بالنسبة لإيش؟ بقى
+
+483
+00:35:32,140 --> 00:35:36,900
+لازم يكون عندى ثقف اللى محققش relation أكمل منه من
+
+484
+00:35:36,900 --> 00:35:40,440
+ال universe of discourse فال universe هي ال .. ال
+
+485
+00:35:40,440 --> 00:35:43,740
+Cartesian product طيب الآن ال compliment لها ال
+
+486
+00:35:43,740 --> 00:35:48,770
+compliment هي ال R نفسهاال inverse of inverse مش
+
+487
+00:35:48,770 --> 00:35:53,490
+مختلفين عليها الجثة ال compliment لا أصغر من ال
+
+488
+00:35:53,490 --> 00:35:57,710
+compliment أصغر من اللي هو أو يساوي بالظبط اللي هو
+
+489
+00:35:57,710 --> 00:36:01,470
+غير أصغر من فإيش اللي بيكمل غير أصغر من أكبر من أو
+
+490
+00:36:01,470 --> 00:36:06,850
+يساوي بالظبط فإذا a و b لا تحقق الأصغر من يعني a
+
+491
+00:36:06,850 --> 00:36:11,150
+ليست أصغر من b فإذا ممكن تسويها و ممكن أكبر منها
+
+492
+00:36:11,150 --> 00:36:16,000
+بدلا من ليست أصغر منها فإذا كأنها بتقولnegation a
+
+493
+00:36:16,000 --> 00:36:20,400
+بمعنى عكس a هو اللي أصغر من b وليس a نفسها وليس a
+
+494
+00:36:20,400 --> 00:36:27,420
+نفسها okay تمام جدا طيب الآن ال binary relation
+
+495
+00:36:27,420 --> 00:36:30,820
+هذه اللي هو يحقق ال relation أو لا يحقق ال
+
+496
+00:36:30,820 --> 00:36:36,970
+relation لما نيجي نطبقها على ال set نفسهاطب هنحتاج
+
+497
+00:36:36,970 --> 00:36:39,630
+نحملها على الست نفسها؟ أه هنحتاج لأنه شوية ال ..
+
+498
+00:36:39,630 --> 00:36:43,350
+هلوجت بدنا نحدد شوية محددات بالنسبالنا هلوجت أنا
+
+499
+00:36:43,350 --> 00:36:47,910
+بقول relation relation لمين؟ للأرقام مع بعضها مثلا
+
+500
+00:36:47,910 --> 00:36:51,810
+الأرقام مع بعضها معناه أن أنا بتكلم عن نفس الست مش
+
+501
+00:36:51,810 --> 00:36:54,970
+عن a و b بتكلم عن natural number فإذا من ال
+
+502
+00:36:54,970 --> 00:36:58,850
+natural number ل natural number أو بتكلم عن
+
+503
+00:36:58,850 --> 00:37:03,670
+relation بين الأشخاص فإذا people من ال people to
+
+504
+00:37:03,670 --> 00:37:09,670
+peopleفإذا ال A هي واحدة هي مش A وB مختلفة عنها هي
+
+505
+00:37:09,670 --> 00:37:14,890
+A ل A فكان من المهم جدا إنه تتحدد إنه relation
+
+506
+00:37:14,890 --> 00:37:20,710
+from a set A ل itself منها لنفسها منها لنفسها و
+
+507
+00:37:20,710 --> 00:37:24,930
+هنا بتسميها relation on the set A على ال set A
+
+508
+00:37:24,930 --> 00:37:28,390
+مباشرة هذا لا يعني إنه أنا بطلت بشتغل كارتيزيا لأ
+
+509
+00:37:28,390 --> 00:37:34,730
+أنا بشتغل كارتيزيا بس بين عناصر A مع عناصر Aحتى لو
+
+510
+00:37:34,730 --> 00:37:39,890
+ظهرت a مع a نفسه كمان حتى لو كانت الزوج المرتل
+
+511
+00:37:39,890 --> 00:37:44,150
+اللي بتفحصه هو a small مع a small أه بمشي الحال
+
+512
+00:37:44,150 --> 00:37:47,690
+هذا واحد من ال elements اللي ينتموا لاي ال
+
+513
+00:37:47,690 --> 00:37:52,890
+Cartesian product في الحالة هذه تمام فإذا في
+
+514
+00:37:52,890 --> 00:37:56,110
+الحالة هذه لو ما نقول أصغر من relation زي ما احنا
+
+515
+00:37:56,110 --> 00:38:00,650
+قلنا سابقا ممكن نعرفها على ال natural number ال
+
+516
+00:38:00,650 --> 00:38:03,750
+natural number و ال natural number هي نفسهافإذا من
+
+517
+00:38:03,750 --> 00:38:09,790
+الست لنفسها .. من الست لنفسها و لكل ال normal أو
+
+518
+00:38:09,790 --> 00:38:14,110
+ال natural numbers طيب ال identity relation او
+
+519
+00:38:14,110 --> 00:38:19,990
+ايه؟ ال I لإيه؟ ال identity relation هي الحالة هذه
+
+520
+00:38:19,990 --> 00:38:25,160
+أنه يجد علاقة بين العنصر و نفسه .. بين العنصرو
+
+521
+00:38:25,160 --> 00:38:28,680
+نفسه كويس بين العنصر و نفسه معناته بقدر أقول أن ال
+
+522
+00:38:28,680 --> 00:38:34,220
+A و A هو ينتمي لل capital A أكيد ينتمي لل 6A كلها
+
+523
+00:38:34,220 --> 00:38:36,620
+بس في الحالة هذه .. هذه الخصية عنده identity
+
+524
+00:38:36,620 --> 00:38:42,860
+relation اللي هي العنصر مع نفسه لما نقول والله في
+
+525
+00:38:42,860 --> 00:38:45,880
+القاعمين بحب نفسه أكتر من غيره أكيد كلنا A مع A
+
+526
+00:38:45,880 --> 00:38:55,890
+صحيح؟ ماتقولليش هلو جتضل في ..تمام؟ اثاره مش اثار
+
+527
+00:38:55,890 --> 00:39:00,370
+ال .. فهي مثلا واحدة من ال relations اللي موجودة و
+
+528
+00:39:00,370 --> 00:39:04,610
+قص على ذلك حاجات كتير هتلاقي فيها identity هتلاقي
+
+529
+00:39:04,610 --> 00:39:07,990
+فيها إيش؟ identity هتلاقي فيها جزئية ال identity و
+
+530
+00:39:07,990 --> 00:39:11,030
+أنا بحاول أجيبلك أمثلة شوية بعيدة عن الأرقام أما
+
+531
+00:39:11,030 --> 00:39:14,230
+أرقام هتلاقي أرقام كتير يعني لما أقولك ال function
+
+532
+00:39:14,230 --> 00:39:20,560
+أو ال .. البلطلةidentity function معناته كل نقطة
+
+533
+00:39:20,560 --> 00:39:24,680
+هي identity مع نفسها صحيح ا مع ا واحد مع واحد
+
+534
+00:39:24,680 --> 00:39:28,540
+اتنين مع اتنين خمسة مع خمسة نص مع نص هتلاقيهم كلهم
+
+535
+00:39:28,540 --> 00:39:32,120
+موجودين بيحققوا ال function أو الخط المستقيم هذا
+
+536
+00:39:32,120 --> 00:39:35,500
+اللي في الزاوية خمسة واربعين فإذا بالأرقام باينة
+
+537
+00:39:35,500 --> 00:39:39,340
+بس أنا بوضحلك أكتر و بحاول أجيبلك أمثلة أكبر من
+
+538
+00:39:39,340 --> 00:39:43,420
+مجرد الأرقام عشان أوضحلك أن ال relation هي أكبر
+
+539
+00:39:43,420 --> 00:39:43,900
+أوسع
+
+540
+00:39:46,550 --> 00:39:51,710
+اه طبعا ال compliment هي العكس ان انت كاره لنفسكأه
+
+541
+00:39:51,710 --> 00:39:53,690
+relation لو مابتش relation بدك تقول ال relation
+
+542
+00:39:53,690 --> 00:39:55,930
+على ال people و احنا هناخد بالمناسبة أمثلة كتير
+
+543
+00:39:55,930 --> 00:39:58,210
+على ال people هم ال .. يعني هم ال universe of
+
+544
+00:39:58,210 --> 00:40:02,710
+discourse و نحاول نطبق عليهم ال relation فحتجت أنه
+
+545
+00:40:02,710 --> 00:40:05,670
+في ناس كتير و خصوصا ساعة الامتحانات انت بتطلع من
+
+546
+00:40:05,670 --> 00:40:08,690
+الامتحان كارح حالك مش شايف انا كيف غلطت هالغلطة
+
+547
+00:40:08,690 --> 00:40:12,310
+كيف عملتها العامل مش شايف فهذه لحظة من اللحظات انت
+
+548
+00:40:12,310 --> 00:40:15,550
+بتحس حالك ان انت أصبحت معظم كسار compliment ل ..
+
+549
+00:40:15,550 --> 00:40:17,650
+لل relation هذه تمام
+
+550
+00:40:21,640 --> 00:40:25,140
+Okay Definition برضه هنرجع نيد ال relation اللي هي
+
+551
+00:40:25,140 --> 00:40:28,500
+على ال 6A فهي relation from A to A زي ما قلنا ناخد
+
+552
+00:40:28,500 --> 00:40:34,040
+المثال طبعنا ال cardinality زي ما قلنا لل universe
+
+553
+00:40:34,040 --> 00:40:38,920
+of discourse ككل هوA Cartesian A فمش معناه ان انا
+
+554
+00:40:38,920 --> 00:40:41,360
+بتكلم عن ايه معناته انا طلعت خارج ال Cartesian لأ
+
+555
+00:40:41,360 --> 00:40:45,720
+انا مازلت ضمن حدود ال Cartesian product تمام لو
+
+556
+00:40:45,720 --> 00:40:50,300
+أخدنا مثلا A عبارة عن واحد اتنين تلاتة أربعة بكفي
+
+557
+00:40:50,300 --> 00:40:57,460
+على جد ال order ال set هذه فهنا محتاجين نحدد من
+
+558
+00:40:57,460 --> 00:41:03,660
+اللي ينطبق عليه relation R A وB such that A أقل من
+
+559
+00:41:03,660 --> 00:41:13,240
+BA أقل من B فبكل بساطة نقدر نقول واحد واحد لأ واحد
+
+560
+00:41:13,240 --> 00:41:19,840
+اتنين اه واحد تلاتة واحد اربعة تمام اتنين واحد
+
+561
+00:41:19,840 --> 00:41:26,100
+اتنين اتنين اتنين تلاتة اتنين اربعة and so on
+
+562
+00:41:26,100 --> 00:41:29,220
+فوضحت الان ال relations في المثال
+
+563
+00:41:32,000 --> 00:41:34,920
+لأ لأ لأ لأ مش ال power لأ ال power مختلفة ال
+
+564
+00:41:34,920 --> 00:41:38,660
+power انت بتعمل كل .. معناها ان كل ال subsets من
+
+565
+00:41:38,660 --> 00:41:42,880
+.. من ال Cartesian product اللي هي كل ال subset من
+
+566
+00:41:42,880 --> 00:41:48,040
+ال setتمام فهنا بتقدر نمثلها بالشكل اللي احنا
+
+567
+00:41:48,040 --> 00:41:52,420
+شايفينه هنا حاطناهم جميع العناصر اللي بيحققوا ال
+
+568
+00:41:52,420 --> 00:41:55,860
+relation بيحققوا ال relation بتقدر طبعا بال
+
+569
+00:41:55,860 --> 00:41:59,420
+bipartate و احنا مثلنا ال set سابقا باستخدام ال
+
+570
+00:41:59,420 --> 00:42:02,480
+bipartate او ال function مثلناها بال bipartate
+
+571
+00:42:02,480 --> 00:42:04,800
+فممكن اقول هاي العناصر تبعتي واحد اتنين تلاتة
+
+572
+00:42:04,800 --> 00:42:10,420
+اربعةواحد لواحد لأ هو مش محقق ال relation فها دي
+
+573
+00:42:10,420 --> 00:42:14,540
+zero واحد اتنين اه واحد تلاتة واحد اربعة اتنين
+
+574
+00:42:14,540 --> 00:42:19,440
+تلاتة اتنين اربعة واحد اربعة نرسمهم بهذا الشكل او
+
+575
+00:42:19,440 --> 00:42:26,980
+بتقدر ترسمهم بشكل table ال table هذا from twoف
+
+576
+00:42:26,980 --> 00:42:33,980
+from ال raw to column from raw ل ال column فإذا
+
+577
+00:42:33,980 --> 00:42:37,380
+بنكتبها بهذا الشكل هذا ال او الأول وهذا التاني
+
+578
+00:42:37,380 --> 00:42:42,920
+تمام فإذا من واحد ل واحد لأ واحد لاتنين yes فهذا
+
+579
+00:42:42,920 --> 00:42:47,360
+موجود ضمن ال relation واحد تلاتة واحد أربعة تمام
+
+580
+00:42:47,360 --> 00:42:51,400
+كلهم موجودين اتنين اتنين مثلا لأ غير موجود و هكذا
+
+581
+00:42:51,400 --> 00:42:59,560
+فبتكتبوا نفسهم بهذا الشكل ماتعكسوشهنا from و هنا
+
+582
+00:42:59,560 --> 00:43:06,020
+to from to تمام فهذه التمثيل اللي هناخده لقدام كيف
+
+583
+00:43:06,020 --> 00:43:08,840
+نمثل ال relations فممكن ييجيك برضه سؤال اعطيك
+
+584
+00:43:08,840 --> 00:43:12,420
+relation معينة او اقولك مثل انياها اما bipartate
+
+585
+00:43:12,420 --> 00:43:16,660
+او اقولك والله بال matrix فبدك تمثلها ما تخربطوا
+
+586
+00:43:16,660 --> 00:43:24,160
+مش مع بعضتمام نختم في حاجة مهمة how many different
+
+587
+00:43:24,160 --> 00:43:29,500
+relations can we define on a set A within elements
+
+588
+00:43:29,500 --> 00:43:39,760
+عندي ال set A هي
+
+589
+00:43:39,760 --> 00:43:48,550
+دي عدد خليني أقول ال cardinality لها Nحسب التعريف
+
+590
+00:43:48,550 --> 00:43:54,910
+check within elements within elements مبدأيا اللي
+
+591
+00:43:54,910 --> 00:43:58,470
+مطلوب جداش عدد ال relations اللي ممكن نعملها من
+
+592
+00:43:58,470 --> 00:44:06,250
+الست هذه مضحك السؤال تمام تمام شوية شوية نركز فيها
+
+593
+00:44:06,250 --> 00:44:08,910
+شوية الآن احنا قولنا إيش ال relation عبارة عن إيش
+
+594
+00:44:08,910 --> 00:44:15,370
+عرفناها subset مش قولنا subset subset من إيش من ال
+
+595
+00:44:15,370 --> 00:44:20,060
+Cartesian productمن Cartesian product يعني from a
+
+596
+00:44:20,060 --> 00:44:23,980
+Cartesian product a يعني هذه ال Cartesian product
+
+597
+00:44:23,980 --> 00:44:29,940
+المفروض انه بدي اخد ال cardinality بتاعتها هي n في
+
+598
+00:44:29,940 --> 00:44:38,740
+في n مظبوط تمام هذه بتساوي n تربيع هاي ال n تربيع
+
+599
+00:44:38,740 --> 00:44:42,940
+اللي بنتكلم عنها ممتازهد مين الـ Interbial؟ هي
+
+600
+00:44:42,940 --> 00:44:47,480
+فعليًا عدد ال elements بتاعة ال Cartesian product
+
+601
+00:44:47,480 --> 00:44:50,880
+لسه مادخلتش ع ال relation ولا اتكلمتش عن ال
+
+602
+00:44:50,880 --> 00:44:54,520
+relation ال relation لسه ماجبناش سرتها حتى الآن
+
+603
+00:44:54,520 --> 00:44:58,840
+جبنا بس ال universe of discourse تبعنا فال
+
+604
+00:44:58,840 --> 00:45:02,560
+universe of discourse إلنا وجدنا إنه طلع مجموعة
+
+605
+00:45:02,560 --> 00:45:03,220
+عناصر
+
+606
+00:45:13,170 --> 00:45:19,450
+الان عشان نعمل منهم relation هاخد
+
+607
+00:45:19,450 --> 00:45:22,790
+كلمة واحد من الشباب اللي سألني فيها أظن مش مهندس
+
+608
+00:45:22,790 --> 00:45:27,170
+قاللي على ال powerال power احنا ايش توجهلناه؟ لما
+
+609
+00:45:27,170 --> 00:45:32,090
+جوابته قلتله هذه هي ال subset من ال set المعطاه
+
+610
+00:45:32,090 --> 00:45:37,570
+عند set كل ال subsets الممكنة بنسميها ال power طيب
+
+611
+00:45:37,570 --> 00:45:42,530
+طب ما احنا كنا بنعرف ان relation هي subset من ال
+
+612
+00:45:42,530 --> 00:45:45,890
+Cartesian product طب قدش عدد ال subsets الممكنين؟
+
+613
+00:45:45,890 --> 00:45:50,510
+لأن كل واحدة منهم تمثل relation لحالها كل واحدة
+
+614
+00:45:50,510 --> 00:45:55,960
+منهم ممكن تتمثل relationcheck تمام فإذن لفنا و
+
+615
+00:45:55,960 --> 00:45:59,060
+دورنا و رجعنا لنفس النقطة إن أنا قاعد بحسب ال
+
+616
+00:45:59,060 --> 00:46:04,540
+power بتاعة ال set بتاعة ال ال ال ال Cartesian
+
+617
+00:46:04,540 --> 00:46:07,860
+product لإن هو هذي هتطني كل ال elements الممكنين
+
+618
+00:46:07,860 --> 00:46:12,840
+داخل ال relation فإذن ممكن يكون 0 0 0 0 0 كلهم
+
+619
+00:46:12,840 --> 00:46:20,260
+zeros بمعنى إنه relation Phi أو العنصر الأول موجود
+
+620
+00:46:20,260 --> 00:46:24,360
+والباقي لأأو العنصر التاني اللي موجود و الباقي لأ
+
+621
+00:46:24,360 --> 00:46:27,480
+أو التالت اللي موجود و الباقي لأ أو الخامس اللي
+
+622
+00:46:27,480 --> 00:46:29,980
+موجود و الباقي لأ أو الانتربيع اللي موجود و الباقي
+
+623
+00:46:29,980 --> 00:46:34,620
+لأ أو الأول و التاني موجودين و الباقي لأ لاحظت جدش
+
+624
+00:46:34,620 --> 00:46:39,340
+عدد ال possibilities ل subset ممكنين منها و احنا
+
+625
+00:46:39,340 --> 00:46:44,660
+أخدناها سابقا كنا بنقول اتنين to the power ال
+
+626
+00:46:44,660 --> 00:46:48,850
+cardinality لإيههذه لما أخدناها بصفة .. بصفة عامة
+
+627
+00:46:48,850 --> 00:46:50,970
+عساسا ان ال cardinality ل a هي اللي بدي أجيبها ال
+
+628
+00:46:50,970 --> 00:46:54,690
+power بس أنا مابديش أجيب ال a لل power الآن مابديش
+
+629
+00:46:54,690 --> 00:46:57,650
+أجيب ال cardinality لل a لل power لأن مابدي أجيبها
+
+630
+00:46:57,650 --> 00:47:05,350
+لمين ال Cartesian product معناته ايوة a Cartesian
+
+631
+00:47:05,350 --> 00:47:09,430
+product a فهيك
+
+632
+00:47:09,430 --> 00:47:12,490
+بنكون جبناها طيب هذه احنا لسه توجب .. اتكلمنا عنها
+
+633
+00:47:12,490 --> 00:47:18,940
+عبارة عن in تربيعin تربية هو ده الكلمة طلع معانا
+
+634
+00:47:18,940 --> 00:47:24,370
+مظبوطهي ال Interbia واضحة درجنا فيها من البداية
+
+635
+00:47:24,370 --> 00:47:27,510
+حينا حددناها ال Cartesian product معناته بتطلع ان
+
+636
+00:47:27,510 --> 00:47:31,130
+Interbia كcardinality total cardinality ال total
+
+637
+00:47:31,130 --> 00:47:34,190
+cardinality هذا معناته عدد العناصر في ال universe
+
+638
+00:47:34,190 --> 00:47:37,750
+of discourse اللي اتفقنا عليه لل relation على
+
+639
+00:47:37,750 --> 00:47:39,650
+اعتبار انه جولنا ال universe of discourse هي ال
+
+640
+00:47:39,650 --> 00:47:44,590
+cardinality لمين؟ لل Cartesian product طيب لما بدي
+
+641
+00:47:44,590 --> 00:47:47,370
+أجيب كل ال subsets الممكنين حسب التعريف ال
+
+642
+00:47:47,370 --> 00:47:51,090
+relation هي subset منالـ Cartesian product معناته
+
+643
+00:47:51,090 --> 00:47:56,510
+كإني بجيب ال power لل universe of discourse واللي
+
+644
+00:47:56,510 --> 00:47:59,390
+هي ال Cartesian product ف2nd to the power ال
+
+645
+00:47:59,390 --> 00:48:02,810
+cardinality لل set اللي بدور عليها أو ال universe
+
+646
+00:48:02,810 --> 00:48:07,030
+of discourse واللي هي N تربيع تمام، هيك و نكون
+
+647
+00:48:07,030 --> 00:48:10,720
+خلصناعلى جد الجزء هذا اللي هي المقدمة لل relations
+
+648
+00:48:10,720 --> 00:48:13,960
+عشان المرة اللي جاية ناخد مجموعة characteristic لل
+
+649
+00:48:13,960 --> 00:48:18,940
+relations و نشوف كيف بنقدر نعرفهم و نكمل في موضوع
+
+650
+00:48:18,940 --> 00:48:20,480
+ال relations يعطوكوا العفو و بركة الله فيكم
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Wt6C7l1t9pk_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Wt6C7l1t9pk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e9892b8da9adfb9dcfd5c2c9535af235ca7b26ef
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Wt6C7l1t9pk_raw.srt
@@ -0,0 +1,2600 @@
+1
+00:00:05,080 --> 00:00:10,040
+طيب، يعطيكوا العفو يا شباب، نكمل اليوم في موضوع ال
+
+2
+00:00:10,040 --> 00:00:13,280
+recurrence relation، المرة الماضية كنا اتكلمنا عن
+
+3
+00:00:13,280 --> 00:00:18,400
+ال recurrence relation و شفنا مجموعة أمثلة اللي
+
+4
+00:00:18,400 --> 00:00:22,990
+احنا بنقدر نقول بتاخد شكل ال relation بتاعتهابين
+
+5
+00:00:22,990 --> 00:00:27,770
+كل قيمة و القيمة السابقة لها بتاخد شكل recurrence
+
+6
+00:00:27,770 --> 00:00:31,470
+relation بمعنى ان كل قيمة هي معتمدة بشكل او باخر
+
+7
+00:00:31,470 --> 00:00:37,270
+ضمن معادلة معينة على القيمة السابقة لها و أخدنا
+
+8
+00:00:37,270 --> 00:00:41,590
+مجموعة أنفلة منها كانت تربيات الأرانب زي ما
+
+9
+00:00:41,590 --> 00:00:46,030
+بتذكرين و إيش علاقتها بين كل شهر و الشهر اللي ورا
+
+10
+00:00:46,030 --> 00:00:48,970
+جدش ممكن يكون العدد او ال couples تبع ال rabbits
+
+11
+00:00:48,970 --> 00:00:54,710
+دولةكويس و بعدين اتكلمنا عن الفائدة
+
+12
+00:00:54,710 --> 00:00:59,530
+المركبة صحيح و وجدنا ان هي فعليا فعلا فائدة على
+
+13
+00:00:59,530 --> 00:01:01,970
+الشهر اللي جابلها طب الشهر اللي جابلها جدش كانت
+
+14
+00:01:01,970 --> 00:01:05,850
+قيمته؟ قيمته اللي جابله مع الفائدة تبعته و اللي
+
+15
+00:01:05,850 --> 00:01:12,390
+جابله و هكذا فبشكل تراكمي هي معادلة او علاقة
+
+16
+00:01:12,390 --> 00:01:19,210
+تكرارية ف recurrence relationاتكلمنا عن ال Hanoi
+
+17
+00:01:19,210 --> 00:01:22,930
+أو ال tower of Hanoi إذا متذكرين و برضه وجدنا إنه
+
+18
+00:01:22,930 --> 00:01:26,990
+عشان نحله بنقدر نعمله بشكل recurrence relation
+
+19
+00:01:26,990 --> 00:01:32,290
+تمام فكانت الفكرة كلها إنه أي recurrence relation
+
+20
+00:01:32,290 --> 00:01:40,520
+هي معتمدة على الحالة السابقة لها سواءعلى الحالة
+
+21
+00:01:40,520 --> 00:01:44,660
+السابقة فقط او اتنين تلاتة من الحالات السابقة حسب
+
+22
+00:01:44,660 --> 00:01:47,880
+فاتنين تلاتة معناه انك تقول ان ناقص واحد ان ناقص
+
+23
+00:01:47,880 --> 00:01:53,500
+اتنين ان ناقص تلاتة جدش عددهم هسميهم in general K
+
+24
+00:01:53,500 --> 00:02:00,850
+فهي معتمدة على K previous terms خليني نسميهافمعتمد
+
+25
+00:02:00,850 --> 00:02:06,350
+على مجموعة قيم سابقة عددهم K مثلا تمام، ضالت الآن
+
+26
+00:02:06,350 --> 00:02:11,450
+الفكرة أنه عشان أعرف قداش قيمة الان هذه في زمن
+
+27
+00:02:11,450 --> 00:02:17,850
+معين أو في N عند ال N مش مضطر أجيب أجيب N ناقص
+
+28
+00:02:17,850 --> 00:02:20,390
+واحد و N ناقص اتنين و N ناقص تلاتة و خصوصا إذا
+
+29
+00:02:20,390 --> 00:02:25,630
+كانت قيمة N أساساهي قيمة كبيرة فمعنى ذلك انه هيكون
+
+30
+00:02:25,630 --> 00:02:30,130
+مضي على الوقت اني اقعد اشتغل كل term باللي قبله
+
+31
+00:02:30,130 --> 00:02:34,770
+لعند ما نصل لمين لل term A naught اللي هو ال
+
+32
+00:02:34,770 --> 00:02:38,470
+initial value تبعتنا هتكون كتير صعبة الجثة بهذا
+
+33
+00:02:38,470 --> 00:02:42,070
+الشكل فكان ضروري جدا ان نروح ل closed form ل
+
+34
+00:02:42,070 --> 00:02:48,080
+relation هي علاقة بال locationو ليست بال term اللي
+
+35
+00:02:48,080 --> 00:02:51,040
+قبله .. و ليست بال term اللي قبله فمعنى ذلك ان ال
+
+36
+00:02:51,040 --> 00:02:54,620
+an هذه لازم تكون هي function في حاجة اللي هي علاقة
+
+37
+00:02:54,620 --> 00:02:59,920
+بال n نفسها ب n مباشرة مش ب n ناقص واحد ليس ب n
+
+38
+00:02:59,920 --> 00:03:05,340
+ناقص واحد جدش هيكون شكلها كيف شكلهامش عارفين مش
+
+39
+00:03:05,340 --> 00:03:09,340
+عارفين لكن هذا هو ال closed form اللي بندور عليه
+
+40
+00:03:09,340 --> 00:03:11,600
+هذا ال closed form اللي بندور عليه ممكن تكون في
+
+41
+00:03:11,600 --> 00:03:15,880
+النهاية متغير او constant اذا بدناها تكون constant
+
+42
+00:03:15,880 --> 00:03:21,400
+to the power قيمة n هذه مثلا فبضل ان انا اعرف جداش
+
+43
+00:03:21,400 --> 00:03:25,120
+ال term هذا بالضبط على اساس انه اجيب form بهذا
+
+44
+00:03:25,120 --> 00:03:29,340
+الشكل قيمة a n اجيبها مباشرة مش محتاج اجيبها من ان
+
+45
+00:03:29,340 --> 00:03:33,060
+ناقص واحد لكن السؤال كيف بده اجيب هذا ال form اصلا
+
+46
+00:03:34,140 --> 00:03:37,700
+الفكرة ان و الله اه هذا ما انتمنى نفعلها نجيبها
+
+47
+00:03:37,700 --> 00:03:43,480
+بهذا الشكل فهي closed form ل a n مباشرة أحسبها و
+
+48
+00:03:43,480 --> 00:03:49,460
+خلصنا لكن كيف نجيب هذا الكلام من علاقة أساسا جياني
+
+49
+00:03:49,460 --> 00:03:54,200
+بال terms السابقة فهذا اللي هنتكلم عنه ابتداء
+
+50
+00:03:54,200 --> 00:03:59,060
+اليوم فاللي هو solving the recurrences و بنستخدم
+
+51
+00:03:59,060 --> 00:04:04,350
+ال linear homogeneous recurrence of degree kK اللي
+
+52
+00:04:04,350 --> 00:04:08,470
+هو كام term سابق انا محتاج عشان احسب ال term
+
+53
+00:04:08,470 --> 00:04:13,010
+اللاحق كام term سابق فبنسميها degree K فهنا عددهم
+
+54
+00:04:13,010 --> 00:04:16,690
+مثلا K فبنسميها degree تبعت الاش تاعة ال
+
+55
+00:04:16,690 --> 00:04:20,250
+recurrence relation with constant coefficient
+
+56
+00:04:20,250 --> 00:04:23,830
+فهنقول انه بدي افترض ان constant ارها دي constant
+
+57
+00:04:25,170 --> 00:04:28,370
+constant خلاص coefficient و بدنا نشوف إيش ال
+
+58
+00:04:28,370 --> 00:04:31,950
+constant المناسب بحيث إنه فعلا a n هدا يكون
+
+59
+00:04:31,950 --> 00:04:35,570
+function في n نفسها في ال location مش في ال terms
+
+60
+00:04:35,570 --> 00:04:39,090
+اللي قبلها مش في ال terms اللي قبلها فإجت الإسم
+
+61
+00:04:39,090 --> 00:04:42,690
+تبعت الطريقة بتاعتنا linear لإن أنا بتعامل معه
+
+62
+00:04:42,690 --> 00:04:43,410
+linear
+
+63
+00:04:46,250 --> 00:04:50,450
+ان بتساوي الناقص واحد الناقص اتنين مش الناقص واحد
+
+64
+00:04:50,450 --> 00:04:54,910
+تربيه الناقص اتنين التكعيب لأ هي linear هي سبب
+
+65
+00:04:54,910 --> 00:05:00,270
+التسميع homogeneous بمعنى انه ان معتمد على ال K
+
+66
+00:05:00,270 --> 00:05:05,970
+اللي جرب منها مش والله افترض ان هنا an ناقص واحد
+
+67
+00:05:05,970 --> 00:05:13,040
+ناقص en ناقص سبعة زائد en ناقص اربعتاشفلأ هي
+
+68
+00:05:13,040 --> 00:05:17,300
+homogeneous هي متجانسة هي متجانسة عشان نقدر نحلها
+
+69
+00:05:17,300 --> 00:05:21,980
+تمام with constant coefficients زي ما قلنا فيندي
+
+70
+00:05:21,980 --> 00:05:26,160
+constant coefficients هنا هذه إلها ثابت ال
+
+71
+00:05:26,160 --> 00:05:29,160
+constants بتاعتها كلها ثابتة وكل ال constants هذه
+
+72
+00:05:29,160 --> 00:05:35,600
+لا تساوي صفر لإن لو واحدة منهم صارت صفرhome genius
+
+73
+00:05:35,600 --> 00:05:39,500
+بطلت home genius بطلت home genius أو متجانسة
+
+74
+00:05:39,500 --> 00:05:42,580
+فمعناه ذلك أن ال term تبعنا به هذا الشكل in
+
+75
+00:05:42,580 --> 00:05:48,480
+general الآن صحيح هي ال a n هي constant في a n نقص
+
+76
+00:05:48,480 --> 00:05:52,600
+واحد constant في a n نقص اتنين لعند c k ال
+
+77
+00:05:52,600 --> 00:05:57,130
+constant رقم k على اعتبار أنه صار عندي k termفي a
+
+78
+00:05:57,130 --> 00:06:03,270
+n ناقص k فهي k بتاعة ال degree بتاعتنا لعندي الان
+
+79
+00:06:03,270 --> 00:06:08,110
+هذا الشكل اللي بدنا نشتغل عليه الشكل الشغلة المهمة
+
+80
+00:06:08,110 --> 00:06:11,370
+ان ال coefficients هدولة لاتوا سوا صفر عشان احقق
+
+81
+00:06:11,370 --> 00:06:15,710
+كلمة homogeneous عشان نحقق كلمة homogeneous تمام
+
+82
+00:06:16,450 --> 00:06:20,650
+معلومة مهمة جدا سواء بدي اشتغل بهذا الشكل او حتى
+
+83
+00:06:20,650 --> 00:06:25,210
+لو حولتها ل closed form ايش هو انه عشان اجيب AN
+
+84
+00:06:25,210 --> 00:06:32,570
+انا محتاج K initial values شك بقول مش هنعرف نحلها
+
+85
+00:06:32,570 --> 00:06:35,930
+يعني اكيد مش هتعرف تحلها انت الان كأنه عندك عدد
+
+86
+00:06:35,930 --> 00:06:41,130
+معادلات بدك إلها عدد مش ههي تكون عارفهم بعدد
+
+87
+00:06:41,130 --> 00:06:45,270
+المعادلات تبعتك كويس واحد اتنين تلاتة فعندي K
+
+88
+00:06:46,340 --> 00:06:48,880
+constants بدنا نجيبهم دول لازم يتجسدوا هنا لازم
+
+89
+00:06:48,880 --> 00:06:54,640
+يكونوا بينين هناطيب معناته بدهم قيم مسبقة معروفة
+
+90
+00:06:54,640 --> 00:06:58,320
+عشان هيك هنكون نفس الشرط هو هو سواء بتشتغل في ال
+
+91
+00:06:58,320 --> 00:07:01,000
+recurrence relation أو في ال closed form انت محتاج
+
+92
+00:07:01,000 --> 00:07:05,580
+k terms ك initial values as a initial values فهم
+
+93
+00:07:05,580 --> 00:07:07,600
+هدول مش همتوا ال conditions ال initial conditions
+
+94
+00:07:07,600 --> 00:07:13,280
+اللي هي من a node to k ناقص واحد فعددهم k عددهم k
+
+95
+00:07:13,280 --> 00:07:19,540
+حسب ال degree اللي بنشتغل عليها تمامفإذن الآن
+
+96
+00:07:19,540 --> 00:07:24,380
+الفرضية اللى بنفرضها أن a n هذا المفروض أنه يكون
+
+97
+00:07:24,380 --> 00:07:31,280
+constant to the power n جداش لازم يكون ال constant
+
+98
+00:07:31,280 --> 00:07:35,100
+هذا أنا مش عارف هل هينضرب برا في constant تاني
+
+99
+00:07:35,100 --> 00:07:38,260
+مثلا يكون والله هنا برضه في عندى طبعا لاحقا
+
+100
+00:07:38,260 --> 00:07:42,360
+هنسميها Alpha Alpha و R معناه اتصل عندى مجهولين
+
+101
+00:07:42,360 --> 00:07:46,020
+هدول لازم أعرفهم لأن هدول ممكن يغيروا ويبدلوا في
+
+102
+00:07:46,020 --> 00:07:51,860
+قيمالـ A N حسب ما يتوافق مع المعادلة الـ
+
+103
+00:07:51,860 --> 00:07:54,840
+Recurrence Relation الحقيقية فعليا فلازم نكون
+
+104
+00:07:54,840 --> 00:07:58,820
+مربطين في بعض بمعنى أن هذه المعادلة هي لازم تيجي
+
+105
+00:07:58,820 --> 00:08:02,580
+من هنا لأن هذا ال given عندي أنا عندي هذه لكن بدا
+
+106
+00:08:02,580 --> 00:08:08,340
+نجيبها بشكل closed form تمام فإذا لو مسكنا هذا ال
+
+107
+00:08:08,340 --> 00:08:13,100
+term هلاجي النهيه بالنسبة لي مكانه بإيش ب R to the
+
+108
+00:08:13,100 --> 00:08:18,530
+power Nتمام الناقص واحد ال C بتاعتها زي ما هي ما
+
+109
+00:08:18,530 --> 00:08:21,130
+هي كانت مضروبة في ال coefficient في C واحد سميناها
+
+110
+00:08:21,130 --> 00:08:25,450
+بس هنا هتصير R to the power الناقص واحد على اعتبار
+
+111
+00:08:25,450 --> 00:08:28,550
+ان ال R هذه زي ما هي ظابطة ل N المفروض انها بتصبط
+
+112
+00:08:28,550 --> 00:08:32,930
+ل الناقص واحد ماهي ده closed form بمعنى انا هقولك
+
+113
+00:08:32,930 --> 00:08:37,620
+جبلنا A عشرةطب إيش يعني لو قلتلك GA تسعة مش هتظبط
+
+114
+00:08:37,620 --> 00:08:41,080
+ال closed form؟ الاصل أنها تظبط الاصبط أن هو
+
+115
+00:08:41,080 --> 00:08:45,320
+المفروض أن هذا general form general form فمعنى ذلك
+
+116
+00:08:45,320 --> 00:08:49,480
+أنه بقدر أقول R to the power الناقص واحد C2 في R
+
+117
+00:08:49,480 --> 00:08:54,300
+to the power الناقص اتنين لما نصل لCK R to the
+
+118
+00:08:54,300 --> 00:08:59,180
+power الناقص Kهكي استعادنا عن المعادلة هذه بال
+
+119
+00:08:59,180 --> 00:09:02,340
+coefficients أو بال roots بتاعتها خلينا نسميها بال
+
+120
+00:09:02,340 --> 00:09:05,680
+Rs بتاعتها اللي المفروض تمثلها لكن أنا مش عارف جدش
+
+121
+00:09:05,680 --> 00:09:10,200
+قيمها فعاليا جدش قيمها حتى اللحظة طيب ال term ده
+
+122
+00:09:10,200 --> 00:09:16,360
+شوية بايخ أو تجيل أو بده تظبط بده تظبط أبسط شغلة
+
+123
+00:09:16,360 --> 00:09:20,920
+أنا صرت أتعامل مع roots مع ال Rs هدولة طيب ال Rs
+
+124
+00:09:20,920 --> 00:09:26,970
+هدولة محتاج أخفف ال weight تبعهمبس relatively ال
+
+125
+00:09:26,970 --> 00:09:30,910
+terms بتظهر زي بعضها بدي أجسم عفوا أجسم على أصغر
+
+126
+00:09:30,910 --> 00:09:34,810
+واحد فيهم انت بتقسم المعادلة كلها على نفس ال term
+
+127
+00:09:34,810 --> 00:09:39,950
+خلاص يمين و شمال مش هتفرج معاك فإذا أصغر term هو
+
+128
+00:09:39,950 --> 00:09:40,870
+هذا ال term
+
+129
+00:09:48,870 --> 00:09:52,050
+وانجلوا كله على ناحية التانية فصار كله بيسوا صفر
+
+130
+00:09:52,050 --> 00:09:55,490
+فمعنى ذلك لما بتقسم مش هتفرج معاك لما انت بتقسم
+
+131
+00:09:55,490 --> 00:09:59,170
+صفر على ال term هذا صفر على هذا ال term خد كل
+
+132
+00:09:59,170 --> 00:10:05,970
+هدولة على ناحية التانية بالسالب صار أيش؟ بيسوا
+
+133
+00:10:05,970 --> 00:10:13,190
+zero بيسوا zero لما نقسم على أصغر term ل Rفانت في
+
+134
+00:10:13,190 --> 00:10:15,950
+الطرف التاني zero هي هي مش هتفرج معاك كتير خدوا
+
+135
+00:10:15,950 --> 00:10:23,110
+common و أشطبه تمام فهنا R to the power N على R to
+
+136
+00:10:23,110 --> 00:10:27,210
+the power N ناقص K فبتصير R to the power K ناقص
+
+137
+00:10:27,210 --> 00:10:31,430
+فهنا برضه K ناقص واحد هنا بتصير K ناقص اتنين لعند
+
+138
+00:10:31,430 --> 00:10:34,930
+اخر term انت قسمت على كل ال term اللي معه فبتضل ال
+
+139
+00:10:34,930 --> 00:10:40,470
+constant لحالها يساوي صفر فصارت معادلة من الدرجة K
+
+140
+00:10:41,430 --> 00:10:44,430
+بينوميال من الدرجة من الدرجة K بدك تجيب ال roots
+
+141
+00:10:44,430 --> 00:10:50,230
+بتاعتها فحولناها لمعادلة جذرية بدك تجيب مجموعة ال
+
+142
+00:10:50,230 --> 00:10:55,730
+roots بتاعتها فقط جداش ال K هي اللي بتفرق معاك هل
+
+143
+00:10:55,730 --> 00:11:00,210
+تربيع تكعيب تتبارخمسة طب مين اللي بيحددها عدد ال
+
+144
+00:11:00,210 --> 00:11:04,710
+terms اللي انا محتاجها عشان اجيب كل قيمةالقيمة هنا
+
+145
+00:11:04,710 --> 00:11:08,670
+محتاجة K مع أنها توحدت درجة K فإذا من ال order K
+
+146
+00:11:08,670 --> 00:11:13,150
+طبعا هتكون صعبة شوية وهذا بتسميه في الآخر كمعادلة
+
+147
+00:11:13,150 --> 00:11:15,170
+أصبحت اسمها characteristic roots
+
+148
+00:11:18,290 --> 00:11:21,590
+كويس عشان نشتغل الكلام هذا و نقدر نحله بيدويا
+
+149
+00:11:21,590 --> 00:11:25,430
+بشغلنا طب انت في الآخر بتقدر تعمم هذا الكلام إذا
+
+150
+00:11:25,430 --> 00:11:28,210
+بتقدر تشتغل لدرجة K بس هيكون عن طريق الحسوب مش
+
+151
+00:11:28,210 --> 00:11:32,870
+هتقدر تشتغل على إيدك يدوي عشان أننا نحل نقدر نشتغل
+
+152
+00:11:32,870 --> 00:11:37,170
+بإيدنا و يدوي فهنحولها لاتنين بكافة و ناخد أمثلتنا
+
+153
+00:11:37,170 --> 00:11:40,550
+كلها علىالاتنين اللي هي بتصير اسمها quadratic form
+
+154
+00:11:40,550 --> 00:11:43,810
+.. quadratic form فتربيعية كلنا بنعرف نحل
+
+155
+00:11:43,810 --> 00:11:47,150
+التربيعية صح كلكوا بتقدروا تجيب ال roots لتربيعية
+
+156
+00:11:47,150 --> 00:11:50,850
+فبتكون سهل الأمور مافيش أي مشكلة otherwise طبعا
+
+157
+00:11:50,850 --> 00:11:53,030
+هتصير على الكمبيوتر بدك تجيبه عن طريق الكمبيوتر
+
+158
+00:11:53,030 --> 00:11:55,450
+تجيب ال code اللي هو يجيب ال roots ال k roots
+
+159
+00:11:55,450 --> 00:11:58,330
+هدولة إذا كان انت اضطرتش في ال k تمام
+
+160
+00:12:01,960 --> 00:12:05,480
+فإذا إذا كان الآل حولنا بدل ما كانت K linear
+
+161
+00:12:05,480 --> 00:12:08,460
+homogeneous recurrence with constant coefficients
+
+162
+00:12:08,460 --> 00:12:12,720
+لأ مش K2 بدنا نقول إن هي من الدرجة التانية من
+
+163
+00:12:12,720 --> 00:12:18,880
+الدرجة التانية معناته أصبحت An زي مين في بناتشي زي
+
+164
+00:12:18,880 --> 00:12:23,860
+في بناتشي مثلا C1 في A N نقص واحد زائد C2 في A نقص
+
+165
+00:12:23,860 --> 00:12:28,100
+اتنينكويس و طبعا في بناتش كانت هنا واحد و واحد
+
+166
+00:12:28,100 --> 00:12:31,360
+صحيح ال C هدولة C واحد و C اتنين كانوا واحد و واحد
+
+167
+00:12:31,360 --> 00:12:34,640
+اللي هي مجموع القيمتين السابقين هدول نفس الكلام
+
+168
+00:12:34,640 --> 00:12:39,780
+اعمل نفس الفكرة عوض بدل كل A ب R to the power ال
+
+169
+00:12:39,780 --> 00:12:42,320
+order تبعها ال N هنا او N ناقص واحد او ناقص اتنين
+
+170
+00:12:42,320 --> 00:12:50,380
+كويس و اقسم على R N ناقص اتنينفبيظل عندك R² ناقص
+
+171
+00:12:50,380 --> 00:12:54,680
+هده هتاخد على ناحية التانية C1 في R ناقص هده هتاخد
+
+172
+00:12:54,680 --> 00:12:58,100
+على ناحية التانية C2 معادلة من ال quadratic form
+
+173
+00:12:58,100 --> 00:13:02,860
+بنقدر نجيب بكل بساطة قيم R وأكيد هيطلع كم قيمة
+
+174
+00:13:02,860 --> 00:13:08,870
+لـR؟ two values فعندي R1 وعندي R2على اعتبار ان هي
+
+175
+00:13:08,870 --> 00:13:11,590
+quadratic form فمعنى ذلك انه هيطلع عندك two roots
+
+176
+00:13:11,590 --> 00:13:16,290
+ال two roots هدولة كيف بقدر امثلهم في ال closed
+
+177
+00:13:16,290 --> 00:13:19,770
+form عشان احطهم في closed form واضح معنى ذلك اذا
+
+178
+00:13:19,770 --> 00:13:23,030
+كانت هنا بتعامل مع قيمة واحدة تطلع بهذا الشكل بس
+
+179
+00:13:23,030 --> 00:13:26,210
+واضح ان انا محتاج قيمتين سابقتين فمعنى ذلك انه
+
+180
+00:13:26,210 --> 00:13:30,310
+برضه هتكون زائد R to the power N تانية بس كل واحدة
+
+181
+00:13:30,310 --> 00:13:36,310
+ب coefficient مختلففحيقولك إيش ال a n closed form
+
+182
+00:13:36,310 --> 00:13:40,490
+اللي هتساوي alpha واحد في ال root الأول to the
+
+183
+00:13:40,490 --> 00:13:43,350
+power n زائد alpha اتنين في ال root التاني to the
+
+184
+00:13:43,350 --> 00:13:45,870
+power n لأنه الآن بدك تحط أنه root من ال two roots
+
+185
+00:13:45,870 --> 00:13:50,450
+هدول احنا قلنا بدنا root okay ماشي هاي R طب أنه
+
+186
+00:13:50,450 --> 00:13:53,950
+واحد هستخدم لأنك هتستخدم الاتنين فعليا هتستخدم
+
+187
+00:13:53,950 --> 00:13:58,570
+الاتنين كويس وكل واحد هتفترض أنه إله constant خاص
+
+188
+00:13:58,570 --> 00:14:02,740
+فيه أو معامل خاص فيه coefficient خاص فيهالـ
+
+189
+00:14:02,740 --> 00:14:05,600
+coefficient الخاص بي فهي الـ root الأول to the
+
+190
+00:14:05,600 --> 00:14:08,560
+power n بالـ root الخاص بي بالـ coefficient الخاص
+
+191
+00:14:08,560 --> 00:14:11,420
+بي زائد الـ root التاني بالـ coefficient الخاص بي
+
+192
+00:14:11,420 --> 00:14:16,520
+و طبعا كلنا بنتكلم عن n من صفر فأكتر عشان أقدر
+
+193
+00:14:16,520 --> 00:14:21,140
+أعبر عنها طيب و بيظل عندنا الشغل المهم بعد ما نحل
+
+194
+00:14:21,140 --> 00:14:25,760
+ال characteristic roots بدك تجيب قيمة ألف واحد و
+
+195
+00:14:25,760 --> 00:14:29,940
+ألف اتنين من وين؟ من ال two initials اللي لازم
+
+196
+00:14:29,940 --> 00:14:33,160
+يكونوا عندكمن ال two initials اللي لازم يكونوا
+
+197
+00:14:33,160 --> 00:14:37,660
+عندك، ما احنا اتفقنا من الأول، عشان تحلل هذه، انت
+
+198
+00:14:37,660 --> 00:14:42,640
+محتاج two values، مدام ال K ب2، معناته انت محتاج
+
+199
+00:14:42,640 --> 00:14:45,960
+قيمتين مسبقتين، هل هي بتقدر تجيب Fibonacci بدون ما
+
+200
+00:14:45,960 --> 00:14:50,310
+تكون عارف القيمتين السابقتين؟ أبداًإطلاقا فمعنى
+
+201
+00:14:50,310 --> 00:14:53,690
+ذلك ان انت محتاج قيمتين سابقتين على الأقل two
+
+202
+00:14:53,690 --> 00:14:56,890
+values حسب ال degree اللي بتشتغل عليها والله لو ال
+
+203
+00:14:56,890 --> 00:15:00,570
+degree تلاتة معناته محتاج تلت قيم initial values و
+
+204
+00:15:00,570 --> 00:15:03,990
+هكذا فإذا ان انا محتاج اتنين محتاج اتنين الاتنين
+
+205
+00:15:03,990 --> 00:15:07,670
+هدولة بتعوض فيهم في المعادلة بيظل عندك الف واحد و
+
+206
+00:15:07,670 --> 00:15:11,890
+الف اتنين المجاهيل تبعتك في معادلتين لما عوضت في
+
+207
+00:15:11,890 --> 00:15:16,650
+القيمتين ال given عندك خلص انحلت الموضوع ناخد مثل
+
+208
+00:15:16,650 --> 00:15:22,820
+انحدد الأموربهذا الشكل طب بدنا نحدد بس شغلة هنا
+
+209
+00:15:22,820 --> 00:15:27,380
+انه هذا الكلام منطقي جدا انه نفصل R1 وR2 على
+
+210
+00:15:27,380 --> 00:15:35,260
+اعتبار انهم مختلفين فبقدرش اقول والله R هذه هي
+
+211
+00:15:35,260 --> 00:15:39,120
+واحد او هي اتنين فانا مضطر اجمعهم الاتنين مع بعض
+
+212
+00:15:39,120 --> 00:15:43,700
+فإذا هذا الكلام النظرية theorem one هذه في حال انه
+
+213
+00:15:43,700 --> 00:15:48,130
+كانوا لايسوا بعض فاحط كل واحد لحاله في termكل واحد
+
+214
+00:15:48,130 --> 00:15:54,090
+هنحط لحاله في term خاص فيه تمام هنشوف مثالنا هاي
+
+215
+00:15:54,090 --> 00:15:59,590
+عندك an بتساوي an نقص واحد زائد اتنين an نقص اتنين
+
+216
+00:15:59,590 --> 00:16:04,310
+فإذن معتمد على القيمة السابقة زائد ضعف القيمة ما
+
+217
+00:16:04,310 --> 00:16:09,490
+قبل السابقة كويس و ال initial conditions بدونها
+
+218
+00:16:09,490 --> 00:16:12,690
+انسى لإنك تحلي حاجة مش هتعرف تحلي حاجة a node
+
+219
+00:16:12,690 --> 00:16:20,110
+بتنين a واحد بسبعة و قلتلك هاتلي aمية انا مش
+
+220
+00:16:20,110 --> 00:16:22,590
+هجيبلك في الامتحان هتلي تلاتة تروح تجمعلي اياهم و
+
+221
+00:16:22,590 --> 00:16:28,750
+تخلص مش هيك اكيد يعني اكيد فمش هتروح تضطر تعملي زي
+
+222
+00:16:28,750 --> 00:16:32,890
+ال summation اللي خدناها سابقا تقعد تعملي terms مش
+
+223
+00:16:32,890 --> 00:16:38,270
+هتعملي terms بدك تعمل terms لمن مية لصفر واحد خلاص
+
+224
+00:16:38,270 --> 00:16:41,350
+ضيع وقتك وراحتك في الحالة هذه فبتصير انت ضيعت وقت
+
+225
+00:16:41,350 --> 00:16:44,530
+على الفاضي لأ بنحولها ل closed form عشان مباشرة
+
+226
+00:16:44,530 --> 00:16:49,990
+تنعوض ب N بمية و خلاصخلصنا هوية واحدة وانتهى طيب
+
+227
+00:16:49,990 --> 00:16:52,750
+هذا الكلام مناسب جدا في بعض الأمثلة حتى جوا في
+
+228
+00:16:52,750 --> 00:16:55,170
+الكتاب اللي هي علاقة بين ال bacteria ال bacteria
+
+229
+00:16:55,170 --> 00:16:59,450
+بشكل بكل ساعة في كل ساعة بتتضعف لتلت أبعاف لما
+
+230
+00:16:59,450 --> 00:17:03,070
+أقولك والله في يوم كامل كام ضعف صارت مش هتقل
+
+231
+00:17:03,070 --> 00:17:07,350
+تتحلليها بإيدك مش هتقل تتحلها بإيدك كويس فبدك تضطر
+
+232
+00:17:07,350 --> 00:17:13,010
+تجيب ال closed form ك term في in و in هنا هتكون
+
+233
+00:17:13,010 --> 00:17:16,590
+عدد الساعات اللي هي بتتضعف فيها لتلت أربع أضعاف
+
+234
+00:17:17,270 --> 00:17:22,430
+عشان في الآخر اتعود بقيمة ال N بس تمام هتنشوف كلام
+
+235
+00:17:22,430 --> 00:17:26,590
+ليه صار معناه بكل بساطة هنا مدام أنا عارف فاهم من
+
+236
+00:17:26,590 --> 00:17:29,410
+الأساس كيف اجت ال characteristic equation فانا
+
+237
+00:17:29,410 --> 00:17:31,990
+عارف مسبقا ان هدولة هوديهم عن ناحية التانية
+
+238
+00:17:31,990 --> 00:17:38,510
+بالسوالب سوالبها كويس و هدى هتروح ل R تربيع ناقص
+
+239
+00:17:38,510 --> 00:17:43,570
+هنا R مافيش اي coefficient معاها و هنا هتصير ناقص
+
+240
+00:17:43,570 --> 00:17:44,250
+اتنين
+
+241
+00:17:48,240 --> 00:17:52,800
+بداك تعمل الطريقة المطولة و تستعود مكان كل N ب R
+
+242
+00:17:52,800 --> 00:17:56,320
+to the power N و بعدين تقسم على ال N الأصغر خلاص
+
+243
+00:17:56,320 --> 00:18:00,960
+ماذا هي؟ ماهي كلها جام كلها تمام خلصنا فهي صارت
+
+244
+00:18:00,960 --> 00:18:02,920
+عندك المعادلة بهذا الشكل اللي هي ال characteristic
+
+245
+00:18:03,960 --> 00:18:07,980
+characteristic equation كويس كلكوا حافظين ال
+
+246
+00:18:07,980 --> 00:18:12,660
+quadratic form ال quadratic form اللي هو سالب ب
+
+247
+00:18:12,660 --> 00:18:16,580
+زائد ناقص الجذر تبع المحدد و اللي هو ب تربية ناقص
+
+248
+00:18:16,580 --> 00:18:21,560
+أربعة a c على اتنين a هذا كلنا حافظينه فعشان هي
+
+249
+00:18:21,560 --> 00:18:23,880
+كان مناسب ان احنا نشتغل على ال degree اتنين بس
+
+250
+00:18:23,880 --> 00:18:28,650
+اكتر من هيك بصير بدك تحلها بطرق تانيةتمام ف R هنا
+
+251
+00:18:28,650 --> 00:18:33,310
+إيش هتسوي في الحالة دي لو عوضنا ب C1 و C2 اللي هي
+
+252
+00:18:33,310 --> 00:18:36,830
+ال coefficients تبعتك هيها عندك ال A بواحد ال B
+
+253
+00:18:36,830 --> 00:18:41,970
+سالب واحد و C سالب اتنين بنعوض عشان يطلع عندك two
+
+254
+00:18:41,970 --> 00:18:46,610
+roots اتنين و سالب واحد فتنين سالب واحد اللي طلعوا
+
+255
+00:18:46,610 --> 00:18:51,010
+عندك هنا بدأك تحطهم في شكل المعادلة تبعتك كل واحدة
+
+256
+00:18:51,010 --> 00:18:54,010
+كان هي ال root فعلا to the power N ال root to the
+
+257
+00:18:54,010 --> 00:18:56,940
+power N وكل واحدة مضروبة في إيش؟في الـ coefficient
+
+258
+00:18:56,940 --> 00:19:02,680
+تبعها خلصنا كل ما مطلوب منك اتعود بالقيمتين هدول ف
+
+259
+00:19:02,680 --> 00:19:08,120
+a zero تساوي اتنين يعني معنى ذلك تساوي alpha واحد
+
+260
+00:19:08,120 --> 00:19:13,860
+و هنا zero انت بتعود عند n ب zero فإذا هذه بواحد و
+
+261
+00:19:13,860 --> 00:19:17,680
+هنا نفس الكلام alpha اتنين و هنا برضه بواحد خلصنا
+
+262
+00:19:17,680 --> 00:19:20,340
+فاتنين تساوي alpha واحد زي ال alpha اتنين هي
+
+263
+00:19:20,340 --> 00:19:25,980
+معادلة أولى بعدين بنعود عند مين عند n بتساوي بواحد
+
+264
+00:19:26,600 --> 00:19:31,260
+and n ساوي واحد فا ايه واحد تساوي سبعة وهذه تساوي
+
+265
+00:19:31,260 --> 00:19:37,440
+اتنين هتصير واحد اتنين Alpha واحد زائد بتصير ناقص
+
+266
+00:19:37,440 --> 00:19:43,680
+واحد مظبوط هنا to the power واحد بتصير اتنين مظبوط
+
+267
+00:19:43,680 --> 00:19:48,300
+و هنا Alpha نزلت زي ما هي بس بالسالب سالب Alpha
+
+268
+00:19:48,300 --> 00:19:55,560
+اتنين مظبوطك احنا عوضنا في واحد اه to the power
+
+269
+00:19:55,560 --> 00:20:01,780
+oneبتبار one اه سالب واحد كويس فهذا كله المفروض
+
+270
+00:20:01,780 --> 00:20:07,180
+انه بيساوي سبعة وهذا بيساوي اتنين بتالي أبسط شغلة
+
+271
+00:20:07,180 --> 00:20:11,420
+ممكن مثلا تجمعهم ضيعت هدولة مثلا هي سبعة فالف واحد
+
+272
+00:20:11,420 --> 00:20:14,640
+بتلاتة هي بيانت لحالها على اعتبار انه تسعة وهدول
+
+273
+00:20:14,640 --> 00:20:19,180
+مجموحهم تلاتة خلصت يعني بتالي مش الحاجة اللي ضخمة
+
+274
+00:20:19,180 --> 00:20:26,380
+صحيح بسيطة جدا الفكرة تمام فخلصنا هى و جابها و
+
+275
+00:20:26,380 --> 00:20:29,880
+اشتغل عليها و فعلا طلع معانا الف و واحد بتلاتة
+
+276
+00:20:29,880 --> 00:20:33,120
+مظبوط الف و واحد بتلاتة و الف و اتنين اب واحد
+
+277
+00:20:33,120 --> 00:20:37,080
+فارجع عوض فيهم في المعادلة تلاتة و واحد هذا closed
+
+278
+00:20:37,080 --> 00:20:42,960
+form خلاص هذا لان لما نطلب منك مية كل ما هتعمله بس
+
+279
+00:20:42,960 --> 00:20:46,880
+تعود هنا بمية و هنا بمية و انتهى و بتجيب القيمة
+
+280
+00:20:46,880 --> 00:20:50,640
+مباشرة طب مابتقدر تعمل check عليها عند الصفر هيطلع
+
+281
+00:20:50,640 --> 00:20:56,040
+لتنين مظبوطةاللي احنا اصلا عوضنا فيها عند الواحد
+
+282
+00:20:56,040 --> 00:20:59,320
+المفروض يطلع السبعة مظبوطة وبعدين بتقدر تكمل ال
+
+283
+00:20:59,320 --> 00:21:03,440
+series تبعتك بتقدر تكمل ال series لو محتاج هتزول
+
+284
+00:21:03,440 --> 00:21:08,000
+.. اتفضل ماكانتش
+
+285
+00:21:08,000 --> 00:21:13,980
+ال quadratic؟
+
+286
+00:21:13,980 --> 00:21:21,140
+معناته ان هي مش ممكنةلأنه complex .. اي عفوًا ..
+
+287
+00:21:21,140 --> 00:21:23,920
+imaginary part هتكون imaginary part في الحالة هذه
+
+288
+00:21:23,920 --> 00:21:26,920
+معناه ذلك أنه .. معناه ذلك أنه المعادلة هذه فيها
+
+289
+00:21:26,920 --> 00:21:32,840
+مشكلة من الأساس في عندك مشكلة فبناتش بتطلع لحل ..
+
+290
+00:21:32,840 --> 00:21:38,420
+لأ فبناتش بتطلع لحل و إجا في امتحان كان واحدة من
+
+291
+00:21:38,420 --> 00:21:41,860
+أسئلة امتحان سابق أنه جبتلهم معادلة فبناتش نفسها و
+
+292
+00:21:41,860 --> 00:21:45,140
+قلتلهم هتقول ال closed form تبعتها و كان فيها أربع
+
+293
+00:21:45,940 --> 00:21:48,180
+متذكر أنه لعندي الآن كان ألف و واحد و ألف اتنين
+
+294
+00:21:48,180 --> 00:21:54,240
+هدول و ربعه حسب ما أذكر لأ لأ جربها جربها ماتحكمش
+
+295
+00:21:54,240 --> 00:21:57,280
+على حاجة بدون ماتجربها الرياضيات بدها التجريب و
+
+296
+00:21:57,280 --> 00:22:00,340
+عشان هيك بيسموه exercise عشان هيك بيسموه دايما في
+
+297
+00:22:00,340 --> 00:22:02,300
+نهاية ال chapters .. ال chapters تبع ال
+
+298
+00:22:02,300 --> 00:22:05,600
+mathematics بيسموهاش problems بيسموه exercise
+
+299
+00:22:05,600 --> 00:22:11,480
+تدريب تدرب حالك تمام لأ لأ بيطلع لحلو ما هي محلولة
+
+300
+00:22:11,480 --> 00:22:13,900
+يعني حلناها بقولك جابل هيك و جيبناها انتحان أصلا
+
+301
+00:22:14,660 --> 00:22:20,800
+طيب الآن السؤال لو ال roots هذه ال roots هي ما
+
+302
+00:22:20,800 --> 00:22:24,820
+طلعتش مختلفة طلعت متشابهة طلعت ال roots متشابهة
+
+303
+00:22:24,820 --> 00:22:29,380
+ففي الحالة هذه إذا طلعت متشابهة يعني one rule ..
+
+304
+00:22:29,380 --> 00:22:34,040
+one root فقط اللي هي R node واحدة مش R واحد وR
+
+305
+00:22:34,040 --> 00:22:39,020
+اتنين فبنقدر نقول أن نفس ال terms لاحظ لنفس ال R
+
+306
+00:22:39,020 --> 00:22:43,420
+بس واحد منهم اضربه في N واحد من ال two terms اضربه
+
+307
+00:22:43,420 --> 00:22:48,140
+في Nالأول التاني بيفرجش بيفرجش كتير يعني ما تقعدش
+
+308
+00:22:48,140 --> 00:22:51,520
+تحفظليها أنه لازم في التاني خلاص هي نفس المعادلة
+
+309
+00:22:51,520 --> 00:22:56,720
+هي .. هي R وقعينا R واحدة .. واحدة متشابهة فR to
+
+310
+00:22:56,720 --> 00:22:58,880
+the power N وR to the power N كل واحدة مضربها في
+
+311
+00:22:58,880 --> 00:23:01,240
+ال coefficient تبعتها Alpha 1 و Alpha 2 واحدة منهم
+
+312
+00:23:01,240 --> 00:23:05,460
+مضربها في N خلاص في النهاية هيثبتلك إياها مين
+
+313
+00:23:05,460 --> 00:23:08,200
+Alpha 1 لما بتعوض فيها و جيب ال .. جيب ال roots مش
+
+314
+00:23:08,200 --> 00:23:11,800
+هتفرج معاك كتير فانت لاجوش من الجثة اضرب أي واحدة
+
+315
+00:23:11,800 --> 00:23:20,080
+منهم في N تمامOkay نجرب مثال على هذا الموضوع هي
+
+316
+00:23:20,080 --> 00:23:27,000
+عندك a n بتساوي ستة a n ناقص واحد ناقص تسعة a n
+
+317
+00:23:27,000 --> 00:23:32,600
+ناقص اتنين و اعطاك two initial values واحد و صفر
+
+318
+00:23:32,600 --> 00:23:35,680
+عند واحد و ست عفوا عند الصفر و الواحد ال
+
+319
+00:23:35,680 --> 00:23:40,380
+characteristic roots بهذا الشكل هذه مباشرة المحددة
+
+320
+00:23:40,380 --> 00:23:46,050
+بتاعتها او اللي تحت الجذر هتساوي zeroما دام بتساوي
+
+321
+00:23:46,050 --> 00:23:50,790
+zero معناته هو root واحد هو root واحد اللي هو سالب
+
+322
+00:23:50,790 --> 00:23:54,230
+بي على المقام اللي هو اتنين ايه فسالب بي على مقام
+
+323
+00:23:54,230 --> 00:23:58,870
+اتنين كلا هما تلاتة خلاص هنعملها زي ما هي هي سيبك
+
+324
+00:23:58,870 --> 00:24:02,430
+من ال N لو جيتها هي تلاتة وهي تلاتة نفس السابق
+
+325
+00:24:02,430 --> 00:24:07,470
+واحدة منهم ضربها في Nواحدة منهم وضربها في N خلاص
+
+326
+00:24:07,470 --> 00:24:12,110
+ضربناها في N في الآخر جابل طبعا منصل ان والله هذه
+
+327
+00:24:12,110 --> 00:24:16,890
+واحد وهذه واحد فعليا هذه اتت من خلال ايش تعويض من
+
+328
+00:24:16,890 --> 00:24:21,130
+خلال تعويض اللي هنا وكانت بسيطة أعتقد مش مش الشغل
+
+329
+00:24:21,130 --> 00:24:29,370
+الصعب كتير A node بتساوي واحد فهنعود هنا صفرو صفر
+
+330
+00:24:29,370 --> 00:24:33,230
+طبعا ترمد كله راح مع الصفر فبتضل هنا صفر يعني
+
+331
+00:24:33,230 --> 00:24:36,710
+بتساوي Alpha واحد فخلصنا هاي Alpha واحد لحالها
+
+332
+00:24:36,710 --> 00:24:42,950
+طلعت خلصت Alpha واحد لحالها A واحد بتساوي ستة وهد
+
+333
+00:24:42,950 --> 00:24:47,390
+بتساوي خلاص هد بواحد انتهى و هنا بضل تلاتة فبتساوي
+
+334
+00:24:47,390 --> 00:24:52,230
+تلاتة زائد Alpha اتنين اللي لسه بدنا نجيبها و هنا
+
+335
+00:24:52,230 --> 00:24:59,120
+واحد في تلاتة يعني تلاتة لأ يعني واحدهذه هتروح
+
+336
+00:24:59,120 --> 00:25:03,680
+الطرف التاني فبصير تلاتة تساوي تلاتة ألف اتنين
+
+337
+00:25:03,680 --> 00:25:09,420
+برضه واحد فإذا برضه تساوي ألف اتنين فهي واحد واحد
+
+338
+00:25:09,420 --> 00:25:13,260
+فصارت هنا كأنه هنا في واحد و هنا في واحد خلصنا جيب
+
+339
+00:25:13,260 --> 00:25:16,080
+كل ال terms اللي بدك هيها بدك ال term رقم مية جيب
+
+340
+00:25:16,080 --> 00:25:20,920
+مية اضرب بس مكان n بمية جيبنا ال term رقم مية
+
+341
+00:25:20,920 --> 00:25:26,240
+فبناتش بتقدر تجيبها و أي series بعد هيك بتقدر
+
+342
+00:25:26,240 --> 00:25:30,060
+تتعامل معاهاتمام هذا كان الجزء اللي ضايلة عندنا في
+
+343
+00:25:30,060 --> 00:25:33,740
+ال linear أو ال solving recurrences في ال solving
+
+344
+00:25:33,740 --> 00:25:37,720
+recurrences طيب ال recurrence هذه احنا ايش كنا
+
+345
+00:25:37,720 --> 00:25:41,860
+نسميها recurrence relation صحيح ال function ال
+
+346
+00:25:41,860 --> 00:25:46,520
+function ايش هي relationصحيح؟ فإذا واضح ان احنا
+
+347
+00:25:46,520 --> 00:25:50,640
+لما متخيلين ان ال function هي أكبر حاجة خدناها و
+
+348
+00:25:50,640 --> 00:25:53,200
+ان الدنيا كلها functions لأ هي في حاجة أكبر من ال
+
+349
+00:25:53,200 --> 00:25:56,300
+function و هي اللي بتشمل ال function ال relation
+
+350
+00:25:56,300 --> 00:26:01,940
+العلاقات ال relation و عشان هيك طبيعي جدا ان احنا
+
+351
+00:26:01,940 --> 00:26:07,060
+نروح لحاجة اسمها relation اللي هي relation ال
+
+352
+00:26:07,060 --> 00:26:10,520
+function هي relation ليش؟ لأنك انت بتجيب بالنسبة
+
+353
+00:26:10,520 --> 00:26:15,190
+لل function العلاقة بين ال input و ال outputفهي
+
+354
+00:26:15,190 --> 00:26:21,090
+relation كأنها function طيب ال .. ال set هي
+
+355
+00:26:21,090 --> 00:26:25,450
+relation لأن أنت بتعمل relation بين العنصر و
+
+356
+00:26:25,450 --> 00:26:28,430
+انتماءه لل set ينتمي أو لا ينتمي فهنا بتصير
+
+357
+00:26:28,430 --> 00:26:32,290
+relation binary relation يعني يا on يا off يا
+
+358
+00:26:32,290 --> 00:26:36,210
+موجود يا غير موجود مثلا كويس؟ طيب في ال series
+
+359
+00:26:36,210 --> 00:26:40,670
+برضه relation relation بين مين و مين بين العنصر
+
+360
+00:26:40,670 --> 00:26:46,140
+نفسه و ال locationفي علاقة ولا مافيش علاقة، واحنا
+
+361
+00:26:46,140 --> 00:26:49,340
+هنا لسه كنا بنشتغل عليها، هيها، high relation بين
+
+362
+00:26:49,340 --> 00:26:54,960
+العنصر وال location تبعه، هي عنصر و location، احنا
+
+363
+00:26:54,960 --> 00:26:56,760
+إيش اللي كنا نعمله هنا؟ ليش قلتلك هاتلي ال
+
+364
+00:26:56,760 --> 00:26:59,620
+location مية، بدي العنصر في ال location مية،
+
+365
+00:26:59,620 --> 00:27:03,460
+معناته المفروض أنه بدلالة المية تعرف قيمة العنصر،
+
+366
+00:27:03,460 --> 00:27:09,520
+فأصبح العنصر معرف بال location تبعهتمام فأول شغلة
+
+367
+00:27:09,520 --> 00:27:13,560
+ال binary relation اللي هي يوجد أو لا يوجد هذه
+
+368
+00:27:13,560 --> 00:27:17,540
+أبسط أنواع ال relations الممكنة كبداية لل
+
+369
+00:27:17,540 --> 00:27:21,760
+relations و اللي زي ما قلنا هي هتشمل كل العلوم
+
+370
+00:27:21,760 --> 00:27:25,280
+هتتفاجأ انها بتشمل كل علوم الرياضيات بتشمل كل
+
+371
+00:27:25,280 --> 00:27:29,920
+المواضيع اللي أخدناها في الرياضيات لإنه ممكن
+
+372
+00:27:29,920 --> 00:27:34,900
+تمثيلها بشكل relation فلما نقولك binary relation
+
+373
+00:27:34,900 --> 00:27:40,760
+بين ال set A و B عندي two sets domain و codomain
+
+374
+00:27:40,760 --> 00:27:43,820
+مش هاي two sets بتاعونك domain و codomain بتجيب
+
+375
+00:27:43,820 --> 00:27:47,340
+منهم function فبقدر أقول ان ال binary relation R
+
+376
+00:27:47,340 --> 00:27:52,260
+from A to B بنكتبها كتالة كأنها function هي
+
+377
+00:27:52,260 --> 00:27:57,320
+لاحظتوا كده ال R أو ال relation أو كأنها ال F مثلا
+
+378
+00:27:57,320 --> 00:28:03,200
+ال R from Ato B هي subset لإيش؟ لل A Cartesian
+
+379
+00:28:03,200 --> 00:28:06,380
+product B ليش Cartesian product B؟ لأنه عارفين إن
+
+380
+00:28:06,380 --> 00:28:09,180
+إحنا في ال Cartesian product B و اللي جيبناها في
+
+381
+00:28:09,180 --> 00:28:13,120
+الامتحان برضه و عملتولنا شوية مشاكل فيها هي معناته
+
+382
+00:28:13,120 --> 00:28:17,520
+أن أنا بجيب أي عنصر من A و سمناها X و أي عنصر من B
+
+383
+00:28:17,520 --> 00:28:21,890
+و سمناها Y، ماينفعش أقول X هنا و هناماكنش بظبط
+
+384
+00:28:21,890 --> 00:28:24,650
+نقول x هنا و هنا لأن معناته أنا بتكلم من ال set
+
+385
+00:28:24,650 --> 00:28:29,110
+لنفسه و هذا ماكنش صحيح ف Cartesian x و y فإذا كل
+
+386
+00:28:29,110 --> 00:28:33,470
+عنصر كزوج مرتب الجزء الأول من الزوج المرتب هو
+
+387
+00:28:33,470 --> 00:28:38,510
+المفروض يكون جاي ينتمي ل a والجزء الثاني ينتمي ل b
+
+388
+00:28:39,580 --> 00:28:43,580
+و بتعمل كل ال possibilities الممكنة فإذا بتاخد
+
+389
+00:28:43,580 --> 00:28:50,000
+عنصر من a بتحطه في البداية ك x axis في ال x axis
+
+390
+00:28:50,000 --> 00:28:57,800
+كويس و كل عناصر بي بتحطه عنصر الأول في هاي حالة مع
+
+391
+00:28:57,800 --> 00:29:01,640
+عنصر التاني هاي حالة مع عنصر التالت حالة خلصتهم
+
+392
+00:29:01,640 --> 00:29:06,000
+بتاخد عنصر التاني من a و بتكرر و بتكرر فمعنى ذلك
+
+393
+00:29:06,000 --> 00:29:11,290
+بطلع عندكالـ cardinality لـ Cartesian product كأنه
+
+394
+00:29:11,290 --> 00:29:16,230
+ضرب ال two cardinalities ال two cardinalities ل A
+
+395
+00:29:16,230 --> 00:29:20,430
+و B اللي هو عدد عناصر A مضروب في عدد عناصر B طيب
+
+396
+00:29:20,430 --> 00:29:25,840
+لما أقول في relation بين عناصر A و Bبين عناصر a و
+
+397
+00:29:25,840 --> 00:29:29,200
+b بمسككم العنصر الأول هل يوجد relation بين العنصر
+
+398
+00:29:29,200 --> 00:29:33,960
+الأول هنا والعنصر الأول في الناحية هذه لأ لا يوجد
+
+399
+00:29:33,960 --> 00:29:38,400
+relation أو يوجد relation بناء على إيش على إيش ال
+
+400
+00:29:38,400 --> 00:29:42,160
+relation اللي أنا بتتكلم عنها بناء على إيش هي ال
+
+401
+00:29:42,160 --> 00:29:45,660
+relation اللي بحكي عنها نتكلم عن relation طيب لما
+
+402
+00:29:45,660 --> 00:29:50,240
+نقول مثلا هي عندنا مستوى التالتكلنا في المستوى
+
+403
+00:29:50,240 --> 00:29:53,240
+التالت طيب هاتنشوف طلبة مستوى أول طب هل يوجد
+
+404
+00:29:53,240 --> 00:29:57,520
+relation ايش نوع ال relation ان حد أخه التاني مثلا
+
+405
+00:29:57,520 --> 00:30:01,740
+relation relation يمكن يطلع five في النهاية يطلع
+
+406
+00:30:01,740 --> 00:30:03,980
+من المستوى التالت مافيش ولا واحد أخوه في المستوى
+
+407
+00:30:03,980 --> 00:30:06,960
+الأول صح في النهاية ممكن تطلع five ماعنديش مشكلة
+
+408
+00:30:06,960 --> 00:30:12,140
+بس تخيل انه كلكوا يطلعلكم في يعني أخه هناك معنى
+
+409
+00:30:12,140 --> 00:30:16,360
+ذلك ان انتوا في الآخر هتكونوا حددتوا بحد أقصىبحد
+
+410
+00:30:16,360 --> 00:30:20,560
+أقصى لا يمكن ال relations الممكنة تزيد عن ال
+
+411
+00:30:20,560 --> 00:30:22,980
+Cartesian product ليش؟ لأن ال Cartesian product
+
+412
+00:30:22,980 --> 00:30:25,960
+انا حطيت كل الاحتمالات ال possibilities الممكنة
+
+413
+00:30:25,960 --> 00:30:30,240
+حطينا كل ال possibilities الممكنة الأول هل أخو
+
+414
+00:30:30,240 --> 00:30:33,520
+الأول هنا؟ طب الأول أخو التاني هنا؟ الأول أخو
+
+415
+00:30:33,520 --> 00:30:36,660
+التالت هنا؟ خلصنا من الأول التاني أخو الأول هنا؟
+
+416
+00:30:36,660 --> 00:30:39,440
+حطيت كل ال possibilities أنت بال Cartesian product
+
+417
+00:30:40,420 --> 00:30:44,400
+فمعنى ذلك لما اقول subset اه انا متأكد تماما ان ال
+
+418
+00:30:44,400 --> 00:30:46,720
+relation هتكون هي subset من ال Cartesian لان ال
+
+419
+00:30:46,720 --> 00:30:50,180
+Cartesian اعطتك كل ال possibilities الممكنة طيب
+
+420
+00:30:50,180 --> 00:30:54,040
+subset ممكن تكون في اجي امسككم واحد واحد و نشوف
+
+421
+00:30:54,040 --> 00:30:59,080
+سنة أولى ولا واحد أخد تاني خلاص معناته في relation
+
+422
+00:30:59,080 --> 00:31:02,880
+لو يوجد relationrelation لا يوجد relation واضحت
+
+423
+00:31:02,880 --> 00:31:07,380
+فكلمة relation انا بالعمدة نقطتي المثال هذا عشان
+
+424
+00:31:07,380 --> 00:31:10,360
+اوضحلك انه مش بالضرورة ال relation تكون ايش رياضي
+
+425
+00:31:10,360 --> 00:31:16,260
+أرقام علاقات الناس في بعض relation عارفت ليش كلمة
+
+426
+00:31:16,260 --> 00:31:19,660
+relation هل وجد موضوع ال relation أكثر عمومية من
+
+427
+00:31:19,660 --> 00:31:23,640
+ال function لأنه انت بتتكلم حتى في الحالات الشخصية
+
+428
+00:31:23,640 --> 00:31:30,480
+relations تقدر تحطها ضغط اه اللغات relationفواضح
+
+429
+00:31:30,480 --> 00:31:34,920
+ان انت الآن احنا بنتكلم عن موضوع شامل كل اللي انت
+
+430
+00:31:34,920 --> 00:31:40,040
+أخدته سابقا كويس هاي subset من ال Cartesian مثال
+
+431
+00:31:40,040 --> 00:31:42,900
+عشان نوضح اللي الموضوع لو أخدنا ال relation أصغر
+
+432
+00:31:42,900 --> 00:31:46,920
+من هاي relation مش أصغر من relation from natural
+
+433
+00:31:46,920 --> 00:31:50,420
+number to natural number معنى ذلك انه set لكل
+
+434
+00:31:53,520 --> 00:31:58,240
+الأزواج المرتبة N و M بشرط أو such that أن N
+
+435
+00:31:58,240 --> 00:32:02,720
+الأولى تكون فعلا تحقق ال relation بالنسبة للتانية
+
+436
+00:32:02,720 --> 00:32:09,600
+فهي N و M معناته أن N أقل من M فمعناه ذلك أن هذا
+
+437
+00:32:09,600 --> 00:32:12,680
+ال relation أقل من هذا ال relation أقل من في
+
+438
+00:32:12,680 --> 00:32:17,180
+الحالة ده بنقدر نقول ال relation A بنقولها A
+
+439
+00:32:17,180 --> 00:32:23,030
+relation Bكأنه A أصغر لأن استعبنا عن ال relation
+
+440
+00:32:23,030 --> 00:32:27,770
+هنا ال relation كانت أصغر منه فحنحط أصغر منه A
+
+441
+00:32:27,770 --> 00:32:33,130
+أصغر من B هاي ال relation طيب فإذا A relation B أو
+
+442
+00:32:33,130 --> 00:32:39,150
+بنكتبها ARB مباشرة أو بمعنى أن A وB ينتموا لل
+
+443
+00:32:39,150 --> 00:32:43,560
+relation Rينتموا لل relation أصغر من .. إذا فعلا
+
+444
+00:32:43,560 --> 00:32:48,200
+حققوا هذا الشرط أن N فعلا أصغر من M فإذا N و M هم
+
+445
+00:32:48,200 --> 00:32:51,860
+ينتموا لأصغر من .. ال relation أصغر من .. كويس
+
+446
+00:32:51,860 --> 00:32:56,360
+فإذا A أصغر من B معناها أن A و B هم ينتموا لل
+
+447
+00:32:56,360 --> 00:33:00,460
+relation أصغر من .. إذا كانت A و B هذه معناها ..
+
+448
+00:33:00,460 --> 00:33:04,880
+بهذا الشكل تحققت فبقدر أقول أن A is related to B
+
+449
+00:33:04,880 --> 00:33:11,850
+by relation Rفهي related ل B تحت ال relation R
+
+450
+00:33:11,850 --> 00:33:17,850
+محقق ال relation R أو A relates to B under
+
+451
+00:33:17,850 --> 00:33:22,850
+relation R relates B فإذا A related أو A relates
+
+452
+00:33:22,850 --> 00:33:28,590
+to Bكلها مصطلحات ننطقها احنا مانشر كتير في النطاق
+
+453
+00:33:28,590 --> 00:33:33,250
+المهم ان نفهم الموضوع فانا بتكلم عن موضوع اشمل من
+
+454
+00:33:33,250 --> 00:33:36,330
+ال function اكثر شمولية شوية من ال function طيب ال
+
+455
+00:33:36,330 --> 00:33:40,830
+complementary ال relation لو فعلا عندك ال relation
+
+456
+00:33:40,830 --> 00:33:47,110
+a from a to b خلصنا منها معنى ذلك انه R complement
+
+457
+00:33:47,110 --> 00:33:53,930
+عملنا شرطة على ال R معناته انهA هو بيلا تحقق أو لا
+
+458
+00:33:53,930 --> 00:33:57,410
+تنتمي لل relation، معناه أنه لا تنتمي لل relation،
+
+459
+00:33:57,410 --> 00:34:01,630
+فإذا لمّانيش نقول مين من مستوى تالت أخو لمستوى
+
+460
+00:34:01,630 --> 00:34:03,810
+أول، يمكن نطلع في النهاية ال compliment كل
+
+461
+00:34:03,810 --> 00:34:08,930
+العلاقات، ليش؟ لأنه مافيش R أصلا، فال compliment
+
+462
+00:34:08,930 --> 00:34:13,290
+هو المكمل تبعها، المكمل تبعها، بالنسبة لمين؟ كلنا
+
+463
+00:34:13,290 --> 00:34:17,290
+عرفنا أنه لما بتكلم عن مكمل في ال 6، معناه ذلك أنه
+
+464
+00:34:17,290 --> 00:34:20,050
+لازم يكون في عند ال universe of discourse، فمين ال
+
+465
+00:34:20,050 --> 00:34:24,690
+universe of discourse تبعنا؟الـ Cartesian product
+
+466
+00:34:24,690 --> 00:34:29,690
+.. ال Cartesian product هي اللي أعطتك كل ال
+
+467
+00:34:29,690 --> 00:34:33,200
+possibilities الممكنةمنها مين بيحقق ال relation
+
+468
+00:34:33,200 --> 00:34:36,660
+ومين بيحققش ال relation إذا بيحققش معناته ال
+
+469
+00:34:36,660 --> 00:34:40,960
+complement المكمل لل relation المكمل لل relation
+
+470
+00:34:40,960 --> 00:34:45,480
+فإذا كأني بقول هيها ال complement لل relation هو
+
+471
+00:34:45,480 --> 00:34:51,100
+كل زوج مرتب لا ينتمي لل relation بمعنى أن هو ال
+
+472
+00:34:51,100 --> 00:34:55,080
+Cartesian product ناقص ال relation فإذا هو موجود
+
+473
+00:34:55,080 --> 00:34:58,480
+في ال Cartesian وغير موجود في ال relation حسب
+
+474
+00:34:58,480 --> 00:35:03,220
+فهمنا لها ال differenceفي ال sets مش هيك تمام و
+
+475
+00:35:03,220 --> 00:35:08,640
+بنقدر نكتبها اما بهذا الشكل خط مائل slash على ال R
+
+476
+00:35:08,640 --> 00:35:12,180
+مباشرة او بكتبها ال bar اللي انتوا عارفينها اللي
+
+477
+00:35:12,180 --> 00:35:15,220
+معناها ال inverse اللي كنا بنفهمها inverse فإذا
+
+478
+00:35:15,220 --> 00:35:18,200
+compliment في الحالة دي و كلنا فهمنا انه ليش ال
+
+479
+00:35:18,200 --> 00:35:19,820
+universive discourse بده يكون هو ال Cartesian
+
+480
+00:35:19,820 --> 00:35:25,300
+product بحيث نقدر نسمي منه ال compliment نقدر نسمي
+
+481
+00:35:25,300 --> 00:35:28,000
+لأن compliment معناته لازم يكون فيه بالنسبة لإيش
+
+482
+00:35:28,000 --> 00:35:32,140
+complimentهذا مكمل لل relation بالنسبة لإيش؟ بقى
+
+483
+00:35:32,140 --> 00:35:36,900
+لازم يكون عندى ثقف اللى محققش relation أكمل منه من
+
+484
+00:35:36,900 --> 00:35:40,440
+ال universe of discourse فال universe هي ال .. ال
+
+485
+00:35:40,440 --> 00:35:43,740
+Cartesian product طيب الآن ال compliment لها ال
+
+486
+00:35:43,740 --> 00:35:48,770
+compliment هي ال R نفسهاال inverse of inverse مش
+
+487
+00:35:48,770 --> 00:35:53,490
+مختلفين عليها الجثة ال compliment لا أصغر من ال
+
+488
+00:35:53,490 --> 00:35:57,710
+compliment أصغر من اللي هو أو يساوي بالظبط اللي هو
+
+489
+00:35:57,710 --> 00:36:01,470
+غير أصغر من فإيش اللي بيكمل غير أصغر من أكبر من أو
+
+490
+00:36:01,470 --> 00:36:06,850
+يساوي بالظبط فإذا a و b لا تحقق الأصغر من يعني a
+
+491
+00:36:06,850 --> 00:36:11,150
+ليست أصغر من b فإذا ممكن تسويها و ممكن أكبر منها
+
+492
+00:36:11,150 --> 00:36:16,000
+بدلا من ليست أصغر منها فإذا كأنها بتقولnegation a
+
+493
+00:36:16,000 --> 00:36:20,400
+بمعنى عكس a هو اللي أصغر من b وليس a نفسها وليس a
+
+494
+00:36:20,400 --> 00:36:27,420
+نفسها okay تمام جدا طيب الآن ال binary relation
+
+495
+00:36:27,420 --> 00:36:30,820
+هذه اللي هو يحقق ال relation أو لا يحقق ال
+
+496
+00:36:30,820 --> 00:36:36,970
+relation لما نيجي نطبقها على ال set نفسهاطب هنحتاج
+
+497
+00:36:36,970 --> 00:36:39,630
+نحملها على الست نفسها؟ أه هنحتاج لأنه شوية ال ..
+
+498
+00:36:39,630 --> 00:36:43,350
+هلوجت بدنا نحدد شوية محددات بالنسبالنا هلوجت أنا
+
+499
+00:36:43,350 --> 00:36:47,910
+بقول relation relation لمين؟ للأرقام مع بعضها مثلا
+
+500
+00:36:47,910 --> 00:36:51,810
+الأرقام مع بعضها معناه أن أنا بتكلم عن نفس الست مش
+
+501
+00:36:51,810 --> 00:36:54,970
+عن a و b بتكلم عن natural number فإذا من ال
+
+502
+00:36:54,970 --> 00:36:58,850
+natural number ل natural number أو بتكلم عن
+
+503
+00:36:58,850 --> 00:37:03,670
+relation بين الأشخاص فإذا people من ال people to
+
+504
+00:37:03,670 --> 00:37:09,670
+peopleفإذا ال A هي واحدة هي مش A وB مختلفة عنها هي
+
+505
+00:37:09,670 --> 00:37:14,890
+A ل A فكان من المهم جدا إنه تتحدد إنه relation
+
+506
+00:37:14,890 --> 00:37:20,710
+from a set A ل itself منها لنفسها منها لنفسها و
+
+507
+00:37:20,710 --> 00:37:24,930
+هنا بتسميها relation on the set A على ال set A
+
+508
+00:37:24,930 --> 00:37:28,390
+مباشرة هذا لا يعني إنه أنا بطلت بشتغل كارتيزيا لأ
+
+509
+00:37:28,390 --> 00:37:34,730
+أنا بشتغل كارتيزيا بس بين عناصر A مع عناصر Aحتى لو
+
+510
+00:37:34,730 --> 00:37:39,890
+ظهرت a مع a نفسه كمان حتى لو كانت الزوج المرتل
+
+511
+00:37:39,890 --> 00:37:44,150
+اللي بتفحصه هو a small مع a small أه بمشي الحال
+
+512
+00:37:44,150 --> 00:37:47,690
+هذا واحد من ال elements اللي ينتموا لاي ال
+
+513
+00:37:47,690 --> 00:37:52,890
+Cartesian product في الحالة هذه تمام فإذا في
+
+514
+00:37:52,890 --> 00:37:56,110
+الحالة هذه لو ما نقول أصغر من relation زي ما احنا
+
+515
+00:37:56,110 --> 00:38:00,650
+قلنا سابقا ممكن نعرفها على ال natural number ال
+
+516
+00:38:00,650 --> 00:38:03,750
+natural number و ال natural number هي نفسهافإذا من
+
+517
+00:38:03,750 --> 00:38:09,790
+الست لنفسها .. من الست لنفسها و لكل ال normal أو
+
+518
+00:38:09,790 --> 00:38:14,110
+ال natural numbers طيب ال identity relation او
+
+519
+00:38:14,110 --> 00:38:19,990
+ايه؟ ال I لإيه؟ ال identity relation هي الحالة هذه
+
+520
+00:38:19,990 --> 00:38:25,160
+أنه يجد علاقة بين العنصر و نفسه .. بين العنصرو
+
+521
+00:38:25,160 --> 00:38:28,680
+نفسه كويس بين العنصر و نفسه معناته بقدر أقول أن ال
+
+522
+00:38:28,680 --> 00:38:34,220
+A و A هو ينتمي لل capital A أكيد ينتمي لل 6A كلها
+
+523
+00:38:34,220 --> 00:38:36,620
+بس في الحالة هذه .. هذه الخصية عنده identity
+
+524
+00:38:36,620 --> 00:38:42,860
+relation اللي هي العنصر مع نفسه لما نقول والله في
+
+525
+00:38:42,860 --> 00:38:45,880
+القاعمين بحب نفسه أكتر من غيره أكيد كلنا A مع A
+
+526
+00:38:45,880 --> 00:38:55,890
+صحيح؟ ماتقولليش هلو جتضل في ..تمام؟ اثاره مش اثار
+
+527
+00:38:55,890 --> 00:39:00,370
+ال .. فهي مثلا واحدة من ال relations اللي موجودة و
+
+528
+00:39:00,370 --> 00:39:04,610
+قص على ذلك حاجات كتير هتلاقي فيها identity هتلاقي
+
+529
+00:39:04,610 --> 00:39:07,990
+فيها إيش؟ identity هتلاقي فيها جزئية ال identity و
+
+530
+00:39:07,990 --> 00:39:11,030
+أنا بحاول أجيبلك أمثلة شوية بعيدة عن الأرقام أما
+
+531
+00:39:11,030 --> 00:39:14,230
+أرقام هتلاقي أرقام كتير يعني لما أقولك ال function
+
+532
+00:39:14,230 --> 00:39:20,560
+أو ال .. البلطلةidentity function معناته كل نقطة
+
+533
+00:39:20,560 --> 00:39:24,680
+هي identity مع نفسها صحيح ا مع ا واحد مع واحد
+
+534
+00:39:24,680 --> 00:39:28,540
+اتنين مع اتنين خمسة مع خمسة نص مع نص هتلاقيهم كلهم
+
+535
+00:39:28,540 --> 00:39:32,120
+موجودين بيحققوا ال function أو الخط المستقيم هذا
+
+536
+00:39:32,120 --> 00:39:35,500
+اللي في الزاوية خمسة واربعين فإذا بالأرقام باينة
+
+537
+00:39:35,500 --> 00:39:39,340
+بس أنا بوضحلك أكتر و بحاول أجيبلك أمثلة أكبر من
+
+538
+00:39:39,340 --> 00:39:43,420
+مجرد الأرقام عشان أوضحلك أن ال relation هي أكبر
+
+539
+00:39:43,420 --> 00:39:43,900
+أوسع
+
+540
+00:39:46,550 --> 00:39:51,710
+اه طبعا ال compliment هي العكس ان انت كاره لنفسكأه
+
+541
+00:39:51,710 --> 00:39:53,690
+relation لو مابتش relation بدك تقول ال relation
+
+542
+00:39:53,690 --> 00:39:55,930
+على ال people و احنا هناخد بالمناسبة أمثلة كتير
+
+543
+00:39:55,930 --> 00:39:58,210
+على ال people هم ال .. يعني هم ال universe of
+
+544
+00:39:58,210 --> 00:40:02,710
+discourse و نحاول نطبق عليهم ال relation فحتجت أنه
+
+545
+00:40:02,710 --> 00:40:05,670
+في ناس كتير و خصوصا ساعة الامتحانات انت بتطلع من
+
+546
+00:40:05,670 --> 00:40:08,690
+الامتحان كارح حالك مش شايف انا كيف غلطت هالغلطة
+
+547
+00:40:08,690 --> 00:40:12,310
+كيف عملتها العامل مش شايف فهذه لحظة من اللحظات انت
+
+548
+00:40:12,310 --> 00:40:15,550
+بتحس حالك ان انت أصبحت معظم كسار compliment ل ..
+
+549
+00:40:15,550 --> 00:40:17,650
+لل relation هذه تمام
+
+550
+00:40:21,640 --> 00:40:25,140
+Okay Definition برضه هنرجع نيد ال relation اللي هي
+
+551
+00:40:25,140 --> 00:40:28,500
+على ال 6A فهي relation from A to A زي ما قلنا ناخد
+
+552
+00:40:28,500 --> 00:40:34,040
+المثال طبعنا ال cardinality زي ما قلنا لل universe
+
+553
+00:40:34,040 --> 00:40:38,920
+of discourse ككل هوA Cartesian A فمش معناه ان انا
+
+554
+00:40:38,920 --> 00:40:41,360
+بتكلم عن ايه معناته انا طلعت خارج ال Cartesian لأ
+
+555
+00:40:41,360 --> 00:40:45,720
+انا مازلت ضمن حدود ال Cartesian product تمام لو
+
+556
+00:40:45,720 --> 00:40:50,300
+أخدنا مثلا A عبارة عن واحد اتنين تلاتة أربعة بكفي
+
+557
+00:40:50,300 --> 00:40:57,460
+على جد ال order ال set هذه فهنا محتاجين نحدد من
+
+558
+00:40:57,460 --> 00:41:03,660
+اللي ينطبق عليه relation R A وB such that A أقل من
+
+559
+00:41:03,660 --> 00:41:13,240
+BA أقل من B فبكل بساطة نقدر نقول واحد واحد لأ واحد
+
+560
+00:41:13,240 --> 00:41:19,840
+اتنين اه واحد تلاتة واحد اربعة تمام اتنين واحد
+
+561
+00:41:19,840 --> 00:41:26,100
+اتنين اتنين اتنين تلاتة اتنين اربعة and so on
+
+562
+00:41:26,100 --> 00:41:29,220
+فوضحت الان ال relations في المثال
+
+563
+00:41:32,000 --> 00:41:34,920
+لأ لأ لأ لأ مش ال power لأ ال power مختلفة ال
+
+564
+00:41:34,920 --> 00:41:38,660
+power انت بتعمل كل .. معناها ان كل ال subsets من
+
+565
+00:41:38,660 --> 00:41:42,880
+.. من ال Cartesian product اللي هي كل ال subset من
+
+566
+00:41:42,880 --> 00:41:48,040
+ال setتمام فهنا بتقدر نمثلها بالشكل اللي احنا
+
+567
+00:41:48,040 --> 00:41:52,420
+شايفينه هنا حاطناهم جميع العناصر اللي بيحققوا ال
+
+568
+00:41:52,420 --> 00:41:55,860
+relation بيحققوا ال relation بتقدر طبعا بال
+
+569
+00:41:55,860 --> 00:41:59,420
+bipartate و احنا مثلنا ال set سابقا باستخدام ال
+
+570
+00:41:59,420 --> 00:42:02,480
+bipartate او ال function مثلناها بال bipartate
+
+571
+00:42:02,480 --> 00:42:04,800
+فممكن اقول هاي العناصر تبعتي واحد اتنين تلاتة
+
+572
+00:42:04,800 --> 00:42:10,420
+اربعةواحد لواحد لأ هو مش محقق ال relation فها دي
+
+573
+00:42:10,420 --> 00:42:14,540
+zero واحد اتنين اه واحد تلاتة واحد اربعة اتنين
+
+574
+00:42:14,540 --> 00:42:19,440
+تلاتة اتنين اربعة واحد اربعة نرسمهم بهذا الشكل او
+
+575
+00:42:19,440 --> 00:42:26,980
+بتقدر ترسمهم بشكل table ال table هذا from twoف
+
+576
+00:42:26,980 --> 00:42:33,980
+from ال raw to column from raw ل ال column فإذا
+
+577
+00:42:33,980 --> 00:42:37,380
+بنكتبها بهذا الشكل هذا ال او الأول وهذا التاني
+
+578
+00:42:37,380 --> 00:42:42,920
+تمام فإذا من واحد ل واحد لأ واحد لاتنين yes فهذا
+
+579
+00:42:42,920 --> 00:42:47,360
+موجود ضمن ال relation واحد تلاتة واحد أربعة تمام
+
+580
+00:42:47,360 --> 00:42:51,400
+كلهم موجودين اتنين اتنين مثلا لأ غير موجود و هكذا
+
+581
+00:42:51,400 --> 00:42:59,560
+فبتكتبوا نفسهم بهذا الشكل ماتعكسوشهنا from و هنا
+
+582
+00:42:59,560 --> 00:43:06,020
+to from to تمام فهذه التمثيل اللي هناخده لقدام كيف
+
+583
+00:43:06,020 --> 00:43:08,840
+نمثل ال relations فممكن ييجيك برضه سؤال اعطيك
+
+584
+00:43:08,840 --> 00:43:12,420
+relation معينة او اقولك مثل انياها اما bipartate
+
+585
+00:43:12,420 --> 00:43:16,660
+او اقولك والله بال matrix فبدك تمثلها ما تخربطوا
+
+586
+00:43:16,660 --> 00:43:24,160
+مش مع بعضتمام نختم في حاجة مهمة how many different
+
+587
+00:43:24,160 --> 00:43:29,500
+relations can we define on a set A within elements
+
+588
+00:43:29,500 --> 00:43:39,760
+عندي ال set A هي
+
+589
+00:43:39,760 --> 00:43:48,550
+دي عدد خليني أقول ال cardinality لها Nحسب التعريف
+
+590
+00:43:48,550 --> 00:43:54,910
+check within elements within elements مبدأيا اللي
+
+591
+00:43:54,910 --> 00:43:58,470
+مطلوب جداش عدد ال relations اللي ممكن نعملها من
+
+592
+00:43:58,470 --> 00:44:06,250
+الست هذه مضحك السؤال تمام تمام شوية شوية نركز فيها
+
+593
+00:44:06,250 --> 00:44:08,910
+شوية الآن احنا قولنا إيش ال relation عبارة عن إيش
+
+594
+00:44:08,910 --> 00:44:15,370
+عرفناها subset مش قولنا subset subset من إيش من ال
+
+595
+00:44:15,370 --> 00:44:20,060
+Cartesian productمن Cartesian product يعني from a
+
+596
+00:44:20,060 --> 00:44:23,980
+Cartesian product a يعني هذه ال Cartesian product
+
+597
+00:44:23,980 --> 00:44:29,940
+المفروض انه بدي اخد ال cardinality بتاعتها هي n في
+
+598
+00:44:29,940 --> 00:44:38,740
+في n مظبوط تمام هذه بتساوي n تربيع هاي ال n تربيع
+
+599
+00:44:38,740 --> 00:44:42,940
+اللي بنتكلم عنها ممتازهد مين الـ Interbial؟ هي
+
+600
+00:44:42,940 --> 00:44:47,480
+فعليًا عدد ال elements بتاعة ال Cartesian product
+
+601
+00:44:47,480 --> 00:44:50,880
+لسه مادخلتش ع ال relation ولا اتكلمتش عن ال
+
+602
+00:44:50,880 --> 00:44:54,520
+relation ال relation لسه ماجبناش سرتها حتى الآن
+
+603
+00:44:54,520 --> 00:44:58,840
+جبنا بس ال universe of discourse تبعنا فال
+
+604
+00:44:58,840 --> 00:45:02,560
+universe of discourse إلنا وجدنا إنه طلع مجموعة
+
+605
+00:45:02,560 --> 00:45:03,220
+عناصر
+
+606
+00:45:13,170 --> 00:45:19,450
+الان عشان نعمل منهم relation هاخد
+
+607
+00:45:19,450 --> 00:45:22,790
+كلمة واحد من الشباب اللي سألني فيها أظن مش مهندس
+
+608
+00:45:22,790 --> 00:45:27,170
+قاللي على ال powerال power احنا ايش توجهلناه؟ لما
+
+609
+00:45:27,170 --> 00:45:32,090
+جوابته قلتله هذه هي ال subset من ال set المعطاه
+
+610
+00:45:32,090 --> 00:45:37,570
+عند set كل ال subsets الممكنة بنسميها ال power طيب
+
+611
+00:45:37,570 --> 00:45:42,530
+طب ما احنا كنا بنعرف ان relation هي subset من ال
+
+612
+00:45:42,530 --> 00:45:45,890
+Cartesian product طب قدش عدد ال subsets الممكنين؟
+
+613
+00:45:45,890 --> 00:45:50,510
+لأن كل واحدة منهم تمثل relation لحالها كل واحدة
+
+614
+00:45:50,510 --> 00:45:55,960
+منهم ممكن تتمثل relationcheck تمام فإذن لفنا و
+
+615
+00:45:55,960 --> 00:45:59,060
+دورنا و رجعنا لنفس النقطة إن أنا قاعد بحسب ال
+
+616
+00:45:59,060 --> 00:46:04,540
+power بتاعة ال set بتاعة ال ال ال ال Cartesian
+
+617
+00:46:04,540 --> 00:46:07,860
+product لإن هو هذي هتطني كل ال elements الممكنين
+
+618
+00:46:07,860 --> 00:46:12,840
+داخل ال relation فإذن ممكن يكون 0 0 0 0 0 كلهم
+
+619
+00:46:12,840 --> 00:46:20,260
+zeros بمعنى إنه relation Phi أو العنصر الأول موجود
+
+620
+00:46:20,260 --> 00:46:24,360
+والباقي لأأو العنصر التاني اللي موجود و الباقي لأ
+
+621
+00:46:24,360 --> 00:46:27,480
+أو التالت اللي موجود و الباقي لأ أو الخامس اللي
+
+622
+00:46:27,480 --> 00:46:29,980
+موجود و الباقي لأ أو الانتربيع اللي موجود و الباقي
+
+623
+00:46:29,980 --> 00:46:34,620
+لأ أو الأول و التاني موجودين و الباقي لأ لاحظت جدش
+
+624
+00:46:34,620 --> 00:46:39,340
+عدد ال possibilities ل subset ممكنين منها و احنا
+
+625
+00:46:39,340 --> 00:46:44,660
+أخدناها سابقا كنا بنقول اتنين to the power ال
+
+626
+00:46:44,660 --> 00:46:48,850
+cardinality لإيههذه لما أخدناها بصفة .. بصفة عامة
+
+627
+00:46:48,850 --> 00:46:50,970
+عساسا ان ال cardinality ل a هي اللي بدي أجيبها ال
+
+628
+00:46:50,970 --> 00:46:54,690
+power بس أنا مابديش أجيب ال a لل power الآن مابديش
+
+629
+00:46:54,690 --> 00:46:57,650
+أجيب ال cardinality لل a لل power لأن مابدي أجيبها
+
+630
+00:46:57,650 --> 00:47:05,350
+لمين ال Cartesian product معناته ايوة a Cartesian
+
+631
+00:47:05,350 --> 00:47:09,430
+product a فهيك
+
+632
+00:47:09,430 --> 00:47:12,490
+بنكون جبناها طيب هذه احنا لسه توجب .. اتكلمنا عنها
+
+633
+00:47:12,490 --> 00:47:18,940
+عبارة عن in تربيعin تربية هو ده الكلمة طلع معانا
+
+634
+00:47:18,940 --> 00:47:24,370
+مظبوطهي ال Interbia واضحة درجنا فيها من البداية
+
+635
+00:47:24,370 --> 00:47:27,510
+حينا حددناها ال Cartesian product معناته بتطلع ان
+
+636
+00:47:27,510 --> 00:47:31,130
+Interbia كcardinality total cardinality ال total
+
+637
+00:47:31,130 --> 00:47:34,190
+cardinality هذا معناته عدد العناصر في ال universe
+
+638
+00:47:34,190 --> 00:47:37,750
+of discourse اللي اتفقنا عليه لل relation على
+
+639
+00:47:37,750 --> 00:47:39,650
+اعتبار انه جولنا ال universe of discourse هي ال
+
+640
+00:47:39,650 --> 00:47:44,590
+cardinality لمين؟ لل Cartesian product طيب لما بدي
+
+641
+00:47:44,590 --> 00:47:47,370
+أجيب كل ال subsets الممكنين حسب التعريف ال
+
+642
+00:47:47,370 --> 00:47:51,090
+relation هي subset منالـ Cartesian product معناته
+
+643
+00:47:51,090 --> 00:47:56,510
+كإني بجيب ال power لل universe of discourse واللي
+
+644
+00:47:56,510 --> 00:47:59,390
+هي ال Cartesian product ف2nd to the power ال
+
+645
+00:47:59,390 --> 00:48:02,810
+cardinality لل set اللي بدور عليها أو ال universe
+
+646
+00:48:02,810 --> 00:48:07,030
+of discourse واللي هي N تربيع تمام، هيك و نكون
+
+647
+00:48:07,030 --> 00:48:10,720
+خلصناعلى جد الجزء هذا اللي هي المقدمة لل relations
+
+648
+00:48:10,720 --> 00:48:13,960
+عشان المرة اللي جاية ناخد مجموعة characteristic لل
+
+649
+00:48:13,960 --> 00:48:18,940
+relations و نشوف كيف بنقدر نعرفهم و نكمل في موضوع
+
+650
+00:48:18,940 --> 00:48:20,480
+ال relations يعطوكوا العفو و بركة الله فيكم
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XMLnhbATUyU.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XMLnhbATUyU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9eadfac2bb4613da2abb46d664383887726f1c35
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XMLnhbATUyU.srt
@@ -0,0 +1,2261 @@
+1
+00:00:05,040 --> 00:00:06,940
+بسم الله الرحمن الرحيم الصلاة والسلام على أشرف
+
+2
+00:00:06,940 --> 00:00:09,460
+الأنبياء والمرسلين سيدنا محمد نبدا اليوم يا شباب ان
+
+3
+00:00:09,460 --> 00:00:13,580
+شاء الله تعالى في chapter 3، chapter الثالث هنتكلم
+
+4
+00:00:13,580 --> 00:00:18,680
+فيه عن algorithms. فالـalgorithms مش هنتكلم فيه عن
+
+5
+00:00:18,680 --> 00:00:22,730
+programming languages. مش هذا الموضوع الـprogramming
+
+6
+00:00:22,730 --> 00:00:25,090
+language as a programming language. لأ احنا هتكلم
+
+7
+00:00:25,090 --> 00:00:30,210
+عن الـalgorithm as a structure،  الـalgorithm نفسه
+
+8
+00:00:30,210 --> 00:00:33,270
+كيف ينكتب الـalgorithm وكيف نتعامل معاه. فعشان هيك
+
+9
+00:00:33,270 --> 00:00:37,390
+بغض النظر ايش الـprogramming languages الجديدة
+
+10
+00:00:37,390 --> 00:00:42,530
+الحديثة او القديمة، احنا مش هنشتغل عليهم. ليش؟ لأنه
+
+11
+00:00:42,530 --> 00:00:46,470
+في النهاية احنا بدنا لغة مشتركة بينهم كلهم، اللغة
+
+12
+00:00:46,470 --> 00:00:49,210
+المشتركة، هذه اللغة الوصفية اللي هنسميها في الآخر
+
+13
+00:00:49,210 --> 00:00:53,230
+pseudocode. فهنتكلم عن حاجة اسمها الـpseudocode
+
+14
+00:00:53,230 --> 00:00:57,790
+اللي هو البرنامج الوصفي، بنوصف كيف بده يشتغل
+
+15
+00:00:57,790 --> 00:01:01,210
+البرنامج، بغض النظر انت ايش بتشتغلي. يعني بمعنى أن
+
+16
+00:01:01,210 --> 00:01:04,090
+المحاضرة هنا، ممكن يكون في شباب بيشتغلوا بيحبوا الـ
+
+17
+00:01:04,090 --> 00:01:06,790
+python، شباب بيحبوا الـJava، شباب بيحبوا الـC++
+
+18
+00:01:06,790 --> 00:01:09,470
+أحرار، بس في النهاية كلهم لازم يكونوا فاهمين
+
+19
+00:01:09,470 --> 00:01:14,130
+عليها، كلهم بدهم يفهموا آلية التفكير في الـ
+
+20
+00:01:14,130 --> 00:01:17,250
+algorithm، في الـcode، في البرنامج، بغض النظر
+
+21
+00:01:17,250 --> 00:01:20,630
+التفاصيل البسيطة اللي بتفرج بين لغة ولغة. فاحنا
+
+22
+00:01:20,630 --> 00:01:24,730
+بنتكلم عن منهجية كتابة برنامج، كيف ممكن أفكر في
+
+23
+00:01:24,730 --> 00:01:28,970
+البرنامج، مش في اللغة نفسها، مش في اللغة نفسها عشان
+
+24
+00:01:28,970 --> 00:01:33,830
+هيك هنستخدم حاجة اسمها الـpseudo code، الوصفة لكن
+
+25
+00:01:33,830 --> 00:01:37,630
+على الأقل كل مبرمج لازم يكون عنده لغة برمجة واحدة
+
+26
+00:01:37,630 --> 00:01:41,050
+على الأقل، بالإضافة للـpseudo code، لأن الـpseudo
+
+27
+00:01:41,050 --> 00:01:43,690
+code هي اللي هتربطك مع كل المبرمجين الآخرين. الـ
+
+28
+00:01:43,690 --> 00:01:47,710
+pseudo code هي اللي هتسمحلك انك تمسك أي كتاب مكتوب
+
+29
+00:01:48,520 --> 00:01:53,200
+عن البرمجة أو في جزء من البرنامج أو جزء من الـsub
+
+30
+00:01:53,200 --> 00:01:57,040
+routine لأي برنامج، تفهمه، مع ايش بتكلمه، بغض النظر
+
+31
+00:01:57,040 --> 00:02:00,220
+اللي اشتغل، ايش كانت اللغة تبعته، اللغة البرمجية طبعا
+
+32
+00:02:00,220 --> 00:02:05,120
+فاتفقنا أن احنا كلامنا هيكون على الـpseudocode. طيب
+
+33
+00:02:05,120 --> 00:02:08,860
+بطريقة وصفية بدون استخدام pseudocode، احنا ممكن
+
+34
+00:02:08,860 --> 00:02:12,740
+نقول مثلا in English. مثلا لو قلنا عندي sequence
+
+35
+00:02:12,740 --> 00:02:17,110
+معين وبدي أجيب الـmaximum value، maximum element،
+
+36
+00:02:17,110 --> 00:02:20,430
+maximum value of element. هنا بكل بساطة اللي هو
+
+37
+00:02:20,430 --> 00:02:24,570
+largest element. هقول: set the value of temporary
+
+38
+00:02:24,570 --> 00:02:29,470
+variable V. هيك باللغة، هقول لكم معناته: جيبوا لنا قيمة
+
+39
+00:02:29,470 --> 00:02:36,490
+مؤقتة، متغير مؤقت وسموه V. كويس، الـV هذا هيكون عبارة
+
+40
+00:02:36,490 --> 00:02:42,990
+عن مؤقت temporary، وحتى اللحظة so far هو اللي
+
+41
+00:02:42,990 --> 00:02:47,800
+بتفترض أن هو أعلى قيمة. أنا قاعد بوصف إيش بدنا نعمل
+
+42
+00:02:47,800 --> 00:02:51,520
+بدون ما أدخل في تفاصيل الـJava والـC++ والـ
+
+43
+00:02:51,520 --> 00:02:55,280
+Python والكلام ده كله إطلاقا. قاعدين نتكلم لغة
+
+44
+00:02:55,280 --> 00:03:00,360
+هقول لكم أفكار بكل بساطة. إذا بدك أكبر رقم في الـarray
+
+45
+00:03:00,360 --> 00:03:06,170
+افرض عندك متغير مؤقت، وافترض أن هو اللي هيحتوي على
+
+46
+00:03:06,170 --> 00:03:09,510
+أكبر قيمة ممكنة، وحتى اللحظة هو أكبر قيمة ممكنة
+
+47
+00:03:09,510 --> 00:03:13,110
+على اعتبار أنه هيحتوي على أول عنصر. انت بتعمل بحث
+
+48
+00:03:13,110 --> 00:03:18,190
+أن أول عنصر هو الـmaximum. الآن بعد هيك، lock العنصر
+
+49
+00:03:18,190 --> 00:03:22,530
+اللي وراه. طلع العنصر اللي وراه. إذا العنصر اللي وراه
+
+50
+00:03:22,530 --> 00:03:29,810
+أكبر من قيمة V، من قيمة الـV، حط V بتساوي قيمة
+
+51
+00:03:29,810 --> 00:03:40,180
+العنصر الجديد، وروح لـA3، لـA4، لما تخلص لـAN. بس تخلص
+
+52
+00:03:40,180 --> 00:03:44,140
+print قيمة V. قيمة V هتكون هي الـmaximum أو الـ
+
+53
+00:03:44,140 --> 00:03:48,100
+largest value. هذا الكلام، هيك لا قلت لك أعمل for loop
+
+54
+00:03:48,100 --> 00:03:53,030
+ولا قلت لك أعمل ولا أي شيء. هي language، ف انت وصلتك الفكرة
+
+55
+00:03:53,030 --> 00:03:55,910
+صحيح، لو بتشتغل C++ على طول، الكلمتين اللي احنا
+
+56
+00:03:55,910 --> 00:03:58,230
+قلناهم بتروح بترجمها بلغتك. اللي بيشتغل Python
+
+57
+00:03:58,230 --> 00:04:01,370
+هيروح يترجمها بلغته. اللي بيشتغل Java هيروح يترجمها
+
+58
+00:04:01,370 --> 00:04:05,270
+بلغته. فهذا هو المقصود أن احنا بنتكلم عن وصف في
+
+59
+00:04:05,270 --> 00:04:09,170
+الآخر، بنعمل return لقيمة V النهائية بعد ما كنت
+
+60
+00:04:09,170 --> 00:04:14,800
+عملت scan على كل الـelements داخل الـarray. خلصنا
+
+61
+00:04:14,800 --> 00:04:19,260
+فبأضمن لك أن الـV.. آخر V وصلت لها هتكون هي الـ
+
+62
+00:04:19,260 --> 00:04:24,420
+maximum، هي فعلا الـlargest value. الكلام هذا بده
+
+63
+00:04:24,420 --> 00:04:29,780
+شوية تثبيت عشان يكون باين ومناسب أكتر، لأن حتى
+
+64
+00:04:29,780 --> 00:04:35,080
+اللغة ممكن تكون فيها تشابه أو فيها اختلافات من فهم
+
+65
+00:04:35,080 --> 00:04:39,940
+لفهمك. فعشان هيك كان ضروري جدا أن يطلع برنامج أو
+
+66
+00:04:39,940 --> 00:04:45,160
+code لفظي، بس يكون الـcode مرتب. بالشكل هذا، okay؟
+
+67
+00:04:45,160 --> 00:04:49,880
+منطقية حاليا، لكن لو بدي أجيب مواضيع أكبر وأضخم، مش
+
+68
+00:04:49,880 --> 00:04:53,020
+هقدر أوصفها هي الكلام ورا بعض، هتكون صعبة جدا لما
+
+69
+00:04:53,020 --> 00:04:56,140
+نوصفها كلام ورا بعض. عشان هيك بدنا نحط structure
+
+70
+00:04:56,140 --> 00:05:03,200
+للغة لفظية، فيها flexibility عالية، لكن أقرب للغة
+
+71
+00:05:03,200 --> 00:05:07,940
+البرمجة، أقرب للغة البرمجة. بمعنى أحط فيها العناصر
+
+72
+00:05:07,940 --> 00:05:12,480
+الأساسية المشتركة في لغة البرمجة. كل لغات البرمجة
+
+73
+00:05:12,480 --> 00:05:17,820
+طريقة شرحها واحدة، كلهم طريقة شرحهم واحدة. كلهم أول
+
+74
+00:05:17,820 --> 00:05:21,180
+ما نبدأ فيهم، نبدأ بنقول مقدمة، كيف تعمل
+
+75
+00:05:21,180 --> 00:05:24,880
+installation للـcompiler. أول نقطة. طيب الدرس اللي
+
+76
+00:05:24,880 --> 00:05:28,790
+ورا الـvariables وأنواعه، وكيف نعرف كل نوع من
+
+77
+00:05:28,790 --> 00:05:30,890
+أنواع الـvariables، ونقعد نتكلم على الـinteger وعلى
+
+78
+00:05:30,890 --> 00:05:36,670
+الـreal values، كيف ممكن تحطها إذا كان fraction،
+
+79
+00:05:36,670 --> 00:05:42,410
+إذا كان character، كيف تعملوا كـinput. بعد هيك بتروح
+
+80
+00:05:42,410 --> 00:05:45,010
+على الـloop، عفوا على الـselection، أول على الـ
+
+81
+00:05:45,010 --> 00:05:48,400
+selection، الـif then، بتدرس فيها الـif then وكل
+
+82
+00:05:48,400 --> 00:05:51,500
+مشتقاتها، وبعدين بتروح على الـloop، وبتاخد الـ
+
+83
+00:05:51,500 --> 00:05:55,100
+while، وبتاخد الـfor loop، وبتاخد كل شغله، وبعدين
+
+84
+00:05:55,100 --> 00:05:57,520
+بتروح إذا كان في، بدك تروح على الـfunction أو كنت
+
+85
+00:05:57,520 --> 00:05:59,820
+بتسموها الـmethod أو بتسموها الـsub routine، اللي
+
+86
+00:05:59,820 --> 00:06:02,960
+هو كيف ممكن أعمل استدعاء لبرنامج انت كتبته عندك، and
+
+87
+00:06:02,960 --> 00:06:07,700
+so on. فإذا هذه عناصر مشتركة. طب نفس الشيء، بدنا نحط
+
+88
+00:06:07,700 --> 00:06:12,660
+العناصر المشتركة هذه في لغة بحيث أن أي مبرمج
+
+89
+00:06:12,660 --> 00:06:18,210
+يفهمها، أي مبرمج يفهمها. فإجتي فكرة أن احنا ممكن نعدل
+
+90
+00:06:18,210 --> 00:06:23,230
+شوية للـpseudocode اللي توه كتبناه، لو بدنا نطبقه
+
+91
+00:06:23,230 --> 00:06:27,430
+هيتطبق، مش هيقول لأ. لكن زي ما قلنا، مش في كل
+
+92
+00:06:27,430 --> 00:06:30,750
+البرامج ممكن تعمل نفس الـdash اللي انت dashيته توه
+
+93
+00:06:30,750 --> 00:06:36,510
+هناك هنا. يعني لو قلنا مثلا بدي أحط AI7123158، أول
+
+94
+00:06:36,510 --> 00:06:41,310
+شغلة بدي أحط المتغير المؤقت هذا، temporary value أو
+
+95
+00:06:41,310 --> 00:06:46,700
+temporary variable V بتساوي أول عنصر، سبعة. وحتى
+
+96
+00:06:46,700 --> 00:06:51,260
+اللحظة هي أكبر عنصر حتى اللحظة. أنا لسه مكملتش، فإذن
+
+97
+00:06:51,260 --> 00:06:55,360
+حتى اللحظة هي الأكبر. بننظر لللي بعده، اللي بعده
+
+98
+00:06:55,360 --> 00:06:59,140
+اثنا عشر. بشوف إذا كان الاثنا عشر هذه أكبر من V، بنحط
+
+99
+00:06:59,140 --> 00:07:05,640
+قيمتها في V، otherwise بنسيبها. فإذن yes it changed
+
+100
+00:07:05,640 --> 00:07:11,000
+V to إيش؟ لقيت اثنين اللي هي اثنا عشر. look at the next
+
+101
+00:07:11,000 --> 00:07:19,000
+element، ثلاثة. No. فإذا A3 ليست أكبر من V، No، leave V
+
+102
+00:07:19,000 --> 00:07:23,260
+alone. سيب V زي ما هي، وشوف اللي وراه، and so on، و
+
+103
+00:07:23,260 --> 00:07:27,320
+هكذا. في الآخر لما تخلص كل الـarray تبعتك أو الـ
+
+104
+00:07:27,320 --> 00:07:32,160
+sequence تبعك، اطبع قيمة V. الـV اللي هتطبعها هي
+
+105
+00:07:32,160 --> 00:07:36,640
+largest element أو largest value للـelements اللي
+
+106
+00:07:36,640 --> 00:07:44,010
+موجودين عندك. فprint it كخطوة أخيرة. الآن، إيش اللي
+
+107
+00:07:44,010 --> 00:07:47,930
+بهمنا لما بتكتب code، لما بتكتب code، بهمك
+
+108
+00:07:47,930 --> 00:07:51,750
+تكون عارف الـinputs كويس، هي كل الـinformation أو
+
+109
+00:07:51,750 --> 00:07:55,310
+الـdata اللي بتروح للبرنامج، بده ياخدها منك
+
+110
+00:07:55,310 --> 00:07:59,750
+البرنامج، فهي رايحة للبرنامج أو comes in للبرنامج
+
+111
+00:07:59,750 --> 00:08:04,110
+للـcode. الـoutput هي، وهذا بده تكون حاذر فيه كتير
+
+112
+00:08:04,110 --> 00:08:07,450
+كويس. انت إيش اللي بدك إياه من الـcode؟ إيش بدك من
+
+113
+00:08:07,450 --> 00:08:10,350
+الـcode؟ outputs. فهذه الـinformation أو الـdata
+
+114
+00:08:10,350 --> 00:08:15,750
+اللي أنت مستنيها من الـcode. كويس. فـthat goes out أو
+
+115
+00:08:15,750 --> 00:08:20,390
+اللي هتطلع لك من الـcode وتاخدها. طيب، في حاجة اسمها
+
+116
+00:08:20,390 --> 00:08:25,250
+الـdefiniteness، هادي اللي هي precisely defined،
+
+117
+00:08:25,250 --> 00:08:30,290
+لازم يكون الـcode برضه معرف بشكل مختصر، بس كافي
+
+118
+00:08:30,290 --> 00:08:34,710
+واضح، بشكل مختصر، بدي يكون واضح. فهدا الوضوح مهم جدا
+
+119
+00:08:34,710 --> 00:08:37,610
+في الـcode. الوضوح بدي يكون كتير مهم في الـcode. الـ
+
+120
+00:08:37,610 --> 00:08:43,850
+correctness، correctness ضرورية، وهدي بتبينش معك إلا
+
+121
+00:08:43,850 --> 00:08:48,450
+مع التجربة. يعني بمعنى لما بتعمل code، جرب مجموعة
+
+122
+00:08:48,450 --> 00:08:54,250
+arguments عليه، مجموعة inputs، ونوعها، ننوع مجموعة الـ
+
+123
+00:08:54,250 --> 00:08:57,190
+inputs، وشوف الـoutput صح ولا غلط. ليش؟ لأنه ممكن
+
+124
+00:08:57,190 --> 00:09:00,910
+يظهر عندك أحد أنواع الـerrors اللي هي
+
+125
+00:09:03,270 --> 00:09:06,610
+لأ، لسه ما وصلناش للـtime في الـcorrectness، الـ
+
+126
+00:09:06,610 --> 00:09:11,930
+logic أو الـalgorithmic logic، في ناس بيسموها
+
+127
+00:09:11,930 --> 00:09:14,650
+algorithmic error، وفي ناس بيسموها الـlogic، الـ
+
+128
+00:09:14,650 --> 00:09:18,850
+logic error، اللي هي بتطلع لك نتائج، بس النتائج
+
+129
+00:09:18,850 --> 00:09:23,830
+مش صح، نتائج مش صحيحة. فهذا نوع من أنواع الـerror.
+
+130
+00:09:23,830 --> 00:09:27,110
+عشان تعمله بدك لازم تحقق الـcorrectness، وعشان
+
+131
+00:09:27,110 --> 00:09:29,990
+تحقق الـcorrectness، ما تستناش الـuser هو اللي يجرب
+
+132
+00:09:29,990 --> 00:09:34,670
+ويقول لك فيه أخطاء. انت بدك تجرب على كذا input، وتكون
+
+133
+00:09:34,670 --> 00:09:39,110
+عارف للـinput هذا، لازم يكون في output إيش بيساوي، و
+
+134
+00:09:39,110 --> 00:09:41,950
+تشوف هل طلع ولا لأ. فالـoutputs related للـ
+
+135
+00:09:41,950 --> 00:09:45,670
+input لازم يكونوا فعلا related لبعض. فبتكون خلصت من
+
+136
+00:09:45,670 --> 00:09:49,050
+أهم مشكلة من المشاكل اللي هي دائما ضايع، اللي انت
+
+137
+00:09:49,050 --> 00:09:53,350
+بيعطيك مش syntax error، اللي هو يطلع لك code syntax
+
+138
+00:09:53,350 --> 00:09:56,530
+error، كلك كلك عارفينه، أنه معناته في الـstructure، في
+
+139
+00:09:56,530 --> 00:10:00,510
+بناء الـ..الـ..الـstatement، في حاجة باينة غلط، في
+
+140
+00:10:00,510 --> 00:10:04,110
+قوس مش موجود، semicolon مش موجودة، في في في..
+
+141
+00:10:04,110 --> 00:10:06,030
+هذه هو لحاله بتطلع لك إياها الـcompiler لحاله
+
+142
+00:10:06,030 --> 00:10:09,270
+بيبين لك إياها، بس النوع اللي بيظهرش عندك وانت
+
+143
+00:10:09,270 --> 00:10:13,230
+بتاخدش بالك منه في الغالب، هو مشاكل الـlogic أو الـ
+
+144
+00:10:13,230 --> 00:10:18,390
+arithmetic، الحسابي، لأنه هتطلع لك نتائج، بس النتائج
+
+145
+00:10:18,390 --> 00:10:25,160
+هذه نتائج خطأ. فلازم تتحقق الـcorrectness في أي code
+
+146
+00:10:25,160 --> 00:10:29,140
+بدك تكتبه. الـfinite..الـfiniteness..الـ
+
+147
+00:10:29,140 --> 00:10:33,500
+finiteness، هنا بنتكلم عن الـforever، لـdescription
+
+148
+00:10:33,500 --> 00:10:37,600
+أو للـ..للـrun، أنه يظل forever. هنا بنتكلم عن الـ
+
+149
+00:10:37,600 --> 00:10:39,860
+runtime error، اللي كان، تبقى بتتكلم عن الـruntime
+
+150
+00:10:39,860 --> 00:10:43,080
+error. اه، هنا معناته انت ممكن في الحالة هذه لو
+
+151
+00:10:43,080 --> 00:10:46,300
+جالك runtime error، معناته ذلك بدك تراجع أهم شغلة
+
+152
+00:10:46,300 --> 00:10:52,900
+الـfor loop، سواء تتكلم عن for أو while، تتأكد هل انت
+
+153
+00:10:52,900 --> 00:10:57,920
+حاطط بالظبط الـstatement اللي بتعمل إيقاف ولا لأ،
+
+154
+00:10:57,920 --> 00:11:00,860
+ولا انت سايبها forever. الشغل التاني والأهم واللي
+
+155
+00:11:00,860 --> 00:11:05,000
+هاد بيضيع أحيانا منكم، هي فكرة أن ممكن تكون انت في
+
+156
+00:11:05,000 --> 00:11:08,920
+معادلة، ومعادلة قسمت على value، وانت مش مدرك أن
+
+157
+00:11:08,920 --> 00:11:13,320
+في حالة من الحالات ممكن تطلع صفر، فبيظهر عندك hit
+
+158
+00:11:13,320 --> 00:11:17,500
+error، خلاص، يعني الجهاز بيروح و بيرجعش، الـcode بيروح و
+
+159
+00:11:17,500 --> 00:11:22,940
+انت مستنيه وهو خلاص مش هيرجع لك، مش هيرجع، انتهى، صار
+
+160
+00:11:22,940 --> 00:11:27,420
+في عندك runtime error. زي ما قلنا، مش بالضروري for
+
+161
+00:11:27,420 --> 00:11:29,920
+loop، لإنه هتراجع الـfor loop، هتلاقي الصحيحة، بس انت
+
+162
+00:11:29,920 --> 00:11:34,460
+ما أخدتش بالك أن واحدة من المعادلات قد تكون الـ
+
+163
+00:11:34,460 --> 00:11:41,820
+input، بحسبة معينة، سبب لك أن في مقام طلع صفر. خذوا
+
+164
+00:11:41,820 --> 00:11:45,740
+بالكم هذا برضه نفس الشيء، هيخلي بالـfiniteness،
+
+165
+00:11:45,740 --> 00:11:49,260
+بالمحدودية للحسابات تبعتك، لأنها هتصير forever،
+
+166
+00:11:49,260 --> 00:11:53,620
+هتبقى شغالة. طيب الـeffectiveness، الـeffectiveness،
+
+167
+00:11:53,620 --> 00:11:58,720
+اللي هي كل step لحالها هي effective لحالها، هي لها
+
+168
+00:11:58,720 --> 00:12:03,400
+فعليتها. فهذه بتوفر عليك أن ما يكونش في عندك خطوات
+
+169
+00:12:03,400 --> 00:12:08,520
+مالهاش لازمة، مالهاش
+
+223
+00:15:34,190 --> 00:15:38,590
+code معناه ديروا بالكم هو اللي بتقرأه algorithm
+
+224
+00:15:38,590 --> 00:15:42,810
+بعرف أن أنا داخل على algorithm الآن، ال procedure و
+
+225
+00:15:42,810 --> 00:15:46,640
+إذا كان مطبوعًا، بتحطه bold، وإذا كانت طباعة،
+
+226
+00:15:46,640 --> 00:15:52,700
+فبتحطه bold. ف ال procedure بتحط اسمه. بعد هيك نفترض
+
+227
+00:15:52,700 --> 00:15:56,300
+زي المثال تبع طوى، كنا بنشتغل على ال largest value
+
+228
+00:15:56,300 --> 00:15:59,660
+ممكن أكتب max، أسمي ال code تبعي على اعتبار أنه إيه؟
+
+229
+00:15:59,660 --> 00:16:03,940
+دلالة بالمحتوى. سميه largest، okay؟ سميه بديكيا بس
+
+230
+00:16:03,940 --> 00:16:07,620
+يكون دلالة لأن أنت في النهاية هو مش القصد أني بدي
+
+231
+00:16:07,620 --> 00:16:12,730
+أطبعه حاليًا، لأ، القصد أني أنا بدي أفهمه. يا مبرمج
+
+232
+00:16:12,730 --> 00:16:16,670
+ثاني معايا، بحيث أنه نتناقش فيه قليلًا. الحل طبعًا أنا
+
+233
+00:16:16,670 --> 00:16:19,770
+بشتغل C++، هو بشتغل Java، بس لا يمنع أن احنا نقعد مع
+
+234
+00:16:19,770 --> 00:16:23,130
+بعض ونحل مشكلة مع بعض. إيش المشكلة؟ ليش لازم يكون
+
+235
+00:16:23,130 --> 00:16:28,610
+نفس اللغة اللي بتعلمّنها؟ لأ، okay. بدي أكون عارف
+
+236
+00:16:28,610 --> 00:16:32,450
+الاسم. الاسم يكون له دلالة، وبعدين الأقواس. هنتكلم
+
+237
+00:16:32,450 --> 00:16:34,910
+عنها. فيه arguments، ونوع ال arguments، هل يوجد
+
+238
+00:16:34,910 --> 00:16:38,730
+هنمسكهم واحدة واحدة. تمام. otherwise باقي الأنواع
+
+239
+00:16:38,730 --> 00:16:43,300
+هنسميها statements. هنسميهم ال statements، والآن
+
+240
+00:16:43,300 --> 00:16:46,880
+هنمسكهم واحدة واحدة. كل واحدة من هدول نشرح بالضبط
+
+241
+00:16:46,880 --> 00:16:50,700
+إيش بتعمل، وأنتوا مبرمجين، وأخذتوا Java واحد و
+
+242
+00:16:50,700 --> 00:16:53,120
+اتنين، فمش هتتغلبوا فيها كتير. على السريع هنبرمج
+
+243
+00:16:53,120 --> 00:16:57,520
+عليها. ال procedure، وهنا ال procedure name اللي هو
+
+244
+00:16:57,520 --> 00:17:01,120
+اسم الإجراء، بمعنى اسم ال code. تفتح أقواس ال
+
+245
+00:17:01,120 --> 00:17:04,340
+arguments، اللي هي ال inputs. إيش ال inputs اللي
+
+246
+00:17:04,340 --> 00:17:11,460
+لازمة لل code هذا؟ زائد إيش نوعه؟ تحط colon ونوعه
+
+247
+00:17:11,460 --> 00:17:16,560
+تمام، فبتعمل declaration لداخل ال text، أنه
+
+248
+00:17:16,560 --> 00:17:20,460
+بتعرفنا أن في procedure احنا داخلين عليه، بمعنى دير
+
+249
+00:17:20,460 --> 00:17:24,040
+بالكم. كل اللي كان فات هذا language عادية، اللي جاي
+
+250
+00:17:24,040 --> 00:17:29,360
+لأ، هذا وصف ل code اللي جاي، وصف ل code كويس. أول شغل
+
+251
+00:17:29,360 --> 00:17:32,240
+ال argument هذا، اللي هي ال inputs، مجموعة ال inputs
+
+252
+00:17:32,240 --> 00:17:38,580
+لل code، وبعدين بنحط له نوعه. إيش نوعه؟ مثال زي طوى
+
+253
+00:17:38,580 --> 00:17:42,500
+لما كنا بندور على ال maximum. بكتب procedure، وبعدين
+
+254
+00:17:42,500 --> 00:17:47,060
+maximum مثلًا، أو max، أو اكتب اللي بدك إياه، المهم تكون
+
+255
+00:17:47,060 --> 00:17:50,460
+لها علاقة بإيش ال functionality ده. أعطي ال code
+
+256
+00:17:50,460 --> 00:17:58,360
+maximum list. هقول مثلًا، محتاج ال ... طب ال ... هاد إيش؟ colon
+
+257
+00:17:58,360 --> 00:18:03,140
+list of integers. فعرفت أن ال ... ال ... هذي لازم تكون
+
+258
+00:18:03,140 --> 00:18:07,900
+integers. لما يجيب لي يدخلني يعطيني list of real
+
+259
+00:18:07,900 --> 00:18:16,060
+values، هقوله لأ، بتشتغلش عندي، لأن ال code بعد هيك
+
+260
+00:18:16,060 --> 00:18:21,090
+هكون أنا كاتبه بما يتناسب مع ال integers، مش مع real
+
+261
+00:18:21,090 --> 00:18:26,830
+values. كويس؟ فهذا هو تعريف بسيط، أنه بس تحط عنوان
+
+262
+00:18:26,830 --> 00:18:31,970
+تعطيه، زي ما بقوله مؤشر للقارئ، يقول للقارئ: stop، أنت
+
+263
+00:18:31,970 --> 00:18:37,050
+داخل على ال algorithm. طيب، ال variable: colon equal
+
+264
+00:18:37,050 --> 00:18:39,550
+أو expression، بتحط ال expression تبعك. فهذه
+
+265
+00:18:39,550 --> 00:18:42,730
+المتغيرات هذه، مش معنى كيف تكتب معادلة، كيف تكتب
+
+266
+00:18:42,730 --> 00:18:48,370
+معادلة. هتحط المتغير وتقول: colon equal. خلاص، بعرف
+
+267
+00:18:48,370 --> 00:18:52,770
+أن هذه هي علامة المساواة في ال pseudocode، وبتحط
+
+268
+00:18:52,770 --> 00:18:56,510
+المعادلة اللي بدك تكتبها. بتحط أي معادلة أنت حابب
+
+269
+00:18:56,510 --> 00:18:59,770
+تكتبها. فهذا ال expression السهل البسيط، زي هنا V
+
+270
+00:18:59,770 --> 00:19:07,130
+colon equal three X plus seven. ال input الآن حسب
+
+271
+00:19:07,130 --> 00:19:12,410
+قيمة X. حاطط لك input ل X، تضرب، فبتعرف قيمة V. بتعرف من
+
+272
+00:19:12,410 --> 00:19:16,510
+خلالها قديش قيمة V. خلصنا، معادلة مش أكثر من هيك في
+
+273
+00:19:16,510 --> 00:19:24,550
+ال pseudocode. لكن مش في ال real-time. احنا ممكن نكتب
+
+274
+00:19:24,550 --> 00:19:28,270
+ال expression هذا بصيغة informal، وهذا بيعطيني
+
+275
+00:19:28,270 --> 00:19:31,130
+أريحية، عشان أقول إن ال code هذا فيه flexibility
+
+276
+00:19:31,130 --> 00:19:36,990
+عن ال real programming language. بمعنى أنت مش
+
+277
+00:19:36,990 --> 00:19:42,150
+مستحيل في ال real code ترجع تكتب مثلًا x colon
+
+278
+00:19:42,150 --> 00:19:47,970
+equal the largest integer in the list L. هنا مسموحة
+
+279
+00:19:47,970 --> 00:19:51,650
+لأنه بعرف إنه في النهاية هذا الجزء لحاله هو
+
+280
+00:19:51,650 --> 00:19:55,950
+function أو sub-routine أو method لحالها. ممكن في
+
+281
+00:19:55,950 --> 00:20:00,220
+الآخر أنا وياك متفقين أن هذه قصة بسيطة. خلّينا في
+
+282
+00:20:00,220 --> 00:20:03,180
+المشكلة الأكبر. في حاجة أكتب لك ... طب احنا ممكن لو
+
+283
+00:20:03,180 --> 00:20:05,540
+افترضنا لو قدرنا نحسب مثلًا X على أساس أن هي the
+
+284
+00:20:05,540 --> 00:20:08,520
+largest integer. أنت مش هتقولي كيف و ليش ومن وين
+
+285
+00:20:08,520 --> 00:20:12,380
+احنا قاعدين فاهمين بعض، بس أنا لغتي غير لغتك كـ real
+
+286
+00:20:12,380 --> 00:20:16,000
+language. لكن بنفكر مع بعض، أو بنفكر مع بعض، مش
+
+287
+00:20:16,000 --> 00:20:18,920
+المشكلة. بقولك أنه آه، ممكن تحسب ال X على أساس أن هي
+
+288
+00:20:18,920 --> 00:20:21,220
+the largest. فيها مشكلة؟ هتقولي لأ، فيش فيها مشكلة.
+
+289
+00:20:21,220 --> 00:20:23,980
+قولت له: هقول لك، خلاص، خلينا نكمل. هذي X ممكن نستخدمها و
+
+290
+00:20:23,980 --> 00:20:29,130
+كذا وكذا ونكمل. مسموح آه، ممكن نكتب هيك ... ممكن
+
+291
+00:20:29,130 --> 00:20:34,010
+نكتب هيك إذا استدعى الأمر. أكيد طبعًا في ال real
+
+292
+00:20:34,010 --> 00:20:37,270
+code مستحيل ... في ال real code مستحيل نعمل هيك. طيب،
+
+293
+00:20:37,270 --> 00:20:40,310
+ال informal statement هذه، ال informal statement
+
+294
+00:20:40,310 --> 00:20:45,670
+ناخد بالنا بس أنه فيها limit لأنك تعمل هيك، لأنه في
+
+295
+00:20:45,670 --> 00:20:47,930
+النهاية معناته ممكن ما تضطر تكتبش ال code كله على
+
+296
+00:20:47,930 --> 00:20:52,520
+بعضه وتقول ما هو هيك وخلاص. أقول لك: بدي code عشان
+
+297
+00:20:52,520 --> 00:20:56,360
+تجيب لي ال largest element، تكتب لي x equal the
+
+298
+00:20:56,360 --> 00:20:58,960
+largest element in the list. يا سلام، خلصنا هيك على
+
+299
+00:20:58,960 --> 00:21:05,300
+طول. ففي limits بدنا ناخد بالنا أنه أحيانًا بنكتب ال
+
+300
+00:21:05,300 --> 00:21:10,010
+statements بـ informal language. في الآخر زي أن أقول
+
+301
+00:21:10,010 --> 00:21:14,150
+بدي أبدّل رقمين، عملية تبديل الرقمين، أنتم كلكم
+
+302
+00:21:14,150 --> 00:21:20,270
+عارفين أنك بدك تضطر تعمل لها متغير مؤقت. لو قلنا
+
+303
+00:21:20,270 --> 00:21:26,590
+مثلًا a و b، بدك تبدل قيمهم مع بعض، أنت عارف أنه لازم
+
+304
+00:21:26,590 --> 00:21:31,070
+يكون في متغير v، هذا اللي هو temporary variable،
+
+305
+00:21:31,070 --> 00:21:36,270
+بحيث أنك تقول: v بتساوي a، ثم بعد هيك رقم واحد، رقم
+
+306
+00:21:36,270 --> 00:21:45,890
+اتنين، تقول: A بتساوي B، ثم B بتساوي v، صحيح؟
+
+307
+00:21:45,890 --> 00:21:49,310
+يعني الحاجة الأبسط اللي ممكن تتبدل في ذهن أي حد. لا،
+
+308
+00:21:49,310 --> 00:21:55,770
+أنت ممكن هنا تكتب swap X and Y، وخلاص. ومتفقين كلنا
+
+309
+00:21:55,770 --> 00:22:00,210
+وصلنا لمرحلة أن احنا مبرمجين كويس، أنت مش لسه
+
+310
+00:22:00,210 --> 00:22:04,270
+بتتعلم برمجة، أنت خلصت جثة البرمجة. فلما أقول لك swap
+
+311
+00:22:04,270 --> 00:22:11,070
+X and Y، مش هتيجي تقولي كيف. مدام الفكرة البسيطة هذه
+
+312
+00:22:11,070 --> 00:22:14,930
+ممكن نحطها بمصطلح زي هذا. بس احنا متفقين إنه هذه
+
+313
+00:22:14,930 --> 00:22:21,390
+ألف باء البرمجة، مش محتاج أجود أعجب فيها، وأي واحد
+
+314
+00:22:21,390 --> 00:22:24,410
+بياخد أقل course في البرمجة بيكون عارفها. فممكن
+
+315
+00:22:24,410 --> 00:22:29,550
+نكتبها بهذا الشكل وخلاص، swap X and Y، انتهينا، تمام.
+
+316
+00:22:29,550 --> 00:22:33,670
+لكن بدأنا ناخد في بالنا إنه في ال real programming
+
+317
+00:22:33,670 --> 00:22:37,010
+language الكلام ده مش مسموح. الكلام ده لازم تروح
+
+318
+00:22:37,010 --> 00:22:43,070
+تعمل code رسمي فعلًا ياخد من إلى ... من إلى ... كويس.
+
+319
+00:22:43,070 --> 00:22:46,410
+طبعًا في بعض ال compilers بالمناسبة هي smart enough
+
+320
+00:22:46,410 --> 00:22:50,250
+أن أنت تقولها بدّلهم مع بعض، وتبدلهم بس من غير ما
+
+321
+00:22:50,250 --> 00:22:57,330
+تقول لك أن هي استخدمت v، هي لحالها استخدمت v، أما مش
+
+322
+00:22:57,330 --> 00:23:00,990
+عملت لك إياها فقط بعمليتين أو عملية واحدة، لأ، هي
+
+323
+00:23:00,990 --> 00:23:06,940
+عملت التلات عمليات، لكن ما أورّجت cash إياها. تمام؟ كويس.
+
+324
+00:23:06,940 --> 00:23:11,800
+الآن، من الحاجات المهمة جدًا أن أنت مش تيجي يكون
+
+325
+00:23:11,800 --> 00:23:15,280
+مطلوب أنك تعمل بعض الأمور، تروح تقول لي: do so and so،
+
+326
+00:23:15,280 --> 00:23:20,340
+أنا طالب منك كذا وكذا، مثلًا تروح تكتب لي: do كذا و
+
+327
+00:23:20,340 --> 00:23:24,140
+كذا، زي توّ بقول لك: بدي منك ال largest element، تقول لي
+
+328
+00:23:24,140 --> 00:23:30,260
+x colon equal the largest element in the list، خلصت
+
+329
+00:23:30,260 --> 00:23:33,680
+البرنامج. إيش اللي خلّصنا البرنامج؟ أنا طالب منك
+
+330
+00:23:33,680 --> 00:23:38,040
+أصلًا so and so، تروح تكتب لي do so and so، وخلصنا
+
+331
+00:23:38,040 --> 00:23:41,480
+هيك؟ لأ، مش لها درجة. ال informal language هتكون، مش
+
+332
+00:23:41,480 --> 00:23:47,750
+لها درجة، كويس؟ فلازم على الأقل so and so هتجسّمها
+
+333
+00:23:47,750 --> 00:23:51,550
+ال algorithm لـ detailed steps، لازم تتجسّم لـ
+
+334
+00:23:51,550 --> 00:23:55,030
+detailed steps، بحيث أنه لو بدّي أكتبها على الوصف
+
+335
+00:23:55,030 --> 00:23:59,310
+تبعك، أكتبها مباشرة statements، عالسريع على اللغة
+
+336
+00:23:59,310 --> 00:24:02,930
+اللي أنا بشتغل عليها، لازم تكون موضّحة كلغة صحيحة. ما
+
+337
+00:24:02,930 --> 00:24:05,730
+جبت ال cash، استخدم ال expression بتاع ال real
+
+338
+00:24:05,730 --> 00:24:09,610
+language اللي أنت بتستخدمها زي ما هي، لكن على الأقل
+
+339
+00:24:09,610 --> 00:24:14,970
+وأنت بتكتب ال code، أنت قاعد بتفكر line by line، وصفه
+
+340
+00:24:14,970 --> 00:24:20,690
+بيختلف آه، لكن مش هتروح تعملي يالا بس. هنعمل كذا، طب
+
+341
+00:24:20,690 --> 00:24:23,630
+ما هو أصلًا المطلوب تعمل كذا. تجيب لي في الامتحان
+
+342
+00:24:23,630 --> 00:24:26,730
+أقول لك: والله جيب لي the largest element في list، و
+
+343
+00:24:26,730 --> 00:24:31,650
+أعطيك ال list، تقول لي: x بتساوي the largest element،
+
+344
+00:24:31,650 --> 00:24:34,370
+جبت لك يا دكتور، ومتوقّع طبعًا تيجي تقول لي: ما هو أنت
+
+345
+00:24:34,370 --> 00:24:36,310
+مش قلت informal statement؟ هاني عملت informal
+
+346
+00:24:36,310 --> 00:24:41,350
+statement، مش لها درجة. طيب، ناخد أول statement من ال
+
+347
+00:24:41,350 --> 00:24:44,660
+statements اللي ... اللي ممكن نبدأ نشتغل عليها هي ال
+
+348
+00:24:44,660 --> 00:24:47,360
+beginning والـ end، واللي أنتم كنتوا بتستخدموها
+
+349
+00:24:47,360 --> 00:24:52,540
+ال curly braces، أخذتوها ال curly braces، مش هيك؟
+
+350
+00:24:52,540 --> 00:24:55,960
+تمام. هذي إيش كنتوا تعملوا؟ يعني إيش بتفهم منها؟ ال
+
+351
+00:24:55,960 --> 00:24:59,820
+block، ال block هذا، بمعنى أن كل ال statements اللي
+
+352
+00:24:59,820 --> 00:25:04,690
+جوا، كأنها one statement، as a one statement، بعملها
+
+353
+00:25:04,690 --> 00:25:07,810
+running، كأنها هي كاملة على بعضها، statement واحدة.
+
+354
+00:25:07,810 --> 00:25:11,510
+بنحتاجها للكلام، بنحتاجه، بنحتاجه أحيانًا مع ال for
+
+355
+00:25:11,510 --> 00:25:19,410
+loop، بنحتاجه مع ال while، مع ال if then، لما يكون ال
+
+356
+00:25:19,410 --> 00:25:23,710
+then هذه هي مش statement واحدة، بدها تتطبّق عدة
+
+357
+00:25:23,710 --> 00:25:29,730
+statements في بعضها، والأكواد بتفهم أن جواب الشرط
+
+358
+00:25:29,730 --> 00:25:34,740
+هو بس السطر اللي ورا then فقط. خدوا بالكم، وهذه أحد
+
+359
+00:25:34,740 --> 00:25:39,400
+الأخطاء بتاعت ال logic، ال code مش هيقول لك أنه غلط،
+
+360
+00:25:39,400 --> 00:25:43,980
+لكن فعليًا حسابيًا هو أخد أول statement. إذا أنت
+
+361
+00:25:43,980 --> 00:25:50,980
+ما حطّيتش ال braces هدول، أول واحدة بس هيعملك ال
+
+362
+00:25:50,980 --> 00:26:00,320
+statement الأولى هذه. مش هيمسكها. is a for loop، هيجي
+
+363
+00:26:00,320 --> 00:26:05,080
+ال for loop بس لهذه فقط. طب لأ، أنا ما بدّيش لها دي
+
+364
+00:26:05,080 --> 00:26:08,860
+لحالها. ليش؟ لأنه هذه ممكن تسبب لك runtime error.
+
+365
+00:26:08,860 --> 00:26:12,800
+أتقول أن أنت بتعمل هنا ال statement هذه عبارة عن X
+
+366
+00:26:12,800 --> 00:26:17,660
+مثلًا، بتساوي معادلة معينة، وهنا أنت حاطط مثلًا ال I،
+
+367
+00:26:17,660 --> 00:26:21,560
+اللي هي بتساوي واحد، بدّاتها بواحد، كذا. هذه المفروض أن
+
+368
+00:26:21,560 --> 00:26:26,940
+أنت بتكتب فيها I زائد واحد، لأنك بتتزود فعليًا.
+
+369
+00:26:26,940 --> 00:26:30,260
+ما عمل لكش التزويد. يعني معنى ذلك أن الفور هيظل
+
+370
+00:26:30,260 --> 00:26:37,630
+forever، هيضل إلى ما لا نهاية. صار عندي error نتيجة أنه
+
+371
+00:26:37,630 --> 00:26:42,130
+ما استخدمتش أهم حاجة عندي اللي كنتوا بتعملوا لها ال
+
+372
+00:26:42,130 --> 00:26:45,890
+braces، اللي هي ال curly braces هذه. فاحنا هنا
+
+373
+00:26:45,890 --> 00:26:51,690
+بنستخدمها برضه. begin، واضحة، بكتب begin وبكتب كل
+
+374
+00:26:51,690 --> 00:26:53,930
+statements اللي بدي إياها، وبعدين بنهي في الآخر بـ end،
+
+375
+00:26:53,930 --> 00:26:58,460
+بفهم أن ما بينهم هو statement واحدة. تمام؟ هي أول
+
+376
+00:26:58,460 --> 00:27:02,060
+حاجة. فـ begin، statement واحد، اتنين، تلاتة، قد ما بدك
+
+377
+00:27:02,060 --> 00:27:04,800
+تكتب، اكتب، وفي الآخر اختمها بإيش؟ بـ end. بفهم أن ما
+
+378
+00:27:04,800 --> 00:27:07,460
+بين ال begin والـ end هدول كلهم كأنهم one
+
+379
+00:27:07,460 --> 00:27:13,480
+statement. كلهم لازم يتنفذوا. طبعًا الكلام اللي مش
+
+380
+00:27:13,480 --> 00:27:15,820
+فيه مشكلة، بنستخدمه في ال if وفي then وفي ال else
+
+381
+00:27:15,820 --> 00:27:19,440
+كمان. إذا أنا محتاج else، اللي هي في حالة ال force لـ
+
+382
+00:27:19,440 --> 00:27:22,440
+ال condition، برضه ممكن يكون أكثر من statement
+
+383
+00:27:22,440 --> 00:27:26,400
+محتاجين نعملها. ما عندناش مشكلة فيها. الجثة في ال for
+
+384
+00:27:26,400 --> 00:27:30,700
+loop وفي ال while نفس الجثة. طيب، كنتوا بتعملوا
+
+385
+00:27:30,700 --> 00:27:37,020
+double slash، صح؟ لما تكون بدك تكتب بس حاجة توضّح لك
+
+386
+00:27:37,020 --> 00:27:40,300
+أنت إيش كان قصدك بالخطوة اللي عملتها هنا، سواء أنت
+
+387
+00:27:40,300 --> 00:27:43,400
+بتشتغلوا مشروع، فأنت بدك توضّحها لزميلك، أو أنت ممكن
+
+388
+00:27:43,400 --> 00:27:46,440
+تنساها، فبتروح بتوضّح أنت ل
+
+445
+00:32:13,670 --> 00:32:16,590
+ال condition ما تحققش، هل معناه ذلك أن ال statement
+
+446
+00:32:16,590 --> 00:32:23,450
+برضه مش هيتحقق؟ ما أعرفش، ماشي، افترض ما كان له فوق،
+
+447
+00:32:23,450 --> 00:32:28,330
+جبل، هل بمعنى أنه لو معرف فوق، هاي سؤالي بتأجيسه
+
+448
+00:32:28,330 --> 00:32:32,430
+بشكل .. لو معرف فوق و متحقق من فوق، ال for loop
+
+449
+00:32:32,430 --> 00:32:36,830
+اللي هي ال if then هذه هتعرف؟
+
+450
+00:32:36,830 --> 00:32:41,670
+لأ، else لازم تكون ما تحققش هنا
+
+451
+00:32:44,740 --> 00:32:50,840
+بمعنى أنك أنت تجاوزت هذه، أنت هل وجدت اللي بدك تفهمه
+
+452
+00:32:50,840 --> 00:32:54,920
+اللي بدك تعممه يعني أن ال if and only if برضه ل
+
+453
+00:32:54,920 --> 00:32:59,060
+then ما
+
+454
+00:32:59,060 --> 00:33:04,380
+.. لأ ما أعتقدش ما أعتقدش خليني أقول شاور فيها برضه ال
+
+455
+00:33:04,380 --> 00:33:11,200
+issue، ال issue أنه بمعنى ال if then برمجيا هل هي
+
+456
+00:33:11,200 --> 00:33:13,660
+implication ولا bi-conditional
+
+457
+00:33:17,640 --> 00:33:22,260
+مش بالضروري قد
+
+458
+00:33:22,260 --> 00:33:27,420
+يكون آه، بس أنا بقولك not necessary يعني هتلاقي أنه
+
+459
+00:33:27,420 --> 00:33:31,020
+في حالات كتير بتحقق بس هل أنه فقط دائما إذا يعني
+
+460
+00:33:31,020 --> 00:33:35,680
+بمعنى إذا ما تحققش مش هتتحقق ال statement، هي السؤال
+
+461
+00:33:36,160 --> 00:33:39,060
+إذا كانت ال statement بس you ولا ال else، فعليا مش
+
+462
+00:33:39,060 --> 00:33:42,620
+هتتحقق إذا كان كان ال truth، إذا أنت هيك بتقول لاحظ
+
+463
+00:33:42,620 --> 00:33:45,600
+أنك أنت ضفت شرط ثاني، ما هو برضه ال else برضه هتكون
+
+464
+00:33:45,600 --> 00:33:49,680
+مدهش الشرط هذا، لأ، ال else، ال else لأن أنا أخليك
+
+465
+00:33:49,680 --> 00:33:53,340
+معايا، ال else أنت استنفذت ال .. ال proposition
+
+466
+00:33:53,340 --> 00:33:58,940
+cases تبعتك اللي هنا، يعني أنت ضمنت أنه if .. if
+
+467
+00:33:58,940 --> 00:34:04,520
+then هي الأولوية، ما تحققش، فأنت مجبر لازم خلاص تروح
+
+468
+00:34:04,520 --> 00:34:10,760
+للتانية، هذه فيها هامش حرية أكثر، هذه أنت مجبور خلاص
+
+469
+00:34:10,760 --> 00:34:15,920
+إذا هذه ما تحققش فأنت مجبر لازم هتروح ل else لازم
+
+470
+00:34:15,920 --> 00:34:20,440
+إجباري لازم تروح ل else، ال
+
+471
+00:34:20,440 --> 00:34:23,000
+while أخدناهم، to while تحديدا صح؟ أخدته في ال logo
+
+472
+00:34:23,000 --> 00:34:26,880
+ال 1010 تمام، ففيش مشكلة، ال while بتحط condition
+
+473
+00:34:26,880 --> 00:34:31,660
+إذا طول ما هو بيتحقق، مش إذا كانت بتحقق، طول ما هو
+
+474
+00:34:31,660 --> 00:34:38,510
+بتحقق بتضلك تعيد ال statement، بمعنى أن هذا loop
+
+475
+00:34:38,510 --> 00:34:43,270
+شغال على طول على ال condition، عشان هيك ال
+
+476
+00:34:43,270 --> 00:34:47,550
+statement هذه لازم تكون حذر جدا وأنت بتكتبها، أنت
+
+477
+00:34:47,550 --> 00:34:51,750
+هتعملك تكسر لك ال while، أنت مش هتسيبها .. بس
+
+478
+00:34:51,750 --> 00:34:55,370
+هتسيبها forever يعني ما تفكرش أبدا أنك أنت تسيبها
+
+479
+00:34:55,370 --> 00:34:59,530
+خلاص ماشية، وأول شغلة فيها زي ما اتكلمنا هي
+
+480
+00:35:02,520 --> 00:35:08,520
+begin و end، لأنه على الأرجح هتضطر تحتاج counter أو
+
+481
+00:35:08,520 --> 00:35:14,380
+كمان statement تغير ال condition في لحظة معينة في
+
+482
+00:35:14,380 --> 00:35:16,920
+لحظة معينة، أما إذا مجرد ال statement تبعتك هي
+
+483
+00:35:16,920 --> 00:35:20,620
+معادلة بتحسبها، هتفضل طول عمرك تشتغل عليها إلا إذا
+
+484
+00:35:20,620 --> 00:35:28,520
+المعادلة بتحسب معامل ال condition نفسه، لاحظته، فإذا
+
+485
+00:35:28,520 --> 00:35:32,000
+كان هنا ال statement لها علاقة بال condition آه
+
+486
+00:35:32,000 --> 00:35:35,200
+عند لحظة معينة هتضطر تطلع، بحيث مش الحالة، لكن إذا
+
+487
+00:35:35,200 --> 00:35:37,460
+مالهمش علاقة ببعض، أنا بقولك من الآن هتبقى forever
+
+488
+00:35:37,460 --> 00:35:43,960
+هتبقى في ال loop، إذا مالهمش علاقة ببعض، بمعنى أن ال
+
+489
+00:35:43,960 --> 00:35:47,800
+statement هنا مجرد معادلة أحسبها، وال condition هو
+
+490
+00:35:47,800 --> 00:35:51,740
+proposition عبارة عن true or false وبس، مالهمش أي
+
+491
+00:35:51,740 --> 00:35:56,600
+علاقة ببعض، أمرك ما حتصل أنك توقفها، طيب إذا كان ال
+
+492
+00:35:56,600 --> 00:35:59,340
+result هي ال true لل condition، فمعنى ذلك بنعمل
+
+493
+00:35:59,340 --> 00:36:03,400
+execution لمين؟ لل statement، otherwise بنعدي ال
+
+494
+00:36:03,400 --> 00:36:06,800
+while كلها، ال while بال statement بتاعتها، بنعديها
+
+495
+00:36:06,800 --> 00:36:09,420
+وبنشوف اللي بعدها، بنكمل اللي بعدها، إذا ال
+
+496
+00:36:09,420 --> 00:36:13,840
+condition false، إذا ال condition false تمام،
+
+497
+00:36:13,840 --> 00:36:17,520
+بنستمر زي ما قلنا وبنكمل فيها، طيب ال while ها دي
+
+498
+00:36:17,520 --> 00:36:23,170
+ممكن تعبير عنها كأنها if لانهائية، ما أعرفش، أخدته
+
+499
+00:36:23,170 --> 00:36:26,090
+يمكن المقاربات هي دي، أن هي في النهاية تمثل إيش
+
+500
+00:36:26,090 --> 00:36:28,510
+فعشان هيك احنا اضطرينا نجيبها، هي عبارة عن مجموعة
+
+501
+00:36:28,510 --> 00:36:32,990
+if then بس، ووجدنا أن ال if ممكن نستخدمها باستمرار
+
+502
+00:36:32,990 --> 00:36:36,230
+وما أعرفش امتى هتوقف، if then if then if then، طب إيش
+
+503
+00:36:36,230 --> 00:36:39,770
+هأسوي؟ فابتكروا كلمة while، ابتكروا كلمة while، إذا
+
+504
+00:36:39,770 --> 00:36:44,210
+كان ال condition، وهي حددناله بدنا نعمل كل هدول
+
+505
+00:36:44,210 --> 00:36:46,430
+إذا كان فعلا ال condition تحقق، أنه أغير ال
+
+506
+00:36:46,430 --> 00:36:49,970
+statement وبعدين ارجع، إذا كان ال condition، وأعمل
+
+507
+00:36:49,970 --> 00:36:54,330
+statement، وأرجع أشوف ال condition، وأرجع أشوف ال
+
+508
+00:36:54,330 --> 00:36:57,930
+condition، طب forever، هفضل مستمر هيك to infinite، لأ
+
+509
+00:36:57,930 --> 00:37:00,630
+مش حاجة طول to infinite، فجاءت كل ال structure هدول
+
+510
+00:37:00,630 --> 00:37:03,650
+احنا هنغيره بحاجة اسمها while وخلاص، فإذا ال while
+
+511
+00:37:03,650 --> 00:37:09,290
+هي فعليا مجموعة if then في بعضها، مجموعة if then في
+
+512
+00:37:09,290 --> 00:37:13,050
+بعضها، ونفس ما قلنا هناك ممكن نقوله هنا، هل ال
+
+513
+00:37:13,050 --> 00:37:15,710
+statement هدول ممكن تغير ال condition ولا لأ، إذا ما
+
+514
+00:37:15,710 --> 00:37:18,270
+غيرتي ال condition هتفضلي forever عن جد فعلا to
+
+515
+00:37:18,270 --> 00:37:19,450
+infinite، هتفضلي
+
+516
+00:37:21,710 --> 00:37:26,990
+infinite nested statement، كويس، statement هذا مهم
+
+517
+00:37:26,990 --> 00:37:30,250
+جدا، خدوا بالكم، ال while من أكثر الأشياء اللي
+
+518
+00:37:30,250 --> 00:37:36,070
+ممكن تعمل لك runtime error، ليش؟ لأنه النوع الثاني ال
+
+519
+00:37:36,070 --> 00:37:38,750
+for loop، أنت عارف أحيانا أنه فيه بداية ونهاية
+
+520
+00:37:38,750 --> 00:37:44,010
+فممكن ممكن يطلع لك errors عبارة عن ال arithmetic أو
+
+521
+00:37:44,010 --> 00:37:48,180
+ال logic، ليش؟ لأنه والله okay، بدأ من ال initial لأن
+
+522
+00:37:48,180 --> 00:37:54,020
+أنا بحدده for وبحدد بالظبط قيمة معينة، value معينة
+
+523
+00:37:54,020 --> 00:37:58,400
+variable معين، وبعطيه initial value وبقوله استمر
+
+524
+00:37:58,400 --> 00:38:01,980
+لحد ال final value، طيب ما بين ال initial لل
+
+525
+00:38:01,980 --> 00:38:05,180
+final value تبعت ال variable، اعمل لي ال statements
+
+526
+00:38:05,180 --> 00:38:09,780
+هذه، فأنا عارف حتى بالظبط في بعض الأحيان بكون عارف
+
+527
+00:38:09,780 --> 00:38:14,820
+تمامًا كام مرة بده يعمل تكرار، بنكون محسوب ال final
+
+528
+00:38:14,820 --> 00:38:19,960
+ناقص ال initial، غير ال while، مختلف عن ال while، هنا
+
+529
+00:38:19,960 --> 00:38:25,180
+طبعًا، فكثير إذا قدرت تشتغل فيها بيكون ربح لك حتى
+
+530
+00:38:25,180 --> 00:38:30,840
+شوية من ال while بدل ما تدخل حالك في مشاكل ال ال
+
+531
+00:38:30,840 --> 00:38:34,940
+runtime error، كويس، ال initial إذا أنت عارف لكن
+
+532
+00:38:34,940 --> 00:38:38,160
+إحنا في أيام كتيرة أو في مواقف كتيرة بنشتغل على
+
+533
+00:38:38,160 --> 00:38:41,440
+برنامج إحنا مش عارفين أنه هينتهي امتى، هنجفها دي، بدك
+
+534
+00:38:41,440 --> 00:38:45,400
+تكون حاضر، وده شيء جيد في ال while، initial هي لل
+
+535
+00:38:45,400 --> 00:38:49,660
+integer اللي هأبدأ منه، قيمة ال variable، ثم ال final
+
+536
+00:38:49,660 --> 00:38:52,440
+اللي هأنتي عنده، واللي بعد هيك خلاص بوقف ال for
+
+537
+00:38:52,440 --> 00:38:56,280
+loop كلها وبطلع منها، بنكمل منها، ال variable بنبدأ
+
+538
+00:38:56,280 --> 00:38:58,940
+بال initial، بعدين initial زائد واحد، initial زائد
+
+539
+00:38:58,940 --> 00:39:00,600
+اثنين، زائد ثلاثة، زائد اثنين، زائد اثنين، زائد اثنين
+
+540
+00:39:00,600 --> 00:39:01,560
+زائد اثنين، زائد اثنين، زائد اثنين، زائد اثنين، زائد
+
+541
+00:39:01,560 --> 00:39:02,640
+اثنين، زائد اثنين، زائد اثنين، زائد اثنين، زائد اثنين
+
+542
+00:39:02,640 --> 00:39:03,870
+زائد اثنين، زائد اثنين، زائد اثنين، زائد برضه مرت
+
+543
+00:39:03,870 --> 00:39:08,290
+عليكم، فمش كتير فيها إشكالية، إن شاء الله تعالى، طيب
+
+544
+00:39:08,290 --> 00:39:12,010
+ال for loop هي عبارة زي برضه زي ما اتكلمنا سابقا
+
+545
+00:39:12,010 --> 00:39:15,430
+هي عبارة عن مجموعة while، الحقيقة بس ال while هنا
+
+546
+00:39:15,430 --> 00:39:20,750
+محكوم بقيمة، هنا محكوم بقيمة، فببدأ begin وبأعطي
+
+547
+00:39:20,750 --> 00:39:24,490
+الكلمة variable، بأعطيها تحديدا ال initial value، ال
+
+548
+00:39:24,490 --> 00:39:26,610
+initial value بتاعتنا، وبعدين بأحسب while ال
+
+549
+00:39:26,610 --> 00:39:30,510
+variable أقل من ال final، إذا أقل أو يساوي ال final
+
+550
+00:39:30,510 --> 00:39:34,670
+استمر، بتضلك ماشي بحيث أنك تحط ال statement وبعدين
+
+551
+00:39:34,670 --> 00:39:40,590
+تفحص، بتحط ال variable هذا، variable زائد واحد عشان
+
+552
+00:39:40,590 --> 00:39:44,730
+ترجع تعيد السؤال، ال variable بعد ما صار زيادة عليه
+
+553
+00:39:44,730 --> 00:39:48,230
+واحد، صار أقل من ال final ولا لسه، نفذ ال statement
+
+554
+00:39:48,230 --> 00:39:53,050
+وبعدين زود واحد، هي اللي كنت بأحكي لك عليها، بدك تأخذ
+
+555
+00:39:53,050 --> 00:39:58,770
+بالك منها في ال while، هي مش statement واحدة، إذا
+
+556
+00:39:58,770 --> 00:40:03,290
+داخل ال while بتحققش حاجة زي هذه، هتضلك forever ..
+
+557
+00:40:03,290 --> 00:40:09,090
+هتظل forever، لازم يكون في المتغير اللي مربوط في ال
+
+558
+00:40:09,090 --> 00:40:13,170
+proposition تبع ال while يكون بيتحرك داخل ال while
+
+559
+00:40:13,170 --> 00:40:19,790
+وإلا هتظل forever، بيولوجيا منطقيا هيك .. صحيح؟
+
+560
+00:40:19,790 --> 00:40:24,370
+أنا حطيت لك condition مش هيتغير، نهاية مش هي .. معناته
+
+561
+00:40:24,370 --> 00:40:27,710
+آه خلاص، شيء اللي بيغيره الجهاز مش هيغيره لحاله
+
+562
+00:40:27,710 --> 00:40:31,050
+هتظل forever، عشان هيك مهمة جدا جزيها دي، قلت لك في
+
+563
+00:40:31,050 --> 00:40:34,170
+الغالب ال while، عشان هيك المتوقع أن في الغالب
+
+564
+00:40:34,170 --> 00:40:37,270
+هتكون فيه beginning و end أو بلغتكم هتكون فيه ال
+
+565
+00:40:37,270 --> 00:40:43,250
+curly braces، طيب
+
+566
+00:40:43,250 --> 00:40:47,190
+ال procedure، أني أكتب اسم ال procedure وأعطيه
+
+567
+00:40:47,190 --> 00:40:50,370
+مجموعة inputs، هذا اللي بتسميه ال calling، أني
+
+568
+00:40:50,370 --> 00:40:57,260
+بستدعي ال function، باستدعي subroutine أو في لغات
+
+569
+00:40:57,260 --> 00:41:01,400
+ثانية بتسميها sub programs أو methods، كل لغة
+
+570
+00:41:01,400 --> 00:41:04,600
+بتسميها باسمها، كل لغة من اللغات الحية اللي احنا
+
+571
+00:41:04,600 --> 00:41:07,360
+بنتكلمها، ال real programming language بتسميها اسم
+
+572
+00:41:07,360 --> 00:41:11,460
+بس، كلهم حاجة واحدة أن أنا بدي استدعي function أو
+
+573
+00:41:11,460 --> 00:41:15,820
+code احنا كاتبينه مسبقا، احنا عاملينه مسبقا، بس
+
+574
+00:41:15,820 --> 00:41:18,920
+فبتعملوا استدعاء من خلال أنك أنت بتكتب اسمه مباشرة
+
+575
+00:41:19,830 --> 00:41:23,910
+اسم البرنامج، وداخل الأقواس بتعطي ال input سبعة،
+
+576
+00:41:24,940 --> 00:41:28,180
+لأنه ما لوش معنى، أنت بتستدعيه وسيبته، طب ما هو
+
+577
+00:41:28,180 --> 00:41:31,940
+بالأساس هذا لما أنت استدعيتة فيه له inputs، وين ال
+
+578
+00:41:31,940 --> 00:41:35,540
+inputs تبعتة؟ يعطيني ال inputs عشان أعرف أرجع لك
+
+579
+00:41:35,540 --> 00:41:41,020
+أعمل لك return بالنتائج، بنعمل return بالنتائج، تجريبًا
+
+580
+00:41:41,020 --> 00:41:45,840
+خلصنا هيك ال structure تبع ال pseudocode، المجموعة
+
+581
+00:41:45,840 --> 00:41:49,340
+هذه مش هنحتاج أكثر منها، otherwise هنشتغل على ال
+
+582
+00:41:49,340 --> 00:41:53,820
+informal language، طيب لما نقول الآن نرجع لكلمة
+
+583
+00:41:53,820 --> 00:41:58,160
+البرنامج اللي كتبناه أول مرة، كتبناه بلغة language
+
+584
+00:41:58,160 --> 00:42:01,260
+عادية، هالوقت بدنا نكتبه باستخدام ال pseudocode
+
+585
+00:42:01,260 --> 00:42:05,380
+هأقول procedure آه، فهمت أن أنا هالوقت داخل على code
+
+586
+00:42:05,380 --> 00:42:09,960
+مش زي طوالي dash فوقه براجراف وتحتة براجراف فهي ضايع
+
+587
+00:42:09,960 --> 00:42:14,260
+في ال .. في ال text، هأقول procedure max، فهمت أنه
+
+588
+00:42:14,260 --> 00:42:16,800
+max آه، معناته بده يعمل maximum أو بده يجيب maximum
+
+589
+00:42:16,800 --> 00:42:23,440
+أو بده يجيب قيمة عالية، قيمة مجموعة ال input، a1, a2,
+
+590
+00:42:23,600 --> 00:42:27,480
+a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13,
+
+591
+00:42:27,480 --> 00:42:30,600
+a14, a15, a16, a17, a18, a19, a20, a21, a22, a23,
+
+592
+00:42:30,600 --> 00:42:31,180
+a22, a22, a23, a22, a22, a22, a22, a22, a22, a22,
+
+593
+00:42:31,760 --> 00:42:32,140
+a22, a22, a22, a22, a22, a22, a22, a22, a22, a22,
+
+594
+00:42:32,140 --> 00:42:35,560
+a22, a22, a22, a22, a22, a22, a22, a22, a22, aV
+
+595
+00:42:35,560 --> 00:42:41,540
+بتساوي A واحد، لاحظ comment، حط comment، largest
+
+596
+00:42:41,540 --> 00:42:45,420
+element so far، حتى اللحظة هو ال maximum حتى اللحظة
+
+597
+00:42:45,420 --> 00:42:48,900
+أنا لسة ما كملتش، أنا حتى الآن شايف أنه أكبر واحد
+
+598
+00:42:48,900 --> 00:42:52,820
+طيب، هتكمل، for loop هيبدأ من اثنين لأن واحد أنا
+
+599
+00:42:52,820 --> 00:42:56,490
+موجود فيه واحد، مش محتاج أبدأ من واحد، فبدأ من ال
+
+600
+00:42:56,490 --> 00:42:58,610
+search تبعي من ال ورا من ال اثنين، أنا موجود في
+
+601
+00:42:58,610 --> 00:43:02,730
+واحد فعليا، فهنبدأ من اثنين to a to n، هاي ال index
+
+602
+00:43:02,730 --> 00:43:05,250
+اللي بنشتغل عليه، وأنتم عارفين أن ال for loop في
+
+603
+00:43:05,250 --> 00:43:10,030
+الغالب بتكون لل index، في الغالب، لكن ما بقدرش أعمم
+
+604
+00:43:10,030 --> 00:43:13,390
+بشكل عام كامل، لكن في الأغلب بتكون هذه اللي هي
+
+605
+00:43:13,390 --> 00:43:16,910
+علاقة بال index تبع ال element داخل ال array تبعتة
+
+606
+00:43:17,780 --> 00:43:23,020
+فمن اثنين to N هنا، إذا والله AI واللي هتبدأ
+
+607
+00:43:23,020 --> 00:43:27,920
+ب اثنين أكبر من V، إذا بنحطها قيمة ال .. ال A2، ال V
+
+608
+00:43:27,920 --> 00:43:31,040
+بتتغير، بتصير هي A2، otherwise لأ، automatically
+
+609
+00:43:31,040 --> 00:43:36,120
+هيسيب السطر هذا وأنا مش محتاج يكون عندي أكثر من
+
+610
+00:43:36,120 --> 00:43:39,220
+ال statement هذه لحالها، عشان ذلك مش محتاج أكتب
+
+611
+00:43:39,220 --> 00:43:44,900
+begin و end، خلاص، فال for loop هذا هو مربوط بس بهذه
+
+612
+00:43:44,900 --> 00:43:51,400
+وبس، أنا عارف أن الآن الاثنين هذول هربوطهم هيك في
+
+6
+
+667
+00:48:11,840 --> 00:48:18,520
+مربوطين ببعض. أنا سبته، احنا سبناه، بمعنى يروح false
+
+668
+00:48:18,520 --> 00:48:21,780
+يروح true، يعمل اللي بدو إياه. ودّحت؟
+
+669
+00:48:23,360 --> 00:48:25,380
+حاجات زي هذه، أنا عارف أن هي كتير بسيطة، وكتير
+
+670
+00:48:25,380 --> 00:48:28,140
+بتعمل لخمة، وممكن تتغير أحياناً من compiler لـ
+
+671
+00:48:28,140 --> 00:48:32,960
+compiler. سنَتعامل الآن مع smart compilers، ممكن
+
+672
+00:48:32,960 --> 00:48:35,500
+تعالج بعض المشاكل هذه، بس هذه لا يمنع أنها
+
+673
+00:48:35,500 --> 00:48:39,340
+مشاكل كانت موجودة، وبعضها ما زال موجود. فهذه خُذ بالك
+
+674
+00:48:39,340 --> 00:48:41,940
+أنه ممكن تكون أحياناً نوع من أنواع الـ error اللي
+
+675
+00:48:41,940 --> 00:48:45,860
+تظهر معاك في البرامج أن أنت مش مصفّر الـ units الـ
+
+676
+00:48:45,860 --> 00:48:49,780
+variables بتاعتك من الأول. فإذا بدك تبقى صح كتير
+
+677
+00:48:49,780 --> 00:48:53,980
+كويس، كل متغيراتك اللي هتستخدمها في الـ code هذا في
+
+678
+00:48:53,980 --> 00:48:57,910
+الـ real language هنا. لأ، أنا مش محتاجها في الصدر، أنا
+
+679
+00:48:57,910 --> 00:49:01,490
+مش محتاج، بس في الـ real language صفرهم في الأول
+
+680
+00:49:01,490 --> 00:49:06,210
+كلهم، خوفاً من حاجة زي هذه. فأنت بتكون ضامن ساعتها
+
+681
+00:49:06,210 --> 00:49:09,250
+أن هي مش بتطلع على أي شيء ثاني، هي فقط مربوطة
+
+682
+00:49:09,250 --> 00:49:12,410
+بتصير هنا، بس in general الـ statement لأ هو ما كانش
+
+683
+00:49:12,410 --> 00:49:16,310
+هيك، بدليل أن لو دخلنا هنا عنصر آخر، الـ statement
+
+684
+00:49:16,310 --> 00:49:20,950
+مش هيعالجه لحاله. هو ما عالجه لحاله. الـ V كانت مخبئة
+
+685
+00:49:20,950 --> 00:49:25,850
+قيمة، مش هيغيرها، مش هيغيرها. همّ جذبهم أنه هذه لو
+
+686
+00:49:25,850 --> 00:49:30,510
+كانت force في I، هو بيحرق الشهادة، بيصير هو مش
+
+687
+00:49:30,510 --> 00:49:33,690
+مسؤول عن تحريكها. مستحيل تكون true. ماشي، أنا معاك.
+
+688
+00:49:33,690 --> 00:49:37,430
+مستحيل تكون true، بس أنا رجاءً، توضحت لك في جزئي الـ
+
+689
+00:49:37,430 --> 00:49:40,330
+implication نفسي اللي بدرس وبده ينجح.
+
+690
+00:49:46,890 --> 00:49:50,270
+و الـ by conditional. من في الأمور هذه بيقول لك: أنا لو
+
+691
+00:49:50,270 --> 00:49:54,530
+عندي كانت false و true، وحقيقي false، لكن أنا
+
+692
+00:49:54,530 --> 00:49:59,150
+أعطانا true في الأمور. يعني، على كلامك، الـ if and
+
+693
+00:49:59,150 --> 00:50:03,270
+only if هذه للـ else، على اعتبار أن أنت بتكون هنا الـ
+
+694
+00:50:03,270 --> 00:50:07,370
+condition. بدنا نقول فرضيّاً، يعني بدك تفرض أن هنا صار
+
+695
+00:50:07,370 --> 00:50:12,650
+else، ومش عارف إيش نعطيله. مثلاً else، نقول مثلاً V
+
+696
+00:50:12,650 --> 00:50:20,830
+تساوي صفر. يعني أي إيص هنا، هالوجد هنا، هذه لو جئنا
+
+697
+00:50:20,830 --> 00:50:28,410
+أكبر من V، ضمنين أنه هذا في حالة تحقق، لكن هو فعلاً
+
+698
+00:50:28,410 --> 00:50:31,670
+في حالة لم يتحقق، المفروض إيش اللي يصير؟
+
+699
+00:50:34,630 --> 00:50:39,430
+عندك false، ممكن true أو false. false ممكن تطلع هيك
+
+700
+00:50:39,430 --> 00:50:44,730
+أو هيك. على الأولى false، عفواً، أن الـ condition هنا
+
+701
+00:50:44,730 --> 00:50:49,950
+إيش بيطلع؟ false. مش هيك؟ اه، false. ممكن بالـ by
+
+702
+00:50:49,950 --> 00:50:52,910
+conditional ممكن يطلع true، ممكن يطلع false. بالـ by
+
+703
+00:50:52,910 --> 00:50:57,710
+conditional ممكن يطلع؟ اه، ممكن. يعني ممكن يطلع صح
+
+704
+00:50:57,710 --> 00:51:01,830
+ممكن يطلع غلط. احنا قلنا مشكلتنا في الـ false، ماشي؟
+
+705
+00:51:01,830 --> 00:51:07,220
+false، معناه ذلك أن هنا false، وهذه معناته الـ else اللي
+
+706
+00:51:07,220 --> 00:51:12,080
+هي الـ inverse تبعها، اللي هي المفروض true، المفروض
+
+707
+00:51:12,080 --> 00:51:18,080
+true. طيب، وممكن تكون false، والـ...وكانت true هنا
+
+708
+00:51:18,080 --> 00:51:25,200
+ما حكمناهاش ليش؟ لأنه كانت، يعني خلينا نقول ممكن تكون
+
+709
+00:51:25,200 --> 00:51:28,500
+true. إذا كانت true، فمعنى ذلك أنه هنا بدّيجي فلأ، هنا
+
+710
+00:51:28,500 --> 00:51:33,040
+مش هيجي false هنا. لازم دائماً true في حالة إنه
+
+711
+00:51:33,040 --> 00:51:38,430
+false. في حالة أنه false. لاحظ أن هنا ممكن تكون true
+
+712
+00:51:38,430 --> 00:51:45,730
+تمام، بس أيوة، لاحظ. لأ، أفضل هذه ممكن تكون true نتيجة
+
+713
+00:51:45,730 --> 00:51:52,430
+خلينا مع بعض. نتيجة أنه معرفة مسبقاً، بمعنى زي بدرس
+
+714
+00:51:52,430 --> 00:52:00,470
+ونجح. هل ودّ درس، النجاح هل هو مربوط بالدراسة؟
+
+715
+00:52:00,470 --> 00:52:06,020
+خلاص، معناته هذه true، مش مربوطة بالـ condition، صح؟
+
+716
+00:52:06,020 --> 00:52:09,260
+ما تيجي تربط لي إياها هالوجه. طب أنت ما ربطنهاش لما شرحنا
+
+717
+00:52:09,260 --> 00:52:13,000
+الـ...اللي نجح واللي رسب، تمام. مش مربوطة، تمام. لكن
+
+718
+00:52:13,000 --> 00:52:18,720
+الآن هنا else، هل معنى ذلك أن أقول: مدام هذه فحصها
+
+719
+00:52:18,720 --> 00:52:21,080
+بدي أفترض أنه smart enough أنه راح يفحصها لجهة أن
+
+720
+00:52:21,080 --> 00:52:24,600
+أنها true، بس مش من هذه يروح يقول لي لأ، معناته هذه
+
+721
+00:52:24,600 --> 00:52:30,400
+false. لأ، لأ، مش مرتبطة فيها. هذه مرتبطة بـ هنا عشان
+
+722
+00:52:30,400 --> 00:52:36,130
+هيك if and only if، مش هتيجي تطلع إن هذه true
+
+723
+00:52:36,130 --> 00:52:40,530
+معناته، هذه false، العكس تبعها، هتقول لك لأ، أنا
+
+724
+00:52:40,530 --> 00:52:44,570
+بعيدة عن الـ inverse تبعي، أنا مربوط بهذه، إذا
+
+725
+00:52:44,570 --> 00:52:50,570
+false لازم أنفذ. مش
+
+726
+00:52:50,570 --> 00:52:53,710
+عارف، إذا واضحة ولا...شكلها مش واضح كتير، ممكن
+
+727
+00:52:53,710 --> 00:52:59,510
+نعمل قعدة ثانية ونرجع نتكلم فيها، تمام. طيب، بكفي
+
+728
+00:52:59,510 --> 00:53:03,070
+هيك، نكمل الباقي للمرة القادمة إن شاء الله تعالى.
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d3d84ccfb9ac87e55c66beea346d9270f10c06f7
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30.srt
@@ -0,0 +1,2020 @@
+1
+00:00:05,030 --> 00:00:07,790
+يعطيكم العفو شباب، بارك الله فيكم، اليوم نبدأ إن
+
+2
+00:00:07,790 --> 00:00:10,530
+شاء الله تعالى مع موضوع الـ recursion بعد ما المرة
+
+3
+00:00:10,530 --> 00:00:13,430
+الماضية كنا أخذنا الـ induction أو الـ inductive
+
+4
+00:00:13,430 --> 00:00:16,050
+step بعد ما شفنا الـ base step و الـ inductive
+
+5
+00:00:16,050 --> 00:00:21,890
+step و أخذنا عملية proving باستخدام الـ inductive
+
+6
+00:00:21,890 --> 00:00:26,090
+step. من الـ inductive step ممكن تتدرج الأمور معنا
+
+7
+00:00:26,090 --> 00:00:28,990
+بحيث أن إحنا نروح لجزئية الـ recursion أو الـ
+
+8
+00:00:28,990 --> 00:00:33,370
+recursive codes بعدها الأكواد التكرارية و التي نشأت
+
+9
+00:00:33,370 --> 00:00:37,050
+بالأساس أساسًا من عملية الـ induction التي أخذناها
+
+10
+00:00:37,050 --> 00:00:42,230
+المرة الماضية بحيث أن الـ recursion هو بكل بساطة هو
+
+11
+00:00:42,230 --> 00:00:48,770
+general term لعملية تعريف الـ object من نفسه، تعريف
+
+12
+00:00:48,770 --> 00:00:53,490
+الـ object من نفسه، ولكن نعرفه في هذا الزمن كأنه
+
+13
+00:00:53,490 --> 00:00:59,370
+function في نفسه في الزمن السابق أو في الحالة التي
+
+14
+00:00:59,370 --> 00:01:01,930
+كانت قبله، في الحالة التي كانت قبله، زي لما أقول أن
+
+15
+00:01:01,930 --> 00:01:05,950
+الـ f of n هي function في f of n ناقص واحد، طب f of
+
+16
+00:01:05,950 --> 00:01:10,100
+n ناقص واحد هي function في f of n ناقص اثنين، وهكذا
+
+17
+00:01:10,100 --> 00:01:16,180
+فإذا، يُعرف من نفسه ببساطة جدًا، هذا ممكن نقول تعريف
+
+18
+00:01:16,180 --> 00:01:21,660
+recursion بشكل مختصر. طيب، زي إنه نقول P of N plus
+
+19
+00:01:21,660 --> 00:01:26,720
+واحد recursively in terms of P of N، فهي معرفة
+
+20
+00:01:26,720 --> 00:01:30,880
+باللي قبلها، معرفة بمن؟ باللي قبلها. طبعًا هذا
+
+21
+00:01:30,880 --> 00:01:34,480
+نستخدمه كـ recursive algorithms وهذه أهم شغلة
+
+22
+00:01:34,480 --> 00:01:37,980
+ويمكن هي النقطة الأهم بالنسبة لكم كمبرمجين أنكم
+
+23
+00:01:37,980 --> 00:01:42,820
+تروحوا لجزئية الـ algorithms بشكل recursively، ممكن
+
+24
+00:01:42,820 --> 00:01:46,780
+تتكرر من نفسها، بمعنى أن الكود يكرر نفسه، وسنأخذ
+
+25
+00:01:46,780 --> 00:01:49,880
+أمثلة على بعض الأكواد خلال محاضرتنا إن شاء الله
+
+26
+00:01:49,880 --> 00:01:54,010
+تعالى. طيب، الـ recursive definitions، الـ recursive
+
+27
+00:01:54,010 --> 00:01:57,150
+functions، الـ recursive sequences، اللي هو الـ
+
+28
+00:01:57,150 --> 00:01:59,570
+sequence نفسه كمان ممكن يكون recursive من نفسه.
+
+29
+00:01:59,570 --> 00:02:03,730
+كويس، and sets، و الـ sets كمان، حتى الـ set نفسها ممكن
+
+30
+00:02:03,730 --> 00:02:07,930
+تُعرف من نفسها، و برضه سنأخذ لها مثال، سنأخذ لها مثال
+
+31
+00:02:07,930 --> 00:02:11,050
+فمعظمهم هؤلاء سنتكلم عنهم أثناء المحاضرة كأمثلة
+
+32
+00:02:11,050 --> 00:02:18,380
+واضحة لهم. نبدأ مثلًا كـ function recursive للـ
+
+33
+00:02:18,380 --> 00:02:22,020
+function، بكل بساطة نقدر نقول أنه أبسط طريقة أني
+
+34
+00:02:22,020 --> 00:02:26,680
+أقول، one way to define a function، أقول if
+
+35
+00:02:26,680 --> 00:02:32,720
+from natural number to set، الـ natural number هذه
+
+36
+00:02:32,720 --> 00:02:38,300
+by default، اللي هي إيش؟ الـ index، الـ index، فعشان هيك
+
+37
+00:02:38,300 --> 00:02:40,660
+بنقول natural number، ممكن الـ index يبدأ معك من
+
+38
+00:02:40,660 --> 00:02:47,340
+صفر، a0، a1، a2، a3، and so on، بتكمل. طيب، الـ a
+
+39
+00:02:47,340 --> 00:02:53,040
+نفسها، a1، و a2، و a3، و a4، و a5، هي العناصر تاعت الـ
+
+40
+00:02:53,040 --> 00:02:56,660
+set، فأنت بتقول الـ set عندنا في الحالة هذه هي
+
+41
+00:02:56,660 --> 00:03:00,480
+العناصر، زي لما نقول عندنا الآن مجموعة الطلاب هؤلاء
+
+42
+00:03:00,480 --> 00:03:04,470
+هم الـ set. Okay، هذه المجموعة خلاص، تمام. لما أجي بدي
+
+43
+00:03:04,470 --> 00:03:08,490
+أعرفهم أو أقيمهم أو بدي أجي أصنفهم، بيصير الآن
+
+44
+00:03:08,490 --> 00:03:13,410
+التصنيف حسب إيش؟ بمعنى، من الذي سيأخذ الـ a0؟ بدي
+
+45
+00:03:13,410 --> 00:03:17,090
+أفترض، مش على الدرجة، بدي أفترض على الترتيب
+
+46
+00:03:17,090 --> 00:03:22,130
+الأبجدي مثلًا، مش هيك. معناته هنا بدي أقول من هو الـ a
+
+47
+00:03:22,130 --> 00:03:27,740
+node أو الـ a صفر، هو عنصر من عناصر الـ set أكيد، فهو
+
+48
+00:03:27,740 --> 00:03:32,360
+ينتمي للـ set صحيح، لكن بدنا نشوف من الذي يحتل هذا
+
+49
+00:03:32,360 --> 00:03:37,470
+المكان حسب Sorting معينة، حسب الـ sort اللي أنا بدي
+
+50
+00:03:37,470 --> 00:03:40,830
+أتكلم عنه، لو افترضنا أن هي بالأرقام الجامعية أو
+
+51
+00:03:40,830 --> 00:03:45,330
+بالـ .. بالأحرف الأبجدية أو حسب الـ grade، حسب ..
+
+52
+00:03:45,330 --> 00:03:49,870
+فيها تصنيفات كثيرة .. فيها تصنيفات كثيرة، فهنا سأقول
+
+53
+00:03:49,870 --> 00:03:53,530
+في الحالة هذه، من natural number to S، اللي هي الـ
+
+54
+00:03:53,530 --> 00:03:59,830
+set. فإذا، for any set S، أو بشكل series ممكن نقول A
+
+55
+00:03:59,830 --> 00:04:06,250
+N هي هالـ N، from N to F of N، F of N من هو هذا؟ يطلع في
+
+56
+00:04:06,250 --> 00:04:12,300
+الآخر عنصر من الـ set. فإذا، من الـ domain، من الـ
+
+57
+00:04:12,300 --> 00:04:17,000
+codomain، ما هي؟ domain to codomain، صح؟ فده هي. فإذا
+
+58
+00:04:17,000 --> 00:04:20,720
+تعريفها as a function، نقول الآن كالتالي عشان
+
+59
+00:04:20,720 --> 00:04:24,620
+نعرفها بشكل recursively، بشكل recursively، سأقول بدنا
+
+60
+00:04:24,620 --> 00:04:29,180
+نعرف أول عنصر، f of zero، رجعنا لنفس الـ induction،
+
+61
+00:04:29,180 --> 00:04:33,900
+رجعنا لنفس الـ induction. طيب، أما if أكبر من صفر،
+
+62
+00:04:33,900 --> 00:04:41,000
+فبتعرف if of n in terms of if zero to n ناقص واحد.
+
+63
+00:04:41,740 --> 00:04:48,340
+من F of 0 إلى F of N ناقص واحد، بمعنى تُعرف بالعناصر
+
+64
+00:04:48,340 --> 00:04:53,440
+السابقة لها، فكل عنصر يُعرف بالعناصر، بالعناصر
+
+65
+00:04:53,440 --> 00:04:57,520
+السابقة للـ function، بيصير اسمها recursively. طيب،
+
+66
+00:04:57,520 --> 00:05:02,040
+مثال، لو قلنا A N تساوي أو equivalent لـ 2 to the
+
+67
+00:05:02,040 --> 00:05:07,560
+power N، فهذا recursively، كأني بقول A node، أبدأ بالـ
+
+68
+00:05:07,560 --> 00:05:10,480
+natural number، حسب التعريف، natural number من الـ
+
+69
+00:05:10,480 --> 00:05:14,940
+نار، بتبدأ بصفر، فإذا a note بتساوي واحد، أكبر من هيك إيش؟
+
+70
+00:05:14,940 --> 00:05:22,970
+بتساوي، بتساوي a n ناقص واحد في اثنين، السابقة في
+
+71
+00:05:22,970 --> 00:05:25,450
+اثنين. فأصبحت فعلاً كأنها function في العنصر الذي
+
+72
+00:05:25,450 --> 00:05:28,710
+جاء قبلها. طب العنصر الذي جاء قبلها برضه اثنين من العنصر
+
+73
+00:05:28,710 --> 00:05:32,690
+الذي جاء قبلها من N ناقص اثنين، N ناقص اثنين هي اثنين
+
+74
+00:05:32,690 --> 00:05:35,790
+في العنصر الذي جاء قبلها، N ناقص ثلاثة، and so on. فإذا
+
+75
+00:05:35,790 --> 00:05:39,130
+لاحظوا أن هذه function بكل بساطة نقدر نحطها بشكل
+
+76
+00:05:39,130 --> 00:05:44,090
+تكراري، شكل تكراري، أن كل عنصر نقدر نحسبه من العنصر
+
+77
+00:05:44,090 --> 00:05:48,490
+الذي جاء قبلها، من العنصر الذي جاء قبلها. مثال على ذلك، نحله
+
+78
+00:05:48,490 --> 00:05:52,590
+مع بعض، مثلًا هذا مثال من الأمثلة، وسنفرض إن أنا فعلاً
+
+79
+00:05:52,590 --> 00:05:56,070
+أتعامل مع function f of n لكل العناصر n belonging
+
+80
+00:05:56,070 --> 00:06:01,770
+to natural number recursively، الـ f of 0 بتساوي 3.
+
+81
+00:06:01,770 --> 00:06:07,470
+طيب، الـ inductive step كمعادلة أقدر أقول إن الـ f of
+
+82
+00:06:07,470 --> 00:06:12,830
+n زائد 1 بتساوي 2 f of n زائد 3. فإذن، بكل بساطة
+
+83
+00:06:12,830 --> 00:06:19,170
+أقدر أقول إن الـ f 1 بتساوي كذا، هاه؟
+
+84
+00:06:20,510 --> 00:06:24,510
+أيوة، اللي هو، جدع، هي عندك كله تسعة، هذه على طول
+
+85
+00:06:24,510 --> 00:06:30,090
+مباشرة، نحل، هي تسعة، اثنان، ثمانية عشر، زي الثلاث، واحد
+
+86
+00:06:30,090 --> 00:06:32,510
+و عشرين، واحد و عشرين في اثنين، اثنان وأربعين، زي
+
+87
+00:06:32,510 --> 00:06:35,390
+الثلاث، خمسة وأربعين، خمسة وأربعين في اثنين، تسعين،
+
+88
+00:06:35,390 --> 00:06:40,030
+تسعين، زي الثلاث، ثلاثة وتسعون، and so on، so on. لاحظ
+
+89
+00:06:40,030 --> 00:06:44,330
+فإذا، كل عنصر بأجيبه من الذي جاء قبلها، فأنت لاحظ كل عنصر
+
+90
+00:06:44,330 --> 00:06:48,400
+و إحنا بنحسبه، ذكرنا العنصر الذي جاء قبلها. فإذا هذه
+
+91
+00:06:48,400 --> 00:06:55,040
+recursive form واضحة جدًا، تمام. recursive definition
+
+92
+00:06:55,040 --> 00:06:58,700
+لها، factorial مثلًا، هاي واحدة من الـ functions التي
+
+93
+00:06:58,700 --> 00:07:04,320
+ممكن برضه نعرفها بشكل recursively، أو recursive
+
+94
+00:07:04,320 --> 00:07:08,220
+form، بكل بساطة، كلنا عارفين الـ F of N، الـ N
+
+95
+00:07:08,220 --> 00:07:11,960
+factorial هي عبارة عن multiplication لكل العناصر
+
+96
+00:07:11,960 --> 00:07:17,820
+من 1 إلى N، واحد في اثنين في ثلاثة في أربعة في N، فكأني
+
+97
+00:07:17,820 --> 00:07:21,460
+بقول N factorial، كأني بقول N factorial. فإذا الـ
+
+98
+00:07:21,460 --> 00:07:24,840
+index I من واحد إلى N، و بكل بساطة بتقدر تبدأ من
+
+99
+00:07:24,840 --> 00:07:28,940
+اثنين لأن واحد مش هيكون كثير مؤثر، أنت بتضرب في
+
+100
+00:07:28,940 --> 00:07:33,220
+واحد فمش هيفرق كثير، فابدأ باثنين مش مشكلة، لكن الـ
+
+101
+00:07:33,220 --> 00:07:37,520
+case تبعتك F of Zero هتكون واحد، هتكون عبارة عن
+
+102
+00:07:37,520 --> 00:07:41,780
+واحد recursively، بتقدر تقول F of واحد، واحد. طيب F
+
+103
+00:07:41,780 --> 00:07:49,490
+of اثنين، F of واحد في قيمة الاثنين. طيب F of ثلاثة
+
+104
+00:07:49,490 --> 00:07:55,750
+هي نفس الثلاثة في F of اثنين، وهكذا. فلاحظ كأنها
+
+105
+00:07:55,750 --> 00:08:00,690
+معرفة بقيمة العنصر الذي قبلها. فلو قلنا F of أربعة
+
+106
+00:08:00,690 --> 00:08:06,850
+هتسوي الأربعة في قيمة الـ F of ثلاثة اللي هي
+
+107
+00:08:06,850 --> 00:08:14,750
+الستة، وهكذا. كل عنصر يُعرف بالذي قبله .. كل عنصر
+
+108
+00:08:14,750 --> 00:08:20,550
+يُعرف بالذي قبله، فهذا طبعًا بتصير أسهل لك لما بدك
+
+109
+00:08:20,550 --> 00:08:24,090
+تشتغل على الـ factorial و بدك تجيب له برنامج تحسبه،
+
+110
+00:08:24,090 --> 00:08:29,710
+برنامج، فبتصير من نفسها .. من نفسها. طيب، بعض الـ easy
+
+111
+00:08:29,710 --> 00:08:32,670
+examples البسيطة جدًا اللي ممكن نتعامل معها، لما
+
+112
+00:08:32,670 --> 00:08:38,350
+بقول a، m A في N، و كلاهما عدد natural number
+
+113
+00:08:38,350 --> 00:08:42,410
+اللي هي الـ N، و real number للـ A، اللي هي مجرد الـ
+
+114
+00:08:42,410 --> 00:08:45,330
+multiplier اللي بنضرب فيه، الـ multiplier، لما بدي
+
+115
+00:08:45,330 --> 00:08:48,930
+أعرف، طبعًا أن هي المتغير، بالمناسبة أن هي المتغير،
+
+116
+00:08:48,930 --> 00:08:51,510
+مدام natural number، معناته هي الـ location، إحنا
+
+117
+00:08:51,510 --> 00:08:54,390
+معطينهم في الـ locations هؤلاء، كل عنصر المفروض أنه
+
+118
+00:08:54,390 --> 00:08:57,630
+بقيمة العنصر الذي في الـ question، الذي جاء قبلها، تمام.
+
+119
+00:08:57,630 --> 00:09:05,980
+أقدر أقول أنه في n هي تساوي a في n ناقص واحد، اللي
+
+120
+00:09:05,980 --> 00:09:12,200
+هي العنصر الذي جاء قبلها، زائد a، فهي الـ term السابق،
+
+121
+00:09:12,200 --> 00:09:19,600
+سنضيف له a. فإذا هنا معامل الـ recursive factor تبعنا
+
+122
+00:09:19,600 --> 00:09:25,560
+هو زائد a، فكل عنصر هو نفس السابق مع إضافة a عليه.
+
+123
+00:09:26,710 --> 00:09:34,290
+فإذا لما بقول a n زائد واحد هي نفسها a n زائد a، لأنك
+
+124
+00:09:34,290 --> 00:09:39,170
+بدك تأخذ في الحالة هذه الـ a common مشترك، و ستجمع
+
+125
+00:09:39,170 --> 00:09:45,210
+هنا، فطلعت الـ n، n ناقص واحد، و هنا زائد واحد، و ستجمع
+
+126
+00:09:45,210 --> 00:09:45,410
+هنا، فطلعت الـ n، n ناقص واحد، و هنا زائد واحد، و ستجمع
+
+127
+00:09:45,410 --> 00:09:45,670
+هنا، فطلعت الـ n، n ناقص واحد، و هنا زائد واحد، و ستجمع
+
+128
+00:09:45,670 --> 00:09:45,690
+هنا، فطلعت الـ n، n ناقص واحد، و هنا زائد واحد، و ستجمع
+
+129
+00:09:45,690 --> 00:09:47,570
+هنا، فطلعت الـ n، n ناقص واحد، و هنا زائد واحد، و ستجمع
+
+130
+00:09:47,570 --> 00:09:53,050
+هنا، فطلعت الـ n، n ناقص واحد، و
+
+131
+00:09:53,220 --> 00:09:56,920
+ضرب a، فأنت كل مرة بتضرب في a، كل مرة بتضرب في a.
+
+132
+00:09:56,920 --> 00:10:04,360
+فمعامل التغيير أو العلاقة بين a of n كـ function في
+
+133
+00:10:04,360 --> 00:10:09,660
+n و a of n ناقص واحد، اللي هي function في n ناقص
+
+134
+00:10:09,660 --> 00:10:14,040
+واحد، الفرق بينهم هو ضرب في a بس، فضربنا في a عشان
+
+135
+00:10:14,040 --> 00:10:18,000
+نحصل عليه. فإذن، واضحة جدًا أن فعلاً الـ function في n
+
+136
+00:10:19,040 --> 00:10:22,260
+لاحظ؟ أقدر أجيبها بدلالة الـ function في N ناقص
+
+137
+00:10:22,260 --> 00:10:26,380
+واحد، اللي هي التي جاءت قبلها .. التي جاءت قبلها. طيب الـ
+
+138
+00:10:26,380 --> 00:10:29,640
+summation .. بسيطة، الـ summation بتتخيل صحيح؟ لما
+
+139
+00:10:29,640 --> 00:10:32,480
+أقول summation to N، طب أنا عارف قيمة الـ summation
+
+140
+00:10:32,480 --> 00:10:35,500
+to N ناقص واحد، ما في داعي أعمل summation to N من
+
+141
+00:10:35,500 --> 00:10:39,200
+الأول و جديد، هي نفس الـ summation لـ N ناقص واحد زائد
+
+142
+00:10:39,200 --> 00:10:43,180
+قيمة الـ N و بس. فإذا، أجمع عليها قيمة N لحالها، نجمع
+
+143
+00:10:43,180 --> 00:10:48,810
+قيمة N لحالها، هي الـ A N نفسها. بنفس الكلام الـ
+
+144
+00:10:48,810 --> 00:10:54,290
+multiplication، أضرب قيمة a of n. فإذا، إذا أنا عارف
+
+145
+00:10:54,290 --> 00:11:03,280
+لعند n ناقص واحد، لـ a of i، هذه عرفها، عرف قيمتها و
+
+146
+00:11:03,280 --> 00:11:07,720
+حسبها. طب هو طالب مني لـ n، فإذا نفس القيمة التي هنا
+
+147
+00:11:07,720 --> 00:11:13,020
+أضربها فقط في a n، اللي هو العنصر الأخير الذي بقي
+
+148
+00:11:13,020 --> 00:11:15,460
+و برضه هذه من الحاجات التي إحنا أخذناها كـ
+
+149
+00:11:15,460 --> 00:11:18,840
+manipulation للـ summation، لو متذكرين لما تكلمنا عن
+
+150
+00:11:18,840 --> 00:11:21,060
+الـ summation، حكينا في الجزء السابق. طيب، أشدر لأن
+
+151
+00:11:21,060 --> 00:11:24,780
+خلصنا .. لا، ولا باقي، لا، الأخيرة الـ .. الـ
+
+152
+00:11:24,780 --> 00:11:32,390
+intersection، لما تقول intersection لـ set I و الـ I
+
+153
+00:11:32,390 --> 00:11:38,090
+هذه مجموعة sets from zero to N، فإذا عندي N sets،
+
+154
+00:11:38,090 --> 00:11:42,370
+بده أجيب التقاطع تبعهم، N هذه خمسة، معناته في عندي
+
+155
+00:11:42,370 --> 00:11:44,870
+خمس مجموعات، بده أجيب تقاطع الخمس مجموعات مع بعض.
+
+156
+00:11:44,870 --> 00:11:49,810
+طيب، هذه كيف أقدر أعرفها بالسابقة تبعها؟ أقدر أقول
+
+157
+00:11:49,810 --> 00:11:54,470
+intersection كأنه أنا عند الـ intersection من صفر إلى
+
+158
+00:11:54,470 --> 00:12:01,950
+N ناقص واحد لـ S I، صحيح؟ طب من هذا الـ term بدي أجيب
+
+159
+00:12:01,950 --> 00:12:06,710
+الـ intersection to
+
+160
+00:12:06,710 --> 00:12:15,610
+N لـ S I. فإذا هنا إيش كمان؟ تقاطع، ما هي تقاطع زائد
+
+161
+00:12:15,610 --> 00:12:23,350
+إيش؟ الـ N التي بقيت، لأن العنصر الوحيد المفقود هو
+
+162
+00:12:23,350 --> 00:12:30,160
+عند الـ N. فإذا، S أو set in هي التي أحتاج أضيفها
+
+163
+00:12:30,160 --> 00:12:35,960
+للتقاطع، بس هي التي نحتاج نضيفها. لماذا؟ للتقاطع طبعًا.
+
+164
+00:12:35,960 --> 00:12:38,780
+الاتحاد نفس الشيء، في الاتحاد نفس الشيء بيصير هنا.
+
+165
+00:12:38,780 --> 00:12:44,870
+اتحاد، مش أكثر. طيب، هـ، أنتم متذكرينها، الـ big arc، الـ
+
+166
+00:12:44,870 --> 00:12:48,110
+Big Arc، تذكرون أخذناها في آخر ما تكلمنا عن الـ
+
+1
+
+223
+00:17:33,240 --> 00:17:39,920
+بساطة بقدر أقول أن if n تساوي if n ناقص واحد زائد
+
+224
+00:17:40,860 --> 00:17:47,800
+ناقص اثنين هذه أكيد صحيح. طيب، بكل بساطة بتقدر تقول
+
+225
+00:17:47,800 --> 00:17:53,380
+هذه صحيحة، مش shake. احنا قلنا بدنا نقول أن هذه is
+
+226
+00:17:53,380 --> 00:17:59,640
+true. فإذاً لازم تكون أكبر من اثنين.
+
+227
+00:17:59,640 --> 00:18:07,160
+to the power ناقص واحد to اثنين if ناقص اثنين.
+
+228
+00:18:11,040 --> 00:18:16,480
+صحيح؟ ليش؟ لأنه ببساطة هذه برضه is true حسب الـ K
+
+229
+00:18:16,480 --> 00:18:21,560
+اللي هي من 2 to N. طب ما هذه في نفس الـ range. فإذاً
+
+230
+00:18:21,560 --> 00:18:25,780
+أنا الـ true، الـ true يعني بقدر أستعيد عنها بـ 2 to the
+
+231
+00:18:25,780 --> 00:18:33,740
+power n ناقص 1 حسب الـ theorem أن هي true ونفس
+
+232
+00:18:33,740 --> 00:18:38,660
+الكلام. أن ناقص اثنين بقدر برضه أستعيد عنها باثنين to the
+
+233
+00:18:38,660 --> 00:18:41,240
+ناقص اثنين، اثنين to the power n ناقص اثنين.
+
+234
+00:18:41,240 --> 00:18:47,980
+فحطيناهم. ممتاز. الآن الاثنين هدول بكل بساطة بتقدر
+
+235
+00:18:47,980 --> 00:18:53,160
+اللي هنتغيرهم بحيث أنك تقول هذا الـ term هيكون أكيد
+
+236
+00:18:53,160 --> 00:19:01,440
+أقل من اثنين to the power n ناقص واحد. صح؟ أكيد. ليش؟
+
+237
+00:19:01,440 --> 00:19:07,470
+لأن كلنا عارفين،  فبالتسلسل، يعني كل عنصر أكيد
+
+238
+00:19:07,470 --> 00:19:12,410
+أكبر من اللي قبله. أكيد أكبر من اللي قبله، معناه
+
+239
+00:19:12,410 --> 00:19:15,950
+ذلك إذا كان استبدلنا عن هذا الـ term باثنين to the
+
+240
+00:19:15,950 --> 00:19:22,190
+power n ناقص واحد. هل هتتغير اتجاه الأكبر من؟ لأ.
+
+241
+00:19:22,190 --> 00:19:26,470
+مش هيتغير. فحتبقى دائماً if of n أقل من هذا الـ term.
+
+242
+00:19:26,470 --> 00:19:32,030
+بالعكس، حتى هتقل بزيادة كمان. فهنا تصبح اثنين if
+
+243
+00:19:32,030 --> 00:19:36,930
+ناقص واحد. لأ f of N. اجمع الاثنين مع بعض كأنك أخدت
+
+244
+00:19:36,930 --> 00:19:42,830
+اثنين عامل مشترك. فبتصير كأنه اثنين مضروبة في هذا
+
+245
+00:19:42,830 --> 00:19:46,550
+الـ term. اجمع فوق فبتصبح أقل من اثنين to the power
+
+246
+00:19:46,550 --> 00:19:46,810
+N
+
+247
+00:19:53,450 --> 00:19:57,770
+لاحظت كيف؟ فـ if of n اللي أنا بدي أثبتها بمعلومة
+
+248
+00:19:57,770 --> 00:20:01,730
+اللي قبلها، على اعتبار أن اللي قبلها أكيد true.
+
+249
+00:20:01,730 --> 00:20:07,310
+أكيد true. ففي الحالة هذه true. فبنستعيد عنها، عفواً،
+
+250
+00:20:07,310 --> 00:20:10,530
+هذه الـ true، بنستعيد عنها بالاثنين to the power n ناقص
+
+251
+00:20:10,530 --> 00:20:13,610
+واحد. بالمناسبة هذا الكلام ينطبق إن هنا ما يكونش
+
+252
+00:20:13,610 --> 00:20:19,450
+لا يساوي أقل من، بس يعني أقل من فقط. ليش؟ لأن احنا
+
+253
+00:20:19,450 --> 00:20:22,150
+ما اشتغلناش على n زائد واحد، اشتغلنا على n نفسها.
+
+254
+00:20:24,060 --> 00:20:29,620
+لاحظت؟ اشتغلنا على n نفسها. فإذاً بتصير لعند n ناقص
+
+255
+00:20:29,620 --> 00:20:35,720
+واحد فعلياً بدون أو يساوي. تمام؟ فهي أثبتناها برضه
+
+256
+00:20:35,720 --> 00:20:38,940
+بالـ inductive step أو الـ proof اللي أخدنا المرة
+
+257
+00:20:38,940 --> 00:20:45,710
+الماضية. طيب في كمان شغلة واضحة جداً فيها جزئية الـ
+
+258
+00:20:45,710 --> 00:20:50,250
+recursion وهي الـ Euclide algorithm اللي أخدناها
+
+259
+00:20:50,250 --> 00:20:52,250
+المرة الماضية لما كنا بدنا نجيب الـ greatest common
+
+260
+00:20:52,250 --> 00:20:56,530
+divisor. ليش؟ لأنه لو متذكرين، هتسترجع شوية، كنت
+
+261
+00:20:56,530 --> 00:21:00,010
+بقول أن الـ greatest common divisor بقدر أجيبها لـ A
+
+262
+00:21:00,010 --> 00:21:05,350
+و B كأنها هي نفس الـ greatest common divisor لـ B مع
+
+263
+00:21:05,350 --> 00:21:12,150
+A modulo B. طب كويس. طب A modulo B مع B هي نفسها كـ
+
+264
+00:21:12,150 --> 00:21:15,780
+greatest common divisor. من برجع بعيد نفس… أيوة… آه
+
+265
+00:21:15,780 --> 00:21:18,720
+لاحظ… بعيد… بعيد. معناته هي recursion. خلاص
+
+266
+00:21:18,720 --> 00:21:22,880
+واضحة recursion. طالع إن لاميه واحد اسمه لاميه
+
+267
+00:21:22,880 --> 00:21:27,000
+وبرضه واضح نصف فرنسي. لاميز هذا عمل، أو لاميه عمل
+
+268
+00:21:27,000 --> 00:21:30,300
+نظرية يسميها لاميز theorem. لاميز theorem بده يقول
+
+269
+00:21:30,300 --> 00:21:35,520
+بالنسبة لـ greatest common divisor لـ A و B، كم مرة
+
+270
+00:21:35,520 --> 00:21:41,200
+عدد مرات تكرارها طبعاً هو، يعني بده يجيب كأنه الـ
+
+271
+00:21:41,200 --> 00:21:44,420
+complexity بتاعتها. الـ complexity بتاع التنقل كم مرة
+
+272
+00:21:44,420 --> 00:21:49,760
+هتتكرر. مش احنا عرفنا سابقاً أن مرات التكرار في
+
+273
+00:21:49,760 --> 00:21:53,880
+الآخر تمثل الـ complexity، الـ complexity بالظبط. طيب إجا
+
+274
+00:21:53,880 --> 00:21:58,960
+جالنا إذا كان والله A و B هما الـ two numbers اللي
+
+275
+00:21:58,960 --> 00:22:00,440
+أنا بدي أجيب الـ greatest common divisor between
+
+276
+00:22:00,440 --> 00:22:06,380
+them. وإيه هي الأكبر؟ فإذاً بقدر أقول أنه باستخدام
+
+277
+00:22:06,380 --> 00:22:10,410
+Euclid's algorithm، الـ greatest common divisor
+
+278
+00:22:10,410 --> 00:22:16,170
+هنعمل كم step منها أقل من أو يساوي بحد أقصى خمسة K
+
+279
+00:22:16,170 --> 00:22:25,030
+بشرط أن K هي عدد الـ decimal digits للرقم الأصغر. هو
+
+280
+00:22:25,030 --> 00:22:30,210
+عبّر عنها رياضياً، اللي هو يعني بمعنى لو كان عندي 121
+
+281
+00:22:30,210 --> 00:22:35,310
+و 96، الأقل منهم two digits number، فـ K باثنين.
+
+282
+00:22:38,280 --> 00:22:41,180
+لكن هو عبّر عنها رياضياً عشان يكتبها رياضياً فقال
+
+283
+00:22:41,180 --> 00:22:50,120
+floor لمن للـ log base 10 لـ B. فهيها. طيب هذه لما نجيب
+
+284
+00:22:50,120 --> 00:22:58,800
+لها log base 10 بتطلع واحد وكسر. زائد الواحد اثنين
+
+285
+00:22:58,800 --> 00:23:05,310
+خلاص. طيب لو بدنا نحسبها لهذه 2 وكسر، فالـ floor 2
+
+286
+00:23:05,310 --> 00:23:08,130
+زائد 1 ثلاثة. ما كان الأول ثلاثة three digits. خلاص
+
+287
+00:23:08,130 --> 00:23:13,210
+مكان الأساس الـ three digits. فبكل بساطة هو في الآخر
+
+288
+00:23:13,210 --> 00:23:16,190
+يعني علقنا عليها، كتبنا أن هي في الآخر هي number of
+
+289
+00:23:16,190 --> 00:23:19,950
+decimal digits. لا بيه. خلاص. يعني احنا ليش مغالبين
+
+290
+00:23:19,950 --> 00:23:24,150
+حالنا؟ لكن في الآخر لو جيت طلعت عليها برضه إطالة
+
+291
+00:23:24,150 --> 00:23:28,560
+كتير. يعني خمسة من الاثنين اللي بتتكلم عن عشرة…
+
+292
+00:23:28,560 --> 00:23:32,960
+عشرة steps. يعني اللي لو أنتو… لو هذا عبارة عن
+
+293
+00:23:32,960 --> 00:23:36,760
+loop، أنت متوقع أنه ما يزيدش عن عشرة. بحيث أنه لو زاد
+
+294
+00:23:36,760 --> 00:23:42,140
+عن عشرة في مشكلة في البرنامج. لو زاد عن عشرة معناته
+
+295
+00:23:42,140 --> 00:23:45,160
+في مشكلة في البرنامج. خد بالك احنا أعطيناك هنا الحد
+
+296
+00:23:45,160 --> 00:23:50,240
+الأقصى لعدد الـ iterations أو الـ recursion steps.
+
+297
+00:23:51,000 --> 00:23:54,060
+زادت عن هيك؟ لأ. خد بالك، يمكن في مشكلة. واضح أن في
+
+298
+00:23:54,060 --> 00:23:58,660
+مشكلة. طيب ففي الحالة هذه الـ Euclid algorithm بنقدر
+
+299
+00:23:58,660 --> 00:24:02,700
+نقول عنه linear لأن هو خطي مع عدد الـ decimal. كل ما
+
+300
+00:24:02,700 --> 00:24:06,720
+زادت الـ decimal بالنسبة لنا كل ما بتزيد عدد الـ
+
+301
+00:24:06,720 --> 00:24:11,120
+steps. كل ما بتزيد one decimal بزيد مقابلها خمسة في
+
+302
+00:24:11,120 --> 00:24:16,020
+الـ times. خمسة في الـ time أو في الـ execution time.
+
+303
+00:24:16,020 --> 00:24:21,470
+فعلياً. طيب الـ recursive لها الـ sets. لما نتكلم عن الـ
+
+304
+00:24:21,470 --> 00:24:25,190
+sets برضه نفس الكلام. رغم أن الـ set في النهاية هي
+
+305
+00:24:25,190 --> 00:24:31,130
+unordered set، هي مش مرتبة. لكن برضه نقدر نعرفها أو
+
+306
+00:24:31,130 --> 00:24:35,390
+نعرف عناصرها من عناصرها. نقدر نعرف عناصرها من
+
+307
+00:24:35,390 --> 00:24:41,470
+عناصرها. زي بكل بساطة ناخد مثلاً لـ a set، أي set ممكن
+
+308
+00:24:41,470 --> 00:24:45,890
+أعرف مجموعة elements، واحد أو اثنين أو ثلاثة بحيث
+
+309
+00:24:45,890 --> 00:24:49,510
+أن هما يكون في بينهم relation بينهم وبين الـ other
+
+310
+00:24:49,510 --> 00:24:53,860
+numbers. relation، وبعرف الـ relation. بس إذا كانت الـ
+
+311
+00:24:53,860 --> 00:24:56,600
+set كبيرة. إذا كانت الـ set عندي كبيرة، واحنا
+
+312
+00:24:56,600 --> 00:24:59,880
+اتكلمنا أنه في عندي infinite sets. في بعض الـ sets
+
+313
+00:24:59,880 --> 00:25:03,640
+infinite بتبقى infinity. فإذاً مش من المناسب أني
+
+314
+00:25:03,640 --> 00:25:08,160
+أقول أكتبها كاملة. فممكن أحط أول عنصرين ثلاثة بس
+
+315
+00:25:08,160 --> 00:25:12,680
+المهم اللي هم يكونوا الـ common اللي بقدر أعمل
+
+316
+00:25:12,680 --> 00:25:17,350
+generation لأي element منهم. زي… فهد… طبعاً احنا
+
+317
+00:25:17,350 --> 00:25:20,330
+كلنا مقتنعين بهذا الكلام أن في عندي small finite
+
+318
+00:25:20,330 --> 00:25:24,210
+بعرف كم element فقط في البداية. على أساس أن هدول الـ
+
+319
+00:25:24,210 --> 00:25:27,830
+base elements بتصير اسمهم. زي الـ base step. هدول الـ
+
+320
+00:25:27,830 --> 00:25:32,250
+base element، وبيكون لازم يكون في عندي rule للـ
+
+321
+00:25:32,250 --> 00:25:35,690
+constructing for other elements. لازم يكون فيه rule
+
+322
+00:25:35,690 --> 00:25:40,230
+وإلا كيف بدي أعرف باقي العناصر؟ باقي العناصر لازم
+
+323
+00:25:40,230 --> 00:25:44,050
+تكون معرفة، معرفة بس مش معرفة كأرقام، معرفة بـ
+
+324
+00:25:44,050 --> 00:25:53,770
+formula، بمعادلة، بـ model أو rule. مثلاً خليني
+
+325
+00:25:53,770 --> 00:25:59,490
+أفترض أن في عندي ثلاثة
+
+326
+00:25:59,490 --> 00:26:07,560
+تنتمي للست S. وجدنا أن كل العناصر تحقق هذه المعادلة
+
+327
+00:26:07,560 --> 00:26:15,400
+لأن x زائد y هي برضه تنتمي لأيش؟ لـ S. و x و y هي
+
+328
+00:26:15,400 --> 00:26:20,420
+عناصر من x من S. كل واحدة منهم عناصر من S. فكل
+
+329
+00:26:20,420 --> 00:26:26,720
+عنصرين هما ضمن الست، مجموعهم لازم يكون ضمن الست. كل
+
+330
+00:26:26,720 --> 00:26:31,010
+عنصرين ضمن الست، مجموعهم برضه ضمن الست. طيب،  قص على
+
+331
+00:26:31,010 --> 00:26:35,330
+ذلك، هتلاقي أن هي لانهائية. بتصير هتصبح لانهائية بكل
+
+332
+00:26:35,330 --> 00:26:38,910
+بساطة. ثلاثة هي تنتمي للـ set. معناه ذلك أنه ثلاثة و
+
+333
+00:26:38,910 --> 00:26:42,730
+ثلاثة، ثلاثة مع نفسها. ليش؟ لأنه في الـ unordered
+
+334
+00:26:42,730 --> 00:26:48,910
+ممكن يكون فيه تكرار. صحيح؟ بمعنى لما نقول ليه set
+
+335
+00:26:48,910 --> 00:26:54,150
+of ثلاثة. أنا عارف أن هو نفسها هذه، ما يُكافئ لثلاثة
+
+336
+00:26:54,150 --> 00:26:54,730
+وثلاثة.
+
+337
+00:26:57,500 --> 00:27:01,240
+فإذن هذه أنا أصلاً هيك بختزلها بثلاثة وأسكت بس.
+
+338
+00:27:01,240 --> 00:27:04,340
+أنا عارف أنه ممكن يكون فيها تكرار، ورغم ذلك بحسبه
+
+339
+00:27:04,340 --> 00:27:08,820
+مرة واحدة. فإذا ثلاثة وثلاثة صار ستة. صار عندي
+
+340
+00:27:08,820 --> 00:27:15,090
+ثلاثة وستة. طيب ثلاثة وستة تسعة، أو الستة مع الستة
+
+341
+00:27:15,090 --> 00:27:18,510
+هي اثنا عشر. آه، اجت الاثنا عشر. اثنا عشر مع الثلاثة، واثنا عشر
+
+342
+00:27:18,510 --> 00:27:20,850
+مع الستة، والتسعة مع الستة، والتسعة مع الثلاثة.
+
+343
+00:27:20,850 --> 00:27:26,010
+صارت تعرف تطلع مضاعفات الثلاثة. فبتلاقيها مضاعفات
+
+344
+00:27:26,010 --> 00:27:30,830
+الثلاثة بشكل infinite set. infinite set. فبكل بساطة
+
+345
+00:27:30,830 --> 00:27:36,210
+ممكن تعرف ثلاثة belong to us، و x زائد y belong to
+
+346
+00:27:36,210 --> 00:27:43,640
+us، إذا x و y belong to us. belong to us. فهيك عرفنا
+
+347
+00:27:43,640 --> 00:27:48,380
+الـ set بشكل recursive. طيب نبدأ في شوية أكواد، أكواد
+
+348
+00:27:48,380 --> 00:27:52,180
+معتمدة، احنا بعضها أخدناها، بس بدنا نحاول أننا
+
+349
+00:27:52,180 --> 00:27:57,160
+نختزلها بشكل recursion model. بشكل recursion model.
+
+350
+00:27:57,160 --> 00:28:02,280
+هفترض أن الأول، إيش بدنا نحسب؟ بدنا نحسب هنا الـ
+
+351
+00:28:02,280 --> 00:28:08,860
+power. فـ example الـ power. طبعاً
+
+352
+00:28:08,860 --> 00:28:10,120
+كتبناها، الـ power بالمناسبة.
+
+353
+00:28:18,800 --> 00:28:25,540
+لما قلنا a to the power n بتساوي a to the power n
+
+354
+00:28:25,540 --> 00:28:35,140
+ناقص واحد في a. خلاص. معناته ذا recursively أنا هضرب
+
+355
+00:28:35,140 --> 00:28:39,920
+بس كل مرة في a. recursively. كل مرة هضرب في a. المثال
+
+356
+00:28:39,920 --> 00:28:44,690
+حاسبة كان التالي. البروسيجر power هنا، حددنا أن أنا
+
+357
+00:28:44,690 --> 00:28:48,110
+فيه code، بدي أكتب فيه code. البروسيجر power اسمه
+
+358
+00:28:48,110 --> 00:28:51,950
+power a و n. دي لا تساوي صفر، لأنه ما لهاش معنى
+
+359
+00:28:51,950 --> 00:28:54,810
+أحطها بتساوي صفر، معناته تبقى power إيش؟ هيكون واحد، و
+
+360
+00:28:54,810 --> 00:28:59,130
+خلاص، a عفواً، أنا هتظل صفر، هتظل دائماً صفر، ما لهاش
+
+361
+00:28:59,130 --> 00:29:04,690
+قيمة. طيب هذه العبارة، الـ a عبارة عن real number، و
+
+362
+00:29:04,690 --> 00:29:09,400
+الـ n natural number، لأن الـ power بده يكون integer.
+
+363
+00:29:09,400 --> 00:29:13,260
+كويس. إذا كانت الـ n اللي هي الـ power اللي فوق
+
+364
+00:29:13,260 --> 00:29:18,480
+بتساوي صفر، إيش return بإيش؟ بواحد. أي حاجة تدور الـ
+
+365
+00:29:18,480 --> 00:29:22,420
+power صفر بدو يرجع بواحد. طب otherwise، لأ، أنا
+
+366
+00:29:22,420 --> 00:29:26,580
+ما بدأت لسه، بدري عليها، بدأت بإيه؟ تدور الـ power
+
+367
+00:29:26,580 --> 00:29:30,460
+اثنين مثلاً، معناته لأ، لا تساوي صفر. في الحالة دي
+
+368
+00:29:30,460 --> 00:29:42,820
+else return إيه؟ هيها، الـ a هي دي في مين؟ في power
+
+369
+00:29:42,820 --> 00:29:46,840
+برضه كمان مرة. بمعنى اعمل method وافتح code كمان
+
+370
+00:29:46,840 --> 00:29:56,800
+مرة، بمرر له الـ a و n ناقص واحد. آه
+
+371
+00:29:56,800 --> 00:30:01,840
+يه، نضربهم في بعض. ممتاز. عشان نجي نفتح هذا الـ term،
+
+372
+00:30:01,840 --> 00:30:06,460
+هذا الـ method. وهذا لسه شغالة موجودة فاضية، قاعدة
+
+373
+00:30:06,460 --> 00:30:10,680
+لسه ما عملتش فيها إشي. كويس، بحيث أنه أنا الـ a لسه
+
+374
+00:30:10,680 --> 00:30:14,480
+بتستنى الناتج. الـ a واقفة هنا بتستنى الناتج. تمام؟
+
+375
+00:30:14,480 --> 00:30:19,340
+الناتج هذا برضه نفس القصة. هفتح من أول وجديد هنا،
+
+376
+00:30:19,340 --> 00:30:25,720
+بس هنا أصبحت بـ n ناقص واحد. هل الـ n ناقص واحد تساوي
+
+377
+00:30:25,720 --> 00:30:26,060
+صفر؟
+
+378
+00:30:29,320 --> 00:30:35,740
+هتساوي واحد، معناه ذلك أنه لأ، هيجي للـ else، روح لي
+
+379
+00:30:35,740 --> 00:30:40,540
+افتح لي a كمان مرة، اضرب a كمان مرة، فهيصير عندي a في
+
+380
+00:30:40,540 --> 00:30:48,700
+a، total a في a وصفر، power الصفر. a في a وراح power
+
+381
+00:30:48,700 --> 00:30:54,640
+الصفر. طيب power الصفر هنا أصبحت zero، فمرر لي zero
+
+382
+00:30:54,640 --> 00:31:01,930
+للميثود الثالثة حتى الآن. صفر؟ لأ. then آه، then return
+
+383
+00:31:01,930 --> 00:31:07,870
+واحد. فبرجع بواحد. طيب لاحظ كيف رجع بواحد. الواحد هذا
+
+384
+00:31:07,870 --> 00:31:13,090
+جابه من الـ method رقم ثلاثة. خلص، سكر الـ method رقم
+
+385
+00:31:13,090 --> 00:31:16,210
+ثلاثة ونهاها ورجع لـ method رقم اثنين. الـ method
+
+386
+00:31:16,210 --> 00:31:21,210
+رقم اثنين الناتج بده يضربه في a، وسكر method
+
+387
+00:31:21,210 --> 00:31:27,990
+رقم اثنين. فرجع لنا بـ a ضربهم. رجع للـ method رقم صفر
+
+388
+00:31:27,990 --> 
+
+445
+00:35:43,540 --> 00:35:45,000
+ال stack space  أه أكيد
+
+446
+00:35:48,460 --> 00:35:50,940
+هي حسب ال method ما أنت إذا كان .. لاحظ إذا كان ال
+
+447
+00:35:50,940 --> 00:35:53,640
+method هي ضخمة كبيرة بمعنى بيقدرش ياخد مجموعة
+
+448
+00:35:53,640 --> 00:35:57,680
+بيانات و يخليها برا و يسكر لأ هي فيها مجموعة كبيرة
+
+449
+00:35:57,680 --> 00:36:01,320
+لأ بيصير بدها شغل تاني لأ أكيد أكيد في الحالة هذه
+
+450
+00:36:01,320 --> 00:36:05,300
+بدك ال stack يكون أصلا كبيرة عندك و ساعتها بيقولك
+
+451
+00:36:05,300 --> 00:36:09,040
+أنه لأ والله صار عندك ال complexity مشكلة في ال
+
+452
+00:36:09,040 --> 00:36:11,740
+space complexity تصبح عندك مشكلة في ال space
+
+453
+00:36:11,740 --> 00:36:16,970
+complexity طيب أخدنا ال linear (linear) سيرش مش ذاكرين
+
+454
+00:36:16,970 --> 00:36:22,930
+طب هاتنعمله code باستخدام ال recursion theorem أو
+
+455
+00:36:22,930 --> 00:36:31,210
+باستخدام ال recursive code كان الشغل كله معتمد على
+
+456
+00:36:31,210 --> 00:36:38,530
+أن في عندي X هذه بدنا نبحث عنها بين I و J و إيش
+
+457
+00:36:38,530 --> 00:36:46,690
+كان مسمى ال series (String) A ببدأ من I location
+
+458
+00:36:46,690 --> 00:36:51,050
+I ل location J فاحنا بدنا نبحث عن X هل هي موجودة
+
+459
+00:36:51,050 --> 00:36:57,550
+داخله ولا مش موجودة فإذا كانت AI أو A1 A2 مباشرة
+
+460
+00:36:57,550 --> 00:37:09,470
+مافيش داعي على I A0 A1 A2 to AN وبدنا نبحث عن X هذا
+
+461
+00:37:09,470 --> 00:37:11,970
+ال code اللي إحنا كتبناه قبل هيك شرحناه و كتبناه
+
+462
+00:37:11,970 --> 00:37:14,770
+أكيد إنتوا كتبينه حتى في مسائل تانية غير مسائلنا
+
+463
+00:37:14,770 --> 00:37:18,610
+اللي إحنا بدنا نكتبه بشكل recursive form بشكل
+
+464
+00:37:18,610 --> 00:37:22,490
+تكراري بشكل تكراري فحتى procedure search زي ما هي
+
+465
+00:37:22,490 --> 00:37:27,550
+هنعرف الـ a طبيعى لأن هذا ال input الأهم هو إيش الـ
+
+466
+00:37:27,550 --> 00:37:31,330
+array اللي بدك تبحث داخلها أو ال string أو الـ
+
+467
+00:37:31,330 --> 00:37:34,850
+series أو ال sequence المهم إن هو ال array اللي
+
+468
+00:37:34,850 --> 00:37:38,130
+بتاخدوها في الـ .. في إيش؟ في البرمجة سموها array و
+
+469
+00:37:38,130 --> 00:37:43,750
+خلاص array A وهذه بتبدأ من I to J طبعا في البداية
+
+470
+00:37:43,750 --> 00:37:48,670
+بتبدأ I بـ 0 عادة و J بـ N صحيح هذه كبداية initially
+
+471
+00:37:48,670 --> 00:37:51,470
+بس إحنا بنحطها in general لإنه أنا عارف إنه ممكن
+
+472
+00:37:51,470 --> 00:37:56,730
+لقدام أفتح نفس ال code كمان مرة بـ I مختلفة فعشان
+
+473
+00:37:56,730 --> 00:38:00,210
+هيك بنعرفها in general I و J هدول عبارة عن
+
+474
+00:38:00,210 --> 00:38:03,610
+integers لإنه locations بينفعش مايكونوش integers
+
+475
+00:38:03,610 --> 00:38:08,150
+أصلا كويس X هي ال term اللي أنا ببحث عنه أو القيمة
+
+476
+00:38:08,150 --> 00:38:12,250
+اللي ببحث عنها و ليست I أو J أو ما بينهما لأ هي
+
+477
+00:38:12,250 --> 00:38:21,930
+القيمة نفسها فهي قيمة ال AI من I لـ J القيمة نفسها
+
+478
+00:38:21,930 --> 00:38:27,150
+تمام هنبدأ إذا كانت والله الـ A I لأن هانبدأ من
+
+479
+00:38:27,150 --> 00:38:32,570
+بداية ال sequence بتاعي بدأت من بداية ال R إذا كانت
+
+480
+00:38:32,570 --> 00:38:37,960
+A I نفسها بتساوي X خير وبركة ارجع لـ mean بـ I فرجعنا بـ
+
+481
+00:38:37,960 --> 00:38:41,400
+I فعليا I مش هي قيمة X كلكم عارفين هذا الكلام
+
+482
+00:38:41,400 --> 00:38:44,160
+بقوله ال index بتاعة X أن X اللي بتدور عليها
+
+483
+00:38:44,160 --> 00:38:48,260
+موجودة في المكان الفلاني بس أنا ماقلتلهش قلتله بس
+
+484
+00:38:48,260 --> 00:38:52,920
+مكانها هنا بدك تروح خدها خدها طبعا أكيد هذه حالة
+
+485
+00:38:52,920 --> 00:38:56,740
+ال best case أن ألاجيها مباشرة لكن فعليا بيصيرش هيك
+
+486
+00:38:56,740 --> 00:39:02,700
+فإيش بيعمل بيسوي إذا كانت I تساوي J بمعنى عملنا
+
+487
+00:39:02,700 --> 00:39:05,160
+وضلنا نعمل عملية recursion step recursion step
+
+488
+00:39:05,160 --> 00:39:06,740
+recursion step recursion step recursion step
+
+489
+00:39:06,740 --> 00:39:07,680
+recursion step recursion step recursion step
+
+490
+00:39:07,680 --> 00:39:08,320
+recursion step recursion step recursion step
+
+491
+00:39:08,320 --> 00:39:08,480
+recursion step recursion step recursion step
+
+492
+00:39:08,480 --> 00:39:08,580
+recursion step recursion step recursion step
+
+493
+00:39:08,580 --> 00:39:08,600
+recursion step recursion step recursion step
+
+494
+00:39:08,600 --> 00:39:08,640
+recursion step recursion step recursion step
+
+495
+00:39:08,640 --> 00:39:09,060
+recursion step recursion step recursion step
+
+496
+00:39:09,060 --> 00:39:11,540
+recursion step recursion step recursion step
+
+497
+00:39:11,540 --> 00:39:15,020
+recursion step recursion step recursion step
+
+498
+00:39:15,020 --> 00:39:16,180
+recursion step recursion step recursion step
+
+499
+00:39:16,180 --> 00:39:23,740
+recursion step recursion step
+
+500
+00:39:23,740 --> 00:39:28,730
+step بمعنى أن أنا ما لاقيتهاش عند I و I ما زالت بعيدة
+
+501
+00:39:28,730 --> 00:39:33,470
+عن ال J بيجي للخيار الثالث اللي هو return  بنسيرش
+
+502
+00:39:33,470 --> 00:39:37,810
+كمان مرة بس يبدأ لي من I زائد واحد الباقي زي ما هو
+
+503
+00:39:37,810 --> 00:39:42,510
+J زي ما هي X كما هي نفس العنصر اللي ببحث عنه زائد
+
+504
+00:39:42,510 --> 00:39:46,340
+واحد كنت في ال element الأول لأ مش هو ال element
+
+505
+00:39:46,340 --> 00:39:48,860
+الأول خلاص ابدء من ال element الثاني ابدا من
+
+506
+00:39:48,860 --> 00:39:52,120
+الثالث ابدا من الرابع ابدا من الخامس and so on
+
+507
+00:39:52,120 --> 00:39:55,400
+طبعا هذه واحدة من ال techniques مثلا في ال linear
+
+508
+00:39:55,400 --> 00:39:59,480
+اللي غير مجدي استخدم فيها ال recursion لأن حصل
+
+509
+00:39:59,480 --> 00:40:04,080
+linear هي كانت linear وضلت linear بس غلبت حالي في
+
+510
+00:40:04,080 --> 00:40:09,600
+ال space يعني أنا فعلا صارت عندي سيئة الأمور أني
+
+511
+00:40:09,600 --> 00:40:15,100
+ماحسنتش في ال time و ال space زودتها بدل ما كنت
+
+512
+00:40:15,100 --> 00:40:17,960
+بشتغل في نفس ال space بتاعة برنامج واحد اضطريت افتح
+
+513
+00:40:17,960 --> 00:40:22,380
+كذا code لنفس البرنامج كذا مرة لنفس ال code هذا
+
+514
+00:40:22,380 --> 00:40:26,560
+معناه أن أنا زودت space ما كانش لها أي لازمة و
+
+515
+00:40:26,560 --> 00:40:31,680
+ماحسنتش في ال time linear ضلت linear لاحظ أنت إيش
+
+516
+00:40:31,680 --> 00:40:36,830
+بتغير كنت I بدأت بـ I بعدين رحت لـ I زائد واحد طب
+
+517
+00:40:36,830 --> 00:40:39,690
+اللي بعد I زائد اثنين I زائد ثلاثة طب إحنا كنا في
+
+518
+00:40:39,690 --> 00:40:43,470
+الأول كنا نعمل for loop نبدأ من I لـ J وكنت
+
+519
+00:40:43,470 --> 00:40:47,510
+برو ح واحد I ثم I زائد واحد ثم I زائد اثنين ثم
+
+520
+00:40:47,510 --> 00:40:50,350
+I زائد ثلاثة يعني فعليا ك time ما تغيرش عن دي
+
+521
+00:40:50,350 --> 00:40:54,770
+فتاخدوا بالكم كويس أن اجانا هذا المثل أنه مش
+
+522
+00:40:54,770 --> 00:40:58,220
+دائما ال recursion كويس مش ده من التعليم كويس
+
+523
+00:40:58,220 --> 00:41:01,900
+عشانك أنت مبرمج human programmer أنت بدك في الآخر
+
+524
+00:41:01,900 --> 00:41:05,560
+أنت مالك الموضوع أنت لابد لك أن تقرر أه هذا مناسب ولا
+
+525
+00:41:05,560 --> 00:41:09,740
+مش مناسب صحيح ال computer و داخل علينا و صار في
+
+526
+00:41:09,740 --> 00:41:13,480
+علم اصطناعي و AI و مش عارف و علم طويل عريض و
+
+527
+00:41:13,480 --> 00:41:16,240
+بيحسب حسابات معقدة أكثر منا بس في النهاية مازلت
+
+528
+00:41:16,240 --> 00:41:22,460
+أنت المالك مازلت أنت مالك الحسابات كويس؟ بدك تقدر
+
+529
+00:41:22,460 --> 00:41:28,370
+هذا أحسن ولا مش أحسن؟ الـ binary الـ binary search
+
+530
+00:41:28,370 --> 00:41:31,190
+برضه من الحاجات اللي أخذناها الـ binary search كيف
+
+531
+00:41:31,190 --> 00:41:34,810
+ممكن أحولها أو أكتبها بشكل recursive code فـ
+
+532
+00:41:34,810 --> 00:41:41,150
+recursive code هنبدأ الـ binary و الـ A زي ما هي X
+
+533
+00:41:41,150 --> 00:41:45,430
+العنصر اللي ببحث عنه و from I to J و زي ما قلنا الـ
+
+534
+00:41:45,430 --> 00:41:47,250
+initial يبدأ من 0 to N
+
+535
+00:41:50,930 --> 00:41:54,650
+و أول شغلة كنا بنعملها بنحسب ال midpoint صحيح الـ
+
+536
+00:41:54,650 --> 00:41:59,170
+midpoint أو النقطة الوسيطية داخل ال array في نص الـ
+
+537
+00:41:59,170 --> 00:42:03,770
+array و بناخد لها floor و بعدين بنبدأ نفحصها هل الـ
+
+538
+00:42:03,770 --> 00:42:07,070
+X تساويها؟ والله خير و بركة بنرجع بقيمتها و خلصنا
+
+539
+00:42:08,480 --> 00:42:11,880
+هذا ال best case أن والله من أول مرة ألاقيها
+
+540
+00:42:11,880 --> 00:42:16,680
+خلصنا طيب أما إذا ما زبطتش بنروح بنبدأ نفحص هل X
+
+541
+00:42:16,680 --> 00:42:20,780
+أقل من العنصر اللي موجود في ال midpoint وطبعا كلنا
+
+542
+00:42:20,780 --> 00:42:24,220
+عارفين أن ال binary search هذه ما بتضبطش إلا إذا كان
+
+543
+00:42:24,220 --> 00:42:30,640
+عندي sorted ال array بتاعتي هي sorted ومن الأقل
+
+544
+00:42:30,640 --> 00:42:38,460
+للأعلى تصاعدي يعني increasing order فإذا X أقل من A
+
+545
+00:42:38,460 --> 00:42:44,100
+معناته إذا أقل من A كل ما هو أكبر من ال M  لا يهمني
+
+546
+00:42:44,100 --> 00:42:48,900
+فأجل ال J صحيح ببقى بنقلل ال J بنقلل ال J وإحنا
+
+547
+00:42:48,900 --> 00:42:56,020
+هنا ما نقولش أو يساوي صحيح
+
+548
+00:42:56,020 --> 00:43:00,680
+معنى ذلك إيش أني ببدء بروحش بحط ال J تساوي ال M
+
+549
+00:43:00,680 --> 00:43:09,170
+نفسها ناقص واحد لاحظ لأنه هي أكيد strictly هي أقل
+
+550
+00:43:09,170 --> 00:43:12,150
+من ولا يمكن أن تساوي معناته خلاص مافيش داعي أفحص
+
+551
+00:43:12,150 --> 00:43:15,930
+كم مرة العنصر هذا بروح العنصر اللي جابله باختصار
+
+552
+00:43:15,930 --> 00:43:21,850
+على عنصر زي هذا كمان كويس و الآن هذا فحصنا كقيمة
+
+553
+00:43:21,850 --> 00:43:26,370
+لكن بدنا نفحص كمان أنه هل فعلا إحنا خلص ال range
+
+554
+00:43:26,370 --> 00:43:31,750
+بتاعنا ولا لسه و I ما زالت أقل من M يعني ما زال
+
+555
+00:43:31,750 --> 00:43:35,210
+في عندي مساحة أبحث فيها لأنه إذا وصلنا أن أنا
+
+556
+00:43:35,210 --> 00:43:41,590
+ماوجدتش لكن I تساوي M طب معناته أن ال midpoint هي
+
+557
+00:43:41,590 --> 00:43:45,110
+نفسها ال first ما ضلش عندك مساحة معنى ذلك
+
+558
+00:43:45,110 --> 00:43:48,610
+automatically بتقول هنا خلاص return بمين؟ بـ zero
+
+559
+00:43:48,610 --> 00:43:55,930
+ما لاقيتهاش ما وجدتش أنت وصلت لـ 0 range ومافيش عنصر خلاص
+
+560
+00:43:55,930 --> 00:44:00,550
+برجع أنه مافيش عنصر وانتهى لكن هذا الكلام إذا حدث
+
+561
+00:44:00,550 --> 00:44:04,130
+هذا الموضوع فبنرجع return هنا باش أنه ما زال في
+
+562
+00:44:04,130 --> 00:44:07,510
+عندي range أبحث فيه برجع return الـ A زي ما هي الـ
+
+563
+00:44:07,510 --> 00:44:13,110
+X زي ما هي الـ I زي ما هي الـ J M ناقص واحد الـ M M
+
+564
+00:44:13,110 --> 00:44:16,510
+ناقص واحد فالعنصر اللي قبل ال midpoint تمام
+
+565
+00:44:16,510 --> 00:44:25,010
+ما تحققش بهذا الشكل بمعنى أنه هنا ليست أقل من هي
+
+566
+00:44:25,010 --> 00:44:29,530
+ليست أقل من فإذا X ليست أقل من A M خلاص بنسيب هذا
+
+567
+00:44:29,530 --> 00:44:33,550
+كل الكلام ما نعملهوش و بنعمل اللي بعدها else إذا كانت
+
+568
+00:44:33,550 --> 00:44:35,210
+أكبر من A M
+
+569
+00:44:39,010 --> 00:44:41,790
+بتلاحظ إحنا كل اللي عملناه ما غيرناش ال notation
+
+570
+00:44:41,790 --> 00:44:46,590
+عكسنا اللي بتاعة ال inequality عكسنا فقط الـ الـ
+
+571
+00:44:46,590 --> 00:44:50,570
+الـ symbols بتاعتنا فهنا صارت الـ AM هي اللي أقل
+
+572
+00:44:50,570 --> 00:44:57,030
+من X فـ X أكبر معناها X أكبر في الحالة هذه إذا بدي
+
+573
+00:44:57,030 --> 00:45:01,310
+أعمل elimination هعمل elimination للجزء اللي قبل M
+
+574
+00:45:01,310 --> 00:45:10,010
+و مدام لا تساوي فهنا في عندي أريحية أقول من زائد
+
+575
+00:45:10,010 --> 00:45:13,710
+واحد لأنها
+
+576
+00:45:13,710 --> 00:45:19,310
+لا تساوي فهنا اختلفت في الجزئية هذه عن ال code
+
+577
+00:45:19,310 --> 00:45:21,890
+اللي كنا كاتبينه سابقا ال code اللي كنا كاتبينه
+
+578
+00:45:21,890 --> 00:45:24,210
+سابقا إذا أنتم متذكرين و أنا شفت السؤال هذا في
+
+579
+00:45:24,210 --> 00:45:28,800
+عين بعضكم إحنا المرة اللي فاتت على أساس أن نوفر
+
+580
+00:45:28,800 --> 00:45:34,140
+على حالنا F كنا F و L و خلاص أما لأ هنا زودنا كمان
+
+581
+00:45:34,140 --> 00:45:39,320
+واحدة فخليناها لها خصوصية ثالثة اليساوي هذه أو
+
+582
+00:45:39,320 --> 00:45:44,960
+يساوي فهنا أقل من أكبر من ما ذكرناش عن اليساوي لسه
+
+583
+00:45:44,960 --> 00:45:48,620
+طيب بس بدنا نأخذ بالنا أن هذا هأحققه و أقول أنه أه
+
+584
+00:45:48,620 --> 00:45:53,820
+والله بدي أروح لـ M زائد واحد إذا كان بأضمن أنه ما
+
+585
+00:45:53,820 --> 00:45:58,790
+زال يوجد range أصلا طيب و الـ M هذه ما زالت أقل من
+
+586
+00:45:58,790 --> 00:46:04,430
+الـ J معناته أنه ما زال فيه range أقدر أبحث فيه ما
+
+587
+00:46:04,430 --> 00:46:10,250
+زال موجود هذا ال range عندي أخذنا midpoint طب مش
+
+588
+00:46:10,250 --> 00:46:15,550
+بدي أضمن أنه بعد ال midpoint بين ال midpoint و الـ
+
+589
+00:46:15,550 --> 00:46:20,370
+J ما زال في مساحة أبحث فيها هذه نفحصها بالـ
+
+590
+00:46:20,370 --> 00:46:25,610
+condition هذا أنه ما زالت M أقل من ال J يعني يوجد
+
+591
+00:46:25,610 --> 00:46:30,090
+مسافة بين ال midpoint ونهاية ال array مازال يوجد
+
+592
+00:46:30,090 --> 00:46:35,350
+مسافة المسافة هذه نبحث عنها مدام موجودة على طول
+
+593
+00:46:35,350 --> 00:46:38,390
+بنقول إيش الـ binary بتاعي binary إيش بنرجع نفتح الـ
+
+594
+00:46:38,390 --> 00:46:42,670
+code كمان مرة ولكن بأرقام مختلفة لمين؟ لـ I لـ I
+
+595
+00:46:42,670 --> 00:46:49,710
+فبتصير A X I هتتغير M زائد واحد افهمنا ليش زائد
+
+596
+00:46:49,710 --> 00:46:53,610
+واحد المرة الماضية ما كناش كاتبين زائد واحد لأن كانت
+
+597
+00:46:53,610 --> 00:46:57,470
+else و ال else على طول معناها النفي لـ ال condition
+
+598
+00:46:57,470 --> 00:47:00,110
+اللي أنت حاطه هنا فمدام كانت أقل من معناته نفيها
+
+599
+00:47:00,110 --> 00:47:04,590
+كان أكبر من أو يساوي لأ هنا أنا ما قلتش else و
+
+600
+00:47:04,590 --> 00:47:08,990
+سكتت أنا كتبت لها condition خاص فيها و كتبت أكبر من
+
+601
+00:47:08,990 --> 00:47:14,370
+أكبر منه ما قلتش أو يساوي فأنا عندي حرية أقول زائد
+
+602
+00:47:14,370 --> 00:47:19,090
+واحد هنا لأنه ضامن أنها لن تتساوي بدليل كان
+
+603
+00:47:19,090 --> 00:47:23,690
+ما تتحققش أصلا شرط هذا طيب else إذا كان فعلا و الله
+
+604
+00:47:23,690 --> 00:47:29,890
+لا هذا تحقق ولا هذا تحقق لاحظ أن أنت شرط اثنين
+
+605
+00:47:29,890 --> 00:47:34,590
+ثلاثة الثلاثة احتمالات الممكن أن أنت حققتها فعليا
+
+606
+00:47:34,590 --> 00:47:46,200
+يساوي هذا ليساوي و هي أقل من و هي أكبر من إيش خلصت
+
+607
+00:47:46,200 --> 00:47:53,140
+فأنت ما خلطتش لل code أي احتمال آخر إلا احتمال أنه
+
+608
+00:47:53,140 --> 00:47:59,900
+لم تتحقق واحدة من ال answers هدول مش هيك لو واحدة
+
+609
+00:47:59,900 --> 00:48:05,240
+منهم false معناته أن I تساوي ال M أو ال M تساوي الـ
+
+610
+00:48:05,240 --> 00:48:09,100
+J في الحالة هذه خلاص ما ضلش عندك range أصلا تبحث
+
+611
+00:48:09,100 --> 00:48:13,290
+فيه أنت ما ضلش عندك range تبحث فيه فعلى طول برجع لنا
+
+612
+00:48:13,290 --> 00:48:18,650
+بإيش؟ بـ zero ما لاقيتهاش خلصت ال range صغر لدرجة أن الـ
+
+613
+00:48:18,650 --> 00:48:21,970
+input و ال output واحد أعفوا أن البداية و النهاية
+
+614
+00:48:21,970 --> 00:48:26,910
+واحدة مافيش عنصر أدور عنه فلأ خلاص رجعنا أن
+
+615
+00:48:26,910 --> 00:48:31,250
+ما لاقيتهاش لأنه فعليا أنت ما لاقيتش عنصر ما ضلش عندك عنصر
+
+616
+00:48:31,250 --> 00:48:33,350
+تمام
+
+617
+00:48:34,780 --> 00:48:37,900
+هيك بنكون أخذنا مجموعة أمثلة برض
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..01958dd441aa491922d84755b0d3a6797e197ee3
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30_postprocess.srt
@@ -0,0 +1,2496 @@
+1
+00:00:05,030 --> 00:00:07,790
+يعطيكوا العفو شباب، بارك الله فيكوا، اليوم نبدأ ان
+
+2
+00:00:07,790 --> 00:00:10,530
+شاء الله تعالى مع موضوع ال recursion بعد ما المرة
+
+3
+00:00:10,530 --> 00:00:13,430
+الماضية كنا أخدنا ال induction أو ال inductive
+
+4
+00:00:13,430 --> 00:00:16,050
+step بعد ما شوفنا ال business step و ال inductive
+
+5
+00:00:16,050 --> 00:00:21,890
+step و أخدنا عملية proving باستخدام ال inductive
+
+6
+00:00:21,890 --> 00:00:26,090
+stepمن ال inductive step ممكن تتدرج الأمور معانا
+
+7
+00:00:26,090 --> 00:00:28,990
+بحيث أن أحنا نروح لجزئية ال recursion أو ال
+
+8
+00:00:28,990 --> 00:00:33,370
+recursive codes بعديك الأكواد التكرارية و اللي قشت
+
+9
+00:00:33,370 --> 00:00:37,050
+بالأساس أساسا من عملية ال induction اللي أخدناها
+
+10
+00:00:37,050 --> 00:00:42,230
+المرة الماضية بحيث أن ال recursion هو بكل بساطة هو
+
+11
+00:00:42,230 --> 00:00:48,770
+general term لعملية تعريف ال object من نفسه تعريف
+
+12
+00:00:48,770 --> 00:00:53,490
+ال object من نفسه ولكن بنعرفه في هذا الزمن كأنه
+
+13
+00:00:53,490 --> 00:00:59,370
+function في نفسه في الزمن السابق أو في الحالة اللي
+
+14
+00:00:59,370 --> 00:01:01,930
+كانت قبله في الحالة اللي كانت قبله زي لما أقول أن
+
+15
+00:01:01,930 --> 00:01:05,950
+ال f of n هي function في f of n ناقص واحد طب f of
+
+16
+00:01:05,950 --> 00:01:10,100
+n ناقص واحد هي function في f of nنقص اتنين و هكذا
+
+17
+00:01:10,100 --> 00:01:16,180
+فإذا بيعرف من نفسه ببساطة جدا هذا ممكن نقول تعريف
+
+18
+00:01:16,180 --> 00:01:21,660
+recursion بشكل مختصر طيب زي إنه نقول P of N plus
+
+19
+00:01:21,660 --> 00:01:26,720
+واحد recursively in terms of P of N فهي معرفة
+
+20
+00:01:26,720 --> 00:01:30,880
+باللي قبلها معرفة بمين باللي قبلهاطبعا هذا
+
+21
+00:01:30,880 --> 00:01:34,480
+بنستخدمه ك recursive algorithms وهذه أهم شغله
+
+22
+00:01:34,480 --> 00:01:37,980
+ويمكن هي النقطة الأهم بالنسبالكم كمبرمجين أنكوا
+
+23
+00:01:37,980 --> 00:01:42,820
+تروحوا لجزئية ال algorithms بشكل recursively ممكن
+
+24
+00:01:42,820 --> 00:01:46,780
+تتكرر من نفسها بمعنى أن الكود يكرر نفسه وحناخد
+
+25
+00:01:46,780 --> 00:01:49,880
+أمثلة على بعض الأكواد خلال محاضرتنا ان شاء الله
+
+26
+00:01:49,880 --> 00:01:54,010
+تعالىطيب ال recursive definitions ال recursive
+
+27
+00:01:54,010 --> 00:01:57,150
+functions ال recursive sequences اللي هو ال
+
+28
+00:01:57,150 --> 00:01:59,570
+sequence نفسه كمان ممكن يكون recursive من نفسه
+
+29
+00:01:59,570 --> 00:02:03,730
+كويس and sets و ال sets كمان حتى ال set نفسها ممكن
+
+30
+00:02:03,730 --> 00:02:07,930
+تعرف من نفسها و برضه هناخدلها مثال هناخدلها مثال
+
+31
+00:02:07,930 --> 00:02:11,050
+فمعظمهم هدولة هنتكلم عنهم أثناء المحاضرة كأمثلة
+
+32
+00:02:11,050 --> 00:02:18,380
+واضحة لهم نبدأ مثلا ك functionrecursive للـ
+
+33
+00:02:18,380 --> 00:02:22,020
+function بكل بساطة بنقدر نقول أنه أبسط طريقة أني
+
+34
+00:02:22,020 --> 00:02:26,680
+أقول الله one way to define a function أقول if
+
+35
+00:02:26,680 --> 00:02:32,720
+from natural number to set ال natural number هادي
+
+36
+00:02:32,720 --> 00:02:38,300
+by default اللي هي إيش ال indexال index فعشان هيك
+
+37
+00:02:38,300 --> 00:02:40,660
+بنقول natural number ممكن ال index يبدأ معاك من
+
+38
+00:02:40,660 --> 00:02:47,340
+صفر نشيك a0 a1 a2 a3 and so on بتكمل طيب ال a
+
+39
+00:02:47,340 --> 00:02:53,040
+نفسها a1 و a2 و a3 و a4 و a5 هي العناصر تاعت ال
+
+40
+00:02:53,040 --> 00:02:56,660
+set فانت بتقول ال set عندنا في الحالة هذه هي
+
+41
+00:02:56,660 --> 00:03:00,480
+العناصر زي لما نقول عندنا الآن مجموعة الطلاب هدولة
+
+42
+00:03:00,480 --> 00:03:04,470
+هم ال setOkay هذه المجموعة خلاص تمام لما أجي بدي
+
+43
+00:03:04,470 --> 00:03:08,490
+أعرفهم أو أقيمهم أو بدي أجي أصنفهم بيصير الآن
+
+44
+00:03:08,490 --> 00:03:13,410
+التصنيف حسب إيش بمعنى مين اللي هياخد ال a 0 بدي
+
+45
+00:03:13,410 --> 00:03:17,090
+أفترض مش على الدرجة اللي بدي أفترض على الترتيب
+
+46
+00:03:17,090 --> 00:03:22,130
+الأبجد مثلا مش هيك معناته هنا بدي أقول مين ال a
+
+47
+00:03:22,130 --> 00:03:27,740
+node أو ال a صفرهو عنصر من عناصر الست أكيد فهو
+
+48
+00:03:27,740 --> 00:03:32,360
+ينتمي للست صحيح لكن بدنا نشوف مين اللي يحتل هذا
+
+49
+00:03:32,360 --> 00:03:37,470
+المكان حسبSorting معينة حسب ال sort اللي انا بدي
+
+50
+00:03:37,470 --> 00:03:40,830
+اتكلم عنه لو افترضنا ان هي بالارقام الجامعية او
+
+51
+00:03:40,830 --> 00:03:45,330
+بال .. بالأحرف الأبجادية او حسب ال grade حسب ..
+
+52
+00:03:45,330 --> 00:03:49,870
+فيها تصنيفات كتير .. فيها تصنيفات كتير فهنا هقول
+
+53
+00:03:49,870 --> 00:03:53,530
+في الحالة هذه من natural number to S اللي هي ال
+
+54
+00:03:53,530 --> 00:03:59,830
+set فإذا for any set S او بشكل series ممكن نقول A
+
+55
+00:03:59,830 --> 00:04:06,250
+N هي هال Nfrom N to F of N F of N مين هذا يطلع في
+
+56
+00:04:06,250 --> 00:04:12,300
+الآخر عنصر من الست فإذا من ال domainمن الـ
+
+57
+00:04:12,300 --> 00:04:17,000
+codomain ما هي domain to codomain صح؟ فده هي فإذا
+
+58
+00:04:17,000 --> 00:04:20,720
+تعريفها as a function بنقول الآن كالتالي عشان
+
+59
+00:04:20,720 --> 00:04:24,620
+نعرفها بشكل recursively بشكل recursively هقول بدنا
+
+60
+00:04:24,620 --> 00:04:29,180
+نعرف أول عنصر f of zero رجعنا لنفس ال induction
+
+61
+00:04:29,180 --> 00:04:33,900
+رجعنا لنفس ال induction طيب أما if أكبر من صفر
+
+62
+00:04:33,900 --> 00:04:41,000
+فبتعرف if of n in terms of if zero to n ناقص واحد
+
+63
+00:04:41,740 --> 00:04:48,340
+من F of 0 ل F of N ناقص واحد بمعنى تعرف بالعناصر
+
+64
+00:04:48,340 --> 00:04:53,440
+السابقة لها فكل عنصر يعرف بالعناصر بالعناصر
+
+65
+00:04:53,440 --> 00:04:57,520
+السابقة لل function بيصير اسمها recursively طيب
+
+66
+00:04:57,520 --> 00:05:02,040
+مثال لو قولنا A N تساوي او equivalent ل 2 to the
+
+67
+00:05:02,040 --> 00:05:07,560
+power N فهذا recursively كأني بقول A nodeابدأ بال
+
+68
+00:05:07,560 --> 00:05:10,480
+natural number حسب التعريف natural number من النار
+
+69
+00:05:10,480 --> 00:05:14,940
+بتبدا بصفر فإذا a note بتساوي واحد أكبر من هيك ايش
+
+70
+00:05:14,940 --> 00:05:22,970
+بتساوي بتساوي a ان ناقص واحد في اتنينالسابقة في
+
+71
+00:05:22,970 --> 00:05:25,450
+اتنين فأصبحت فعلا كأنها function في العنصر اللي
+
+72
+00:05:25,450 --> 00:05:28,710
+جابلها طب العنصر اللي جابلها برضه اتنين من العنصر
+
+73
+00:05:28,710 --> 00:05:32,690
+اللي جابله من N ناقص اتنين N ناقص اتنين هي اتنين
+
+74
+00:05:32,690 --> 00:05:35,790
+في العنصر اللي جابله N ناقص تلاتة and so on فإذا
+
+75
+00:05:35,790 --> 00:05:39,130
+لاحظوا أن هذه function بكل بساطة بنقدر نحطها بشكل
+
+76
+00:05:39,130 --> 00:05:44,090
+تكراري شكل تكراري أن كل عنصر نقدر نحسبه من العنصر
+
+77
+00:05:44,090 --> 00:05:48,490
+اللي جابله من العنصر اللي جابله مثال على ذلك نحله
+
+78
+00:05:48,490 --> 00:05:52,590
+مع بعض مثلا هذا مثال من الأمثلةوهنفترض إن أنا فعلا
+
+79
+00:05:52,590 --> 00:05:56,070
+بتعامل مع function f of n لكل العناصر n belonging
+
+80
+00:05:56,070 --> 00:06:01,770
+to natural number recursively ال f of 0 بتساوي 3
+
+81
+00:06:01,770 --> 00:06:07,470
+طيب ال inductive step كمعادلة بقدر أقول إن ال f of
+
+82
+00:06:07,470 --> 00:06:12,830
+n زائد 1 بتساوي 2 f of n زائد 3 فإذن بكل بساطة
+
+83
+00:06:12,830 --> 00:06:19,170
+بقدر أقول إن ال f 1 بتساوي كدهش؟
+
+84
+00:06:20,510 --> 00:06:24,510
+أيوة اللي هو جداش هي عندك كله تسعة هذه على طول
+
+85
+00:06:24,510 --> 00:06:30,090
+مباشرة نحل هي تسعة اتنين تمانتاش زي التلاتة واحد
+
+86
+00:06:30,090 --> 00:06:32,510
+وعشرين وواحد وعشرين في اتنين اتنين واربعين زي
+
+87
+00:06:32,510 --> 00:06:35,390
+التلاتة خمسة واربعين خمسة واربعين في اتنين تسعين
+
+88
+00:06:35,390 --> 00:06:40,030
+تسعين زي التلاتة تلاتة وتسعين and so on so on لاحظ
+
+89
+00:06:40,030 --> 00:06:44,330
+فإذا كل عنصر بجيبه من اللي جابله فانت لاحظ كل عنصر
+
+90
+00:06:44,330 --> 00:06:48,400
+واحنا بنحسبه ذكرنا العنصر اللي جابلهفإذا هذه
+
+91
+00:06:48,400 --> 00:06:55,040
+recursive form واضح جدا تمام recursive definition
+
+92
+00:06:55,040 --> 00:06:58,700
+لها factorial مثلا هاي واحدة من ال functions اللي
+
+93
+00:06:58,700 --> 00:07:04,320
+ممكن برضه نعرفها بشكل recursively أو recursive
+
+94
+00:07:04,320 --> 00:07:08,220
+form بكل بساطة كلنا عارفين ال F of N ال N
+
+95
+00:07:08,220 --> 00:07:11,960
+factorial هي عبارة عن multiplication لكل العناصر
+
+96
+00:07:11,960 --> 00:07:17,820
+من 1 ل Nواحد في اتنين في تلاتة في اربعة في N فكأني
+
+97
+00:07:17,820 --> 00:07:21,460
+بقول N factorial كأني بقول N factorial فإذا ال
+
+98
+00:07:21,460 --> 00:07:24,840
+index I من واحد to N و بكل بساطة بتقدر تبدأ من
+
+99
+00:07:24,840 --> 00:07:28,940
+اتنين لإن واحد مش هيكون كتير مؤثر انت بتضرب في
+
+100
+00:07:28,940 --> 00:07:33,220
+واحد فمش هيفرق كتير فابدأ باتنين مش مشكلة لكن ال
+
+101
+00:07:33,220 --> 00:07:37,520
+case تبعتك F of Zero هتكون واحد هتكون عبارة عن
+
+102
+00:07:37,520 --> 00:07:41,780
+واحد recursively بتقدر تقول F of واحد واحد طيب F
+
+103
+00:07:41,780 --> 00:07:49,490
+of اتنينF of واحد في قيمة الاتنين طيب F of تلاتة
+
+104
+00:07:49,490 --> 00:07:55,750
+هي نفس التلاتة في F of اتنين و هكذا فلاحظ كأنها
+
+105
+00:07:55,750 --> 00:08:00,690
+معرفة بقيمة العنصر اللي قبلها فلو قلنا F of أربعة
+
+106
+00:08:00,690 --> 00:08:06,850
+هتسوي الأربعة لاحظ في قيمة ال F of تلاتة اللي هي
+
+107
+00:08:06,850 --> 00:08:14,750
+الستة و هكذافكل عنصر بيعرف باللي قبله .. كل عنصر
+
+108
+00:08:14,750 --> 00:08:20,550
+بيعرف باللي قبله فهذا طبعا بتصير أسهل لك لما بدك
+
+109
+00:08:20,550 --> 00:08:24,090
+تشتغل على ال factorial و بدك تجيبله برنامج تحسبله
+
+110
+00:08:24,090 --> 00:08:29,710
+برنامج فبتصير من نفسها .. من نفسها طيب بعض ال easy
+
+111
+00:08:29,710 --> 00:08:32,670
+examples البسيطة جدا اللي ممكن نتعامل معها لما
+
+112
+00:08:32,670 --> 00:08:38,350
+بقول a, mA في N و كلا هما واحدة natural number
+
+113
+00:08:38,350 --> 00:08:42,410
+اللي هي ال N و real number لل A اللي هي مجرد ال
+
+114
+00:08:42,410 --> 00:08:45,330
+multiplier اللي بنضرب فيه ال multiplier لما بدي
+
+115
+00:08:45,330 --> 00:08:48,930
+أعرف طبعا أن هي المتغير بالمناسبة أن هي المتغير
+
+116
+00:08:48,930 --> 00:08:51,510
+مدام natural number معناته هي ال location احنا
+
+117
+00:08:51,510 --> 00:08:54,390
+عاطينهم في ال locations هدول كل عنصر المفروض انه
+
+118
+00:08:54,390 --> 00:08:57,630
+بقيمة العنصر اللي في ال question اللي جابله تمام
+
+119
+00:08:57,630 --> 00:09:05,980
+بقدر اقول انهفي n هي تساوي a في n ناقص واحد اللي
+
+120
+00:09:05,980 --> 00:09:12,200
+هي العنصر اللي جابله زائد a فهي ال term السابق
+
+121
+00:09:12,200 --> 00:09:19,600
+هنضفله a فإذا هنا معامل ال recursive factor تبعنا
+
+122
+00:09:19,600 --> 00:09:25,560
+هي زائد a فكل عنصر هو نفس السابق مع إضافة a عليه
+
+123
+00:09:26,710 --> 00:09:34,290
+فإذا لما بقول a زائد واحد هي نفسها an زائد a لأنك
+
+124
+00:09:34,290 --> 00:09:39,170
+بدك تاخد في الحالة هذه ال a common مشترك و هتجمع
+
+125
+00:09:39,170 --> 00:09:45,210
+هنا فطلعت ال n ن ناقص واحد و هنا زائد واحد و هتجمع
+
+126
+00:09:45,210 --> 00:09:45,410
+هنا فطلعت ال n ن ناقص واحد و هنا زائد واحد و هتجمع
+
+127
+00:09:45,410 --> 00:09:45,670
+هنا فطلعت ال n ن ناقص واحد و هنا زائد واحد و هتجمع
+
+128
+00:09:45,670 --> 00:09:45,690
+هنا فطلعت ال n ن ناقص واحد و هنا زائد واحد و هتجمع
+
+129
+00:09:45,690 --> 00:09:47,570
+هنا فطلعت ال n ن ناقص واحد و هنا زائد واحد و هتجمع
+
+130
+00:09:47,570 --> 00:09:53,050
+هنا فطلعت ال n ن ناقص واحد و
+
+131
+00:09:53,220 --> 00:09:56,920
+درب a فانت كل مرة بتضرب في a كل مرة بتضرب في a
+
+132
+00:09:56,920 --> 00:10:04,360
+فمعامل التغيير او العلاقة بين a of n ك function في
+
+133
+00:10:04,360 --> 00:10:09,660
+n و a of n ناقص واحد اللي هي function في n ناقص
+
+134
+00:10:09,660 --> 00:10:14,040
+واحد الفرق بينهم هو ضرب في a بس فضربنا في a عشان
+
+135
+00:10:14,040 --> 00:10:18,000
+نحصل عليه فإذن واضحة جدا ان فعلا ال function في n
+
+136
+00:10:19,040 --> 00:10:22,260
+لاحظ؟ بقدر أجيبها بدلالة الـ function في N نقص
+
+137
+00:10:22,260 --> 00:10:26,380
+واحد اللي هي اللي جابلها .. اللي جابلها طيب ال
+
+138
+00:10:26,380 --> 00:10:29,640
+summation .. بسيطة ال summation بتتخيل صحيح؟ لما
+
+139
+00:10:29,640 --> 00:10:32,480
+أقول summation to N طب أنا عارف قيمة ال summation
+
+140
+00:10:32,480 --> 00:10:35,500
+to N نقص واحد مافيش داعي أعمل summation to N من
+
+141
+00:10:35,500 --> 00:10:39,200
+أول و جديد هي نفس ال summation ل N نقص واحد زائد
+
+142
+00:10:39,200 --> 00:10:43,180
+قيمة ال N و بس فإذا بجمع عليها قيمة N لحالها نجمع
+
+143
+00:10:43,180 --> 00:10:48,810
+قيمة N لحالها هي ال A N نفسها بسنفس الكلام ال
+
+144
+00:10:48,810 --> 00:10:54,290
+multiplication بضرب قيمة a of n فإذا إذا أنا عارف
+
+145
+00:10:54,290 --> 00:11:03,280
+لعند n ناقص واحد ل a of iهذه عرفها عرف قيمتها و
+
+146
+00:11:03,280 --> 00:11:07,720
+حسبها طب هو طالب مني ل n فإذا نفس القيمة اللي هنا
+
+147
+00:11:07,720 --> 00:11:13,020
+بضربها فقط في a n اللي هو العنصر الأخير اللي ضايل
+
+148
+00:11:13,020 --> 00:11:15,460
+و برضه هذه من الحاجات اللي احنا خدناها ك
+
+149
+00:11:15,460 --> 00:11:18,840
+manipulation لل summation لو متذكرين لما تكلمنا عن
+
+150
+00:11:18,840 --> 00:11:21,060
+ال summation حكينا في الجزء السابق طيب أشدر لإن
+
+151
+00:11:21,060 --> 00:11:24,780
+خلصنا .. لا ولا دايل لا الأخيرة ال .. ال
+
+152
+00:11:24,780 --> 00:11:32,390
+intersection لما تقول intersection لset I و ال I
+
+153
+00:11:32,390 --> 00:11:38,090
+هذه مجموعة sets from zero to N فإذا عندي N sets
+
+154
+00:11:38,090 --> 00:11:42,370
+بده أجيب التقاطع تبعهم N هذه خمسة معناته في عندي
+
+155
+00:11:42,370 --> 00:11:44,870
+خمس مجموعات بده أجيب تقاطع الخمس مجموعات مع بعض
+
+156
+00:11:44,870 --> 00:11:49,810
+طيب هذه كيف بقدر أعرفها بالسابق تبعها بقدر أقول
+
+157
+00:11:49,810 --> 00:11:54,470
+intersection كأنه أنا عند ال intersection من صفر ل
+
+158
+00:11:54,470 --> 00:12:01,950
+N ناقص واحدلـ S I صحيح؟ طب من هذا ال term بدي أجيب
+
+159
+00:12:01,950 --> 00:12:06,710
+ال intersection to
+
+160
+00:12:06,710 --> 00:12:15,610
+N ل S I فإذا هنا إيش كمان؟ تقاطع ما هي تقاطع زاد
+
+161
+00:12:15,610 --> 00:12:23,350
+إيش؟ ال N اللي ضايلة لأن الانصر الوحيد المفقود هي
+
+162
+00:12:23,350 --> 00:12:30,160
+عند ال N فإذا Sأو sit in هي اللي محتاج أضيفها
+
+163
+00:12:30,160 --> 00:12:35,960
+للتقاطع بس هي اللي محتاجين نضيفها ليش للتقاطع طبعا
+
+164
+00:12:35,960 --> 00:12:38,780
+الاتحاد نفس الشيء في الاتحاد نفس الشيء بيصير هنا
+
+165
+00:12:38,780 --> 00:12:44,870
+اتحاد مش أكتر طيب هد انتوا متذكرينها ال big arcالـ
+
+166
+00:12:44,870 --> 00:12:48,110
+Big Arc تذكرين أخدناها في آخر ما اتكلمنا عن الـ
+
+167
+00:12:48,110 --> 00:12:51,890
+Sets طيب فى Bonacci Series فى Bonacci Series برضه
+
+168
+00:12:51,890 --> 00:12:56,870
+واحدة من الأمثلة الواضحة لل Recursion ليش؟ لأن هو
+
+169
+00:12:56,870 --> 00:13:00,710
+كل عنصر في ال Series هذه هو معتمد على الإتنين اللي
+
+170
+00:13:00,710 --> 00:13:04,530
+جابله مش على واحد جابله فى Bonacci Series بكل
+
+171
+00:13:04,530 --> 00:13:10,150
+بساطة هي Series كل عنصر يساوي مجموع العنصرين اللي
+
+172
+00:13:10,150 --> 00:13:15,150
+جابلهببساطة يعني هذه هي ال series اللي بنتكلم عنها
+
+173
+00:13:15,150 --> 00:13:19,170
+فإذا إذا اتكلمنا عن عنصرين initially لازم أبدأ
+
+174
+00:13:19,170 --> 00:13:24,750
+فيهم معناته ال basis step هي مش قيمة واحدة لازم
+
+175
+00:13:24,750 --> 00:13:28,710
+يكونوا قيمتين عشان أقدر أكمل بادي ال series مدام
+
+176
+00:13:28,710 --> 00:13:32,190
+أنا بقول كل عنصر مجموع الإتنين اللي جابله معناته
+
+177
+00:13:32,190 --> 00:13:36,550
+محتاج اتنين في البداية كبداية محتاج اتنين فكبداية
+
+178
+00:13:36,550 --> 00:13:42,400
+هي صفر واحدخلاص هدول الوحيدين اللي بنعرفهم في
+
+179
+00:13:42,400 --> 00:13:45,240
+البداية و الباقي خلاص بيجي منهم الباقي كله بيجي
+
+180
+00:13:45,240 --> 00:13:53,380
+منهم ف 0 1 هدول ال initial او ال basis step اجمعهم
+
+181
+00:13:53,380 --> 00:13:59,350
+بطلع واحد طيب صار عندي واحد واحدأتنين طيب صار عند
+
+182
+00:13:59,350 --> 00:14:04,550
+اتنين و واحد تلاتة اتنين و تلاتة خمسة خمسة و تلاتة
+
+183
+00:14:04,550 --> 00:14:08,770
+تمانية خمسة و تمانية تلتاش تلتاش و تمانية واحد و
+
+184
+00:14:08,770 --> 00:14:13,810
+عشرين واحد و عشرين و تلتاش واستمر تستمر فالفبناتش
+
+185
+00:14:13,810 --> 00:14:20,070
+بتظل ماشية مستمرة تمام فإذا بتبدأ بصفر واحد و
+
+186
+00:14:20,070 --> 00:14:23,990
+بعدين تكتب المعادلة خلاص أما صفر واحد لابد تبدأ
+
+187
+00:14:23,990 --> 00:14:28,470
+فيهملو واحد منهم مش موجود مش هتقدر تكمل لإن كل
+
+188
+00:14:28,470 --> 00:14:33,910
+عنصر هيه كل عنصر f of n بشرط إنه n أكبر أو تساوي 2
+
+189
+00:14:33,910 --> 00:14:38,130
+هيكون عبارة عن f of n ناقص 1 زائد f of n ناقص 2
+
+190
+00:14:38,130 --> 00:14:41,570
+العنصرين اللي جابله عنصرين اللي جابله فهذه واضحة
+
+191
+00:14:41,570 --> 00:14:46,990
+جدا إن هي بتعتمد على ال recursive theory تماما
+
+192
+00:14:46,990 --> 00:14:52,830
+واضحةطيب بدنا من خلالها من خلال ال series هذه نثبت
+
+193
+00:14:52,830 --> 00:14:58,410
+إثبات إنه بالنسبة لفبناتش series دائما f of n أقل
+
+194
+00:14:58,410 --> 00:15:05,610
+من 2 to the power n بالإيش بال inductive step أو
+
+195
+00:15:05,610 --> 00:15:12,750
+induction proof بكل بساطة عندي basis case أو ال
+
+196
+00:15:12,750 --> 00:15:20,600
+basis step و لازم يكونوا 2 فإذا ببدأنوت تسوى صفر
+
+197
+00:15:20,600 --> 00:15:24,540
+هل الصفر فعلا أقل من اتنين to the power صفر حسب
+
+198
+00:15:24,540 --> 00:15:30,660
+التعريف مظبوط طيب واحد F واحد معناته ما وجدتش
+
+199
+00:15:30,660 --> 00:15:33,540
+قيمتها F واحد واحد لإن هاي الأول answer in صفر
+
+200
+00:15:33,540 --> 00:15:36,420
+واحد هل الواحد أقل من اتنين to the power واحد
+
+201
+00:15:36,420 --> 00:15:41,320
+مظبوط أقل منه طيب بعد ذلك بنروح لمين لل inductive
+
+202
+00:15:41,320 --> 00:15:44,220
+step وال inductive step كلنا عارفين يريدوني أفترض
+
+203
+00:15:44,220 --> 00:15:52,580
+أنه هنا مسمينا F F of N is trueوبال direct proof
+
+204
+00:15:52,580 --> 00:15:59,040
+بدنا نثبت منها ان f of n زائد واحد is true ولا لأ
+
+205
+00:15:59,040 --> 00:16:07,160
+فإذا هفترض فعلا ان f of n is true ايش يعني is
+
+206
+00:16:07,160 --> 00:16:13,720
+true؟معناه ان هي تحقق هذه ال rule اللي هم
+
+207
+00:16:17,270 --> 00:16:19,990
+صحيح، بدأ تعتمد على الإتنين في الحالة هذه، مظبوط،
+
+208
+00:16:19,990 --> 00:16:23,410
+ففي الحالة هذه، بدنا نفرض إنه إذا كانت فعلاً F of
+
+209
+00:16:23,410 --> 00:16:26,730
+N بس طبعاً recursively، إحنا عارفين إنه N هنا لن
+
+210
+00:16:26,730 --> 00:16:31,930
+تبدأ إلا من بعد الإتنينواضحت؟ فالشرطين اللي بتحكي
+
+211
+00:16:31,930 --> 00:16:35,530
+عنهم هدولة احنا غطيناهم في ال business step بعد
+
+212
+00:16:35,530 --> 00:16:39,030
+هيك لأ خلاص مادام ال business step تحققت بعد هيك
+
+213
+00:16:39,030 --> 00:16:43,150
+بنشتغل على انت يعني اللي انت قلته هو فتحلنا موضوع
+
+214
+00:16:43,150 --> 00:16:47,990
+مهم ان احنا هنشتغل على ال first principle هنشتغل
+
+215
+00:16:47,990 --> 00:16:53,470
+على ال second principle بمعنى بدنا نثبت ان if
+
+216
+00:16:57,090 --> 00:17:04,450
+و خلّينا نسميها K مثلا is true بشرط انه K from
+
+217
+00:17:04,450 --> 00:17:11,440
+اتنين اتنين المفروض صحيح من اتنين لقيمة Nis it
+
+218
+00:17:11,440 --> 00:17:15,260
+true فهذه ال strong proof strong اه ال strong
+
+219
+00:17:15,260 --> 00:17:18,260
+proof سميناها اللي هو ال second principle آخر جزء
+
+220
+00:17:18,260 --> 00:17:22,360
+أخدناه المرة الماضية صحيح كويس انت نبحتنا عشان
+
+221
+00:17:22,360 --> 00:17:28,140
+الكل ينتبه فيها تمام منها بدنا نثبت ان n زائد واحد
+
+222
+00:17:28,140 --> 00:17:33,240
+برضه is it true برضه ايش is it true جيد فإذن بكل
+
+223
+00:17:33,240 --> 00:17:39,920
+بساطة بقدرقول ان if n تساوي if n ناقص واحد زائد
+
+224
+00:17:40,860 --> 00:17:47,800
+ناقص اتنين هذه اكيد صحيح طيب بكل بساطة بتقدر تقول
+
+225
+00:17:47,800 --> 00:17:53,380
+هذه صحيحة مش shake احنا قلنا بدنا نقول ان هذه is
+
+226
+00:17:53,380 --> 00:17:59,640
+true فإذا لازم تكون اكبر من اتنين
+
+227
+00:17:59,640 --> 00:18:07,160
+to the power ناقص واحد to اتنين if ناقص اتنين
+
+228
+00:18:11,040 --> 00:18:16,480
+صحيح؟ ليش؟ لأنه ببساطة هذه برضه is true حسب ال K
+
+229
+00:18:16,480 --> 00:18:21,560
+اللي هي من 2 to N طب ما هذه في نفس ال range فإذا
+
+230
+00:18:21,560 --> 00:18:25,780
+أنا true ال true يعني بقدر أستعيد عنها ب2 to the
+
+231
+00:18:25,780 --> 00:18:33,740
+power n ناقص 1 حسب ال theorem إن هي true و نفس
+
+232
+00:18:33,740 --> 00:18:38,660
+الكلامإن ناقص اتنين بقدر برضه أستعيد عنها بتنين إن
+
+233
+00:18:38,660 --> 00:18:41,240
+ناقص اتنين اتنين to the power إن ناقص اتنين
+
+234
+00:18:41,240 --> 00:18:47,980
+فحطناهم ممتاز الآن التنتين هدولة بكل بساطة بتقدر
+
+235
+00:18:47,980 --> 00:18:53,160
+اللي هنتغيرهم بحيث إنك تقول هذا ال term هيكون أكيد
+
+236
+00:18:53,160 --> 00:19:01,440
+أقل من اتنين to the power إن ناقص واحد صح أكيد ليش
+
+237
+00:19:01,440 --> 00:19:07,470
+لأن كلنا عارفين فبناتشة تسعوديةيعني كل عنصر أكيد
+
+238
+00:19:07,470 --> 00:19:12,410
+أكبر من اللي جابله أكيد أكبر من اللي جابله معناه
+
+239
+00:19:12,410 --> 00:19:15,950
+ذلك إذا كان استعبنا عن هذا ال term بتنين to the
+
+240
+00:19:15,950 --> 00:19:22,190
+power n ناقص واحد هل هتتغير اتجاه الأكبر من .. لأ
+
+241
+00:19:22,190 --> 00:19:26,470
+مش هيتغير فحتبال دايما if of n أقل من هذا ال term
+
+242
+00:19:26,470 --> 00:19:32,030
+بالعكس حتى هتقل بزيادة كمان فهنا تصبح اتنين if
+
+243
+00:19:32,030 --> 00:19:36,930
+ناقص واحدلأ F of N اجمع الاتنين مع بعض كأنك أخدت
+
+244
+00:19:36,930 --> 00:19:42,830
+اتنين عامل مشترك فبتصير كأنه اتنين مضروبة في هذا
+
+245
+00:19:42,830 --> 00:19:46,550
+ال term اجمع فوق فبتصبح اقل من اتنين to the power
+
+246
+00:19:46,550 --> 00:19:46,810
+N
+
+247
+00:19:53,450 --> 00:19:57,770
+نحظت كيف ف if of n اللي انا بدي اثبتها بمعلومة
+
+248
+00:19:57,770 --> 00:20:01,730
+اللي جابلها على اعتبار ان اللي جابلها اكيد true
+
+249
+00:20:01,730 --> 00:20:07,310
+اكيد true ففي الحالة هذه true فبنستعيد عنها عفوا
+
+250
+00:20:07,310 --> 00:20:10,530
+هذه true بنستعيد عنها بالاتنين to the power n نقص
+
+251
+00:20:10,530 --> 00:20:13,610
+واحد بالمناسبة هذا الكلام ينطبق ان هنا مايكونش
+
+252
+00:20:13,610 --> 00:20:19,450
+لايساوي اقل من بس يعني اقل من فقط ليش لأن احنا
+
+253
+00:20:19,450 --> 00:20:22,150
+ماشتغلناش على n زائد واحد اشتغلنا على n نفسها
+
+254
+00:20:24,060 --> 00:20:29,620
+لاحظته؟ اشتغلنا على N نفسها فإذا بتصير لعند N نقص
+
+255
+00:20:29,620 --> 00:20:35,720
+واحد فعليا بدون أو يساوي تمام فهي أثبتناها برضه
+
+256
+00:20:35,720 --> 00:20:38,940
+بال inductive step أو ال proof اللي أخدنا المرة
+
+257
+00:20:38,940 --> 00:20:45,710
+الماضية طيب في كمان شغلةواضحة جدا فيها جزئية الـ
+
+258
+00:20:45,710 --> 00:20:50,250
+Recursion وهي الـ Euclide algorithm اللي أخدناها
+
+259
+00:20:50,250 --> 00:20:52,250
+المرة الماضية لما كنا بدنا نجيب ال greatest common
+
+260
+00:20:52,250 --> 00:20:56,530
+divisor ليش؟ لأنه لو متذكرين هتنسترجع شوية كنت
+
+261
+00:20:56,530 --> 00:21:00,010
+بقول أن ال greatest common divisor بقدر أجيبها ل A
+
+262
+00:21:00,010 --> 00:21:05,350
+و Bكأنها هي نفس ال greatest common divisor ل B مع
+
+263
+00:21:05,350 --> 00:21:12,150
+A modulo B طب كويس طب A modulo B مع B هي نفسها ك
+
+264
+00:21:12,150 --> 00:21:15,780
+greatest common divisor من برجع بعيد نفسأيوة .. أه
+
+265
+00:21:15,780 --> 00:21:18,720
+لاحظ .. بعيد .. بعيد معناته هي recursion خلاص
+
+266
+00:21:18,720 --> 00:21:22,880
+واضحة recursion طالع إن لاميه واحد اسمه لاميه
+
+267
+00:21:22,880 --> 00:21:27,000
+وبرضه واضح نصف فرنساوي فلاميز هذا عمل أو لاميه عمل
+
+268
+00:21:27,000 --> 00:21:30,300
+نظري يسميها لاميز theorem لاميز theorem بده يقول
+
+269
+00:21:30,300 --> 00:21:35,520
+بالنسبة ل greatest common divisor ل A و B أكم مرة
+
+270
+00:21:35,520 --> 00:21:41,200
+عدد مرات تكرارها طبعا هو يعني بده يجيب كأنه ال
+
+271
+00:21:41,200 --> 00:21:44,420
+complexity بتاعتهاالكمplexity بتاع التنقل كان مرة
+
+272
+00:21:44,420 --> 00:21:49,760
+هتتكرر مش احنا عرفنا سابقا انه مرات التكرار في
+
+273
+00:21:49,760 --> 00:21:53,880
+الآخر تمثل الكمplexity، الكمplexity بالظبط طيب إجا
+
+274
+00:21:53,880 --> 00:21:58,960
+جالنا إذا كان والله A وB هما ال two numbers اللي
+
+275
+00:21:58,960 --> 00:22:00,440
+أنا بدي أجيب ل greatest common divisor between
+
+276
+00:22:00,440 --> 00:22:06,380
+them وإيه هي الأكبر فإذا بقدر أقول أنه باستخدام
+
+277
+00:22:06,380 --> 00:22:10,410
+Duclid's algorithmالـ greatest common divisor
+
+278
+00:22:10,410 --> 00:22:16,170
+هنعمل أكم step منها أقل من أو يسوى بحد أقصى خمسة K
+
+279
+00:22:16,170 --> 00:22:25,030
+بشرط أن K هي عدد ال decimal digits للرقم الأصغر هو
+
+280
+00:22:25,030 --> 00:22:30,210
+عبّر عنها رياضيا اللي هو يعني بمعنى لو كان عند 121
+
+281
+00:22:30,210 --> 00:22:35,310
+و 96 الأقل منهم two digits number فK باتنين
+
+282
+00:22:38,280 --> 00:22:41,180
+لكن هو عبّر عنها رياضيا عشان يكتبها رياضا فقال
+
+283
+00:22:41,180 --> 00:22:50,120
+floor لمن ل log base 10 ل B فهيها طيب هذه لما نجيب
+
+284
+00:22:50,120 --> 00:22:58,800
+لها log base 10 بتطلع واحد وكسر زائد الواحد اتنين
+
+285
+00:22:58,800 --> 00:23:05,310
+خلاص طيب لو بدنا نحسبها لهذه2 مكسر ف ال floor 2
+
+286
+00:23:05,310 --> 00:23:08,130
+زائد 1 ثلاثة ماكان الأول ثلاثة three digits خلاص
+
+287
+00:23:08,130 --> 00:23:13,210
+مكان الأساس ال three digits فبكل بساطة هو في الآخر
+
+288
+00:23:13,210 --> 00:23:16,190
+يعني علقنا عليها كتبنا ان هي في الآخر هي number of
+
+289
+00:23:16,190 --> 00:23:19,950
+decimal digits لا بيه خلاص يعني احنا ليش مغالبين
+
+290
+00:23:19,950 --> 00:23:24,150
+حالنا لكن في الآخر لو جيتل طلعت عليها برضه فاطفاضة
+
+291
+00:23:24,150 --> 00:23:28,560
+كتيريعني خمسة من الأتنين اللي بتتكلم عن عشرة ..
+
+292
+00:23:28,560 --> 00:23:32,960
+عشرة steps يعني اللي لو انتوا .. لو هذا عبارة عن
+
+293
+00:23:32,960 --> 00:23:36,760
+loop انت متوقع انه مايزدش عن عشرة بحيث انه لو زاد
+
+294
+00:23:36,760 --> 00:23:42,140
+عن عشرة في مشكلة في البرنامج لو زاد عن عشرة معناته
+
+295
+00:23:42,140 --> 00:23:45,160
+في مشكلة في البرنامج خد بالك احنا أعطيناك هنا الحد
+
+296
+00:23:45,160 --> 00:23:50,240
+الأقصى لعدد ال iterations أو ال recursion steps
+
+297
+00:23:51,000 --> 00:23:54,060
+زادت عن هيك لأ خد بالك يمكن في مشكلة واضح انه في
+
+298
+00:23:54,060 --> 00:23:58,660
+مشكلة طيب ففي الحالة هذه اليقليد algorithm بنقدر
+
+299
+00:23:58,660 --> 00:24:02,700
+نقول عنه linear لأن هو خطي مع عدد ال decimal كل ما
+
+300
+00:24:02,700 --> 00:24:06,720
+زادت ال decimal بالنسبالنا كل ما بتزيد عدد ال
+
+301
+00:24:06,720 --> 00:24:11,120
+steps كل ما بتزيد one decimal بزيد مقابلها خمسة في
+
+302
+00:24:11,120 --> 00:24:16,020
+ال times خمسة في ال time او في ال execution time
+
+303
+00:24:16,020 --> 00:24:21,470
+فعلياطيب ال recursive لها ال sets لما نتكلم عن ال
+
+304
+00:24:21,470 --> 00:24:25,190
+sets برضه نفس الكلام رغم ان ال set في النهاية هي
+
+305
+00:24:25,190 --> 00:24:31,130
+unordered set هي مش مرتبة لكن برضه نقدر نعرفها أو
+
+306
+00:24:31,130 --> 00:24:35,390
+نعرف عناصرها من عناصرهانقدر نعرف عناصرها من
+
+307
+00:24:35,390 --> 00:24:41,470
+عناصرها زي بكل بساطة ناخد مثلا ل a set اي set ممكن
+
+308
+00:24:41,470 --> 00:24:45,890
+اعرف مجموعة elements واحد او اتنين او تلاتة بحيث
+
+309
+00:24:45,890 --> 00:24:49,510
+ان هما يكون في بينهم relation بينهم وبين ال other
+
+310
+00:24:49,510 --> 00:24:53,860
+numbers relation و بعرف ال relation بسإذا كانت ال
+
+311
+00:24:53,860 --> 00:24:56,600
+set كبيرة إذا كانت ال set عندي كبيرة و احنا
+
+312
+00:24:56,600 --> 00:24:59,880
+اتكلمنا إنه في عندي infinite sets في بعض ال sets
+
+313
+00:24:59,880 --> 00:25:03,640
+infinite بتبقى infinity فإذا مش من المناسب أني
+
+314
+00:25:03,640 --> 00:25:08,160
+أقول أكتبها كاملة فممكن أحط أول عنصرين تلاتة بس
+
+315
+00:25:08,160 --> 00:25:12,680
+المهم اللي هم يكونوا ال common اللي بقدر أعمل
+
+316
+00:25:12,680 --> 00:25:17,350
+generation لأي element منهم زيفهد .. طبعا احنا
+
+317
+00:25:17,350 --> 00:25:20,330
+كلنا مقتنعين بهذا الكلام ان في عندي small finite
+
+318
+00:25:20,330 --> 00:25:24,210
+بعرف أكمن element فقط في البداية عساس ان هدولة ال
+
+319
+00:25:24,210 --> 00:25:27,830
+base elements بتصير اسمهم زي ال base step هدولة ال
+
+320
+00:25:27,830 --> 00:25:32,250
+base element وبيكون لازم يكون في عندي rule ل ال
+
+321
+00:25:32,250 --> 00:25:35,690
+constructing for other elements لازم يكون فيه rule
+
+322
+00:25:35,690 --> 00:25:40,230
+وإلا كيف بدي أعرف باقي العناصر؟باجي العناصر لازم
+
+323
+00:25:40,230 --> 00:25:44,050
+تكون معرفة، معرفة بس مش معرفة كأرقام، معرفة ب
+
+324
+00:25:44,050 --> 00:25:53,770
+formula، بمعادلة، ب model أو rule مثلًا خلّيني
+
+325
+00:25:53,770 --> 00:25:59,490
+أفترض إن في عندي تلاتة
+
+326
+00:25:59,490 --> 00:26:07,560
+تمتم لست Sو جلنا ان كل العناصر تحقق هذه المعادلة
+
+327
+00:26:07,560 --> 00:26:15,400
+لان X زائد Y هي برضه تنتمي لايش ل S و X و Y هي
+
+328
+00:26:15,400 --> 00:26:20,420
+عناصر من X من S كل واحدة منهم عناصر من S فكل
+
+329
+00:26:20,420 --> 00:26:26,720
+عنصرين هم ضمن الست مجموحهم لازم يكون ضمن الست كل
+
+330
+00:26:26,720 --> 00:26:31,010
+عنصرين ضمن الست مجموحهم برضه ضمن الستطيب قص على
+
+331
+00:26:31,010 --> 00:26:35,330
+ذلك هتلاقي أن هي لانهائية بتصير هتصبح لانهائية بكل
+
+332
+00:26:35,330 --> 00:26:38,910
+بساطة تلاتة هي تنتمي لل set معناه ذلك أنه تلاتة و
+
+333
+00:26:38,910 --> 00:26:42,730
+تلاتة تلاتة مع نفسها ليش؟ لأنه في ال unordered
+
+334
+00:26:42,730 --> 00:26:48,910
+ممكن يكون فيه تكرار صحيح؟ بمعنى لما نقول ليه set
+
+335
+00:26:48,910 --> 00:26:54,150
+of تلاتة أنا عارف أن هو نفسها هذه ما يمكافئ لتلاتة
+
+336
+00:26:54,150 --> 00:26:54,730
+و تلاتة
+
+337
+00:26:57,500 --> 00:27:01,240
+فإذن هذه انا اصلا هيكي بختزلها بتلاتة و اسكت بس
+
+338
+00:27:01,240 --> 00:27:04,340
+انا عارف انه ممكن يكون فيها تكرار و رغم ذلك بحسمه
+
+339
+00:27:04,340 --> 00:27:08,820
+مرة واحدة فإذا تلاتة و تلاتة صار ستة صار عندي
+
+340
+00:27:08,820 --> 00:27:15,090
+تلاتة و ستة طيب تلاتة و ستةتسعة أو الستة مع الستة
+
+341
+00:27:15,090 --> 00:27:18,510
+هي اتناش اه اجت الاتناش اتناش مع التلاتة و اتناش
+
+342
+00:27:18,510 --> 00:27:20,850
+مع الستة و التسعة مع الستة و التسعة مع التلاتة
+
+343
+00:27:20,850 --> 00:27:26,010
+صارت تعرف تطلع مضاعفات التلاتة فبتلاقيها مضاعفات
+
+344
+00:27:26,010 --> 00:27:30,830
+التلاتة بشكل infinite set infinite set فبكل بساطة
+
+345
+00:27:30,830 --> 00:27:36,210
+ممكن تعرف تلاتة belong to us و x زائد y belong to
+
+346
+00:27:36,210 --> 00:27:43,640
+us إذا x و y belong to us belong to usفهيك عرفنا
+
+347
+00:27:43,640 --> 00:27:48,380
+ال set بشكل recursive طيب نبدأ فى شوية أكواد أكواد
+
+348
+00:27:48,380 --> 00:27:52,180
+معتمدة احنا بعضها أخدناها بس بدنا نحاول اننا
+
+349
+00:27:52,180 --> 00:27:57,160
+نختزلوا بشكل recursion model بشكل recursion model
+
+350
+00:27:57,160 --> 00:28:02,280
+هفترض ان الأول ايش بدنا نحسب بدنا نحسب هنا ال
+
+351
+00:28:02,280 --> 00:28:08,860
+power ف example ال power طوى
+
+352
+00:28:08,860 --> 00:28:10,120
+كتبناها ال power بالمناسبة
+
+353
+00:28:18,800 --> 00:28:25,540
+لما قلنا a to the power n بتساوي a to the power n
+
+354
+00:28:25,540 --> 00:28:35,140
+ناقص واحد في a خلاص معناه ذا recursively أنا هضرب
+
+355
+00:28:35,140 --> 00:28:39,920
+بس كل مرة في a recursively كل مرة هضرب في a المثال
+
+356
+00:28:39,920 --> 00:28:44,690
+حاسير كان التاليالبروسيجر باور هنا احددنا ان انا
+
+357
+00:28:44,690 --> 00:28:48,110
+فيه code بدي اكتب فيه code البروسيجر باور اسمه
+
+358
+00:28:48,110 --> 00:28:51,950
+باور ايه و ايه دي لا تسوى صفر لانه مالهاش معنى
+
+359
+00:28:51,950 --> 00:28:54,810
+احطها بتسوى صفر معناته تبقى باور ايش هيكون واحد و
+
+360
+00:28:54,810 --> 00:28:59,130
+خلاص ايه عفوا انا هتظل صفر هتظل دائما صفر مالهاش
+
+361
+00:28:59,130 --> 00:29:04,690
+قيمة طيب هذه العبارة ال a عبارة عن real number و
+
+362
+00:29:04,690 --> 00:29:09,400
+ال nnatural number لأن ال power بدو يكون integer
+
+363
+00:29:09,400 --> 00:29:13,260
+كويس إذا كانت ال n اللي هي ال power اللي فوق
+
+364
+00:29:13,260 --> 00:29:18,480
+بتساوي صفر إيش return بإيش؟ بواحد أي حاجة تدور ال
+
+365
+00:29:18,480 --> 00:29:22,420
+power صفر بدو يرجع بواحد طب otherwise لأ أنا
+
+366
+00:29:22,420 --> 00:29:26,580
+مابدأتش لسه بدري عليها بدأت بإيه تدور ال power
+
+367
+00:29:26,580 --> 00:29:30,460
+اتنين مثلا معناته لأ لا تساوي صفر في الحالة دي
+
+368
+00:29:30,460 --> 00:29:42,820
+else return إيههيها ال A هى دى فى مين فى power
+
+369
+00:29:42,820 --> 00:29:46,840
+برضه كمان مرة بمعنى اعمل method و افتح code كمان
+
+370
+00:29:46,840 --> 00:29:56,800
+مرة بسمررله ال A وإن ناقص واحد اه
+
+371
+00:29:56,800 --> 00:30:01,840
+يه انضربناهم في بعضممتاز عشان نجي نفتح هذا ال term
+
+372
+00:30:01,840 --> 00:30:06,460
+هذا ال method وهذا لسه شغالة موجودة فاضية جاعدة
+
+373
+00:30:06,460 --> 00:30:10,680
+لسه ماعملتش فيها إشي كويس بحيث أنه أنا ال a لسه
+
+374
+00:30:10,680 --> 00:30:14,480
+بتستنى الناتج ال a واقفة هنا بتستنى الناتج تمام
+
+375
+00:30:14,480 --> 00:30:19,340
+الناتج هذا برضه نفس القصة هفتح من أول و جديد هنا
+
+376
+00:30:19,340 --> 00:30:25,720
+بس هنا أصبحت ب n ناقص واحد هل ال n ناقص واحد تساوي
+
+377
+00:30:25,720 --> 00:30:26,060
+صفر
+
+378
+00:30:29,320 --> 00:30:35,740
+هتساوي واحد معناه ذلك انه لأ هيجي ل else روحلي
+
+379
+00:30:35,740 --> 00:30:40,540
+افتحلي a كمان مرة اضرب a كمان مرة فهيصار عندي a في
+
+380
+00:30:40,540 --> 00:30:48,700
+a total a في a و صفر و بور الصفر a في a وراح بور
+
+381
+00:30:48,700 --> 00:30:54,640
+الصفر طيب بور الصفر هنا أصبحت zero فمررلي zero
+
+382
+00:30:54,640 --> 00:31:01,930
+لالميثود التالت حتى الآنصفر لأ then اه then return
+
+383
+00:31:01,930 --> 00:31:07,870
+واحد فبرجع بواحد طيب لاحظ كيف رجع بواحد الواحد هذا
+
+384
+00:31:07,870 --> 00:31:13,090
+جابه من ال method رقم تلاتة خلص سكر ال method رقم
+
+385
+00:31:13,090 --> 00:31:16,210
+تلاتة و نهاها و رجع ل method رقم اتنين ال method
+
+386
+00:31:16,210 --> 00:31:21,210
+رقم اتنين الناتج بده يضربه في ايه؟ و سكر method
+
+387
+00:31:21,210 --> 00:31:27,990
+رقم اتنينفرجعلنا ب A ضربهم رجع لل method رقم صفر
+
+388
+00:31:27,990 --> 00:31:31,970
+الأولى رقم واحد أول واحدة عشان الناتج اللى رجع فيه
+
+389
+00:31:31,970 --> 00:31:37,970
+يضربه في A فرجعلنا A تربيع رجعلنا بمين ب A تربيع
+
+390
+00:31:37,970 --> 00:31:47,010
+فعملها بشكل recursive method او recursive code انا
+
+391
+00:31:47,010 --> 00:31:49,490
+اتوقع انه مرت عليكوا هذه قبل هيكوا واشتغلت عليها
+
+392
+00:31:54,230 --> 00:31:59,050
+كمان مثل على اليوكليد احنا أخدنا اليوكليد و لماه
+
+393
+00:31:59,050 --> 00:32:03,530
+طالع لنا و جالنا فيه إلها الوثيوريم و تلاتة أو
+
+394
+00:32:03,530 --> 00:32:06,930
+خمسة كيو و ماخمسة كيو و بدنا نستطيع خلاص خلينا
+
+395
+00:32:06,930 --> 00:32:09,650
+نكتب لها code بالمرة نكتب لنا code إلها ف
+
+396
+00:32:09,650 --> 00:32:14,790
+procedure ل grade is common divisor B و A و لحظوا
+
+397
+00:32:14,790 --> 00:32:20,390
+B و A ترتيبها كيف نحط مهم جدا الترتيب لما بتستخدم
+
+398
+00:32:20,390 --> 00:32:24,300
+المثل دهالمفروض ان انتوا عادي ماجولكمش عليها انتوا
+
+399
+00:32:24,300 --> 00:32:27,840
+عارفينها لحالكوا ترتيب ال arguments او ال input
+
+400
+00:32:27,840 --> 00:32:32,080
+arguments كتير مهم في البرمجة كتير مهم ماتروحش
+
+401
+00:32:32,080 --> 00:32:36,980
+تحطهم a و b و بعدين تعمل أثناء ال steps تعمل
+
+402
+00:32:36,980 --> 00:32:44,520
+method و انت مرتب اللي عملتله pass له a و b بدل b
+
+403
+00:32:44,520 --> 00:32:48,980
+و a أكيد هتطلع نتائج كلها غلط في غلط و هتضلك تجري
+
+404
+00:32:48,980 --> 00:32:54,000
+وراالـ Logic Error أو يمكن .. ما بتعرفش يمكن تصدف
+
+405
+00:32:54,000 --> 00:32:58,300
+بعض الأحيان Run Error أو Run Time Error أه ممكن
+
+406
+00:32:58,300 --> 00:33:00,640
+يطلع Run Time Error ليش؟ لأن ال condition اللي
+
+407
+00:33:00,640 --> 00:33:05,420
+بيوقف عمره ما هيتحقق يعني عمرك ما هتصل لل return
+
+408
+00:33:05,420 --> 00:33:10,400
+النهائية اللي اتوقف عندها فاخدوا بالكوا جدا من
+
+409
+00:33:10,400 --> 00:33:15,400
+جزئية الـ من جاب المن في عملية ال passing فهنا بي
+
+410
+00:33:15,400 --> 00:33:20,720
+و ايه؟ يعني من الأصغر لأكبرمن الأصغر فالأكبر فانا
+
+411
+00:33:20,720 --> 00:33:25,420
+عارف أني بمرر الرقم الصغير في الأول طيب فهمناها؟
+
+412
+00:33:25,420 --> 00:33:29,400
+خلاص تمام إذا كانت ال B اللي هو الرقم الصغير اللي
+
+413
+00:33:29,400 --> 00:33:35,560
+هو جاي في الأول صفر خلاص ارجعلي بال A لأنه ال A في
+
+414
+00:33:35,560 --> 00:33:38,610
+الحالة ده هو ال commonالـ greatest common divisor
+
+415
+00:33:38,610 --> 00:33:42,810
+صح هذا اللي يقولي اتجلنا هيك تمام إذا ماوصلناش لسه
+
+416
+00:33:42,810 --> 00:33:47,110
+للصفر return برضه ارجع افتح كمان برنامج كمان مرة
+
+417
+00:33:47,110 --> 00:33:52,090
+الكود ارجع عيده كمان مرة ك method و مررله A modulo
+
+418
+00:33:52,090 --> 00:33:57,950
+B فانا دعم ان ال term اللي هنا هو الأصغر صح أكيد
+
+419
+00:33:57,950 --> 00:34:02,890
+هو الأصغر فهيتمرر كأنه الرقم الأصغر وال B هتصبح هي
+
+420
+00:34:02,890 --> 00:34:08,580
+الأكبر فعلياالـ B فعلا هتكون هي الأكبر لأن ناتج ال
+
+421
+00:34:08,580 --> 00:34:13,620
+module لـ B أكيد هتكون أصغر من B أكيد و حتما هتكون
+
+422
+00:34:13,620 --> 00:34:17,780
+أصغر من B تمام فإذا ال code بكل بساطة هي كله سطرين
+
+423
+00:34:17,780 --> 00:34:23,280
+.. كله سطرين على بعض عشان تحسب ال greatest common
+
+424
+00:34:23,280 --> 00:34:23,980
+divisor
+
+425
+00:34:26,940 --> 00:34:31,500
+Okay بتحيل؟ Okay بدنا نتكلم عن هنا جزئية ال space
+
+426
+00:34:31,500 --> 00:34:36,800
+أنه أحيانا إذا كان ال compiler تبعك مش smart
+
+427
+00:34:36,800 --> 00:34:40,140
+enough طبعا معظم الآن ال compilers يلاقي smart
+
+428
+00:34:40,140 --> 00:34:44,000
+enough أنه بيقدر يخزنلك على جد النتائج و يسكر ال
+
+429
+00:34:44,000 --> 00:34:47,770
+methodبسكّر المثل بيخلّي فقط قيمة النتائج بتاعتها
+
+430
+00:34:47,770 --> 00:34:50,510
+عشان يوفّر على حاله فتح برامج لإن هو دي بالنسبالك
+
+431
+00:34:50,510 --> 00:34:53,210
+أنت برنامج مفتوح برنامج مفتوح برنامج مفتوح إذا كان
+
+432
+00:34:53,210 --> 00:34:57,440
+ال compiler نسبيا قديم هيجع في الفخ هذاهتلاقي
+
+433
+00:34:57,440 --> 00:35:01,360
+بيفتح البرنامج و هتعمله من جوا method فهيرجع يفتح
+
+434
+00:35:01,360 --> 00:35:05,300
+كمان مرة البرنامج في space تانية و بعدين يفتح كمان
+
+435
+00:35:05,300 --> 00:35:08,320
+مرة في space تالتة على نفس المساحة او ال work
+
+436
+00:35:08,320 --> 00:35:10,780
+space اللي انت شغال عليه فال work space ايش بده
+
+437
+00:35:10,780 --> 00:35:15,160
+يصير فيه؟ بده يتعبى، بده يتعبى هذا ال compilers
+
+438
+00:35:15,160 --> 00:35:19,240
+القديمة، اذا كان ال compiler smart enough الحديث
+
+439
+00:35:19,240 --> 00:35:22,900
+معظمه، لهو بياخد النتائج و بيخلي النتائج عنده، اما
+
+440
+00:35:22,900 --> 00:35:25,960
+ما بيخلي البرنامج كله مفتوحبشوف إيش النتائج اللي
+
+441
+00:35:25,960 --> 00:35:31,480
+مضطر يضرب فيها و بس على نفس ال space اه فبيخفف قدر
+
+442
+00:35:31,480 --> 00:35:35,020
+الإمكان ال space تبعه فهذه نقطة مهمة جدا إذا بدنا
+
+443
+00:35:35,020 --> 00:35:38,660
+نشتغل على ال method ال method هل ال compiler اللي
+
+444
+00:35:38,660 --> 00:35:43,540
+عندك بساعد ولا بساعدش اللي هو ال stack memory او
+
+445
+00:35:43,540 --> 00:35:45,000
+ال stack space اه أكيد
+
+446
+00:35:48,460 --> 00:35:50,940
+هي حسب ال method ما انت إذا كان .. لاحظ إذا كان ال
+
+447
+00:35:50,940 --> 00:35:53,640
+method هي ضخمة كبيرة بمعنى بيقدرش ياخد مجموعة
+
+448
+00:35:53,640 --> 00:35:57,680
+بيانات و يخليها برا و يسكر لأ هي فيها مجموعة كبيرة
+
+449
+00:35:57,680 --> 00:36:01,320
+لأ بيصير بدها شغل تاني لأ أكيد أكيد في الحالة هذه
+
+450
+00:36:01,320 --> 00:36:05,300
+بدك ال stack يكون أصلا كبيرة عندك و ساعتها بيقولك
+
+451
+00:36:05,300 --> 00:36:09,040
+أنه لأ والله صار عندك ال complexity مشكلة في ال
+
+452
+00:36:09,040 --> 00:36:11,740
+space complexity تصبح عندك مشكلة في ال space
+
+453
+00:36:11,740 --> 00:36:16,970
+complexity طيب أخدنا ال linearلينير سيرش مش ذاكرين
+
+454
+00:36:16,970 --> 00:36:22,930
+طب هاتنعمله code باستخدام ال recursion theorem او
+
+455
+00:36:22,930 --> 00:36:31,210
+باستخدام ال recursive code كان الشغل كله معتمد على
+
+456
+00:36:31,210 --> 00:36:38,530
+انه في عندى X X هذه بدنا نبحث عنها بين I و J و إيش
+
+457
+00:36:38,530 --> 00:36:46,690
+كان مسم ال series تبقىString A ببدأ من I location
+
+458
+00:36:46,690 --> 00:36:51,050
+I ل location J فاحنا بدنا نبحث عن X هل هي موجودة
+
+459
+00:36:51,050 --> 00:36:57,550
+داخله ولا مش موجودة فإذا كأنها AI او A1 A2 مباشرة
+
+460
+00:36:57,550 --> 00:37:09,470
+مافيش داعي على I A0 A1 A2 to AN وبدنا نبحث عن Xهذا
+
+461
+00:37:09,470 --> 00:37:11,970
+ال code اللي احنا كتبناه قبل هيك شرحناه و كتبناه
+
+462
+00:37:11,970 --> 00:37:14,770
+اكيد انتوا كتبينه حتى في مصاقات تانية غير مصارنا
+
+463
+00:37:14,770 --> 00:37:18,610
+اللي انا بدنا نكتبه بشكل recursively form بشكل
+
+464
+00:37:18,610 --> 00:37:22,490
+تكراري بشكل تكراري فحته procedure search زي ما هي
+
+465
+00:37:22,490 --> 00:37:27,550
+هنعرف ال aطبيعي لأن هذا ال input الأهم هو إيش ال
+
+466
+00:37:27,550 --> 00:37:31,330
+array اللى بدك تبحث داخلها أو ال string أو ال
+
+467
+00:37:31,330 --> 00:37:34,850
+series أو ال sequence المهم إن هو ال array اللى
+
+468
+00:37:34,850 --> 00:37:38,130
+بتاخدوها في ال .. في إيش؟ في البرمجة سموها array و
+
+469
+00:37:38,130 --> 00:37:43,750
+خلاص array A وهذه بتبدأ من I to J طبعا في البداية
+
+470
+00:37:43,750 --> 00:37:48,670
+بتبدأ I ب 0 عادة و J ب Nصحيح هذه كبداية initially
+
+471
+00:37:48,670 --> 00:37:51,470
+بس احنا بنحطها in general لإنه انا عارف انه ممكن
+
+472
+00:37:51,470 --> 00:37:56,730
+لجدام افتح نفس ال code كمان مرة ب I مختلفة فعشان
+
+473
+00:37:56,730 --> 00:38:00,210
+هيك بنعرفها in general I و J هدول عبارة عن
+
+474
+00:38:00,210 --> 00:38:03,610
+integers لإنه locations بينفعش مايكونوش integers
+
+475
+00:38:03,610 --> 00:38:08,150
+أصلا كويس X هي ال term اللي أنا ببحث عنه أو القيمة
+
+476
+00:38:08,150 --> 00:38:12,250
+اللي ببحث عنها و ليست I أو J أو ما بينهما لأ هي
+
+477
+00:38:12,250 --> 00:38:21,930
+القيمة نفسها فهي قيمة ال AI من I ل J القيمة نفسها
+
+478
+00:38:21,930 --> 00:38:27,150
+تمام هانبدأ إذا كانت والله ال A I لأن هاني بدأت من
+
+479
+00:38:27,150 --> 00:38:32,570
+بداية ال sequence تبعي بدأت من بداية ال R إذا كانت
+
+480
+00:38:32,570 --> 00:38:37,960
+E نفسها بتسوي X خير وبركة ارجع ل meanب I فرجعنا ب
+
+481
+00:38:37,960 --> 00:38:41,400
+I فعليا I مش هي قيمة X كلكم عارفين هذا الكلام
+
+482
+00:38:41,400 --> 00:38:44,160
+بقوله ال index بتاعة X ان X اللي بتدور عليها
+
+483
+00:38:44,160 --> 00:38:48,260
+موجودة في المكان الفلاني بس أنا ماقلتلهش قلتله بس
+
+484
+00:38:48,260 --> 00:38:52,920
+مكانها هنا بدك تروح خدها خدها طبعا أكيد هذه حالة
+
+485
+00:38:52,920 --> 00:38:56,740
+ال best caseإن ألاجيها مباشرة لكن فعليا بيصيرش هيك
+
+486
+00:38:56,740 --> 00:39:02,700
+فإيش بيزاكي بيسوي إذا كانت I تساوي J بمعنى عملنا
+
+487
+00:39:02,700 --> 00:39:05,160
+وضلنا نعمل عملية recursion step recursion step
+
+488
+00:39:05,160 --> 00:39:06,740
+recursion step recursion step recursion step
+
+489
+00:39:06,740 --> 00:39:07,680
+recursion step recursion step recursion step
+
+490
+00:39:07,680 --> 00:39:08,320
+recursion step recursion step recursion step
+
+491
+00:39:08,320 --> 00:39:08,480
+recursion step recursion step recursion step
+
+492
+00:39:08,480 --> 00:39:08,580
+recursion step recursion step recursion step
+
+493
+00:39:08,580 --> 00:39:08,600
+recursion step recursion step recursion step
+
+494
+00:39:08,600 --> 00:39:08,640
+recursion step recursion step recursion step
+
+495
+00:39:08,640 --> 00:39:09,060
+recursion step recursion step recursion step
+
+496
+00:39:09,060 --> 00:39:11,540
+recursion step recursion step recursion step
+
+497
+00:39:11,540 --> 00:39:15,020
+recursion step recursion step recursion step
+
+498
+00:39:15,020 --> 00:39:16,180
+recursion step recursion step recursion step
+
+499
+00:39:16,180 --> 00:39:23,740
+recursion step recursion step recursion
+
+500
+00:39:23,740 --> 00:39:28,730
+stepبمعنى ان انا مالجتهاش عند I و I ما زالت بعيدة
+
+501
+00:39:28,730 --> 00:39:33,470
+عن ال J بيجي للخيار التالت اللي هو return بسيرش
+
+502
+00:39:33,470 --> 00:39:37,810
+كمان مرة بس يبدأ لي من I زائد واحد الباقي زي ما هو
+
+503
+00:39:37,810 --> 00:39:42,510
+J زي ما هي X كما هي نفس العنصر اللي ببحث عنه زائد
+
+504
+00:39:42,510 --> 00:39:46,340
+واحدكنت في ال element الأول لأ مش هو ال element
+
+505
+00:39:46,340 --> 00:39:48,860
+الأول خلاص ابدالي من ال element التاني ابدا من
+
+506
+00:39:48,860 --> 00:39:52,120
+التالت ابدا من الرابع ابدا من الخامس and so on
+
+507
+00:39:52,120 --> 00:39:55,400
+طبعا هذه واحدة من ال techniques مثلا في ال linear
+
+508
+00:39:55,400 --> 00:39:59,480
+اللي غير مجدى استخدم فيها ال recursion لأن حضّال
+
+509
+00:39:59,480 --> 00:40:04,080
+linear هي كانت linear وضلت linear بس غلبت حالي في
+
+510
+00:40:04,080 --> 00:40:09,600
+ال space يعني أنا فعلا صارت عندى سيئة الأمور اني
+
+511
+00:40:09,600 --> 00:40:15,100
+ماحسنتش في ال time و ال space زودتهابدل ما كنت
+
+512
+00:40:15,100 --> 00:40:17,960
+بصغل في نفس ال space بتاعت برنامج واحد اضطريت افتح
+
+513
+00:40:17,960 --> 00:40:22,380
+كذا code لنفس البرنامج كذا مرة لنفس ال code هذا
+
+514
+00:40:22,380 --> 00:40:26,560
+معناه ان انا زودت space ماكنش لها اي لازمة و
+
+515
+00:40:26,560 --> 00:40:31,680
+ماحسنتش في ال time linear ضالت linear لاحظ انت ايش
+
+516
+00:40:31,680 --> 00:40:36,830
+بتغير كنت I بديت ب I بعدين روحت ل I زائد واحدطب
+
+517
+00:40:36,830 --> 00:40:39,690
+اللي بعد اي زائد اتنين اي زائد تلتة طب احنا كنا في
+
+518
+00:40:39,690 --> 00:40:43,470
+الأول كنا نعمل هات for loop نبدأ من I لت جيه وكنت
+
+519
+00:40:43,470 --> 00:40:47,510
+بروح واحد اي ثم اي زائد واحد ثم اي زائد اتنين ثم
+
+520
+00:40:47,510 --> 00:40:50,350
+اي زائد تلتة يعني فعليا ك time ما تغيرش عن دي
+
+521
+00:40:50,350 --> 00:40:54,770
+فتاخدوا بالكوا و كويس ان اجانا هذا المثل انه مش
+
+522
+00:40:54,770 --> 00:40:58,220
+دايما ال recursion كويسمش ده من ال education كويس
+
+523
+00:40:58,220 --> 00:41:01,900
+عشانك انت مبرمج human programmer انت بدك في الآخر
+
+524
+00:41:01,900 --> 00:41:05,560
+انت مالك الموضوع انت لابدك تقرر اه هذا مناسب ولا
+
+525
+00:41:05,560 --> 00:41:09,740
+مش مناسب صحيح ال computer و داخل علينا و صار في
+
+526
+00:41:09,740 --> 00:41:13,480
+علم كاصطناعي و AI و مش عارفش و علم طويل عريض و
+
+527
+00:41:13,480 --> 00:41:16,240
+بحسب حسابات معقدة اكتر مننا بس في النهاية مازلت
+
+528
+00:41:16,240 --> 00:41:22,460
+انت المالك مازلت انت مالك الحسابات كويس؟ بدك تقدر
+
+529
+00:41:22,460 --> 00:41:28,370
+هذا احسن ولا مش احسن؟الـ binary ال binary search
+
+530
+00:41:28,370 --> 00:41:31,190
+برضه من الحاجات اللي أخدناها ال binary search كيف
+
+531
+00:41:31,190 --> 00:41:34,810
+ممكن أحولها أو أكتبها بشكل recursive code ف
+
+532
+00:41:34,810 --> 00:41:41,150
+recursive code هنبدأ ال binary وال A زي ما هي X
+
+533
+00:41:41,150 --> 00:41:45,430
+العنصر اللي ببحث عنه و from I to J و زي ما قلنا ال
+
+534
+00:41:45,430 --> 00:41:47,250
+initial يبدأ من 0 to N
+
+535
+00:41:50,930 --> 00:41:54,650
+و أول شغلة كنا بنعملها بنحسب ال midpoint صحيح ال
+
+536
+00:41:54,650 --> 00:41:59,170
+midpoint أو النقطة الوساطية داخل ال array في نص ال
+
+537
+00:41:59,170 --> 00:42:03,770
+array و بناخد لها floor و بعدين بنبدا نفحصها هل ال
+
+538
+00:42:03,770 --> 00:42:07,070
+X تسويها؟ والله خير و بركة بنرجع بقيمتها و خلصنا
+
+539
+00:42:08,480 --> 00:42:11,880
+هذا ال best case انه والله من أول مرة أخبط لجناها
+
+540
+00:42:11,880 --> 00:42:16,680
+خلصنا طيب أما إذا ما زبطتش بنروح بنبدأ نفحص هل X
+
+541
+00:42:16,680 --> 00:42:20,780
+أقل من العنصر اللي موجود في ال midpoint وطبعا كلنا
+
+542
+00:42:20,780 --> 00:42:24,220
+عارفين أن ال binary search هدى تظبطش إلا إذا كان
+
+543
+00:42:24,220 --> 00:42:30,640
+عندي sorted ال array تبعتي هي sorted ومن الأقل
+
+544
+00:42:30,640 --> 00:42:38,460
+فالأعلى تصعدي يعني increasing order فإذا Xأقل من A
+
+545
+00:42:38,460 --> 00:42:44,100
+معناته إذا أقل من A كل ما هو أكبر من ال M بلزمنيش
+
+546
+00:42:44,100 --> 00:42:48,900
+فجلل ال J صحيح ببقى بنقلل ال J بنقلل ال J وإحنا
+
+547
+00:42:48,900 --> 00:42:56,020
+هنا مقولاش أو يساوي صحيح
+
+548
+00:42:56,020 --> 00:43:00,680
+معنى ذلك إيش أني ببداش بروحش بحط ال J تساوي ال M
+
+549
+00:43:00,680 --> 00:43:09,170
+نفسها ناقص واحدلاحظ لأنه هي أكيد strictly هي أقل
+
+550
+00:43:09,170 --> 00:43:12,150
+من ولا يمكن أن تساوي معناته خلاص مافيش داعي أفحص
+
+551
+00:43:12,150 --> 00:43:15,930
+كم مرة العنصر هذا بروح العنصر اللي جابله باختصر
+
+552
+00:43:15,930 --> 00:43:21,850
+علي عنصر زي هذا كمان كويس andالان هذا فحصنا كقيمة
+
+553
+00:43:21,850 --> 00:43:26,370
+لكن بدنا نفحص كمان انه هل فعلا احنا خلص ال range
+
+554
+00:43:26,370 --> 00:43:31,750
+تبعنا ولا لسه and I ما زالت اقل من M يعني ما زال
+
+555
+00:43:31,750 --> 00:43:35,210
+في عندي مساحة ابحث فيها لأنه اذا وصلنا انه انا
+
+556
+00:43:35,210 --> 00:43:41,590
+ماوجدتش لكن I تسوى M طب معناته انت ال midpoint هي
+
+557
+00:43:41,590 --> 00:43:45,110
+نفسها ال first ماضلش عندك مساحة معنى ذلك
+
+558
+00:43:45,110 --> 00:43:48,610
+automatically بتقول هنا خلاص return بمين؟ ب zero
+
+559
+00:43:48,610 --> 00:43:55,930
+مالجتشماوجدتش انت وصلت لـ 0 range ومافيش عنصر خلاص
+
+560
+00:43:55,930 --> 00:44:00,550
+برجع انه مافيش عنصر وانتهى لكن هذا الكلام اذا حدث
+
+561
+00:44:00,550 --> 00:44:04,130
+هذا الموضوع فبنرجع return هنا باش انه ما زال في
+
+562
+00:44:04,130 --> 00:44:07,510
+عندي range ابحث فيه برجع return الـ A زي ما هي ال
+
+563
+00:44:07,510 --> 00:44:13,110
+X زي ما هي ال I زي ما هي ال J M ناقص واحد ال M M
+
+564
+00:44:13,110 --> 00:44:16,510
+ناقص واحد فالعنصر اللي جاب ال midpoint تمام
+
+565
+00:44:16,510 --> 00:44:25,010
+ماتحققش بهذا الشكل بمعنى انه هيهنا ليست أقل من هي
+
+566
+00:44:25,010 --> 00:44:29,530
+ليست أقل من فإذا X ليست أقل من A M خلاص بنسيب هذا
+
+567
+00:44:29,530 --> 00:44:33,550
+كل الكلام نعملهش و بنجعله اللي بعدها else إذا كانت
+
+568
+00:44:33,550 --> 00:44:35,210
+أكبر من A M
+
+569
+00:44:39,010 --> 00:44:41,790
+بتلاحظ احنا كل اللي عملناه مغيرناش ال notation
+
+570
+00:44:41,790 --> 00:44:46,590
+عكسنا اللي بتاعة ال inequality عكسنا فقط ال .. ال
+
+571
+00:44:46,590 --> 00:44:50,570
+.. ال symbols تبعتنا فهنا صارت ال aM هي اللي أقل
+
+572
+00:44:50,570 --> 00:44:57,030
+من X ف X أكبر معناها X أكبر في الحالة هذه إذا بدي
+
+573
+00:44:57,030 --> 00:45:01,310
+أعمل elimination هعمل elimination للجزء اللي قبل M
+
+574
+00:45:01,310 --> 00:45:10,010
+ومدام لا تساوي فهنا في عندي أريحية أقول منمزاد
+
+575
+00:45:10,010 --> 00:45:13,710
+واحد لأنها
+
+576
+00:45:13,710 --> 00:45:19,310
+لا تساوي فهنا اختلفت في الجزئية هذه عن ال code
+
+577
+00:45:19,310 --> 00:45:21,890
+اللي كنا كاتبينه سابقا ال code اللي كنا كاتبينه
+
+578
+00:45:21,890 --> 00:45:24,210
+سابقا إذا انتوا متذاكرين و أنا شوفت السؤال هذا في
+
+579
+00:45:24,210 --> 00:45:28,800
+عين بعضكملأ احنا المرة اللي فاتت على اساس ان نوفر
+
+580
+00:45:28,800 --> 00:45:34,140
+على حالنا F كنا F و L و خلاص أما لأ هنا زودنا كمان
+
+581
+00:45:34,140 --> 00:45:39,320
+واحدة فخلناها لها خصوصية تالتة اليساوي هذه او
+
+582
+00:45:39,320 --> 00:45:44,960
+يساوي فهنا أقل من أكبر من ماذكرناش عن اليساوي لسه
+
+583
+00:45:44,960 --> 00:45:48,620
+طيب بس بدنا ناخد بالنا أن هذا هحققه و أقول أنه أه
+
+584
+00:45:48,620 --> 00:45:53,820
+والله بدي أروح ل M زائد واحد إذا كان بأضمن أنه ما
+
+585
+00:45:53,820 --> 00:45:58,790
+زال يوجد range أصلاطيب and ال M هذه ما زالت أقل من
+
+586
+00:45:58,790 --> 00:46:04,430
+ال J معناته أنه ما زال فيه range أقدر أبحث فيه ما
+
+587
+00:46:04,430 --> 00:46:10,250
+زال موجود هاي ال range عندي أخدنا midpoint طب مش
+
+588
+00:46:10,250 --> 00:46:15,550
+بدي أضمن أنه بعد ال midpoint بين ال midpoint و ال
+
+589
+00:46:15,550 --> 00:46:20,370
+J ما زال في مساحة أبحث فيها هذه نفحصها بال
+
+590
+00:46:20,370 --> 00:46:25,610
+condition هذا أنه ما زالت M أقل من ال Jيعني يوجد
+
+591
+00:46:25,610 --> 00:46:30,090
+مسافة بين ال midpoint ونهاية ال array مازال يوجد
+
+592
+00:46:30,090 --> 00:46:35,350
+مسافة المسافة هذه نبحث عنها مدام موجودة على طول
+
+593
+00:46:35,350 --> 00:46:38,390
+بنقول إيش ال binary تبعي binary إيش بنرجع نفتح ال
+
+594
+00:46:38,390 --> 00:46:42,670
+code كمان مرة ولكن بأرقام مختلفة لمين ل I ل I
+
+595
+00:46:42,670 --> 00:46:49,710
+فبتصير A X I هتتغير ام زائد واحد افهمنا ليش زائد
+
+596
+00:46:49,710 --> 00:46:53,610
+واحدالمرة الماضية ماكنتش كتبين زائد واحد لإن كانت
+
+597
+00:46:53,610 --> 00:46:57,470
+else و ال else على طول معناها النفي ل ال condition
+
+598
+00:46:57,470 --> 00:47:00,110
+اللي انت حاطه هنا فمدار كانت أقل من معناته النفيها
+
+599
+00:47:00,110 --> 00:47:04,590
+كان أكبر من أو يساوي لأ هنا أنا ماجولتش else و
+
+600
+00:47:04,590 --> 00:47:08,990
+سكتت أنا كتبتلها condition خاص فيها و كتبت أكبر من
+
+601
+00:47:08,990 --> 00:47:14,370
+أكبر منه ماجولتش أو يساوي فأنا عنده حرية أقول زائد
+
+602
+00:47:14,370 --> 00:47:19,090
+واحد هنالأنه ضامن أنها لن تتساوي بدليل كان
+
+603
+00:47:19,090 --> 00:47:23,690
+ماتتحققش أصلا شرط هذا طيب else إذا كان فعلا و الله
+
+604
+00:47:23,690 --> 00:47:29,890
+لا هذا اتحقق ولا هذا اتحقق لاحظ أن أنت شرط اتنين
+
+605
+00:47:29,890 --> 00:47:34,590
+تلاتة التلت احتمالات الممكن أن انت حققتها فعليا
+
+606
+00:47:34,590 --> 00:47:46,200
+يساوي هاي ليساوي وهي أقل من وهي أكبر من اشضلخلصت
+
+607
+00:47:46,200 --> 00:47:53,140
+فانت ماخلطش لل code اي احتمال اخر الا احتمال انه
+
+608
+00:47:53,140 --> 00:47:59,900
+لم تتحقق واحدة من ال ans هدوله مش هيك لو واحدة
+
+609
+00:47:59,900 --> 00:48:05,240
+منهم false معناته ان I تساوي ال M او ال M تساوي ال
+
+610
+00:48:05,240 --> 00:48:09,100
+J في الحالة هذه خلاص ماضلش عندك range اصلا تبحث
+
+611
+00:48:09,100 --> 00:48:13,290
+فيهانت ماضلش عندك range تبحث فيه فعلى طول بترجعلنا
+
+612
+00:48:13,290 --> 00:48:18,650
+بإيش؟ ب zero مالجتش خلصت ال range صغر لدرجة انه ال
+
+613
+00:48:18,650 --> 00:48:21,970
+input و ال output واحد اعفوا ان البداية و النهاية
+
+614
+00:48:21,970 --> 00:48:26,910
+واحدة مافيش عنصر أدور عنه فلأ خلاص رجعلنا ان
+
+615
+00:48:26,910 --> 00:48:31,250
+مالجتش لأنه فعليا انت مالجتش عنصر ماضلش عندك عنصر
+
+616
+00:48:31,250 --> 00:48:33,350
+تمام
+
+617
+00:48:34,780 --> 00:48:37,900
+هيك بنكون أخدنا مجموعة أمثلة برضه على ال recursion
+
+618
+00:48:37,900 --> 00:48:43,040
+code و خلصنا الجزء تبع ال recursion المرة القادمة
+
+619
+00:48:43,040 --> 00:48:47,060
+ان شاء الله تعالى بنبدأ في ال counting بمعنى أن
+
+620
+00:48:47,060 --> 00:48:52,800
+احنا بتذكرين أخدنا ال numbers و نظرية الأعداد و
+
+621
+00:48:52,800 --> 00:48:57,300
+ختمت معانا في الآخر لأكواد و لتشفير الآن بدنا نروح
+
+622
+00:48:57,300 --> 00:49:02,070
+للعد كيف أنا بقدر أعدونشوف كيف وين بتوصلنا طرق
+
+623
+00:49:02,070 --> 00:49:04,610
+العد بعد ذلك ياطيكوا ألف عافية ونشوفكوا المرة
+
+624
+00:49:04,610 --> 00:49:04,910
+القادمة
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..9d0b2a8b6d911beffe2419de15c2a1c3b5dd44bd
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30_raw.json
@@ -0,0 +1 @@
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algorithms وهذه أهم شغله ويمكن هي النقطة الأهم بالنسبالكم كمبرمجين أنكوا تروحوا لجزئية ال algorithms بشكل recursively ممكن تتكرر من نفسها بمعنى أن الكود يكرر نفسه وحناخد أمثلة على بعض الأكواد خلال محاضرتنا ان شاء الله تعالى", "tokens": [9566, 3555, 3615, 995, 23758, 44945, 14851, 9778, 40448, 3224, 9122, 20560, 488, 14642, 37037, 24192, 5551, 16095, 13412, 17082, 43761, 4032, 32640, 19452, 39896, 28239, 47432, 3660, 16247, 16095, 20666, 1863, 35457, 6027, 24793, 9122, 2304, 26890, 2304, 7435, 9957, 14739, 4117, 14407, 6055, 32887, 5016, 14407, 5296, 7435, 11622, 19986, 10632, 2423, 14642, 4724, 8592, 28820, 20560, 3413, 3714, 43020, 6055, 2655, 37983, 2288, 9154, 8717, 36178, 11296, 4724, 2304, 3615, 1863, 7578, 14739, 33251, 23328, 7251, 37983, 2288, 8717, 36178, 3224, 4032, 5016, 1863, 47283, 3215, 5551, 2304, 12984, 37977, 15844, 45030, 11242, 16247, 4117, 14407, 3215, 16490, 1211, 6027, 3714, 5016, 46958, 43500, 8315, 16472, 13412, 16606, 21984, 37279, 6027, 7578], "avg_logprob": 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{"start": 1236.64, "end": 1237.02, "word": " أو", "probability": 0.6328125}, {"start": 1237.02, "end": 1237.16, "word": " ال", "probability": 0.56396484375}, {"start": 1237.16, "end": 1238.04, "word": " proof", "probability": 0.94189453125}, {"start": 1238.04, "end": 1238.2, "word": " اللي", "probability": 0.9072265625}, {"start": 1238.2, "end": 1238.52, "word": " أخدنا", "probability": 0.910400390625}, {"start": 1238.52, "end": 1238.94, "word": " المرة", "probability": 0.7119140625}, {"start": 1238.94, "end": 1240.06, "word": " الماضية", "probability": 0.9752604166666666}, {"start": 1240.06, "end": 1241.72, "word": " طيب", "probability": 0.8525390625}, {"start": 1241.72, "end": 1241.9, "word": " في", "probability": 0.65673828125}, {"start": 1241.9, "end": 1242.22, "word": " كمان", "probability": 0.9498697916666666}, {"start": 1242.22, "end": 1242.66, "word": " شغلة", "probability": 0.9344075520833334}], "temperature": 1.0}, {"id": 52, "seek": 126036, "start": 1243.79, "end": 1260.37, "text": "واضحة جدا فيها جزئية الـ Recursion وهي الـ Euclide algorithm اللي أخدناها المرة الماضية لما كنا بدنا نجيب ال greatest common divisor ليش؟ لأنه لو متذكرين هتنسترجع شوية كنت بقول أن ال greatest common divisor بقدر أجيبها ل A و B", "tokens": [2407, 46958, 5016, 3660, 10874, 28259, 8978, 11296, 10874, 11622, 19986, 10632, 2423, 39184, 9647, 2156, 313, 37037, 1829, 2423, 39184, 462, 1311, 31264, 9284, 13672, 1829, 5551, 9778, 3215, 8315, 11296, 9673, 25720, 9673, 46958, 10632, 5296, 15042, 9122, 8315, 47525, 8315, 8717, 7435, 1829, 3555, 2423, 6636, 2689, 25974, 284, 32239, 8592, 22807, 5296, 33456, 3224, 45164, 44650, 8848, 37983, 9957, 8032, 2655, 1863, 14851, 47341, 3615, 13412, 2407, 10632, 9122, 29399, 4724, 39648, 14739, 2423, 6636, 2689, 25974, 284, 4724, 28543, 2288, 5551, 7435, 1829, 3555, 11296, 5296, 316, 4032, 363], "avg_logprob": -0.20230263879424648, "compression_ratio": 1.53125, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1243.79, "end": 1244.39, "word": "واضحة", "probability": 0.911865234375}, {"start": 1244.39, "end": 1244.63, "word": " جدا", "probability": 0.907470703125}, {"start": 1244.63, "end": 1245.01, "word": " فيها", "probability": 0.80419921875}, {"start": 1245.01, "end": 1245.55, "word": " جزئية", "probability": 0.800537109375}, {"start": 1245.55, "end": 1245.71, "word": " الـ", "probability": 0.5816650390625}, {"start": 1245.71, "end": 1246.31, "word": " Recursion", "probability": 0.77685546875}, {"start": 1246.31, "end": 1247.73, "word": " وهي", "probability": 0.628173828125}, {"start": 1247.73, "end": 1248.55, "word": " الـ", "probability": 0.785400390625}, {"start": 1248.55, "end": 1249.15, "word": " Euclide", "probability": 0.83642578125}, {"start": 1249.15, "end": 1249.69, "word": " algorithm", "probability": 0.443359375}, {"start": 1249.69, "end": 1249.91, "word": " اللي", "probability": 0.8251953125}, {"start": 1249.91, "end": 1250.25, "word": " أخدناها", "probability": 0.901953125}, {"start": 1250.25, "end": 1250.51, "word": " المرة", "probability": 0.91845703125}, {"start": 1250.51, "end": 1250.79, "word": " الماضية", "probability": 0.9554036458333334}, {"start": 1250.79, "end": 1250.95, "word": " لما", "probability": 0.857177734375}, {"start": 1250.95, "end": 1251.15, "word": " كنا", "probability": 0.98828125}, {"start": 1251.15, "end": 1251.43, "word": " بدنا", "probability": 0.71728515625}, {"start": 1251.43, "end": 1251.67, "word": " نجيب", "probability": 0.991455078125}, {"start": 1251.67, "end": 1251.75, "word": " ال", "probability": 0.5107421875}, {"start": 1251.75, "end": 1251.99, "word": " greatest", "probability": 0.81689453125}, {"start": 1251.99, "end": 1252.25, "word": " common", "probability": 0.93603515625}, {"start": 1252.25, "end": 1252.79, "word": " divisor", "probability": 0.96630859375}, {"start": 1252.79, "end": 1253.83, "word": " ليش؟", "probability": 0.7071940104166666}, {"start": 1253.83, "end": 1254.17, "word": " لأنه", "probability": 0.8391927083333334}, {"start": 1254.17, "end": 1254.41, "word": " لو", "probability": 0.96044921875}, {"start": 1254.41, "end": 1255.03, "word": " متذكرين", "probability": 0.9031982421875}, {"start": 1255.03, "end": 1255.63, "word": " هتنسترجع", "probability": 0.7544759114583334}, {"start": 1255.63, "end": 1256.03, "word": " شوية", "probability": 0.9069010416666666}, {"start": 1256.03, "end": 1256.53, "word": " كنت", "probability": 0.869140625}, {"start": 1256.53, "end": 1256.95, "word": " بقول", "probability": 0.98583984375}, {"start": 1256.95, "end": 1257.47, "word": " أن", "probability": 0.36669921875}, {"start": 1257.47, "end": 1257.59, "word": " ال", "probability": 0.76416015625}, {"start": 1257.59, "end": 1257.87, "word": " greatest", "probability": 0.9560546875}, {"start": 1257.87, "end": 1258.23, "word": " common", "probability": 0.94091796875}, {"start": 1258.23, "end": 1258.79, "word": " divisor", "probability": 0.975830078125}, {"start": 1258.79, "end": 1259.19, "word": " بقدر", "probability": 0.9832356770833334}, {"start": 1259.19, "end": 1259.63, "word": " أجيبها", "probability": 0.9794921875}, {"start": 1259.63, "end": 1259.85, "word": " ل", "probability": 0.9609375}, {"start": 1259.85, "end": 1260.01, "word": " A", "probability": 0.248046875}, {"start": 1260.01, "end": 1260.13, "word": " و", "probability": 0.94189453125}, {"start": 1260.13, "end": 1260.37, "word": " B", "probability": 0.6064453125}], "temperature": 1.0}, {"id": 53, "seek": 127451, "start": 1261.67, "end": 1274.51, "text": "كأنها هي نفس ال greatest common divisor ل B مع A modulo B طب كويس طب A modulo B مع B هي نفسها ك greatest common divisor من برجع بعيد نفس", "tokens": [4117, 33456, 11296, 39896, 8717, 36178, 2423, 6636, 2689, 25974, 284, 5296, 363, 20449, 316, 1072, 13455, 363, 23032, 3555, 9122, 45865, 3794, 23032, 3555, 316, 1072, 13455, 363, 20449, 363, 39896, 8717, 36178, 11296, 9122, 6636, 2689, 25974, 284, 9154, 4724, 47341, 3615, 45030, 25708, 8717, 36178], "avg_logprob": -0.2230548518044608, "compression_ratio": 1.4330708661417322, "no_speech_prob": 0.0, "words": [{"start": 1261.67, "end": 1262.23, "word": "كأنها", "probability": 0.7581380208333334}, {"start": 1262.23, "end": 1262.43, "word": " هي", "probability": 0.2322998046875}, {"start": 1262.43, "end": 1262.69, "word": " نفس", "probability": 0.991943359375}, {"start": 1262.69, "end": 1262.79, "word": " ال", "probability": 0.251708984375}, {"start": 1262.79, "end": 1263.07, "word": " greatest", "probability": 0.75537109375}, {"start": 1263.07, "end": 1263.35, "word": " common", "probability": 0.94580078125}, {"start": 1263.35, "end": 1263.97, "word": " divisor", "probability": 0.9658203125}, {"start": 1263.97, "end": 1264.45, "word": " ل", "probability": 0.90234375}, {"start": 1264.45, "end": 1264.73, "word": " B", "probability": 0.386474609375}, {"start": 1264.73, "end": 1265.35, "word": " مع", "probability": 0.9755859375}, {"start": 1265.35, "end": 1266.09, "word": " A", "probability": 0.822265625}, {"start": 1266.09, "end": 1267.17, "word": " modulo", "probability": 0.869140625}, {"start": 1267.17, "end": 1267.79, "word": " B", "probability": 0.89599609375}, {"start": 1267.79, "end": 1268.47, "word": " طب", "probability": 0.6181640625}, {"start": 1268.47, "end": 1268.87, "word": " كويس", "probability": 0.9562174479166666}, {"start": 1268.87, "end": 1269.23, "word": " طب", "probability": 0.6829833984375}, {"start": 1269.23, "end": 1269.55, "word": " A", "probability": 0.58251953125}, {"start": 1269.55, "end": 1269.99, "word": " modulo", "probability": 0.88916015625}, {"start": 1269.99, "end": 1270.27, "word": " B", "probability": 0.974609375}, {"start": 1270.27, "end": 1270.85, "word": " مع", "probability": 0.9931640625}, {"start": 1270.85, "end": 1271.23, "word": " B", "probability": 0.9560546875}, {"start": 1271.23, "end": 1271.67, "word": " هي", "probability": 0.90673828125}, {"start": 1271.67, "end": 1272.07, "word": " نفسها", "probability": 0.90869140625}, {"start": 1272.07, "end": 1272.15, "word": " ك", "probability": 0.9599609375}, {"start": 1272.15, "end": 1272.43, "word": " greatest", "probability": 0.69970703125}, {"start": 1272.43, "end": 1272.75, "word": " common", "probability": 0.94287109375}, {"start": 1272.75, "end": 1273.23, "word": " divisor", "probability": 0.95458984375}, {"start": 1273.23, "end": 1273.43, "word": " من", "probability": 0.9921875}, {"start": 1273.43, "end": 1273.93, "word": " برجع", "probability": 0.82958984375}, {"start": 1273.93, "end": 1274.17, "word": " بعيد", "probability": 0.90185546875}, {"start": 1274.17, "end": 1274.51, "word": " نفس", "probability": 0.997314453125}], "temperature": 1.0}, {"id": 54, "seek": 130209, "start": 1275.22, "end": 1302.1, "text": "أيوة .. أه لاحظ .. بعيد .. بعيد معناته هي recursion خلاص واضحة recursion طالع إن لاميه واحد اسمه لاميه وبرضه واضح نصف فرنساوي فلاميز هذا عمل أو لاميه عمل نظري يسميها لاميز theorem لاميز theorem بده يقول بالنسبة ل greatest common divisor ل A و B أكم مرة عدد مرات تكرارها طبعا هو يعني بده يجيب كأنه ال complexity بتاعتها", "tokens": [10721, 1829, 2407, 3660, 4386, 5551, 3224, 20193, 5016, 19913, 4386, 45030, 25708, 4386, 45030, 25708, 20449, 8315, 47395, 39896, 20560, 313, 16490, 1211, 33546, 4032, 46958, 5016, 3660, 20560, 313, 23032, 6027, 3615, 36145, 5296, 10943, 1829, 3224, 36764, 24401, 24525, 2304, 3224, 5296, 10943, 1829, 3224, 4032, 26890, 11242, 3224, 4032, 46958, 5016, 8717, 9381, 5172, 6156, 2288, 1863, 3794, 995, 45865, 6156, 37440, 1829, 11622, 23758, 6225, 42213, 34051, 5296, 10943, 1829, 3224, 6225, 42213, 8717, 19913, 16572, 7251, 38251, 1829, 11296, 5296, 10943, 1829, 11622, 20904, 5296, 10943, 1829, 11622, 20904, 47525, 3224, 7251, 39648, 20666, 1863, 35457, 3660, 5296, 6636, 2689, 25974, 284, 5296, 316, 4032, 363, 5551, 24793, 3714, 25720, 6225, 3215, 3215, 3714, 2288, 9307, 6055, 37983, 9640, 11296, 23032, 3555, 3615, 995, 31439, 37495, 22653, 47525, 3224, 7251, 7435, 1829, 3555, 9122, 33456, 3224, 2423, 14024, 39894, 995, 34268, 11296], "avg_logprob": -0.2422399392864048, "compression_ratio": 1.7474048442906573, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 1275.22, "end": 1275.58, "word": "أيوة", "probability": 0.7525634765625}, {"start": 1275.58, "end": 1275.6, "word": " ..", "probability": 0.404052734375}, {"start": 1275.6, "end": 1275.78, "word": " أه", "probability": 0.645751953125}, {"start": 1275.78, "end": 1276.12, "word": " لاحظ", "probability": 0.9446614583333334}, {"start": 1276.12, "end": 1276.2, "word": " ..", "probability": 0.2349853515625}, {"start": 1276.2, "end": 1276.7, "word": " بعيد", "probability": 0.95654296875}, {"start": 1276.7, "end": 1277.26, "word": " ..", "probability": 0.42822265625}, {"start": 1277.26, "end": 1277.48, "word": " بعيد", "probability": 0.88232421875}, {"start": 1277.48, "end": 1277.76, "word": " معناته", "probability": 0.8043619791666666}, {"start": 1277.76, "end": 1277.88, "word": " هي", "probability": 0.91796875}, {"start": 1277.88, "end": 1278.36, 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0.82958984375}, {"start": 1288.92, "end": 1289.48, "word": " لاميز", "probability": 0.789825439453125}, {"start": 1289.48, "end": 1289.76, "word": " theorem", "probability": 0.7421875}, {"start": 1289.76, "end": 1290.06, "word": " بده", "probability": 0.5015869140625}, {"start": 1290.06, "end": 1290.3, "word": " يقول", "probability": 0.992919921875}, {"start": 1290.3, "end": 1291.4, "word": " بالنسبة", "probability": 0.987060546875}, {"start": 1291.4, "end": 1291.6, "word": " ل", "probability": 0.9189453125}, {"start": 1291.6, "end": 1292.2, "word": " greatest", "probability": 0.2144775390625}, {"start": 1292.2, "end": 1292.48, "word": " common", "probability": 0.955078125}, {"start": 1292.48, "end": 1293.18, "word": " divisor", "probability": 0.9609375}, {"start": 1293.18, "end": 1293.34, "word": " ل", "probability": 0.927734375}, {"start": 1293.34, "end": 1293.6, "word": " A", "probability": 0.283447265625}, {"start": 1293.6, "end": 1293.9, "word": " و", "probability": 0.958984375}, {"start": 1293.9, "end": 1294.18, "word": " B", "probability": 0.69140625}, {"start": 1294.18, "end": 1295.04, "word": " أكم", "probability": 0.6807861328125}, {"start": 1295.04, "end": 1295.52, "word": " مرة", "probability": 0.985595703125}, {"start": 1295.52, "end": 1296.24, "word": " عدد", "probability": 0.9632161458333334}, {"start": 1296.24, "end": 1296.54, "word": " مرات", "probability": 0.97900390625}, {"start": 1296.54, "end": 1297.12, "word": " تكرارها", "probability": 0.9873046875}, {"start": 1297.12, "end": 1298.72, "word": " طبعا", "probability": 0.8941650390625}, {"start": 1298.72, "end": 1298.88, "word": " هو", "probability": 0.97265625}, {"start": 1298.88, "end": 1299.52, "word": " يعني", "probability": 0.96923828125}, {"start": 1299.52, "end": 1300.68, "word": " بده", "probability": 0.77783203125}, {"start": 1300.68, "end": 1300.84, "word": " يجيب", "probability": 0.800537109375}, {"start": 1300.84, "end": 1301.12, "word": " كأنه", "probability": 0.9069010416666666}, {"start": 1301.12, "end": 1301.2, "word": " ال", "probability": 0.83349609375}, {"start": 1301.2, "end": 1301.58, "word": " complexity", "probability": 0.95703125}, {"start": 1301.58, "end": 1302.1, "word": " بتاعتها", "probability": 0.98681640625}], "temperature": 1.0}, {"id": 55, "seek": 132732, "start": 1303.14, "end": 1327.32, "text": "الكمplexity بتاع التنقل كان مرة هتتكرر مش احنا عرفنا سابقا انه مرات التكرار في الآخر تمثل الكمplexity، الكمplexity بالظبط طيب إجا جالنا إذا كان والله A وB هما ال two numbers اللي أنا بدي أجيب ل greatest common divisor between them وإيه هي الأكبر فإذا بقدر أقول أنه باستخدام Duclid's algorithm", "tokens": [6027, 24793, 18945, 507, 39894, 45761, 16712, 1863, 4587, 1211, 25961, 3714, 25720, 8032, 2655, 2655, 37983, 2288, 37893, 1975, 5016, 8315, 6225, 28480, 8315, 8608, 16758, 4587, 995, 16472, 3224, 3714, 2288, 9307, 16712, 37983, 9640, 8978, 6024, 95, 34740, 46811, 12984, 1211, 2423, 24793, 18945, 507, 12399, 2423, 24793, 18945, 507, 20666, 19913, 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"probability": 0.93310546875}, {"start": 1320.74, "end": 1322.4, "word": " وإيه", "probability": 0.857421875}, {"start": 1322.4, "end": 1322.56, "word": " هي", "probability": 0.8701171875}, {"start": 1322.56, "end": 1323.06, "word": " الأكبر", "probability": 0.99267578125}, {"start": 1323.06, "end": 1324.32, "word": " فإذا", "probability": 0.8102213541666666}, {"start": 1324.32, "end": 1324.72, "word": " بقدر", "probability": 0.9832356770833334}, {"start": 1324.72, "end": 1325.06, "word": " أقول", "probability": 0.913330078125}, {"start": 1325.06, "end": 1325.64, "word": " أنه", "probability": 0.7022705078125}, {"start": 1325.64, "end": 1326.38, "word": " باستخدام", "probability": 0.977783203125}, {"start": 1326.38, "end": 1326.92, "word": " Duclid's", "probability": 0.544580078125}, {"start": 1326.92, "end": 1327.32, "word": " algorithm", "probability": 0.81591796875}], "temperature": 1.0}, {"id": 56, "seek": 135531, "start": 1329.11, "end": 1355.31, "text": "الـ greatest common divisor هنعمل أكم step منها أقل من أو يسوى بحد أقصى خمسة K بشرط أن K هي عدد ال decimal digits للرقم الأصغر هو عبّر عنها رياضيا اللي هو يعني بمعنى لو كان عند 121 و 96 الأقل منهم two digits number فK باتنين", "tokens": [6027, 39184, 6636, 2689, 25974, 284, 8032, 1863, 25957, 1211, 5551, 24793, 1823, 9154, 11296, 5551, 4587, 1211, 9154, 34051, 7251, 3794, 2407, 7578, 4724, 24401, 5551, 4587, 9381, 7578, 16490, 2304, 3794, 3660, 591, 4724, 46309, 9566, 14739, 591, 39896, 6225, 3215, 3215, 2423, 26601, 27011, 24976, 2288, 4587, 2304, 16247, 9381, 17082, 2288, 31439, 6225, 3555, 11703, 2288, 18871, 11296, 12602, 1829, 46958, 25528, 13672, 1829, 31439, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 45164, 25961, 43242, 2272, 16, 4032, 24124, 16247, 4587, 1211, 9154, 16095, 732, 27011, 1230, 6156, 42, 4724, 9307, 1863, 9957], "avg_logprob": -0.20328444075219484, "compression_ratio": 1.4327731092436975, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1329.11, "end": 1329.37, "word": 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رياضا فقال floor لمن ل log base 10 ل B فهيها طيب هذه لما نجيب لها log base 10 بتطلع واحد وكسر زائد الواحد اتنين خلاص طيب لو بدنا نحسبها لهذه", "tokens": [1211, 19452, 31439, 6225, 3555, 11703, 2288, 18871, 11296, 12602, 1829, 46958, 25528, 6225, 8592, 7649, 7251, 4117, 2655, 3555, 11296, 12602, 1829, 46958, 995, 6156, 4587, 6027, 4123, 5296, 27842, 5296, 3565, 3096, 1266, 5296, 363, 6156, 3224, 1829, 11296, 23032, 1829, 3555, 29538, 5296, 15042, 8717, 7435, 1829, 3555, 5296, 11296, 3565, 3096, 1266, 39894, 9566, 1211, 3615, 36764, 24401, 4032, 4117, 3794, 2288, 30767, 16373, 3215, 2423, 14407, 24401, 1975, 2655, 1863, 9957, 16490, 1211, 33546, 23032, 1829, 3555, 45164, 47525, 8315, 8717, 5016, 35457, 11296, 46740, 24192], "avg_logprob": -0.19021739470569984, "compression_ratio": 1.598901098901099, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 1358.28, "end": 1358.62, "word": "لكن", "probability": 0.82568359375}, {"start": 1358.62, "end": 1358.76, "word": " هو", 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{"start": 1683.16, "end": 1683.94, "word": " example", "probability": 0.6904296875}, {"start": 1683.94, "end": 1684.38, "word": " ال", "probability": 0.52490234375}, {"start": 1684.38, "end": 1685.6, "word": " power", "probability": 0.9130859375}, {"start": 1685.6, "end": 1688.86, "word": " طوى", "probability": 0.5009765625}, {"start": 1688.86, "end": 1689.26, "word": " كتبناها", "probability": 0.9759765625}, {"start": 1689.26, "end": 1689.36, "word": " ال", "probability": 0.9482421875}, {"start": 1689.36, "end": 1689.52, "word": " power", "probability": 0.916015625}, {"start": 1689.52, "end": 1690.12, "word": " بالمناسبة", "probability": 0.96416015625}], "temperature": 1.0}, {"id": 71, "seek": 172078, "start": 1698.8, "end": 1720.78, "text": "لما قلنا a to the power n بتساوي a to the power n ناقص واحد في a خلاص معناه ذا recursively أنا هضرب بس كل مرة في a recursively كل مرة هضرب في a المثال حاسير كان التالي", "tokens": [1211, 15042, 12174, 1211, 8315, 257, 281, 264, 1347, 297, 39894, 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هيكون", "probability": 0.661376953125}, {"start": 1734.43, "end": 1734.73, "word": " واحد", "probability": 0.976806640625}, {"start": 1734.73, "end": 1734.81, "word": " و", "probability": 0.66650390625}, {"start": 1734.81, "end": 1735.11, "word": " خلاص", "probability": 0.8507486979166666}, {"start": 1735.11, "end": 1735.37, "word": " ايه", "probability": 0.6488444010416666}, {"start": 1735.37, "end": 1735.63, "word": " عفوا", "probability": 0.84912109375}, {"start": 1735.63, "end": 1735.73, "word": " انا", "probability": 0.5938720703125}, {"start": 1735.73, "end": 1735.95, "word": " هتظل", "probability": 0.6502685546875}, {"start": 1735.95, "end": 1736.35, "word": " صفر", "probability": 0.9778645833333334}, {"start": 1736.35, "end": 1737.13, "word": " هتظل", "probability": 0.9287109375}, {"start": 1737.13, "end": 1738.41, "word": " دائما", "probability": 0.8610026041666666}, {"start": 1738.41, "end": 1738.69, "word": " صفر", "probability": 0.97900390625}, {"start": 1738.69, "end": 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"word": " ال", "probability": 0.94189453125}, {"start": 1744.83, "end": 1745.07, "word": " n", "probability": 0.8232421875}], "temperature": 1.0}, {"id": 73, "seek": 177340, "start": 1745.94, "end": 1773.4, "text": "natural number لأن ال power بدو يكون integer كويس إذا كانت ال n اللي هي ال power اللي فوق بتساوي صفر إيش return بإيش؟ بواحد أي حاجة تدور ال power صفر بدو يرجع بواحد طب otherwise لأ أنا مابدأتش لسه بدري عليها بدأت بإيه تدور ال power اتنين مثلا معناته لأ لا تساوي صفر في الحالة دي else return إيه", "tokens": [16296, 1230, 5296, 33456, 2423, 1347, 47525, 2407, 7251, 30544, 24922, 9122, 45865, 3794, 11933, 15730, 25961, 2655, 2423, 297, 13672, 1829, 39896, 2423, 1347, 13672, 1829, 6156, 30543, 39894, 3794, 995, 45865, 20328, 5172, 2288, 11933, 1829, 8592, 2736, 4724, 28814, 1829, 8592, 22807, 4724, 14407, 24401, 36632, 11331, 26108, 3660, 6055, 3215, 13063, 2423, 1347, 20328, 5172, 2288, 47525, 2407, 7251, 47341, 3615, 4724, 14407, 24401, 23032, 3555, 5911, 5296, 10721, 41850, 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فاضية جاعدة لسه ماعملتش فيها إشي كويس بحيث أنه أنا ال a لسه بتستنى الناتج ال a واقفة هنا بتستنى الناتج تمام الناتج هذا برضه نفس القصة هفتح من أول و جديد هنا بس هنا أصبحت ب n ناقص واحد هل ال n ناقص واحد تساوي صفر", "tokens": [2304, 2304, 2655, 31377, 6225, 8592, 7649, 8717, 7435, 1829, 8717, 5172, 2655, 5016, 23758, 2423, 1433, 23758, 2423, 3170, 37037, 15730, 5296, 3794, 3224, 13412, 17082, 6027, 3660, 3714, 29245, 23328, 3660, 6156, 46958, 10632, 10874, 995, 22488, 3660, 5296, 3794, 3224, 19446, 25957, 1211, 2655, 8592, 8978, 11296, 11933, 8592, 1829, 9122, 45865, 3794, 4724, 5016, 1829, 12984, 14739, 3224, 41850, 2423, 257, 5296, 3794, 3224, 39894, 14851, 1863, 7578, 28239, 9307, 7435, 2423, 257, 36764, 4587, 5172, 3660, 34105, 39894, 14851, 1863, 7578, 28239, 9307, 7435, 46811, 10943, 28239, 9307, 7435, 23758, 4724, 43042, 3224, 8717, 36178, 25062, 9381, 3660, 8032, 5172, 2655, 5016, 9154, 5551, 12610, 4032, 10874, 16254, 3215, 34105, 4724, 3794, 34105, 5551, 9381, 3555, 33753, 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sequence المهم إن هو ال array اللى بتاخدوها في ال .. في إيش؟ في البرمجة سموها array و خلاص array A وهذه بتبدأ من I to J طبعا في البداية بتبدأ I ب 0 عادة و J ب N", "tokens": [9566, 21292, 3615, 1829, 5296, 33456, 23758, 2423, 4846, 16247, 16095, 31439, 11933, 1829, 8592, 2423, 10225, 13672, 7578, 47525, 4117, 6055, 49628, 12984, 11778, 47283, 1211, 11296, 34051, 2423, 6798, 34051, 2423, 2638, 34051, 2423, 8310, 9673, 16095, 36145, 31439, 2423, 10225, 13672, 7578, 39894, 47283, 3215, 2407, 11296, 8978, 2423, 4386, 8978, 11933, 1829, 8592, 22807, 8978, 2423, 26890, 2304, 7435, 3660, 8608, 2304, 2407, 11296, 10225, 4032, 16490, 1211, 33546, 10225, 316, 37037, 24192, 39894, 44510, 10721, 9154, 286, 281, 508, 23032, 3555, 3615, 995, 8978, 29739, 28259, 10632, 39894, 44510, 10721, 286, 4724, 1958, 6225, 18513, 3660, 4032, 508, 4724, 426], "avg_logprob": -0.20489386862741327, "compression_ratio": 1.7241379310344827, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 2244.53, "end": 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"start": 2383.96, "end": 2412.94, "text": "كنت في ال element الأول لأ مش هو ال element الأول خلاص ابدالي من ال element التاني ابدا من التالت ابدا من الرابع ابدا من الخامس and so on طبعا هذه واحدة من ال techniques مثلا في ال linear اللي غير مجدى استخدم فيها ال recursion لأن حضّال linear هي كانت linear وضلت linear بس غلبت حالي في ال space يعني أنا فعلا صارت عندى سيئة الأمور اني ماحسنتش في ال time و ال space زودتها", "tokens": [19452, 2655, 8978, 2423, 4478, 16247, 12610, 5296, 10721, 37893, 31439, 2423, 4478, 16247, 12610, 16490, 1211, 33546, 48127, 3215, 6027, 1829, 9154, 2423, 4478, 16712, 7649, 1829, 48127, 28259, 9154, 16712, 6027, 2655, 48127, 28259, 9154, 34892, 16758, 3615, 48127, 28259, 9154, 33962, 10943, 3794, 293, 370, 322, 23032, 3555, 3615, 995, 29538, 36764, 24401, 3660, 9154, 2423, 7512, 50113, 15040, 8978, 2423, 8213, 13672, 1829, 32771, 13546, 3714, 7435, 3215, 7578, 44713, 9778, 40448, 8978, 11296, 2423, 20560, 313, 5296, 33456, 11331, 11242, 11703, 6027, 8213, 39896, 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ماكنش لها اي لازمة و ماحسنتش في ال time linear ضالت linear لاحظ انت ايش بتغير كنت I بديت ب I بعدين روحت ل I زائد واحد", "tokens": [44510, 1211, 19446, 9122, 29399, 4724, 9381, 17082, 1211, 8978, 8717, 36178, 2423, 1901, 39894, 995, 34268, 4724, 2288, 8315, 2304, 7435, 36764, 24401, 1975, 11242, 9566, 16572, 2655, 1975, 5172, 2655, 5016, 9122, 15730, 3089, 5296, 1863, 36178, 2423, 26890, 8315, 2304, 7435, 9122, 15730, 3714, 25720, 5296, 1863, 36178, 2423, 3089, 23758, 20449, 8315, 3224, 16472, 1975, 8315, 30767, 23328, 2655, 1901, 19446, 19452, 8592, 5296, 11296, 1975, 1829, 5296, 31377, 46007, 4032, 19446, 5016, 3794, 29399, 8592, 8978, 2423, 565, 8213, 48812, 6027, 2655, 8213, 20193, 5016, 19913, 16472, 2655, 1975, 1829, 8592, 39894, 17082, 13546, 9122, 29399, 286, 47525, 36081, 4724, 286, 39182, 9957, 12602, 2407, 33753, 5296, 286, 30767, 16373, 3215, 36764, 24401], "avg_logprob": -0.16596638755638057, "compression_ratio": 1.8185840707964602, "no_speech_prob": 6.556510925292969e-07, 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{"start": 2503.67, "end": 2504.11, "word": " I", "probability": 0.80126953125}, {"start": 2504.11, "end": 2504.57, "word": " to", "probability": 0.953125}, {"start": 2504.57, "end": 2504.81, "word": " J", "probability": 0.91015625}, {"start": 2504.81, "end": 2504.95, "word": " و", "probability": 0.75146484375}, {"start": 2504.95, "end": 2505.03, "word": " زي", "probability": 0.797607421875}, {"start": 2505.03, "end": 2505.13, "word": " ما", "probability": 0.9658203125}, {"start": 2505.13, "end": 2505.35, "word": " قلنا", "probability": 0.8714192708333334}, {"start": 2505.35, "end": 2505.43, "word": " ال", "probability": 0.488037109375}, {"start": 2505.43, "end": 2505.67, "word": " initial", "probability": 0.802734375}, {"start": 2505.67, "end": 2506.03, "word": " يبدأ", "probability": 0.7900390625}, {"start": 2506.03, "end": 2506.17, "word": " من", "probability": 0.98388671875}, {"start": 2506.17, "end": 2506.47, "word": " 0", "probability": 0.365478515625}, {"start": 2506.47, "end": 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{"start": 2520.17, "end": 2520.55, "word": " بناخد", "probability": 0.8684895833333334}, {"start": 2520.55, "end": 2520.73, "word": " لها", "probability": 0.758056640625}, {"start": 2520.73, "end": 2521.01, "word": " floor", "probability": 0.875}, {"start": 2521.01, "end": 2521.39, "word": " و", "probability": 0.779296875}, {"start": 2521.39, "end": 2521.67, "word": " بعدين", "probability": 0.95703125}, {"start": 2521.67, "end": 2521.89, "word": " بنبدا", "probability": 0.5948079427083334}, {"start": 2521.89, "end": 2522.45, "word": " نفحصها", "probability": 0.9583984375}, {"start": 2522.45, "end": 2523.65, "word": " هل", "probability": 0.6982421875}, {"start": 2523.65, "end": 2523.77, "word": " ال", "probability": 0.95751953125}, {"start": 2523.77, "end": 2523.97, "word": " X", "probability": 0.4609375}, {"start": 2523.97, "end": 2525.07, "word": " تسويها؟", "probability": 0.7373779296875}, {"start": 2525.07, "end": 2525.39, "word": " والله", "probability": 0.7376708984375}, {"start": 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2923.34, "end": 2923.64, "word": " تعالى", "probability": 0.94482421875}, {"start": 2923.64, "end": 2924.14, "word": " بنبدأ", "probability": 0.93994140625}, {"start": 2924.14, "end": 2924.56, "word": " في", "probability": 0.90576171875}, {"start": 2924.56, "end": 2925.1, "word": " ال", "probability": 0.9560546875}, {"start": 2925.1, "end": 2925.68, "word": " counting", "probability": 0.9580078125}, {"start": 2925.68, "end": 2926.92, "word": " بمعنى", "probability": 0.9654296875}, {"start": 2926.92, "end": 2927.06, "word": " أن", "probability": 0.52783203125}, {"start": 2927.06, "end": 2927.34, "word": " احنا", "probability": 0.8219401041666666}, {"start": 2927.34, "end": 2927.84, "word": " بتذكرين", "probability": 0.829833984375}, {"start": 2927.84, "end": 2928.26, "word": " أخدنا", "probability": 0.967529296875}, {"start": 2928.26, "end": 2928.72, "word": " ال", "probability": 0.97314453125}, {"start": 2928.72, "end": 2929.56, "word": " numbers", "probability": 0.828125}, {"start": 2929.56, "end": 2930.72, "word": " و", "probability": 0.98046875}, {"start": 2930.72, "end": 2931.54, "word": " نظرية", "probability": 0.7587890625}, {"start": 2931.54, "end": 2932.12, "word": " الأعداد", "probability": 0.8942057291666666}, {"start": 2932.12, "end": 2932.8, "word": " و", "probability": 0.94970703125}, {"start": 2932.8, "end": 2933.32, "word": " ختمت", "probability": 0.9646809895833334}, {"start": 2933.32, "end": 2933.64, "word": " معانا", "probability": 0.8868815104166666}, {"start": 2933.64, "end": 2933.76, "word": " في", "probability": 0.95166015625}, {"start": 2933.76, "end": 2934.24, "word": " الآخر", "probability": 0.9661458333333334}, {"start": 2934.24, "end": 2935.06, "word": " لأكواد", "probability": 0.953125}, {"start": 2935.06, "end": 2935.36, "word": " و", "probability": 0.78955078125}, {"start": 2935.36, "end": 2936.22, "word": " لتشفير", "probability": 0.96640625}, {"start": 2936.22, "end": 2936.86, "word": " الآن", "probability": 0.542724609375}, {"start": 2936.86, "end": 2937.08, "word": " بدنا", "probability": 0.946533203125}, {"start": 2937.08, "end": 2937.3, "word": " نروح", "probability": 0.9938151041666666}, {"start": 2937.3, "end": 2937.8, "word": " للعد", "probability": 0.8115234375}, {"start": 2937.8, "end": 2938.34, "word": " كيف", "probability": 0.862060546875}, {"start": 2938.34, "end": 2938.44, "word": " أنا", "probability": 0.51123046875}, {"start": 2938.44, "end": 2938.78, "word": " بقدر", "probability": 0.9803059895833334}, {"start": 2938.78, "end": 2939.1, "word": " أعد", "probability": 0.879638671875}], "temperature": 1.0}, {"id": 121, "seek": 294491, "start": 2940.15, "end": 2944.91, "text": "ونشوف كيف وين بتوصلنا طرق العد بعد ذلك ياطيكوا ألف عافية ونشوفكوا المرة القادمة", "tokens": [11536, 8592, 38688, 9122, 33911, 4032, 9957, 39894, 2407, 36520, 8315, 23032, 2288, 4587, 18863, 3215, 39182, 29910, 23275, 7251, 41193, 1829, 4117, 14407, 5551, 46538, 6225, 31845, 10632, 4032, 1863, 8592, 38688, 4117, 14407, 9673, 25720, 25062, 18513, 46007], "avg_logprob": -0.25209604240045314, "compression_ratio": 1.4215686274509804, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2940.15, "end": 2940.73, "word": "ونشوف", "probability": 0.7431640625}, {"start": 2940.73, "end": 2940.99, "word": " كيف", "probability": 0.920654296875}, {"start": 2940.99, "end": 2941.15, "word": " وين", "probability": 0.64208984375}, {"start": 2941.15, "end": 2941.79, "word": " بتوصلنا", "probability": 0.67938232421875}, {"start": 2941.79, "end": 2942.07, "word": " طرق", "probability": 0.9296875}, {"start": 2942.07, "end": 2942.47, "word": " العد", "probability": 0.947998046875}, {"start": 2942.47, "end": 2943.13, "word": " بعد", "probability": 0.87451171875}, {"start": 2943.13, "end": 2943.37, "word": " ذلك", "probability": 0.9873046875}, {"start": 2943.37, "end": 2943.69, "word": " ياطيكوا", "probability": 0.588623046875}, {"start": 2943.69, "end": 2943.83, "word": " ألف", "probability": 0.796630859375}, {"start": 2943.83, "end": 2944.07, "word": " عافية", "probability": 0.892578125}, {"start": 2944.07, "end": 2944.43, "word": " ونشوفكوا", "probability": 0.8457845052083334}, {"start": 2944.43, "end": 2944.61, "word": " المرة", "probability": 0.8720703125}, {"start": 2944.61, "end": 2944.91, "word": " القادمة", "probability": 0.98486328125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2944.963625, "duration_after_vad": 2844.408124999989}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9b56161c4ffc93d87ba0ec7b5603fb6a56e87668
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/XjaPIh8Er30_raw.srt
@@ -0,0 +1,2520 @@
+1
+00:00:05,030 --> 00:00:07,790
+يعطيكوا العفو شباب، بارك الله فيكوا، اليوم نبدأ ان
+
+2
+00:00:07,790 --> 00:00:10,530
+شاء الله تعالى مع موضوع ال recursion بعد ما المرة
+
+3
+00:00:10,530 --> 00:00:13,430
+الماضية كنا أخدنا ال induction أو ال inductive
+
+4
+00:00:13,430 --> 00:00:16,050
+step بعد ما شوفنا ال business step و ال inductive
+
+5
+00:00:16,050 --> 00:00:21,890
+step و أخدنا عملية proving باستخدام ال inductive
+
+6
+00:00:21,890 --> 00:00:26,090
+stepمن ال inductive step ممكن تتدرج الأمور معانا
+
+7
+00:00:26,090 --> 00:00:28,990
+بحيث أن أحنا نروح لجزئية ال recursion أو ال
+
+8
+00:00:28,990 --> 00:00:33,370
+recursive codes بعديك الأكواد التكرارية و اللي قشت
+
+9
+00:00:33,370 --> 00:00:37,050
+بالأساس أساسا من عملية ال induction اللي أخدناها
+
+10
+00:00:37,050 --> 00:00:42,230
+المرة الماضية بحيث أن ال recursion هو بكل بساطة هو
+
+11
+00:00:42,230 --> 00:00:48,770
+general term لعملية تعريف ال object من نفسه تعريف
+
+12
+00:00:48,770 --> 00:00:53,490
+ال object من نفسه ولكن بنعرفه في هذا الزمن كأنه
+
+13
+00:00:53,490 --> 00:00:59,370
+function في نفسه في الزمن السابق أو في الحالة اللي
+
+14
+00:00:59,370 --> 00:01:01,930
+كانت قبله في الحالة اللي كانت قبله زي لما أقول أن
+
+15
+00:01:01,930 --> 00:01:05,950
+ال f of n هي function في f of n ناقص واحد طب f of
+
+16
+00:01:05,950 --> 00:01:10,100
+n ناقص واحد هي function في f of nنقص اتنين و هكذا
+
+17
+00:01:10,100 --> 00:01:16,180
+فإذا بيعرف من نفسه ببساطة جدا هذا ممكن نقول تعريف
+
+18
+00:01:16,180 --> 00:01:21,660
+recursion بشكل مختصر طيب زي إنه نقول P of N plus
+
+19
+00:01:21,660 --> 00:01:26,720
+واحد recursively in terms of P of N فهي معرفة
+
+20
+00:01:26,720 --> 00:01:30,880
+باللي قبلها معرفة بمين باللي قبلهاطبعا هذا
+
+21
+00:01:30,880 --> 00:01:34,480
+بنستخدمه ك recursive algorithms وهذه أهم شغله
+
+22
+00:01:34,480 --> 00:01:37,980
+ويمكن هي النقطة الأهم بالنسبالكم كمبرمجين أنكوا
+
+23
+00:01:37,980 --> 00:01:42,820
+تروحوا لجزئية ال algorithms بشكل recursively ممكن
+
+24
+00:01:42,820 --> 00:01:46,780
+تتكرر من نفسها بمعنى أن الكود يكرر نفسه وحناخد
+
+25
+00:01:46,780 --> 00:01:49,880
+أمثلة على بعض الأكواد خلال محاضرتنا ان شاء الله
+
+26
+00:01:49,880 --> 00:01:54,010
+تعالىطيب ال recursive definitions ال recursive
+
+27
+00:01:54,010 --> 00:01:57,150
+functions ال recursive sequences اللي هو ال
+
+28
+00:01:57,150 --> 00:01:59,570
+sequence نفسه كمان ممكن يكون recursive من نفسه
+
+29
+00:01:59,570 --> 00:02:03,730
+كويس and sets و ال sets كمان حتى ال set نفسها ممكن
+
+30
+00:02:03,730 --> 00:02:07,930
+تعرف من نفسها و برضه هناخدلها مثال هناخدلها مثال
+
+31
+00:02:07,930 --> 00:02:11,050
+فمعظمهم هدولة هنتكلم عنهم أثناء المحاضرة كأمثلة
+
+32
+00:02:11,050 --> 00:02:18,380
+واضحة لهم نبدأ مثلا ك functionrecursive للـ
+
+33
+00:02:18,380 --> 00:02:22,020
+function بكل بساطة بنقدر نقول أنه أبسط طريقة أني
+
+34
+00:02:22,020 --> 00:02:26,680
+أقول الله one way to define a function أقول if
+
+35
+00:02:26,680 --> 00:02:32,720
+from natural number to set ال natural number هادي
+
+36
+00:02:32,720 --> 00:02:38,300
+by default اللي هي إيش ال indexال index فعشان هيك
+
+37
+00:02:38,300 --> 00:02:40,660
+بنقول natural number ممكن ال index يبدأ معاك من
+
+38
+00:02:40,660 --> 00:02:47,340
+صفر نشيك a0 a1 a2 a3 and so on بتكمل طيب ال a
+
+39
+00:02:47,340 --> 00:02:53,040
+نفسها a1 و a2 و a3 و a4 و a5 هي العناصر تاعت ال
+
+40
+00:02:53,040 --> 00:02:56,660
+set فانت بتقول ال set عندنا في الحالة هذه هي
+
+41
+00:02:56,660 --> 00:03:00,480
+العناصر زي لما نقول عندنا الآن مجموعة الطلاب هدولة
+
+42
+00:03:00,480 --> 00:03:04,470
+هم ال setOkay هذه المجموعة خلاص تمام لما أجي بدي
+
+43
+00:03:04,470 --> 00:03:08,490
+أعرفهم أو أقيمهم أو بدي أجي أصنفهم بيصير الآن
+
+44
+00:03:08,490 --> 00:03:13,410
+التصنيف حسب إيش بمعنى مين اللي هياخد ال a 0 بدي
+
+45
+00:03:13,410 --> 00:03:17,090
+أفترض مش على الدرجة اللي بدي أفترض على الترتيب
+
+46
+00:03:17,090 --> 00:03:22,130
+الأبجد مثلا مش هيك معناته هنا بدي أقول مين ال a
+
+47
+00:03:22,130 --> 00:03:27,740
+node أو ال a صفرهو عنصر من عناصر الست أكيد فهو
+
+48
+00:03:27,740 --> 00:03:32,360
+ينتمي للست صحيح لكن بدنا نشوف مين اللي يحتل هذا
+
+49
+00:03:32,360 --> 00:03:37,470
+المكان حسبSorting معينة حسب ال sort اللي انا بدي
+
+50
+00:03:37,470 --> 00:03:40,830
+اتكلم عنه لو افترضنا ان هي بالارقام الجامعية او
+
+51
+00:03:40,830 --> 00:03:45,330
+بال .. بالأحرف الأبجادية او حسب ال grade حسب ..
+
+52
+00:03:45,330 --> 00:03:49,870
+فيها تصنيفات كتير .. فيها تصنيفات كتير فهنا هقول
+
+53
+00:03:49,870 --> 00:03:53,530
+في الحالة هذه من natural number to S اللي هي ال
+
+54
+00:03:53,530 --> 00:03:59,830
+set فإذا for any set S او بشكل series ممكن نقول A
+
+55
+00:03:59,830 --> 00:04:06,250
+N هي هال Nfrom N to F of N F of N مين هذا يطلع في
+
+56
+00:04:06,250 --> 00:04:12,300
+الآخر عنصر من الست فإذا من ال domainمن الـ
+
+57
+00:04:12,300 --> 00:04:17,000
+codomain ما هي domain to codomain صح؟ فده هي فإذا
+
+58
+00:04:17,000 --> 00:04:20,720
+تعريفها as a function بنقول الآن كالتالي عشان
+
+59
+00:04:20,720 --> 00:04:24,620
+نعرفها بشكل recursively بشكل recursively هقول بدنا
+
+60
+00:04:24,620 --> 00:04:29,180
+نعرف أول عنصر f of zero رجعنا لنفس ال induction
+
+61
+00:04:29,180 --> 00:04:33,900
+رجعنا لنفس ال induction طيب أما if أكبر من صفر
+
+62
+00:04:33,900 --> 00:04:41,000
+فبتعرف if of n in terms of if zero to n ناقص واحد
+
+63
+00:04:41,740 --> 00:04:48,340
+من F of 0 ل F of N ناقص واحد بمعنى تعرف بالعناصر
+
+64
+00:04:48,340 --> 00:04:53,440
+السابقة لها فكل عنصر يعرف بالعناصر بالعناصر
+
+65
+00:04:53,440 --> 00:04:57,520
+السابقة لل function بيصير اسمها recursively طيب
+
+66
+00:04:57,520 --> 00:05:02,040
+مثال لو قولنا A N تساوي او equivalent ل 2 to the
+
+67
+00:05:02,040 --> 00:05:07,560
+power N فهذا recursively كأني بقول A nodeابدأ بال
+
+68
+00:05:07,560 --> 00:05:10,480
+natural number حسب التعريف natural number من النار
+
+69
+00:05:10,480 --> 00:05:14,940
+بتبدا بصفر فإذا a note بتساوي واحد أكبر من هيك ايش
+
+70
+00:05:14,940 --> 00:05:22,970
+بتساوي بتساوي a ان ناقص واحد في اتنينالسابقة في
+
+71
+00:05:22,970 --> 00:05:25,450
+اتنين فأصبحت فعلا كأنها function في العنصر اللي
+
+72
+00:05:25,450 --> 00:05:28,710
+جابلها طب العنصر اللي جابلها برضه اتنين من العنصر
+
+73
+00:05:28,710 --> 00:05:32,690
+اللي جابله من N ناقص اتنين N ناقص اتنين هي اتنين
+
+74
+00:05:32,690 --> 00:05:35,790
+في العنصر اللي جابله N ناقص تلاتة and so on فإذا
+
+75
+00:05:35,790 --> 00:05:39,130
+لاحظوا أن هذه function بكل بساطة بنقدر نحطها بشكل
+
+76
+00:05:39,130 --> 00:05:44,090
+تكراري شكل تكراري أن كل عنصر نقدر نحسبه من العنصر
+
+77
+00:05:44,090 --> 00:05:48,490
+اللي جابله من العنصر اللي جابله مثال على ذلك نحله
+
+78
+00:05:48,490 --> 00:05:52,590
+مع بعض مثلا هذا مثال من الأمثلةوهنفترض إن أنا فعلا
+
+79
+00:05:52,590 --> 00:05:56,070
+بتعامل مع function f of n لكل العناصر n belonging
+
+80
+00:05:56,070 --> 00:06:01,770
+to natural number recursively ال f of 0 بتساوي 3
+
+81
+00:06:01,770 --> 00:06:07,470
+طيب ال inductive step كمعادلة بقدر أقول إن ال f of
+
+82
+00:06:07,470 --> 00:06:12,830
+n زائد 1 بتساوي 2 f of n زائد 3 فإذن بكل بساطة
+
+83
+00:06:12,830 --> 00:06:19,170
+بقدر أقول إن ال f 1 بتساوي كدهش؟
+
+84
+00:06:20,510 --> 00:06:24,510
+أيوة اللي هو جداش هي عندك كله تسعة هذه على طول
+
+85
+00:06:24,510 --> 00:06:30,090
+مباشرة نحل هي تسعة اتنين تمانتاش زي التلاتة واحد
+
+86
+00:06:30,090 --> 00:06:32,510
+وعشرين وواحد وعشرين في اتنين اتنين واربعين زي
+
+87
+00:06:32,510 --> 00:06:35,390
+التلاتة خمسة واربعين خمسة واربعين في اتنين تسعين
+
+88
+00:06:35,390 --> 00:06:40,030
+تسعين زي التلاتة تلاتة وتسعين and so on so on لاحظ
+
+89
+00:06:40,030 --> 00:06:44,330
+فإذا كل عنصر بجيبه من اللي جابله فانت لاحظ كل عنصر
+
+90
+00:06:44,330 --> 00:06:48,400
+واحنا بنحسبه ذكرنا العنصر اللي جابلهفإذا هذه
+
+91
+00:06:48,400 --> 00:06:55,040
+recursive form واضح جدا تمام recursive definition
+
+92
+00:06:55,040 --> 00:06:58,700
+لها factorial مثلا هاي واحدة من ال functions اللي
+
+93
+00:06:58,700 --> 00:07:04,320
+ممكن برضه نعرفها بشكل recursively أو recursive
+
+94
+00:07:04,320 --> 00:07:08,220
+form بكل بساطة كلنا عارفين ال F of N ال N
+
+95
+00:07:08,220 --> 00:07:11,960
+factorial هي عبارة عن multiplication لكل العناصر
+
+96
+00:07:11,960 --> 00:07:17,820
+من 1 ل Nواحد في اتنين في تلاتة في اربعة في N فكأني
+
+97
+00:07:17,820 --> 00:07:21,460
+بقول N factorial كأني بقول N factorial فإذا ال
+
+98
+00:07:21,460 --> 00:07:24,840
+index I من واحد to N و بكل بساطة بتقدر تبدأ من
+
+99
+00:07:24,840 --> 00:07:28,940
+اتنين لإن واحد مش هيكون كتير مؤثر انت بتضرب في
+
+100
+00:07:28,940 --> 00:07:33,220
+واحد فمش هيفرق كتير فابدأ باتنين مش مشكلة لكن ال
+
+101
+00:07:33,220 --> 00:07:37,520
+case تبعتك F of Zero هتكون واحد هتكون عبارة عن
+
+102
+00:07:37,520 --> 00:07:41,780
+واحد recursively بتقدر تقول F of واحد واحد طيب F
+
+103
+00:07:41,780 --> 00:07:49,490
+of اتنينF of واحد في قيمة الاتنين طيب F of تلاتة
+
+104
+00:07:49,490 --> 00:07:55,750
+هي نفس التلاتة في F of اتنين و هكذا فلاحظ كأنها
+
+105
+00:07:55,750 --> 00:08:00,690
+معرفة بقيمة العنصر اللي قبلها فلو قلنا F of أربعة
+
+106
+00:08:00,690 --> 00:08:06,850
+هتسوي الأربعة لاحظ في قيمة ال F of تلاتة اللي هي
+
+107
+00:08:06,850 --> 00:08:14,750
+الستة و هكذافكل عنصر بيعرف باللي قبله .. كل عنصر
+
+108
+00:08:14,750 --> 00:08:20,550
+بيعرف باللي قبله فهذا طبعا بتصير أسهل لك لما بدك
+
+109
+00:08:20,550 --> 00:08:24,090
+تشتغل على ال factorial و بدك تجيبله برنامج تحسبله
+
+110
+00:08:24,090 --> 00:08:29,710
+برنامج فبتصير من نفسها .. من نفسها طيب بعض ال easy
+
+111
+00:08:29,710 --> 00:08:32,670
+examples البسيطة جدا اللي ممكن نتعامل معها لما
+
+112
+00:08:32,670 --> 00:08:38,350
+بقول a, mA في N و كلا هما واحدة natural number
+
+113
+00:08:38,350 --> 00:08:42,410
+اللي هي ال N و real number لل A اللي هي مجرد ال
+
+114
+00:08:42,410 --> 00:08:45,330
+multiplier اللي بنضرب فيه ال multiplier لما بدي
+
+115
+00:08:45,330 --> 00:08:48,930
+أعرف طبعا أن هي المتغير بالمناسبة أن هي المتغير
+
+116
+00:08:48,930 --> 00:08:51,510
+مدام natural number معناته هي ال location احنا
+
+117
+00:08:51,510 --> 00:08:54,390
+عاطينهم في ال locations هدول كل عنصر المفروض انه
+
+118
+00:08:54,390 --> 00:08:57,630
+بقيمة العنصر اللي في ال question اللي جابله تمام
+
+119
+00:08:57,630 --> 00:09:05,980
+بقدر اقول انهفي n هي تساوي a في n ناقص واحد اللي
+
+120
+00:09:05,980 --> 00:09:12,200
+هي العنصر اللي جابله زائد a فهي ال term السابق
+
+121
+00:09:12,200 --> 00:09:19,600
+هنضفله a فإذا هنا معامل ال recursive factor تبعنا
+
+122
+00:09:19,600 --> 00:09:25,560
+هي زائد a فكل عنصر هو نفس السابق مع إضافة a عليه
+
+123
+00:09:26,710 --> 00:09:34,290
+فإذا لما بقول a زائد واحد هي نفسها an زائد a لأنك
+
+124
+00:09:34,290 --> 00:09:39,170
+بدك تاخد في الحالة هذه ال a common مشترك و هتجمع
+
+125
+00:09:39,170 --> 00:09:45,210
+هنا فطلعت ال n ن ناقص واحد و هنا زائد واحد و هتجمع
+
+126
+00:09:45,210 --> 00:09:45,410
+هنا فطلعت ال n ن ناقص واحد و هنا زائد واحد و هتجمع
+
+127
+00:09:45,410 --> 00:09:45,670
+هنا فطلعت ال n ن ناقص واحد و هنا زائد واحد و هتجمع
+
+128
+00:09:45,670 --> 00:09:45,690
+هنا فطلعت ال n ن ناقص واحد و هنا زائد واحد و هتجمع
+
+129
+00:09:45,690 --> 00:09:45,690
+هنا فطلعت ال n ن ناقص واحد و هنا زائد واحد و هتجمع
+
+130
+00:09:45,690 --> 00:09:47,570
+هنا فطلعت ال n ن ناقص واحد و هنا زائد واحد و هتجمع
+
+131
+00:09:47,570 --> 00:09:53,050
+هنا فطلعت ال n ن ناقص واحد و
+
+132
+00:09:53,220 --> 00:09:56,920
+درب a فانت كل مرة بتضرب في a كل مرة بتضرب في a
+
+133
+00:09:56,920 --> 00:10:04,360
+فمعامل التغيير او العلاقة بين a of n ك function في
+
+134
+00:10:04,360 --> 00:10:09,660
+n و a of n ناقص واحد اللي هي function في n ناقص
+
+135
+00:10:09,660 --> 00:10:14,040
+واحد الفرق بينهم هو ضرب في a بس فضربنا في a عشان
+
+136
+00:10:14,040 --> 00:10:18,000
+نحصل عليه فإذن واضحة جدا ان فعلا ال function في n
+
+137
+00:10:19,040 --> 00:10:22,260
+لاحظ؟ بقدر أجيبها بدلالة الـ function في N نقص
+
+138
+00:10:22,260 --> 00:10:26,380
+واحد اللي هي اللي جابلها .. اللي جابلها طيب ال
+
+139
+00:10:26,380 --> 00:10:29,640
+summation .. بسيطة ال summation بتتخيل صحيح؟ لما
+
+140
+00:10:29,640 --> 00:10:32,480
+أقول summation to N طب أنا عارف قيمة ال summation
+
+141
+00:10:32,480 --> 00:10:35,500
+to N نقص واحد مافيش داعي أعمل summation to N من
+
+142
+00:10:35,500 --> 00:10:39,200
+أول و جديد هي نفس ال summation ل N نقص واحد زائد
+
+143
+00:10:39,200 --> 00:10:43,180
+قيمة ال N و بس فإذا بجمع عليها قيمة N لحالها نجمع
+
+144
+00:10:43,180 --> 00:10:48,810
+قيمة N لحالها هي ال A N نفسها بسنفس الكلام ال
+
+145
+00:10:48,810 --> 00:10:54,290
+multiplication بضرب قيمة a of n فإذا إذا أنا عارف
+
+146
+00:10:54,290 --> 00:11:03,280
+لعند n ناقص واحد ل a of iهذه عرفها عرف قيمتها و
+
+147
+00:11:03,280 --> 00:11:07,720
+حسبها طب هو طالب مني ل n فإذا نفس القيمة اللي هنا
+
+148
+00:11:07,720 --> 00:11:13,020
+بضربها فقط في a n اللي هو العنصر الأخير اللي ضايل
+
+149
+00:11:13,020 --> 00:11:15,460
+و برضه هذه من الحاجات اللي احنا خدناها ك
+
+150
+00:11:15,460 --> 00:11:18,840
+manipulation لل summation لو متذكرين لما تكلمنا عن
+
+151
+00:11:18,840 --> 00:11:21,060
+ال summation حكينا في الجزء السابق طيب أشدر لإن
+
+152
+00:11:21,060 --> 00:11:24,780
+خلصنا .. لا ولا دايل لا الأخيرة ال .. ال
+
+153
+00:11:24,780 --> 00:11:32,390
+intersection لما تقول intersection لset I و ال I
+
+154
+00:11:32,390 --> 00:11:38,090
+هذه مجموعة sets from zero to N فإذا عندي N sets
+
+155
+00:11:38,090 --> 00:11:42,370
+بده أجيب التقاطع تبعهم N هذه خمسة معناته في عندي
+
+156
+00:11:42,370 --> 00:11:44,870
+خمس مجموعات بده أجيب تقاطع الخمس مجموعات مع بعض
+
+157
+00:11:44,870 --> 00:11:49,810
+طيب هذه كيف بقدر أعرفها بالسابق تبعها بقدر أقول
+
+158
+00:11:49,810 --> 00:11:54,470
+intersection كأنه أنا عند ال intersection من صفر ل
+
+159
+00:11:54,470 --> 00:12:01,950
+N ناقص واحدلـ S I صحيح؟ طب من هذا ال term بدي أجيب
+
+160
+00:12:01,950 --> 00:12:06,710
+ال intersection to
+
+161
+00:12:06,710 --> 00:12:15,610
+N ل S I فإذا هنا إيش كمان؟ تقاطع ما هي تقاطع زاد
+
+162
+00:12:15,610 --> 00:12:23,350
+إيش؟ ال N اللي ضايلة لأن الانصر الوحيد المفقود هي
+
+163
+00:12:23,350 --> 00:12:30,160
+عند ال N فإذا Sأو sit in هي اللي محتاج أضيفها
+
+164
+00:12:30,160 --> 00:12:35,960
+للتقاطع بس هي اللي محتاجين نضيفها ليش للتقاطع طبعا
+
+165
+00:12:35,960 --> 00:12:38,780
+الاتحاد نفس الشيء في الاتحاد نفس الشيء بيصير هنا
+
+166
+00:12:38,780 --> 00:12:44,870
+اتحاد مش أكتر طيب هد انتوا متذكرينها ال big arcالـ
+
+167
+00:12:44,870 --> 00:12:48,110
+Big Arc تذكرين أخدناها في آخر ما اتكلمنا عن الـ
+
+168
+00:12:48,110 --> 00:12:51,890
+Sets طيب فى Bonacci Series فى Bonacci Series برضه
+
+169
+00:12:51,890 --> 00:12:56,870
+واحدة من الأمثلة الواضحة لل Recursion ليش؟ لأن هو
+
+170
+00:12:56,870 --> 00:13:00,710
+كل عنصر في ال Series هذه هو معتمد على الإتنين اللي
+
+171
+00:13:00,710 --> 00:13:04,530
+جابله مش على واحد جابله فى Bonacci Series بكل
+
+172
+00:13:04,530 --> 00:13:10,150
+بساطة هي Series كل عنصر يساوي مجموع العنصرين اللي
+
+173
+00:13:10,150 --> 00:13:15,150
+جابلهببساطة يعني هذه هي ال series اللي بنتكلم عنها
+
+174
+00:13:15,150 --> 00:13:19,170
+فإذا إذا اتكلمنا عن عنصرين initially لازم أبدأ
+
+175
+00:13:19,170 --> 00:13:24,750
+فيهم معناته ال basis step هي مش قيمة واحدة لازم
+
+176
+00:13:24,750 --> 00:13:28,710
+يكونوا قيمتين عشان أقدر أكمل بادي ال series مدام
+
+177
+00:13:28,710 --> 00:13:32,190
+أنا بقول كل عنصر مجموع الإتنين اللي جابله معناته
+
+178
+00:13:32,190 --> 00:13:36,550
+محتاج اتنين في البداية كبداية محتاج اتنين فكبداية
+
+179
+00:13:36,550 --> 00:13:42,400
+هي صفر واحدخلاص هدول الوحيدين اللي بنعرفهم في
+
+180
+00:13:42,400 --> 00:13:45,240
+البداية و الباقي خلاص بيجي منهم الباقي كله بيجي
+
+181
+00:13:45,240 --> 00:13:53,380
+منهم ف 0 1 هدول ال initial او ال basis step اجمعهم
+
+182
+00:13:53,380 --> 00:13:59,350
+بطلع واحد طيب صار عندي واحد واحدأتنين طيب صار عند
+
+183
+00:13:59,350 --> 00:14:04,550
+اتنين و واحد تلاتة اتنين و تلاتة خمسة خمسة و تلاتة
+
+184
+00:14:04,550 --> 00:14:08,770
+تمانية خمسة و تمانية تلتاش تلتاش و تمانية واحد و
+
+185
+00:14:08,770 --> 00:14:13,810
+عشرين واحد و عشرين و تلتاش واستمر تستمر فالفبناتش
+
+186
+00:14:13,810 --> 00:14:20,070
+بتظل ماشية مستمرة تمام فإذا بتبدأ بصفر واحد و
+
+187
+00:14:20,070 --> 00:14:23,990
+بعدين تكتب المعادلة خلاص أما صفر واحد لابد تبدأ
+
+188
+00:14:23,990 --> 00:14:28,470
+فيهملو واحد منهم مش موجود مش هتقدر تكمل لإن كل
+
+189
+00:14:28,470 --> 00:14:33,910
+عنصر هيه كل عنصر f of n بشرط إنه n أكبر أو تساوي 2
+
+190
+00:14:33,910 --> 00:14:38,130
+هيكون عبارة عن f of n ناقص 1 زائد f of n ناقص 2
+
+191
+00:14:38,130 --> 00:14:41,570
+العنصرين اللي جابله عنصرين اللي جابله فهذه واضحة
+
+192
+00:14:41,570 --> 00:14:46,990
+جدا إن هي بتعتمد على ال recursive theory تماما
+
+193
+00:14:46,990 --> 00:14:52,830
+واضحةطيب بدنا من خلالها من خلال ال series هذه نثبت
+
+194
+00:14:52,830 --> 00:14:58,410
+إثبات إنه بالنسبة لفبناتش series دائما f of n أقل
+
+195
+00:14:58,410 --> 00:15:05,610
+من 2 to the power n بالإيش بال inductive step أو
+
+196
+00:15:05,610 --> 00:15:12,750
+induction proof بكل بساطة عندي basis case أو ال
+
+197
+00:15:12,750 --> 00:15:20,600
+basis step و لازم يكونوا 2 فإذا ببدأنوت تسوى صفر
+
+198
+00:15:20,600 --> 00:15:24,540
+هل الصفر فعلا أقل من اتنين to the power صفر حسب
+
+199
+00:15:24,540 --> 00:15:30,660
+التعريف مظبوط طيب واحد F واحد معناته ما وجدتش
+
+200
+00:15:30,660 --> 00:15:33,540
+قيمتها F واحد واحد لإن هاي الأول answer in صفر
+
+201
+00:15:33,540 --> 00:15:36,420
+واحد هل الواحد أقل من اتنين to the power واحد
+
+202
+00:15:36,420 --> 00:15:41,320
+مظبوط أقل منه طيب بعد ذلك بنروح لمين لل inductive
+
+203
+00:15:41,320 --> 00:15:44,220
+step وال inductive step كلنا عارفين يريدوني أفترض
+
+204
+00:15:44,220 --> 00:15:52,580
+أنه هنا مسمينا F F of N is trueوبال direct proof
+
+205
+00:15:52,580 --> 00:15:59,040
+بدنا نثبت منها ان f of n زائد واحد is true ولا لأ
+
+206
+00:15:59,040 --> 00:16:07,160
+فإذا هفترض فعلا ان f of n is true ايش يعني is
+
+207
+00:16:07,160 --> 00:16:13,720
+true؟معناه ان هي تحقق هذه ال rule اللي هم
+
+208
+00:16:17,270 --> 00:16:19,990
+صحيح، بدأ تعتمد على الإتنين في الحالة هذه، مظبوط،
+
+209
+00:16:19,990 --> 00:16:23,410
+ففي الحالة هذه، بدنا نفرض إنه إذا كانت فعلاً F of
+
+210
+00:16:23,410 --> 00:16:26,730
+N بس طبعاً recursively، إحنا عارفين إنه N هنا لن
+
+211
+00:16:26,730 --> 00:16:31,930
+تبدأ إلا من بعد الإتنينواضحت؟ فالشرطين اللي بتحكي
+
+212
+00:16:31,930 --> 00:16:35,530
+عنهم هدولة احنا غطيناهم في ال business step بعد
+
+213
+00:16:35,530 --> 00:16:39,030
+هيك لأ خلاص مادام ال business step تحققت بعد هيك
+
+214
+00:16:39,030 --> 00:16:43,150
+بنشتغل على انت يعني اللي انت قلته هو فتحلنا موضوع
+
+215
+00:16:43,150 --> 00:16:47,990
+مهم ان احنا هنشتغل على ال first principle هنشتغل
+
+216
+00:16:47,990 --> 00:16:53,470
+على ال second principle بمعنى بدنا نثبت ان if
+
+217
+00:16:57,090 --> 00:17:04,450
+و خلّينا نسميها K مثلا is true بشرط انه K from
+
+218
+00:17:04,450 --> 00:17:11,440
+اتنين اتنين المفروض صحيح من اتنين لقيمة Nis it
+
+219
+00:17:11,440 --> 00:17:15,260
+true فهذه ال strong proof strong اه ال strong
+
+220
+00:17:15,260 --> 00:17:18,260
+proof سميناها اللي هو ال second principle آخر جزء
+
+221
+00:17:18,260 --> 00:17:22,360
+أخدناه المرة الماضية صحيح كويس انت نبحتنا عشان
+
+222
+00:17:22,360 --> 00:17:28,140
+الكل ينتبه فيها تمام منها بدنا نثبت ان n زائد واحد
+
+223
+00:17:28,140 --> 00:17:33,240
+برضه is it true برضه ايش is it true جيد فإذن بكل
+
+224
+00:17:33,240 --> 00:17:39,920
+بساطة بقدرقول ان if n تساوي if n ناقص واحد زائد
+
+225
+00:17:40,860 --> 00:17:47,800
+ناقص اتنين هذه اكيد صحيح طيب بكل بساطة بتقدر تقول
+
+226
+00:17:47,800 --> 00:17:53,380
+هذه صحيحة مش shake احنا قلنا بدنا نقول ان هذه is
+
+227
+00:17:53,380 --> 00:17:59,640
+true فإذا لازم تكون اكبر من اتنين
+
+228
+00:17:59,640 --> 00:18:07,160
+to the power ناقص واحد to اتنين if ناقص اتنين
+
+229
+00:18:11,040 --> 00:18:16,480
+صحيح؟ ليش؟ لأنه ببساطة هذه برضه is true حسب ال K
+
+230
+00:18:16,480 --> 00:18:21,560
+اللي هي من 2 to N طب ما هذه في نفس ال range فإذا
+
+231
+00:18:21,560 --> 00:18:25,780
+أنا true ال true يعني بقدر أستعيد عنها ب2 to the
+
+232
+00:18:25,780 --> 00:18:33,740
+power n ناقص 1 حسب ال theorem إن هي true و نفس
+
+233
+00:18:33,740 --> 00:18:38,660
+الكلامإن ناقص اتنين بقدر برضه أستعيد عنها بتنين إن
+
+234
+00:18:38,660 --> 00:18:41,240
+ناقص اتنين اتنين to the power إن ناقص اتنين
+
+235
+00:18:41,240 --> 00:18:47,980
+فحطناهم ممتاز الآن التنتين هدولة بكل بساطة بتقدر
+
+236
+00:18:47,980 --> 00:18:53,160
+اللي هنتغيرهم بحيث إنك تقول هذا ال term هيكون أكيد
+
+237
+00:18:53,160 --> 00:19:01,440
+أقل من اتنين to the power إن ناقص واحد صح أكيد ليش
+
+238
+00:19:01,440 --> 00:19:07,470
+لأن كلنا عارفين فبناتشة تسعوديةيعني كل عنصر أكيد
+
+239
+00:19:07,470 --> 00:19:12,410
+أكبر من اللي جابله أكيد أكبر من اللي جابله معناه
+
+240
+00:19:12,410 --> 00:19:15,950
+ذلك إذا كان استعبنا عن هذا ال term بتنين to the
+
+241
+00:19:15,950 --> 00:19:22,190
+power n ناقص واحد هل هتتغير اتجاه الأكبر من .. لأ
+
+242
+00:19:22,190 --> 00:19:26,470
+مش هيتغير فحتبال دايما if of n أقل من هذا ال term
+
+243
+00:19:26,470 --> 00:19:32,030
+بالعكس حتى هتقل بزيادة كمان فهنا تصبح اتنين if
+
+244
+00:19:32,030 --> 00:19:36,930
+ناقص واحدلأ F of N اجمع الاتنين مع بعض كأنك أخدت
+
+245
+00:19:36,930 --> 00:19:42,830
+اتنين عامل مشترك فبتصير كأنه اتنين مضروبة في هذا
+
+246
+00:19:42,830 --> 00:19:46,550
+ال term اجمع فوق فبتصبح اقل من اتنين to the power
+
+247
+00:19:46,550 --> 00:19:46,810
+N
+
+248
+00:19:53,450 --> 00:19:57,770
+نحظت كيف ف if of n اللي انا بدي اثبتها بمعلومة
+
+249
+00:19:57,770 --> 00:20:01,730
+اللي جابلها على اعتبار ان اللي جابلها اكيد true
+
+250
+00:20:01,730 --> 00:20:07,310
+اكيد true ففي الحالة هذه true فبنستعيد عنها عفوا
+
+251
+00:20:07,310 --> 00:20:10,530
+هذه true بنستعيد عنها بالاتنين to the power n نقص
+
+252
+00:20:10,530 --> 00:20:13,610
+واحد بالمناسبة هذا الكلام ينطبق ان هنا مايكونش
+
+253
+00:20:13,610 --> 00:20:19,450
+لايساوي اقل من بس يعني اقل من فقط ليش لأن احنا
+
+254
+00:20:19,450 --> 00:20:22,150
+ماشتغلناش على n زائد واحد اشتغلنا على n نفسها
+
+255
+00:20:24,060 --> 00:20:29,620
+لاحظته؟ اشتغلنا على N نفسها فإذا بتصير لعند N نقص
+
+256
+00:20:29,620 --> 00:20:35,720
+واحد فعليا بدون أو يساوي تمام فهي أثبتناها برضه
+
+257
+00:20:35,720 --> 00:20:38,940
+بال inductive step أو ال proof اللي أخدنا المرة
+
+258
+00:20:38,940 --> 00:20:45,710
+الماضية طيب في كمان شغلةواضحة جدا فيها جزئية الـ
+
+259
+00:20:45,710 --> 00:20:50,250
+Recursion وهي الـ Euclide algorithm اللي أخدناها
+
+260
+00:20:50,250 --> 00:20:52,250
+المرة الماضية لما كنا بدنا نجيب ال greatest common
+
+261
+00:20:52,250 --> 00:20:56,530
+divisor ليش؟ لأنه لو متذكرين هتنسترجع شوية كنت
+
+262
+00:20:56,530 --> 00:21:00,010
+بقول أن ال greatest common divisor بقدر أجيبها ل A
+
+263
+00:21:00,010 --> 00:21:05,350
+و Bكأنها هي نفس ال greatest common divisor ل B مع
+
+264
+00:21:05,350 --> 00:21:12,150
+A modulo B طب كويس طب A modulo B مع B هي نفسها ك
+
+265
+00:21:12,150 --> 00:21:15,780
+greatest common divisor من برجع بعيد نفسأيوة .. أه
+
+266
+00:21:15,780 --> 00:21:18,720
+لاحظ .. بعيد .. بعيد معناته هي recursion خلاص
+
+267
+00:21:18,720 --> 00:21:22,880
+واضحة recursion طالع إن لاميه واحد اسمه لاميه
+
+268
+00:21:22,880 --> 00:21:27,000
+وبرضه واضح نصف فرنساوي فلاميز هذا عمل أو لاميه عمل
+
+269
+00:21:27,000 --> 00:21:30,300
+نظري يسميها لاميز theorem لاميز theorem بده يقول
+
+270
+00:21:30,300 --> 00:21:35,520
+بالنسبة ل greatest common divisor ل A و B أكم مرة
+
+271
+00:21:35,520 --> 00:21:41,200
+عدد مرات تكرارها طبعا هو يعني بده يجيب كأنه ال
+
+272
+00:21:41,200 --> 00:21:44,420
+complexity بتاعتهاالكمplexity بتاع التنقل كان مرة
+
+273
+00:21:44,420 --> 00:21:49,760
+هتتكرر مش احنا عرفنا سابقا انه مرات التكرار في
+
+274
+00:21:49,760 --> 00:21:53,880
+الآخر تمثل الكمplexity، الكمplexity بالظبط طيب إجا
+
+275
+00:21:53,880 --> 00:21:58,960
+جالنا إذا كان والله A وB هما ال two numbers اللي
+
+276
+00:21:58,960 --> 00:22:00,440
+أنا بدي أجيب ل greatest common divisor between
+
+277
+00:22:00,440 --> 00:22:06,380
+them وإيه هي الأكبر فإذا بقدر أقول أنه باستخدام
+
+278
+00:22:06,380 --> 00:22:10,410
+Duclid's algorithmالـ greatest common divisor
+
+279
+00:22:10,410 --> 00:22:16,170
+هنعمل أكم step منها أقل من أو يسوى بحد أقصى خمسة K
+
+280
+00:22:16,170 --> 00:22:25,030
+بشرط أن K هي عدد ال decimal digits للرقم الأصغر هو
+
+281
+00:22:25,030 --> 00:22:30,210
+عبّر عنها رياضيا اللي هو يعني بمعنى لو كان عند 121
+
+282
+00:22:30,210 --> 00:22:35,310
+و 96 الأقل منهم two digits number فK باتنين
+
+283
+00:22:38,280 --> 00:22:41,180
+لكن هو عبّر عنها رياضيا عشان يكتبها رياضا فقال
+
+284
+00:22:41,180 --> 00:22:50,120
+floor لمن ل log base 10 ل B فهيها طيب هذه لما نجيب
+
+285
+00:22:50,120 --> 00:22:58,800
+لها log base 10 بتطلع واحد وكسر زائد الواحد اتنين
+
+286
+00:22:58,800 --> 00:23:05,310
+خلاص طيب لو بدنا نحسبها لهذه2 مكسر ف ال floor 2
+
+287
+00:23:05,310 --> 00:23:08,130
+زائد 1 ثلاثة ماكان الأول ثلاثة three digits خلاص
+
+288
+00:23:08,130 --> 00:23:13,210
+مكان الأساس ال three digits فبكل بساطة هو في الآخر
+
+289
+00:23:13,210 --> 00:23:16,190
+يعني علقنا عليها كتبنا ان هي في الآخر هي number of
+
+290
+00:23:16,190 --> 00:23:19,950
+decimal digits لا بيه خلاص يعني احنا ليش مغالبين
+
+291
+00:23:19,950 --> 00:23:24,150
+حالنا لكن في الآخر لو جيتل طلعت عليها برضه فاطفاضة
+
+292
+00:23:24,150 --> 00:23:28,560
+كتيريعني خمسة من الأتنين اللي بتتكلم عن عشرة ..
+
+293
+00:23:28,560 --> 00:23:32,960
+عشرة steps يعني اللي لو انتوا .. لو هذا عبارة عن
+
+294
+00:23:32,960 --> 00:23:36,760
+loop انت متوقع انه مايزدش عن عشرة بحيث انه لو زاد
+
+295
+00:23:36,760 --> 00:23:42,140
+عن عشرة في مشكلة في البرنامج لو زاد عن عشرة معناته
+
+296
+00:23:42,140 --> 00:23:45,160
+في مشكلة في البرنامج خد بالك احنا أعطيناك هنا الحد
+
+297
+00:23:45,160 --> 00:23:50,240
+الأقصى لعدد ال iterations أو ال recursion steps
+
+298
+00:23:51,000 --> 00:23:54,060
+زادت عن هيك لأ خد بالك يمكن في مشكلة واضح انه في
+
+299
+00:23:54,060 --> 00:23:58,660
+مشكلة طيب ففي الحالة هذه اليقليد algorithm بنقدر
+
+300
+00:23:58,660 --> 00:24:02,700
+نقول عنه linear لأن هو خطي مع عدد ال decimal كل ما
+
+301
+00:24:02,700 --> 00:24:06,720
+زادت ال decimal بالنسبالنا كل ما بتزيد عدد ال
+
+302
+00:24:06,720 --> 00:24:11,120
+steps كل ما بتزيد one decimal بزيد مقابلها خمسة في
+
+303
+00:24:11,120 --> 00:24:16,020
+ال times خمسة في ال time او في ال execution time
+
+304
+00:24:16,020 --> 00:24:21,470
+فعلياطيب ال recursive لها ال sets لما نتكلم عن ال
+
+305
+00:24:21,470 --> 00:24:25,190
+sets برضه نفس الكلام رغم ان ال set في النهاية هي
+
+306
+00:24:25,190 --> 00:24:31,130
+unordered set هي مش مرتبة لكن برضه نقدر نعرفها أو
+
+307
+00:24:31,130 --> 00:24:35,390
+نعرف عناصرها من عناصرهانقدر نعرف عناصرها من
+
+308
+00:24:35,390 --> 00:24:41,470
+عناصرها زي بكل بساطة ناخد مثلا ل a set اي set ممكن
+
+309
+00:24:41,470 --> 00:24:45,890
+اعرف مجموعة elements واحد او اتنين او تلاتة بحيث
+
+310
+00:24:45,890 --> 00:24:49,510
+ان هما يكون في بينهم relation بينهم وبين ال other
+
+311
+00:24:49,510 --> 00:24:53,860
+numbers relation و بعرف ال relation بسإذا كانت ال
+
+312
+00:24:53,860 --> 00:24:56,600
+set كبيرة إذا كانت ال set عندي كبيرة و احنا
+
+313
+00:24:56,600 --> 00:24:59,880
+اتكلمنا إنه في عندي infinite sets في بعض ال sets
+
+314
+00:24:59,880 --> 00:25:03,640
+infinite بتبقى infinity فإذا مش من المناسب أني
+
+315
+00:25:03,640 --> 00:25:08,160
+أقول أكتبها كاملة فممكن أحط أول عنصرين تلاتة بس
+
+316
+00:25:08,160 --> 00:25:12,680
+المهم اللي هم يكونوا ال common اللي بقدر أعمل
+
+317
+00:25:12,680 --> 00:25:17,350
+generation لأي element منهم زيفهد .. طبعا احنا
+
+318
+00:25:17,350 --> 00:25:20,330
+كلنا مقتنعين بهذا الكلام ان في عندي small finite
+
+319
+00:25:20,330 --> 00:25:24,210
+بعرف أكمن element فقط في البداية عساس ان هدولة ال
+
+320
+00:25:24,210 --> 00:25:27,830
+base elements بتصير اسمهم زي ال base step هدولة ال
+
+321
+00:25:27,830 --> 00:25:32,250
+base element وبيكون لازم يكون في عندي rule ل ال
+
+322
+00:25:32,250 --> 00:25:35,690
+constructing for other elements لازم يكون فيه rule
+
+323
+00:25:35,690 --> 00:25:40,230
+وإلا كيف بدي أعرف باقي العناصر؟باجي العناصر لازم
+
+324
+00:25:40,230 --> 00:25:44,050
+تكون معرفة، معرفة بس مش معرفة كأرقام، معرفة ب
+
+325
+00:25:44,050 --> 00:25:53,770
+formula، بمعادلة، ب model أو rule مثلًا خلّيني
+
+326
+00:25:53,770 --> 00:25:59,490
+أفترض إن في عندي تلاتة
+
+327
+00:25:59,490 --> 00:26:07,560
+تمتم لست Sو جلنا ان كل العناصر تحقق هذه المعادلة
+
+328
+00:26:07,560 --> 00:26:15,400
+لان X زائد Y هي برضه تنتمي لايش ل S و X و Y هي
+
+329
+00:26:15,400 --> 00:26:20,420
+عناصر من X من S كل واحدة منهم عناصر من S فكل
+
+330
+00:26:20,420 --> 00:26:26,720
+عنصرين هم ضمن الست مجموحهم لازم يكون ضمن الست كل
+
+331
+00:26:26,720 --> 00:26:31,010
+عنصرين ضمن الست مجموحهم برضه ضمن الستطيب قص على
+
+332
+00:26:31,010 --> 00:26:35,330
+ذلك هتلاقي أن هي لانهائية بتصير هتصبح لانهائية بكل
+
+333
+00:26:35,330 --> 00:26:38,910
+بساطة تلاتة هي تنتمي لل set معناه ذلك أنه تلاتة و
+
+334
+00:26:38,910 --> 00:26:42,730
+تلاتة تلاتة مع نفسها ليش؟ لأنه في ال unordered
+
+335
+00:26:42,730 --> 00:26:48,910
+ممكن يكون فيه تكرار صحيح؟ بمعنى لما نقول ليه set
+
+336
+00:26:48,910 --> 00:26:54,150
+of تلاتة أنا عارف أن هو نفسها هذه ما يمكافئ لتلاتة
+
+337
+00:26:54,150 --> 00:26:54,730
+و تلاتة
+
+338
+00:26:57,500 --> 00:27:01,240
+فإذن هذه انا اصلا هيكي بختزلها بتلاتة و اسكت بس
+
+339
+00:27:01,240 --> 00:27:04,340
+انا عارف انه ممكن يكون فيها تكرار و رغم ذلك بحسمه
+
+340
+00:27:04,340 --> 00:27:08,820
+مرة واحدة فإذا تلاتة و تلاتة صار ستة صار عندي
+
+341
+00:27:08,820 --> 00:27:15,090
+تلاتة و ستة طيب تلاتة و ستةتسعة أو الستة مع الستة
+
+342
+00:27:15,090 --> 00:27:18,510
+هي اتناش اه اجت الاتناش اتناش مع التلاتة و اتناش
+
+343
+00:27:18,510 --> 00:27:20,850
+مع الستة و التسعة مع الستة و التسعة مع التلاتة
+
+344
+00:27:20,850 --> 00:27:26,010
+صارت تعرف تطلع مضاعفات التلاتة فبتلاقيها مضاعفات
+
+345
+00:27:26,010 --> 00:27:30,830
+التلاتة بشكل infinite set infinite set فبكل بساطة
+
+346
+00:27:30,830 --> 00:27:36,210
+ممكن تعرف تلاتة belong to us و x زائد y belong to
+
+347
+00:27:36,210 --> 00:27:43,640
+us إذا x و y belong to us belong to usفهيك عرفنا
+
+348
+00:27:43,640 --> 00:27:48,380
+ال set بشكل recursive طيب نبدأ فى شوية أكواد أكواد
+
+349
+00:27:48,380 --> 00:27:52,180
+معتمدة احنا بعضها أخدناها بس بدنا نحاول اننا
+
+350
+00:27:52,180 --> 00:27:57,160
+نختزلوا بشكل recursion model بشكل recursion model
+
+351
+00:27:57,160 --> 00:28:02,280
+هفترض ان الأول ايش بدنا نحسب بدنا نحسب هنا ال
+
+352
+00:28:02,280 --> 00:28:08,860
+power ف example ال power طوى
+
+353
+00:28:08,860 --> 00:28:10,120
+كتبناها ال power بالمناسبة
+
+354
+00:28:18,800 --> 00:28:25,540
+لما قلنا a to the power n بتساوي a to the power n
+
+355
+00:28:25,540 --> 00:28:35,140
+ناقص واحد في a خلاص معناه ذا recursively أنا هضرب
+
+356
+00:28:35,140 --> 00:28:39,920
+بس كل مرة في a recursively كل مرة هضرب في a المثال
+
+357
+00:28:39,920 --> 00:28:44,690
+حاسير كان التاليالبروسيجر باور هنا احددنا ان انا
+
+358
+00:28:44,690 --> 00:28:48,110
+فيه code بدي اكتب فيه code البروسيجر باور اسمه
+
+359
+00:28:48,110 --> 00:28:51,950
+باور ايه و ايه دي لا تسوى صفر لانه مالهاش معنى
+
+360
+00:28:51,950 --> 00:28:54,810
+احطها بتسوى صفر معناته تبقى باور ايش هيكون واحد و
+
+361
+00:28:54,810 --> 00:28:59,130
+خلاص ايه عفوا انا هتظل صفر هتظل دائما صفر مالهاش
+
+362
+00:28:59,130 --> 00:29:04,690
+قيمة طيب هذه العبارة ال a عبارة عن real number و
+
+363
+00:29:04,690 --> 00:29:09,400
+ال nnatural number لأن ال power بدو يكون integer
+
+364
+00:29:09,400 --> 00:29:13,260
+كويس إذا كانت ال n اللي هي ال power اللي فوق
+
+365
+00:29:13,260 --> 00:29:18,480
+بتساوي صفر إيش return بإيش؟ بواحد أي حاجة تدور ال
+
+366
+00:29:18,480 --> 00:29:22,420
+power صفر بدو يرجع بواحد طب otherwise لأ أنا
+
+367
+00:29:22,420 --> 00:29:26,580
+مابدأتش لسه بدري عليها بدأت بإيه تدور ال power
+
+368
+00:29:26,580 --> 00:29:30,460
+اتنين مثلا معناته لأ لا تساوي صفر في الحالة دي
+
+369
+00:29:30,460 --> 00:29:42,820
+else return إيههيها ال A هى دى فى مين فى power
+
+370
+00:29:42,820 --> 00:29:46,840
+برضه كمان مرة بمعنى اعمل method و افتح code كمان
+
+371
+00:29:46,840 --> 00:29:56,800
+مرة بسمررله ال A وإن ناقص واحد اه
+
+372
+00:29:56,800 --> 00:30:01,840
+يه انضربناهم في بعضممتاز عشان نجي نفتح هذا ال term
+
+373
+00:30:01,840 --> 00:30:06,460
+هذا ال method وهذا لسه شغالة موجودة فاضية جاعدة
+
+374
+00:30:06,460 --> 00:30:10,680
+لسه ماعملتش فيها إشي كويس بحيث أنه أنا ال a لسه
+
+375
+00:30:10,680 --> 00:30:14,480
+بتستنى الناتج ال a واقفة هنا بتستنى الناتج تمام
+
+376
+00:30:14,480 --> 00:30:19,340
+الناتج هذا برضه نفس القصة هفتح من أول و جديد هنا
+
+377
+00:30:19,340 --> 00:30:25,720
+بس هنا أصبحت ب n ناقص واحد هل ال n ناقص واحد تساوي
+
+378
+00:30:25,720 --> 00:30:26,060
+صفر
+
+379
+00:30:29,320 --> 00:30:35,740
+هتساوي واحد معناه ذلك انه لأ هيجي ل else روحلي
+
+380
+00:30:35,740 --> 00:30:40,540
+افتحلي a كمان مرة اضرب a كمان مرة فهيصار عندي a في
+
+381
+00:30:40,540 --> 00:30:48,700
+a total a في a و صفر و بور الصفر a في a وراح بور
+
+382
+00:30:48,700 --> 00:30:54,640
+الصفر طيب بور الصفر هنا أصبحت zero فمررلي zero
+
+383
+00:30:54,640 --> 00:31:01,930
+لالميثود التالت حتى الآنصفر لأ then اه then return
+
+384
+00:31:01,930 --> 00:31:07,870
+واحد فبرجع بواحد طيب لاحظ كيف رجع بواحد الواحد هذا
+
+385
+00:31:07,870 --> 00:31:13,090
+جابه من ال method رقم تلاتة خلص سكر ال method رقم
+
+386
+00:31:13,090 --> 00:31:16,210
+تلاتة و نهاها و رجع ل method رقم اتنين ال method
+
+387
+00:31:16,210 --> 00:31:21,210
+رقم اتنين الناتج بده يضربه في ايه؟ و سكر method
+
+388
+00:31:21,210 --> 00:31:27,990
+رقم اتنينفرجعلنا ب A ضربهم رجع لل method رقم صفر
+
+389
+00:31:27,990 --> 00:31:31,970
+الأولى رقم واحد أول واحدة عشان الناتج اللى رجع فيه
+
+390
+00:31:31,970 --> 00:31:37,970
+يضربه في A فرجعلنا A تربيع رجعلنا بمين ب A تربيع
+
+391
+00:31:37,970 --> 00:31:47,010
+فعملها بشكل recursive method او recursive code انا
+
+392
+00:31:47,010 --> 00:31:49,490
+اتوقع انه مرت عليكوا هذه قبل هيكوا واشتغلت عليها
+
+393
+00:31:54,230 --> 00:31:59,050
+كمان مثل على اليوكليد احنا أخدنا اليوكليد و لماه
+
+394
+00:31:59,050 --> 00:32:03,530
+طالع لنا و جالنا فيه إلها الوثيوريم و تلاتة أو
+
+395
+00:32:03,530 --> 00:32:06,930
+خمسة كيو و ماخمسة كيو و بدنا نستطيع خلاص خلينا
+
+396
+00:32:06,930 --> 00:32:09,650
+نكتب لها code بالمرة نكتب لنا code إلها ف
+
+397
+00:32:09,650 --> 00:32:14,790
+procedure ل grade is common divisor B و A و لحظوا
+
+398
+00:32:14,790 --> 00:32:20,390
+B و A ترتيبها كيف نحط مهم جدا الترتيب لما بتستخدم
+
+399
+00:32:20,390 --> 00:32:24,300
+المثل دهالمفروض ان انتوا عادي ماجولكمش عليها انتوا
+
+400
+00:32:24,300 --> 00:32:27,840
+عارفينها لحالكوا ترتيب ال arguments او ال input
+
+401
+00:32:27,840 --> 00:32:32,080
+arguments كتير مهم في البرمجة كتير مهم ماتروحش
+
+402
+00:32:32,080 --> 00:32:36,980
+تحطهم a و b و بعدين تعمل أثناء ال steps تعمل
+
+403
+00:32:36,980 --> 00:32:44,520
+method و انت مرتب اللي عملتله pass له a و b بدل b
+
+404
+00:32:44,520 --> 00:32:48,980
+و a أكيد هتطلع نتائج كلها غلط في غلط و هتضلك تجري
+
+405
+00:32:48,980 --> 00:32:54,000
+وراالـ Logic Error أو يمكن .. ما بتعرفش يمكن تصدف
+
+406
+00:32:54,000 --> 00:32:58,300
+بعض الأحيان Run Error أو Run Time Error أه ممكن
+
+407
+00:32:58,300 --> 00:33:00,640
+يطلع Run Time Error ليش؟ لأن ال condition اللي
+
+408
+00:33:00,640 --> 00:33:05,420
+بيوقف عمره ما هيتحقق يعني عمرك ما هتصل لل return
+
+409
+00:33:05,420 --> 00:33:10,400
+النهائية اللي اتوقف عندها فاخدوا بالكوا جدا من
+
+410
+00:33:10,400 --> 00:33:15,400
+جزئية الـ من جاب المن في عملية ال passing فهنا بي
+
+411
+00:33:15,400 --> 00:33:20,720
+و ايه؟ يعني من الأصغر لأكبرمن الأصغر فالأكبر فانا
+
+412
+00:33:20,720 --> 00:33:25,420
+عارف أني بمرر الرقم الصغير في الأول طيب فهمناها؟
+
+413
+00:33:25,420 --> 00:33:29,400
+خلاص تمام إذا كانت ال B اللي هو الرقم الصغير اللي
+
+414
+00:33:29,400 --> 00:33:35,560
+هو جاي في الأول صفر خلاص ارجعلي بال A لأنه ال A في
+
+415
+00:33:35,560 --> 00:33:38,610
+الحالة ده هو ال commonالـ greatest common divisor
+
+416
+00:33:38,610 --> 00:33:42,810
+صح هذا اللي يقولي اتجلنا هيك تمام إذا ماوصلناش لسه
+
+417
+00:33:42,810 --> 00:33:47,110
+للصفر return برضه ارجع افتح كمان برنامج كمان مرة
+
+418
+00:33:47,110 --> 00:33:52,090
+الكود ارجع عيده كمان مرة ك method و مررله A modulo
+
+419
+00:33:52,090 --> 00:33:57,950
+B فانا دعم ان ال term اللي هنا هو الأصغر صح أكيد
+
+420
+00:33:57,950 --> 00:34:02,890
+هو الأصغر فهيتمرر كأنه الرقم الأصغر وال B هتصبح هي
+
+421
+00:34:02,890 --> 00:34:08,580
+الأكبر فعلياالـ B فعلا هتكون هي الأكبر لأن ناتج ال
+
+422
+00:34:08,580 --> 00:34:13,620
+module لـ B أكيد هتكون أصغر من B أكيد و حتما هتكون
+
+423
+00:34:13,620 --> 00:34:17,780
+أصغر من B تمام فإذا ال code بكل بساطة هي كله سطرين
+
+424
+00:34:17,780 --> 00:34:23,280
+.. كله سطرين على بعض عشان تحسب ال greatest common
+
+425
+00:34:23,280 --> 00:34:23,980
+divisor
+
+426
+00:34:26,940 --> 00:34:31,500
+Okay بتحيل؟ Okay بدنا نتكلم عن هنا جزئية ال space
+
+427
+00:34:31,500 --> 00:34:36,800
+أنه أحيانا إذا كان ال compiler تبعك مش smart
+
+428
+00:34:36,800 --> 00:34:40,140
+enough طبعا معظم الآن ال compilers يلاقي smart
+
+429
+00:34:40,140 --> 00:34:44,000
+enough أنه بيقدر يخزنلك على جد النتائج و يسكر ال
+
+430
+00:34:44,000 --> 00:34:47,770
+methodبسكّر المثل بيخلّي فقط قيمة النتائج بتاعتها
+
+431
+00:34:47,770 --> 00:34:50,510
+عشان يوفّر على حاله فتح برامج لإن هو دي بالنسبالك
+
+432
+00:34:50,510 --> 00:34:53,210
+أنت برنامج مفتوح برنامج مفتوح برنامج مفتوح إذا كان
+
+433
+00:34:53,210 --> 00:34:57,440
+ال compiler نسبيا قديم هيجع في الفخ هذاهتلاقي
+
+434
+00:34:57,440 --> 00:35:01,360
+بيفتح البرنامج و هتعمله من جوا method فهيرجع يفتح
+
+435
+00:35:01,360 --> 00:35:05,300
+كمان مرة البرنامج في space تانية و بعدين يفتح كمان
+
+436
+00:35:05,300 --> 00:35:08,320
+مرة في space تالتة على نفس المساحة او ال work
+
+437
+00:35:08,320 --> 00:35:10,780
+space اللي انت شغال عليه فال work space ايش بده
+
+438
+00:35:10,780 --> 00:35:15,160
+يصير فيه؟ بده يتعبى، بده يتعبى هذا ال compilers
+
+439
+00:35:15,160 --> 00:35:19,240
+القديمة، اذا كان ال compiler smart enough الحديث
+
+440
+00:35:19,240 --> 00:35:22,900
+معظمه، لهو بياخد النتائج و بيخلي النتائج عنده، اما
+
+441
+00:35:22,900 --> 00:35:25,960
+ما بيخلي البرنامج كله مفتوحبشوف إيش النتائج اللي
+
+442
+00:35:25,960 --> 00:35:31,480
+مضطر يضرب فيها و بس على نفس ال space اه فبيخفف قدر
+
+443
+00:35:31,480 --> 00:35:35,020
+الإمكان ال space تبعه فهذه نقطة مهمة جدا إذا بدنا
+
+444
+00:35:35,020 --> 00:35:38,660
+نشتغل على ال method ال method هل ال compiler اللي
+
+445
+00:35:38,660 --> 00:35:43,540
+عندك بساعد ولا بساعدش اللي هو ال stack memory او
+
+446
+00:35:43,540 --> 00:35:45,000
+ال stack space اه أكيد
+
+447
+00:35:48,460 --> 00:35:50,940
+هي حسب ال method ما انت إذا كان .. لاحظ إذا كان ال
+
+448
+00:35:50,940 --> 00:35:53,640
+method هي ضخمة كبيرة بمعنى بيقدرش ياخد مجموعة
+
+449
+00:35:53,640 --> 00:35:57,680
+بيانات و يخليها برا و يسكر لأ هي فيها مجموعة كبيرة
+
+450
+00:35:57,680 --> 00:36:01,320
+لأ بيصير بدها شغل تاني لأ أكيد أكيد في الحالة هذه
+
+451
+00:36:01,320 --> 00:36:05,300
+بدك ال stack يكون أصلا كبيرة عندك و ساعتها بيقولك
+
+452
+00:36:05,300 --> 00:36:09,040
+أنه لأ والله صار عندك ال complexity مشكلة في ال
+
+453
+00:36:09,040 --> 00:36:11,740
+space complexity تصبح عندك مشكلة في ال space
+
+454
+00:36:11,740 --> 00:36:16,970
+complexity طيب أخدنا ال linearلينير سيرش مش ذاكرين
+
+455
+00:36:16,970 --> 00:36:22,930
+طب هاتنعمله code باستخدام ال recursion theorem او
+
+456
+00:36:22,930 --> 00:36:31,210
+باستخدام ال recursive code كان الشغل كله معتمد على
+
+457
+00:36:31,210 --> 00:36:38,530
+انه في عندى X X هذه بدنا نبحث عنها بين I و J و إيش
+
+458
+00:36:38,530 --> 00:36:46,690
+كان مسم ال series تبقىString A ببدأ من I location
+
+459
+00:36:46,690 --> 00:36:51,050
+I ل location J فاحنا بدنا نبحث عن X هل هي موجودة
+
+460
+00:36:51,050 --> 00:36:57,550
+داخله ولا مش موجودة فإذا كأنها AI او A1 A2 مباشرة
+
+461
+00:36:57,550 --> 00:37:09,470
+مافيش داعي على I A0 A1 A2 to AN وبدنا نبحث عن Xهذا
+
+462
+00:37:09,470 --> 00:37:11,970
+ال code اللي احنا كتبناه قبل هيك شرحناه و كتبناه
+
+463
+00:37:11,970 --> 00:37:14,770
+اكيد انتوا كتبينه حتى في مصاقات تانية غير مصارنا
+
+464
+00:37:14,770 --> 00:37:18,610
+اللي انا بدنا نكتبه بشكل recursively form بشكل
+
+465
+00:37:18,610 --> 00:37:22,490
+تكراري بشكل تكراري فحته procedure search زي ما هي
+
+466
+00:37:22,490 --> 00:37:27,550
+هنعرف ال aطبيعي لأن هذا ال input الأهم هو إيش ال
+
+467
+00:37:27,550 --> 00:37:31,330
+array اللى بدك تبحث داخلها أو ال string أو ال
+
+468
+00:37:31,330 --> 00:37:34,850
+series أو ال sequence المهم إن هو ال array اللى
+
+469
+00:37:34,850 --> 00:37:38,130
+بتاخدوها في ال .. في إيش؟ في البرمجة سموها array و
+
+470
+00:37:38,130 --> 00:37:43,750
+خلاص array A وهذه بتبدأ من I to J طبعا في البداية
+
+471
+00:37:43,750 --> 00:37:48,670
+بتبدأ I ب 0 عادة و J ب Nصحيح هذه كبداية initially
+
+472
+00:37:48,670 --> 00:37:51,470
+بس احنا بنحطها in general لإنه انا عارف انه ممكن
+
+473
+00:37:51,470 --> 00:37:56,730
+لجدام افتح نفس ال code كمان مرة ب I مختلفة فعشان
+
+474
+00:37:56,730 --> 00:38:00,210
+هيك بنعرفها in general I و J هدول عبارة عن
+
+475
+00:38:00,210 --> 00:38:03,610
+integers لإنه locations بينفعش مايكونوش integers
+
+476
+00:38:03,610 --> 00:38:08,150
+أصلا كويس X هي ال term اللي أنا ببحث عنه أو القيمة
+
+477
+00:38:08,150 --> 00:38:12,250
+اللي ببحث عنها و ليست I أو J أو ما بينهما لأ هي
+
+478
+00:38:12,250 --> 00:38:21,930
+القيمة نفسها فهي قيمة ال AI من I ل J القيمة نفسها
+
+479
+00:38:21,930 --> 00:38:27,150
+تمام هانبدأ إذا كانت والله ال A I لأن هاني بدأت من
+
+480
+00:38:27,150 --> 00:38:32,570
+بداية ال sequence تبعي بدأت من بداية ال R إذا كانت
+
+481
+00:38:32,570 --> 00:38:37,960
+E نفسها بتسوي X خير وبركة ارجع ل meanب I فرجعنا ب
+
+482
+00:38:37,960 --> 00:38:41,400
+I فعليا I مش هي قيمة X كلكم عارفين هذا الكلام
+
+483
+00:38:41,400 --> 00:38:44,160
+بقوله ال index بتاعة X ان X اللي بتدور عليها
+
+484
+00:38:44,160 --> 00:38:48,260
+موجودة في المكان الفلاني بس أنا ماقلتلهش قلتله بس
+
+485
+00:38:48,260 --> 00:38:52,920
+مكانها هنا بدك تروح خدها خدها طبعا أكيد هذه حالة
+
+486
+00:38:52,920 --> 00:38:56,740
+ال best caseإن ألاجيها مباشرة لكن فعليا بيصيرش هيك
+
+487
+00:38:56,740 --> 00:39:02,700
+فإيش بيزاكي بيسوي إذا كانت I تساوي J بمعنى عملنا
+
+488
+00:39:02,700 --> 00:39:05,160
+وضلنا نعمل عملية recursion step recursion step
+
+489
+00:39:05,160 --> 00:39:06,740
+recursion step recursion step recursion step
+
+490
+00:39:06,740 --> 00:39:07,680
+recursion step recursion step recursion step
+
+491
+00:39:07,680 --> 00:39:08,320
+recursion step recursion step recursion step
+
+492
+00:39:08,320 --> 00:39:08,480
+recursion step recursion step recursion step
+
+493
+00:39:08,480 --> 00:39:08,580
+recursion step recursion step recursion step
+
+494
+00:39:08,580 --> 00:39:08,580
+recursion step recursion step recursion step
+
+495
+00:39:08,580 --> 00:39:08,600
+recursion step recursion step recursion step
+
+496
+00:39:08,600 --> 00:39:08,600
+recursion step recursion step recursion step
+
+497
+00:39:08,600 --> 00:39:08,600
+recursion step recursion step recursion step
+
+498
+00:39:08,600 --> 00:39:08,600
+recursion step recursion step recursion step
+
+499
+00:39:08,600 --> 00:39:08,640
+recursion step recursion step recursion step
+
+500
+00:39:08,640 --> 00:39:08,640
+recursion step recursion step recursion step
+
+501
+00:39:08,640 --> 00:39:09,060
+recursion step recursion step recursion step
+
+502
+00:39:09,060 --> 00:39:11,540
+recursion step recursion step recursion step
+
+503
+00:39:11,540 --> 00:39:15,020
+recursion step recursion step recursion step
+
+504
+00:39:15,020 --> 00:39:16,180
+recursion step recursion step recursion step
+
+505
+00:39:16,180 --> 00:39:23,740
+recursion step recursion step recursion
+
+506
+00:39:23,740 --> 00:39:28,730
+stepبمعنى ان انا مالجتهاش عند I و I ما زالت بعيدة
+
+507
+00:39:28,730 --> 00:39:33,470
+عن ال J بيجي للخيار التالت اللي هو return بسيرش
+
+508
+00:39:33,470 --> 00:39:37,810
+كمان مرة بس يبدأ لي من I زائد واحد الباقي زي ما هو
+
+509
+00:39:37,810 --> 00:39:42,510
+J زي ما هي X كما هي نفس العنصر اللي ببحث عنه زائد
+
+510
+00:39:42,510 --> 00:39:46,340
+واحدكنت في ال element الأول لأ مش هو ال element
+
+511
+00:39:46,340 --> 00:39:48,860
+الأول خلاص ابدالي من ال element التاني ابدا من
+
+512
+00:39:48,860 --> 00:39:52,120
+التالت ابدا من الرابع ابدا من الخامس and so on
+
+513
+00:39:52,120 --> 00:39:55,400
+طبعا هذه واحدة من ال techniques مثلا في ال linear
+
+514
+00:39:55,400 --> 00:39:59,480
+اللي غير مجدى استخدم فيها ال recursion لأن حضّال
+
+515
+00:39:59,480 --> 00:40:04,080
+linear هي كانت linear وضلت linear بس غلبت حالي في
+
+516
+00:40:04,080 --> 00:40:09,600
+ال space يعني أنا فعلا صارت عندى سيئة الأمور اني
+
+517
+00:40:09,600 --> 00:40:15,100
+ماحسنتش في ال time و ال space زودتهابدل ما كنت
+
+518
+00:40:15,100 --> 00:40:17,960
+بصغل في نفس ال space بتاعت برنامج واحد اضطريت افتح
+
+519
+00:40:17,960 --> 00:40:22,380
+كذا code لنفس البرنامج كذا مرة لنفس ال code هذا
+
+520
+00:40:22,380 --> 00:40:26,560
+معناه ان انا زودت space ماكنش لها اي لازمة و
+
+521
+00:40:26,560 --> 00:40:31,680
+ماحسنتش في ال time linear ضالت linear لاحظ انت ايش
+
+522
+00:40:31,680 --> 00:40:36,830
+بتغير كنت I بديت ب I بعدين روحت ل I زائد واحدطب
+
+523
+00:40:36,830 --> 00:40:39,690
+اللي بعد اي زائد اتنين اي زائد تلتة طب احنا كنا في
+
+524
+00:40:39,690 --> 00:40:43,470
+الأول كنا نعمل هات for loop نبدأ من I لت جيه وكنت
+
+525
+00:40:43,470 --> 00:40:47,510
+بروح واحد اي ثم اي زائد واحد ثم اي زائد اتنين ثم
+
+526
+00:40:47,510 --> 00:40:50,350
+اي زائد تلتة يعني فعليا ك time ما تغيرش عن دي
+
+527
+00:40:50,350 --> 00:40:54,770
+فتاخدوا بالكوا و كويس ان اجانا هذا المثل انه مش
+
+528
+00:40:54,770 --> 00:40:58,220
+دايما ال recursion كويسمش ده من ال education كويس
+
+529
+00:40:58,220 --> 00:41:01,900
+عشانك انت مبرمج human programmer انت بدك في الآخر
+
+530
+00:41:01,900 --> 00:41:05,560
+انت مالك الموضوع انت لابدك تقرر اه هذا مناسب ولا
+
+531
+00:41:05,560 --> 00:41:09,740
+مش مناسب صحيح ال computer و داخل علينا و صار في
+
+532
+00:41:09,740 --> 00:41:13,480
+علم كاصطناعي و AI و مش عارفش و علم طويل عريض و
+
+533
+00:41:13,480 --> 00:41:16,240
+بحسب حسابات معقدة اكتر مننا بس في النهاية مازلت
+
+534
+00:41:16,240 --> 00:41:22,460
+انت المالك مازلت انت مالك الحسابات كويس؟ بدك تقدر
+
+535
+00:41:22,460 --> 00:41:28,370
+هذا احسن ولا مش احسن؟الـ binary ال binary search
+
+536
+00:41:28,370 --> 00:41:31,190
+برضه من الحاجات اللي أخدناها ال binary search كيف
+
+537
+00:41:31,190 --> 00:41:34,810
+ممكن أحولها أو أكتبها بشكل recursive code ف
+
+538
+00:41:34,810 --> 00:41:41,150
+recursive code هنبدأ ال binary وال A زي ما هي X
+
+539
+00:41:41,150 --> 00:41:45,430
+العنصر اللي ببحث عنه و from I to J و زي ما قلنا ال
+
+540
+00:41:45,430 --> 00:41:47,250
+initial يبدأ من 0 to N
+
+541
+00:41:50,930 --> 00:41:54,650
+و أول شغلة كنا بنعملها بنحسب ال midpoint صحيح ال
+
+542
+00:41:54,650 --> 00:41:59,170
+midpoint أو النقطة الوساطية داخل ال array في نص ال
+
+543
+00:41:59,170 --> 00:42:03,770
+array و بناخد لها floor و بعدين بنبدا نفحصها هل ال
+
+544
+00:42:03,770 --> 00:42:07,070
+X تسويها؟ والله خير و بركة بنرجع بقيمتها و خلصنا
+
+545
+00:42:08,480 --> 00:42:11,880
+هذا ال best case انه والله من أول مرة أخبط لجناها
+
+546
+00:42:11,880 --> 00:42:16,680
+خلصنا طيب أما إذا ما زبطتش بنروح بنبدأ نفحص هل X
+
+547
+00:42:16,680 --> 00:42:20,780
+أقل من العنصر اللي موجود في ال midpoint وطبعا كلنا
+
+548
+00:42:20,780 --> 00:42:24,220
+عارفين أن ال binary search هدى تظبطش إلا إذا كان
+
+549
+00:42:24,220 --> 00:42:30,640
+عندي sorted ال array تبعتي هي sorted ومن الأقل
+
+550
+00:42:30,640 --> 00:42:38,460
+فالأعلى تصعدي يعني increasing order فإذا Xأقل من A
+
+551
+00:42:38,460 --> 00:42:44,100
+معناته إذا أقل من A كل ما هو أكبر من ال M بلزمنيش
+
+552
+00:42:44,100 --> 00:42:48,900
+فجلل ال J صحيح ببقى بنقلل ال J بنقلل ال J وإحنا
+
+553
+00:42:48,900 --> 00:42:56,020
+هنا مقولاش أو يساوي صحيح
+
+554
+00:42:56,020 --> 00:43:00,680
+معنى ذلك إيش أني ببداش بروحش بحط ال J تساوي ال M
+
+555
+00:43:00,680 --> 00:43:09,170
+نفسها ناقص واحدلاحظ لأنه هي أكيد strictly هي أقل
+
+556
+00:43:09,170 --> 00:43:12,150
+من ولا يمكن أن تساوي معناته خلاص مافيش داعي أفحص
+
+557
+00:43:12,150 --> 00:43:15,930
+كم مرة العنصر هذا بروح العنصر اللي جابله باختصر
+
+558
+00:43:15,930 --> 00:43:21,850
+علي عنصر زي هذا كمان كويس andالان هذا فحصنا كقيمة
+
+559
+00:43:21,850 --> 00:43:26,370
+لكن بدنا نفحص كمان انه هل فعلا احنا خلص ال range
+
+560
+00:43:26,370 --> 00:43:31,750
+تبعنا ولا لسه and I ما زالت اقل من M يعني ما زال
+
+561
+00:43:31,750 --> 00:43:35,210
+في عندي مساحة ابحث فيها لأنه اذا وصلنا انه انا
+
+562
+00:43:35,210 --> 00:43:41,590
+ماوجدتش لكن I تسوى M طب معناته انت ال midpoint هي
+
+563
+00:43:41,590 --> 00:43:45,110
+نفسها ال first ماضلش عندك مساحة معنى ذلك
+
+564
+00:43:45,110 --> 00:43:48,610
+automatically بتقول هنا خلاص return بمين؟ ب zero
+
+565
+00:43:48,610 --> 00:43:55,930
+مالجتشماوجدتش انت وصلت لـ 0 range ومافيش عنصر خلاص
+
+566
+00:43:55,930 --> 00:44:00,550
+برجع انه مافيش عنصر وانتهى لكن هذا الكلام اذا حدث
+
+567
+00:44:00,550 --> 00:44:04,130
+هذا الموضوع فبنرجع return هنا باش انه ما زال في
+
+568
+00:44:04,130 --> 00:44:07,510
+عندي range ابحث فيه برجع return الـ A زي ما هي ال
+
+569
+00:44:07,510 --> 00:44:13,110
+X زي ما هي ال I زي ما هي ال J M ناقص واحد ال M M
+
+570
+00:44:13,110 --> 00:44:16,510
+ناقص واحد فالعنصر اللي جاب ال midpoint تمام
+
+571
+00:44:16,510 --> 00:44:25,010
+ماتحققش بهذا الشكل بمعنى انه هيهنا ليست أقل من هي
+
+572
+00:44:25,010 --> 00:44:29,530
+ليست أقل من فإذا X ليست أقل من A M خلاص بنسيب هذا
+
+573
+00:44:29,530 --> 00:44:33,550
+كل الكلام نعملهش و بنجعله اللي بعدها else إذا كانت
+
+574
+00:44:33,550 --> 00:44:35,210
+أكبر من A M
+
+575
+00:44:39,010 --> 00:44:41,790
+بتلاحظ احنا كل اللي عملناه مغيرناش ال notation
+
+576
+00:44:41,790 --> 00:44:46,590
+عكسنا اللي بتاعة ال inequality عكسنا فقط ال .. ال
+
+577
+00:44:46,590 --> 00:44:50,570
+.. ال symbols تبعتنا فهنا صارت ال aM هي اللي أقل
+
+578
+00:44:50,570 --> 00:44:57,030
+من X ف X أكبر معناها X أكبر في الحالة هذه إذا بدي
+
+579
+00:44:57,030 --> 00:45:01,310
+أعمل elimination هعمل elimination للجزء اللي قبل M
+
+580
+00:45:01,310 --> 00:45:10,010
+ومدام لا تساوي فهنا في عندي أريحية أقول منمزاد
+
+581
+00:45:10,010 --> 00:45:13,710
+واحد لأنها
+
+582
+00:45:13,710 --> 00:45:19,310
+لا تساوي فهنا اختلفت في الجزئية هذه عن ال code
+
+583
+00:45:19,310 --> 00:45:21,890
+اللي كنا كاتبينه سابقا ال code اللي كنا كاتبينه
+
+584
+00:45:21,890 --> 00:45:24,210
+سابقا إذا انتوا متذاكرين و أنا شوفت السؤال هذا في
+
+585
+00:45:24,210 --> 00:45:28,800
+عين بعضكملأ احنا المرة اللي فاتت على اساس ان نوفر
+
+586
+00:45:28,800 --> 00:45:34,140
+على حالنا F كنا F و L و خلاص أما لأ هنا زودنا كمان
+
+587
+00:45:34,140 --> 00:45:39,320
+واحدة فخلناها لها خصوصية تالتة اليساوي هذه او
+
+588
+00:45:39,320 --> 00:45:44,960
+يساوي فهنا أقل من أكبر من ماذكرناش عن اليساوي لسه
+
+589
+00:45:44,960 --> 00:45:48,620
+طيب بس بدنا ناخد بالنا أن هذا هحققه و أقول أنه أه
+
+590
+00:45:48,620 --> 00:45:53,820
+والله بدي أروح ل M زائد واحد إذا كان بأضمن أنه ما
+
+591
+00:45:53,820 --> 00:45:58,790
+زال يوجد range أصلاطيب and ال M هذه ما زالت أقل من
+
+592
+00:45:58,790 --> 00:46:04,430
+ال J معناته أنه ما زال فيه range أقدر أبحث فيه ما
+
+593
+00:46:04,430 --> 00:46:10,250
+زال موجود هاي ال range عندي أخدنا midpoint طب مش
+
+594
+00:46:10,250 --> 00:46:15,550
+بدي أضمن أنه بعد ال midpoint بين ال midpoint و ال
+
+595
+00:46:15,550 --> 00:46:20,370
+J ما زال في مساحة أبحث فيها هذه نفحصها بال
+
+596
+00:46:20,370 --> 00:46:25,610
+condition هذا أنه ما زالت M أقل من ال Jيعني يوجد
+
+597
+00:46:25,610 --> 00:46:30,090
+مسافة بين ال midpoint ونهاية ال array مازال يوجد
+
+598
+00:46:30,090 --> 00:46:35,350
+مسافة المسافة هذه نبحث عنها مدام موجودة على طول
+
+599
+00:46:35,350 --> 00:46:38,390
+بنقول إيش ال binary تبعي binary إيش بنرجع نفتح ال
+
+600
+00:46:38,390 --> 00:46:42,670
+code كمان مرة ولكن بأرقام مختلفة لمين ل I ل I
+
+601
+00:46:42,670 --> 00:46:49,710
+فبتصير A X I هتتغير ام زائد واحد افهمنا ليش زائد
+
+602
+00:46:49,710 --> 00:46:53,610
+واحدالمرة الماضية ماكنتش كتبين زائد واحد لإن كانت
+
+603
+00:46:53,610 --> 00:46:57,470
+else و ال else على طول معناها النفي ل ال condition
+
+604
+00:46:57,470 --> 00:47:00,110
+اللي انت حاطه هنا فمدار كانت أقل من معناته النفيها
+
+605
+00:47:00,110 --> 00:47:04,590
+كان أكبر من أو يساوي لأ هنا أنا ماجولتش else و
+
+606
+00:47:04,590 --> 00:47:08,990
+سكتت أنا كتبتلها condition خاص فيها و كتبت أكبر من
+
+607
+00:47:08,990 --> 00:47:14,370
+أكبر منه ماجولتش أو يساوي فأنا عنده حرية أقول زائد
+
+608
+00:47:14,370 --> 00:47:19,090
+واحد هنالأنه ضامن أنها لن تتساوي بدليل كان
+
+609
+00:47:19,090 --> 00:47:23,690
+ماتتحققش أصلا شرط هذا طيب else إذا كان فعلا و الله
+
+610
+00:47:23,690 --> 00:47:29,890
+لا هذا اتحقق ولا هذا اتحقق لاحظ أن أنت شرط اتنين
+
+611
+00:47:29,890 --> 00:47:34,590
+تلاتة التلت احتمالات الممكن أن انت حققتها فعليا
+
+612
+00:47:34,590 --> 00:47:46,200
+يساوي هاي ليساوي وهي أقل من وهي أكبر من اشضلخلصت
+
+613
+00:47:46,200 --> 00:47:53,140
+فانت ماخلطش لل code اي احتمال اخر الا احتمال انه
+
+614
+00:47:53,140 --> 00:47:59,900
+لم تتحقق واحدة من ال ans هدوله مش هيك لو واحدة
+
+615
+00:47:59,900 --> 00:48:05,240
+منهم false معناته ان I تساوي ال M او ال M تساوي ال
+
+616
+00:48:05,240 --> 00:48:09,100
+J في الحالة هذه خلاص ماضلش عندك range اصلا تبحث
+
+617
+00:48:09,100 --> 00:48:13,290
+فيهانت ماضلش عندك range تبحث فيه فعلى طول بترجعلنا
+
+618
+00:48:13,290 --> 00:48:18,650
+بإيش؟ ب zero مالجتش خلصت ال range صغر لدرجة انه ال
+
+619
+00:48:18,650 --> 00:48:21,970
+input و ال output واحد اعفوا ان البداية و النهاية
+
+620
+00:48:21,970 --> 00:48:26,910
+واحدة مافيش عنصر أدور عنه فلأ خلاص رجعلنا ان
+
+621
+00:48:26,910 --> 00:48:31,250
+مالجتش لأنه فعليا انت مالجتش عنصر ماضلش عندك عنصر
+
+622
+00:48:31,250 --> 00:48:33,350
+تمام
+
+623
+00:48:34,780 --> 00:48:37,900
+هيك بنكون أخدنا مجموعة أمثلة برضه على ال recursion
+
+624
+00:48:37,900 --> 00:48:43,040
+code و خلصنا الجزء تبع ال recursion المرة القادمة
+
+625
+00:48:43,040 --> 00:48:47,060
+ان شاء الله تعالى بنبدأ في ال counting بمعنى أن
+
+626
+00:48:47,060 --> 00:48:52,800
+احنا بتذكرين أخدنا ال numbers و نظرية الأعداد و
+
+627
+00:48:52,800 --> 00:48:57,300
+ختمت معانا في الآخر لأكواد و لتشفير الآن بدنا نروح
+
+628
+00:48:57,300 --> 00:49:02,070
+للعد كيف أنا بقدر أعدونشوف كيف وين بتوصلنا طرق
+
+629
+00:49:02,070 --> 00:49:04,610
+العد بعد ذلك ياطيكوا ألف عافية ونشوفكوا المرة
+
+630
+00:49:04,610 --> 00:49:04,910
+القادمة
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/YJtMKeajHsA.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/YJtMKeajHsA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e0553519cd3bab1847025dbb9312050c45d03691
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/YJtMKeajHsA.srt
@@ -0,0 +1,2046 @@
+1
+00:00:05,520 --> 00:00:08,520
+السلام عليكم، بتكونوا عافية يا شباب، اليوم إن شاء
+
+2
+00:00:08,520 --> 00:00:12,460
+الله تعالى، بنبدأ في موضوع جديد، ما حاجتهوش من المرة
+
+3
+00:00:12,460 --> 00:00:16,540
+الماضية، اللي هو الـ function، بحيث أنه إنكم بدأنا
+
+4
+00:00:16,540 --> 00:00:20,060
+فيه خلال هذا الأسبوع، إن شاء الله تعالى، بعد ما
+
+5
+00:00:20,060 --> 00:00:26,220
+اتكلمنا عن الـ sets، أخدنا الـ set كـ theory، ثم أخدنا
+
+6
+00:00:26,220 --> 00:00:30,180
+الـ set باستخدام الـ operations الخاصة بالـ sets
+
+7
+00:00:30,180 --> 00:00:34,480
+اليوم هنتكلم عن الـ functions كأحد الأدوات المهمة
+
+8
+00:00:34,480 --> 00:00:39,540
+جدا في الـ discrete math، فكل حاجة في الدنيا ممكن
+
+9
+00:00:39,540 --> 00:00:44,290
+اتعامل معها كـ function، تحديدا من الحاجات اللي
+
+10
+00:00:44,290 --> 00:00:48,470
+أخدناها حتى الآن في الـ math، في كتير شواهد، وفي
+
+11
+00:00:48,470 --> 00:00:51,930
+كتير أمثلة لفكرة الـ function، الـ function اللي هي
+
+12
+00:00:51,930 --> 00:00:55,830
+ببساطة، بقدر أسميها، اختصارا، في معظم الكتب بيسموها F
+
+13
+00:00:55,830 --> 00:01:01,650
+ولكن هي مش حكرا على الـ letter case F بس لحاله، لأ
+
+14
+00:01:01,650 --> 00:01:05,950
+هي ممكن تكون لأي حاجة تانية، لكن باستمرار بيقول F
+
+15
+00:01:05,950 --> 00:01:09,230
+على أساس إن هي function، وهذه بتحدد لنا أو بتعين لنا
+
+16
+00:01:09,230 --> 00:01:18,260
+لكل X قيمة Y، هذه معناها كأنك أنت بتعمل mapping بين
+
+17
+00:01:18,260 --> 00:01:22,400
+مجموعة أرقام أو مجموعة أعداد أو مجموعة in general
+
+18
+00:01:22,400 --> 00:01:26,240
+objects، واتكلمنا إن إحنا دائما هنحاول نروح للـ
+
+19
+00:01:26,240 --> 00:01:31,320
+general، إن هي مجموعة objects، فبعين ليه؟ لأي حد من
+
+20
+00:01:31,320 --> 00:01:35,420
+مجموعة الـ objects هذه، حد من مجموعة objects تانية،
+
+21
+00:01:35,420 --> 00:01:39,140
+بيعمل علاقة بينهم، بيعمل رابط بينهم، فالعلاقة هذه
+
+22
+00:01:39,140 --> 00:01:42,220
+أو الـ relation هذه بيكون اسمها function إذا كان
+
+23
+00:01:42,220 --> 00:01:47,190
+relation واضحة وبتتغيرش مع الزمن، مش كل ما بدي أعمل
+
+24
+00:01:47,190 --> 00:01:49,950
+الـ function، وأدخل نفس الرقم أو نفس الـ object
+
+25
+00:01:49,950 --> 00:01:53,450
+ألاقي object مختلف بيطلع، إذا كان حافظنا على نفس الـ
+
+26
+00:01:53,450 --> 00:01:57,110
+object باستمرار، فهذه بتصير relation ثابتة، function
+
+27
+00:01:57,110 --> 00:02:02,350
+تصبح كأنها دالة، كويس؟ فهذه تعريفة ببساطة جدا أننا
+
+28
+00:02:02,350 --> 00:02:08,380
+بنعمل تعيين لكل رقم X، كل رقم X belong to real
+
+29
+00:02:08,380 --> 00:02:12,260
+number، a particular value، يكون له particular value
+
+30
+00:02:12,260 --> 00:02:18,020
+كنتيجة، اسمها Y، اسمها Y، الـ Y هذه هتكون عبارة عن X
+
+31
+00:02:18,020 --> 00:02:24,460
+applied عليه، التأثير بتاع الـ function، فكأنه طبقت الـ
+
+32
+00:02:24,460 --> 00:02:28,600
+function هنا دي على X، فالتأثير اللي ظهر بعد تطبيق
+
+33
+00:02:28,600 --> 00:02:32,760
+الـ function على X هيكون عبارة عن value جديدة اسمها
+
+34
+00:02:32,760 --> 00:02:37,180
+Y، فصارت X مربوطة في Y، وبرضه Y المفروض إن هي
+
+35
+00:02:37,180 --> 00:02:42,300
+belong to R، لكن فعليا الـ function زي ما قلنا هي مش
+
+36
+00:02:42,300 --> 00:02:45,560
+مجرد الأرقام أو الـ elements بتاعتها، ممكن تكون أي
+
+37
+00:02:45,560 --> 00:02:52,080
+set، آه رجعنا هنا لموضوع الـ set، بمعنى هنا X زي ما
+
+38
+00:02:52,080 --> 00:02:55,680
+قلنا مش ضروري تكون رقم فقط، ممكن تكون أي object، و
+
+39
+00:02:55,680 --> 00:03:01,300
+ينتمي لأي set، ممكن ينتمي لأي set من الـ sets اللي
+
+40
+00:03:01,300 --> 00:03:04,620
+ممكن يخطر على بالك، ونفس الكلام بحيث إن يكون في
+
+41
+00:03:04,620 --> 00:03:11,100
+بينهم علاقة، و object آخر موجود برضه كـ Y belong to
+
+42
+00:03:11,100 --> 00:03:20,390
+set، مثلا T، تمام؟ أو نفسها S، أو نفسها S، فـ in general
+
+43
+00:03:20,390 --> 00:03:24,230
+أول شغل إحنا ما نتعاملش مع فقط numbers، الشغل الثاني
+
+44
+00:03:24,230 --> 00:03:30,790
+ممكن يكون أي set، أستخدمها لـ .. كفضاء عينة لمجموعة
+
+45
+00:03:30,790 --> 00:03:34,610
+X اللي بدي أطبق عليها الـ function، أو أطبق عليها
+
+46
+00:03:34,610 --> 00:03:38,570
+الـ relation اللي هنسميها function، كويس؟ فهذا هيك
+
+47
+00:03:38,570 --> 00:03:46,070
+بشكل مبسط كمفاهيم، ونكمل شغلنا، okay، الـ function
+
+48
+00:03:46,070 --> 00:03:49,770
+formally بيكون هنا، مدام اتفقنا على sets، إنه بدنا
+
+49
+00:03:49,770 --> 00:03:54,670
+ناخد قيم X، وتأثيرها لازم برضه يكون ضمن الـ set
+
+50
+00:03:54,670 --> 00:03:59,690
+فبنقدر نقول الآن بداية تعريفنا، any sets A و B، الـ
+
+51
+00:03:59,690 --> 00:04:03,690
+function هتكون F، الـ function F اللي رمزناها بـ F
+
+52
+00:04:03,690 --> 00:04:08,170
+على أساس إن هي function، هتكون بتعمل mapping between
+
+53
+00:04:08,170 --> 00:04:16,750
+عناصر A لعناصر B، عناصر A لعناصر B، لأن A بالنسبة لنا
+
+54
+00:04:16,750 --> 00:04:24,290
+هنا بأخد منه قيم X لـ الـ function F of X، فـ X هذه
+
+55
+00:04:24,290 --> 00:04:30,370
+بأخدها لازم تكون belong to capital A، الناتج هنا
+
+56
+00:04:30,370 --> 00:04:35,130
+كقيمة اللي هي المفروض يساوي Y، Y هذه المفروض إن هي
+
+57
+00:04:35,130 --> 00:04:41,880
+برضه belong to B، to set B، فهي مش مجرد قيمة واحدة بس
+
+58
+00:04:41,880 --> 00:04:46,140
+كل الـ function، الـ result هتكون فقط قيمة، ولا هتكون
+
+59
+00:04:46,140 --> 00:04:50,420
+مجموعة قيم، مجموعة القيم هذه محطوطة داخل set، فالـ
+
+60
+00:04:50,420 --> 00:04:53,740
+set اسمها B، فهنا بنسميها لأي A و B، الـ function
+
+61
+00:04:53,740 --> 00:05:00,240
+هتكون from A to B، بنكتبها كتالي: if الـ function if
+
+62
+00:05:00,240 --> 00:05:08,780
+from A to B، بتكتب بهذا الشكل، فإذا الـ function f، و
+
+63
+00:05:08,780 --> 00:05:12,280
+اللي إحنا رمزناها بـ f، ممكن تكتبها أي عنصر آخر، أي
+
+64
+00:05:12,280 --> 00:05:16,640
+حاجة، g، بتكون تكتبها g، أو تكتبها g from capital a
+
+65
+00:05:16,640 --> 00:05:19,820
+لـ b، فخلاص بعرف إن الـ function g أو الـ function f
+
+66
+00:05:19,820 --> 00:05:26,360
+هذه هي عبارة عن f of x، y تساوي f of x، بحيث إن x
+
+67
+00:05:26,360 --> 00:05:33,280
+لازم تكون belong to set A، و Y كنتيجة لازم تكون برضه
+
+68
+00:05:33,280 --> 00:05:39,320
+belong to set B، ببساطة جدا، هذه كل الفكرة، فإذا
+
+69
+00:05:39,320 --> 00:05:45,000
+عرفنا الـ functions بدلالة الـ sets تبعتها، بدلالة
+
+70
+00:05:45,000 --> 00:05:47,680
+الـ sets، ليش بدلالة الـ sets؟ لأن في إلها مفهوم
+
+71
+00:05:47,680 --> 00:05:50,360
+لحقيقة الـ set، لأن ببساطة جدا بقدر أسميها الـ
+
+72
+00:05:50,360 --> 00:05:54,210
+domain، بنقدر الآن نتعامل، أنتم أخدتوا
+
+73
+00:05:54,210 --> 00:05:59,790
+المصطلح ده قبل، هي الـ domain أو المجال، المجال تبع
+
+74
+00:05:59,790 --> 00:06:04,330
+X، تبع قيم X، والمجال تبع قيم Y، هذه في النهاية
+
+75
+00:06:04,330 --> 00:06:10,430
+domain هذه عبارة عن set، هي في النهاية ستة، تمام؟ فهي
+
+76
+00:06:10,430 --> 00:06:13,570
+التعريف المبسط للـ functions اللي هنستخدمه الآن على
+
+77
+00:06:13,570 --> 00:06:17,850
+طول، فهذا بحدد لنا الحقيقة من هذا التعريف، بفهم منه
+
+78
+00:06:17,850 --> 00:06:21,130
+أنه عمل assignment أو عمل تعيين، exactly one
+
+79
+00:06:21,130 --> 00:06:26,890
+element، if of X belong to P، لكل element من A، لكل
+
+80
+00:06:26,890 --> 00:06:32,150
+element من A، فهو حدد لنا element و element واحد من B
+
+81
+00:06:33,580 --> 00:06:38,960
+corresponding أو يمثل، represented لعنصر من مين؟ من
+
+82
+00:06:38,960 --> 00:06:43,610
+إيه؟ اللي هو قيمة X، تمام؟ في نفس الـ function f of x
+
+83
+00:06:43,610 --> 00:06:49,010
+بس بشوية فلسفة، هيك فلسفناها بشكل sets، بشكل الـ sets
+
+84
+00:06:49,010 --> 00:06:52,290
+تبعتنا اللي إحنا أخدناها، لأن هذه هتساعدنا لقدام في
+
+85
+00:06:52,290 --> 00:06:56,030
+تعريف أمور كتيرة بالطريقة، هذه هتساعدنا بتعريف أمور
+
+86
+00:06:56,030 --> 00:06:58,950
+كتيرة، مجرد إن أنا بقدر مجموعة elements أحطها داخل
+
+87
+00:06:58,950 --> 00:07:03,590
+set، خلاص بقدر أعرف function أو relation على آخر
+
+88
+00:07:03,590 --> 00:07:06,090
+الفصل، هنتكلم إن الله في عندي حاجة اسمها relation
+
+89
+00:07:06,090 --> 00:07:09,710
+علاقة ما بين كذا وكذا، العلاقة هذه بصورة أو بأخرى
+
+90
+00:07:09,710 --> 00:07:15,610
+هي function، تمام؟ تمثيلها شكل، بشكل، التمثيل بقدر أقول
+
+91
+00:07:15,610 --> 00:07:18,830
+إن عندي، هي الـ Venn diagram، باستخدام الـ Venn
+
+92
+00:07:18,830 --> 00:07:21,830
+diagram، هي عندي المجموعة الأولى capital A، وهي
+
+93
+00:07:21,830 --> 00:07:25,430
+المجموعة الثانية capital B، وبالمناسبة ممكن يكون
+
+94
+00:07:25,430 --> 00:07:30,070
+في intersection between them، أو unjoined، أو
+
+95
+00:07:30,070 --> 00:07:34,770
+unjoined، منفصلين، لكن في النهاية اللي بيهمني نقاش إن
+
+96
+00:07:34,770 --> 00:07:41,940
+كل عنصر من capital A، في قلة قارنه في B، مين اللي حدد
+
+97
+00:07:41,940 --> 00:07:46,180
+مين قارن مين؟ الـ function، قيمة الـ function، عشان هيك
+
+98
+00:07:46,180 --> 00:07:50,600
+حسب قيمة الـ function هتتغير قيمة B اللي
+
+99
+00:07:50,600 --> 00:07:54,620
+corresponding لـ A، اللي corresponding لـ A، صحيح أنت
+
+100
+00:07:54,620 --> 00:07:57,280
+ممكن نفس العنصر يدخله على الـ function الأولى، يعطيه
+
+101
+00:07:57,280 --> 00:08:00,320
+قيمة، على الـ function الثانية يعطيه قيمة ثانية، يعطيك
+
+102
+00:08:00,320 --> 00:08:05,240
+قيمة ثانية، تمام؟ فبنرسمها بهذا الشكل، أما if من الـ
+
+103
+00:08:05,240 --> 00:08:09,680
+set كلها للـ set كلها، خلاص بفهم إن الـ function if
+
+104
+00:08:09,680 --> 00:08:15,580
+نفس التعريف اللي كتبناه توّه، فكأني بقول if from a
+
+105
+00:08:15,580 --> 00:08:21,960
+to b، from
+
+106
+00:08:21,960 --> 00:08:27,960
+a to b، أو بالطريقة الثانية اللي هي b تساوي f of a
+
+107
+00:08:30,540 --> 00:08:39,560
+بحيث إن A belong to capital A، and B belong to
+
+108
+00:08:39,560 --> 00:08:45,400
+capital B، بس هي كل طريقة الرسم بالـ Venn diagram، أو
+
+109
+00:08:45,400 --> 00:08:54,060
+ممكن نرسمها bipartite، by ثنائي، وpartite جزء فجزء
+
+110
+00:08:54,060 --> 00:09:02,980
+ثنائي، أو بنجزئها لجزئين، جزء أول هم عناصر a، جزء
+
+111
+00:09:02,980 --> 00:09:07,060
+ثاني عناصر b، وبنعمل relation، الـ relation هذا أو
+
+112
+00:09:07,060 --> 00:09:12,860
+السهم هذا from a to b، أو أي element من a لـ element
+
+113
+00:09:12,860 --> 00:09:19,060
+من b، مين اللي حدد العلاقة هذه؟ الـ function .. الـ
+
+114
+00:09:19,060 --> 00:09:21,460
+function، فعليا الـ function هو اللي هي لغاية ..
+
+115
+00:09:21,460 --> 00:09:24,900
+لأن أول عنصر هنا، إذا طبقنا عليه الـ function، if
+
+116
+00:09:24,900 --> 00:09:28,720
+هيعطينا العنصر الثاني من الـ .. okay، مافيش مشكلة
+
+117
+00:09:28,720 --> 00:09:30,840
+العنصر الثاني، إذا طبقنا عليه if، هيعطينا العنصر ..
+
+118
+00:09:30,840 --> 00:09:35,360
+okay، ماشي، يطلع اللي يطلع، بس في النهاية هيكون عندي
+
+119
+00:09:35,360 --> 00:09:41,320
+علاقة بين مجموعة العناصر بتاعة a ومجموعة العناصر لـ
+
+120
+00:09:41,320 --> 00:09:48,170
+b، أو الطريقة الأشهر، لـ plot X و Y، و X belong to
+
+121
+00:09:48,170 --> 00:09:54,230
+capital A، و Y belong to capital B، وبنحط النقاط، فـ
+
+122
+00:09:54,230 --> 00:09:58,870
+relation الآن هي فعليا بين A و B
+
+123
+00:10:02,700 --> 00:10:07,680
+عند A تطلع B هذه، عند A2 تطلع B ثانية، عند A3 تطلع
+
+124
+00:10:07,680 --> 00:10:11,660
+B ثالثة، وهكذا، لما في الآخر نحطهم كنقاط، كأزواج
+
+125
+00:10:11,660 --> 00:10:18,360
+مرتبة، ونعمل plot، فهي الثلاث طرق لتمثيل أي function
+
+126
+00:10:23,600 --> 00:10:26,340
+Okay، طيب الـ functions اللي عندي الآن، وين شفناها؟
+
+127
+00:10:26,340 --> 00:10:28,880
+الحقيقة اللي حتى الآن، كل اللي درسناه من أول الفصل
+
+128
+00:10:28,880 --> 00:10:33,180
+إلى الآن، بقدر أمثله بشكل functions، نقدر نمثله بشكل
+
+129
+00:10:33,180 --> 00:10:36,400
+functions، ابتداء من الـ proposition، الـ proposition
+
+130
+00:10:36,400 --> 00:10:40,680
+هو function من إيش لإيش؟ من، معناته هنا بنتكلم عن
+
+131
+00:10:40,680 --> 00:10:47,010
+اللي بينتمي لإيه؟ to إيش؟ بينتمي للـ input، والـ
+
+132
+00:10:47,010 --> 00:10:51,570
+output، فإذا ممكن نمثلها كـ function from situations
+
+133
+00:10:51,570 --> 00:10:56,330
+to truth values، للـ truth values، زي لما أقول إن الـ
+
+134
+00:10:56,330 --> 00:11:01,090
+proposition P، it's raining، it's raining، طبعا أنا
+
+135
+00:11:01,090 --> 00:11:07,230
+الوضع العادي مش قادر أقول true ولا false، صح؟ لكن
+
+136
+00:11:07,230 --> 00:11:12,770
+لو قلت لي إن الـ situation إن إحنا في شهر يناير، و
+
+137
+00:11:12,770 --> 00:11:18,850
+مبارح كان مطر، بدي أقول لك yes to a true، أو تطلع من
+
+138
+00:11:18,850 --> 00:11:24,310
+الشمس، أقول لك الـ situation إنه مغيم، cloudy، خلاص حفظت
+
+139
+00:11:24,310 --> 00:11:28,110
+معناته إن هي مغيمة، okay، هتكون في مقر أو drizzle
+
+140
+00:11:28,920 --> 00:11:33,060
+اللي هي بتنزل من نقطة خفيفة، تمام؟ فالـ situation
+
+141
+00:11:33,060 --> 00:11:37,960
+هنا حسب قيمة الـ situation، فالـ function اللي هي الـ
+
+142
+00:11:37,960 --> 00:11:40,400
+P أو الـ proposition أصبحت function في الـ
+
+143
+00:11:40,400 --> 00:11:43,360
+situation، حسب الـ situation اللي أنت هتحطّني فيه،
+
+144
+00:11:43,360 --> 00:11:50,060
+هقدر أقول لك هي true ولا false؟ كان ناتج للـ function
+
+145
+00:11:50,060 --> 00:11:54,580
+فالـ function تبعتي أصبحت الـ F هي الـ P، أصبحت هي الـ
+
+146
+00:11:54,580 --> 00:11:58,080
+P، الـ function في مين؟ في الـ situation، في الـ
+
+147
+00:11:58,080 --> 00:12:00,680
+situation، تقول لي والله إحنا في شهر .. في عزيزي
+
+148
+00:12:00,680 --> 00:12:04,940
+شهر ثمانية، هقول لك false، خلاص false، معناته وإحنا
+
+149
+00:12:04,940 --> 00:12:08,640
+عارفين إن إحنا في غزة مافيش مطر في شهر ثمانية، خلاص
+
+150
+00:12:08,640 --> 00:12:13,850
+حسب الـ situation بتقدر تحكمه، حطينا هنا belong to
+
+151
+00:12:13,850 --> 00:12:18,390
+set، عرفناها هي بـ set، والـ set هذا إحنا من الأساس
+
+152
+00:12:18,390 --> 00:12:21,470
+عارفين إنه الـ outputs تبعتها true أو false، فشيء
+
+153
+00:12:21,470 --> 00:12:25,490
+ثالث، فبقدر مباشرة أكتبهم بهذا الشكل، كويس؟ الـ
+
+154
+00:12:25,490 --> 00:12:30,670
+propositional operator هو نفسه function، هي نفسها
+
+155
+00:12:30,670 --> 00:12:34,070
+function، كل الـ operators اللي أخذناها سابقا هي بحد
+
+156
+00:12:34,070 --> 00:12:38,600
+ذاتها function، كيف؟ زي لما أقول مثلا، بنحطها طبعا
+
+157
+00:12:38,600 --> 00:12:43,580
+بشكل ordered pairs، الـ pairs هذه، ممكن أقول الـ
+
+158
+00:12:43,580 --> 00:12:48,740
+operator أو الـ function، this junction، لإيش؟ from
+
+159
+00:12:48,740 --> 00:12:55,840
+from false to true، from false to true، يعني كأني
+
+160
+00:12:55,840 --> 00:13:05,120
+طبقت الـ operator هذه على two operands، الأول false
+
+161
+00:13:05,120 --> 00:13:11,700
+والثاني الـ true، فنتجها كاملة الـ true، طيب لو قلنا
+
+162
+00:13:11,700 --> 00:13:19,260
+الـ implication كـ operator، كـ function، applied from
+
+163
+00:13:19,260 --> 00:13:25,400
+true to false، false، طب لو كده اللي قلت، applied from
+
+164
+00:13:25,400 --> 00:13:30,880
+false to true، true، فالآن هذه واضحة أكثر إن هذا
+
+165
+00:13:30,880 --> 00:13:37,040
+function، يعني بيفرج مين اللي جوا الـ function هذه
+
+166
+00:13:37,040 --> 00:13:40,700
+كأنه لو بتفترض إن هذه بدل كلمة if، هذه الـ function
+
+167
+00:13:40,700 --> 00:13:47,980
+طبيعة الـ function، وكتبت from true، و if بهذا الشكل
+
+168
+00:13:49,830 --> 00:13:53,490
+false، فأنا عارف إنه هذه بتعطينا نتيجة اللي هي
+
+169
+00:13:53,490 --> 00:13:58,430
+المفروض y، إيش الـ y؟ false، أصبحت كأنه هذه بالظبط
+
+170
+00:13:58,430 --> 00:14:03,350
+بتلعب دور إيش؟ دور function، كأنها هي ال
+
+223
+00:17:47,400 --> 00:17:51,650
+elements هذه هي نفسها الـ X ممكن أتعامل معاها أن هي
+
+224
+00:17:51,650 --> 00:17:56,050
+نفس الـ X فالـ X أصبحت عندي من واحد to N واحد to N،
+
+225
+00:17:56,050 --> 00:17:59,930
+مدام إحنا عرفنا الـ length تبعه N فإذن أبدأ من
+
+226
+00:17:59,930 --> 00:18:03,030
+واحد، من أول location لـ maximum location لأن هو
+
+227
+00:18:03,030 --> 00:18:07,150
+أصلًا الـ length كله على بعضه N okay انتهى، فبتظهر
+
+228
+00:18:07,150 --> 00:18:11,890
+عندي كـ function من number من واحد to N هذه أشبه
+
+229
+00:18:13,480 --> 00:18:16,500
+position الـ position لكل bit من الـ bits اللي
+
+230
+00:18:16,500 --> 00:18:20,780
+موجودة عندك فإذا عرفلي الـ location عشان أعرفلك
+
+231
+00:18:20,780 --> 00:18:24,820
+القيمة الـ value اللي بتاعة الـ bit بدون هيك مش هعرف
+
+232
+00:18:24,820 --> 00:18:28,500
+أعرفلك إياها، أقول لي في أي location موجودة بقول لك
+
+233
+00:18:28,500 --> 00:18:33,660
+إيش هي بالظبط قيمتها، خلاص فإذن to the bit الـ bit
+
+234
+00:18:33,660 --> 00:18:36,580
+هذه أكيد يا صفر يا واحد مدام إحنا بنتكلم من الأساس
+
+235
+00:18:36,580 --> 00:18:40,840
+على bit string و bit كلمة bit binary خلاص bit
+
+236
+00:18:40,840 --> 00:18:46,120
+معناته binary ثنائية صفر يا واحد زي الـ bit string
+
+237
+00:18:46,120 --> 00:18:52,100
+101 وبقول لك P of 3 الـ P of 3 هذه يعني كأنك بقول
+
+238
+00:18:52,100 --> 00:18:55,040
+الـ location التالت، أنت إيش على طول هتقول له بتساوي
+
+239
+00:18:55,040 --> 00:18:57,480
+واحد، أنك هتشوف واحد اتنين تلاتة، إيش القيمة؟ آه واحد
+
+240
+00:18:57,480 --> 00:19:02,500
+خلاص function هيها، هي أصبحت function، وأنتم فعلا
+
+241
+00:19:02,500 --> 00:19:04,360
+كنتم تعملوا هذا الكلام في البرمجة اللي ما كنتم
+
+242
+00:19:04,360 --> 00:19:08,460
+تبرمجوا الـ array، أنتم كنتم تعرفوا الـ element بالـ
+
+243
+00:19:08,460 --> 00:19:11,900
+location تبعه صح؟ function أنتم كنتم فعلا بتبرمجوا
+
+244
+00:19:11,900 --> 00:19:17,910
+كأنكم تشتغلوا function تمام، برضه في الـ sets نفسها الـ
+
+245
+00:19:17,910 --> 00:19:21,930
+set نفسها الـ universe of discourse U مثلا فبقدر
+
+246
+00:19:21,930 --> 00:19:27,620
+أقول أنه كـ function from elements of U الـ elements
+
+247
+00:19:27,620 --> 00:19:31,040
+of U هل الـ element موجود في الـ U ولا مش موجود
+
+248
+00:19:31,040 --> 00:19:33,840
+فهيقول لك الـ membership، متذكرين الـ membership
+
+249
+00:19:33,840 --> 00:19:37,940
+table خلاص فإذن الـ membership table يا موجود يا
+
+250
+00:19:37,940 --> 00:19:42,260
+غير موجود، belong أو not belong فإما true أو false
+
+251
+00:19:42,260 --> 00:19:50,120
+إما true أو false زي S الـ set S عبارة عن set of
+
+252
+00:19:50,120 --> 00:19:56,390
+three طيب لما أقول لك S of zero يعني بمعنى هل الـ
+
+253
+00:19:56,390 --> 00:20:00,690
+element الصفر ينتمي ولا لا ينتمي؟ لا ينتمي، false
+
+254
+00:20:00,690 --> 00:20:07,710
+طيب الـ element three ينتمي للـ set؟ three آه ينتمي
+
+255
+00:20:07,710 --> 00:20:11,990
+فعلا هو العنصر أصلًا اللي موجود فـ true طيب التمثيل
+
+256
+00:20:11,990 --> 00:20:16,490
+نفسه هذا، هيكة function، تمثيل كتمثيل هو فعلا
+
+257
+00:20:16,490 --> 00:20:21,410
+function جيد، هذه برضه كنتم تستخدموها نفس الشيء
+
+258
+00:20:21,410 --> 00:20:26,710
+في البرمجة لما كنت في عندك مجموعة عناصر داخل الـ
+
+259
+00:20:26,710 --> 00:20:30,970
+database وبدك تعمل check عليها، query عليها هل هي
+
+260
+00:20:30,970 --> 00:20:34,170
+موجودة ولا مش موجودة، العنصر موجود ولا غير موجود
+
+261
+00:20:34,170 --> 00:20:39,050
+طيب نفس الفكرة زي ما عملنا فيه الـ implication
+
+262
+00:20:39,050 --> 00:20:43,590
+وقلنا هي نفس الـ implication والـ disjoint أو الـ
+
+263
+00:20:43,590 --> 00:20:48,720
+disjunction هم نفسهم function برضه في الـ set الـ
+
+264
+00:20:48,720 --> 00:20:52,960
+union والـ intersection والـ complement برضه نفس
+
+265
+00:20:52,960 --> 00:20:57,060
+الفكرة، بقدر أحطهم في بداية التعريف كـ function from
+
+266
+00:20:57,060 --> 00:21:05,640
+A to A زي لما نقول الـ intersection from الـ 6 و1 و
+
+267
+00:21:05,640 --> 00:21:12,810
+3 to 6، 3 و4 بالظبط حيكون عندك تلاتة،  الاعتبار أنت
+
+268
+00:21:12,810 --> 00:21:16,370
+بتقوله intersection ما بين عنصرين، فالعنصرين هدول
+
+269
+00:21:16,370 --> 00:21:20,070
+هم المتغيرين للـ function، هل فيه intersection بدون
+
+270
+00:21:20,070 --> 00:21:23,550
+ما يكون فيه عندك two sets؟ مفيش، أنت بدك
+
+271
+00:21:23,550 --> 00:21:26,390
+intersection أو union معناته لازم يكون يعطيك إيش؟
+
+272
+00:21:26,390 --> 00:21:30,150
+إيش؟ two sets مجموعتين عشان فعلا أجيب الـ operation
+
+273
+00:21:30,150 --> 00:21:34,250
+هذه، أشوف تأثير الـ operation، حقيقة كويس، فمعنى ذلك
+
+274
+00:21:34,250 --> 00:21:39,710
+بالنسبة لك أنت هي function محتاجة two inputs X1 X2
+
+275
+00:21:39,710 --> 00:21:43,950
+فهنا عرفنا له X أولى و X ثانية، الآن بيطلق النتيجة
+
+276
+00:21:43,950 --> 00:21:49,390
+بدونها ما لها معنى لأنه هيطلقها هي هي، فإذن نقول لها أي
+
+277
+00:21:49,390 --> 00:21:53,890
+معنى، تمام فهنا واضحة، تلاتة واضحة أكثر أنه إحنا
+
+278
+00:21:53,890 --> 00:21:55,510
+بنتعامل مع function
+
+279
+00:21:57,720 --> 00:22:01,660
+تمام، الآن بدنا نحط شوية terminology لـ function
+
+280
+00:22:01,660 --> 00:22:04,560
+هذه، بعد ما فهمنا أن فعلا حياتنا اللي عندنا من أول
+
+281
+00:22:04,560 --> 00:22:09,060
+الفصل حتى اللحظة، كل اللي أخذناه هم بنقدر بكل بساطة
+
+282
+00:22:09,060 --> 00:22:11,840
+نمثلهم بشكل functions، الآن بدنا نفهم الـ function
+
+283
+00:22:11,840 --> 00:22:18,440
+بشكلها اللي أنتم كنتم تأخذوه حول if function if
+
+284
+00:22:18,440 --> 00:22:25,050
+from A to B هذا معناه أن f of A و A لابد أن تكون
+
+285
+00:22:25,050 --> 00:22:30,270
+belong to capital A بتساوي B، و B لازم تظهر في الـ
+
+286
+00:22:30,270 --> 00:22:37,930
+set B، في الحالة هذه بقدر أقول أن capital A بيسموها
+
+287
+00:22:37,930 --> 00:22:45,210
+domain، هذا الـ domain، فإذن الـ domain هي الـ set of
+
+288
+00:22:45,210 --> 00:22:52,570
+input argument للـ input argument أو لـ small a أي
+
+289
+00:22:52,570 --> 00:22:57,370
+small a ممكنة أو ممكن تكون input للـ function فهي
+
+290
+00:22:57,370 --> 00:23:01,190
+لازم تكون تنتمي للـ domain، لازم تكون موجودة في الـ
+
+291
+00:23:01,190 --> 00:23:05,850
+domain، زي لما كنتم بترسموا الرسم الطبيعي تبعكم
+
+292
+00:23:05,850 --> 00:23:14,120
+اللي هي العلاقة بين y تساوي f of x، X هذا كل هذه
+
+293
+00:23:14,120 --> 00:23:17,160
+القيم اللي ممكن تظهر فيها الـ function أو ممكن
+
+294
+00:23:17,160 --> 00:23:21,100
+applied عليها الـ function كلها هذه اسمها domain
+
+295
+00:23:21,100 --> 00:23:27,000
+كلها اسمها domain، تمام، في المقابل B بيسموها الـ
+
+296
+00:23:27,000 --> 00:23:34,020
+codomain، الـ codomain المجال المقارن اللي هو
+
+297
+00:23:34,020 --> 00:23:37,300
+هيكون مقترن بالـ domain نفسه، فعشان هيك بيسموها codomain
+
+298
+00:23:37,300 --> 00:23:42,960
+اللي هو مقارن، المقارن للـ domain نفسه، كويس، لاحظ أن
+
+299
+00:23:42,960 --> 00:23:52,140
+أنت بتعمل هنا B تساوي f of A، B هذه هي صورة للـ
+
+300
+00:23:52,140 --> 00:23:58,380
+input A فإذن هي الصورة للـ pre-image، image ناتج
+
+301
+00:23:58,380 --> 00:24:08,420
+مقبل الصورة اللي هي B هي الـ image of A بناء على
+
+302
+00:24:08,420 --> 00:24:14,650
+إيش؟ with respect to F أو under F بالنسبة لـ F فمعنى
+
+303
+00:24:14,650 --> 00:24:17,250
+ذلك أن الـ image هذه مش دائمًا هتكون نفس الشيء
+
+304
+00:24:17,250 --> 00:24:22,890
+لو أعطيتها A حسب الـ function، حسب الـ function تربيع
+
+305
+00:24:22,890 --> 00:24:26,610
+غير تكعيب، مع أنه أنا بكون بيعطيها نفس الـ X لكن
+
+306
+00:24:26,610 --> 00:24:31,490
+بيختلف الـ output طبعًا، الـ Y بناء على الـ function
+
+307
+00:24:31,490 --> 00:24:34,450
+فإذن الـ function عامل مؤثر، كويس، الـ A هنا بتصير
+
+308
+00:24:34,450 --> 00:24:41,080
+اسمها الـ pre-image، الـ pre-image of B under F فهذه
+
+309
+00:24:41,080 --> 00:24:46,520
+المعطى اللي أنتج B على الـ function F باستخدام الـ
+
+310
+00:24:46,520 --> 00:24:50,580
+function F فهي صارت الـ pre-image ما قبل الصورة اللي
+
+311
+00:24:50,580 --> 00:24:55,520
+أنتجت لنا الصورة باستخدام الـ function F، طيب، فـ in
+
+312
+00:24:55,520 --> 00:24:59,600
+general we may have more than one pre-image
+
+313
+00:25:01,740 --> 00:25:05,640
+فإذن الـ image ممكن يكون لها أكثر أو ممكن يكون لها أكثر
+
+314
+00:25:05,640 --> 00:25:09,940
+من pre-image، صحيح الكلام هذا؟ صحيح، صحيح جدًا، هاي
+
+315
+00:25:09,940 --> 00:25:18,020
+مثال، هاي
+
+316
+00:25:18,020 --> 00:25:25,060
+X واحد، هاي X اتنين، وكلاهما لهم نفس الـ Y فهي مش
+
+317
+00:25:25,060 --> 00:25:29,910
+image واحدة، image لها two pre-image لها two pre-image، طيب
+
+318
+00:25:29,910 --> 00:25:35,750
+مثال ثاني كان قال لي معناته أن هي two pre-image مثلا
+
+319
+00:25:35,750 --> 00:25:41,530
+وخلاص لأ هي أكثر من هيك زي
+
+320
+00:25:41,530 --> 00:25:46,780
+sinusoidal مثلا اللي هي الـ periodic functions هذه
+
+321
+00:25:46,780 --> 00:25:50,620
+عدد لانهائي اللي لها من الـ pre-images، مش هيك، مش pre-
+
+322
+00:25:50,620 --> 00:25:54,740
+image واحدة، تمام فإذن اقتنعنا بهذه الجملة، فاهمينها؟
+
+323
+00:25:54,740 --> 00:26:00,860
+مفهوم، مش مشكلة، الـ range، الـ range الآن، الـ range هي
+
+324
+00:26:00,860 --> 00:26:06,360
+عبارة عن set R، subset من B، فهي جزء من الـ codomain
+
+325
+00:26:06,360 --> 00:26:11,860
+بس هذه الجزء الحقيقي للـ function من الـ codomain
+
+326
+00:26:11,860 --> 00:26:16,170
+بمعنى لو... لو أنا بتكلم عن الـ function f
+
+327
+00:26:16,170 --> 00:26:22,130
+هذه، هتكون عبارة عن set of B، لاحظ set of B فهي
+
+328
+00:26:22,130 --> 00:26:27,230
+عناصر الـ... الـ B، الـ images، الصور، هذه واضح أن هي الـ
+
+329
+00:26:27,230 --> 00:26:36,610
+images بشرط أن يوجد A لإنتاج B، يوجد A لو طبقت عليه
+
+330
+00:26:36,610 --> 00:26:41,890
+الـ function تطلع B، تطلع B، أحيانًا في بعض الأمور زي
+
+331
+00:26:41,890 --> 00:26:49,950
+هنا مش كل الـ B's تظهر معاه، هاي الصورة واضحة، B in
+
+332
+00:26:49,950 --> 00:26:57,450
+general، الـ capital B بقول إن هي real number أو
+
+333
+00:26:57,450 --> 00:27:00,810
+exactly حتى الـ real number هيها من minus infinity
+
+334
+00:27:00,810 --> 00:27:06,590
+to infinity in general لكن actual النتائج الحقيقية
+
+335
+00:27:06,590 --> 00:27:13,340
+للـ small B تبدأ من صفر، صح؟ فعليًا بتبدأ من صفر، فهذه
+
+336
+00:27:13,340 --> 00:27:16,540
+بتختلف حسب الـ function، فهنا أنا بعمل رغم أنه
+
+337
+00:27:16,540 --> 00:27:21,080
+استخدمنا هنا كل العناصر في الـ domain من minus
+
+338
+00:27:21,080 --> 00:27:24,120
+infinity to infinity لكن في الـ codomain ما ظهرتش
+
+339
+00:27:24,120 --> 00:27:28,120
+كلها، ظهر فقط من الصفر to infinity، طب والجزء
+
+340
+00:27:28,120 --> 00:27:34,180
+السالب ما ظهرش، لا يوجد أي عنصر B يظهر أصلًا، يعني ما فيش
+
+341
+00:27:34,180 --> 00:27:42,200
+عندك أي عنصر A هنا هيظهر لك بالسالب، فلابد أن يكون
+
+342
+00:27:42,200 --> 00:27:45,740
+العناصر، عشان أقول أن هذه اسمها range لابد أن يكون
+
+343
+00:27:45,740 --> 00:27:53,260
+العنصر فيه عنصر pre-image له، بقدر ينتجه، بيقدر ينتجه
+
+344
+00:27:53,260 --> 00:27:58,420
+فهنا كل ما يتم إنتاجه فعليًا، حقيقة، بنحطه كله في set
+
+345
+00:27:58,420 --> 00:28:02,860
+واحدة بنسميها range، والـ range أكيد هتكون مجموعة
+
+346
+00:28:02,860 --> 00:28:06,640
+جزئية من الـ codomain، قد يكون الـ codomain كله
+
+347
+00:28:06,640 --> 00:28:10,160
+وقد تكون مجموعة جزئية زي مثلا sinusoidal
+
+348
+00:28:10,160 --> 00:28:15,280
+sinusoidal عندك الـ peaks، الـ upper والـ lower peaks
+
+349
+00:28:15,280 --> 00:28:21,070
+تبعونك، خلاص، هاي كل الـ range otherwise مش موجود
+
+350
+00:28:21,070 --> 00:28:26,630
+ما فيش أي قيمة أصلًا لـ X بتقدر تنتج لك أكثر من
+
+351
+00:28:26,630 --> 00:28:33,370
+هالرقمين، أكبر أو أقل، نهائي، فأنت عندك range R رغم
+
+352
+00:28:33,370 --> 00:28:40,570
+أن أنت اسميًا عندك R للـ B فهي الـ real number بس
+
+353
+00:28:40,570 --> 00:28:45,230
+فعليًا الـ range لأ ما يأخذش كل هذا الكلام، تمام فهي...
+
+354
+00:28:45,230 --> 00:28:48,900
+آه تفضل، هو أنا على أي أساس بحدد الـ codomain mainly الـ
+
+355
+00:28:48,900 --> 00:28:53,240
+codomain... لأ الـ codomain بن... بناء على الـ
+
+356
+00:28:53,240 --> 00:28:57,000
+domain، أنت لاحظ إحنا لسة منا codomain مقترن
+
+357
+00:28:57,000 --> 00:29:00,940
+بمين؟ خلاص، أنت إيش العناصر اللي أخذتها في الـ
+
+358
+00:29:00,940 --> 00:29:07,210
+domain؟ تمام؟ هذا إذا كانوا الاتنين اللي هو نفس...
+
+359
+00:29:07,210 --> 00:29:10,870
+نفس المعنى أو نفس المصطلح real numbers خلاص فيه
+
+360
+00:29:10,870 --> 00:29:15,870
+real numbers، في أحيانًا الـ application نفسه بيأثر
+
+361
+00:29:15,870 --> 00:29:19,110
+في اختيارنا، هناخد مثال عليها، قاعدين هناخد مثال
+
+362
+00:29:19,110 --> 00:29:22,750
+مثلا، بس أنت بتحط جميع الاحتمالات الممكنة للـ codomain
+
+363
+00:29:22,750 --> 00:29:27,190
+قاعدين هنشوفها، جينا مثال لها، هيو، على طول
+
+364
+00:29:27,190 --> 00:29:32,300
+إتجاه أي مثال، مثلا لو افترضنا أن في عندنا الـ F، الـ F
+
+365
+00:29:32,300 --> 00:29:36,780
+هي function، الـ function هذه بتعمل mapping، mapping
+
+366
+00:29:36,780 --> 00:29:40,460
+معناته بتعمل كأنه دور الـ function نفسها، دور الـ
+
+367
+00:29:40,460 --> 00:29:43,960
+function اللي هي عملية الـ modification لـ X بحيث
+
+368
+00:29:43,960 --> 00:29:49,160
+أنه يطلع Y أو small A لـ small B، بتعمل mapping للـ
+
+369
+00:29:49,160 --> 00:29:55,300
+students in this class to the set of grades طيب in
+
+370
+00:29:55,300 --> 00:29:59,100
+general هيكون grades، الشمة يا إيه اللي هو ممتاز
+
+371
+00:29:59,100 --> 00:30:04,840
+جيد جدًا، جيد، مقبول أو راسب؟ عندنا شيء ثاني؟ فأنت
+
+372
+00:30:04,840 --> 00:30:09,320
+عايز... المثال وضح لك أنه إيش الممكن؟ الممكن هي
+
+373
+00:30:09,320 --> 00:30:14,120
+الخمسة هدول، خلاص، بتحط الخمسة A أو B أو C أو D أو
+
+374
+00:30:14,120 --> 00:30:18,500
+F هي الـ codomain، واضحة الآن كيف هي الـ codomain؟
+
+375
+00:30:18,500 --> 00:30:21,880
+لأنه مختلف عن الـ students، الـ students
+
+376
+00:30:21,880 --> 00:30:24,760
+أعداد، العدد ممكن يكون مئة، ممكن خمسين، ممكن
+
+377
+00:30:24,760 --> 00:30:27,440
+سبعين، ممكن ثمانين، كل مرة بيختلف، بس الـ grades
+
+378
+00:30:27,440 --> 00:30:32,480
+معروف أنه... معروفين، limited، بيقعوا من A to F حسب
+
+379
+00:30:32,480 --> 00:30:41,480
+المعدلات، تمام، at this point حتى اللحظة، حتى اللحظة
+
+380
+00:30:42,230 --> 00:30:44,710
+اللي إحنا فيها إحنا ما زلنا في أول الفصل لنعرف
+
+381
+00:30:44,710 --> 00:30:47,250
+خيركم، من شركه، لسه ما عملناش أي امتحانات ولا بنعرف
+
+382
+00:30:47,250 --> 00:30:52,570
+كيف الوضع معانا، تمام؟ حتى اللحظة، if أو الـ... الـ
+
+383
+00:30:52,570 --> 00:30:57,410
+codomain تبعنا إيش يعني؟
+
+384
+00:30:57,410 --> 00:31:00,670
+الآن كلكم مرشحين اللي ممكن تاخدوا أي شيء، صحيح، فـ in
+
+385
+00:31:00,670 --> 00:31:06,190
+general كله، طيب، الـ range أكيد مش هيكون معروفة، أنا
+
+386
+00:31:06,190 --> 00:31:08,450
+بقول لكم حتى اللحظة أنا لسة ما عرفتش خيركم و أسوأكم
+
+387
+00:31:08,450 --> 00:31:13,250
+صح؟ ما عرفناش لسه كيف أدائكم ولا شفنا الامتحانات
+
+388
+00:31:13,250 --> 00:31:16,270
+كيف هتكون ولا كيف الـ response ولا أنتم شفتوا كيف
+
+389
+00:31:16,270 --> 00:31:20,950
+الامتحانات بتاعتي هتصير، حتى اللحظة الـ noun الـ range
+
+390
+00:31:20,950 --> 00:31:26,910
+الـ noun لأنه لسة ما طبقناش الـ function، شكل الـ
+
+391
+00:31:26,910 --> 00:31:30,230
+function لسة ما شفناش نتائجه، مدام لسة ما شفنا
+
+392
+00:31:30,230 --> 00:3
+
+445
+00:36:10,910 --> 00:36:15,850
+function G تكون هي الـ input للـ F، الـ input للـ F
+
+446
+00:36:15,850 --> 00:36:21,870
+فهتكون بهذا الشكل بحيث أن الـ input للـ F هي هي
+
+447
+00:36:21,870 --> 00:36:30,230
+الـ B فأصبحت كأنه F of B، وهدي تتفق تماما مع هنا من
+
+448
+00:36:30,230 --> 00:36:36,250
+B to C فهتسوي للمفروض small c، و small c هذه حتما
+
+449
+00:36:36,250 --> 00:36:39,790
+لازم تكون belong to ايش capital C
+
+450
+00:36:43,420 --> 00:36:49,300
+تمام الـ .. الـ composition هي زيها زي الـ Cartesian
+
+451
+00:36:49,300 --> 00:36:54,660
+product ايش يعني؟ ليس التبادلية، يعني if compose G
+
+452
+00:36:54,660 --> 00:36:59,900
+مش بالضروري تساوي G compose F، حالات كتير نادرة ممكن
+
+453
+00:36:59,900 --> 00:37:03,460
+تظبط بس in general لأ، بيساووا بعض in general لأ، ما
+
+454
+00:37:03,460 --> 00:37:09,820
+بيساوا بعض، تمام، هاي اتكلمنا عن نفس القاعدة
+
+455
+00:37:15,360 --> 00:37:19,820
+Okay، أنواع الـ functions بعد ما أن تعرفنا عنه على
+
+456
+00:37:19,820 --> 00:37:24,320
+مجموعة operators وكانت plus و ضرب، مافيش فيهم مشاكل
+
+457
+00:37:24,320 --> 00:37:27,860
+هدولة الـ composition أتوقع مش كتير صعبة، بسيطة جدا
+
+458
+00:37:27,860 --> 00:37:31,080
+سهلة، مش كتير لما بتعمل function compose function
+
+459
+00:37:31,080 --> 00:37:34,680
+تانية، مش هالأشي اللي ضخم، الأن أنواع الـ functions
+
+460
+00:37:34,680 --> 00:37:39,080
+وكيف ممكن نعرفهم، في function اسمها one to one
+
+461
+00:37:39,780 --> 00:37:43,560
+business بيسموها أحيانا injection، injection اللي
+
+462
+00:37:43,560 --> 00:37:46,840
+هو حقن، بمعنى الحقن دايما بتقطع، لو واحد صح فالـ
+
+463
+00:37:46,840 --> 00:37:51,100
+input له output واحد بس، خلاص من input لـ output
+
+464
+00:37:51,100 --> 00:37:56,740
+انتهى حقن، فالحقن من الا بس، فبيسموها one to one
+
+465
+00:37:56,740 --> 00:38:00,040
+injective أو injection، if and only if every
+
+466
+00:38:00,040 --> 00:38:05,470
+element of its range has only one preimage، كل
+
+467
+00:38:05,470 --> 00:38:09,610
+element في الـ range، في الـ actual output هو فعليا
+
+468
+00:38:09,610 --> 00:38:15,150
+مالوش إلا preimage واحدة، وليس أكثر من ذلك، كويس
+
+469
+00:38:15,150 --> 00:38:20,770
+فعلينا نوضح تماما أن حالة زي التربيع مش هتكون ضمن
+
+470
+00:38:20,770 --> 00:38:25,590
+هذا التعريف إطلاقا، كويس، formally كيف ممكن نكتبها؟
+
+471
+00:38:25,590 --> 00:38:31,250
+لو عندي الـ function from a to b، a to b فبقدر
+
+472
+00:38:31,250 --> 00:38:35,220
+أسميها هي one to one أو injective، if and only if
+
+473
+00:38:35,220 --> 00:38:41,940
+فهي equivalent لأنة لا يوجد عنصرين مختلفين
+
+474
+00:38:41,940 --> 00:38:52,420
+عنصرين مختلفين كمان، والـ image تبعتهم متساوية، يعني
+
+475
+00:38:52,420 --> 00:38:56,320
+مش هاد الـ f of x، الـ image بتاعت الأول، والـ f of y
+
+476
+00:38:56,320 --> 00:39:00,600
+الـ image بتاعت التاني، لا يساووا بعض، يعني لا يوجد
+
+477
+00:39:00,600 --> 00:39:06,900
+image لأكثر من preimage واحد، لا يوجد، بدأناها بلا
+
+478
+00:39:06,900 --> 00:39:11,240
+يوجد، فإذا هذا معناه أن هنا هذه ليست one to one على
+
+479
+00:39:11,240 --> 00:39:16,280
+طول، ليست one to one، تمام، فـ only one element of the
+
+480
+00:39:16,280 --> 00:39:22,820
+domain is mapped to any given one element of range
+
+481
+00:39:22,820 --> 00:39:30,880
+فقط preimage واحدة لكل element في الـ range، طيب في
+
+482
+00:39:30,880 --> 00:39:36,280
+الحالة دي الـ domain والـ range حتما هيساووا بعض، صح
+
+483
+00:39:36,280 --> 00:39:39,500
+لأن كل عنصر في الـ domain هيروح يما الـ mapping
+
+484
+00:39:39,500 --> 00:39:44,000
+لعنصر واحد في الـ range، وكل عنصر في الـ range احنا
+
+485
+00:39:44,000 --> 00:39:48,820
+جابينه من عنصر واحد في الـ domain فقط، فإذا أكيد
+
+486
+00:39:48,820 --> 00:39:52,340
+هيكون الـ اتنين have the same cardinality، نفس
+
+487
+00:39:52,340 --> 00:39:56,020
+العناصر اللي في الـ domain، في الـ range، طب والـ
+
+488
+00:39:56,020 --> 00:39:56,400
+codomain؟
+
+489
+00:39:59,670 --> 00:40:04,250
+نعرفش، احنا العلاقة الواضحة actually أن كل واحد في
+
+490
+00:40:04,250 --> 00:40:07,690
+الـ range هو يقابل واحد في الـ domain، الـ code domain
+
+491
+00:40:07,690 --> 00:40:10,230
+نعرفش، لأن الـ application هو اللي بيحددنا الـ code
+
+492
+00:40:10,230 --> 00:40:15,070
+domain، يمكن يكون أكثر أو أقل، بيعرفش، تمام، فممكن
+
+493
+00:40:15,070 --> 00:40:20,720
+يكون أكثر، ممكن الأن كل element في الـ domain هو
+
+494
+00:40:20,720 --> 00:40:25,440
+injected، بيحقق أن كل element في الـ domain فعليا
+
+495
+00:40:25,440 --> 00:40:30,280
+عشان أشوف تأثير الـ function عليه، هيوح على عنصر
+
+496
+00:40:30,280 --> 00:40:35,700
+واحد فقط في الـ range، فكل واحد له different element
+
+497
+00:40:35,700 --> 00:40:38,560
+of range، عشان هيك طبعا قلنا الملاحظة الأولى أن
+
+498
+00:40:38,560 --> 00:40:42,440
+أكيد لازم الـ domain هيساوي الـ range، كيف بنمثلها زي
+
+499
+00:40:42,440 --> 00:40:46,340
+ما قلنا بالـ bipartate؟ بالـ bipartate، حالة زي اللي
+
+500
+00:40:46,340 --> 00:40:49,080
+.. اللي هنا هي واحدة، اتنين، تلاتة، نبدأ في الأولى
+
+501
+00:40:49,080 --> 00:40:56,520
+الأولى one to one، باينة كل عنصر mapping أو بيصير له
+
+502
+00:40:56,520 --> 00:41:01,240
+mapped أو بيصير له under if عنصر واحد فقط، وهنا نفس
+
+503
+00:41:01,240 --> 00:41:04,220
+الكلام، عنصر، عنصر، عنصر، الـ domain والـ codomain
+
+504
+00:41:04,220 --> 00:41:07,220
+بيفرجش معانا حجمهم، لكن اللي بيفرج معايا أن الـ
+
+505
+00:41:07,220 --> 00:41:11,680
+range يساوي الـ domain بالظبط، الـ domain هنا أربعة
+
+506
+00:41:11,680 --> 00:41:16,060
+الـ range أربعة، خلاص، الـ code domain ايش ما يطلع يطلع
+
+507
+00:41:16,060 --> 00:41:22,760
+فهذي one to one، التانية أكيد لأ، هذي function فعليا
+
+508
+00:41:22,760 --> 00:41:26,720
+function، هاندي two pre-image اللي هم نفس الـ output
+
+509
+00:41:26,720 --> 00:41:30,120
+زي الحالة اللي عندنا هنا، أي حالة من الحالات، okay
+
+510
+00:41:30,120 --> 00:41:38,380
+لكن ليست one to one، الطيب، التالتة ليش unstable؟
+
+511
+00:41:42,110 --> 00:41:45,930
+هنا غير مستقرة الـ function، يعني بمعنى أنت بتعطيها
+
+512
+00:41:45,930 --> 00:41:50,750
+الـ input كل مرة بتعطيك output شكل، مرة بتعطيك الـ
+
+513
+00:41:50,750 --> 00:41:53,470
+output هذا، ومرة بتعطيك الـ output هذا، مع أنه نفس
+
+514
+00:41:53,470 --> 00:41:58,330
+الـ input، فهذه unstable، هيك الـ function unstable
+
+515
+00:41:58,330 --> 00:42:02,350
+فهذه ليست function من الأساس، هذه بالأساس ليست
+
+516
+00:42:02,350 --> 00:42:04,610
+function، بتعاملش معها أن هي function، هذه
+
+517
+00:42:04,610 --> 00:42:08,190
+بالنسبة لنا حتى لو في الـ signal ولا في أي مادة
+
+518
+00:42:08,190 --> 00:42:10,830
+أخدتوها، بتسموها unstable، بمعنى أن هي غير مقبول
+
+519
+00:42:10,830 --> 00:42:13,930
+أصلا، تتسيبوها بهذا الشكل، غير مقبول تركها بهذا
+
+520
+00:42:13,930 --> 00:42:18,850
+الشكل، طيب في المقابل الـ into هذا ممكن يعطيني عشان
+
+521
+00:42:18,850 --> 00:42:22,710
+أقول أن هي unto، عفوا one to one، لسة ما وصلناش للـ unto
+
+522
+00:42:22,710 --> 00:42:27,460
+الـ one to one sufficient condition، يعني لازم يكون
+
+523
+00:42:27,460 --> 00:42:30,260
+في شرط كافي أني أقول والله الـ function هتكون فعلا
+
+524
+00:42:30,260 --> 00:42:36,740
+one to one، في شرط أو أحد الشرطين يتحقق، الحقيقة بس
+
+525
+00:42:36,740 --> 00:42:41,800
+هم مفهوما شرط واحد، أنه يكون monotonically
+
+526
+00:42:41,800 --> 00:42:47,180
+increasing أو decreasing، mono monotonic من كلمة
+
+527
+00:42:47,180 --> 00:42:52,580
+mono، أحادي، غير stereo، مش mono و stereo، الأعوان كله
+
+528
+00:42:52,580 --> 00:42:57,090
+stereo، mono اللي هو كان أحاديا، وحدي معناته وحدي
+
+529
+00:42:57,090 --> 00:43:00,590
+الاتجاه، أما في اتجاه الـ increasing أو الـ
+
+530
+00:43:00,590 --> 00:43:03,810
+decreasing، بمعنى أن الـ function أما تساعدية أو
+
+531
+00:43:03,810 --> 00:43:11,170
+تنازلية، بس، طيب المثال اللي شفناه اللي قلنا عليه
+
+532
+00:43:11,170 --> 00:43:15,370
+ليست onto، هي تنازلية، ممتاز، بس اجت عند نقطة معينة
+
+533
+00:43:15,370 --> 00:43:18,450
+ورجعت تساعدية، فـ not mono
+
+534
+00:43:21,030 --> 00:43:25,710
+not mono، لكن لما تقول ليه هي تصاعدية وبس
+
+535
+00:43:25,710 --> 00:43:29,470
+monotonic
+
+536
+00:43:29,470 --> 00:43:36,530
+increasing، فهي أحدية التصاعد، أحدية التصاعد، خلاص، من
+
+537
+00:43:36,530 --> 00:43:40,870
+minus infinity to infinity بيبقى المتصاعدة، معدل
+
+538
+00:43:40,870 --> 00:43:44,090
+التصاعد بيجل، بيزيد، مش مشكلة، يعني هنا مثلا كان حاد
+
+539
+00:43:44,090 --> 00:43:47,490
+جدا، وبعدين بدأ يجل، زي الـ exponential مثلا، بس
+
+540
+00:43:47,490 --> 00:43:52,060
+تصاعدية، دلتا بتبقى اسمها تصاعدية، هادي one to one أو
+
+541
+00:43:52,060 --> 00:43:58,340
+تنازلية، decreasing
+
+542
+00:43:58,340 --> 00:44:03,800
+بس monotonic في الآخر، و أحادية الاتجاه، إذا هذا
+
+543
+00:44:03,800 --> 00:44:07,900
+الكلام تحقق، وأنت بتحقق، خليني هنا في الأولى بتحقق
+
+544
+00:44:07,900 --> 00:44:10,600
+إذا كان بتكلم عن الـ increasing في البداية
+
+545
+00:44:10,600 --> 00:44:15,820
+increasing لـ X واحد و X اتنين، يعني لأي two points
+
+546
+00:44:16,830 --> 00:44:23,090
+لأي two points، إذا X1 أصغر من X2 فالـ functional
+
+547
+00:44:23,090 --> 00:44:25,370
+value بتاعتها برضه أصغر من الـ functional value لـ
+
+548
+00:44:25,370 --> 00:44:34,610
+X2، X1
+
+549
+00:44:34,610 --> 00:44:41,230
+أصغر من X2، معناه ذلك أن الـ F of X1 لازم تكون برضه
+
+550
+00:44:41,230 --> 00:44:47,400
+أقل من F of X2، بمعنى إذا كان X1 أصغر من X2 لازم
+
+551
+00:44:47,400 --> 00:44:53,800
+تكون Y1 أصغر من Y2، في نفس الاتجاه، تمام، أما في حالة
+
+552
+00:44:53,800 --> 00:44:58,760
+الـ decreasing بالعكس هتكون ايش؟ بالعكس، خلّيني أنا
+
+553
+00:44:58,760 --> 00:45:02,560
+أخذ مثلا هنا، لأ، خلّيني أنا أخذها في الموجب عشان
+
+554
+00:45:02,560 --> 00:45:06,700
+بدّيش تتخربطوا معاه في السالب، هاي حالتين زي هدول
+
+555
+00:45:10,040 --> 00:45:21,120
+هي X1 و X2، وهنا X1، F of X1، F of X2، لاحظوا X1 أصغر
+
+556
+00:45:21,120 --> 00:45:28,280
+من X2، بس في المقابل F of X1 أكبر من F of X2، إذا
+
+557
+00:45:28,280 --> 00:45:34,220
+فعلا لطول الـ function، أي قيمتين بتاخدهم دايما نفس
+
+558
+00:45:34,220 --> 00:45:36,520
+الـ relation، هيك معناته دايما increasing،
+
+559
+00:45:36,520 --> 00:45:43,050
+decreasing، لأي نقطتين .. أي نقطتين بتاخدهم على الـ
+
+560
+00:45:43,050 --> 00:45:48,510
+curve، يعني بمعنى أي two elements من الـ domain، من
+
+561
+00:45:48,510 --> 00:45:51,510
+الـ domain، الـ ratio بتاعهم بهذا الشكل دائما ..
+
+562
+00:45:51,510 --> 00:45:54,910
+دائما عكسية، فهي دائما decreasing .. دائما
+
+563
+00:45:54,910 --> 00:45:58,250
+decreasing، أما إذا ترضية والله بيزيدوا مع بعض
+
+564
+00:45:58,250 --> 00:46:00,910
+معناته بتزيد كمان الـ y's تبعتهم، أو الـ output تبعهم
+
+565
+00:46:00,910 --> 00:46:05,290
+خلاص، معناته دائما increasing، فـ automatic بقول عنها
+
+566
+00:46:05,290 --> 00:46:09,940
+one to one، على طول بنقول عنها ايش؟ one to one، أمثلة
+
+567
+00:46:09,940 --> 00:46:17,940
+عليها زي مثلا الـ X تكعيب، الـ X تكعيب من الأمثلة
+
+568
+00:46:17,940 --> 00:46:30,720
+المشهورة جدا لـ الـ one to one، هاي
+
+569
+00:46:30,720 --> 00:46:35,240
+X تكعيب
+
+570
+00:46:37,650 --> 00:46:44,770
+Y تساوي X تكعيب، أو Y = F of X تكعيب، of X تكعيب، وين
+
+571
+00:46:44,770 --> 00:46:54,390
+روحت الـ .. نكتبها بشكل أوضح، تكعيب
+
+572
+00:46:54,390 --> 00:46:59,770
+أو Y تساوي F of X، و F of X هنا تساوي X تكعيب، هذه
+
+573
+00:46:59,770 --> 00:47:03,690
+واحدة من الحالات اللي دائما increasing ولا
+
+574
+00:47:03,690 --> 00:47:07,880
+decreasing، increasing، بازدياد .. باستمرار، مستمر ..
+
+575
+00:47:07,880 --> 00:47:11,720
+monotonic، فإذا هذه على طول one to one، طب في
+
+576
+00:47:11,720 --> 00:47:19,100
+المقابل واحد على X، واحد على X، نرسمها على نفس الـ
+
+577
+00:47:19,100 --> 00:47:24,780
+curve بس بلون ثاني، تكون
+
+578
+00:47:24,780 --> 00:47:29,320
+بهذا الشكل، اللون الأحمر، الأحمر هذا اللي هو واحد
+
+579
+00:47:29,320 --> 00:47:35,220
+على X، مالها
+
+580
+00:47:35,220 --> 00:47:35,680
+هذه؟
+
+581
+00:47:38,460 --> 00:47:45,400
+ليش؟ هي .. يعني مش من minus infinity؟ هي من minus
+
+582
+00:47:45,400 --> 00:47:52,680
+infinity وتنازلية، وهي تنازلية، ايش
+
+583
+00:47:52,680 --> 00:47:57,840
+مشكلتكم معها؟
+
+584
+00:47:57,840 --> 00:48:04,690
+at صفر، أيوة، two values، عند الصفر في عندك two values
+
+585
+00:48:04,690 --> 00:48:17,050
+فهي not continuous، هي ليست مستمرة، الصفر
+
+586
+00:48:17,050 --> 00:48:23,910
+من الـ domain ولا لأ؟ من الـ domain، خلينا خطوة خطوة
+
+587
+00:48:23,910 --> 00:48:25,010
+هي من الـ domain
+
+588
+00:48:27,880 --> 00:48:32,680
+لأ، سيبك منه، إن سال الـ function، الـ domain، الـ domain
+
+589
+00:48:32,680 --> 00:48:36,360
+تبعنا مش من minus infinity to infinity، domain
+
+590
+00:48:36,360 --> 00:48:39,660
+ما تكلمتش عن الـ code domain، بتكلم عن الـ domain
+
+591
+00:48:39,660 --> 00:48:44,460
+بمعنى القيم اللي ممكن تكون input للـ function، بغض
+
+592
+00:48:44,460 --> 00:48:48,720
+النظر أنا عارف الـ function ولا مش عارفها، لسة موجود
+
+593
+00:48:48,720 --> 00:48:55,760
+موجود، يعني فعلا موجود، بمعنى أنه ممكن اعتباره a
+
+594
+00:49:01,650 --> 00:49:04,530
+يا جماعة، يا جماعة أنتم خربطتوا الـ domain مع الـ code
+
+595
+00:49:04,530 --> 00:49:07,450
+domain، في الـ domain، الـ domain بعرفه من الأول وخلصنا
+
+596
+00:49:08,280 --> 00:49:10,940
+الـ domain تبعنا من minus infinity to infinity، خلاص
+
+597
+00:49:10,940 --> 00:49:15,660
+الأن مش ذنب الـ domain أنه في عنصر الـ function
+
+598
+00:49:15,660 --> 00:49:21,800
+undefined بالنسبة للـ function، من الـ range، اتكلملي
+
+599
+00:49:21,800 --> 00:49:24,680
+في الـ range، أنت حر، قول لي اه ولا ما ظهرش في الـ range
+
+600
+00:49:24,680 --> 00:49:28,340
+ماشي، بس ما تتكلمش على الـ domain، الـ domain عرفناه من
+
+601
+00:49:28,340 --> 00:49:31,780
+الأول، قلنا من minus infinity to infinity، بمعنى أن
+
+602
+00:49:31,780 --> 00:49:38,670
+الـ X belong to R، الـ Range بمعنى الـ .. الـ .. الـ ..
+
+603
+00:49:38,670 --> 00:49:42,790
+الـ belonging to mean to R، خلاص، فإذا هذا معناه أنه
+
+604
+00:49:42,790 --> 00:49:47,710
+A الممكنة، المفروض أنها belong to capital R، لأن هذا
+
+605
+00:49:47,710 --> 00:49:52,370
+هو الـ domain، هذا هو ايش؟ الـ domain اللي عندنا، خلاص
+
+606
+00:49:52,370 --> 00:49:58,530
+بتعامل معاه، نتعامل معاه، وجدنا أنه عند نقطة معينة
+
+607
+00:49:58,530 --> 00:50:07,410
+عند input معين يوجد two outputs، هي هي، عند نقطة معينة
+
+608
+00:50:07,410 --> 00:50:10,450
+هي هي في الـ domain، تيجي هالوقت على الرسمة هذه تقولي
+
+609
+00:50:10,450 --> 00:50:13,430
+لأ، معناته هذا مش في الـ domain، طب هو في الـ domain
+
+610
+00:50:13,430 --> 00:50:19,230
+ايش هساوي فيه؟ طب هو قاعد هي، أيوة، قولي هنا بطل
+
+611
+00:50:19,230 --> 00:50:22,310
+function، أنت حر، هقول لك أين بالظبط بطلت الـ function
+
+612
+00:50:22,310 --> 00:50:23,970
+لأن هذه الـ function معروفة، هتقول لي لأ، هي مش
+
+613
+00:50:23,970 --> 00:50:27,970
+function عند صفر، هقول لك okay، مافيش مشكلة، بتصير لما
+
+614
+00:50:27,970 --> 00:50:32,250
+بدنا نستخدمها، بدنا نأخذ بالنا من هذه النقطة أن
+
+615
+00:50:32,250 --> 00:50:36,460
+عند صفر ما نستخدمهاش الـ function هذه، بس أما مش تقولي
+
+616
+00:50:36,460 --> 00:50:39,860
+لأ هي
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Z4_jnPs62Eo.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Z4_jnPs62Eo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fb826c07a3b463d0def16e1e25932fae80174828
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Z4_jnPs62Eo.srt
@@ -0,0 +1,787 @@
+1
+00:00:04,990 --> 00:00:09,190
+نقول بسم الله الرحمن الرحيم، المرة الماضية كنا أخذنا
+
+2
+00:00:09,190 --> 00:00:11,850
+الـ algorithm كان ضايق لنا جزئية بسيطة منه، يعني
+
+3
+00:00:11,850 --> 00:00:15,930
+فعلا خلصنا الملف تبع الـ algorithms، اللي ضايل كان
+
+4
+00:00:15,930 --> 00:00:18,590
+هي مجموعة تطبيقات، كنا بدنا نبدأ نعطيكم شوية أمثلة
+
+5
+00:00:18,590 --> 00:00:22,950
+يعني بمعنى أنه ستذهبون لعملية تفكير، كيف نبدأ نفكر في
+
+6
+00:00:22,950 --> 00:00:27,050
+بعض الـ problems، و نكتبها بالـ pseudocode، فهنخليها
+
+7
+00:00:27,050 --> 00:00:30,350
+للأسبوع القادم إن شاء الله، يوم السبت نبدأ، نأخذ هلأ
+
+8
+00:00:30,350 --> 00:00:33,450
+كم من مثال اللي ضايقين، ثم نبدأ في الـ complexity و
+
+9
+00:00:33,450 --> 00:00:38,120
+نبدأ نفهم إيش يعني complexity، بحيث أنه بعدها مباشرة
+
+10
+00:00:38,120 --> 00:00:43,680
+ليوم الاثنين، ممكن نكون روحنا لمفهوم الـ big O و الـ
+
+11
+00:00:43,680 --> 00:00:47,760
+theta، و نفهمها الأمور كلها، و نحاول نستخدمها في بعض
+
+12
+00:00:47,760 --> 00:00:53,280
+algorithms أو أكواد نكتبها، و نحسب لها الـ complexity
+
+13
+00:00:53,280 --> 00:00:57,380
+بتاعتها، تمام. فالجزئية اللي كانت متبقية، مش كتير
+
+14
+00:00:57,380 --> 00:01:01,160
+كبيرة، هي جزئية أمثلة فعليا، و أتوقع أن معظمها مرت
+
+15
+00:01:01,160 --> 00:01:06,560
+عليكم في الـ data structure، و في الـ code السابقة، لو
+
+16
+00:01:06,560 --> 00:01:08,980
+اطلعتوا عليها، حتى في الملفات اللي موجودة على الـ
+
+17
+00:01:08,980 --> 00:01:13,400
+model، ستجدون أن معظمها مرت عليكم، فبنعملها هيك بس
+
+18
+00:01:13,400 --> 00:01:16,560
+بنكتبها بالـ pseudocode، فمش ضايل كتير، فخلينا اليوم
+
+19
+00:01:16,560 --> 00:01:21,770
+نستغل محاضرتنا لمجموعة أمثلة محلولة، خلينا برضه
+
+20
+00:01:21,770 --> 00:01:24,950
+نجيبها من الامتحانات، في العادة من الامتحانات أو من
+
+21
+00:01:24,950 --> 00:01:28,610
+جزء الكتاب اللي عادة بنأخذ منه، و بنجيب منه
+
+22
+00:01:28,610 --> 00:01:32,470
+امتحانات، تمام. و بنختم في الآخر بالـ quiz اللي
+
+23
+00:01:32,470 --> 00:01:36,550
+اتفقنا عليه، الـ quiz بسيط، مجرد بس أنه خلاص بدنا
+
+24
+00:01:36,550 --> 00:01:40,550
+نعمل مراجعات، و إحنا الأصل نبدأ الآن، لأنه مش ضايل
+
+25
+00:01:40,550 --> 00:01:43,610
+كتير، أعتقد للنصف، الناس في كتير قاعد شوية شوية
+
+26
+00:01:43,610 --> 00:01:47,990
+بيجرب علينا، فمناسب جدا نبدأ نفعل هيك نشاطاتكم بالـ
+
+27
+00:01:47,990 --> 00:01:51,870
+quizات، نلين أيديكم، عشان تقدروا تتعاملوا بكرا مع
+
+28
+00:01:51,870 --> 00:01:57,070
+الامتحانات، طيب نبدأ بأول سؤال كان له علاقة بالـ
+
+29
+00:01:57,070 --> 00:02:01,330
+functions، كويس. جزئية الـ function، و بعدين نشوف إيش
+
+30
+00:02:01,330 --> 00:02:03,490
+بدنا نتكلم فيه في جزئية الـ function، واحدة من
+
+31
+00:02:03,490 --> 00:02:06,850
+الأسئلة اللي ممكن تيجي، و ليه يتطلع فيها يفكر إن هي
+
+32
+00:02:06,850 --> 00:02:11,510
+يعني فكرة ضخمة، و .. و إيش صعب، و إيش تعقيدي، و إيش ..
+
+33
+00:02:11,840 --> 00:02:14,720
+هذا للمميزين، و هذا للمش عارفين، بينما هو سؤال عادي
+
+34
+00:02:14,720 --> 00:02:17,780
+جدا، و ما فيه إشي إطلاقا، كل المطلوب أن لو افترضنا
+
+35
+00:02:17,780 --> 00:02:21,220
+أن الـ f of x given، عندك الـ g of x برضه given عندك
+
+36
+00:02:21,220 --> 00:02:26,300
+و given بالمتغيرات الـ parameters، مش معرفة معرفة in
+
+37
+00:02:26,300 --> 00:02:30,460
+general، كويس، اللي هي بـ الـ coefficients تبعتك كلها
+
+38
+00:02:30,460 --> 00:02:35,010
+a, b, c, d، فالـ C هنا اللي هو الميل أو الـ slope تبعك
+
+39
+00:02:35,010 --> 00:02:40,330
+مش مُعطى، هو given كـ parameter، C، و جزء الـ DC اللي
+
+40
+00:02:40,330 --> 00:02:42,350
+موجود في الـ signal أو في الإشارة تبعتك في الـ
+
+41
+00:02:42,350 --> 00:02:45,570
+function، برضه مُعطى بهذا الشكل، نفس الشيء للاتنين
+
+42
+00:02:45,570 --> 00:02:49,570
+مطلوب إيش؟ كلهم constants، هدول كلهم constants
+
+43
+00:02:49,570 --> 00:02:52,370
+لأنه coefficients، بدنا نحسب necessary and
+
+44
+00:02:52,370 --> 00:02:57,010
+sufficient conditions، فمحتاجين الشروط الضرورية
+
+45
+00:02:57,010 --> 00:03:04,210
+والكافية، ضرورية وكافية لإيش؟ لـ الـ a و b و c بحيث
+
+46
+00:03:04,210 --> 00:03:12,990
+أنه تضمن لنا f compose g تساوي g compose f، مش أكثر
+
+47
+00:03:12,990 --> 00:03:18,460
+من هيك، السؤال direct، السؤال direct، ما فيه لا
+
+48
+00:03:18,460 --> 00:03:21,860
+لعبة شمال ولا لعبة يمين، ولا فيه أي حاجة إطلاقا على
+
+49
+00:03:21,860 --> 00:03:26,660
+طول، بتبدأ تقول إيش يعني الـ composition، if compose
+
+50
+00:03:26,660 --> 00:03:33,580
+g، فهي الـ function f لمخرج الـ function g بس، ونفس
+
+51
+00:03:33,580 --> 00:03:38,920
+الكلام g compose f، فنبدأهم واحدة واحدة، هي عند الـ f
+
+52
+00:03:38,920 --> 00:03:47,800
+وهي عند الـ g، نبدأ أول واحدة منهم، F compose G، فمعنى
+
+53
+00:03:47,800 --> 00:03:56,820
+ذلك أنه بتصير F of مخرج G، طب G هي G بننزلها وبس
+
+54
+00:03:56,820 --> 00:04:03,320
+مش أكثر من هيك، و عوض بالـ function F، فالـ term هذا
+
+55
+00:04:03,320 --> 00:04:07,680
+هيك، حنحطه مكان الـ X، كله على بعضه بيجي مكان x عشان
+
+56
+00:04:07,680 --> 00:04:14,620
+تصبح a في c x plus d كله plus b، هذه الأولى، اعمل
+
+57
+00:04:14,620 --> 00:04:18,100
+نفس الكلام لمين؟ للتانية، ممكن طبعا هنا تبدأ تفك
+
+58
+00:04:18,100 --> 00:04:22,200
+فيها شوية شوية، بحيث أن الـ a إتدخله أو تسيبه في
+
+59
+00:04:22,200 --> 00:04:25,560
+النهاية، مش إشكال كبير، لأنه هتسويهم ببعض في الآخر
+
+60
+00:04:25,560 --> 00:04:31,200
+هناخذ جزء ثاني برضه، نفس القضية، الـ two terms هدول
+
+61
+00:04:31,200 --> 00:04:36,770
+بدك تسويهم ببعض، عشان تشوف إمتى لازم يساووا بعض، الشكل
+
+62
+00:04:36,770 --> 00:04:43,030
+مباشر كتير، فما حدش سؤال زي هذا يعمل لي كارثة في صرف
+
+63
+00:04:43,030 --> 00:04:45,930
+الامتحان، و هذا شيء، و شيء صعب، و شيء ما فيه
+
+64
+00:04:45,930 --> 00:04:51,090
+شيء إطلاقا، فحاجة إنه في حاجات حتى هتروح مع بعض، بس
+
+65
+00:04:51,090 --> 00:04:54,810
+هذول الشرطين، لهم فعليا إيش؟ قال لك necessary and
+
+66
+00:04:54,810 --> 00:04:59,930
+sufficient، فخلاص هم sufficient، كافي، الشرط في
+
+67
+00:04:59,930 --> 00:05:04,270
+الحالة هذه، كافي جدا، إيش هو الشرط الكافي هنا؟ أنه
+
+68
+00:05:05,130 --> 00:05:13,030
+علاقتهم ببعض بهذا الشكل، إذا فعلا AD بلس B تساوي BC
+
+69
+00:05:13,030 --> 00:05:17,610
+بلس D، معناته الـ two compositions بيساووا بعض، خلاص
+
+70
+00:05:17,610 --> 00:05:22,560
+هذا الشرط كله على بعضه، هي كل شرط، والله بدك يعني
+
+71
+00:05:22,560 --> 00:05:26,300
+تعمل فيه شوية اختصارات، وتظبطه، سيبته هيك كويس خير و
+
+72
+00:05:26,300 --> 00:05:29,200
+بركة، بدك تظبطه أكثر، أن الـ D هذه ممكن تيجي مع الـ D
+
+73
+00:05:29,200 --> 00:05:31,340
+هذه، و الـ B هذه ممكن تيجي مع الـ B هذه، و تأخذ عوامل
+
+74
+00:05:31,340 --> 00:05:36,520
+مشتركة، تظبطها، تشيكها أكثر، سيبته هيك، فليكن، مش أكثر من
+
+75
+00:05:36,520 --> 00:05:41,980
+هيك طبعا، فسؤال نوعية أسئلة بسيطة، ما فيه شيء، لكن
+
+76
+00:05:41,980 --> 00:05:46,120
+لو روح في الامتحان، نسكه، هيعمل جثة منه، نسكه هيعمل
+
+77
+00:05:46,120 --> 00:05:49,740
+جثة، لأنه هيظن أنه مش فاهم إيش المطلوب، فهي كل
+
+78
+00:05:49,740 --> 00:05:53,560
+المطلوب، لا أكثر ولا أقل، طيب أنواع ثانية طبعا هذه
+
+79
+00:05:53,560 --> 00:05:57,460
+أنواع كتير بسيطة، سهلة، زمان كنا نجيبها في بداية ما
+
+80
+00:05:57,460 --> 00:06:00,860
+كنا بندرس المادة، لغاية بطلنا نجيبها، لأنه مش كتير
+
+81
+00:06:00,860 --> 00:06:04,700
+محتاجة، آه، كنا نجيبها في الزمنات، في الأول لما يقول لك
+
+82
+00:06:04,700 --> 00:06:08,700
+والله، اعملي عندك مجموعة bits، و اعملي إياها كم
+
+83
+00:06:08,700 --> 00:06:13,720
+byte، يعني الفكرة فيها .. الفكرة فيها هي عملية الـ
+
+84
+00:06:13,720 --> 00:06:17,560
+scaling، مش أكثر، عارفين الـ scaling؟ أنتم عارفين
+
+85
+00:06:17,560 --> 00:06:21,260
+الفرق بين الـ bit و الـ byte إيش؟ هي ثمانية، تقسم على
+
+86
+00:06:21,260 --> 00:06:24,040
+ثمانية، عشان الـ جي بيعطيك عدد الـ bytes، لكن في الآخر
+
+87
+00:06:24,040 --> 00:06:27,780
+بتجد أنه أحيانا خارج القسمة بيكون fraction، عشان
+
+88
+00:06:27,780 --> 00:06:31,080
+هيك، بيدخل هذا النوع من أنواع الأسئلة في جزئية الـ
+
+89
+00:06:31,080 --> 00:06:34,060
+function، يعني function اللي هي الـ floor و الـ ceiling
+
+90
+00:06:34,060 --> 00:06:36,580
+ففي عملية الـ ceiling، أنت المفروض تكون عارف إنك أنت
+
+91
+00:06:36,580 --> 00:06:40,000
+لازم تأخذ ceiling، لازم تأخذ ceiling، مش الـ floor، مش
+
+92
+00:06:40,000 --> 00:06:44,220
+الـ floor، ففي الحالة هذه، على طول مثلا، فاصلة ثمانية
+
+93
+00:06:44,220 --> 00:06:48,340
+مش حتقولي معناته صفر، حتقول واحد، and so on، يعني
+
+94
+00:06:50,030 --> 00:06:53,430
+لمجرد أنه كانت كانت نوع من أنواع الأسئلة، يعني لو
+
+95
+00:06:53,430 --> 00:06:58,290
+وجع في يدك، امتحان كتير جديد شوية للمادة، حتجد نوع
+
+96
+00:06:58,290 --> 00:07:05,710
+أسئلة بهذا الشكل، طيب هي بنفس الفكرة برضه، كل مجموعة
+
+97
+00:07:06,790 --> 00:07:11,230
+بايتز، بدنا نحطهم بلوك، ده نعملهم بلوك، خلينا نقول
+
+98
+00:07:11,230 --> 00:07:14,450
+البلوك هذا، الـ frame، خلينا نقول، بدنا نعمل
+
+99
+00:07:14,450 --> 00:07:17,650
+transmission للـ data، و بدنا نعملها مجموعة frames
+
+100
+00:07:17,650 --> 00:07:23,440
+فبهذا الشكل، لو قلنا كم frame أو كم block، في حال
+
+101
+00:07:23,440 --> 00:07:27,900
+أن كان عندك 150 kilobytes، حيكون عندك طبعا كلنا في
+
+102
+00:07:27,900 --> 00:07:31,300
+الآخر عارفين أنه بدنا نقسم على 1500، بس طبعا بعد ما
+
+103
+00:07:31,300 --> 00:07:33,420
+تضرب في الـ unit اللي موجودة عندك، kilo معناته أنك
+
+104
+00:07:33,420 --> 00:07:38,200
+بتتكلم عن ألف، يعني هذه 150 ألف byte الأولى، فبدك
+
+105
+00:07:38,200 --> 00:07:42,960
+تقول 150 ألف byte، و تقسم على الـ 1500، الأول ما فيه
+
+106
+00:07:42,960 --> 00:07:46,680
+شيء، بيطلع عدد صحيح، integer، ما فيه مشكلة، التاني برضه
+
+107
+00:07:46,680 --> 00:07:49,700
+بتهيأ لي بيطلع برضه integer، برضه ما فيه قصة كبيرة
+
+108
+00:07:49,700 --> 00:07:53,800
+فالتالتة، بده يفهم إنك أنت عارف الـ ceiling، مش أكثر
+
+109
+00:07:53,800 --> 00:08:00,140
+من هيك، ما تعملهاش floor، بالضبط ليش؟ عشان القصور هذه،
+
+110
+00:08:00,140 --> 00:08:03,340
+بمعنى أنه آخر block، okay، أنت مش حتكمل الـ block
+
+111
+00:08:03,340 --> 00:08:08,120
+كامل، بس فيه مجموعة bytes لازم تنبعت، ما تقول لي
+
+112
+00:08:08,120 --> 00:08:11,040
+بدي أجف عنده، طب، مجموعة الـ bytes اللي زادت هذه
+
+113
+00:08:11,040 --> 00:08:13,760
+معناته ما انبعتش، معناته ما انبعتش، لأ، بنعمل
+
+114
+00:08:13,760 --> 00:08:18,300
+scaling، بس هيك، فكرة السؤال، لا أكثر ولا أقل،
+
+115
+00:08:18,300 --> 00:08:20,280
+تخيلوا أننا كنا في سنة من السنوات نجيب امتحانات
+
+116
+00:08:20,280 --> 00:08:26,510
+بهذا الشكل، طيب، رسم، طبعا هذه الواجهة، عفوا، عليه، زمان
+
+117
+00:08:26,510 --> 00:08:33,070
+كانت، نيجي نرسم، مش محتاجينها، بس الفكرة أنا بحاول
+
+118
+00:08:33,070 --> 00:08:37,690
+إيش بده أقول لك؟ أن نوعية الامتحانات بسيطة، مش زي ما
+
+119
+00:08:37,690 --> 00:08:42,190
+بينقل لكم، هذه الواجهة، نوع من أنواع الأسئلة زي هيك، F
+
+120
+00:08:42,190 --> 00:08:47,410
+of X، اتنين X، و عاملينها floor، مطلوب ارسمها، إحنا
+
+121
+00:08:47,410 --> 00:08:50,470
+رسمناها أصلا في المحاضرة، رسمنا زيها، بس كانت أظن
+
+122
+00:08:50,470 --> 00:08:53,970
+على ثلاثة X، على ثلاثة في وجهتها، فنفس الفكرة بدك
+
+123
+00:08:53,970 --> 00:08:57,510
+ترسم الـ units تبعتك، و تبدأ من الصفر، أعوض في صفر
+
+124
+00:08:57,510 --> 00:09:01,170
+فتطلع صفر، أعوض فيه، باعتبار هذا مضروبة في اتنين،
+
+125
+00:09:01,170 --> 00:09:04,110
+فبدك تأخذ بالك أن الـ step تبعتك بتكون صغيرة، لأن
+
+126
+00:09:04,110 --> 00:09:07,950
+أنت ضارب في اتنين، إذا أنت راسم بالضبط، راسم على عدد
+
+127
+00:09:07,950 --> 00:09:11,290
+معناته الـ step تبعتك شوية، ممكن تختارها كبيرة، عشان
+
+128
+00:09:11,290 --> 00:09:14,150
+تلحق تخلص الشغل، فأنت ضارب، معناته بدك تأخذ step
+
+129
+00:09:14,150 --> 00:09:18,770
+شوية صغيرة، خليني أقول نصف، عند نصف، هيطلع واحد، مش هيك؟
+
+130
+00:09:18,770 --> 00:09:26,900
+طيب، أجل من النص، صفر، طيب، ما بعد النص، واحد، فإذا في
+
+131
+00:09:26,900 --> 00:09:34,000
+عندي نقطة انتقال، عند النص، عند النص، حيكون في نقطة
+
+132
+00:09:34,000 --> 00:09:39,320
+انتقال، طيب النص فعليا مع مين؟ مع الواحد، بعملها
+
+133
+00:09:39,320 --> 00:09:44,210
+solid، مع الواحد بتيجي solid، بس هي كل الفكرة، و بتكمل
+
+134
+00:09:44,210 --> 00:09:49,530
+بعد ذلك، عشان تجد أن هي فعليا بهذا الشكل، شكل
+
+135
+00:09:49,530 --> 00:09:53,610
+المعادلة تبعتك، طول الدرجة مثلا نصف، كيف؟ طول
+
+136
+00:09:53,610 --> 00:09:59,150
+الدرجة مثلا نصف، نصف، ما هي، ليش النصف؟ فأنت بتتكلم عن
+
+137
+00:09:59,150 --> 00:10:02,290
+إيش الـ term اللي بدي يعطيك قيمة الواحد؟ لأن الواحد
+
+138
+00:10:02,290 --> 00:10:06,550
+هو الـ integer، هو الـ step للـ integers، فواحد، تمام.
+
+139
+00:10:06,550 --> 00:10:10,970
+تالي، نفس الكلام برضه بتعمله، بنفس القضية، لهيك سؤال
+
+140
+00:10:10,970 --> 00:10:13,230
+ده، نوع من الأسئلة هذه، مش كنا نقولها اللي زمان كنا
+
+141
+00:10:13,230 --> 00:10:17,900
+نجيبهم زمان، الحاجات هذه، كوزات وامتحانات، لا خلصنا
+
+142
+00:10:17,900 --> 00:10:22,660
+عدناها، الجثة والله!
+
+143
+00:10:22,660 --> 00:10:27,300
+يعني أن ننصحكم، نجيبها، طيب هذه نوع من أنواع الأسئلة
+
+144
+00:10:27,300 --> 00:10:34,780
+مثلا، بدنا نعرف هل بدك تعمل prove أو disprove
+
+145
+00:10:34,780 --> 00:10:40,030
+لمجموعة الـ rules اللي معطيك إياها، أو مجموعة الـ
+
+146
+00:10:40,030 --> 00:10:43,410
+relations اللي معطيك إياها، أول relation بيقول لك أن
+
+147
+00:10:43,410 --> 00:10:47,910
+ceiling of floor x بيساوي floor x، true ولا false، و
+
+148
+00:10:47,910 --> 00:10:55,510
+ليش true؟ ليش integer؟
+
+149
+00:10:55,510 --> 00:10:58,950
+خلاص، بالضبط، هذه integer، أصبحت integer أصلا، فالـ
+
+150
+00:10:58,950 --> 00:11:03,300
+ceiling ما له قيمة، بالضبط، الـ ceiling ما له قيمة، و
+
+151
+00:11:03,300 --> 00:11:07,760
+إحنا قلنا rule كانت واضحة جدا، الـ integer يساوي الـ
+
+152
+00:11:07,760 --> 00:11:11,760
+ceiling و يساوي الـ floor، ما له، خلصنا، فإذا فعليا
+
+153
+00:11:11,760 --> 00:11:15,140
+مدام أخذت floor، فهو أصبحت automatically integer، الـ
+
+154
+00:11:15,140 --> 00:11:18,900
+integer هذا ما له قيمة، الـ ceiling ما له قيمة،
+
+155
+00:11:18,900 --> 00:11:23,080
+فإذا صارت floor هو نفسه floor، okay، صح، مش مشكلة،
+
+156
+00:11:23,080 --> 00:11:30,460
+تمام، الثانية ليش؟ بدنا .. بدنا مثال لحالة .. من
+
+157
+00:11:30,460 --> 00:11:34,780
+الحالات، مثلا النص، مثلا النص، okay، ممتاز، النص هنا
+
+158
+00:11:34,780 --> 00:11:39,400
+هيطلع واحد، النص هنا صفر، فإذا هذه برضه واضحة جدا،
+
+159
+00:11:39,400 --> 00:11:45,140
+ما أعتقدش أن فيها جثة كتير كبيرة، الـ C،  أصبرنا عليها، C
+
+160
+00:11:45,140 --> 00:11:50,250
+بدها شغل، حنحلها على الـ slide اللي وراها، كويس.
+
+161
+00:11:50,250 --> 00:11:53,590
+استثنينا C، لأن لأنه بدها شغل، نأخذ الاتنين السهلين
+
+162
+00:11:53,590 --> 00:11:55,930
+اللي ممكن نحلهم في هالسطرين اللي ضايلين، و هدول
+
+163
+00:11:55,930 --> 00:11:59,030
+نجولها معانا للي بعد هيك، نرجع نفكر فيها لإنه بدها
+
+164
+00:11:59,030 --> 00:12:10,270
+شوية شغل، طيب، floor X by Y بيساوي floor X floor، عفوا
+
+223
+00:16:58,100 --> 00:17:04,400
+إبسلون up لواحد أو
+
+224
+00:17:04,400 --> 00:17:07,800
+ممكن يكون كل مجْموع أكبر من الواحد فبيعمل up
+
+225
+00:17:07,800 --> 00:17:15,420
+لاتنين فإذا أنا عندي احتمالين ممكنين واردين لكل
+
+226
+00:17:15,420 --> 00:17:18,780
+.. احنا بنتكلم for all real numbers لكل الأعداد الحقيقية
+
+227
+00:17:18,780 --> 00:17:24,430
+ممكن تكون هيك وممكن تكون هيك،  كلهم طيب، في الحالة
+
+228
+00:17:24,430 --> 00:17:28,030
+هذه نمسكهم واحدة واحدة، معنا ذلك أنه بنقدر نقول اما
+
+229
+00:17:28,030 --> 00:17:31,890
+نشتغل
+
+230
+00:17:31,890 --> 00:17:39,950
+عليهم فوق، على الحالة اللي عندنا، اما انه x هذه اللي
+
+231
+00:17:39,950 --> 00:17:46,620
+هي عبارة عن جولنا n زائد إبسلون، هتكون زائد واحد
+
+232
+00:17:46,620 --> 00:17:51,360
+هذا أكيد هتكون زائد واحد لأنه في كسر، والكسر هذا
+
+233
+00:17:51,360 --> 00:17:54,840
+مع الـ ceiling هيصير زائد واحد، والـ M برضه هتصير
+
+234
+00:17:54,840 --> 00:18:00,380
+زائد واحد، ناقص هنا بختلف عن الـ term هذا، واللي
+
+235
+00:18:00,380 --> 00:18:04,060
+احنا الآن قلنا له حلتين، اما هيطلع، ممكن يطلع هيك أو
+
+236
+00:18:04,060 --> 00:18:07,320
+ممكن يطلع هيك، فنمسكهم واحدة واحدة، ممكن يطلع بهذا
+
+237
+00:18:07,320 --> 00:18:11,360
+الشكل، ممكن يكون بهذا الشكل، الكسور، مجموعة الكسور
+
+238
+00:18:11,360 --> 00:18:16,680
+مكمّلش الواحد، فالـ ceiling تبعه واحد بس، ففي الحالة
+
+239
+00:18:16,680 --> 00:18:22,540
+هذه، اطرحهم من بعض، هيطلع واحد، okay ماشي
+
+240
+00:18:22,540 --> 00:18:26,740
+طيب، ناخد الحالة الثانية، هو ممكن يكون في قيم فعلا
+
+241
+00:18:26,740 --> 00:18:31,960
+كون كسورها أكبر من نص، ونعود بهذا الشكل اللي
+
+242
+00:18:31,960 --> 00:18:36,080
+احنا شايفينه، هاتيج اتطلعت لجهة صفر فأخذنا كل
+
+243
+00:18:36,080 --> 00:18:41,880
+احتمالات الآن، اما integers وفي الحالة دي هيطلع صفر
+
+244
+00:18:41,880 --> 00:18:47,000
+وهو معقول، أنه اه ممكن تساوي صفر أو أنه لأ، هم real
+
+245
+00:18:47,000 --> 00:18:50,720
+وليسوا integers، بمعنى في كسور، وهدي الها احتماليا
+
+246
+00:18:50,720 --> 00:18:54,760
+أن مجموع الكسور أقل من الواحد أو أكبر من الواحد، و
+
+247
+00:18:54,760 --> 00:18:59,260
+في الحالتين ناتج العملية يا صفر يا واحد، فـ is not
+
+248
+00:18:59,260 --> 00:19:07,930
+true، فإذا true تمام، فهي هذه فكرة .. فكرتها بسيطة بس
+
+249
+00:19:07,930 --> 00:19:10,870
+زي ما بيقولوا، بتحتاج تركيز عشان تتكلم فيها، تعرف
+
+250
+00:19:10,870 --> 00:19:16,090
+تجيبها، بس فعليا هل جبنا أي شيء مش معروف، كلها
+
+251
+00:19:16,090 --> 00:19:20,690
+علاقات عادية جدا، و relations لموضوعنا البسيط جدا
+
+252
+00:19:20,690 --> 00:19:25,110
+تمام، خلصنا، هيك ما بدي أطول عليها المرة هذه عشان
+
+253
+00:19:25,110 --> 00:19:30,230
+تركزوا في الـ .. في الـ quiz، فخلوني أتكلم عن الـ quiz
+
+254
+00:19:30,230 --> 00:19:35,050
+أجهزوا، ممكن، احنا خلصنا زي ما بيقولوا محاضرتنا
+
+255
+00:19:35,050 --> 00:19:35,810
+فعليا
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Z4_jnPs62Eo_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Z4_jnPs62Eo_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..49f82e25e611178cb3ea239c121f2ab54c7fe24e
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/Z4_jnPs62Eo_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 625, "start": 4.99, "end": 6.25, "text": "نقول بسم الله الرحمن الرحيم", "tokens": [1863, 39648, 4724, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640], "avg_logprob": -0.11621093253294627, "compression_ratio": 1.0638297872340425, "no_speech_prob": 0.0, "words": [{"start": 4.99, "end": 5.29, "word": "نقول", "probability": 0.850830078125}, {"start": 5.29, "end": 5.45, "word": " بسم", "probability": 0.954833984375}, {"start": 5.45, "end": 5.57, "word": " الله", "probability": 0.96826171875}, {"start": 5.57, "end": 5.83, "word": " الرحمن", "probability": 0.9713541666666666}, {"start": 5.83, "end": 6.25, "word": " الرحيم", "probability": 0.9943033854166666}], "temperature": 1.0}, {"id": 2, "seek": 3653, "start": 7.81, "end": 36.53, "text": "المرة الماضية كنا أخدنا ال algorithm كان ضايق لنا جزئية بسيطة منها يعني فعلا خلصنا الملف تبع ال algorithms اللي ضايل كان هي مجموعة تطبيقات كنا بدنا نبدأ نعطيكوا شوية أمثلة يعني بمعنى أنه هتروح لعملية تفكير كيف نبدأ نفكر في بعض ال problems و نكتبها بال pseudocode فهنخليها للأسبوع القادم ان شاء الله يوم السبت نبدأ ناخد هلأ كم من مثال اللي ضايقين ثم نبدأ في ال complexity و نبدأ نفهم إيش يعني complexity بحيث أنه", "tokens": [45340, 25720, 9673, 46958, 10632, 9122, 8315, 5551, 9778, 3215, 8315, 2423, 9284, 25961, 48812, 47302, 4587, 5296, 8315, 10874, 11622, 19986, 10632, 4724, 3794, 1829, 9566, 3660, 9154, 11296, 37495, 22653, 6156, 3615, 15040, 16490, 1211, 9381, 8315, 9673, 46538, 6055, 3555, 3615, 2423, 14642, 13672, 1829, 48812, 995, 26895, 25961, 39896, 3714, 7435, 2304, 45367, 3660, 6055, 9566, 21292, 4587, 9307, 9122, 8315, 47525, 8315, 8717, 44510, 10721, 8717, 3615, 9566, 1829, 4117, 14407, 13412, 2407, 10632, 5551, 2304, 12984, 37977, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 14739, 3224, 8032, 2655, 32887, 5016, 5296, 25957, 1211, 10632, 6055, 5172, 4117, 13546, 9122, 33911, 8717, 44510, 10721, 8717, 5172, 37983, 8978, 45030, 11242, 2423, 2740, 4032, 8717, 4117, 2655, 3555, 11296, 20666, 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constants هدولة كلهم constants لإنه coefficients بدنا نحسب necessary and sufficient conditions فمحتاجين الشروط الدرورية والكافية", "tokens": [5172, 6027, 39184, 383, 34105, 13672, 1829, 31439, 9673, 1829, 15040, 34051, 2423, 13525, 6055, 3555, 3615, 4117, 37893, 3714, 10859, 3615, 9566, 6808, 7578, 31439, 2212, 9122, 13075, 383, 4032, 10874, 11622, 38207, 2423, 9114, 13672, 1829, 3714, 29245, 23328, 8978, 2423, 6358, 34051, 8978, 33688, 8592, 9640, 3660, 6055, 3555, 34268, 4117, 8978, 2423, 2445, 4724, 43042, 3224, 3714, 10859, 3615, 9566, 6808, 7578, 39627, 15730, 25124, 28820, 8717, 36178, 2423, 33599, 1829, 24976, 2655, 29399, 9957, 3714, 9566, 1211, 37746, 36632, 8592, 22807, 28242, 16095, 35870, 8032, 3215, 12610, 3660, 28242, 16095, 35870, 5296, 28814, 1863, 3224, 31994, 47525, 8315, 8717, 5016, 35457, 4818, 293, 11563, 4487, 6156, 2304, 33753, 26108, 9957, 25124, 32887, 9566, 32748, 2288, 13063, 10632, 16070, 4117, 31845, 10632], "avg_logprob": -0.19623524161774342, 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"start": 178.87, "end": 194.57, "text": "بارورية وكافية لإيش ل ال a و b و c بحيث أنه تضمن لنا f compose g تساوي g compose f مش أكتر من هيك السؤال direct", "tokens": [3555, 9640, 13063, 10632, 4032, 4117, 31845, 10632, 5296, 28814, 1829, 8592, 5296, 2423, 257, 4032, 272, 4032, 269, 4724, 5016, 1829, 12984, 14739, 3224, 6055, 11242, 27842, 5296, 8315, 283, 35925, 290, 6055, 3794, 995, 45865, 290, 35925, 283, 37893, 5551, 4117, 2655, 2288, 9154, 39896, 4117, 21136, 33604, 6027, 2047], "avg_logprob": -0.23540683849802557, "compression_ratio": 1.310077519379845, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 178.87, "end": 179.55, "word": "بارورية", "probability": 0.6021728515625}, {"start": 179.55, "end": 180.33, "word": " وكافية", "probability": 0.9056396484375}, {"start": 180.33, "end": 181.19, "word": " لإيش", "probability": 0.8306884765625}, {"start": 181.19, "end": 182.09, "word": " ل", "probability": 0.5244140625}, {"start": 182.09, "end": 182.55, "word": " ال", 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compose g فهي ال function if لمخرج ال function g بس و نفس الكلام g compose f فنبدأهم واحدة واحدة هي عند ال f وهي عند ال g نبدأ أول واحدة منهم", "tokens": [6027, 3794, 33604, 6027, 2047, 19446, 41185, 8592, 8978, 3224, 20193, 5296, 3615, 49401, 13412, 2304, 6027, 49429, 5296, 3615, 49401, 3714, 6027, 9957, 49429, 8978, 1975, 1829, 11331, 26108, 3660, 1975, 9566, 15040, 4587, 995, 15844, 23032, 12610, 39894, 44510, 10721, 6055, 39648, 1975, 1829, 8592, 37495, 22653, 2423, 12686, 498, 35925, 290, 6156, 3224, 1829, 2423, 2445, 498, 5296, 2304, 34740, 7435, 2423, 2445, 290, 4724, 3794, 4032, 8717, 36178, 2423, 28820, 10943, 290, 35925, 283, 6156, 1863, 44510, 10721, 16095, 36764, 24401, 3660, 36764, 24401, 3660, 39896, 43242, 2423, 283, 37037, 1829, 43242, 2423, 290, 8717, 44510, 10721, 5551, 12610, 36764, 24401, 3660, 9154, 16095], "avg_logprob": -0.1903669697429062, "compression_ratio": 1.9158878504672898, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 195.46, "end": 196.18, 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1148.19, "end": 1148.43, "word": " بيقولوا", "probability": 0.814697265625}, {"start": 1148.43, "end": 1148.61, "word": " بتها", "probability": 0.5108642578125}, {"start": 1148.61, "end": 1148.97, "word": " تركيز", "probability": 0.9544677734375}, {"start": 1148.97, "end": 1149.27, "word": " عشان", "probability": 0.9654947916666666}, {"start": 1149.27, "end": 1150.31, "word": " تتكلم", "probability": 0.9764404296875}, {"start": 1150.31, "end": 1150.59, "word": " فيها", "probability": 0.98681640625}, {"start": 1150.59, "end": 1150.87, "word": " تعرف", "probability": 0.7820638020833334}, {"start": 1150.87, "end": 1151.23, "word": " تجيبها", "probability": 0.98212890625}, {"start": 1151.23, "end": 1151.63, "word": " بس", "probability": 0.970458984375}, {"start": 1151.63, "end": 1152.09, "word": " فعليا", "probability": 0.9324951171875}, {"start": 1152.09, "end": 1152.63, "word": " هل", "probability": 0.919189453125}, {"start": 1152.63, "end": 1153.01, "word": " جبنا", "probability": 0.8474934895833334}, {"start": 1153.01, "end": 1153.35, "word": " أي", "probability": 0.751953125}, {"start": 1153.35, "end": 1154.27, "word": " إشي", "probability": 0.888671875}, {"start": 1154.27, "end": 1154.49, "word": " مش", "probability": 0.99267578125}, {"start": 1154.49, "end": 1155.03, "word": " معروف", "probability": 0.9910481770833334}, {"start": 1155.03, "end": 1156.09, "word": " كلها", "probability": 0.93359375}, {"start": 1156.09, "end": 1156.47, "word": " علاقات", "probability": 0.9896240234375}, {"start": 1156.47, "end": 1156.71, "word": " عادية", "probability": 0.9527994791666666}, {"start": 1156.71, "end": 1156.99, "word": " جدا", "probability": 0.995849609375}, {"start": 1156.99, "end": 1157.15, "word": " و", "probability": 0.46484375}, {"start": 1157.15, "end": 1157.55, "word": " relations", "probability": 0.85546875}, {"start": 1157.55, "end": 1159.39, "word": " لموضوعنا", "probability": 0.9453938802083334}, {"start": 1159.39, "end": 1159.83, "word": " البسيط", "probability": 0.99267578125}, {"start": 1159.83, "end": 1160.69, "word": " الجدا", "probability": 0.795654296875}, {"start": 1160.69, "end": 1161.89, "word": " تمام", "probability": 0.981201171875}, {"start": 1161.89, "end": 1162.91, "word": " خلصنا", "probability": 0.989013671875}, {"start": 1162.91, "end": 1163.41, "word": " هيك", "probability": 0.972412109375}, {"start": 1163.41, "end": 1164.03, "word": " ماديش", "probability": 0.4837239583333333}, {"start": 1164.03, "end": 1164.27, "word": " أطول", "probability": 0.9329427083333334}, {"start": 1164.27, "end": 1164.49, "word": " عليها", "probability": 0.78369140625}, {"start": 1164.49, "end": 1164.71, "word": " المرة", "probability": 0.777099609375}, {"start": 1164.71, "end": 1164.85, "word": " هذه", "probability": 0.400634765625}, {"start": 1164.85, "end": 1165.11, "word": " عشان", "probability": 0.9890950520833334}, {"start": 1165.11, "end": 1165.99, "word": " تركزوا", "probability": 0.9085693359375}, {"start": 1165.99, "end": 1166.11, "word": " في", "probability": 0.7939453125}, {"start": 1166.11, "end": 1166.35, "word": " ال", "probability": 0.96728515625}, {"start": 1166.35, "end": 1166.69, "word": " ..", "probability": 0.57373046875}, {"start": 1166.69, "end": 1167.15, "word": " في", "probability": 0.95166015625}, {"start": 1167.15, "end": 1167.25, "word": " ال", "probability": 0.97509765625}, {"start": 1167.25, "end": 1167.57, "word": " quiz", "probability": 0.9921875}, {"start": 1167.57, "end": 1169.13, "word": " فخلوني", "probability": 0.89658203125}, {"start": 1169.13, "end": 1169.47, "word": " أتكلم", "probability": 0.96337890625}, {"start": 1169.47, "end": 1169.73, "word": " عن", "probability": 0.9931640625}, {"start": 1169.73, "end": 1169.95, "word": " ال", "probability": 0.360107421875}, {"start": 1169.95, "end": 1170.23, "word": " quiz", "probability": 0.9951171875}, {"start": 1170.23, "end": 1170.81, "word": " اجهزوا", "probability": 0.90341796875}], "temperature": 1.0}, {"id": 51, "seek": 117581, "start": 1172.29, "end": 1175.81, "text": "ممكن يك احنا خلصنا زي ما بيقولوا محاضرتنا فعليا", "tokens": [2304, 43020, 7251, 4117, 1975, 5016, 8315, 16490, 1211, 9381, 8315, 30767, 1829, 19446, 4724, 1829, 39648, 14407, 3714, 5016, 46958, 43500, 8315, 6156, 3615, 20292, 995], "avg_logprob": -0.13734654071075575, "compression_ratio": 1.1466666666666667, "no_speech_prob": 0.0, "words": [{"start": 1172.29, "end": 1172.65, "word": "ممكن", "probability": 0.760009765625}, {"start": 1172.65, "end": 1172.77, "word": " يك", "probability": 0.566650390625}, {"start": 1172.77, "end": 1172.91, "word": " احنا", "probability": 0.84130859375}, {"start": 1172.91, "end": 1173.35, "word": " خلصنا", "probability": 0.9764404296875}, {"start": 1173.35, "end": 1173.49, "word": " زي", "probability": 0.911865234375}, {"start": 1173.49, "end": 1173.55, "word": " ما", "probability": 0.88720703125}, {"start": 1173.55, "end": 1174.23, "word": " بيقولوا", "probability": 0.961669921875}, {"start": 1174.23, "end": 1175.05, "word": " محاضرتنا", "probability": 0.9681640625}, {"start": 1175.05, "end": 1175.81, "word": " فعليا", "probability": 0.9163818359375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1176.2068125, "duration_after_vad": 1142.3831249999996}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aNdhsDDrcFQ_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aNdhsDDrcFQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..281c85a99c15d94f0185e6dae61882710eee34a4
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aNdhsDDrcFQ_postprocess.srt
@@ -0,0 +1,2620 @@
+1
+00:00:04,980 --> 00:00:07,940
+بسم الله الرحمن الرحيم يعطيكوا العفو يا شباب و
+
+2
+00:00:07,940 --> 00:00:10,200
+الحقيقة الأسبوع اللي فاتش تجنالكوا فيه ما ..
+
+3
+00:00:10,200 --> 00:00:17,080
+ماشوفناكمش فالكويس أن احنا رجعنا نحاول نستفكر و
+
+4
+00:00:17,080 --> 00:00:20,840
+نوصلنا .. احنا كنا خلصنا ال algorithm خلصنا ال ..
+
+5
+00:00:20,840 --> 00:00:24,700
+ال .. ال complexity تبعته و اتكلمنا عن مجموعة
+
+6
+00:00:24,700 --> 00:00:28,440
+examples له اتكلمنا اذا متذكرين اخر اشي على ال
+
+7
+00:00:28,440 --> 00:00:33,150
+tractable و ال intractable و ..مجدش هي مهمة النقطة
+
+8
+00:00:33,150 --> 00:00:36,150
+هذه اللي هي tractable و intractable هدولة الجزئية
+
+9
+00:00:36,150 --> 00:00:38,850
+هذه و زي ما قلتلكم فيها .. فيها ناس بيعملوا
+
+10
+00:00:38,850 --> 00:00:41,530
+دكتوراه فيها و هي واحدة من الرسالة اللي هتتكلم
+
+11
+00:00:41,530 --> 00:00:45,290
+فيها اللي هي ال tractable و intractable و إيش ال
+
+12
+00:00:45,290 --> 00:00:47,150
+algorithms اللي ممكن نستخدمها في حالة ال
+
+13
+00:00:47,150 --> 00:00:50,610
+intractable فهذه كانت أخر حاجة احنا خطبناها المرة
+
+14
+00:00:50,610 --> 00:00:54,970
+الماضية عشان اليوم نبدأ ان شاء الله تعالىفي موضوع
+
+15
+00:00:54,970 --> 00:00:59,190
+جديد في chapter جديد زي ما بقوله صفحة جديدة و زي
+
+16
+00:00:59,190 --> 00:01:03,230
+ما قلتلكم اللي فات راح فنبدأ اليوم صفحة جديدة
+
+17
+00:01:03,230 --> 00:01:07,310
+كأننا بنبدأ course جديد تعمل refreshment هيك خلاص
+
+18
+00:01:07,310 --> 00:01:11,870
+بدنا نبدأ من أول و جديد فاليوم هنبدأ في جزئية ال
+
+19
+00:01:11,870 --> 00:01:17,170
+basic number theory و هنبدأمن ال ABC ل ال
+
+20
+00:01:17,170 --> 00:01:20,250
+mathematics من أول حاجة أخدتها في الرياضيات نبدأ
+
+21
+00:01:20,250 --> 00:01:24,910
+شوية شوية فهبدأ تعاملي مع الرياضيات من الأرقام
+
+22
+00:01:24,910 --> 00:01:28,530
+الصحيحة كأن احنا ماعرفش الأرقام الصحيحة كويس
+
+23
+00:01:28,530 --> 00:01:33,500
+فببساطة جدا لو قولنا a و bهي أرقام صحيحة integers
+
+24
+00:01:33,500 --> 00:01:37,660
+مجموعة integers و a لا تساوي صفر فبقدر اقول ان a
+
+25
+00:01:37,660 --> 00:01:43,780
+divides b لما اقول a divides b يعني كأنه b موجودة
+
+26
+00:01:43,780 --> 00:01:49,420
+هنا و a هي اللي بتقسمها ف a هي ال denominator و ال
+
+27
+00:01:49,420 --> 00:01:52,640
+b هي ال numerator او ال bust و المقام فهنا ايش
+
+28
+00:01:52,640 --> 00:01:58,740
+بقولDivides P يعني ايه هي تقسم P فعلياً فP قيمة
+
+29
+00:01:58,740 --> 00:02:03,540
+كبيرة واتقسمت بالمعامل ايه اللي هنسميه لاحقا
+
+30
+00:02:03,540 --> 00:02:09,690
+Divisorبنشيك divisor كويس فإذا هنا a divides b فa
+
+31
+00:02:09,690 --> 00:02:13,090
+بهذا الشكل اللي بننطقها معناته ان there exist c
+
+32
+00:02:13,090 --> 00:02:19,430
+برضه integer خارج عملية القسمة بمعنى إنه ال c هذا
+
+33
+00:02:19,430 --> 00:02:22,630
+لو ضربت في ال denominator في a المفروض يرجع ليه
+
+34
+00:02:22,630 --> 00:02:27,290
+قيمة b فإذا هذا المفروض يساوي c فإذا there exist c
+
+35
+00:02:27,290 --> 00:02:31,790
+اللي هي belong to زرد فانا كل كلام الأعلى على
+
+36
+00:02:31,790 --> 00:02:36,790
+integersعلى أرقام صحيحة لسه مارح نهرش لل fractions
+
+37
+00:02:36,790 --> 00:02:41,470
+كويس نحاول نمضل نمركزين لهنا و نفهم شويه شويه كل
+
+38
+00:02:41,470 --> 00:02:47,750
+الحاجات البسيطة فإذا there is integer c such that
+
+39
+00:02:47,750 --> 00:02:51,770
+c times a equals b بأي نوة واضحة مش فاقة مشكلة
+
+40
+00:02:51,770 --> 00:02:58,600
+مثال three divides minus twelvetrue ليش؟ لأنه
+
+41
+00:02:58,600 --> 00:03:03,180
+الناتج هيطلع integer فمش الحال لكن لما أقول three
+
+42
+00:03:03,180 --> 00:03:08,260
+divides seven false لأنه مش integer مش integer في
+
+43
+00:03:08,260 --> 00:03:12,700
+الحالة دي طيب if and only if a divides b إذن بنقدر
+
+44
+00:03:12,700 --> 00:03:19,980
+نقول أنه a هي factor ofof B المفروض أو هي factor
+
+45
+00:03:19,980 --> 00:03:26,240
+of a divisor هذه B هي اللي هتسميها .. نقدر نسميها
+
+46
+00:03:26,240 --> 00:03:32,160
+هنا A divides B إذا في ناقصة حاجة ناقصة هنا or اه
+
+47
+00:03:32,160 --> 00:03:39,180
+تمام or هنا or فإذا هي factor أو divisor إما
+
+48
+00:03:39,180 --> 00:03:43,660
+factor أو divisorتمام لما اكون جريب اشوفهاش لازم
+
+49
+00:03:43,660 --> 00:03:49,440
+الواحد دي بعد عشان يشوف فإذا اما factor او divisor
+
+50
+00:03:49,440 --> 00:03:55,040
+كويس المقسم اللي لها و B بنسميها ال multiple لإيه
+
+51
+00:03:55,040 --> 00:04:00,650
+هي تكرار من ايه تكرار هنا مثلا بقداش ب C مرةمكرر
+
+52
+00:04:00,650 --> 00:04:08,150
+بي مكرر من a بc بc مرة فإذا هي تكرار منها بي is
+
+53
+00:04:08,150 --> 00:04:12,750
+even بقدر أعبر عنها بال divisor هذا أنه two
+
+54
+00:04:12,750 --> 00:04:16,910
+divides بي إذا والله فعلا two divides بي is true
+
+55
+00:04:16,910 --> 00:04:22,650
+معناته بي even أكيد أكيد هتكون even طيب ال zero
+
+56
+00:04:22,650 --> 00:04:33,000
+evenتخيلوا نفس الفكرة ال zero even يعني بمعنى هل
+
+57
+00:04:33,000 --> 00:04:36,980
+بقدر أقول اتنين divide zero okay ليش لأنه بيطلع
+
+58
+00:04:36,980 --> 00:04:42,080
+الناتج zero شك و ال zero integer ال zero الناتج
+
+59
+00:04:42,080 --> 00:04:46,160
+integer فمعناته there exist number و integer
+
+60
+00:04:46,160 --> 00:04:50,040
+number تحديدا كخارج عامل القسمة و اللي هو ال zero
+
+61
+00:04:50,040 --> 00:04:53,240
+تمام طيب ال minus four
+
+62
+00:04:55,630 --> 00:05:00,730
+even أكيد even برضه لأنه two divides minus four
+
+63
+00:05:00,730 --> 00:05:05,130
+أكيد هيطلع ليه integer هيكون ناتجها integer تمام
+
+64
+00:05:05,130 --> 00:05:13,220
+مجموعة facts أولها أنه ممكن نقول a divides zeroزي
+
+65
+00:05:13,220 --> 00:05:17,560
+2 divides 0 فإذا في حاجة اسمها a divides 0 بمشي
+
+66
+00:05:17,560 --> 00:05:20,280
+الحل هذا طبعا إذا كان افترضنا ان كل الرموز اللي
+
+67
+00:05:20,280 --> 00:05:24,840
+هناخدها ال a و b و c هي كلها integers بنقدر نقول
+
+68
+00:05:24,840 --> 00:05:31,420
+ان a divides b and a divides c فبالضروري معنى ذلك
+
+69
+00:05:31,420 --> 00:05:37,880
+ان a divides مجموحهم a أكيد هيكون divides مجموحهم
+
+70
+00:05:38,610 --> 00:05:43,550
+نفس الكلام a divides b إذا a divides b مضروبة في
+
+71
+00:05:43,550 --> 00:05:50,890
+أي integer صحيح فإتزادت التكرارات مش أكتر مدام b
+
+72
+00:05:50,890 --> 00:05:55,170
+بتقسم على a فb مضروبة في c أكيد ك total هتقسم برضه
+
+73
+00:05:55,170 --> 00:05:58,890
+على a لأنه في عامل مشترك أن ال b أصلا هي بتقسم
+
+74
+00:05:58,890 --> 00:06:05,230
+أصلا لحالها على a تمام a divides b و and b divides
+
+75
+00:06:05,230 --> 00:06:12,370
+cفإذا أكيد a divide c أكيد هتكون a divide c بمعنى
+
+76
+00:06:12,370 --> 00:06:20,330
+لو كانت b على a بتعطيني integer و c على b بتعطي
+
+77
+00:06:20,330 --> 00:06:25,510
+برضه integer أكيد هتكون c على a برضه بتعطي integer
+
+78
+00:06:25,510 --> 00:06:31,770
+لأ
+
+79
+00:06:31,770 --> 00:06:38,670
+مش بالضروري a divide c هذه عكس هذهفاهمت جزدك هذه
+
+80
+00:06:38,670 --> 00:06:44,950
+تقرأ بالعكس denominator divides numerator هذا ال
+
+81
+00:06:44,950 --> 00:06:50,030
+divisor وهذا ال multiple تمام فهي تقرأ عكس ما أنت
+
+82
+00:06:50,030 --> 00:06:54,670
+فاهمها الكثور العادية غير عكس ما أنت بتفهم الكثور
+
+83
+00:06:54,670 --> 00:06:58,390
+العادية فهنا a divides b معناته هذا فعليا كأنها b
+
+84
+00:06:58,390 --> 00:07:04,530
+على a تمامطبعا اثبات رقم اتنين هيكون سهل جدا بكل
+
+85
+00:07:04,530 --> 00:07:08,150
+بساطة مادام A divides B معناته بقدر اقول انه B
+
+86
+00:07:08,150 --> 00:07:12,710
+تساوي هيلاحظ A مضروبة في some integers في some
+
+87
+00:07:12,710 --> 00:07:20,790
+integers S نفس الكلام اذا A C او B او اين احنا كنا
+
+88
+00:07:20,790 --> 00:07:26,480
+هنا A divides C اكيد هتكون C برضه تساوي A فيمضروبة
+
+89
+00:07:26,480 --> 00:07:32,020
+في ايش؟ في تكرار معين في T معناه ذلك ان بي زائد C
+
+90
+00:07:32,020 --> 00:07:40,340
+هتساوي AS plus AT و بتقدر تاخد ال A common يعني
+
+91
+00:07:40,340 --> 00:07:45,540
+بتقبل القسمة ك total بيقبل القسمة على A فإذا A
+
+92
+00:07:45,540 --> 00:07:50,340
+divides بتصير B plus C فإذا إثباتها واضح وبالتالي
+
+93
+00:07:50,340 --> 00:07:53,700
+مافيش محتاج أصلا كنا نعمله إثبات
+
+94
+00:07:57,750 --> 00:08:03,490
+الـ Primes نبدأ شوية نتصاعد في الرياضيات في ال ABC
+
+95
+00:08:03,490 --> 00:08:09,510
+Math ال Primes كلنا عارفين انه لما بقول Prime هذا
+
+96
+00:08:09,510 --> 00:08:13,670
+بقدر أسمي أي عنصر Prime if and only if there is no
+
+97
+00:08:13,670 --> 00:08:18,510
+product أو هو فعليا لا يمكن يكون product لأي two
+
+98
+00:08:18,510 --> 00:08:24,290
+other integerأكبر من واحد لأنه ممكن يكون الواحد و
+
+99
+00:08:24,290 --> 00:08:27,750
+تقولي أه ما هي الواحد زي مثلا السبعة تقولي ما هي
+
+100
+00:08:27,750 --> 00:08:33,730
+السبعة بتساوي سبعة في واحد هيها ضربتني لأ أكبر من
+
+101
+00:08:33,730 --> 00:08:40,490
+الواحد أكبر من الواحد تمام فإذا لا يوجد العنصر
+
+102
+00:08:40,490 --> 00:08:43,530
+بقدر أقولها ال prime إذا لا يمكن إنه يكون هو ضرب
+
+103
+00:08:43,530 --> 00:08:48,330
+رقمين أكبر من الواحد كلاهما أكبر من إيش من الواحد
+
+104
+00:08:48,330 --> 00:08:53,890
+فنقدر نعبّر عنه كتاليprime أكبر من الواحد and
+
+105
+00:08:53,890 --> 00:08:59,870
+there is no exist لا يوجد a و b هايهم عنصرين
+
+106
+00:08:59,870 --> 00:09:07,510
+natural number عنصرين integer بحيث أنه الأتنين
+
+107
+00:09:07,510 --> 00:09:11,490
+أكبر من واحد عشان نوضح أنها greater than one قلنا
+
+108
+00:09:11,490 --> 00:09:14,350
+كلا هم لازم يكونوا أكبر من واحد بحيث أن ضربهم
+
+109
+00:09:14,350 --> 00:09:22,000
+يساوي ال prime لا يوجد عنصريندربهم يساوي هذا ال
+
+110
+00:09:22,000 --> 00:09:25,440
+prime فإذا ال prime لا يمكن أنه يكون يعكسها ال
+
+111
+00:09:25,440 --> 00:09:31,300
+prime لا يمكن يكون مضروب to integers أكبر من واحد،
+
+112
+00:09:31,300 --> 00:09:36,860
+هي معناها، هي معناها، كويس فهذه هي الترجمة
+
+113
+00:09:36,860 --> 00:09:39,200
+بتاعتها، طبعا باستثناء زي ما قلنا ال prime ممكن
+
+114
+00:09:39,200 --> 00:09:46,490
+يكون الواحد في نفسه فقطالواحد فى نفسه فقط كويس بعض
+
+115
+00:09:46,490 --> 00:09:49,450
+ال primes اللى كلكم عارفين هتنين تلاتة خمسة سبعة
+
+116
+00:09:49,450 --> 00:09:54,410
+and so on مجموعات ال primes اللى قولنا انها مجموعة
+
+117
+00:09:54,410 --> 00:09:58,330
+لا نهائية مش شير و أثبتنا سابقا انها مجموعة لا
+
+118
+00:09:58,330 --> 00:10:02,970
+نهائية صحيح أثبتنا بالقرار انها لا نهائية لكن
+
+119
+00:10:02,970 --> 00:10:08,000
+ماقدرناش نثبت ان كل عناصرها وهذا اتكلمنا عنهالما
+
+120
+00:10:08,000 --> 00:10:13,860
+كنا بنتكلم عن إن هي يمكن إثباتها ولا يمكن قرار
+
+121
+00:10:13,860 --> 00:10:19,200
+الحكم على عنصر، إن نحكم على عنصر هو صح ولا مش صح،
+
+122
+00:10:19,200 --> 00:10:22,000
+هو prime ولا مش prime، ماشي، لكن إن أحكم على كل
+
+123
+00:10:22,000 --> 00:10:24,920
+primes، قولنا المرة اللي فاتت، قولنا هذا ختمنا
+
+124
+00:10:24,920 --> 00:10:27,340
+فيها المرة اللي فاتت، قولنا إن هذه ال complexity
+
+125
+00:10:27,340 --> 00:10:31,850
+بتكون عالية جدا للنوحدة من أنواع المشاكلطيب ال non
+
+126
+00:10:31,850 --> 00:10:37,070
+-prime أكيد هيكون العكس كل عنصر بقدر أعبر عنه ال
+
+127
+00:10:37,070 --> 00:10:41,310
+two integers مضروبين في بعض فهو أكيد مش ال prime
+
+128
+00:10:41,310 --> 00:10:48,070
+فبنقول عليه composed number اللي هو رقم مؤلف من
+
+129
+00:10:48,070 --> 00:10:54,130
+رقمين أو من two integers مضروبين في بعض ف
+
+130
+00:10:54,130 --> 00:10:58,780
+compositeأو ليش composite لأن هو composed ل
+
+131
+00:10:58,780 --> 00:11:02,980
+multiplication ل two other طبعا أكيد هيكون أصغر
+
+132
+00:11:02,980 --> 00:11:07,220
+منه ل two other integers تانين لرقمين تانين زي لما
+
+133
+00:11:07,220 --> 00:11:13,440
+نقول ستة فهي تلاتة في اتنين هي تلاتة في من؟ في
+
+134
+00:11:13,440 --> 00:11:19,180
+اتنين فإذا يوجد رقمين integers مضروبهم يساوي ال
+
+135
+00:11:19,180 --> 00:11:24,360
+composite number composite number اللي هو مركب رقم
+
+136
+00:11:24,950 --> 00:11:29,230
+أو قيمة مُركّبة، ليش مُركّبة؟ لأنها عبارة عن two
+
+137
+00:11:29,230 --> 00:11:32,330
+values مضربين في بعضهم، two values مضربين في
+
+138
+00:11:32,330 --> 00:11:35,530
+بعضهم، بعكس الـprime، بعكس الـprime، لا يمكن يكون
+
+139
+00:11:35,530 --> 00:11:39,750
+composite لأن هو فعليًا مستقل بذاته، لا يمكن يكون
+
+140
+00:11:39,750 --> 00:11:42,830
+فيه رقمين مضربين في بعض باقين الـprime إلا نفسه،
+
+141
+00:11:42,830 --> 00:11:48,930
+إلا نفسهOkay مجموعة عناصر الواحد أكيد هو empty لإن
+
+142
+00:11:48,930 --> 00:11:52,210
+احنا قولنا الprimes بيبدأ من أكبر من واحد فهذه
+
+143
+00:11:52,210 --> 00:11:57,370
+خارج ال series بتاعتنا بتاعة الprimes هي خارج ال
+
+144
+00:11:57,370 --> 00:12:02,230
+series بتاعة الprimes الاتنين هو نفسه مين؟ هو نفسه
+
+145
+00:12:02,230 --> 00:12:08,750
+prime مش هتلاقي أجل منه عنصر أو عنصرين تضربهم في
+
+146
+00:12:08,750 --> 00:12:15,190
+بعض يطلع اتنين مافيش طيب الأربعة لأ compositeليش؟
+
+147
+00:12:15,190 --> 00:12:18,510
+لأنه عبارة عن اتنين في اتنين، فهذا ليس prime
+
+148
+00:12:18,510 --> 00:12:22,670
+الألفين لأ مش prime، ليش؟ لأنه مبدأيا بيكبر الجسم
+
+149
+00:12:22,670 --> 00:12:26,630
+على اتنين، لما بيكبر الجسم على اتنين، بيضال
+
+150
+00:12:26,630 --> 00:12:30,610
+خمسمية، ماجدديش بيضال الف، طيب الألف برضه بيكبر
+
+151
+00:12:30,610 --> 00:12:33,980
+الجسم على اتنينطيب ده بيصير خمس مية، الخمس مية
+
+152
+00:12:33,980 --> 00:12:37,000
+بتجبر الجسم على اتنين، بتقنه خمسين، بتجبر الجسم
+
+153
+00:12:37,000 --> 00:12:39,400
+على اتنين، مية خمسة وعشرين، بعد هيك بتجبر على
+
+154
+00:12:39,400 --> 00:12:42,440
+خمسة، مية خمسة وعشرين، بتصير خمسة وعشرين، خمسة
+
+155
+00:12:42,440 --> 00:12:46,300
+وعشرين، بتجبر على خمسة، الخمسة هي نفسها خمسة، فلأ
+
+156
+00:12:46,300 --> 00:12:51,260
+هي مؤلفة من مجموعة عناصر أقل منها، ودائما هتلاقي
+
+157
+00:12:51,260 --> 00:12:54,970
+أن مجموعة العناصر are primesفإذا أي composite
+
+158
+00:12:54,970 --> 00:12:59,030
+number في الدنيا هو مؤلف من مجموعة primes مضروبين
+
+159
+00:12:59,030 --> 00:13:02,390
+في بعض من مجموعة primes مضروبة في بعضها بهذا الشكل
+
+160
+00:13:02,390 --> 00:13:05,730
+اللي احنا شايفينه 2001 مثلا هتلاقي ان هي بتقبل
+
+161
+00:13:05,730 --> 00:13:08,850
+جسمها على تلاتة باعتبار ان مجموحهم يقبل القسم على
+
+162
+00:13:08,850 --> 00:13:11,810
+تلاتة عارفين القاعدة هذا صحيح؟ اتنين زائد واحد
+
+163
+00:13:11,810 --> 00:13:14,970
+تلاتة فإذا بتقبل قسمها على تلاتة فعلا بتقبل جسمها
+
+164
+00:13:14,970 --> 00:13:18,850
+على تلاتة طيب بعد هيك هتجد انه الناتج لا يقبل لا
+
+165
+00:13:18,850 --> 00:13:23,220
+على تلاتة ولا على خمسة ولا على سبعة ولاهل معناه
+
+166
+00:13:23,220 --> 00:13:26,460
+ذلك انه بيبطل يبقى لأ بتستمر فيه هتصل عند ال 23
+
+167
+00:13:26,460 --> 00:13:32,500
+هيقبل جسمها ال 23ثم للتسعة و عشرين كلهم primes
+
+168
+00:13:32,500 --> 00:13:37,040
+التلات .. تلاتة primes في النهاية فهذا composite
+
+169
+00:13:37,040 --> 00:13:42,820
+number أو non-prime مش prime الالفين و اتنين نفس
+
+170
+00:13:42,820 --> 00:13:45,600
+الجثة هي باينة من أولها بتقبل جسمها على اتنين فإذا
+
+171
+00:13:45,600 --> 00:13:49,560
+not prime على طول هي composite هي composite بتقبل
+
+172
+00:13:49,560 --> 00:13:53,640
+جسمها على اتنين طيب الأرقام هذه اللي هي الprimes
+
+173
+00:13:53,640 --> 00:13:57,320
+بنسميها ال prime factorization لأي composition ..
+
+174
+00:13:57,320 --> 00:14:01,210
+composite number في الدنياأى number بتقدر تجيبله
+
+175
+00:14:01,210 --> 00:14:05,010
+ال factors أو ال prime factors تبعته فبتعمل ال
+
+176
+00:14:05,010 --> 00:14:10,510
+prime factorization okay طيب ألفين ألفين و تلاتة
+
+177
+00:14:10,510 --> 00:14:13,350
+طب ألفين ألفين و أتنين ألفين و واحد ألفين و أتنين
+
+178
+00:14:13,350 --> 00:14:21,170
+ألفين و تلاتة هو نفسه primeفهذا هو نفسه أساسا ال
+
+179
+00:14:21,170 --> 00:14:24,690
+prime فإذا ال primes ممكن تكون أرقام كبيرة جدا
+
+180
+00:14:24,690 --> 00:14:27,470
+أكبر مما أنت تتخيل كمان يعني احنا حتى هذا الرقم
+
+181
+00:14:27,470 --> 00:14:32,390
+يعتبر متواضع ك prime كرقم ال primeو اتوقع قلتلك
+
+182
+00:14:32,390 --> 00:14:36,630
+القاعدة سابقا إذا أخدتهم متسلسلين من أول ال series
+
+183
+00:14:36,630 --> 00:14:40,090
+تبع ال prime series و ضربتهم في بعض و اضرب جد ما
+
+184
+00:14:40,090 --> 00:14:44,170
+بدك المهم انك انت ماتنساش answer في النص اضربهم جد
+
+185
+00:14:44,170 --> 00:14:47,290
+ما بدك و بعدين اجمع واحد اكيد هيطلع ال prime فأكيد
+
+186
+00:14:47,290 --> 00:14:53,150
+هنتجاوز حتى الرقم هذا ب .. بمئات المرات طيب ال
+
+187
+00:14:53,150 --> 00:14:56,350
+division مدام ان انا كنت بتكلم عن ايه divides
+
+188
+00:14:59,070 --> 00:15:02,570
+CAB مثلاً A divides B كنا بنتكلم عنها معنا ذلك انه
+
+189
+00:15:02,570 --> 00:15:05,390
+الناتج انا متوقع ان هو هيكون ناتج ال division
+
+190
+00:15:05,390 --> 00:15:10,030
+algorithm او القسمة خارج القسمة مش هيك عشان انا
+
+191
+00:15:10,030 --> 00:15:13,690
+بده اجيبها لوجة C بدنا نجيب C فمعنا ذلك ان انا بده
+
+192
+00:15:13,690 --> 00:15:16,850
+اجيب ناتج القسمة هذا عشان هيك بدنا نبدأ نرجع
+
+193
+00:15:16,850 --> 00:15:21,940
+لعملية القسمة فلأي integer بنسميه dividendالـ
+
+194
+00:15:21,940 --> 00:15:26,220
+dividend هذا ايه؟ او المقسوم؟ المقسوم معناته ايش؟
+
+195
+00:15:26,220 --> 00:15:31,780
+بده يكون كبير فهذا العنصر الكبير ال dividend اللي
+
+196
+00:15:31,780 --> 00:15:37,320
+هو المقسوم اللي بده يتقسم كويس و القاسم ال divisor
+
+197
+00:15:37,320 --> 00:15:43,380
+اللي هو هيقوم بعملية القسمةD و طبعا دي هنا في
+
+198
+00:15:43,380 --> 00:15:46,380
+الحالة دي لازم يكون لا يساوي صفر و إلا العملية
+
+199
+00:15:46,380 --> 00:15:50,340
+هتطلع .. هتروح لإيش ل Undefined result ل Undefined
+
+200
+00:15:50,340 --> 00:15:54,720
+result مش معرفة فإذا هدي لازم تكون إيش لاتساوي
+
+201
+00:15:54,720 --> 00:15:58,940
+Zero لاتساوي Zero فهي نفس الكلام إحنا ماشيين فيه
+
+202
+00:15:58,940 --> 00:16:04,540
+في الحالة هدي يوجد unique انتجر إيش Quotient ال
+
+203
+00:16:04,540 --> 00:16:08,040
+Quotient هذا اللي هو خارج القسمة Quotient اللي هو
+
+204
+00:16:08,040 --> 00:16:13,820
+المفروض خارج القسمة ال Q ناتجالـ quotient هذا خارج
+
+205
+00:16:13,820 --> 00:16:19,200
+القسمة طيب إذا كان الاتنين هدولة ناتجهم بيطلعش
+
+206
+00:16:19,200 --> 00:16:23,820
+integer فإذن هي لأ مع ال quotient اللي طلع هذه Q
+
+207
+00:16:23,820 --> 00:16:30,200
+في متبقي فبنسميه remainder عادي متبقي with R فإذن
+
+208
+00:16:30,200 --> 00:16:34,440
+بيظل متبقي زي القسمة المطولة اللي بتعملوها هيكون
+
+209
+00:16:34,440 --> 00:16:37,560
+عندك هنا ال dividend هيكون عندك هنا ال divisor
+
+210
+00:16:38,310 --> 00:16:43,730
+هتكون ال quotient و هيتبقى في الآخر remainder ال R
+
+211
+00:16:43,730 --> 00:16:49,210
+فهي الأربع عناصر الأساسيين اللي بنتكلم عنهم في أي
+
+212
+00:16:49,210 --> 00:16:56,090
+قسمة مطولة الكلام بتهيأ ليه؟ كتير basic طيب في
+
+213
+00:16:56,090 --> 00:17:01,610
+الآخر A أكيد هتساوي D في Q divisor في ال quotient
+
+214
+00:17:01,610 --> 00:17:05,830
+plus ال R أكيد أكيد جدا طيب ال R عشان أقول عليها
+
+215
+00:17:05,830 --> 00:17:10,070
+فعلا R لازم تكون أقل من Dمش هيك أقل من ال divisor
+
+216
+00:17:10,070 --> 00:17:15,170
+وإلا لأ هي القسمة ما زالت مستمرة إذا كان لسه أكبر
+
+217
+00:17:15,170 --> 00:17:18,970
+من دي معناته لأ هي ما زالت مستمرة بتاكي تكمل عملية
+
+218
+00:17:18,970 --> 00:17:22,950
+القسمة المطولة لسه ماصلتش لل R المطلوبة كويس فإذا
+
+219
+00:17:22,950 --> 00:17:26,070
+R لازم تكون أكبر أو يساوي صفر أو يساوي صفر أو ممكن
+
+220
+00:17:26,070 --> 00:17:29,310
+تكون أو يساوي صفر اللي هي ناتج بدون متبقي خلاص بمش
+
+221
+00:17:29,310 --> 00:17:33,290
+الحال و أقل من absolute دي لإنك انت ممكن تكون تقسم
+
+222
+00:17:33,290 --> 00:17:36,930
+على سالب ممكن تكون تقسم على سالب أو ال R المتبقي
+
+223
+00:17:36,930 --> 00:17:42,520
+سالبتمام ففي الحالة هذه بنقدر نقوله لكل a و d
+
+224
+00:17:42,520 --> 00:17:47,160
+integers و d لازم تكون أكبر من صفر لأنه مانفعش ال
+
+225
+00:17:47,160 --> 00:17:52,140
+denominator او ال bust المقام يكون صفر there exist
+
+226
+00:17:52,140 --> 00:18:03,050
+only one Q and R أكيدأكيد صحيح دايما ل D A وD A
+
+227
+00:18:03,050 --> 00:18:07,990
+قسم ال D لازم يكون فيه Q وحيدة وR وحيدة مستحيل
+
+228
+00:18:07,990 --> 00:18:11,390
+يعني كل واحد ييجي يعمل عملية القسم المطولة وكل
+
+229
+00:18:11,390 --> 00:18:14,190
+واحد يطلع نتائج غير التاني اعناته في واحد منهم غلط
+
+230
+00:18:14,190 --> 00:18:20,480
+فإذا هيطلعonly there exist او exist only one ل Q و
+
+231
+00:18:20,480 --> 00:18:27,640
+R بحيث ان R لازم تكون اقل من D و A تساوي DQ plus R
+
+232
+00:18:27,640 --> 00:18:32,540
+طيب كيف بقدر احسب ال Q و ال R؟ ال Q بكل بساطة
+
+233
+00:18:32,540 --> 00:18:37,670
+بتخسم A على D و بتاخد floorفجبنا ال Q لحالها او ال
+
+234
+00:18:37,670 --> 00:18:42,310
+quotient لحالها خارج القسمة لحالها ناتج القسمة و
+
+235
+00:18:42,310 --> 00:18:47,930
+ال R هتساوي ال A الكبيرة اللي اتقسمت ناقص ال Q في
+
+236
+00:18:47,930 --> 00:18:54,510
+ال D فبيعطيك المتبقىواللي المفروض يكون أقل من D
+
+237
+00:18:54,510 --> 00:18:58,750
+أقل من مين؟ من D مفاهيم بسيطة مش فيها مشكلة حتى
+
+238
+00:18:58,750 --> 00:19:02,830
+اللحظة طيب مدام في عملية قسمة عملية القسمة هذه
+
+239
+00:19:02,830 --> 00:19:05,350
+ممكن تقودنا لحاجة اسمها greatest common divisor
+
+240
+00:19:05,350 --> 00:19:08,690
+مدام أنا بحكي على divisor D D D Divisor Divisor
+
+241
+00:19:08,690 --> 00:19:15,410
+Divisor وبدأت فيها شغلD divides A اللي هو قيمة
+
+242
+00:19:15,410 --> 00:19:21,070
+بدها تقسم قيمة أكبر فاللي قامت بالتقسيم القاسم
+
+243
+00:19:21,070 --> 00:19:25,610
+اللي هو القاسم divisor فال divisor هذا ممكن يكون
+
+244
+00:19:25,610 --> 00:19:29,730
+للقيمة أكتر من divisor مش هيك؟ طيب ممكن أقول
+
+245
+00:19:29,730 --> 00:19:34,070
+greatest common divisor هنا لما نقول قاسم مشترك
+
+246
+00:19:34,070 --> 00:19:39,370
+أكبر معناته هذا القاسم بدي يكون لأكتر من قيمةزي
+
+247
+00:19:39,370 --> 00:19:46,850
+طوى لما قلنا a divides b و a divides c فإذا عندي
+
+248
+00:19:46,850 --> 00:19:53,470
+divisor بيقسم أكتر من قيمة ففي الحالة هذه القيمتين
+
+249
+00:19:53,470 --> 00:19:59,610
+هدول في عامل مشترك قاسم مشترك بينهم يوجد قاسم
+
+250
+00:19:59,610 --> 00:20:06,110
+مشترك بينهم بمعنى ان بي تسمح انهاتقسم على A و C
+
+251
+00:20:06,110 --> 00:20:11,390
+تسمح أنها تقسم على A فإذاً A هنا مشترك كعامل تقسيم
+
+252
+00:20:11,390 --> 00:20:16,970
+ف divisor طيب و مشترك بس هنا بنتكلم عن greater أو
+
+253
+00:20:16,970 --> 00:20:23,070
+أكبر معامل مشترك أكبر فبنسميه GCD او greatest
+
+254
+00:20:23,070 --> 00:20:27,310
+common divisor between A و B معناته أنا بتكلم عن D
+
+255
+00:20:27,310 --> 00:20:33,160
+الناتج يعني هنا بالنسبالنا كانت Aففي الحالة هذه
+
+256
+00:20:33,160 --> 00:20:40,580
+إذا هذا الكلام صحيح كأنه D divide A و D divide B
+
+257
+00:20:40,580 --> 00:20:48,580
+تشيك كأنني بدي أطلع القيمة الناتج اللي هي D العامل
+
+258
+00:20:48,580 --> 00:20:53,620
+المشترك الأكبر لكلاهما لكلاهما فبنقدر نقول إن هي
+
+259
+00:20:53,620 --> 00:21:00,330
+ال maximum لل D لأنه قلنا greatestطيب الأرقام ممكن
+
+260
+00:21:00,330 --> 00:21:02,530
+يكون فيها اكتر من عامل مشترك او ممكن يكون اكتر من
+
+261
+00:21:02,530 --> 00:21:06,750
+عامل مشترك احنا بدنا اكبر عامل مشترك ممكن بحيث انه
+
+262
+00:21:06,750 --> 00:21:11,610
+دي هذه ال maximum دي تسمح انه دي divides a و دي
+
+263
+00:21:11,610 --> 00:21:16,350
+divides b معطلة بسيطة وسهلة جدا طيب مجموعة امثلة
+
+264
+00:21:16,350 --> 00:21:22,290
+greatest common divisor ال 24 و 36 جداش بدنا
+
+265
+00:21:22,290 --> 00:21:25,830
+نجيبكم كل المعاملات اللي بينهم الاتنين اه معامل
+
+266
+00:21:25,830 --> 00:21:30,930
+لان كلا هماeven فإذا الاتنين ممكن الواحد سيبك منها
+
+267
+00:21:30,930 --> 00:21:34,910
+حنتكلم حالة خاصة شوية الواحد حنتكلم عندنا بس
+
+268
+00:21:34,910 --> 00:21:38,610
+الاتنين موجودة كلاهما هذه ستة وهذه تسعة مجموحهم
+
+269
+00:21:38,610 --> 00:21:43,830
+فإذا التلاتة برضه divides both numbers التلاتة
+
+270
+00:21:43,830 --> 00:21:47,950
+بتقدر تجسم كلاهما هاي التلاتة الأربعة ممكن الستة
+
+271
+00:21:47,950 --> 00:21:51,250
+ممكن الأتناش ممكن في أكتر من هيك خلاص أكتر من
+
+272
+00:21:51,250 --> 00:21:55,310
+الأتناش مش هينفع أصلا انت ماتفحصش أكتر من نص قيمة
+
+273
+00:21:55,310 --> 00:22:01,460
+منهمخلاص مش هتفحص اكتر من نص قيمة لان بعد هيك اكيد
+
+274
+00:22:01,460 --> 00:22:05,220
+هيكون عنصر مكرر من ال divisors اللي طلعوا مين ال
+
+275
+00:22:05,220 --> 00:22:08,160
+common divisor بينهم اكيد اكبر واحد اللي هو ال 12
+
+276
+00:22:08,160 --> 00:22:10,480
+في ال greatest is 12
+
+277
+00:22:12,800 --> 00:22:15,400
+مش عارف انا عارف ان انتوا هالوقت حاسين حالكوا لسه
+
+278
+00:22:15,400 --> 00:22:19,440
+في ابتدائي و عدايا ده ايش اللي بنحكيه مش هيك لكن
+
+279
+00:22:19,440 --> 00:22:22,620
+المصطلحات هذه مهمة لأنه بعد هيك بدك تحولها لأكواد
+
+280
+00:22:22,620 --> 00:22:27,580
+بعد هيك بدك انت تكتب أكواد ال division algorithm
+
+281
+00:22:27,580 --> 00:22:33,410
+هذا طيب الطريقة التانيةاللي ممكن نستخدمها بدل ما
+
+282
+00:22:33,410 --> 00:22:38,050
+انت تقعد تتخمن ايش العوامل المشتركة و تجيب ال
+
+283
+00:22:38,050 --> 00:22:41,150
+maximum منهم احنا خدنا توي ال prime factorization
+
+284
+00:22:41,150 --> 00:22:45,130
+مش هي برضه هاد الطريقة خدتوها سابقا كل اللي بعمله
+
+285
+00:22:45,130 --> 00:22:48,450
+انه a و b اللي بدي اجيب ال greatest common divisor
+
+286
+00:22:48,450 --> 00:22:54,410
+between them بجيب ال prime factors تبعتهم لل a و
+
+287
+00:22:54,410 --> 00:23:00,890
+لل b و بنشوف اذا كان في prime تكرركمعامل لكلهما
+
+288
+00:23:00,890 --> 00:23:07,790
+باخده و باخد ال power الأقل منهما ناخد ال power
+
+289
+00:23:07,790 --> 00:23:12,450
+الأقل منهما بحيث أنه نمسك ال prime الأول و ناخد ال
+
+290
+00:23:12,450 --> 00:23:17,770
+minimum between a1 او b1 و نفس الكلام ال prime
+
+291
+00:23:17,770 --> 00:23:23,010
+التاني من الأقل تكرار هنا ولا هنا فباخده من الأقل
+
+292
+00:23:23,010 --> 00:23:25,890
+تكرار لما نخلص كل ال primes اللي موجودين اللي
+
+293
+00:23:25,890 --> 00:23:28,170
+ظهروا معناها اللي و كده هنشوف الأمثلة فونرجع
+
+294
+00:23:28,170 --> 00:23:33,580
+نضربهمبتكون ال greatest common divisor زي ال 84 و
+
+295
+00:23:33,580 --> 00:23:38,940
+ال 96 بمسك ال 84 و بنبدأ بقسم على 2 او بقبل 2 طيب
+
+296
+00:23:38,940 --> 00:23:42,120
+اللي ضال جديش 42 ال 42 بتقبل على 2 او بتقبل على 2
+
+297
+00:23:42,120 --> 00:23:46,800
+تكمل and so on بتكمل لما تخلص و دايما عشان تريح
+
+298
+00:23:46,800 --> 00:23:50,400
+حالك و تجيبهم ابدا دايما من الصغير يعني ابدا اطلب
+
+299
+00:23:50,400 --> 00:23:54,590
+القسم على 2خلصت من الأتنين الأولى، ضلك في الأتنين،
+
+300
+00:23:54,590 --> 00:23:57,230
+ما تسيبش الأتنين إلا لما الرقم خلاص بيقسمش على
+
+301
+00:23:57,230 --> 00:23:59,890
+اتنين نهائيًا، ما تقعدش تخربط حالك مرة اتنين و مرة
+
+302
+00:23:59,890 --> 00:24:03,910
+تلاتة و مرة خمسة، و ترجع تاني على اتنين، هقولك،
+
+303
+00:24:03,910 --> 00:24:08,030
+هتتخربط، هتتخربط، أكيد، فابتنسك من أصغر عنصر في
+
+304
+00:24:08,030 --> 00:24:12,870
+الprimes، و لما تستنفظ تمامًا، خلصته، ابدا أنجل عن
+
+305
+00:24:12,870 --> 00:24:16,490
+اللي بعده، and so on بهذا الشكل، فبتضلك مرتب، و ان
+
+306
+00:24:16,490 --> 00:24:20,830
+شاء الله بتغلطش فيهاتمام اتنين اتنين تلاتة سبعة
+
+307
+00:24:20,830 --> 00:24:24,930
+كويس فهذه معناته كأنه عند الاتنين متكررة مرتين فهي
+
+308
+00:24:24,930 --> 00:24:29,150
+اتنين تتطور اتنين التلاتة متكررة مرة واحدة والسبعة
+
+309
+00:24:29,150 --> 00:24:34,480
+مرة واحدةطيب ال 96 برضه نفس الكلام هتبدأ تقسم على
+
+310
+00:24:34,480 --> 00:24:38,640
+2 طيب لسه بتقبل على 2 اه اكمل على 2 ع 2 ع 2 لما ت
+
+311
+00:24:38,640 --> 00:24:42,620
+stand في رقم 2 تماما انت بتكون مطمن انك انت هالوقت
+
+312
+00:24:42,620 --> 00:24:46,100
+هتبدأ تقسم على 3 و عمرك ماهي ترجع لل 2 عمره
+
+313
+00:24:46,100 --> 00:24:50,580
+ماهيطلع الناتج برجع يقسم على 2 تمام فظهر بهذا
+
+314
+00:24:50,580 --> 00:24:56,220
+الشكل ف2 تتباور 5 3 تتباور 1 7 المشتركة هنا هي هنا
+
+315
+00:24:56,220 --> 00:25:00,110
+فعليا تتباور 0to the power صفر أنا ماكنش في عندي
+
+316
+00:25:00,110 --> 00:25:02,410
+سبعة هنا يعني كأنها سبعة to the power صفر و احنا
+
+317
+00:25:02,410 --> 00:25:05,370
+عارفين ان اي حاجة to the power صفر بواحد مش هيك؟
+
+318
+00:25:05,370 --> 00:25:08,590
+كويس كأنها بهذا الشكل ليش عملنا هيك؟ لمجرد بس ناخد
+
+319
+00:25:08,590 --> 00:25:13,170
+ال minimum هلقيت ال minimum هنا اتنين فال greatest
+
+320
+00:25:13,170 --> 00:25:16,550
+common divisor هي اتنين هيقوم مشترك to the power
+
+321
+00:25:16,550 --> 00:25:20,530
+الأقل منهم اتنين الواحد واحد زي ما هي والسبعة
+
+322
+00:25:20,530 --> 00:25:26,000
+هناخد الصفرفكأنه مش موجود تمام فهنا صارت اربعة في
+
+323
+00:25:26,000 --> 00:25:30,480
+تلاتة اتن عاش فال greatest common divisor between
+
+324
+00:25:30,480 --> 00:25:33,960
+them هو اتن عاش هذا ال algorithm ممكن تشتغل عليه ك
+
+325
+00:25:33,960 --> 00:25:39,680
+algorithm تعملوا برمجة و تطلع النتج النهائي طبعا
+
+326
+00:25:39,680 --> 00:25:46,900
+طيب بيصير معنى كتير ان a و b هم فعليا كل واحد
+
+327
+00:25:46,900 --> 00:25:52,030
+لحاله composite number لكن related لبعضrelated
+
+328
+00:25:52,030 --> 00:25:58,490
+لبعض هم بالنسبة لبعض كأنهم primes بالنسبة لبعض ايش
+
+329
+00:25:58,490 --> 00:26:01,950
+معنى ان هم بالنسبة لبعض كأنهم primes معناته ان
+
+330
+00:26:01,950 --> 00:26:05,150
+لايوجد greatest common divisor between them هم
+
+331
+00:26:05,150 --> 00:26:08,450
+مافيش عامل مشترك بينهم مافيش حد منهم مضاعف للتاني
+
+332
+00:26:08,450 --> 00:26:12,290
+ولا يوجد اي divisor مشترك بينهم ففي الحالة هذه
+
+333
+00:26:12,290 --> 00:26:18,210
+بنسميهم co-prime او relatively prime بنسميهم
+
+334
+00:26:18,210 --> 00:26:24,950
+relatively prime او co-primeكأنه لا يوجد أي عامل
+
+335
+00:26:24,950 --> 00:26:28,930
+مشترك بينهم، مافيش بينهم أي عامل مشترك، يعني لو
+
+336
+00:26:28,930 --> 00:26:34,150
+قدر لواحد منهم يكون هو المرجعية بتاعتنا في العد،
+
+337
+00:26:34,150 --> 00:26:36,970
+احنا المرجعية بتاعتنا مين؟ صفر، مش هيك بنبدأ من
+
+338
+00:26:36,970 --> 00:26:40,710
+صفر، لو قدر ان واحد من الرقمين هدول هو المرجعية
+
+339
+00:26:40,710 --> 00:26:46,460
+للعد، التاني هيكون ال primeلو فهم relatively
+
+340
+00:26:46,460 --> 00:26:49,660
+prime، بنسميهم في الحالة هذه، فإذا بنقول
+
+341
+00:26:49,660 --> 00:26:53,200
+relatively prime أو coprime if and only if the
+
+342
+00:26:53,200 --> 00:26:55,240
+greatest common divisor between them equaled to
+
+343
+00:26:55,240 --> 00:26:59,060
+one يعني لاوجد عامل مشترك بينهم، one معناه أنه
+
+344
+00:26:59,060 --> 00:27:03,820
+لاوجد عامل مشتركتمام مثال ال 21 و العشرة هما
+
+345
+00:27:03,820 --> 00:27:08,580
+كلاهما مش prime لا هدا prime ولا هدا prime لكن مع
+
+346
+00:27:08,580 --> 00:27:11,880
+بعض هما co-prime ليش هما اتنين مع بعض co-prime
+
+347
+00:27:11,880 --> 00:27:15,920
+لأنه ببساطة ال 21 هذه هي عبارة عن تلاتة في سبعة
+
+348
+00:27:15,920 --> 00:27:20,240
+هدا واحد كأنه مش هم ال two to the power of zero
+
+349
+00:27:20,240 --> 00:27:24,760
+طيب و العشرة هي اتنين في خمسة جيبلي greatest
+
+350
+00:27:24,760 --> 00:27:31,740
+common divisor between them صفر صفر صفر صفرفأرقام
+
+351
+00:27:31,740 --> 00:27:36,660
+تتطور صفر واحد يعني في الآخر بتطلع واحد فهم
+
+352
+00:27:36,660 --> 00:27:40,400
+بالنسبالهم لو قدر لو واحد منهم ان هو يكون ال
+
+353
+00:27:40,400 --> 00:27:44,120
+reference بتاع العد تبعنا التاني اكيد هيكون ايش
+
+354
+00:27:44,120 --> 00:27:48,480
+prime بالنسباله هتكون
+
+355
+00:27:48,480 --> 00:27:52,240
+كأنه prime بالنسبة لبعض كذا فبنسميهم co-prime في
+
+356
+00:27:52,240 --> 00:27:57,710
+الحالة هذهالهم تطبيقات اه تطبيقات كتيرة و تحديدا
+
+357
+00:27:57,710 --> 00:27:59,930
+في ال security و في ال encryption و هده هناخدوا
+
+358
+00:27:59,930 --> 00:28:03,690
+الكلام هده دي ربعكوا احنا بدأنا لحظة من اوله
+
+359
+00:28:03,690 --> 00:28:07,430
+ابتدائي جاعدين نبدأ بس ال chapter هده جاعدين نتدرج
+
+360
+00:28:07,430 --> 00:28:11,330
+فيه لما هتصل لمرحلة ال encryption لما تصل لمرحلة
+
+361
+00:28:11,330 --> 00:28:16,390
+انك انت تعمل security code عشان هيك انا بادئ
+
+362
+00:28:16,390 --> 00:28:21,140
+معاكوا من اولهركزوا معانا لأن هذا كله هو هذا اللي
+
+363
+00:28:21,140 --> 00:28:24,240
+هنستخدمه في ال encryption ال encryption مش اختراع
+
+364
+00:28:24,240 --> 00:28:29,440
+كبير يعني ان اعمل تشفير للبيانات مش اختراع كبير هي
+
+365
+00:28:29,440 --> 00:28:33,800
+بادية من الأرقام هي numbers فعليا وهي نبديين
+
+366
+00:28:33,800 --> 00:28:38,480
+رايحين في هذا الاتجاه طيب في حاجة اسمها least
+
+367
+00:28:38,480 --> 00:28:43,500
+common multiple اللي هو المضاعف المشترك الأصغرلما
+
+368
+00:28:43,500 --> 00:28:46,740
+يكون عندك عنصرين طب هذا مضاعفاته و هذا مضاعفاته
+
+369
+00:28:46,740 --> 00:28:50,400
+امتى هيلتقوا بمضاعف مشترك بينهم بس الامتى هيلتقوا
+
+370
+00:28:50,400 --> 00:28:56,420
+بمضاعف مشترك بينهم اول مضاعف مشترك هسميه ال Lcm او
+
+371
+00:28:56,420 --> 00:29:01,660
+ال less common multiple نفس فكرة ال prime
+
+372
+00:29:01,660 --> 00:29:05,700
+factorization لكن باخد ال power الأكبر هنافي ال
+
+373
+00:29:05,700 --> 00:29:07,400
+greatest common divisor باخد ال power الأقل
+
+374
+00:29:07,400 --> 00:29:12,700
+للمشتركات ل ال primes المشتركة هنا بناخد الأكبر ..
+
+375
+00:29:12,700 --> 00:29:17,600
+بناخد الأكبر يعني لو قلنا ستة و عشرة في الحلقة هذه
+
+376
+00:29:17,600 --> 00:29:23,380
+ممكن ال A نفصل ال primes تبعته و ال B نفصل ال
+
+377
+00:29:23,380 --> 00:29:26,700
+primes تبعته و ناخد ال maximum بينهم .. ناخد بينهم
+
+378
+00:29:27,540 --> 00:29:33,160
+ال maximum ببساطة جدا هات ناخد ال 6 و العشرة ال 6
+
+379
+00:29:33,160 --> 00:29:39,200
+و العشرة نبدأ مع بعض ناخد مين الأول اجت 6 ايش ال
+
+380
+00:29:39,200 --> 00:29:52,770
+primes تبعتها 2 في 3 شك؟ طيب العشرة 2 في 52×5 فإذن
+
+381
+00:29:52,770 --> 00:29:56,090
+بدنا نقول هالوجد هنا كأنها to the power one to the
+
+382
+00:29:56,090 --> 00:29:57,890
+power one to the power one كأنها تلاتة to the
+
+383
+00:29:57,890 --> 00:30:02,110
+power صفر في خمسة to the power one و هنا كأنها
+
+384
+00:30:02,110 --> 00:30:05,690
+خمسة to the power zero معناته واحد يعني هدولة بس
+
+385
+00:30:05,690 --> 00:30:10,030
+عشان ناخد مين ال maximum فال maximum هي نفسها طيب
+
+386
+00:30:10,030 --> 00:30:17,070
+ال maximum تلاتة و هنا ال maximum خمسة صحيح طيب
+
+387
+00:30:17,070 --> 00:30:23,060
+اضربههذه ستة في خمسة وهذه تلاتين فإذا التلاتين هو
+
+388
+00:30:23,060 --> 00:30:29,120
+العامل المضاعف الأصغر لكلهما فإذا هو لازم يكون
+
+389
+00:30:29,120 --> 00:30:32,480
+مضاعف من المضاعفات تبع كلاهما التلاتين من
+
+390
+00:30:32,480 --> 00:30:36,100
+المضاعفات العشر أه ما هي عشر عشرين تلاتين والستة
+
+391
+00:30:36,100 --> 00:30:40,660
+نفس الكلام ستة اتناشر تمانتعشر اربع عشرين تلاتين
+
+392
+00:30:40,660 --> 00:30:45,320
+فإذا هي مضاعف للاتنين و هم أصغر مضاعف اشتركوا فيه
+
+393
+00:30:45,320 --> 00:30:54,060
+كلهمابنسميه ال LCM تمام هذه فكرة ال LCM okay نبدأ
+
+394
+00:30:54,060 --> 00:31:00,200
+شوية شوية نبدأ في ال modulo ال modulo operator
+
+395
+00:31:00,200 --> 00:31:05,960
+ببساطة جدا هي عملية بنحسب منها ال remainder أو ال
+
+396
+00:31:05,960 --> 00:31:12,300
+division remainder ال R اللي سبناها تحت معلجة هذه
+
+397
+00:31:12,300 --> 00:31:16,870
+بدنا إيقهاخارج عملية القسمة ال R اللي بتسيبها في
+
+398
+00:31:16,870 --> 00:31:19,310
+الآخر كأنها فاضلة من الفضالة خلاص بدناش هي لأ هذه
+
+399
+00:31:19,310 --> 00:31:23,010
+هي اللي بدناها هي المتبقى هي الفاضل يعني اللي ضال
+
+400
+00:31:23,010 --> 00:31:28,330
+جويس هذه اللي بدناها فلو قلنا A و D هما integers
+
+401
+00:31:28,330 --> 00:31:32,530
+مجموعة integers او two integers و D لازم تكون اكبر
+
+402
+00:31:32,530 --> 00:31:37,350
+من واحد بحيث ان يكون في خارج القسمة اصلا جويس اذا
+
+403
+00:31:37,350 --> 00:31:45,270
+Amodulo D كإني بقول A تقسيم D، بديش الناتج ال
+
+404
+00:31:45,270 --> 00:31:48,570
+quotient، ال quotient بديش إياه، أنا بده ال R،
+
+405
+00:31:48,570 --> 00:31:56,310
+بدنا ال R، فنتج هذه العملية ال modulo هي ال Rهي ال
+
+406
+00:31:56,310 --> 00:31:59,870
+R كويس ف ال division هذا بنسميها من division
+
+407
+00:31:59,870 --> 00:32:03,890
+algorithm ايش متبقي من ال division algorithm R هي
+
+408
+00:32:03,890 --> 00:32:10,270
+ناتج المدلو A مدلو D ففي الحالة هذه D هذا بنسميه
+
+409
+00:32:10,270 --> 00:32:18,470
+ال modulus او هو معامل التكرار تبعناه هو divisor
+
+410
+00:32:18,470 --> 00:32:24,040
+تبعكوالناتج لإلها كلها هي ال R وليست ال quotient،
+
+411
+00:32:24,040 --> 00:32:26,280
+وليست ال quotient اللي .. اللي كل متوقع أنه هي ال
+
+412
+00:32:26,280 --> 00:32:30,210
+quotient، لأ هي مش ال quotientطيب فال dividend زي
+
+413
+00:32:30,210 --> 00:32:35,510
+ما هي A ال divisor زي ما هي D و ناتجهم كلاهما هو
+
+414
+00:32:35,510 --> 00:32:40,350
+المتبقي متبقي ناتج المخدمة طيب فبنستخدم ال long
+
+415
+00:32:40,350 --> 00:32:45,490
+division العادية جدا ممكن تستخدم القسمة المطولة
+
+416
+00:32:45,490 --> 00:32:53,010
+يعني طيب بنبقى بنحسب ال A modulo D باستخدام A ناقص
+
+417
+00:32:53,010 --> 00:32:59,730
+D في ال quotient ما هي هذه في النهاية ما هي ال Qمش
+
+418
+00:32:59,730 --> 00:33:04,730
+هذه ال Q كانت؟ هي ال quotient خارج أو ناتج القسمة
+
+419
+00:33:04,730 --> 00:33:12,030
+A على D اخد floor فلما تيجي تعمل عملية A و D هنا
+
+420
+00:33:12,030 --> 00:33:18,610
+هتكون ال Q وهنا هتظل ال R ففعليا هذا ال term A على
+
+421
+00:33:18,610 --> 00:33:25,620
+D floor هو ال Q هي فعليا ال Qتمام هد في ال C++ أو
+
+422
+00:33:25,620 --> 00:33:29,100
+في ال C أو في ال Java بنستخدم العلامة المئوية فهد
+
+423
+00:33:29,100 --> 00:33:33,260
+هي ال mod أو ال modulo أو ال modulo operation هد
+
+424
+00:33:33,260 --> 00:33:39,420
+لو جربتها في اكتبلك كده صغير هيك سطر اعملك مثلا اي
+
+425
+00:33:39,420 --> 00:33:42,960
+رقمين و اعمل بينهم العلامة هد الناتج هتلاقي هو
+
+426
+00:33:42,960 --> 00:33:51,240
+متبقي القسم بينهم هو متبقي القسم ما بينهم كيف؟
+
+427
+00:34:03,260 --> 00:34:08,000
+الإشارة في واحد منهم هو تكرار و في واحد لأ الإشارة
+
+428
+00:34:08,000 --> 00:34:12,420
+بتفرج لأ اصبر علينا اصبر علينا الموجلة الموجلات
+
+429
+00:34:12,420 --> 00:34:16,500
+هلوجة الموجلات هنتكلم عنه أعتقد جاينا هيا الموجلات
+
+430
+00:34:16,500 --> 00:34:22,490
+congrance congrance هنا نتكلم عنو هنا ال
+
+431
+00:34:22,490 --> 00:34:26,230
+congruence هتوضحلك أن ال R ممكن أن أنا أستخدمها أي
+
+432
+00:34:26,230 --> 00:34:31,870
+شيء في ال modulo لكن في ال R الطبيعية لأ هي قيمة و
+
+433
+00:34:31,870 --> 00:34:35,290
+احنا قلنا unique تولما اتكلمنا قبل slideين تلاتة
+
+434
+00:34:35,290 --> 00:34:40,470
+قلنا هي unique صحيح؟ هنا لأ هنا لما نيجي نقول إذا
+
+435
+00:34:40,470 --> 00:34:45,110
+كان عندي positive integer positive integer هاي في
+
+436
+00:34:45,110 --> 00:34:48,850
+علامة ال positive integerهي عبارة عن natural
+
+437
+00:34:48,850 --> 00:34:52,030
+number أكيد مدام positive معناته بدأنا دخلنا في ال
+
+438
+00:34:52,030 --> 00:34:55,970
+natural number تنتمي ل z و ال n هذا لازم تكون أكبر
+
+439
+00:34:55,970 --> 00:35:01,070
+من من صفر لأنه لازم تكون positive فهذا تعريف كلمة
+
+440
+00:35:01,070 --> 00:35:06,490
+z plus فإذا كان positive integer بهذا الشكل اللي
+
+441
+00:35:06,490 --> 00:35:10,170
+هنكتبه وعندي a و b هي مجموعة integers هذه هنسميها
+
+442
+00:35:10,170 --> 00:35:16,590
+ال modulus ال modulus بمعنى هيمعامل التكرار إيش
+
+443
+00:35:16,590 --> 00:35:20,110
+يعني معامل التكرار أنت فعليًا لما بتجي بتعمل عملية
+
+444
+00:35:20,110 --> 00:35:28,170
+القسمة A على D A تقسيم D أنت فعليًا قاعد بتشوف مرة
+
+445
+00:35:28,170 --> 00:35:37,590
+تكرار أنت بتشوف جداش D multiple من A multiple من D
+
+446
+00:35:37,590 --> 00:35:44,090
+بمعنى D أكام مرة متكررةفي Q صحيح طيب لو قلنا مثلا
+
+447
+00:35:44,090 --> 00:35:50,730
+متكررة خمس مرات او Q مرة Q مرة عشان يظل عندك R مرة
+
+448
+00:35:50,730 --> 00:35:53,850
+طيب في الحالة هذه لو انت تخيلت ان انت بتتكلم عن
+
+449
+00:35:53,850 --> 00:35:59,930
+ساعة ساعة ساعة العجارب ساعة العجارب ساعة العقارب
+
+450
+00:35:59,930 --> 00:36:01,270
+انت بتتكلم عن اتناش هنا
+
+451
+00:36:04,270 --> 00:36:09,570
+بمعنى الزمن انت مجسمه لـ12 و بس 12 فبتجسمه كل مرة
+
+452
+00:36:09,570 --> 00:36:13,750
+على الـ12 الساعة اللي في إيدك لو هي عجارب أو انت
+
+453
+00:36:13,750 --> 00:36:17,430
+حاطط على جوالك ساعة عجارب مش هتنط عن الـ12 يعني او
+
+454
+00:36:17,430 --> 00:36:21,230
+مرة ماحتجيك قيمة أكبر غير الـ12 صحيح؟ مدام هي
+
+455
+00:36:21,230 --> 00:36:25,650
+عقارب قاعدة بتلف او مرة ماحتجيش تقولك انا 13 الا
+
+456
+00:36:25,650 --> 00:36:31,580
+رقميةوالرقمية ساعتها حتى ال .. ال modulus تبحر 24
+
+457
+00:36:31,580 --> 00:36:34,580
+و بوقف مافيش ساعة خمسة و عشرين مافيش ساعة سبعة و
+
+458
+00:36:34,580 --> 00:36:37,540
+عشرين مش شئ طيب ها إيش اللي بيصير فعليا السبعة و
+
+459
+00:36:37,540 --> 00:36:40,460
+عشرين إجت ما إحنا إلنا عاشين عمر لما تيجي بدك تحسب
+
+460
+00:36:40,460 --> 00:36:45,300
+عمرك بالساعات كده بدك تحسبه بدك تقول والله اليوم
+
+461
+00:36:45,300 --> 00:36:49,400
+24 ساعة المش عارف الأسبوع سبعة أيام و هكذا طيب أكم
+
+462
+00:36:49,400 --> 00:36:54,350
+يوم فيها بتبدأ تضرب في مين؟ في ال modulusفبتصير
+
+463
+00:36:54,350 --> 00:36:58,710
+تبدأ تشتغل على ال modular congrance بحيث انه تقول
+
+464
+00:36:58,710 --> 00:37:05,790
+والله من الساعة اتناش ستة تلاتة تسعة الساعة تلتاش
+
+465
+00:37:05,790 --> 00:37:14,870
+هي congrance او congrant to واحد مش هيك مش هيك
+
+466
+00:37:14,870 --> 00:37:18,530
+احنا هنحسبها هي نفس الساعة واحدة الظهر الساعة
+
+467
+00:37:18,530 --> 00:37:24,110
+تلتاش هي واحدة الظهرطيب، فإذا في تكافؤ بينهم، في
+
+468
+00:37:24,110 --> 00:37:29,010
+عملية congruence congruence هي التكافؤ تبع ال
+
+469
+00:37:29,010 --> 00:37:35,970
+modulus أو ال modular congruence فهي أنت بتشتغل
+
+470
+00:37:35,970 --> 00:37:43,490
+على المدلو والمدلو مدام أنت جسمت على D فالناتج أو
+
+471
+00:37:43,490 --> 00:37:51,470
+اللي هو بدك إياه كR هوناتج بعد عدد مرات تكرار D من
+
+472
+00:37:51,470 --> 00:37:54,850
+A D
+
+473
+00:37:54,850 --> 00:38:00,170
+من A فلما بتقول والله عندي ستة وعشرين هنا ستة
+
+474
+00:38:00,170 --> 00:38:05,790
+وعشرين وانا بتكلم عن ساعة فإذا أكمرة معامل الساعة
+
+475
+00:38:05,790 --> 00:38:14,520
+هذا المجلس اتكرر قد أخصم منهاهي مرة اتناش شيلنا
+
+476
+00:38:14,520 --> 00:38:17,820
+اتناش فبضل اربعتاش الاربعتاش مازالت اكبر يعني تقدر
+
+477
+00:38:17,820 --> 00:38:22,100
+تعمل كمان لفة اربعة اتناش ساعة بيضل اتنين فالاتنين
+
+478
+00:38:22,100 --> 00:38:28,800
+هذا المتبقي فعليا هو مكافئ لاربعة وعشرين هو مكافئ
+
+479
+00:38:28,800 --> 00:38:35,700
+لاربعة وعشرين طيب الاربعتاش برضه مكافئ لهم بطلنا
+
+480
+00:38:35,700 --> 00:38:43,270
+نحكي عن R لحظت فصار عندك اتنين congruentللـ 14 و
+
+481
+00:38:43,270 --> 00:38:47,710
+هما كلاهما congruent ل 26 و كلاهما congruent ل 26
+
+482
+00:38:47,710 --> 00:38:53,810
+زاد 12 زاد 12 زاد 12 زاد 12 بضلك زيد زاد 12 براحتك
+
+483
+00:38:54,640 --> 00:38:58,680
+كل رقم بتضيفه الناتج هو congruent له اللي بدأت منه
+
+484
+00:38:58,680 --> 00:39:03,700
+مدام انت بتجمع قيمة ال modulus فقط ال modulus ده
+
+485
+00:39:03,700 --> 00:39:08,940
+هو اللي هي العداد تبعك عدادك طيب ناس بيشتغلوا في
+
+486
+00:39:08,940 --> 00:39:14,060
+الهندسة هتكون بالنسبالهم تلت مية و ستين الزوايا مش
+
+487
+00:39:14,060 --> 00:39:19,380
+هيك اكم درجة لما تقولي تلت مية و سبعين فبفهم ان
+
+488
+00:39:19,380 --> 00:39:23,890
+انت بتتكلم عن عشر درجات بس في اتجاه الموجببنفهم إن
+
+489
+00:39:23,890 --> 00:39:27,990
+إيه عشر درجات لما تيجي تحسب عملية حسابية بدك تحسب
+
+490
+00:39:27,990 --> 00:39:31,430
+مجموعة Sines فيه Cos فيه ومش عارفاش وكلها زوايا
+
+491
+00:39:31,430 --> 00:39:35,730
+واتجمعت معاك مجموعة زوايا طلعت يعني عدت الـ360 مش
+
+492
+00:39:35,730 --> 00:39:40,910
+مشكلة إيش المشكلة صارت 720 أنت عارف أن الـ720 هي
+
+493
+00:39:40,910 --> 00:39:44,290
+نفس الـ360 هي نفس الصفر يعني أنت بتتكلم عن زاوية
+
+494
+00:39:44,290 --> 00:39:48,570
+صفر معناه أن أنت في الاتجاه نفسه مش هتضطر تغير أنت
+
+495
+00:39:48,570 --> 00:39:51,590
+ما زلت في الاتجاه الصحيح مش مضطر تغير
+
+496
+00:39:56,400 --> 00:40:01,500
+فهو رجع لقى وضعه هو بس أخد لفة جولة هيك ورجع مكانه
+
+497
+00:40:01,500 --> 00:40:10,080
+كما كان تمام فهي الفكرة الأساسية طيب انشوف هنا إيش
+
+498
+00:40:10,080 --> 00:40:15,940
+بدناه كمان فإذا بقدر أقول A congruent congruent
+
+499
+00:40:15,940 --> 00:40:26,210
+لإيش ل B modulo M وزي ما قلنا A هيناتج الموديلو و
+
+500
+00:40:26,210 --> 00:40:32,550
+B هي برضه ناتج لموديلو الموديلوس
+
+501
+00:40:32,550 --> 00:40:39,550
+M باستخدام الموديلوس M زي ما قلنا اتنين واربعتاش
+
+502
+00:40:39,550 --> 00:40:44,770
+ل M جداش اتناش نفس الكلامفانت لو ماتجيش تطلع
+
+503
+00:40:44,770 --> 00:40:48,810
+الساعة و جلبت لحالها رقمي و لجيتها 14 فانت فاهم ان
+
+504
+00:40:48,810 --> 00:40:51,810
+انت بتتكلم عن الساعتين و الظهر انت فاهم الكلام هذا
+
+505
+00:40:51,810 --> 00:40:55,410
+فانت automatic انت برمج حالك على قصة ال congrance
+
+506
+00:40:55,410 --> 00:41:00,570
+المكافئة ان هذا تكافئ الساعتين تان بس بتحطلها
+
+507
+00:41:00,570 --> 00:41:03,590
+التمييز تبعها انه ظهرا بتحطلها تميزها ظهرا طيب
+
+508
+00:41:03,590 --> 00:41:10,090
+الحاجة اللي واضحة جدا هنا ان ايه ناقص بيه ايه ناقص
+
+509
+00:41:10,090 --> 00:41:15,360
+بيه لازم يساوي قيمة المجلسعشان يكونوا فعلا
+
+510
+00:41:15,360 --> 00:41:21,840
+متكافئين مع بعض أو congruent لبعض ف A ناقص B مدله
+
+511
+00:41:21,840 --> 00:41:27,320
+M لازم يسووا Zero لما كنا متكلم عن اربعتاش ناقص
+
+512
+00:41:27,320 --> 00:41:35,460
+اتنين كلهما لما نيجي نقول عليهم مد اتناش لازم
+
+513
+00:41:35,460 --> 00:41:43,830
+يسووا صفر لازم يطلع صفرلما كنا نقول 24 .. اه 26 زي
+
+514
+00:41:43,830 --> 00:41:52,370
+توي يقولنا congruent لبعض 26 و 14 برضه يساوي صفر
+
+515
+00:41:52,370 --> 00:41:56,850
+فبقدر نقول ان اه الاتنين هدول congruent لبعض نقدر
+
+516
+00:41:56,850 --> 00:42:04,750
+نقول ان هم congruent لبعض لما اتكلمنا عن 25 و 1 اه
+
+517
+00:42:04,750 --> 00:42:12,940
+الاتنين لازم في الآخر بيساوي صفرلما اتكلمنا عن سبع
+
+518
+00:42:12,940 --> 00:42:18,740
+.. خلّيني اقول مثلا تلاتمية و تمانين و انا بتكلم
+
+519
+00:42:18,740 --> 00:42:23,760
+عن عشرين
+
+520
+00:42:23,760 --> 00:42:27,620
+كدرجة لتلاتمية
+
+521
+00:42:27,620 --> 00:42:32,700
+و ستين درجة اكيد بده يساوي صفر فإذا انت فاهم ان
+
+522
+00:42:32,700 --> 00:42:36,460
+تلاتمية و تمانين درجة معناته ان في النهاية عشرين
+
+523
+00:42:36,460 --> 00:42:41,730
+درجةعشرين درجة طيب انت بتعمل كمان حاجة اكتر من هيك
+
+524
+00:42:41,730 --> 00:42:46,770
+ايش بتعمل اكتر من هيك انك انت تقول تلاتمية وسبعين
+
+525
+00:42:46,770 --> 00:42:55,730
+هي سالب عشرة يعني عفوا تلاتمية وخمسين انت
+
+526
+00:42:55,730 --> 00:42:58,290
+ممكن تصل لمرحلة انك تقول تلاتمية وخمسين يعني سالب
+
+527
+00:42:58,290 --> 00:43:05,990
+عشرة يعني بروح في الاتجاه العكسى بدل ماأحسب تلاتي
+
+528
+00:43:05,990 --> 00:43:09,530
+عشرة مش شكلها دلوقت بحسب العشرة اللي تحت سالب عشرة
+
+529
+00:43:09,530 --> 00:43:15,710
+فبتقول اه هاي الزاوجة تبعتي طيب ما هي السالب عشرة
+
+530
+00:43:15,710 --> 00:43:20,650
+هذه هي نفسها تكافئ تلاتمية وخمسين يعني امشي من هنا
+
+531
+00:43:20,650 --> 00:43:26,490
+تلاتمية وخمسين هتصل نفس الشيء هتصل نفس الشغلاء هذه
+
+532
+00:43:26,490 --> 00:43:28,730
+هناخدها لجدام برضه الاتجاهات لما نيجي نعكس في
+
+533
+00:43:28,730 --> 00:43:32,790
+الاتجاهات لما نيجي نعكس اتجاهات هناخدها
+
+534
+00:43:38,930 --> 00:43:42,930
+Okay فشرحت ان هما لازم يكونوا في الآخر difference
+
+535
+00:43:42,930 --> 00:43:46,510
+between them مساوي ل ال modulus و مادام ساوى ال
+
+536
+00:43:46,510 --> 00:43:50,730
+modulus معناته اكيد ناتج ال modulo لازم يطلع zero
+
+537
+00:43:50,730 --> 00:43:54,430
+لابد يطلع zero ف difference between them كذا طيب
+
+538
+00:43:54,430 --> 00:43:59,430
+العلم هذه زي ما قولنا هي مش معناها is defined as
+
+539
+00:43:59,430 --> 00:44:04,770
+يعني هي مش معناها انه زي زي ال R لأ هنا congruent
+
+540
+00:44:04,770 --> 00:44:08,250
+مش معناها equalمش معناها equal عمرها مكنت
+
+541
+00:44:08,250 --> 00:44:12,950
+الاربعتاش بتساوي الاتنين عمرها مكنت هنا بتكافئ
+
+542
+00:44:12,950 --> 00:44:17,510
+الاتنين لإن حتى واحدة صباح و واحدة مساء يعني عمرك
+
+543
+00:44:17,510 --> 00:44:22,650
+ماحد تقولي ال 360 هي نفس الصفر الصفر بل ماشي عدل
+
+544
+00:44:22,650 --> 00:44:26,110
+على كلامك و جلب ال 360 بل ماشي عدل ماصلش اشي بس
+
+545
+00:44:26,110 --> 00:44:29,090
+هذا جلب ال 360 يمكن مات في ال 360 و رجع بعدين صفر
+
+546
+00:44:29,090 --> 00:44:31,210
+تقولي مهي و رجع زي ما كان لأ مارجعش زي ما كان
+
+547
+00:44:31,210 --> 00:44:35,690
+مارجعش زي ما كان على الأجال الخافةمش هيك؟ فهو
+
+548
+00:44:35,690 --> 00:44:40,750
+مرجعش زي ما كان congruent اه congruent المحصلة زي
+
+549
+00:44:40,750 --> 00:44:45,230
+بعض لكن ال action ما بين الفعل و المحصلة لأ مش زي
+
+550
+00:44:45,230 --> 00:44:49,370
+بعض مش زي بعض اصلا جاوبتك هيك على تساؤلك هم
+
+551
+00:44:49,370 --> 00:44:54,050
+الاتنين فعليا مش نفس الاشي طيب spiral
+
+552
+00:44:54,050 --> 00:45:02,420
+visualization of modulo هنا مثال نوضح فيهابشكل
+
+553
+00:45:02,420 --> 00:45:05,780
+واضح طبعا هنا ينطبق على زي ما قلنا بدنا نشتغل على
+
+554
+00:45:05,780 --> 00:45:10,840
+12 فانت بتتكلم عن ساعة بدت تشتغل على ال .. اللهم
+
+555
+00:45:10,840 --> 00:45:13,160
+صلى الله عليه و سلم يا محمد على 360 فانت بتشتغل
+
+556
+00:45:13,160 --> 00:45:18,300
+على ال degrees للزوايا بدت تشتغل على 2 πاي برضه
+
+557
+00:45:18,300 --> 00:45:22,900
+للزوايا بس بال radianmeasure فتشتغل بالدكيار معناه
+
+558
+00:45:22,900 --> 00:45:28,400
+ذلك أن هذه حاجة حيوية نستخدمها نستعملها في حياتنا
+
+559
+00:45:28,400 --> 00:45:35,140
+فعلا كويس هنا المثال اللي واضح لتمثيل
+
+560
+00:45:35,140 --> 00:45:43,080
+الحلزوني لmodulo ففعلا نستخدمه لخمسة فتبدأ من صفر
+
+561
+00:45:43,080 --> 00:45:47,320
+كأن هذه الساعة بدأت من الاتناش بدأنا نشتغل و بتلف
+
+562
+00:45:47,320 --> 00:45:53,380
+بس بتجسمها لخمسةفي ال 12 بتجسمها ل 12 في ال 360 زي
+
+563
+00:45:53,380 --> 00:45:56,420
+المنقلة اللي بتكون عندك بتجسمها ل 360 طبعا أنت
+
+564
+00:45:56,420 --> 00:46:00,140
+بتاخد نص اللي 180 يعني بتشتغلها فلازم يكون مجسم لك
+
+565
+00:46:00,140 --> 00:46:02,380
+كل ما جسملك إيها أكتر كل ما أعطاك دقة أكتر في
+
+566
+00:46:02,380 --> 00:46:07,480
+القياس كل ما أعطاك دقة أكتر لما بنتكلم عن خمسة فقط
+
+567
+00:46:07,480 --> 00:46:12,520
+فال modulus تبعك هو خمسة فقط فمعيارك خمسة
+
+568
+00:46:12,520 --> 00:46:15,440
+بالمناسبة modulus معناها المعيار اللي هو قيمة
+
+569
+00:46:15,440 --> 00:46:20,180
+المعيارية تبعتككويس فالميار تبعك هنا للتكرار هي
+
+570
+00:46:20,180 --> 00:46:24,320
+الخمسة فخلاص بقول فيها صفر واحد اتنين تلاتة اربعة
+
+571
+00:46:24,320 --> 00:46:29,920
+خمسة الخمسة بترجع للصفر زي الاطمعاش الاطمعاش هي
+
+572
+00:46:29,920 --> 00:46:34,580
+مكانها الصفر مكانها زي الصفر الاربعة عشرين مكانها
+
+573
+00:46:34,580 --> 00:46:39,380
+برضه بترجع للصفر ترجع للصفر فإذنبنبدأ من الصفر
+
+574
+00:46:39,380 --> 00:46:42,560
+واحد اتنين تلات اربع and so on هتيجي طبعا تلاقي كل
+
+575
+00:46:42,560 --> 00:46:46,440
+اللي على نفس الخط هي هم عناصر congruent ل بعض
+
+576
+00:46:46,440 --> 00:46:51,760
+فبقدر اقول انه الواحد congruent ل السبت عشر الست
+
+577
+00:46:51,760 --> 00:46:57,920
+congruent ل الواحد وعشرين بس كل هذا ايه؟ مدله خمسة
+
+578
+00:46:57,920 --> 00:47:02,940
+لو ال modulus مختلف لأ هيطلع اشي تاني اكيد هيطلع
+
+579
+00:47:02,940 --> 00:47:07,420
+اشي تاني اكيد هيطلع حاجة مختلفة تماما عن هيك تمام
+
+580
+00:47:10,310 --> 00:47:16,410
+Okay يعني نختم بشوية facts حوالين الموضوع هذا لو
+
+581
+00:47:16,410 --> 00:47:23,010
+قلنا a و b هم integers و m لاحظ هنا ال modulus
+
+582
+00:47:23,010 --> 00:47:27,550
+تبعك بكون positive لأن انت بتتكلم عن تكرار مش اكتر
+
+583
+00:47:27,550 --> 00:47:30,090
+من هيك هتقول طب ماهو ممكن يكون بالسلب لأ مش هيكون
+
+584
+00:47:30,090 --> 00:47:34,090
+بالسلب هيكون اتجاه الحركة ممكن يكون عكس اقارب
+
+585
+00:47:34,090 --> 00:47:40,350
+الساعة بس اما المعيار مش هيتغيريعني كمعيار مش
+
+586
+00:47:40,350 --> 00:47:44,430
+هيتغير انت إيش اللي بتعمله إيش اللي عملته اللي
+
+587
+00:47:44,430 --> 00:47:48,270
+أسبوع اللي فات انت غيرته الساعة عكس عقارب الساعة
+
+588
+00:47:48,270 --> 00:47:54,470
+لفة كاملة مش هيك فانت بتغير عقارب الدقائق كنت بس
+
+589
+00:47:54,470 --> 00:47:57,630
+عكس .. انت هيك بالنسبالك عكس عقارب الساعة صح
+
+590
+00:47:57,630 --> 00:48:03,670
+لفتوها بالعكس جداش لفة كاملة فعملته shift ساعة
+
+591
+00:48:03,670 --> 00:48:07,170
+لجدامقدمتها الساعة بدل ما الساعة تمانية صارت
+
+592
+00:48:07,170 --> 00:48:09,510
+الساعة سبعة الشيك اللي صار معاكه الأسبوع اللي فات
+
+593
+00:48:09,510 --> 00:48:13,230
+بالضبط هو اللي صار معناه ففيش حاجة اسمها سالب سالب
+
+594
+00:48:13,230 --> 00:48:17,170
+اتناش موجلس لأ انت بتقول أنا بدمشي في اتجاه عقارب
+
+595
+00:48:17,170 --> 00:48:21,910
+الساعة ولا ضد عقارب الساعة بس هي كل الفرق فإذا
+
+596
+00:48:21,910 --> 00:48:26,470
+دايما بستخدموله positive integer positive integer
+
+597
+00:48:26,470 --> 00:48:32,630
+للتعبير عنه تمام
+
+598
+00:48:32,630 --> 00:48:40,970
+فإذا في الآخر بقول acongruent B modulo M معناته
+
+599
+00:48:40,970 --> 00:48:46,910
+انه there exist K يوجد فارق زمني فارق و عدد مرات
+
+600
+00:48:46,910 --> 00:48:52,750
+تكرار هذه عبارة عن نستخدمها ك Z integer بحيث انه A
+
+601
+00:48:52,750 --> 00:48:57,750
+تساوي B اللي هم الاتنين ال congruent لبعض زائد
+
+602
+00:48:57,750 --> 00:49:01,570
+قيمة المجلس او تكراراته
+
+603
+00:49:03,300 --> 00:49:10,480
+أو تكراراته فإذا ال modulus مضروف في sum k و sum k
+
+604
+00:49:10,480 --> 00:49:16,820
+معناته تكرارات منه زي الساعة برضه هي الأقرب لذهن
+
+605
+00:49:16,820 --> 00:49:22,400
+عندكم اللي ممكن نعبر فيها لما أقول الساعة اتنين هي
+
+606
+00:49:22,400 --> 00:49:27,940
+نفس الساعة اتنينطيب، زود قيمة M، معناته بأتكلم عن
+
+607
+00:49:27,940 --> 00:49:32,320
+الساعة 2 زائد 12، 14، معناته هي congruent لل 14
+
+608
+00:49:32,320 --> 00:49:35,380
+طيب، نفس الكلام، لأ، ممكن ما تكونش الأتنين،
+
+609
+00:49:35,380 --> 00:49:39,220
+ماتكونش الأربعة عشر، ممكن تكون اتنين و زود، مش
+
+610
+00:49:39,220 --> 00:49:43,820
+اتناش، اتناش في اتنين اتناش في اتنين، اربع عشرين،
+
+611
+00:49:43,820 --> 00:49:47,260
+زاد الأتنين، ستة و عشرين، فإذا الأتنين هي
+
+612
+00:49:47,260 --> 00:49:51,020
+congruent للستة و عشرين فلاحظوا أن ال K ممكن تكون
+
+613
+00:49:51,020 --> 00:49:56,070
+عدد التكرارات، مرات التكرار كمانمرات اتكرار بتبقى
+
+614
+00:49:56,070 --> 00:50:00,690
+مستمر زي تاوه ما شوفنا الحلزون اللي قدامنا الخامسة
+
+615
+00:50:00,690 --> 00:50:04,130
+.. الخامسة كانت مظبوطة؟ لأ الستة الستة كانت كرمت
+
+616
+00:50:04,130 --> 00:50:13,210
+للواحد و عشرين للواحد و عشرين هنا ال K جدش كانت؟
+
+617
+00:50:13,210 --> 00:50:19,970
+تلاتة الستة جدش جمعت عليها عشان تصبح واحد و عشرين؟
+
+618
+00:50:19,970 --> 00:50:25,080
+التلاتة .. التلاتة .. عفوا .. التلاتةلفات كل لفة
+
+619
+00:50:25,080 --> 00:50:31,040
+بخمسة تلت لفات هيصار خمستاش على الستة واحد وعشرين
+
+620
+00:50:31,040 --> 00:50:34,280
+فصارت الستة congruent للواحد وعشرين صارت الستة
+
+621
+00:50:34,280 --> 00:50:37,180
+congruent للواحد وعشرين بتهيألي واضحة الأن الشي ال
+
+622
+00:50:37,180 --> 00:50:41,840
+K كرر هذا عدد اللفات لف جد ما بدك تلف لف في
+
+623
+00:50:41,840 --> 00:50:45,520
+النهاية هترجع لنفس ال congruent المكافئله مش نفس
+
+624
+00:50:45,520 --> 00:50:49,240
+القيمة كويس؟ بيانت معناه؟ تمام
+
+625
+00:50:52,260 --> 00:50:57,000
+Okay A B C D كلهم هدولة integers واتفقنا ال M
+
+626
+00:50:57,000 --> 00:51:00,240
+تحديدا بدنا نحدده أكثر نقوله هو positive integer
+
+627
+00:51:00,240 --> 00:51:03,180
+positive integer لأنه مالوش معنى يكون negative ال
+
+628
+00:51:03,180 --> 00:51:05,320
+negative احنا بنعالجها باشي تاني و هناخدها لاحقا
+
+629
+00:51:05,320 --> 00:51:08,920
+لأنه هنحتاجها تكون بال negative أحيانا بس هنحتاجها
+
+630
+00:51:08,920 --> 00:51:11,380
+في نظريات سابقة يمكن المحاضرة الجاية أو اللي بعدها
+
+631
+00:51:12,190 --> 00:51:15,950
+هنتعامل معاها كاتجاه انا بتتحرك عكس عقارب الساعة
+
+632
+00:51:15,950 --> 00:51:20,790
+بس اما هو ك modulus لأ هو هيظل positive integer
+
+633
+00:51:20,790 --> 00:51:25,790
+فبقدر اقول ان اذا a congruent ل b لنفس ال modulus
+
+634
+00:51:25,790 --> 00:51:30,650
+و c congruent ل d برضه لنفس ال modulus تلاحظ انه
+
+635
+00:51:30,650 --> 00:51:37,150
+مشترك في الحالة هذه بقدر اقول ان a زائد c
+
+636
+00:51:37,150 --> 00:51:43,030
+congruent ل b زائد dعلى اعتبار ان الفروقات هنا و
+
+637
+00:51:43,030 --> 00:51:51,510
+هنا واحدة و كلاهما متشابه الفرق الفرق بين a و b م
+
+638
+00:51:51,510 --> 00:51:55,430
+أو مضاعفاتها و هنا نفس الكلام الفرق بين c و d م و
+
+639
+00:51:55,430 --> 00:51:59,290
+مضاعفاتها فإذا لما جمعهم مع بعض الفرق اللي كان هنا
+
+640
+00:51:59,290 --> 00:52:01,530
+و الفرق اللي كان هنا هينجمع بس هم في جميع الأحوال
+
+641
+00:52:01,530 --> 00:52:05,730
+هم مضاعفات بم مدام مشتركة ما تروحش تطبق للقاعدة
+
+642
+00:52:05,730 --> 00:52:10,590
+هذه و هذه غير هذه أكيد مش هيطلع صحفإذا هذا في حالة
+
+643
+00:52:10,590 --> 00:52:16,790
+ان الموجلص مشترك a زائد b حيو كافق congruent لمن b
+
+644
+00:52:16,790 --> 00:52:23,890
+plus d لنفس الموجلص طيب a مضروب في c برضه
+
+645
+00:52:23,890 --> 00:52:32,030
+congruent لb مضروب في d لنفس الموجلص لنفس الموجلص
+
+646
+00:52:32,030 --> 00:52:38,980
+تمام okayOkay المرة الجاية هذه هنرجع ناخد ال
+
+647
+00:52:38,980 --> 00:52:41,920
+greatest common divisor بس باستخدام ال modulo
+
+648
+00:52:41,920 --> 00:52:46,220
+باستخدام ال modulo كتير أسهل و ببساطة بتقدر تعمل
+
+649
+00:52:46,220 --> 00:52:49,980
+لها code تكتبها code صغير جدا حق و كله تلت أسطور
+
+650
+00:52:49,980 --> 00:52:54,240
+فبيكون مناسبة جدا هنتعلمها المرة القادمة و نكمل
+
+651
+00:52:54,240 --> 00:52:57,140
+نتصعد يعني احنا يمكن تصعدنا اليوم أخدنا لسنتين
+
+652
+00:52:57,140 --> 00:53:00,700
+تلاتة من سنة أولى لجدش لسادس ابتداية خلصنا اشي زي
+
+653
+00:53:00,700 --> 00:53:04,000
+هيك يعني المرة الجاية بنطلعكم و بنخلص اعدادي و
+
+654
+00:53:04,000 --> 00:53:07,340
+اللي بعدها بنخلصنا و بعدين بندخلكم في ال ..يعطيكوا
+
+655
+00:53:07,340 --> 00:53:08,500
+الفعف، يا بارك الله فيكوا الشباب
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aNdhsDDrcFQ_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aNdhsDDrcFQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..b3386faa232de14a148b46bfabaa567d34e45bf4
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aNdhsDDrcFQ_raw.json
@@ -0,0 +1 @@
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"text": "الواحد فى نفسه فقط كويس بعض ال primes اللى كلكم عارفين هتنين تلاتة خمسة سبعة and so on مجموعات ال primes اللى قولنا انها مجموعة لا نهائية مش شير و أثبتنا سابقا انها مجموعة لا نهائية صحيح أثبتنا بالقرار انها لا نهائية لكن ماقدرناش نثبت ان كل عناصرها وهذا اتكلمنا عنها", "tokens": [6027, 14407, 24401, 6156, 7578, 8717, 36178, 3224, 6156, 47432, 9122, 45865, 3794, 45030, 11242, 2423, 2886, 279, 13672, 7578, 9122, 23275, 2304, 6225, 9640, 5172, 9957, 8032, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 16490, 2304, 3794, 3660, 8608, 3555, 27884, 293, 370, 322, 3714, 7435, 2304, 45367, 9307, 2423, 2886, 279, 13672, 7578, 12174, 12610, 8315, 16472, 11296, 3714, 7435, 2304, 45367, 3660, 20193, 8717, 3224, 16373, 10632, 37893, 13412, 13546, 4032, 5551, 12984, 3555, 2655, 8315, 8608, 16758, 4587, 995, 16472, 11296, 3714, 7435, 2304, 2407, 27884, 20193, 8717, 3224, 16373, 10632, 20328, 5016, 1829, 5016, 5551, 12984, 3555, 2655, 8315, 20666, 4587, 2288, 9640, 16472, 11296, 20193, 8717, 3224, 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number", "probability": 0.97998046875}, {"start": 681.48, "end": 681.62, "word": " اللي", "probability": 0.928466796875}, {"start": 681.62, "end": 681.84, "word": " هو", "probability": 0.97802734375}, {"start": 681.84, "end": 682.48, "word": " مركب", "probability": 0.8619791666666666}, {"start": 682.48, "end": 684.36, "word": " رقم", "probability": 0.88330078125}], "temperature": 1.0}, {"id": 29, "seek": 70345, "start": 684.95, "end": 703.45, "text": "أو قيمة مُركّبة، ليش مُركّبة؟ لأنها عبارة عن two values مضربين في بعضهم، two values مضربين في بعضهم، بعكس الـprime، بعكس الـprime، لا يمكن يكون composite لأن هو فعليًا مستقل بذاته، لا يمكن يكون فيه رقمين مضربين في بعض باقين الـprime إلا نفسه، إلا نفسه", "tokens": [10721, 2407, 12174, 32640, 3660, 3714, 10859, 31747, 11703, 49401, 12399, 32239, 8592, 3714, 10859, 31747, 11703, 49401, 22807, 5296, 33456, 11296, 6225, 3555, 9640, 3660, 18871, 732, 4190, 3714, 11242, 25513, 9957, 8978, 45030, 11242, 16095, 12399, 732, 4190, 3714, 11242, 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"probability": 0.7890625}, {"start": 1116.81, "end": 1116.99, "word": " Q", "probability": 0.2056884765625}, {"start": 1116.99, "end": 1117.41, "word": " لحالها", "probability": 0.9666748046875}, {"start": 1117.41, "end": 1117.57, "word": " او", "probability": 0.735595703125}, {"start": 1117.57, "end": 1117.67, "word": " ال", "probability": 0.78955078125}, {"start": 1117.67, "end": 1118.01, "word": " quotient", "probability": 0.950439453125}, {"start": 1118.01, "end": 1118.41, "word": " لحالها", "probability": 0.9892578125}, {"start": 1118.41, "end": 1119.07, "word": " خارج", "probability": 0.9786783854166666}, {"start": 1119.07, "end": 1119.63, "word": " القسمة", "probability": 0.9674479166666666}, {"start": 1119.63, "end": 1120.05, "word": " لحالها", "probability": 0.9931640625}, {"start": 1120.05, "end": 1120.79, "word": " ناتج", "probability": 0.9423828125}, {"start": 1120.79, "end": 1121.73, "word": " القسمة", "probability": 0.97998046875}, {"start": 1121.73, "end": 1122.31, 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فإذا عندي divisor بيقسم أكتر من قيمة ففي الحالة هذه القيمتين هدول في عامل مشترك قاسم مشترك بينهم يوجد قاسم مشترك بينهم بمعنى ان بي تسمح انها", "tokens": [11622, 1829, 23032, 2407, 7578, 5296, 15042, 12174, 1211, 8315, 257, 41347, 272, 4032, 257, 41347, 269, 6156, 28814, 15730, 18871, 16254, 25974, 284, 4724, 1829, 4587, 38251, 5551, 4117, 2655, 2288, 9154, 12174, 32640, 3660, 6156, 41185, 21542, 6027, 3660, 29538, 25062, 32640, 2655, 9957, 8032, 3215, 12610, 8978, 6225, 10943, 1211, 37893, 2655, 31747, 12174, 32277, 2304, 37893, 2655, 31747, 49374, 16095, 7251, 29245, 3215, 12174, 32277, 2304, 37893, 2655, 31747, 49374, 16095, 4724, 2304, 3615, 1863, 7578, 16472, 4724, 1829, 6055, 38251, 5016, 16472, 11296], "avg_logprob": -0.1512464927823356, "compression_ratio": 1.696629213483146, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 1179.07, "end": 1179.37, "word": "زي", "probability": 0.799072265625}, {"start": 1179.37, "end": 1179.91, "word": " طوى", "probability": 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كأنه مش هم ال two to the power of zero طيب و العشرة هي اتنين في خمسة جيبلي greatest common divisor between them صفر صفر صفر صفر", "tokens": [39237, 10943, 50113, 6027, 2423, 5080, 4032, 18863, 8592, 25720, 8032, 15042, 9122, 15040, 3224, 15042, 37893, 5835, 20193, 8032, 28259, 5835, 49429, 8032, 28259, 5835, 44381, 20449, 45030, 11242, 8032, 15042, 598, 12, 1424, 1312, 32239, 8592, 8032, 15042, 1975, 2655, 1863, 9957, 20449, 45030, 11242, 598, 12, 1424, 1312, 5296, 33456, 3224, 4724, 3555, 3794, 41193, 3660, 2423, 5080, 29538, 39896, 6225, 3555, 9640, 3660, 18871, 6055, 1211, 9307, 3660, 8978, 8608, 3555, 27884, 8032, 28259, 36764, 24401, 9122, 33456, 3224, 37893, 8032, 2304, 2423, 732, 281, 264, 1347, 295, 4018, 23032, 1829, 3555, 4032, 18863, 8592, 25720, 39896, 1975, 2655, 1863, 9957, 8978, 16490, 2304, 3794, 3660, 10874, 1829, 3555, 20292, 6636, 2689, 25974, 284, 1296, 552, 20328, 5172, 2288, 20328, 5172, 2288, 20328, 5172, 2288, 20328, 5172, 2288], "avg_logprob": 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واحد منهم ان هو يكون ال reference بتاع العد تبعنا التاني اكيد هيكون ايش prime بالنسباله هتكون كأنه prime بالنسبة لبعض كذا فبنسميهم co-prime في الحالة هذه", "tokens": [5172, 10721, 2288, 4587, 10943, 6055, 2655, 9566, 13063, 20328, 5172, 2288, 36764, 24401, 37495, 22653, 8978, 6024, 95, 34740, 39894, 9566, 1211, 3615, 36764, 24401, 6156, 16095, 20666, 1863, 35457, 6027, 16095, 45164, 12174, 3215, 2288, 45164, 36764, 24401, 9154, 16095, 16472, 31439, 7251, 30544, 2423, 6408, 39894, 45761, 18863, 3215, 6055, 3555, 3615, 8315, 16712, 7649, 1829, 1975, 4117, 25708, 39896, 30544, 1975, 1829, 8592, 5835, 20666, 1863, 35457, 6027, 3224, 8032, 2655, 30544, 9122, 33456, 3224, 5835, 20666, 1863, 35457, 3660, 5296, 3555, 3615, 11242, 9122, 15730, 6156, 3555, 1863, 38251, 1829, 16095, 598, 12, 1424, 1312, 8978, 21542, 6027, 3660, 29538], "avg_logprob": -0.20135612560893004, "compression_ratio": 1.8502415458937198, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1650.92, "end": 1651.74, 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اتجاه عقارب الساعة ولا ضد عقارب الساعة بس هي كل الفرق فإذا دايما بستخدموله positive integer positive integer للتعبير عنه تمام فإذا في الآخر بقول a", "tokens": [28543, 2304, 2655, 11296, 21136, 995, 27884, 47525, 1211, 19446, 21136, 995, 27884, 46811, 7649, 10632, 20328, 9640, 2655, 21136, 995, 27884, 8608, 3555, 27884, 25124, 1829, 4117, 13672, 1829, 20328, 9640, 20449, 995, 4117, 3224, 16247, 35457, 45367, 13672, 1829, 6156, 9307, 20666, 11242, 3555, 9566, 31439, 13672, 1829, 20328, 9640, 20449, 8315, 3224, 6156, 41185, 8592, 11331, 26108, 3660, 24525, 2304, 11296, 8608, 6027, 3555, 8608, 6027, 3555, 1975, 2655, 1863, 33599, 3714, 29245, 1211, 3794, 5296, 10721, 16472, 2655, 39894, 39648, 41850, 4724, 40448, 8592, 1829, 8978, 1975, 2655, 7435, 40294, 6225, 4587, 9640, 3555, 21136, 995, 27884, 49429, 48812, 3215, 6225, 4587, 9640, 3555, 21136, 995, 27884, 4724, 3794, 39896, 28242, 27188, 2288, 4587, 6156, 28814, 15730, 11778, 47302, 15042, 4724, 14851, 9778, 40448, 12610, 3224, 3353, 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{"start": 2900.29, "end": 2901.05, "word": " الفرق", "probability": 0.7838541666666666}, {"start": 2901.05, "end": 2901.91, "word": " فإذا", "probability": 0.8323567708333334}, {"start": 2901.91, "end": 2902.53, "word": " دايما", "probability": 0.8341471354166666}, {"start": 2902.53, "end": 2903.27, "word": " بستخدموله", "probability": 0.8001708984375}, {"start": 2903.27, "end": 2903.89, "word": " positive", "probability": 0.92138671875}, {"start": 2903.89, "end": 2905.35, "word": " integer", "probability": 0.9453125}, {"start": 2905.35, "end": 2905.85, "word": " positive", "probability": 0.607421875}, {"start": 2905.85, "end": 2906.47, "word": " integer", "probability": 0.96630859375}, {"start": 2906.47, "end": 2907.81, "word": " للتعبير", "probability": 0.976953125}, {"start": 2907.81, "end": 2908.23, "word": " عنه", "probability": 0.980224609375}, {"start": 2908.23, "end": 2912.63, "word": " تمام", "probability": 0.828125}, {"start": 2912.63, "end": 2913.07, "word": " فإذا", 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2928.63, "end": 2928.91, "word": " عن", "probability": 0.98828125}, {"start": 2928.91, "end": 2930.95, "word": " نستخدمها", "probability": 0.874169921875}, {"start": 2930.95, "end": 2931.13, "word": " ك", "probability": 0.96826171875}, {"start": 2931.13, "end": 2931.31, "word": " Z", "probability": 0.70166015625}, {"start": 2931.31, "end": 2931.71, "word": " integer", "probability": 0.828125}, {"start": 2931.71, "end": 2932.17, "word": " بحيث", "probability": 0.97705078125}, {"start": 2932.17, "end": 2932.49, "word": " انه", "probability": 0.7509765625}, {"start": 2932.49, "end": 2932.75, "word": " A", "probability": 0.87255859375}, {"start": 2932.75, "end": 2933.61, "word": " تساوي", "probability": 0.8770751953125}, {"start": 2933.61, "end": 2934.09, "word": " B", "probability": 0.94287109375}, {"start": 2934.09, "end": 2934.35, "word": " اللي", "probability": 0.771728515625}, {"start": 2934.35, "end": 2934.49, "word": " هم", "probability": 0.8359375}, {"start": 2934.49, "end": 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هنتعلمها", "probability": 0.95576171875}, {"start": 3172.12, "end": 3172.36, "word": " المرة", "probability": 0.986083984375}, {"start": 3172.36, "end": 3172.66, "word": " القادمة", "probability": 0.9881184895833334}, {"start": 3172.66, "end": 3173.28, "word": " و", "probability": 0.6865234375}, {"start": 3173.28, "end": 3174.24, "word": " نكمل", "probability": 0.8865559895833334}, {"start": 3174.24, "end": 3174.98, "word": " نتصعد", "probability": 0.82373046875}, {"start": 3174.98, "end": 3175.14, "word": " يعني", "probability": 0.855224609375}, {"start": 3175.14, "end": 3175.3, "word": " احنا", "probability": 0.91357421875}, {"start": 3175.3, "end": 3175.48, "word": " يمكن", "probability": 0.640380859375}, {"start": 3175.48, "end": 3176.24, "word": " تصعدنا", "probability": 0.82611083984375}, {"start": 3176.24, "end": 3176.46, "word": " اليوم", "probability": 0.963623046875}, {"start": 3176.46, "end": 3176.74, "word": " أخدنا", "probability": 0.843505859375}, {"start": 3176.74, "end": 3177.14, "word": " لسنتين", "probability": 0.8583984375}, {"start": 3177.14, "end": 3177.46, "word": " تلاتة", "probability": 0.86181640625}, {"start": 3177.46, "end": 3177.58, "word": " من", "probability": 0.94775390625}, {"start": 3177.58, "end": 3177.8, "word": " سنة", "probability": 0.8653971354166666}, {"start": 3177.8, "end": 3178.04, "word": " أولى", "probability": 0.7894694010416666}, {"start": 3178.04, "end": 3178.58, "word": " لجدش", "probability": 0.8446044921875}, {"start": 3178.58, "end": 3178.92, "word": " لسادس", "probability": 0.8719482421875}, {"start": 3178.92, "end": 3179.2, "word": " ابتداية", "probability": 0.73095703125}, {"start": 3179.2, "end": 3179.66, "word": " خلصنا", "probability": 0.9896240234375}, {"start": 3179.66, "end": 3180.54, "word": " اشي", "probability": 0.7052408854166666}, {"start": 3180.54, "end": 3180.7, "word": " زي", "probability": 0.976318359375}, {"start": 3180.7, "end": 3180.9, "word": " هيك", "probability": 0.938232421875}, {"start": 3180.9, "end": 3181.46, "word": " يعني", "probability": 0.84423828125}, {"start": 3181.46, "end": 3182.12, "word": " المرة", "probability": 0.94775390625}, {"start": 3182.12, "end": 3182.42, "word": " الجاية", "probability": 0.97314453125}, {"start": 3182.42, "end": 3182.96, "word": " بنطلعكم", "probability": 0.812109375}, {"start": 3182.96, "end": 3183.08, "word": " و", "probability": 0.267578125}, {"start": 3183.08, "end": 3183.52, "word": " بنخلص", "probability": 0.916748046875}, {"start": 3183.52, "end": 3183.92, "word": " اعدادي", "probability": 0.7354736328125}, {"start": 3183.92, "end": 3184.0, "word": " و", "probability": 0.80078125}, {"start": 3184.0, "end": 3184.1, "word": " اللي", "probability": 0.723388671875}, {"start": 3184.1, "end": 3184.36, "word": " بعدها", "probability": 0.84619140625}, {"start": 3184.36, "end": 3184.8, "word": " بنخلصنا", "probability": 0.86103515625}, {"start": 3184.8, "end": 3184.88, "word": " و", "probability": 0.810546875}, {"start": 3184.88, "end": 3185.06, "word": " بعدين", "probability": 0.920166015625}, {"start": 3185.06, "end": 3185.48, "word": " بندخلكم", "probability": 0.86826171875}, {"start": 3185.48, "end": 3185.6, "word": " في", "probability": 0.91162109375}, {"start": 3185.6, "end": 3185.88, "word": " ال", "probability": 0.794921875}, {"start": 3185.88, "end": 3185.88, "word": " ..", "probability": 0.79296875}], "temperature": 1.0}, {"id": 129, "seek": 318850, "start": 3186.9, "end": 3188.5, "text": "يعطيكوا الفعف، يا بارك الله فيكوا الشباب", "tokens": [40228, 9566, 1829, 4117, 14407, 27188, 3615, 5172, 12399, 35186, 4724, 9640, 4117, 21984, 8978, 4117, 14407, 25124, 3555, 16758], "avg_logprob": -0.20554315476190477, "compression_ratio": 1.15625, "no_speech_prob": 0.0, "words": [{"start": 3186.9, "end": 3187.34, "word": "يعطيكوا", "probability": 0.8982421875}, {"start": 3187.34, "end": 3187.66, "word": " الفعف،", "probability": 0.71148681640625}, {"start": 3187.66, "end": 3187.7, "word": " يا", "probability": 0.375244140625}, {"start": 3187.7, "end": 3187.92, "word": " بارك", "probability": 0.9580078125}, {"start": 3187.92, "end": 3188.0, "word": " الله", "probability": 0.96533203125}, {"start": 3188.0, "end": 3188.22, "word": " فيكوا", "probability": 0.8042805989583334}, {"start": 3188.22, "end": 3188.5, "word": " الشباب", "probability": 0.9881184895833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3188.6803125, "duration_after_vad": 3100.0824999999895}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aX4ewdPoCoU.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aX4ewdPoCoU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4fad8380cb71158d17244f7c7b5f06b39a8e5739
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@@ -0,0 +1,1966 @@
+1
+00:00:04,960 --> 00:00:08,360
+طيب، يعطيكم العفو يا شباب، نبدأ اليوم إن شاء الله.
+
+2
+00:00:08,360 --> 00:00:13,000
+تعالوا في جزئية جديدة في مساقنا، واللي هي الـ proof
+
+3
+00:00:13,000 --> 00:00:17,560
+strategies أو الـ proof methods. فمن المرات الماضية
+
+4
+00:00:17,560 --> 00:00:20,640
+اتكلمنا أن واحدة من مفردات المساق هتكون نتكلم
+
+5
+00:00:20,640 --> 00:00:24,600
+فيها عن الـ strategies اللي ممكن نتباحثها لعملية الـ
+
+6
+00:00:24,600 --> 00:00:30,250
+proving، اللي هي الإثباتات. فاليوم هيكون مساقنا أو ما
+
+7
+00:00:30,250 --> 00:00:34,150
+حضرتنا في هذا المجال، فهنتكلم أنه فعلياً الـ proof
+
+8
+00:00:34,150 --> 00:00:37,550
+methods هي methods of mathematical argument أو
+
+9
+00:00:37,550 --> 00:00:43,190
+للنقاش الرياضي. أن احنا نناقش ونحاول نثبت relation
+
+10
+00:00:43,190 --> 00:00:49,270
+معينة، هل هي موجودة أو لا. أو لا، فهذه ممكن can be
+
+11
+00:00:49,270 --> 00:00:54,960
+formalized، ممكن نوضح بشكل أو نعملها formalization
+
+12
+00:00:54,960 --> 00:00:59,900
+باستخدام terms of rules of logical inference. فالـ
+
+13
+00:00:59,900 --> 00:01:04,180
+inference، اللي هي الاستدلال. نتكلم عن الـ rules of
+
+14
+00:01:04,180 --> 00:01:07,700
+inference، بمعنى قواعد الاستدلال. فطبيعي قواعد
+
+15
+00:01:07,700 --> 00:01:12,880
+الاستدلال اللي أنتم كنتوا بتاخدوها بشكل قوانين، اللي
+
+16
+00:01:12,880 --> 00:01:16,500
+هو القانون، هذا الاستدلال اللي أنت بتحط مجموعة الـ
+
+17
+00:01:16,500 --> 00:01:20,460
+antecedents تبعته، وهي بتستنى أو بتشوف إيش الـ
+
+18
+00:01:20,460 --> 00:01:25,380
+consequence أو الـ conclusion اللي ممكن يظهر، يطلع
+
+19
+00:01:25,380 --> 00:01:29,850
+منه. فبنسميها هنا logical mathematical inference.
+
+20
+00:01:29,850 --> 00:01:34,330
+فطبعاً في حاجات، أحياناً استدلال منطقي، اللي هي قبل ما
+
+21
+00:01:34,330 --> 00:01:38,950
+تبدأ تثبت theorem معينة، أنت بتثبت الـ theorem أساساً
+
+22
+00:01:38,950 --> 00:01:43,190
+بتحطها بشكل قانون. لكن من الأساس، إيش اللي أثبت لك أن
+
+23
+00:01:43,190 --> 00:01:45,830
+هذا الـ theorem هي صحيحة؟ فمن خلال حاجة
+
+24
+00:01:52,130 --> 00:01:55,630
+be represented formally as discrete structures. هي
+
+25
+00:01:55,630 --> 00:01:59,610
+نفسها أصلاً عملية الـ proving هي discrete structures
+
+26
+00:01:59,610 --> 00:02:02,770
+من خلال الـ rules اللي أنت بتستخدمها. هذه من خلال الـ
+
+27
+00:02:02,770 --> 00:02:07,750
+rules اللي أنت بتستعملها. فخلال اليوم هناخد جزئية
+
+28
+00:02:07,750 --> 00:02:11,350
+نعمل revision فيها على الـ inference rules، و
+
+29
+00:02:11,350 --> 00:02:16,450
+المحاضرة القادمة بناخد several proof methods، طرق
+
+30
+00:02:16,450 --> 00:02:20,190
+إثباتات معتمدة أو مستخدمة. اليوم هناخد الـ
+
+31
+00:02:20,190 --> 00:02:23,530
+introduction، المقدمة اللي هنتكلم فيها عن الـ
+
+32
+00:02:23,530 --> 00:02:28,850
+inference نفسه، عملية الاستدلال نفسها، وكيف تنعمل
+
+33
+00:02:28,850 --> 00:02:31,910
+عملية الاستدلال، وإيش الـ .. الـ .. خلّيني أقول الـ
+
+34
+00:02:31,910 --> 00:02:36,330
+rules البسيطة، الـ basics اللي ممكن استخدامها في الـ
+
+35
+00:02:36,330 --> 00:02:41,710
+inference أو الاستدلال. نبدأ بشوية terminology اللي
+
+36
+00:02:41,710 --> 00:02:46,370
+هي terms نفهمها، مجموعة terms، مصطلحات بدنا
+
+37
+00:02:46,370 --> 00:02:49,450
+نفهمها. الـ theorem، أول شغلة، كلمة theorem اللي هي
+
+38
+00:02:49,450 --> 00:02:54,770
+نظرية. النظرية هي عبارة عن statement، طبيعي، تصريح أو
+
+39
+00:02:54,770 --> 00:03:00,290
+حاجة معلنة that has been proven to be true. هي
+
+40
+00:03:00,290 --> 00:03:04,330
+مثبتة أن هي صحيحة. فأي شيء مثبت أنه هو صحيح، بقدر
+
+41
+00:03:04,330 --> 00:03:08,910
+أستخده في الاستدلال، لأنه كلنا عارفين أنه صحيح. كلنا
+
+42
+00:03:08,910 --> 00:03:12,670
+عارفين أنه صحيح. الـ assumptions، الـ assumptions أو
+
+43
+00:03:12,670 --> 00:03:16,370
+الفرضيات، واللي مش بالضروري أن هي proven، هي
+
+44
+00:03:16,370 --> 00:03:21,590
+unproven، بمعنى هي مش مثبتة، ولكن فرضية ممكن واضحة.
+
+45
+00:03:21,590 --> 00:03:25,210
+فالفرضية هذه، تعرف على أساس أن هي structure about
+
+46
+00:03:25,210 --> 00:03:31,590
+which we are reasoning. هي structure مخصوص للشغل
+
+47
+00:03:31,590 --> 00:03:33,970
+اللي إحنا بنفكر فيها. بمعنى أن إحنا بنفكر في حال
+
+48
+00:03:33,970 --> 00:03:39,490
+مشكلة، فأنا بحطها ضمن فرضية معينة، عشان أبدأ أشتغل وأـ
+
+49
+00:03:39,490 --> 00:03:45,540
+أحاول أثبت. الـ object هذا، هل هو true or false؟ تمام؟
+
+50
+00:03:45,540 --> 00:03:50,240
+هنشوفها طبعاً في شغلنا. الـ rules of inference أو
+
+51
+00:03:50,240 --> 00:03:54,760
+قواعد الاستدلال. قاعدة استدلال زيها زي القانون، فهي
+
+52
+00:03:54,760 --> 00:03:58,700
+بتكون عبارة عن pattern، نموذج، قالب. قالب، خلاص
+
+53
+00:03:58,700 --> 00:04:03,940
+عارفين أنه هذا صحيح. عارفين أنه صحيح، زي أي قانون،
+
+54
+00:04:03,940 --> 00:04:10,620
+قانون. قانون بيكون فيه right and left terms، واتنين
+
+55
+00:04:10,620 --> 00:04:16,680
+equal لبعض، وبنحط أي problem ضمن هذا الـ pattern.
+
+56
+00:04:16,680 --> 00:04:21,680
+فهي عبارة عن patterns أو قوالب، منطقياً valid
+
+57
+00:04:21,680 --> 00:04:27,780
+deductions from hypotheses to conclusions. فهي
+
+58
+00:04:27,780 --> 00:04:33,460
+فعلياً بتقودنا من الفرضيات للنتائج. من الفرضيات
+
+59
+00:04:33,460 --> 00:04:36,760
+للنتائج. بس طبعاً بيكون زي ما قلنا، الـ rule هذه أو
+
+60
+00:04:36,760 --> 00:04:41,020
+القاعدة هذه، أو الـ inference هذه، اللي هي قاعدة
+
+61
+00:04:41,020 --> 00:04:44,680
+الاستدلال، بدها تكون دائماً valid، بمعنى هي دائماً
+
+62
+00:04:44,680 --> 00:04:49,260
+صحيحة، هي دائماً صح. ما تكونش والله مرات صح ومرات
+
+63
+00:04:49,260 --> 00:04:54,020
+غلط، حسب الـ option، حسب خلّيني أقول الـ case، و
+
+64
+00:04:54,020 --> 00:04:57,660
+أفترض أن هي rule خلاص، لأ لأ، الـ rule لازم تكون
+
+65
+00:04:57,660 --> 00:05:01,640
+دائماً، ضامن أن هي دائماً صح، دائماً صح. طبعاً هناخد
+
+66
+00:05:01,640 --> 00:05:06,120
+أمثلة كثيرة لها. إذن مبدئياً، الـ basic definition
+
+67
+00:05:06,120 --> 00:05:10,300
+لـ theorem، اتفقنا عليه، هي أي حاجة بتكون مبين
+
+68
+00:05:10,300 --> 00:05:14,620
+أن هي دائماً صحيحة، أو proven، هي مثبتة أن هي دائماً
+
+69
+00:05:14,620 --> 00:05:19,520
+صحيحة. مبدئياً، دائماً نفترض أنه عندي مجموعة hypothesis
+
+70
+00:05:19,520 --> 00:05:27,620
+H1 and H2، اللي هي premises، المقدمات أو المعطيات.
+
+71
+00:05:27,620 --> 00:05:34,350
+premises، معطى hypothesis، اللي هي الفرضيات. فإذن هذه
+
+72
+00:05:34,350 --> 00:05:37,550
+أو هذه الاثنين، بمشي الحال، المهم أن هما antecedents
+
+73
+00:05:37,550 --> 00:05:42,070
+اللي هي المعطيات، المقدمات، للـ rule اللي أطبق عليها.
+
+74
+00:05:42,070 --> 00:05:46,070
+الـ rule. هنطبق الـ rule على مجموعة h1, h2 to hn.
+
+75
+00:05:46,070 --> 00:05:52,630
+فعندي n hypothesis، بحيث أنه يعطوني إيش conclusion
+
+76
+00:05:53,240 --> 00:05:57,440
+نستنتج منهم، conclusion معين. فهذه الـ form، الأبسط
+
+77
+00:05:57,440 --> 00:06:02,480
+الأصغر، اللي هو الـ if then، إذا تحققت الـ antecedents،
+
+78
+00:06:02,480 --> 00:06:07,000
+إذا الـ conclusion هيتحقق. بس rule بسيطة جداً مبدئياً،
+
+79
+00:06:07,000 --> 00:06:11,820
+هنبني عليها جميع الـ rules اللاحقة. كمان ما زلنا في
+
+80
+00:06:11,820 --> 00:06:15,580
+الـ terminology، ما زلنا في شوية terms بدنا نفهمها.
+
+81
+00:06:15,580 --> 00:06:18,580
+اتكلمنا عن الـ theorem، مش مشكلة، الـ theorem هذه
+
+82
+00:06:18,580 --> 00:06:24,220
+أحياناً مجرد أن أنا أثبتتها، أثبتتها، أنا ضامن أن الـ
+
+83
+00:06:24,220 --> 00:06:28,710
+conclusion تبعها مرتبط بـ other term، مرتبط بـ other
+
+84
+00:06:28,710 --> 00:06:31,770
+term، في relation بينه وبين other term. فأنا بمجرد ما
+
+85
+00:06:31,770 --> 00:06:35,830
+أثبتت صحة الـ conclusion هذا، من خلال الـ rule، من
+
+86
+00:06:35,830 --> 00:06:41,170
+خلال الـ theorem، أكيد أنا بكون بكل بساطة الـ
+
+87
+00:06:41,170 --> 00:06:47,370
+premises تبعت الـ theorem، بقدر أربطها بمين؟ بالـ
+
+88
+00:06:47,370 --> 00:06:50,850
+term اللي مرتبط بالـ conclusion. فممكن أطلع منها
+
+89
+00:06:50,850 --> 00:06:55,750
+نظرية ثانية، بتعطيني نفس الـ conclusion، هو هو، بإنعكاس
+
+90
+00:06:55,750 --> 00:07:02,070
+بمعنى، خلّيني أفترض أن عندي h1 and h2 and h3، بكفي
+
+91
+00:07:02,070 --> 00:07:08,930
+هدول، إذا تحققوا، بيعطيني c1، okay، خلاص، تمام. إذا
+
+92
+00:07:08,930 --> 00:07:15,450
+تحقق كذا وكذا وكذا، إذا أكيد في كذا، تمام؟ كويس.
+
+93
+00:07:15,450 --> 00:07:19,210
+خلّيني أفترض بهذا الشكل. طيب، ولكن عندي برضه في نفس
+
+94
+00:07:19,210 --> 00:07:26,160
+الوقت، عندي rule ثانية بتقول أنه c1، مم تمام، or مثلاً
+
+95
+00:07:26,160 --> 00:07:36,360
+c2، بيضمن لي c3. مبدئياً هذه، إذا تحققت نتيجة الـ h1 h2
+
+96
+00:07:36,360 --> 00:07:41,440
+h3 تحققت، خلاص، معناه ذلك أن أكيد c1 تحققت. فبقدر
+
+97
+00:07:41,440 --> 00:07:47,620
+أقول أن هذه نظرية، ممكن أسميها theorem، صحيح. خلّصنا
+
+98
+00:07:47,620 --> 00:07:51,660
+من الـ theorem الأولى. طيب، لكن في عندي ارتباط بين c1
+
+99
+00:07:53,190 --> 00:08:02,830
+و c3. معنى ذلك أنه لو تحققت H1, H2, H3، إذا C3 is
+
+100
+00:08:02,830 --> 00:08:08,910
+true، صح؟ لاحظ؟ مجرد أنه C1 is true، خلاص، لأنه or
+
+101
+00:08:08,910 --> 00:08:14,530
+مثلاً نتكلم هنا، القصد أنه النظرية، تحقيقها، ممكن يؤدي
+
+102
+00:08:14,530 --> 00:08:18,670
+بسهولة لتحقيق نظرية أخرى. فالنظريّة الأخرى، نسميها
+
+103
+00:08:18,670 --> 00:08:24,570
+الليمة، نسميها lemma. الـ lemma هذه هي نظرية، هيتم
+
+104
+00:08:24,570 --> 00:08:27,950
+إثباتها بسهولة، نتيجة أنه تحققت النظرية اللي إحنا
+
+105
+00:08:27,950 --> 00:08:32,720
+بنحكي عنها، اللي إحنا بصددها، هذه اللي إحنا بنثبتها.
+
+106
+00:08:32,720 --> 00:08:37,960
+واضحة؟ فإذا نتكلم عن النظرية أو الـ theorem اللي
+
+107
+00:08:37,960 --> 00:08:41,580
+إحنا بنتكلم عنها، بيصير اسمها brae theorem، brae
+
+108
+00:08:41,580 --> 00:08:46,480
+theorem. لابد تحقيقها، عشان أقول أنه صار في عندي
+
+109
+00:08:46,480 --> 00:08:58,540
+theorem كالتالي: H1 and H2 and H3 implies C3. فهذه هي
+
+110
+00:08:58,540 --> 00:09:04,740
+النظرية اللي بنحكي عنها الآن، اللي اسمها theorem. طيب،
+
+111
+00:09:04,740 --> 00:09:11,660
+هذه بالنسبة لها إيش؟ اللي ما أعتمدتها؟ عشان نحقق هذه
+
+112
+00:09:11,660 --> 00:09:18,760
+لاحظوا ما فيش مباشر بين مجموعة الـ H's اللي عندي، أو
+
+113
+00:09:18,760 --> 00:09:25,240
+الـ hypothesis اللي عندي، و C3. لكن C3 مربوطة بـ C1، و
+
+114
+00:09:25,240 --> 00:09:31,530
+قدرنا نثبت نظرية بين مجموعة الـ H's تبعتي، و C1 هذه
+
+115
+00:09:31,530 --> 00:09:37,430
+اسمها lemma. بمجرد ما تحققت، فـ automatically الـ
+
+116
+00:09:37,430 --> 00:09:42,070
+theorem اللي بنحكي عنها تتحقق. فاسمها pre-theorem.
+
+117
+00:09:42,070 --> 00:09:48,650
+العكس صحيح لـ الـ corollary. الـ corollary هي العكس
+
+118
+00:09:48,650 --> 00:09:53,690
+تبعها، هي العكس تبعنا. فصارت بالنسبة لنا هذه النظرية
+
+119
+00:09:53,690 --> 00:09:55,230
+هي corollary لهذه.
+
+120
+00:09:58,010 --> 00:10:01,710
+بمجرد ما هذه تحققت، أوتوماتيك، بقدر منها، ممكن تكون
+
+121
+00:10:01,710 --> 00:10:04,070
+هذه هي النظرية اللي أنا بدور عليها، وبدي أثبتها.
+
+122
+00:10:04,070 --> 00:10:09,070
+Okay، أثبتناها، بس by default، ممكن بالطريقة، كنتيجة
+
+123
+00:10:09,070 --> 00:10:15,890
+لها، تتحقق نظرية أخرى. فصارت corollary بالنسبة لها
+
+124
+00:10:15,890 --> 00:10:18,530
+الأولى بالنسبة للثانية. لما
+
+125
+00:10:21,010 --> 00:10:25,810
+في مصطلحين، واحدة نظرية سابقة للنظرية اللي بنبحث
+
+126
+00:10:25,810 --> 00:10:28,730
+فيها، طبيعي. لأن في نظرية أنا جاي أحاول أثبتها أو
+
+127
+00:10:28,730 --> 00:10:34,870
+أحاول أبحث فيها، إذا كان حدوثها يلزمني إني لازم
+
+128
+00:10:34,870 --> 00:10:39,830
+أثبت نظرية سابقة لها. فهي لما النظرية السابقة لها
+
+129
+00:10:39,830 --> 00:10:44,450
+طيب، حققناها وخلصنا، بس by default أنا عارف إن مجرد
+
+130
+00:10:44,450 --> 00:10:48,530
+تحقيقها، بيضمن لي حدوث شيء ثاني. فالشيء الثاني هذا صار
+
+131
+00:10:48,530 --> 00:10:52,370
+نظرية برضه، ممكن يطلق عليه نظرية لحالها، خلاص، بيصير
+
+132
+00:10:52,370 --> 00:10:58,150
+اسمه corollary، أو post-theorem، ما بعد النظرية، ما بعد
+
+133
+00:10:58,150 --> 00:11:02,830
+النظرية. فإذن الـ corollary هذه، ما ظهرت إلا نتيجة أن
+
+134
+00:11:02,830 --> 00:11:08,230
+الـ theorem تحققت. فهذه كانت ما بعدها. طيب، إذا لم
+
+135
+00:11:08,230 --> 00:11:13,210
+تتحقق نظرية، ما فيش corollary، مش هتقدر تثبتها. لأن أنت
+
+136
+00:11:13,210 --> 00:11:18,450
+عشان تثبت أنه فيه relation between h1, h2, h3 و c3،
+
+137
+00:11:18,450 --> 00:11:23,770
+لازم تكون أثبتت أولاً أن h1, h2, h3، في بينهم.. بين
+
+138
+00:11:23,770 --> 00:11:31,250
+الـ c1 relation، تمام؟ تمام. فهي.. اه، في الأخيرة لسه
+
+139
+00:11:31,250 --> 00:11:34,750
+الـ conjecture، الـ conjectures، مجموعة الـ
+
+140
+00:11:34,750 --> 00:11:37,810
+conjectures هذه، عادة اللي إحنا بنسميها الحدث، اللي
+
+141
+00:11:37,810 --> 00:11:43,090
+هو بيكون عندك حالة، وأنت دائماً بتقول عليها true،
+
+142
+00:11:43,090 --> 00:11:49,890
+لكن ما فيش إثبات لها، ما لهاش إثبات. زي لما تقول
+
+143
+00:11:49,890 --> 00:11:53,370
+ما فيش عدد prime أكبر
+
+144
+00:11:57,000 --> 00:12:00,340
+إحنا هيك بنقول صحيح، لإنه كل ما بيتقدم علم
+
+145
+00:12:00,340 --> 00:12:04,160
+الرياضيات، بنجد أنه بيكتشفوا كمان عدد prime، ممكن من
+
+146
+00:12:04,160 --> 00:12:07,940
+عشرين خانة، ولا من خمس عشرة خانة، لكنه prime، لا يقسم
+
+147
+00:12:07,940 --> 00:12:13,220
+على كل اللي أقل منه. لكن مش قادرين نثبت إن فعلاً لا
+
+148
+00:12:13,220 --> 00:12:18,440
+يوجد prime أكبر. لإنه عشان تثبت هذا الكلام، معناته
+
+149
+00:12:18,440 --> 00:12:22,240
+بدأت تكون وصلت للـ infinity. فإذن هذا حدث بالنسبة لنا
+
+150
+00:12:22,240 --> 00:12:27,520
+ما نعرفش حتى اللحظة، إمكانية الـ computers بتاعتنا، ما
+
+151
+00:12:27,520 --> 00:12:30,420
+خدمتناش في هالجثة. كل الأرقام اللي بيقدر الكمبيوتر
+
+152
+00:12:30,420 --> 00:12:36,340
+يصلها، فيه دائماً رقم أكبر، فيه دائماً رقم أكبر. بس في
+
+153
+00:12:36,340 --> 00:12:40,460
+النهاية، أنا عامل حسابي أنه ممكن يكون فيه أكبر منه،
+
+154
+00:12:40,460 --> 00:12:44,280
+لكن الحواسيب بتاعتنا مش قادرة تصل له. فعشان هيك الـ
+
+155
+00:12:44,280 --> 00:12:46,660
+conjecture تبعته، هنا في الحالة هذه، الحدث تبعي
+
+156
+00:12:46,660 --> 00:12:51,900
+أنه لا يوجد عدد أولي أكبر، يعني ما فيش عدد أولي
+
+157
+00:12:51,900 --> 00:12:57,870
+وبعده، خلاص، بطل العدد الأولي، خلصت، ما فيش. ما في حدّ
+
+158
+00:12:57,870 --> 00:13:01,190
+بيقدر يقول لك الكلام هذا، ما في حد بيقدر يقول لك، لكن
+
+159
+00:13:01,190 --> 00:13:04,470
+الحدث هيك بيقول لنا إنه ما فيش عدد أكبر، خلاص، طول ما
+
+160
+00:13:04,470 --> 00:13:07,410
+أنت ماشي، والأعداد بيخترعوا أعداد جديدة، وبيسموا
+
+161
+00:13:07,410 --> 00:13:12,010
+تسمية جديدة للأعداد. ممكن يظهر لنا رقم أكبر من اللي
+
+162
+00:13:12,010 --> 00:13:17,260
+إحنا عارفينه، أو اللي إحنا موجود عندنا، تمام؟ ليش؟
+
+163
+00:13:17,260 --> 00:13:23,800
+وخصوصاً إنه بالعادة، في نظرية بنعمل منها creation
+
+164
+00:13:23,800 --> 00:13:29,760
+للأرقام الأولية. وحتى الآن، النظرية هذه صحيحة، بس
+
+165
+00:13:29,760 --> 00:13:35,660
+ما أقدرش أقول عليها نظرية، بنسميها حدث، زي العدد الأولي.
+
+166
+00:13:35,660 --> 00:13:38,880
+يبقى باعتبار أنه إجتها سرتها ده، إن خلّيني أقول لك إن
+
+167
+00:13:38,880 --> 00:13:42,440
+العدد الأولي بتبدأ مثلاً من اثنين، ثلاثة، إيش
+
+168
+00:13:42,440 --> 00:13:48,580
+بعدها؟ خمسة، سبعة.. لأ، تصبح تجيب.. لأ، تجيب لش.. 
+
+223
+00:18:15,700 --> 00:18:21,420
+الكلام في معنى ذلك لاحظوا أن الـ antecedent one,
+
+224
+00:18:22,000 --> 00:18:25,940
+antecedent two and antecedent two and antecedent
+
+225
+00:18:25,940 --> 00:18:32,300
+three and four and so on to end. مثلاً إذا كل هذه
+
+226
+00:18:32,300 --> 00:18:38,960
+is true.  و أخذنا implication .. implication  للـ
+
+227
+00:18:38,960 --> 00:18:42,000
+conclusion أو الـ consequent. فإذا لازم تطلع
+
+228
+00:18:42,000 --> 00:18:49,620
+tautology. لازم يطلع tautology بمعنى إنه H1, H2, H3
+
+229
+00:18:49,620 --> 00:18:57,010
+employees. C1 is true. ليش؟ لأن هذه أصلاً rule of
+
+230
+00:18:57,010 --> 00:19:01,510
+inference أو هي فعلاً مستدل عليها كنظرية. معنى ذلك
+
+231
+00:19:01,510 --> 00:19:06,410
+إذا تحقق الشمال لابد أن يتحقق اليمين، وإذا لم يتحقق
+
+232
+00:19:06,410 --> 00:19:11,870
+الشمال، فاليمين لم يتحقق. وهذا معناه أن الـ relation
+
+233
+00:19:11,870 --> 00:19:16,630
+بهذا الشكل ستطلع دائماً true. الأصل إنها دائماً true
+
+234
+00:19:16,630 --> 00:19:21,250
+وإلا بطلت rule. إذا مش دائماً true معناته بطلت rule.
+
+235
+00:19:21,250 --> 00:19:24,470
+مش هيقدر أستخدمها كـ rule. ما أقدر أقولك أحفظها
+
+236
+00:19:24,470 --> 00:19:27,790
+زي ما هي هيك. ليش؟ لأنه مش دائماً true. لأ هي دائماً
+
+237
+00:19:27,790 --> 00:19:33,430
+true. وعشان هي أصبحت بالنسبالي theorem أو rule. مدام
+
+238
+00:19:33,430 --> 00:19:37,660
+أصبحت rule فهي tautology. Tautology. اتكلمنا عن الـ ..
+
+239
+00:19:37,660 --> 00:19:41,980
+عن الـ .. Tautology. المصطلح دائماً صحيحة، وإلا ما حد
+
+240
+00:19:41,980 --> 00:19:45,540
+ما بيقدر أقولك لأ هي أحفظها أو هي rule. لأ مش بتبطل
+
+241
+00:19:45,540 --> 00:19:48,500
+rule في الحالة دي. فإذا الـ relation الأخيرة أكيد
+
+242
+00:19:48,500 --> 00:19:55,660
+لازم تظل دائماً Tautology. دائماً صحيحة بالمناسبة.
+
+243
+00:19:55,660 --> 00:19:59,840
+الأخيرة دائماً صحيحة. هذا لا يعني أن لو كل الـ
+
+244
+00:19:59,840 --> 00:20:04,140
+antecedents تحققت، لم يتحقق، يعني واحدة منهم لم تتحقق.
+
+245
+00:20:04,140 --> 00:20:08,540
+أن الـ .. الـ .. الـ consequent مش هيتحقق، دي  ربالكم،
+
+246
+00:20:08,540 --> 00:20:12,080
+إحنا إيش اللي عاملينه؟ عاملين implication، دائماً
+
+247
+00:20:12,080 --> 00:20:17,160
+في بالكم مين؟ الـ truth table تبع الـ implication و
+
+248
+00:20:17,160 --> 00:20:20,480
+يبدو أن إحنا لازم نحطه ده على جنب لأنه من الآن
+
+249
+00:20:20,480 --> 00:20:24,660
+هنبدأ هو شغلنا الشاغل. بمعنى أنه أقول هذا صح ولا
+
+250
+00:20:24,660 --> 00:20:29,580
+غلط بناء عليه، وليس بناء على تخيلك المنطقي اللي
+
+251
+00:20:29,580 --> 00:20:32,840
+أنت بتفترض أنه منطقي، بينما هو مش منطقي. فهنا بدنا
+
+252
+00:20:32,840 --> 00:20:38,540
+نحطها هي P و Q. نكتبه على جنب، و الـ implication false
+
+253
+00:20:38,540 --> 00:20:43,380
+false. خليها دائماً على جنب. الـ true. طيب false true
+
+254
+00:20:43,380 --> 00:20:47,280
+true. بالظبط هي هذه حالة من الحالات بقولك مش مضرورة
+
+255
+00:20:47,280 --> 00:20:50,660
+كل الـ antecedents يكونوا صح، لكن رغم ذلك الـ
+
+256
+00:20:50,660 --> 00:20:56,860
+consequence صح. هتقول true. طيب true false. الحالة
+
+257
+00:20:56,860 --> 00:21:01,140
+الوحيدة اللي مستثنى، و true true is true. خلي هذه
+
+258
+00:21:01,140 --> 00:21:04,060
+على جنب. بدنا عشان نمحيها طول ما إحنا ماشيين في
+
+259
+00:21:04,060 --> 00:21:05,720
+شغلنا لأنه هنحتاجها كتير.
+
+260
+00:21:08,530 --> 00:21:14,570
+بعض الاستدلالات. نأخذ بعض الـ inference rules. بعض
+
+261
+00:21:14,570 --> 00:21:17,930
+الاستدلالات المنطقية اللي ممكن نبني عليها شغلنا
+
+262
+00:21:17,930 --> 00:21:25,690
+لإثبات نظريات. بعد هيك لو كانت P is true. معنى ذلك
+
+263
+00:21:25,690 --> 00:21:32,870
+أنه في or أو disjunction in a proposition is true.
+
+264
+00:21:32,870 --> 00:21:37,530
+بغض النظر عن Q. الشيء بغض النظر إيش Q. حاجة بسيطة جداً
+
+265
+00:21:37,530 --> 00:21:41,850
+صحيح، لكن منها بنبني استدلالنا على النظريات الكبيرة
+
+266
+00:21:41,850 --> 00:21:45,750
+الضخمة. في حاجات صغيرة زي هيك. في حاجات صغيرة زي هيك.
+
+267
+00:21:45,750 --> 00:21:52,330
+طيب إذا كانت P and Q is true. معنى ذلك أن P is
+
+268
+00:21:52,330 --> 00:22:01,670
+true و Q is true. صح تمام. P is true لحالها. الـ Q is
+
+269
+00:22:01,670 --> 00:22:04,430
+true. معنى ذلك الـ conjunction تبعهم is true.
+
+270
+00:22:04,430 --> 00:22:08,410
+ملاحظين؟ كده بسيطة مفاهيمنا، بس هاد بنبني عليها شغل
+
+271
+00:22:08,410 --> 00:22:15,790
+كتير كبير. من حاجات بسيطة. فمبدأياً عملية الإثبات
+
+272
+00:22:15,790 --> 00:22:22,050
+بسيطة. مبنية على حاجات biological أنت عارفها، لكن خلاص
+
+273
+00:22:22,050 --> 00:22:26,620
+ما جاكتش على بالك لحظة ما بدأت تعمل إثباتك. طيب إذا
+
+274
+00:22:26,620 --> 00:22:31,140
+كانت P. وهنا بدنا عشان هي مكتوبة لكم هذه. إذا كانت P
+
+275
+00:22:31,140 --> 00:22:38,040
+is true. لاحظ. و P implies Q is true. يعني هذه true
+
+276
+00:22:38,040 --> 00:22:45,120
+وهذه true. طلع ليها على الجدول. الـ Q لابد تطلع true.
+
+277
+00:22:45,120 --> 00:22:53,590
+لاحظ العمود الأول والثالث في الجدول. true true. وين
+
+278
+00:22:53,590 --> 00:23:00,650
+فيه بيكونوا true true؟  فيش. للأخيرة صح؟ فإذا بنتكلم
+
+279
+00:23:00,650 --> 00:23:10,310
+عن q لازم تطلع true. okay. طيب هذه اللي هي الـ
+
+280
+00:23:10,310 --> 00:23:13,590
+affirming أو التأكيد. affirming اللي هي التأكيد.
+
+281
+00:23:13,590 --> 00:23:20,530
+لأنه أكدنا قيمة q. طيب في الـ denying أو الإنكار.
+
+282
+00:23:20,530 --> 00:23:25,530
+الإنكار إني أنكر قيمة أو أقول false لـ P. أن هي الـ
+
+283
+00:23:25,530 --> 00:23:29,330
+false. هو التأكيد تبعها. لو كانت negation الـ Q is
+
+284
+00:23:29,330 --> 00:23:34,530
+true. يعني الـ Q false. طيب و الـ implication is true
+
+285
+00:23:34,530 --> 00:23:40,170
+برضه تطلع هيك على الـ column الثاني والثالث. الـ
+
+286
+00:23:40,170 --> 00:23:45,850
+column الثاني لازم يكون false و الثالث true. إيه
+
+287
+00:23:45,850 --> 00:23:52,000
+أنت بتحقق هذا الكلام؟ فقط. فإذا هذا بيأكد أن P is
+
+288
+00:23:52,000 --> 00:23:58,740
+false. يعني negation P هي الـ true. negation P. تمام.
+
+289
+00:23:58,740 --> 00:24:02,040
+عشان كنت قلت لكم هذا. بدنا .. بدنا .. خلاص ما فيش
+
+290
+00:24:02,040 --> 00:24:06,440
+مجال هذا. معظم المسائل مبني على الجدول هذا. معظم
+
+291
+00:24:06,440 --> 00:24:09,460
+مسائلنا مبنية على الجدول هذا. تمام. فإذا حتى الآن
+
+292
+00:24:09,460 --> 00:24:13,320
+استدلالات بسيطة جداً. استدلالات بسيطة جداً. طيب كمان
+
+293
+00:24:13,320 --> 00:24:21,320
+استدلال. إذا كانت P implies Q is true and. قلنا مدام
+
+294
+00:24:21,320 --> 00:24:26,740
+الاثنين الـ premises. معناته and بينهم. Q implies R
+
+295
+00:24:26,740 --> 00:24:34,300
+is true. فهذا بضمن لي. مدام الاثنين هدول صحيحين is
+
+296
+00:24:34,300 --> 00:24:42,960
+true. معناته إذا كانت P is true. إذا R is true. تمام؟
+
+297
+00:24:42,960 --> 00:24:47,490
+تمام. السيلوجيزم هذه. هذه نظرية السيلوجيزم أو
+
+298
+00:24:47,490 --> 00:24:53,290
+المنطقية. الاستدلال المنطقية أو الاستنتاجي. مدام P
+
+299
+00:24:53,290 --> 00:24:58,190
+تضمن لـ Q و Q تضمن لـ R. فإذا من الأساس P تضمن لـ R
+
+300
+00:24:58,190 --> 00:25:04,810
+تضمن R. كويس. كمان واحدة. P this junction Q is true.
+
+301
+00:25:04,810 --> 00:25:12,830
+تمام. واحدة منهم false. فأكيد الثانية حتماً .. حتماً is
+
+302
+00:25:12,830 --> 00:25:18,550
+true. صح؟ أكيد. فإذا negation P is true. يعني Q is
+
+303
+00:25:18,550 --> 00:25:24,610
+true. حتى الآن أنا عارف بسيطة جداً وسهلة جداً، ومع ذلك
+
+304
+00:25:24,610 --> 00:25:29,310
+ماشي معك بشويش لأنه بعدين هنستخدمها في أكبر من
+
+305
+00:25:29,310 --> 00:25:33,840
+هيك. تمام؟ كمان revision سريع عليها. أخذنا معظم
+
+306
+00:25:33,840 --> 00:25:37,760
+الحالات هنا. إذا كانت P is true. معنى ذلك أن P or
+
+307
+00:25:37,760 --> 00:25:43,400
+أي شيء ستطلع برضه true. P and Q is true. معناته كل
+
+308
+00:25:43,400 --> 00:25:49,480
+كل من هما لحاله منفرد هو is true. تمام. P true. Q
+
+309
+00:25:49,480 --> 00:25:52,120
+true. فإذا الاثنين مع بعض. conjunction أو
+
+310
+00:25:52,120 --> 00:25:58,190
+conjunction هي true. Okay. أخذنا برضه الـ denying. إذا
+
+311
+00:25:58,190 --> 00:26:03,090
+كانت negation Q هي الـ true و الـ implication Q. فإذا
+
+312
+00:26:03,090 --> 00:26:07,830
+negation P هي الـ true. بعدين أخذنا الـ .. الـ affirming
+
+313
+00:26:07,830 --> 00:26:12,570
+اللي هي الـ .. الـ .. الـ syllogism. اللي هي P
+
+314
+00:26:13,540 --> 00:26:17,860
+implies Q is true و Q implies R is true. فإذا
+
+315
+00:26:17,860 --> 00:26:23,020
+automatically by default أو by logic. P implies R
+
+316
+00:26:23,020 --> 00:26:30,480
+برضه is true. جيد. فإذا الآن مبدأياً خلصنا مجموعة
+
+317
+00:26:30,480 --> 00:26:35,360
+استدلالات. هنشتغل فيها في الأمثلة اللي جاية، بس
+
+318
+00:26:35,360 --> 00:26:42,130
+بدنا نعرف أنه الآن كل اللي واضح لنا أنه الـ proof
+
+319
+00:26:42,130 --> 00:26:47,210
+نفسه كـ rule. هو المفروض إنه relation .. relation الـ
+
+320
+00:26:47,210 --> 00:26:51,430
+proof هو relation. يعني demonstrates. يوضح لنا إذا
+
+321
+00:26:51,430 --> 00:26:55,370
+كانت مجموعة الـ premises اللي سميناها antecedents.  تُو
+
+322
+00:26:55,370 --> 00:27:00,210
+مجموعة الـ premises. المعطيات كلهم is true. كل واحدة
+
+323
+00:27:00,210 --> 00:27:04,790
+لحالها هي true. فإذا كلهم مجموعة are true. كلهم. معنى
+
+324
+00:27:04,790 --> 00:27:09,860
+ذلك أن الـ conclusion C is true. فإذن هذه بشكل أساسي
+
+325
+00:27:09,860 --> 00:27:13,980
+النظرية العامة لأي فكرة إثبات. بدك تبدأ، بدك تشوف
+
+326
+00:27:13,980 --> 00:27:16,600
+مجموعة الـ premises. إيش المعطيات؟ وهذه اللي كنتوا
+
+327
+00:27:16,600 --> 00:27:19,320
+تاخدوها في كل إثباتها اللي كانت سابقة في أي مرحلة
+
+328
+00:27:19,320 --> 00:27:22,160
+من مراحل تعليمكم. كنتوا إيش بتدوروا على المعطيات في
+
+329
+00:27:22,160 --> 00:27:27,020
+البداية. ومن المعطيات بتحاولوا تروحوا للـ conclusion
+
+330
+00:27:27,020 --> 00:27:34,210
+أو للاستنتاج. للاستنتاج. فإذن أي proof هي
+
+331
+00:27:34,210 --> 00:27:37,530
+استراتيجيته الأساسية. مش هنطلع عن نفس الاستراتيجية.
+
+332
+00:27:37,530 --> 00:27:44,410
+هي هي. okay. نأخذ مثال هالوقت. it's not sunny and
+
+333
+00:27:44,410 --> 00:27:52,150
+it's cold. هي الدنيا مش مشمسة والجو بارد. هي نعبة.
+
+334
+00:27:52,150 --> 00:27:57,970
+هذه مجموعة premises. خلي هذه بدنية، أو خليني أقول
+
+335
+00:27:57,970 --> 00:28:03,230
+على الأقل أنتم هتحتاجوها. وأنا بشرح دائماً إذا
+
+336
+00:28:03,230 --> 00:28:08,930
+التبس عندك هو صح، وارجع له. سأحسب لك إياه هنا طبعاً.
+
+337
+00:28:08,930 --> 00:28:12,970
+فهذا مبدأياً هاي أول مجموعة premises. لو في عندي
+
+338
+00:28:12,970 --> 00:28:17,710
+premises واحدة، اثنين، ثلاثة، أربعة. مطلوب بدنا نثبت
+
+339
+00:28:17,710 --> 00:28:21,490
+الـ conclusion الأخيرة. مطلوب نثبت الـ conclusion
+
+340
+00:28:21,490 --> 00:28:25,670
+الأخيرة بشوية خطوات. الخطوات كلها لن تخرج عن مجموعة
+
+341
+00:28:25,670 --> 00:28:30,980
+الـ rule of inference أو الـ rules. الـ rules اللي
+
+342
+00:28:30,980 --> 00:28:35,660
+أخذناهم قبل شوية فقط لا أكثر ولا أقل. هيجيب لك طريقة
+
+343
+00:28:35,660 --> 00:28:41,720
+نظرية واضحة ومتسلسلة. خلينا نبدأ الأولى. it's not
+
+344
+00:28:41,720 --> 00:28:46,260
+sunny. معنى ذلك أنه معطى أنه فعلياً ما فيش شمس اليوم و
+
+345
+00:28:46,260 --> 00:28:52,900
+كذلك and cold. الجو فيه برد. we will swim only if
+
+346
+00:28:52,900 --> 00:28:58,480
+it's sunny. إحنا هنسبح إذا كانت فقط sunny. إذا كانت
+
+347
+00:28:58,480 --> 00:29:02,880
+الدنيا مشمسة. طيب if we don't swim. إذا إحنا
+
+348
+00:29:02,880 --> 00:29:06,420
+ما سبحناش. إذا we will play volley. هنلعب طائرة. و
+
+349
+00:29:06,420 --> 00:29:09,840
+ما فيش داعي نسبح على البحر. خليني على الشط نلعب كرة
+
+350
+00:29:09,840 --> 00:29:14,740
+طائرة. نحط الشبك ونلعب طائرة وخلاص. طيب if we
+
+351
+00:29:14,740 --> 00:29:19,960
+play volley then we will be home early. معناته
+
+352
+00:29:19,960 --> 00:29:23,660
+هنروح بدري. هنروح بدري. بدنا نثبت أنه إحنا فعلاً
+
+353
+00:29:23,660 --> 00:29:27,220
+هنروح بدري. هي طبعاً بيولوجياً منطقية شايفينها أنتم
+
+354
+00:29:27,220 --> 00:29:30,820
+لحالها. هي باينة. هي باينة. أنا عارف أنها باينة، بس
+
+355
+00:29:30,820 --> 00:29:34,600
+الهدف الرئيسي منها كيف استخدام الـ rules عليها بس
+
+356
+00:29:34,600 --> 00:29:41,060
+الآن. أول شغلة بدنا نعمل الـ notation. أول حاجة
+
+357
+00:29:41,060 --> 00:29:45,060
+أخذناها بتذاكرين في أول حصة في المساق. قلنا إن
+
+358
+00:29:45,060 --> 00:29:47,340
+الخطوات بتاعتنا. بدنا نفهم الـ language. concise
+
+359
+00:29:47,340 --> 00:29:50,840
+language. مش هيك. وبعدين بدنا نعملها، نعمل notations
+
+360
+00:29:50,840 --> 00:29:54,480
+لها. وبعدين نبدأ في الاستدلالات بتاعتها، أو نبدأ
+
+361
+00:29:54,480 --> 00:29:56,900
+في الـ logic اللي إحنا شغالين عليه كـ mathematical
+
+362
+00:29:56,900 --> 00:30:01,620
+logic. فإحنا لأن في نقطة الـ notations بدنا نختصر
+
+363
+00:30:01,620 --> 00:30:04,660
+اللغة. مش معقول بدي أقعد كل شوية أكتب الجملة كاملة.
+
+364
+00:30:04,660 --> 00:30:07,960
+فبدنا نختصرها. نقول sunny. خلاص هذا بدي أعتبره كإني
+
+365
+00:30:07,960 --> 00:30:13,050
+بقول P. P. it's sunny. لأ بدي أسميها sunny وخلاص.
+
+366
+00:30:13,050 --> 00:30:15,430
+what's cool. فبتعامل معاها إنه هذه هيك على بعضها
+
+367
+00:30:15,430 --> 00:30:22,220
+أصبحت إيش؟ هذه المتغير. هذه الـproposition.
+
+368
+00:30:22,220 --> 00:30:26,660
+هذه الـ proposition. تمام. اللي هي it's sunny. طيب
+
+369
+00:30:26,660 --> 00:30:31,340
+cold. خلصنا. swim. اختصرناهم بس عشان نستخدم الـ
+
+370
+00:30:31,340 --> 00:30:34,620
+notations هذه كمختصرات وخلصناها. اللي كان الـ
+
+371
+00:30:34,620 --> 00:30:37,560
+premises اللي كانت موجودة. بدنا نحولها لـ
+
+372
+00:30:37,560 --> 00:30:43,120
+mathematical forms. عشان نبدأ نحط عليها الـ rules
+
+373
+00:30:43,120 --> 00:30:46,680
+اللي اتكلمنا عنها قبل شوية. تمام. فإذا أول rule كانت
+
+374
+00:30:46,680 --> 00:30:52,550
+إيش متذكرين؟ it's not sunny and it's cold. negation
+
+375
+00:30:52,550 --> 00:31:00,890
+sunny and cold. تمام. الثانية. swim if only if sunny.
+
+376
+00:31:00,890 --> 00:31:05,930
+وهذه واحدة لو رجعتم لمحاضرة الـ implication و
+
+377
+00:31:05,930 --> 00:31:10,170
+حطيتكم مجموعة forms. كانت if. في الحالة هذه اللي هي
+
+378
+00:31:10,170 --> 00:31:16,170
+only if. only if. معناته اللي في الأول هي الـ P وفي
+
+379
+00:31:16,170 --> 00:31:21,920
+الـ A وبعدها الـ Q. ده و متذكرين لأن only هذه هتنفي لك
+
+380
+00:31:21,920 --> 00:31:28,300
+الحالة هذه. فمعنى ذلك أنه ما ينفعش تفهموها إنها
+
+381
+00:31:28,300 --> 00:31:32,860
+معكوسة. هذه يمكن واحدة من الحالات اللي إذا ما جتش
+
+382
+00:31:32,860 --> 00:31:36,940
+كويس فيها كـ language ممكن تتخربط. فكتير كويس إنك
+
+383
+00:31:36,940 --> 00:31:40,460
+ترجعوا لمحاضرة الـ implication وتشوفوا مجموعة الـ
+
+384
+00:31:40,460 --> 00:31:46,300
+forms. وهذه تحديدا أركز فيها كويس لأن by logic
+
+385
+00:31:47,260 --> 00:31:51,180
+المنطق ممكن الكل يفهمها. هنا لاحظ لي أجربها كمان مرة
+
+386
+00:31:51,180 --> 00:31:54,540
+هتقول
+
+387
+00:31:54,540 --> 00:32:02,440
+يا إيه if. معناته if sunny then we will swim. غلط.
+
+388
+00:32:02,440 --> 00:32:12,740
+غلط. هيكون غلط بالظبط. only هذه هتنفي لك حالة الـ
+
+389
+00:32:12,740 --> 00:32:13,460
+false هنا.
+
+390
+00:32:16,540 --> 0
+
+445
+00:36:34,530 --> 00:36:40,570
+modest الاثبات المهم أنك تثبته okay نصل لحاجة
+
+446
+00:36:40,570 --> 00:36:44,510
+مهمة هي الـ rules أو الـ inference rules للـ
+
+447
+00:36:44,510 --> 00:36:48,790
+quantifiers ليش؟ للـ quantifiers في عندي مجموعة
+
+448
+00:36:48,790 --> 00:36:54,150
+quantifiers أخذناهم المرة الماضية كان في عندي إذا
+
+449
+00:36:54,150 --> 00:36:56,850
+متذكرين الـ for all و there exist؟ طب هدول لما
+
+450
+00:36:56,850 --> 00:36:59,730
+يكونوا موجودين هل فيهم استدلالات؟ اه فيهم
+
+451
+00:36:59,730 --> 00:37:05,410
+استدلالات بقدر استدل منهم على بعض الأمور زي if for
+
+452
+00:37:05,410 --> 00:37:11,070
+all x P of X is true معناته كل عنصر داخل الـ
+
+453
+00:37:11,070 --> 00:37:15,170
+universe of discourse تاعة X هو true، صح؟ معناته ذلك
+
+454
+00:37:15,170 --> 00:37:18,530
+أن P of O و O هذا أي واحد داخل الـ universe of
+
+455
+00:37:18,530 --> 00:37:22,590
+discourse،  التالية المنطقية وما فيها غلبة هذه...هذه
+
+456
+00:37:22,590 --> 00:37:27,570
+ما فيها غلبة universal instantiational...instantiational...
+
+457
+00:37:27,570 --> 00:37:33,170
+instantiational كويس، فإذا أي واحدة هي true خلصنا
+
+458
+00:37:33,170 --> 00:37:40,450
+طيب هذه اللي شوية بدها تركزوا معايا، طيب if P of G
+
+459
+00:37:40,450 --> 00:37:49,460
+is true، إذا for all X P of X is true بالشكل هذا، و
+
+460
+00:37:49,460 --> 00:37:53,880
+بدون ما أوضح الشيء الـ G الكلام مش صح، الكلام مش صح
+
+461
+00:37:53,880 --> 00:38:00,380
+صحيح، لكن لما أقول G arbitrary element from
+
+462
+00:38:00,380 --> 00:38:04,860
+universe of discourse، arbitrary
+
+463
+00:38:04,860 --> 00:38:13,380
+بمعنى بشكل اعتباطي، بشكل عشوائي، أخذناها بمعنى أن G
+
+464
+00:38:13,380 --> 00:38:16,880
+ممكن تكون أي element داخل universe of discourse
+
+465
+00:38:19,450 --> 00:38:23,610
+هقول: طلاب كلهم هينجحوا، امتى الكلام هذا؟ الكلام هذا
+
+466
+00:38:23,610 --> 00:38:26,510
+إذا كان على الغمض، شاورت على أي واحد وقلت هذا
+
+467
+00:38:26,510 --> 00:38:31,430
+هينجح true، طيب هذا هينجح true، هذا هينجح true، طب ع
+
+468
+00:38:31,430 --> 00:38:35,170
+مين هيجي تيجي؟ هذا هينجح true وأنا مغمض وعارف...
+
+469
+00:38:35,170 --> 00:38:37,930
+هيقولي: غمض هناك وشاور على أي واحد وبدنا نخربطهم
+
+470
+00:38:37,930 --> 00:38:41,250
+إذا أنا عارف أن كله هينجح وهينجحوا...هينجحوا
+
+471
+00:38:41,250 --> 00:38:44,610
+كلكم مش هيفرق معايا وين هشاور، صح؟ arbitrarily
+
+472
+00:38:45,780 --> 00:38:49,380
+arbitrary، بشكل عشوائي، مش فارقة معايا وين أصبعي
+
+473
+00:38:49,380 --> 00:38:54,200
+هيروح، فإذا هاختار أي حد والأصبع هيجي على أي حد مش
+
+474
+00:38:54,200 --> 00:39:00,640
+مشكلة وهقول: is it true؟ إذا فعلاً تحقق هذا الـ
+
+475
+00:39:00,640 --> 00:39:06,020
+condition، فإذا for all is true، واضحت؟ فإذا
+
+476
+00:39:06,020 --> 00:39:10,300
+بالمطلق لا، هو كلام مش صح، لكن لما أقول G arbitrary
+
+477
+00:39:10,300 --> 00:39:15,500
+element، اه بتصير صحيحة، ليش؟ لأن أنا ماخذة بدون
+
+478
+00:39:15,500 --> 00:39:19,620
+تعيين، أنا مش محدد واحد معين قلت عليه: اه هذا هينجح
+
+479
+00:39:19,620 --> 00:39:24,440
+أنا أي واحد هيجي قدامي هقول له: اه هينجح من الـ
+
+480
+00:39:24,440 --> 00:39:27,100
+universe of discourse، فهذا automatically هيقودني
+
+481
+00:39:27,100 --> 00:39:30,680
+لفكرة أن معناته أنا مش فارقة معايا كلهم هينجحوا، أنا
+
+482
+00:39:30,680 --> 00:39:33,200
+عامل fast seven، كلهم هينجحوا مدام مش فارقة عند مين
+
+483
+00:39:33,200 --> 00:39:39,140
+هيجي أصبعي، واضحة الآن، إذا كانت arbitrary هينجح إن
+
+484
+00:39:39,140 --> 00:39:47,770
+شاء الله، إذا بتصير for all x P of X، طيب في الـ exist
+
+485
+00:39:47,770 --> 00:39:53,490
+there exist x P of X، إذا
+
+486
+00:39:53,490 --> 00:40:00,150
+هذه true على طول، معناته P of C is true برضه
+
+487
+00:40:00,150 --> 00:40:07,290
+بالمطلق هيك مش منطقية كتير، مش معناته C، يعني لكن
+
+488
+00:40:07,290 --> 00:40:13,130
+لاحظ لما أقول هذه C، الخصوصية هذه، a new constant C
+
+489
+00:40:13,130 --> 00:40:21,230
+a new constant C، فإذن هقول there exist أن في حد
+
+490
+00:40:21,230 --> 00:40:26,610
+هينجح، لإن عكسناها للأسف أن والله في حد هينجح، طب
+
+491
+00:40:26,610 --> 00:40:30,330
+أمش مضطر لكل، في الحالة هذه ويمكن واحد بس، طيب لما
+
+492
+00:40:30,330 --> 00:40:34,010
+أقول في حد هينجح وأقول في الآخر اللي هينجح هذا X
+
+493
+00:40:34,010 --> 00:40:38,680
+بس أنا ما حددتش X، أنا قلت إنه في الـ new constant الـ
+
+494
+00:40:38,680 --> 00:40:42,580
+new constant هذا اسمه X، و X هينجح، X هذا هيطلع في
+
+495
+00:40:42,580 --> 00:40:46,320
+الآخر محمد، هيطلع أحمد، هيطلع عمر، المهم إنه هيطلع
+
+496
+00:40:46,320 --> 00:40:49,660
+حدا من مين؟ من الـ universe of discourse، من فضاء
+
+497
+00:40:49,660 --> 00:40:54,080
+العينة، أنا حاطط له new constant عشان ما يكونش حدًا
+
+498
+00:40:54,080 --> 00:41:01,040
+تحديدًا من العينة، محدد شخصًا، لا، أنا قلت هو X وهو
+
+499
+00:41:01,040 --> 00:41:06,500
+موجود في العينة، أنت حاطط لك الآن مين X؟ مش فاهم، كويس
+
+500
+00:41:06,500 --> 00:41:13,200
+واضحت؟ فإذا كمان مرة، C هذه الـ new constant مش
+
+501
+00:41:13,200 --> 00:41:16,960
+بالضروري أن هو موجود من الـ elements بتاعة مين؟
+
+502
+00:41:16,960 --> 00:41:20,560
+بتاعة الـ universe of discourse، أنا بقول C هو
+
+503
+00:41:20,560 --> 00:41:25,800
+constant موجود وبيحقق، مدام there exist، بس مين؟
+
+504
+00:41:25,800 --> 00:41:31,640
+أي واحد ممكن يكون C، أي واحد فيكم ممكن يكون C من الـ
+
+505
+00:41:31,640 --> 00:41:35,710
+universe of discourse، كويس؟ وهذا ممكن يكون منطبق
+
+506
+00:41:35,710 --> 00:41:39,630
+عادي، C هذا ممكن يكون أكثر من واحد، ممكن يكون أكثر
+
+507
+00:41:39,630 --> 00:41:44,990
+من واحد، لكن في النهاية في حد هيحقق الـ constant C،
+
+508
+00:41:44,990 --> 00:41:49,950
+واضحت؟ ما أقدرش أحدد تحديدًا C هو، أقول والله P of
+
+509
+00:41:49,950 --> 00:41:54,470
+Ahmed، بس Ahmed، لا هي غلط، هي غلط، there exist
+
+510
+00:41:54,470 --> 00:41:57,550
+معناته بضمن لي  تحديدًا Ahmed، الـ there exist اللي
+
+511
+00:41:57,550 --> 00:42:00,490
+is a true، لا ما حدش قال إنه Ahmed تحديدًا، يمكن
+
+512
+00:42:00,490 --> 00:42:04,980
+محمد، يمكن عمرو، يمكن خالد، صحيح، فإذا بقول C، و C هذا
+
+513
+00:42:04,980 --> 00:42:11,660
+ممكن يكون أي حد، بس أنا ضامن إنه في حد هيكون حقق الـ
+
+514
+00:42:11,660 --> 00:42:17,540
+P of X، في حد، صحيح؟ تمام، فحطينا له a new constant
+
+515
+00:42:17,540 --> 00:42:22,940
+عشان نطلع من مطب أنه هيك حددته، لا أنا ما حددتش هذا
+
+516
+00:42:22,940 --> 00:42:28,540
+new constant، طيب هذا بهيأ لي واضحة، object داخل الـ
+
+517
+00:42:28,540 --> 00:42:31,700
+universe of discourse، إذا هو true فمعناته there
+
+518
+00:42:31,700 --> 00:42:36,780
+exist، خلاص في معه حدا، فليكن، إذا هو لحاله، فليكن في
+
+519
+00:42:36,780 --> 00:42:39,640
+الحالتين اتحققت there exist، there exist في
+
+520
+00:42:39,640 --> 00:42:44,080
+الحالتين حتى اتحققت، خلاص مش هندا مشكلة، مش هيكون فيه
+
+521
+00:42:44,080 --> 00:42:51,120
+مشكلة، okay، بيظهر لنا مشكلة كبيرة من وراء عدم فهمنا
+
+522
+00:42:51,120 --> 00:42:55,760
+للـ implication، هذا الشيء اللي هي الـ fallacy
+
+523
+00:42:55,760 --> 00:43:01,480
+المغالطة أو الـ fallacies، المغالطات، أحيانًا المغالطات
+
+524
+00:43:01,480 --> 00:43:06,480
+هذه إما بتصير في عملية التأكيد أو في عملية الإنكار،
+
+525
+00:43:06,480 --> 00:43:09,920
+احنا أخذناها مرتين الـ implication في الـ F بذاته
+
+526
+00:43:09,920 --> 00:43:14,220
+توي، صح؟ أخذناها مرة لما قلنا affirming إن والله
+
+527
+00:43:14,220 --> 00:43:18,840
+بدنا نؤكد فيها الـ consequence اللي هو الـ
+
+528
+00:43:18,840 --> 00:43:23,900
+conclusion، أو denying للـ premise للـ P لما
+
+529
+00:43:23,900 --> 00:43:29,620
+نفينا الـ P وقلنا بنستنتج negation P من negation Q
+
+530
+00:43:30,320 --> 00:43:35,180
+كويس، فإذا في عندي كانوا حالتين بس، هل الحالتين هدول
+
+531
+00:43:35,180 --> 00:43:38,320
+واضحين جدًا؟ لا، ممكن نصيبهم مغالطات، أحيانًا من وراء
+
+532
+00:43:38,320 --> 00:43:43,580
+حالتين هنتكلم عنهم، ممكن جدًا، الفلسفة الأولى اللي هي
+
+533
+00:43:43,580 --> 00:43:47,900
+للـ affirming، أني أؤكد الـ conclusion بينما هو مش
+
+534
+00:43:47,900 --> 00:43:51,360
+بالضروري يكون مؤكد، زي لما أقول إذا كان ظهر عندي P
+
+535
+00:43:51,360 --> 00:43:57,160
+implies Q is true، هذا true خلاص مية بالمية، و Q is
+
+536
+00:43:57,160 --> 00:44:01,800
+true، تروح تأكد الـ premise، التأكيد بيجي على الـ
+
+537
+00:44:01,800 --> 00:44:06,620
+conclusion مش على الـ premise، توي النظرية اللي
+
+538
+00:44:06,620 --> 00:44:09,940
+أخذناها، الـ rule اللي أخذناها كانت تأكيد للـ
+
+539
+00:44:09,940 --> 00:44:16,640
+conclusion و denying للـ premise، خذوا بالكم، طيب
+
+540
+00:44:16,640 --> 00:44:22,500
+بمعنى أنه هنا لما يقول لي P implication
+
+541
+00:44:22,500 --> 00:44:26,920
+أو employs Q is true، و Q is true، ما حدش يجي يقول
+
+542
+00:44:26,920 --> 00:44:32,120
+ليه؟ معناته P is true، العكس صح بس هذه لا، إذا كان
+
+543
+00:44:32,120 --> 00:44:36,440
+هنا P is true، بقول لك اه Q is true، أما Q is true
+
+544
+00:44:36,440 --> 00:44:37,500
+شوفوا لي
+
+545
+00:44:41,910 --> 00:44:47,890
+الـ Q اللي هو العمود الثاني والثالث، الاثنين true
+
+546
+00:44:47,890 --> 00:44:53,390
+true، شوفوا ليه؟ ايش لازم تكون P؟ يعني أنت بتحتمل
+
+547
+00:44:53,390 --> 00:44:56,190
+الحالتين، ليش؟ أنت راحت قررت أن هي لازم تكون true
+
+548
+00:44:56,190 --> 00:45:03,950
+خطأ، فالـ affirming هادي للـ conclusion مش للـ premise
+
+549
+00:45:03,950 --> 00:45:07,410
+...مش للـ premise، طيب والعكس صحيح، لما نيجي نتكلم عن
+
+550
+00:45:07,410 --> 00:45:10,650
+الـ premise اللي هو في عملية الـ denying اللي هو
+
+551
+00:45:10,650 --> 00:45:15,670
+الإنكار، أو اللي هو الفلسفي أن أقول: الله دي false، زي
+
+552
+00:45:15,670 --> 00:45:21,250
+حالة أن أقول P implies Q is true، تمام، اتفجنا الـ
+
+553
+00:45:21,250 --> 00:45:27,010
+column الثالث و P is false، أما أنت هيك قلت يا
+
+554
+00:45:27,010 --> 00:45:31,070
+دكتور لا استنى، أنا ما قلتش هيك، أنا قلت إذا تم إنكار
+
+555
+00:45:31,070 --> 00:45:35,950
+الـ conclusion، استنتج أنه الـ premise منكرة، بس اللي
+
+556
+00:45:35,950 --> 00:45:40,530
+هنا تم إنكار الـ premise، ما تقدرش بناء عليها تنكر الـ
+
+557
+00:45:40,530 --> 00:45:44,710
+conclusion، تروح تقول الـ Q معناته false، شوف العمود
+
+558
+00:45:44,710 --> 00:45:49,730
+الأول والثالث، false true، شوف ليه false true
+
+559
+00:45:49,730 --> 00:45:54,230
+العمود الأول والثالث، الـ Q لها الحالتين، فأنت بناء
+
+560
+00:45:54,230 --> 00:45:59,340
+عليها راحت حكمت، إذن هذه مغلطة بتصير، والواحد بيضل
+
+561
+00:45:59,340 --> 00:46:05,300
+فيها بيفكر أنه لا هي منطقي، بيفكر أنه لا أنا صح، ليش
+
+562
+00:46:05,300 --> 00:46:09,640
+هتقول غلط، لأنه بتكون حالة من الحالتين هذول في
+
+563
+00:46:09,640 --> 00:46:13,080
+الغالب، في الغالب، هذه معظم الحالات اللي بتصير فيها
+
+564
+00:46:13,080 --> 00:46:18,680
+fallacy أو مغلطة بتكون من الحالتين، طيب ننهي بمثال
+
+565
+00:46:21,500 --> 00:46:28,280
+ننهي بالمثال هذا ونشوف وين الخلل في الموضوع هذا،
+
+566
+00:46:28,280 --> 00:46:33,780
+أقول أن a و b هي positive integers، a تساوي b، تمام؟
+
+567
+00:46:33,780 --> 00:46:38,680
+هضرب الاثنين في a، كلاهما هضربوا في a، a تربيع و a
+
+568
+00:46:38,680 --> 00:46:42,640
+في b، وبعدين كلاهما طرحنا منه b تربيع على الطرفين
+
+569
+00:46:42,640 --> 00:46:46,620
+طرحنا من الـ...هي b تربيع و b تربيع، كلاهما أخذنا
+
+570
+00:46:46,620 --> 00:46:53,610
+منهم common الـ a ناقص b، أخذناها common، طبعًا هنا
+
+571
+00:46:53,610 --> 00:46:59,990
+لاحظوا أن هذه طرح مربعين، فلما بناخد الـ a ناقص b
+
+572
+00:46:59,990 --> 00:47:03,590
+بتصير مضروبة في a زائد b، هدول لو ضربتهم في بعض
+
+573
+00:47:03,590 --> 00:47:08,130
+هيرجعوا للثاني، تمام، هنا ناخد الـ a ناقص b فبتضل الـ
+
+574
+00:47:08,130 --> 00:47:12,110
+b برة لحالها، بعدين اختصر الاثنين هدول مع بعض
+
+575
+00:47:12,110 --> 00:47:20,070
+اختصرناهم واتبقى a ناقص b، صارت هنا a هي نفسها b، 2A
+
+576
+00:47:20,070 --> 00:47:26,190
+2E، مين الرجال اللي بتظبطش؟ ليش
+
+577
+00:47:26,190 --> 00:47:32,090
+بتظبطش؟ تجسم على صفر؟ ليش بدك تجسم على صفر؟
+
+578
+00:47:32,090 --> 00:47:37,070
+اختصرتهم اختصار مع بعض، أنا بس اختصرتهم اختصار
+
+579
+00:47:37,070 --> 00:47:41,850
+واحدة على اليمين، واحدة على الشمال واختصرتهم، أحسنت
+
+580
+00:47:41,850 --> 00:47:45,150
+أحسنت، الاختصار مش معناته زي ما أنا قاعد بقول، اختصر
+
+581
+00:47:45,150 --> 00:47:48,990
+وخلصنا، ضيعناهم مع بعض، الاختصار معناه قسمة، هي
+
+582
+00:47:48,990 --> 00:47:52,650
+policy واضحة جدًا وكتير ممكن تصير معانا، ليش؟ لأن
+
+583
+00:47:52,650 --> 00:47:57,110
+أنا بتلّوي الإثبات غصب عنه، بدي أمشي فبتصير معاكم
+
+584
+00:47:57,110 --> 00:48:00,210
+إنك بدك تلّوي غصب عنه، بدك تمشي، بدك تطلع إن لا
+
+585
+00:48:00,210 --> 00:48:04,450
+وصلت لنتيجة بينما أنت عارف إن هي مش مقنعة وقد
+
+586
+00:48:04,450 --> 00:48:07,690
+تكون مش عارف، يعني أنا مثلًا هنا قاعدة قدامك وطلعت
+
+587
+00:48:07,690 --> 00:48:12,720
+مش عارف، راحت ايش سويت؟ اختصرتهم مع بعض، لا، فيش حاجة
+
+588
+00:48:12,720 --> 00:48:17,020
+اسمها اختصرتهم مع بعض، في حاجة اسمها قسمت كل طرفين
+
+589
+00:48:17,020 --> 00:48:20,700
+على نفس الـ term، ما فيش حاجة أقول اختصر مع
+
+590
+00:48:20,700 --> 00:48:24,020
+بعض، ما فيش حاجة هيك اسمها، في إن هذه لحالها أنا راحت
+
+591
+00:48:24,020 --> 00:48:27,080
+قسمتها على a ناقص واحد، وأنا من الأول قاعد بقول a
+
+592
+00:48:27,080 --> 00:48:33,640
+تساوي b، فإذا قسمت على term ناقص نفسه، يعني صار
+
+593
+00:48:33,640 --> 00:48:36,120
+كأنني بقسم على صفر، undefined
+
+594
+00:48:37,960 --> 00:48:42,480
+إن هاتش هيطلع undefined، غير معرف، معنى ذلك أنه اللي
+
+595
+00:48:42,480 --> 00:48:47,020
+طلع في الآخر undefined، يساوي undefined وليس زي ما
+
+596
+00:48:47,020 --> 00:48:53,720
+أنا قلت هيك، A زائد B تساوي B، هذا undefined، تمام
+
+597
+00:48:53,720 --> 00:48:58,120
+واضحت؟ الكل واضحت معاه؟ ما تيجيش تقصر لاختصارات؟
+
+598
+00:48:58,120 --> 00:49:03,160
+الاختصارات دي هي زي ما أقول لك إحنا بنعمل اختصار
+
+599
+00:49:03,160 --> 00:49:07,460
+للعملية... لعملية قسمة... لعملية قسمة، يلا يعطيك
+
+600
+00:49:07,460 --> 00:49:08,500
+الله، عفا شباب، خلصنا هي
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aX4ewdPoCoU_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aX4ewdPoCoU_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..dca9417f1a57cf9f244fc4718c4150adab6d926a
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aX4ewdPoCoU_raw.json
@@ -0,0 +1 @@
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{"start": 211.85, "end": 212.33, "word": " بنفكر", "probability": 0.96923828125}, {"start": 212.33, "end": 212.57, "word": " فيها", "probability": 0.98193359375}, {"start": 212.57, "end": 212.93, "word": " بمعنى", "probability": 0.9623046875}, {"start": 212.93, "end": 213.07, "word": " ان", "probability": 0.7822265625}, {"start": 213.07, "end": 213.25, "word": " احنا", "probability": 0.95849609375}, {"start": 213.25, "end": 213.65, "word": " بنفكر", "probability": 0.94580078125}, {"start": 213.65, "end": 213.81, "word": " في", "probability": 0.90478515625}, {"start": 213.81, "end": 213.97, "word": " حال", "probability": 0.943359375}, {"start": 213.97, "end": 214.49, "word": " مشكلة", "probability": 0.9168294270833334}, {"start": 214.49, "end": 214.93, "word": " فانا", "probability": 0.97509765625}, {"start": 214.93, "end": 215.49, "word": " بحطها", "probability": 0.9896240234375}, {"start": 215.49, "end": 216.19, "word": " ضمن", "probability": 0.993896484375}, {"start": 216.19, "end": 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بتكون", "probability": 0.950439453125}, {"start": 235.22, "end": 235.44, "word": " عبارة", "probability": 0.992919921875}, {"start": 235.44, "end": 235.6, "word": " عن", "probability": 0.99365234375}, {"start": 235.6, "end": 236.2, "word": " pattern،", "probability": 0.736572265625}, {"start": 236.2, "end": 236.86, "word": " نموذج،", "probability": 0.988525390625}, {"start": 236.86, "end": 237.72, "word": " قالب،", "probability": 0.9012451171875}, {"start": 237.72, "end": 238.3, "word": " قالب", "probability": 0.9529622395833334}, {"start": 238.3, "end": 238.7, "word": " خلاص", "probability": 0.94970703125}, {"start": 238.7, "end": 239.14, "word": " عارفين", "probability": 0.9498291015625}, {"start": 239.14, "end": 239.34, "word": " أنه", "probability": 0.4149169921875}, {"start": 239.34, "end": 239.46, "word": " هذا", "probability": 0.85400390625}, {"start": 239.46, "end": 239.96, "word": " صحيح", "probability": 0.990478515625}, {"start": 239.96, "end": 240.62, "word": " عارفين", "probability": 0.9029541015625}, {"start": 240.62, "end": 241.12, "word": " أنه", "probability": 0.837890625}, {"start": 241.12, "end": 241.58, "word": " صحيح", "probability": 0.9981689453125}, {"start": 241.58, "end": 241.88, "word": " زي", "probability": 0.967041015625}, {"start": 241.88, "end": 243.06, "word": " اي", "probability": 0.6881103515625}, {"start": 243.06, "end": 243.94, "word": " قانون،", "probability": 0.8489990234375}, {"start": 243.94, "end": 244.22, "word": " قانون", "probability": 0.96435546875}], "temperature": 1.0}, {"id": 12, "seek": 26436, "start": 245.06, "end": 264.36, "text": "قانون بيكون في right and left terms و اتنين equal لبعض و بنحط اي problem ضمن هذا ال pattern فهي عبارة عن patterns او قوالب منطقيا valid dedications from", "tokens": [4587, 7649, 11536, 4724, 1829, 30544, 8978, 558, 293, 1411, 2115, 4032, 1975, 2655, 1863, 9957, 2681, 5296, 3555, 3615, 11242, 4032, 44945, 5016, 9566, 1975, 1829, 1154, 48812, 27842, 23758, 2423, 5102, 6156, 3224, 1829, 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250.62, "end": 251.0, "word": " equal", "probability": 0.93896484375}, {"start": 251.0, "end": 252.16, "word": " لبعض", "probability": 0.947021484375}, {"start": 252.16, "end": 252.76, "word": " و", "probability": 0.66064453125}, {"start": 252.76, "end": 253.6, "word": " بنحط", "probability": 0.9578450520833334}, {"start": 253.6, "end": 253.98, "word": " اي", "probability": 0.730712890625}, {"start": 253.98, "end": 254.64, "word": " problem", "probability": 0.96875}, {"start": 254.64, "end": 255.58, "word": " ضمن", "probability": 0.98095703125}, {"start": 255.58, "end": 256.12, "word": " هذا", "probability": 0.96044921875}, {"start": 256.12, "end": 256.26, "word": " ال", "probability": 0.97607421875}, {"start": 256.26, "end": 256.68, "word": " pattern", "probability": 0.9677734375}, {"start": 256.68, "end": 257.3, "word": " فهي", "probability": 0.9685872395833334}, {"start": 257.3, "end": 257.56, "word": " عبارة", "probability": 0.9874267578125}, {"start": 257.56, "end": 257.72, 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rule خلاص، لأ لأ ال rule لازم تكون دائما، ضامن أن هي دائما صح، دائما صح، طبعا هناخد أنثى الاكتيف لإلها", "tokens": [6027, 20292, 39896, 12174, 995, 22488, 3660, 42963, 14851, 3215, 1211, 6027, 12399, 47525, 11296, 6055, 30544, 11778, 16373, 15042, 7363, 12399, 4724, 2304, 3615, 1863, 7578, 39896, 11778, 16373, 15042, 20328, 5016, 1829, 5016, 3660, 12399, 39896, 11778, 16373, 15042, 20328, 5016, 12399, 3714, 9307, 30544, 8592, 16070, 43761, 3714, 2288, 9307, 20328, 5016, 4032, 29973, 9307, 32771, 1211, 9566, 12399, 11331, 35457, 2423, 3614, 12399, 11331, 35457, 16490, 1211, 11703, 9957, 1829, 8717, 39648, 2423, 1389, 12399, 4032, 5551, 5172, 2655, 43042, 14739, 39896, 4978, 16490, 1211, 33546, 12399, 5296, 10721, 5296, 10721, 2423, 4978, 5296, 31377, 2304, 6055, 30544, 11778, 16373, 15042, 12399, 48812, 10943, 1863, 14739, 39896, 11778, 16373, 15042, 20328, 5016, 12399, 11778, 16373, 15042, 20328, 5016, 12399, 23032, 3555, 3615, 995, 8032, 1863, 47283, 3215, 14739, 12984, 7578, 42963, 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198234, "start": 1966.02, "end": 1982.34, "text": "only if بدون ال F الأولى، لاحظ، هذه حالة و هذه حالة و بدون only حالة تالتة كمان، يعني لاحظ هنا بدون هذه، هذه P وهذه Q", "tokens": [25202, 498, 47525, 11536, 2423, 479, 16247, 12610, 7578, 12399, 20193, 5016, 19913, 12399, 29538, 11331, 6027, 3660, 4032, 29538, 11331, 6027, 3660, 4032, 47525, 11536, 787, 11331, 6027, 3660, 6055, 6027, 2655, 3660, 9122, 2304, 7649, 12399, 37495, 22653, 20193, 5016, 19913, 34105, 47525, 11536, 29538, 12399, 29538, 430, 37037, 24192, 1249], "avg_logprob": -0.24030671185917324, "compression_ratio": 1.652542372881356, "no_speech_prob": 3.814697265625e-06, "words": [{"start": 1966.02, "end": 1966.44, "word": "only", "probability": 0.1822509765625}, {"start": 1966.44, "end": 1966.86, "word": " if", "probability": 0.77587890625}, {"start": 1966.86, "end": 1967.28, "word": " بدون", "probability": 0.72412109375}, {"start": 1967.28, "end": 1967.38, "word": " ال", "probability": 0.697265625}, {"start": 1967.38, 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"probability": 0.875}, {"start": 2000.72, "end": 2000.94, "word": " لو", "probability": 0.9892578125}, {"start": 2000.94, "end": 2001.4, "word": " مولنا", "probability": 0.81591796875}, {"start": 2001.4, "end": 2003.58, "word": " if", "probability": 0.92724609375}, {"start": 2003.58, "end": 2004.22, "word": " and", "probability": 0.93994140625}], "temperature": 1.0}, {"id": 82, "seek": 202688, "start": 2005.58, "end": 2026.88, "text": "only if لأ أصلح أصبحت كلها مختلفة ك operator ال operator كله بطل بطل ال if then أصلا صارت حاجة تاني مختلفة تمام okay خلاص هي ده اللي كنت بدأ أوضحها أركز عليها فصارت هنا swim employs sunny", "tokens": [25202, 498, 5296, 10721, 5551, 36520, 5016, 5551, 9381, 3555, 33753, 28242, 11296, 3714, 46456, 46538, 3660, 9122, 12973, 2423, 12973, 28242, 3224, 4724, 9566, 1211, 4724, 9566, 1211, 2423, 498, 550, 5551, 9381, 15040, 20328, 9640, 2655, 11331, 26108, 3660, 6055, 7649, 1829, 3714, 46456, 46538, 3660, 46811, 10943, 1392, 16490, 1211, 33546, 39896, 11778, 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" تاني", "probability": 0.8069661458333334}, {"start": 2016.22, "end": 2017.16, "word": " مختلفة", "probability": 0.988525390625}, {"start": 2017.16, "end": 2017.94, "word": " تمام", "probability": 0.75439453125}, {"start": 2017.94, "end": 2018.48, "word": " okay", "probability": 0.607421875}, {"start": 2018.48, "end": 2022.2, "word": " خلاص", "probability": 0.9720052083333334}, {"start": 2022.2, "end": 2022.36, "word": " هي", "probability": 0.84423828125}, {"start": 2022.36, "end": 2022.5, "word": " ده", "probability": 0.5693359375}, {"start": 2022.5, "end": 2022.62, "word": " اللي", "probability": 0.949462890625}, {"start": 2022.62, "end": 2022.76, "word": " كنت", "probability": 0.988037109375}, {"start": 2022.76, "end": 2022.98, "word": " بدأ", "probability": 0.4495849609375}, {"start": 2022.98, "end": 2023.4, "word": " أوضحها", "probability": 0.874609375}, {"start": 2023.4, "end": 2023.76, "word": " أركز", "probability": 0.89306640625}, {"start": 2023.76, "end": 2024.12, "word": " عليها", "probability": 0.99169921875}, {"start": 2024.12, "end": 2024.7, "word": " فصارت", "probability": 0.9720458984375}, {"start": 2024.7, "end": 2024.94, "word": " هنا", "probability": 0.98974609375}, {"start": 2024.94, "end": 2025.42, "word": " swim", "probability": 0.90234375}, {"start": 2025.42, "end": 2026.4, "word": " employs", "probability": 0.766845703125}, {"start": 2026.4, "end": 2026.88, "word": " sunny", "probability": 0.85302734375}], "temperature": 1.0}, {"id": 83, "seek": 205446, "start": 2027.9, "end": 2054.46, "text": "و بعد هيك خلاص اذا احنا ماسبحناش اذا هنلعب volley ماسبحناش هنا negation swim negation swim اذا volley طيب و اذا احنا volley اذا early هنروح بدري طيب بسيط اذا كان هذه الموقعات نبدأ فيهم واحدة واحدة اول موقع هي ال premise number one negation sunny and cold معناته هذه لحالها بحثتها true وهذه لحالها true", "tokens": [2407, 39182, 39896, 4117, 16490, 1211, 33546, 1975, 15730, 1975, 5016, 8315, 19446, 35457, 5016, 1863, 33599, 1975, 15730, 8032, 1863, 1211, 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"probability": 0.89794921875}, {"start": 2052.4, "end": 2052.9, "word": " بحثتها", "probability": 0.78720703125}, {"start": 2052.9, "end": 2053.22, "word": " true", "probability": 0.9892578125}, {"start": 2053.22, "end": 2053.86, "word": " وهذه", "probability": 0.845458984375}, {"start": 2053.86, "end": 2054.16, "word": " لحالها", "probability": 0.9940185546875}, {"start": 2054.16, "end": 2054.46, "word": " true", "probability": 0.98779296875}], "temperature": 1.0}, {"id": 84, "seek": 208250, "start": 2056.52, "end": 2082.5, "text": "خلاص معناته هي فعلا not sunny فإذا not sunny لحالها is true طيب في اندرامس تانية كانت بتقول ليه swim if sunny only if sunny تمام فإذا كانت swim employees sunny طيب لاحظوا هنا negation sunny الحالة بتاعة ال denying او الانكار معناه ذلك انه", "tokens": [9778, 1211, 33546, 20449, 8315, 47395, 39896, 6156, 3615, 15040, 406, 20412, 6156, 28814, 15730, 406, 20412, 5296, 5016, 6027, 11296, 307, 2074, 23032, 1829, 3555, 8978, 16472, 3215, 2288, 10943, 3794, 6055, 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{"start": 2058.08, "end": 2059.28, "word": " فإذا", "probability": 0.7810872395833334}, {"start": 2059.28, "end": 2059.62, "word": " not", "probability": 0.85986328125}, {"start": 2059.62, "end": 2059.86, "word": " sunny", "probability": 0.9521484375}, {"start": 2059.86, "end": 2060.32, "word": " لحالها", "probability": 0.965087890625}, {"start": 2060.32, "end": 2060.48, "word": " is", "probability": 0.9384765625}, {"start": 2060.48, "end": 2060.82, "word": " true", "probability": 0.9853515625}, {"start": 2060.82, "end": 2063.6, "word": " طيب", "probability": 0.7018636067708334}, {"start": 2063.6, "end": 2063.72, "word": " في", "probability": 0.83935546875}, {"start": 2063.72, "end": 2064.22, "word": " اندرامس", "probability": 0.4826416015625}, {"start": 2064.22, "end": 2064.54, "word": " تانية", "probability": 0.8642578125}, {"start": 2064.54, "end": 2064.86, "word": " كانت", "probability": 0.973388671875}, {"start": 2064.86, "end": 2065.2, "word": " بتقول", "probability": 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"probability": 0.7576904296875}, {"start": 2081.2, "end": 2081.92, "word": " معناه", "probability": 0.9519856770833334}, {"start": 2081.92, "end": 2082.16, "word": " ذلك", "probability": 0.988525390625}, {"start": 2082.16, "end": 2082.5, "word": " انه", "probability": 0.866455078125}], "temperature": 1.0}, {"id": 85, "seek": 211204, "start": 2083.84, "end": 2112.04, "text": "negation swim هتطلع negation swim هاي واحدة من ال rules اللي كنا بتكلم عنها واحدة من ال rules اللي حكينا عنهم قبل شوية فإذا negation swim is true طيب برضه في عندى premise رقم تلاتة كانت بتقول ال negation swim هي بيضمن ليه او predicate volley تمام هنا التأكيد لإن فعلا هذه true هذه true", "tokens": [28561, 399, 7110, 8032, 2655, 9566, 1211, 3615, 2485, 399, 7110, 8032, 47302, 36764, 24401, 3660, 9154, 2423, 4474, 13672, 1829, 9122, 8315, 39894, 4117, 19528, 18871, 11296, 36764, 24401, 3660, 9154, 2423, 4474, 13672, 1829, 11331, 4117, 1829, 8315, 18871, 16095, 12174, 36150, 13412, 2407, 10632, 6156, 28814, 15730, 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بمعنى انه هنا لما يقول لي P of P implication او employs Q is true و Q is true ماحدش يجي يقول ليه معناته P is true العكس صح بس هذه لأ اذا كان هنا P is true بقولك اه Q is true اما Q is true شوفولي", "tokens": [9778, 3215, 14407, 20666, 4117, 14407, 23032, 1829, 3555, 4724, 2304, 3615, 1863, 7578, 16472, 3224, 34105, 5296, 15042, 7251, 39648, 32239, 430, 295, 430, 37814, 1975, 2407, 846, 49522, 1249, 307, 2074, 4032, 1249, 307, 2074, 19446, 24401, 8592, 7251, 7435, 1829, 7251, 39648, 32239, 3224, 20449, 8315, 47395, 430, 307, 2074, 18863, 4117, 3794, 20328, 5016, 4724, 3794, 29538, 5296, 10721, 1975, 15730, 25961, 34105, 430, 307, 2074, 4724, 39648, 4117, 1975, 3224, 1249, 307, 2074, 1975, 15042, 1249, 307, 2074, 13412, 38688, 12610, 1829], "avg_logprob": -0.21466619876975362, "compression_ratio": 1.654054054054054, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 2654.96, "end": 2655.32, "word": "خدوا", "probability": 0.9064127604166666}, {"start": 2655.32, "end": 2655.86, 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"probability": 0.7457682291666666}, {"start": 2906.5, "end": 2906.8, "word": " بقول", "probability": 0.936767578125}, {"start": 2906.8, "end": 2907.08, "word": " a", "probability": 0.92041015625}, {"start": 2907.08, "end": 2907.98, "word": " تساوي", "probability": 0.8909912109375}, {"start": 2907.98, "end": 2908.72, "word": " b", "probability": 0.80810546875}, {"start": 2908.72, "end": 2909.48, "word": " فإذا", "probability": 0.69580078125}, {"start": 2909.48, "end": 2909.92, "word": " قسمت", "probability": 0.9866536458333334}, {"start": 2909.92, "end": 2910.12, "word": " على", "probability": 0.64013671875}, {"start": 2910.12, "end": 2911.28, "word": " term", "probability": 0.97216796875}, {"start": 2911.28, "end": 2911.84, "word": " ناقص", "probability": 0.990966796875}, {"start": 2911.84, "end": 2912.38, "word": " نفسه", "probability": 0.9973958333333334}, {"start": 2912.38, "end": 2913.42, "word": " يعني", "probability": 0.95263671875}, {"start": 2913.42, "end": 2913.64, "word": " 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1829, 19446, 41850, 12174, 1211, 2655, 39896, 4117, 316, 30767, 16373, 3215, 363, 6055, 3794, 2407, 7578, 363, 8032, 18513, 2719, 5666, 2001], "avg_logprob": -0.24285714370863778, "compression_ratio": 1.4930555555555556, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2917.96, "end": 2918.22, "word": "إن", "probability": 0.54779052734375}, {"start": 2918.22, "end": 2918.46, "word": " هاتش", "probability": 0.5023600260416666}, {"start": 2918.46, "end": 2918.7, "word": " هيطلع", "probability": 0.860888671875}, {"start": 2918.7, "end": 2919.2, "word": " Undefined", "probability": 0.8255208333333334}, {"start": 2919.2, "end": 2920.06, "word": " غير", "probability": 0.82666015625}, {"start": 2920.06, "end": 2920.66, "word": " معرف", "probability": 0.885986328125}, {"start": 2920.66, "end": 2921.26, "word": " معنا", "probability": 0.840087890625}, {"start": 2921.26, "end": 2921.62, "word": " ذلك", "probability": 0.867919921875}, {"start": 2921.62, "end": 2922.02, "word": " إنه", "probability": 0.5006103515625}, {"start": 2922.02, "end": 2922.48, "word": " اللي", "probability": 0.95947265625}, {"start": 2922.48, "end": 2922.82, "word": " طلع", "probability": 0.97216796875}, {"start": 2922.82, "end": 2922.94, "word": " في", "probability": 0.923828125}, {"start": 2922.94, "end": 2923.44, "word": " الآخر", "probability": 0.9783528645833334}, {"start": 2923.44, "end": 2924.5, "word": " Undefined", "probability": 0.9446614583333334}, {"start": 2924.5, "end": 2924.84, "word": " يسوى", "probability": 0.79827880859375}, {"start": 2924.84, "end": 2925.42, "word": " Undefined", "probability": 0.978515625}, {"start": 2925.42, "end": 2926.76, "word": " وليس", "probability": 0.8785807291666666}, {"start": 2926.76, "end": 2926.94, "word": " زي", "probability": 0.981201171875}, {"start": 2926.94, "end": 2927.02, "word": " ما", "probability": 0.91162109375}, {"start": 2927.02, "end": 2927.2, "word": " أنا", "probability": 0.68408203125}, {"start": 2927.2, "end": 2927.44, "word": " قلت", "probability": 0.857421875}, {"start": 2927.44, "end": 2927.96, "word": " هيك", "probability": 0.6072998046875}, {"start": 2927.96, "end": 2928.62, "word": " A", "probability": 0.52783203125}, {"start": 2928.62, "end": 2929.4, "word": " زائد", "probability": 0.6895345052083334}, {"start": 2929.4, "end": 2929.66, "word": " B", "probability": 0.9287109375}, {"start": 2929.66, "end": 2930.16, "word": " تسوى", "probability": 0.8824462890625}, {"start": 2930.16, "end": 2930.4, "word": " B", "probability": 0.97216796875}, {"start": 2930.4, "end": 2930.96, "word": " هاد", "probability": 0.426513671875}, {"start": 2930.96, "end": 2931.46, "word": " Undefined", "probability": 0.9280598958333334}], "temperature": 1.0}, {"id": 118, "seek": 294850, "start": 2933.26, "end": 2948.5, "text": "تمام واضحت؟ الكل واضحت معاه؟ ماتيجيش تقتصر لاختصارات؟ الاختصارات دي هي زي ما اقوله احنا بنعمل اختصار للعملية .. لعملية قسمة .. لعملية قسمة يلا يعطيك الله عفا شباب خلصنا هي", "tokens": [39237, 10943, 4032, 46958, 33753, 22807, 2423, 28820, 4032, 46958, 33753, 20449, 40294, 22807, 3714, 9307, 1829, 7435, 1829, 8592, 6055, 38149, 9381, 2288, 5296, 47283, 2655, 9381, 9640, 9307, 22807, 2423, 47283, 2655, 9381, 9640, 9307, 11778, 1829, 39896, 30767, 1829, 19446, 1975, 39648, 3224, 1975, 5016, 8315, 44945, 25957, 1211, 1975, 46456, 9381, 9640, 24976, 25957, 1211, 10632, 4386, 5296, 25957, 1211, 10632, 12174, 38251, 3660, 4386, 5296, 25957, 1211, 10632, 12174, 38251, 3660, 7251, 15040, 37495, 9566, 1829, 4117, 21984, 6225, 5172, 995, 13412, 3555, 16758, 16490, 1211, 9381, 8315, 39896], "avg_logprob": -0.21249999309840956, "compression_ratio": 1.9012345679012346, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 2933.26, "end": 2933.72, "word": "تمام", "probability": 0.7333984375}, {"start": 2933.72, "end": 2934.88, "word": " واضحت؟", "probability": 0.72467041015625}, {"start": 2934.88, "end": 2935.2, "word": " الكل", "probability": 0.8974609375}, {"start": 2935.2, "end": 2935.46, "word": " واضحت", "probability": 0.94873046875}, {"start": 2935.46, "end": 2936.18, "word": " معاه؟", "probability": 0.8912760416666666}, {"start": 2936.18, "end": 2936.6, "word": " ماتيجيش", "probability": 0.8017985026041666}, {"start": 2936.6, "end": 2937.08, "word": " تقتصر", "probability": 0.8685302734375}, {"start": 2937.08, "end": 2938.12, "word": " لاختصارات؟", "probability": 0.8343680245535714}, {"start": 2938.12, "end": 2938.7, "word": " الاختصارات", "probability": 0.92236328125}, {"start": 2938.7, "end": 2939.74, "word": " دي", "probability": 0.59130859375}, {"start": 2939.74, "end": 2940.08, "word": " هي", "probability": 0.89501953125}, {"start": 2940.08, "end": 2940.74, "word": " زي", "probability": 0.683837890625}, {"start": 2940.74, "end": 2940.82, "word": " ما", "probability": 0.97119140625}, {"start": 2940.82, "end": 2941.08, "word": " اقوله", "probability": 0.5791829427083334}, {"start": 2941.08, "end": 2941.2, "word": " احنا", "probability": 0.8844401041666666}, {"start": 2941.2, "end": 2941.78, "word": " بنعمل", "probability": 0.9775390625}, {"start": 2941.78, "end": 2943.16, "word": " اختصار", "probability": 0.983154296875}, {"start": 2943.16, "end": 2944.24, "word": " للعملية", "probability": 0.9608154296875}, {"start": 2944.24, "end": 2944.8, "word": " ..", "probability": 0.307861328125}, {"start": 2944.8, "end": 2945.18, "word": " لعملية", "probability": 0.8997802734375}, {"start": 2945.18, "end": 2945.62, "word": " قسمة", "probability": 0.9095052083333334}, {"start": 2945.62, "end": 2945.68, "word": " ..", "probability": 0.85986328125}, {"start": 2945.68, "end": 2946.04, "word": " لعملية", "probability": 0.94140625}, {"start": 2946.04, "end": 2946.72, "word": " قسمة", "probability": 0.99609375}, {"start": 2946.72, "end": 2947.2, "word": " يلا", "probability": 0.58349609375}, {"start": 2947.2, "end": 2947.46, "word": " يعطيك", "probability": 0.88134765625}, {"start": 2947.46, "end": 2947.54, "word": " الله", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aX4ewdPoCoU_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aX4ewdPoCoU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c88bc2b49b7185003488ceee652e7f9342eb943e
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/aX4ewdPoCoU_raw.srt
@@ -0,0 +1,2400 @@
+1
+00:00:04,960 --> 00:00:08,360
+طيب يعطيكوا العفو يا شباب نبدأ اليوم ان شاء الله
+
+2
+00:00:08,360 --> 00:00:13,000
+تعالى في جزئية جديدة في مصاقنا و اللي هي ال proof
+
+3
+00:00:13,000 --> 00:00:17,560
+strategies او ال proof methods فمن المرات الماضية
+
+4
+00:00:17,560 --> 00:00:20,640
+اتكلمنا ان واحدة من مفارضات المصاق هتكون نتكلم
+
+5
+00:00:20,640 --> 00:00:24,600
+فيها عن ال strategies اللي ممكن اتباحها لعملية ال
+
+6
+00:00:24,600 --> 00:00:30,250
+proving اللي هي الاثباتاتفاليوم هيكون مساقنا او ما
+
+7
+00:00:30,250 --> 00:00:34,150
+حضرتنا في هذا المجال فهنتكلم انه فعليا ال proof
+
+8
+00:00:34,150 --> 00:00:37,550
+methods هي methods of mathematical argument او
+
+9
+00:00:37,550 --> 00:00:43,190
+للنقاش الرياضي ان احنا نناقش و نحاول نثبت relation
+
+10
+00:00:43,190 --> 00:00:49,270
+معينة هل هي موجودة او لا او لا فهذه ممكن can be
+
+11
+00:00:49,270 --> 00:00:54,960
+formalized ممكن وضح بشكلأو نعملها formalization
+
+12
+00:00:54,960 --> 00:00:59,900
+باستخدام term of rules of logical inference فال
+
+13
+00:00:59,900 --> 00:01:04,180
+inference اللي هي الاستدلال نتكلم عن ال rule of
+
+14
+00:01:04,180 --> 00:01:07,700
+inference بمعنى قواعد الاستدلال فطبيعي قواعد
+
+15
+00:01:07,700 --> 00:01:12,880
+الاستدلال اللي انتوا كنتوا تاخدوها بشكلقوانين اللي
+
+16
+00:01:12,880 --> 00:01:16,500
+هو القانون هذا الاستدلال اللي انت بتحط مجموعة ال
+
+17
+00:01:16,500 --> 00:01:20,460
+antecedents تبعته و هي بتستنى او بتشوف ايش ال
+
+18
+00:01:20,460 --> 00:01:25,380
+consequence او ال conclusion اللي ممكن يظهر يطلع
+
+19
+00:01:25,380 --> 00:01:29,850
+منه فبنسميها هنا logicalmathematical inference
+
+20
+00:01:29,850 --> 00:01:34,330
+فطبعا في حاجات أحيانا استدلال منطقي اللي هي قبل ما
+
+21
+00:01:34,330 --> 00:01:38,950
+تبدأ تثبت theorem معينة أنت بتثبت ال theorem أساسا
+
+22
+00:01:38,950 --> 00:01:43,190
+بتحطها بشكل قانون لكن من الأساس إيش اللي أثبتلك أن
+
+23
+00:01:43,190 --> 00:01:45,830
+هذا ال theorem هي صحيحة فمن خلال حاجة
+
+24
+00:01:52,130 --> 00:01:55,630
+be represented formally as discrete structures هي
+
+25
+00:01:55,630 --> 00:01:59,610
+نفسها أصلا عملية ال proving هي discrete structures
+
+26
+00:01:59,610 --> 00:02:02,770
+من خلال ال rules اللي أنت بتستخدمها هذه من خلال ال
+
+27
+00:02:02,770 --> 00:02:07,750
+rules اللي أنت بتستعملها فخلال اليوم هناخد جزئية
+
+28
+00:02:07,750 --> 00:02:11,350
+نعمل revision فيها على ال inference rules و
+
+29
+00:02:11,350 --> 00:02:16,450
+المحاضرة القادمة بناخد several proof methodsطرق
+
+30
+00:02:16,450 --> 00:02:20,190
+إثباتات معتمدة أو مستخدمة اليوم هناخد ال
+
+31
+00:02:20,190 --> 00:02:23,530
+introduction المقدمة اللي هنتكلم فيها عن ال
+
+32
+00:02:23,530 --> 00:02:28,850
+inference نفسهعملية الاستدلال نفسها و كيف تنعمل
+
+33
+00:02:28,850 --> 00:02:31,910
+عملية الاستدلال و إيش ال .. ال .. خلّيني أقول ال
+
+34
+00:02:31,910 --> 00:02:36,330
+rules البسيطة ال basics اللي ممكن استخدامها في ال
+
+35
+00:02:36,330 --> 00:02:41,710
+inference أو الاستدلال نبدأ بشوية terminology اللي
+
+36
+00:02:41,710 --> 00:02:46,370
+هي terms نفهمها، مجموعة terms، مصطلحات بدنا
+
+37
+00:02:46,370 --> 00:02:49,450
+نفهمها، ال theorem أول شغلة كلمة theorem اللي هي
+
+38
+00:02:49,450 --> 00:02:54,770
+نظريةالنظرية هي عبارة عن statement طبيعي تصريح أو
+
+39
+00:02:54,770 --> 00:03:00,290
+حاجة معلنة that has been proven to be true هي
+
+40
+00:03:00,290 --> 00:03:04,330
+مثبتة أن هي صحيحة فأي شيء مثبت أن هو صحيح بقدر
+
+41
+00:03:04,330 --> 00:03:08,910
+أستخده في الاستدلال لأنه كلنا عارفين أنه صحيح كلنا
+
+42
+00:03:08,910 --> 00:03:12,670
+عارفين أنه صحيح ال assumptionsال assumptions أو
+
+43
+00:03:12,670 --> 00:03:16,370
+الفرضيات و اللي مش بالضروري ان هي proven هي
+
+44
+00:03:16,370 --> 00:03:21,590
+unproven بمعنى هي مش مثبتة ولكن فرضية ممكن واضحة
+
+45
+00:03:21,590 --> 00:03:25,210
+فالفرضية هذه تعرف على اساس ان هي structure about
+
+46
+00:03:25,210 --> 00:03:31,590
+which we are reasoning هي structure مخصوص للشغل
+
+47
+00:03:31,590 --> 00:03:33,970
+اللي احنا بنفكر فيها بمعنى ان احنا بنفكر في حال
+
+48
+00:03:33,970 --> 00:03:39,490
+مشكلة فانا بحطها ضمن فرضية معينة عشان ابدأ أشتغل و
+
+49
+00:03:39,490 --> 00:03:45,540
+أحاول أثبتال object هذا هل هو true or false تمام؟
+
+50
+00:03:45,540 --> 00:03:50,240
+هنشوفها طبعا في شغلنا ال rules of inference أو
+
+51
+00:03:50,240 --> 00:03:54,760
+قواعد الاستدلال قاعدة استدلال زيها زي القانون فهي
+
+52
+00:03:54,760 --> 00:03:58,700
+بتكون عبارة عن pattern، نموذج، قالب، قالب خلاص
+
+53
+00:03:58,700 --> 00:04:03,940
+عارفين أنه هذا صحيح عارفين أنه صحيح زي اي قانون،
+
+54
+00:04:03,940 --> 00:04:10,620
+قانونقانون بيكون في right and left terms و اتنين
+
+55
+00:04:10,620 --> 00:04:16,680
+equal لبعض و بنحط اي problem ضمن هذا ال pattern
+
+56
+00:04:16,680 --> 00:04:21,680
+فهي عبارة عن patterns او قوالب منطقيا valid
+
+57
+00:04:21,680 --> 00:04:27,780
+dedications fromhypotheses to conclusions فهي
+
+58
+00:04:27,780 --> 00:04:33,460
+فعليا بتقودنا من الفرضيات للنتائج من الفرضيات
+
+59
+00:04:33,460 --> 00:04:36,760
+للنتائج بس طبعا بيكون زي ما قولنا ال rule هذه او
+
+60
+00:04:36,760 --> 00:04:41,020
+القاعدة هذه او ال inference هذهاللي هي قاعدة
+
+61
+00:04:41,020 --> 00:04:44,680
+الاستدلال، بدها تكون دائما valid، بمعنى هي دائما
+
+62
+00:04:44,680 --> 00:04:49,260
+صحيحة، هي دائما صح، ماتكونش والله مرات صح ومرات
+
+63
+00:04:49,260 --> 00:04:54,020
+غلط، حسب ال option، حسب خلّيني نقول ال case، و
+
+64
+00:04:54,020 --> 00:04:57,660
+أفترض أن هي rule خلاص، لأ لأ ال rule لازم تكون
+
+65
+00:04:57,660 --> 00:05:01,640
+دائما، ضامن أن هي دائما صح، دائما صح، طبعا هناخد
+
+66
+00:05:01,640 --> 00:05:06,120
+أنثى الاكتيف لإلهافإذن مبدأيا ال basic definition
+
+67
+00:05:06,120 --> 00:05:10,300
+لها ال theorem اتفقنا عليه هي أي حاجة بتكون مبين
+
+68
+00:05:10,300 --> 00:05:14,620
+ان هي دائما صحيحة او proven هي مثبتة ان هي دائما
+
+69
+00:05:14,620 --> 00:05:19,520
+صحيحة مبدأيا دائما نفترض انه عند مجموعة hypothesis
+
+70
+00:05:19,520 --> 00:05:27,620
+H1 and H2 اللي هي premises المقدمات او المعطيات
+
+71
+00:05:27,620 --> 00:05:34,350
+premises معطة hypothesis اللي هي الفرضيات فإذنهذه
+
+72
+00:05:34,350 --> 00:05:37,550
+او هذه الاتنين بمشي الحال المهم ان هما antecedents
+
+73
+00:05:37,550 --> 00:05:42,070
+اللي هي المعطية المقدمات لل rule اللي اطبق عليها
+
+74
+00:05:42,070 --> 00:05:46,070
+ال rule هنطبق ال rule على مجموعة h1, h2 to hn
+
+75
+00:05:46,070 --> 00:05:52,630
+فعندي n hypothesis بحيث انه يعطوني ايش conclusion
+
+76
+00:05:53,240 --> 00:05:57,440
+نستنتج منهم conclusion معين فهذه ال form الأبسط
+
+77
+00:05:57,440 --> 00:06:02,480
+الأصغر اللي هو ال if then إذا تحققت ال antecedents
+
+78
+00:06:02,480 --> 00:06:07,000
+إذا ال conclusion هيتحقق بس rule بسيطة جدا مبدئيا
+
+79
+00:06:07,000 --> 00:06:11,820
+هنبني عليها جميع ال rules اللاحقة كمان ما زلنا في
+
+80
+00:06:11,820 --> 00:06:15,580
+ال terminology ما زلنا في شويةterms بدنا نفهمها
+
+81
+00:06:15,580 --> 00:06:18,580
+اتكلمنا عن ال theorem مش مشكلة ال theorem هذه
+
+82
+00:06:18,580 --> 00:06:24,220
+احيانا مجرد ان انا اثبتتها اثبتتها انا ضامن ان ال
+
+83
+00:06:24,220 --> 00:06:28,710
+conclusion تبعها مرتبط ب other termمرتبط ب other
+
+84
+00:06:28,710 --> 00:06:31,770
+term في relation بينه بين other term فانا بمجرد ما
+
+85
+00:06:31,770 --> 00:06:35,830
+أثبتت صحة ال conclusion هدا من خلال ال rule من
+
+86
+00:06:35,830 --> 00:06:41,170
+خلال ال theorem أكيد انا بكون بكل بساطة ال
+
+87
+00:06:41,170 --> 00:06:47,370
+premises تبعت ال theorem بقدر أربطها بمين؟ بال
+
+88
+00:06:47,370 --> 00:06:50,850
+term اللي مرتبط بال conclusion فممكن أطلع منها
+
+89
+00:06:50,850 --> 00:06:55,750
+نظرية تانية بتطليليش نفس ال conclusion هو هو بإنعب
+
+90
+00:06:55,750 --> 00:07:02,070
+بمعنىخلّيني افترض ان عندي h1 and h2 and h3 بكفي
+
+91
+00:07:02,070 --> 00:07:08,930
+هدولة إذا تحققوا بيعطيني c1 okay خلاص تمام إذا
+
+92
+00:07:08,930 --> 00:07:15,450
+تحقق كذا و كذا و كذا إذا أكيد في كذا تمام؟ كويس
+
+93
+00:07:15,450 --> 00:07:19,210
+خلّيني افترض بهذا الشكل طيب ولكن عندي برضه في نفس
+
+94
+00:07:19,210 --> 00:07:26,160
+الوقت عندي rule تانية بتقول انه c1مم تمام or مثلا
+
+95
+00:07:26,160 --> 00:07:36,360
+c2 بيضمن لي c3 مبدأيا هذه إذا تحققت نتيجة ال h1 h2
+
+96
+00:07:36,360 --> 00:07:41,440
+h3 تحققت خلاص معناه ذلك أن أكيد c1 تحققت فبقدر
+
+97
+00:07:41,440 --> 00:07:47,620
+أقول أن هذه نظرية ممكن أسميها theorem صحيح خلصنا
+
+98
+00:07:47,620 --> 00:07:51,660
+من ال theorem الأولى طيب لكن في عندي ارتباط بين c1
+
+99
+00:07:53,190 --> 00:08:02,830
+و C3 معنى ذلك أنه لو تحققت H1, H2, H3 إذا C3 is
+
+100
+00:08:02,830 --> 00:08:08,910
+true صح؟ لاحظ؟ مجرد أنه C1 is true خلاص لأنه or
+
+101
+00:08:08,910 --> 00:08:14,530
+مثلا نتكلم هنا القصد أنه النظرية تحققها ممكن يؤدي
+
+102
+00:08:14,530 --> 00:08:18,670
+بسهولة لتحقيق نظرية أخرى فالنظرية الأخرى نسميها
+
+103
+00:08:18,670 --> 00:08:24,570
+الليمةسميها lima، ال lima هذه هي نظرية هيتم
+
+104
+00:08:24,570 --> 00:08:27,950
+إثباتها بسهولة نتيجة انه تحققت النظرية اللي احنا
+
+105
+00:08:27,950 --> 00:08:32,720
+بنحكي عنها اللي احنا بصددها هذهاللي احنا بيصطادها
+
+106
+00:08:32,720 --> 00:08:37,960
+واضحت؟ فإذا نتكلم عن النظرية أو ال theorem اللي
+
+107
+00:08:37,960 --> 00:08:41,580
+احنا بنتكلم عنها بيصير اسمها brae theorem brae
+
+108
+00:08:41,580 --> 00:08:46,480
+theorem لابد تحقيقها عشان اقول انه صار في عندي
+
+109
+00:08:46,480 --> 00:08:58,540
+theorem كتالي H1 and H2 and H3 implies C3 فهذه هي
+
+110
+00:08:58,540 --> 00:09:04,740
+النظرية اللي بنحكي عنها الآناللي اسمها theorem طيب
+
+111
+00:09:04,740 --> 00:09:11,660
+هذه بالنسبالها إيش؟ اللي ماتعتها؟ عشان نحقق هذه
+
+112
+00:09:11,660 --> 00:09:18,760
+لاحظوا مافيش مباشر بين مجموعة ال H's اللي عندي أو
+
+113
+00:09:18,760 --> 00:09:25,240
+ال hypothesis اللي عندي و C3 لكن C3 مربوطة بC1 و
+
+114
+00:09:25,240 --> 00:09:31,530
+اقدرنا نثبت نظريةبين مجموعة الـ H's تبعتي و C1 هذه
+
+115
+00:09:31,530 --> 00:09:37,430
+اسمها Lima بمجرد ما تحققت ف automatically ال
+
+116
+00:09:37,430 --> 00:09:42,070
+theorem اللي بنحكي عنها تتحقق فاسمها Pre theorem
+
+117
+00:09:42,070 --> 00:09:48,650
+العكس صحيح ل ال corollary ال corollary هي العكس
+
+118
+00:09:48,650 --> 00:09:53,690
+تبعنا هي العكس تبعنا فصارت بالنسبالنا هذه النظرية
+
+119
+00:09:53,690 --> 00:09:55,230
+هي corollary لهذه
+
+120
+00:09:58,010 --> 00:10:01,710
+بمجرد ما هذه تحققت اتوماتيك بقدر منها ممكن تكون
+
+121
+00:10:01,710 --> 00:10:04,070
+هذه هي النظرية اللي انا بدور عليها و بدي اثبتها
+
+122
+00:10:04,070 --> 00:10:09,070
+okay أثبتناها بس by default ممكن بالطريق كنتيجة
+
+123
+00:10:09,070 --> 00:10:15,890
+لها تتحقق نظرية أخرى فصارت corollary بالنسبة لها
+
+124
+00:10:15,890 --> 00:10:18,530
+الأولى بالنسبة للتانية لما
+
+125
+00:10:21,010 --> 00:10:25,810
+في مصطلحين واحدة نظرية سابقة للنظرية اللي بنبحث
+
+126
+00:10:25,810 --> 00:10:28,730
+فيها طبيعي لإن في نظرية أنا جاعت بحاول أثبتها أو
+
+127
+00:10:28,730 --> 00:10:34,870
+بحاول أبحث فيها إذا كان حدوثها يلزمني إني لازم
+
+128
+00:10:34,870 --> 00:10:39,830
+أثبت نظرية سابقة لها فهي لما النظرية السابقة لها
+
+129
+00:10:39,830 --> 00:10:44,450
+طيب حققناها وخلصنا بس by default أنا عارف إن مجرد
+
+130
+00:10:44,450 --> 00:10:48,530
+تحقيقها بيضمنلي حدوث إشي تانيفالاشي التاني هذا صار
+
+131
+00:10:48,530 --> 00:10:52,370
+نظرية برضه ممكن يطلق عليه نظرية لحاله خلاص بيصير
+
+132
+00:10:52,370 --> 00:10:58,150
+اسمه Corollary أو Post ما بعد النظرية ما بعد
+
+133
+00:10:58,150 --> 00:11:02,830
+النظرية فإذا ال Corollary هذه ما زهرت إلا نتيجة أن
+
+134
+00:11:02,830 --> 00:11:08,230
+ال theorem تحققت فهذه كانت ما بعدها طيب إذا لم
+
+135
+00:11:08,230 --> 00:11:13,210
+تتحقق نظرية مافيش Corollaryمش هتقدر تثبتها لإن انت
+
+136
+00:11:13,210 --> 00:11:18,450
+عشان تثبت انه فيه relation between h1, h2, h3 و c3
+
+137
+00:11:18,450 --> 00:11:23,770
+لازم تكون أثبتت أولا ان h1, h2, h3 في بينهم .. بين
+
+138
+00:11:23,770 --> 00:11:31,250
+ال c1 relation تمام؟ تمام فهي .. اه في الأخيرة لسه
+
+139
+00:11:31,250 --> 00:11:34,750
+ال conjuncture ال conjunctures مجموعة ال
+
+140
+00:11:34,750 --> 00:11:37,810
+conjunctures هذه عادة اللي احنا بنسميها الحدثاللي
+
+141
+00:11:37,810 --> 00:11:43,090
+هو بيكون عندك حالة و أنت دايما بتقول عليها true
+
+142
+00:11:43,090 --> 00:11:49,890
+لكن مافيش إثبات إلها، ماهاش إثبات زي لما تقول
+
+143
+00:11:49,890 --> 00:11:53,370
+مافيش عدد prime أكبر
+
+144
+00:11:57,000 --> 00:12:00,340
+أحنا هيك بنقول صحيح لإنه كل ما بيتقدم علم
+
+145
+00:12:00,340 --> 00:12:04,160
+الرياضيات بنجد إنه بيكتشفوا كمان عدد prime ممكن من
+
+146
+00:12:04,160 --> 00:12:07,940
+عشرين خانة و لا من خمستاشر خانة لكنه prime لا يقسم
+
+147
+00:12:07,940 --> 00:12:13,220
+على كل اللي أقل منه لكن مش جادرين نثبت إن فعلا لا
+
+148
+00:12:13,220 --> 00:12:18,440
+يوجد prime أكبر لإنه عشان تثبت هذا الكلام معناته
+
+149
+00:12:18,440 --> 00:12:22,240
+بدأت تكون وصلت لل infinity فإذن هذا حدث بالنسبالنا
+
+150
+00:12:22,240 --> 00:12:27,520
+بنعرفش حتى اللحظة إمكانية ال computers بتاعتناما
+
+151
+00:12:27,520 --> 00:12:30,420
+خدمتناش في هالجثة كل الأرقام اللي بيقدر الكمبيوتر
+
+152
+00:12:30,420 --> 00:12:36,340
+يصلها فيه دائما رقم أكبر فيه دائما رقم أكبر بس في
+
+153
+00:12:36,340 --> 00:12:40,460
+النهاية أنا عامل حسابي أنه ممكن يكون فيه أكبر منه
+
+154
+00:12:40,460 --> 00:12:44,280
+لكن الحواسيب بتاعتنا مش قادر يتصلوا فعشان هيك ال
+
+155
+00:12:44,280 --> 00:12:46,660
+conjecture تبعته هنا في الحالة هذه الحادثة تبعي
+
+156
+00:12:46,660 --> 00:12:51,900
+أنه لا يوجد عدد أولي أكبر يعني مافيش عدد أولي
+
+157
+00:12:51,900 --> 00:12:57,870
+وبعده خلاص بطلت العدد الأولي خلصت مافيشمافي حدش
+
+158
+00:12:57,870 --> 00:13:01,190
+بيقدر يقولك الكلام هذا، مافيش حد بيقدر يقولك، لكن
+
+159
+00:13:01,190 --> 00:13:04,470
+الحدث هيك بيقولنا إنه مافيش عدد أكبر، خلاص طول ما
+
+160
+00:13:04,470 --> 00:13:07,410
+أنت ماشي و الأعداد بيخترعوا أعداد جديدة و بيسموا
+
+161
+00:13:07,410 --> 00:13:12,010
+تسمية جديدة للأعداد، ممكن يظهرلنا رقم أكبر من اللي
+
+162
+00:13:12,010 --> 00:13:17,260
+احنا عارفينه أو اللي احنا موجود عندنا، تمامليش؟
+
+163
+00:13:17,260 --> 00:13:23,800
+وخصوصا إنه بالعادة في نظرية بنعمل منها creation
+
+164
+00:13:23,800 --> 00:13:29,760
+للأرقام الأولية وحتى الآن النظرية هذه صحيحة بس
+
+165
+00:13:29,760 --> 00:13:35,660
+ماقدرش أقول عليها نظرية بنسميها حدث زي العدد الأول
+
+166
+00:13:35,660 --> 00:13:38,880
+يبقى باعتبار أنه إجت سرتها ده إن خليني أقولك إن
+
+167
+00:13:38,880 --> 00:13:42,440
+العدد الأولي بتبدأ مثلا من اتنين شك تلاتة إيش
+
+168
+00:13:42,440 --> 00:13:48,580
+بعدها؟ خمسة سبعةلأ تصحى تجبه .. لأ تجبه لش .. 11
+
+169
+00:13:48,580 --> 00:13:51,980
+and so on مبدايا خليني على جد تهدي بس عشان أوريك
+
+170
+00:13:51,980 --> 00:13:58,680
+ال relation اللي حطوها و بقى اسمها conjunctures او
+
+171
+00:13:58,680 --> 00:14:03,960
+conjuncture بمعنى حدث هل في رقم أكبر بيعرفوش لو
+
+172
+00:14:03,960 --> 00:14:10,220
+أخدنا بتبدأ دايما من البداية لو أخدت الأعداد و ال
+
+173
+00:14:10,220 --> 00:14:13,900
+primes اللي موجودة زائد واحد او ضربهم
+
+174
+00:14:16,570 --> 00:14:20,570
+multiplication of primes زائد واحد يعني الاتنين
+
+175
+00:14:20,570 --> 00:14:26,530
+مثلا لحالها زائد واحد تلاتة التلاتة prime طيب
+
+176
+00:14:26,530 --> 00:14:33,330
+اتنين في تلاتة ستة زائد واحد السبعة prime اتنين في
+
+177
+00:14:33,330 --> 00:14:40,110
+تلاتة ستة في خمسة تلاتين زائد واحد الواحد تلاتين
+
+178
+00:14:40,110 --> 00:14:46,940
+prime and so on and so on طيبهذا مبني .. اتفضل بجد
+
+179
+00:14:46,940 --> 00:14:50,640
+ا دكتور يقول ال truth value بتاعها true force لكن
+
+180
+00:14:50,640 --> 00:14:55,040
+بدون اثبات ولا .. بدون اثبات هو حدث حتى لان محدش
+
+181
+00:14:55,040 --> 00:14:58,520
+اثبت عكسه يعني ايه له القيمة يعني انا .. لاحظ هي
+
+182
+00:14:58,520 --> 00:15:02,740
+اني قاعد بقولك ان النظرية هذه صحيحة اثبتلي عكسها
+
+183
+00:15:02,740 --> 00:15:08,740
+مالهاش مالهاش لان هذه مبنية على infinity عكس الدول
+
+184
+00:15:08,740 --> 00:15:12,960
+فلا انت بدك .. لأ انت مش قادر تقول صح ولا غلط اصلا
+
+185
+00:15:13,750 --> 00:15:16,510
+لأن عشان تقول صح ولا غلط لازم تكون عملت check على
+
+186
+00:15:16,510 --> 00:15:22,370
+كل الأرقام صح؟ طب لا إيه انت هتضلك تعمل يعني إيه؟
+
+187
+00:15:22,370 --> 00:15:25,910
+لأ انت هتضلك ماشي و بعدين كل رقم هتقعد تضرب
+
+188
+00:15:25,910 --> 00:15:30,130
+الأرقام في طلعنا 31 مش بدك تعمل test عليه عشان
+
+189
+00:15:30,130 --> 00:15:37,250
+تتأكد طيب وصلنا في الآخر لأرقام بال 11 أو 15 خانة
+
+190
+00:15:37,250 --> 00:15:40,690
+بدك تقوم تعمل check على كل أرقام اللي أقل منه أن
+
+191
+00:15:40,690 --> 00:15:45,360
+هي لا يقبل قسم عليهافالعملية مرهقة حتى اللحظة
+
+192
+00:15:45,360 --> 00:15:48,980
+ماحدش جادر يقولك صح ولا غلط أما لعندي اللحظة أه
+
+193
+00:15:48,980 --> 00:15:54,420
+تطبيقها صح هل ممكن تكون بالصدفة لعند مجموعة
+
+194
+00:15:54,420 --> 00:15:58,980
+الأرقام لعند أقل يعني أقل من رقم معين بعد هت
+
+195
+00:15:58,980 --> 00:16:04,600
+نتفاجأ أنه لا ولا مش صحيحة هي حدث حتى الآن كلامها
+
+196
+00:16:04,600 --> 00:16:09,870
+صح لكن ماحدش أثبتهكل ما في الموضوع وحط الاجال لو
+
+197
+00:16:09,870 --> 00:16:12,730
+عملته كذا هيطلع الـ prime طب ماشي اثبتلنا الكلام
+
+198
+00:16:12,730 --> 00:16:17,990
+هذا جالك بكل بساطة انا بقولك هيك انت اثبت عكسه بس
+
+199
+00:16:17,990 --> 00:16:23,470
+اما انا مش قادر اثبتلكيا بشكل واقعي ان ليش انت
+
+200
+00:16:23,470 --> 00:16:26,190
+اثبت عكسه اذا بتقدر بس وضلت على هيك هي مش دايما
+
+201
+00:16:26,190 --> 00:16:30,270
+صحيح لأ احنا حتى لو مش دايما صحيح كان بطلت نظرية
+
+202
+00:16:30,270 --> 00:16:34,940
+اصلا كان وجفنا كان جولنا لأ هذا غلطاحنا مابعتبرها
+
+203
+00:16:34,940 --> 00:16:39,200
+دائما صحيح الحدث هو relation بعتبرها دائما صحيحة
+
+204
+00:16:39,200 --> 00:16:45,440
+بس مالهاش formula واضحة logically form مالهاش يعني
+
+205
+00:16:45,440 --> 00:16:49,740
+ان اقول والله في استدلال بقدر أثبتها كنظرية اثبات
+
+206
+00:16:49,740 --> 00:16:54,560
+كنظرية مافيش فهي نظرية وبس احنا عارفين موضوعنا
+
+207
+00:16:54,560 --> 00:16:58,020
+اليوم هو على ال proving أصلا مش على النظرية نفسها
+
+208
+00:16:58,020 --> 00:17:04,940
+موضوعنا اليوم للإثبات أن أثبت النظريةفنظرية زي هذه
+
+209
+00:17:04,940 --> 00:17:08,980
+ماحدش قادر اثبتها في نفس الوقت ماحدش قادر ينفيها
+
+210
+00:17:08,980 --> 00:17:14,040
+تمام فهي بالنسبالنا لموضوعنا اليوم اللي هو ال
+
+211
+00:17:14,040 --> 00:17:19,680
+proving عشان نعمل اثبات مش قادر اثبتها فبسميها
+
+212
+00:17:19,680 --> 00:17:25,200
+conjecture او حدث حدث اشي بديهي و خلاص حدث تمام
+
+213
+00:17:25,200 --> 00:17:30,420
+okay اتفقنا زي ما قلنا ال inference rules بشكل
+
+214
+00:17:30,420 --> 00:17:34,890
+أساسي هي عبارة عن مجموعة of antecedentsإذا تحققت
+
+215
+00:17:34,890 --> 00:17:40,790
+فيتبع ذلك بالتالي مباشرة إن ال consequence هيتحقق
+
+216
+00:17:40,790 --> 00:17:46,130
+أو ال conclusion مجموعة premises إذا كلها تحققت
+
+217
+00:17:46,130 --> 00:17:50,490
+إيش يعني كلها تحققت؟ معناته antecedent one and
+
+218
+00:17:50,490 --> 00:17:55,210
+antecedent two and antecedent three and so on and
+
+219
+00:17:55,210 --> 00:17:59,550
+so on كلهم إذا تحققوا معنى ذلك إن ال consequence
+
+220
+00:17:59,550 --> 00:18:06,080
+أو ال conclusion is true هيتحقق معاهاOkay زي ما
+
+221
+00:18:06,080 --> 00:18:10,060
+قلنا هي النظرية بالبساطة نقدر نترجمها بالشكل اللي
+
+222
+00:18:10,060 --> 00:18:15,700
+حنا شايفينه الان طيب إذا فعلا إذا فعلا عملنا هذا
+
+223
+00:18:15,700 --> 00:18:21,420
+الكلام فمعنى ذلك لاحظوا أن ال antecedent one,
+
+224
+00:18:22,000 --> 00:18:25,940
+antecedent two and antecedent two and antecedent
+
+225
+00:18:25,940 --> 00:18:32,300
+three and four and so on to end مثلاإذا كل هدولة
+
+226
+00:18:32,300 --> 00:18:38,960
+is true و أخدنا implication .. implication ل ال
+
+227
+00:18:38,960 --> 00:18:42,000
+conclusion أو ال consequent فإذا لازم تطلع
+
+228
+00:18:42,000 --> 00:18:49,620
+tautology لازم يطلع tautology بمعنى إنه H1, H2, H3
+
+229
+00:18:49,620 --> 00:18:57,010
+employees C1 is trueليش؟ لأن هذه أصلا rule of
+
+230
+00:18:57,010 --> 00:19:01,510
+inference أو هي فعلا مستدل عليها كنظرية معنى ذلك
+
+231
+00:19:01,510 --> 00:19:06,410
+إذا تحقق الشمال لابد هيتحقق اليمين وإذا لم يتحقق
+
+232
+00:19:06,410 --> 00:19:11,870
+الشمال فاليمين ماتحققش وهذا معناه إن ال relation
+
+233
+00:19:11,870 --> 00:19:16,630
+بهذا الشكل هتطلع دائما trueالأصل إنها دائما true
+
+234
+00:19:16,630 --> 00:19:21,250
+وإلا بطلت rule إذا مش دائما true معناته بطلت rule
+
+235
+00:19:21,250 --> 00:19:24,470
+مش هي بقدرش أستخدمها ك rule ما بقدر أقولك أحفظها
+
+236
+00:19:24,470 --> 00:19:27,790
+زي ما هي هيك ليش؟ لأنه مش دائما true لأ هي دائما
+
+237
+00:19:27,790 --> 00:19:33,430
+true وعشان هي أصبحت بالنسبالي theorem أو rule مدام
+
+238
+00:19:33,430 --> 00:19:37,660
+أصبحت rule فهي tautologyTautology اتكلمنا عن ال ..
+
+239
+00:19:37,660 --> 00:19:41,980
+عن ال .. Tautology المصطلح دائما صحيحة وإلا ماحد
+
+240
+00:19:41,980 --> 00:19:45,540
+مابقدر أقولك لأ هي أحفظها أو هي rule لأ مش بتبطر
+
+241
+00:19:45,540 --> 00:19:48,500
+rule في الحالة دي فإذا ال relation الأخيرة أكيد
+
+242
+00:19:48,500 --> 00:19:55,660
+لازم تظل دائما Tautology دائما صح بالمناسبة
+
+243
+00:19:55,660 --> 00:19:59,840
+الأخيرة دائما صح هذا لا يعني أن لو كل ال
+
+244
+00:19:59,840 --> 00:20:04,140
+antecedents تحققلم يتحقق يعني واحدة منهم لم تتحقق
+
+245
+00:20:04,140 --> 00:20:08,540
+ان ال .. ال .. ال consequent مش هيتحقق، دي ربالكو،
+
+246
+00:20:08,540 --> 00:20:12,080
+احنا إيش اللي عاملينه؟ عاملين implication، دايما
+
+247
+00:20:12,080 --> 00:20:17,160
+في بالك مين؟الـ truth table تبع ال implication و
+
+248
+00:20:17,160 --> 00:20:20,480
+يبدو ان احنا لازم نحطه ده على جنب لأنه من الآن
+
+249
+00:20:20,480 --> 00:20:24,660
+هنبدأ هو شغلنا الشاغل بمعنى انه اقول هذا صح ولا
+
+250
+00:20:24,660 --> 00:20:29,580
+غلط بناء عليه و ليس بناء على تخيلك المنطقي اللي
+
+251
+00:20:29,580 --> 00:20:32,840
+انت بتفترض انه منطقي بيضا ما هو مش منطقي فهنا بدنا
+
+252
+00:20:32,840 --> 00:20:38,540
+نحطها هي P و Q نكتبه على جنب و ال implicationfalse
+
+253
+00:20:38,540 --> 00:20:43,380
+false خلّيها دايما على جنب ال true طيب false true
+
+254
+00:20:43,380 --> 00:20:47,280
+true بالظبط هي هذه حالة من الحلات بقولك مش مضرور
+
+255
+00:20:47,280 --> 00:20:50,660
+كل ال antecedents يكونوا صح لكن رغم ذلك ال
+
+256
+00:20:50,660 --> 00:20:56,860
+consequence صح هتقول true طيب true false الحالة
+
+257
+00:20:56,860 --> 00:21:01,140
+الوحيدة اللي مستثنى و true true is true خلّي هذه
+
+258
+00:21:01,140 --> 00:21:04,060
+على جنب بدنا عشان نمحاها طول ما احنا ماشيين في
+
+259
+00:21:04,060 --> 00:21:05,720
+شغلنا لأنه هنحتاجها كتير
+
+260
+00:21:08,530 --> 00:21:14,570
+بعض الاستدلالات ناخد بعض ال inference rules بعض
+
+261
+00:21:14,570 --> 00:21:17,930
+الاستدلالات المنطقية اللى ممكن نبني عليها شغلنا
+
+262
+00:21:17,930 --> 00:21:25,690
+لإثبات نظريات بعد هيك لو كانت P is true معناه ذلك
+
+263
+00:21:25,690 --> 00:21:32,870
+انه في or او disjunction in a propositionis true
+
+264
+00:21:32,870 --> 00:21:37,530
+بغض النظر Q الشيء بغض النظر إيش Q حاجة بسيطة جدا
+
+265
+00:21:37,530 --> 00:21:41,850
+صح لكن منها بنبني استدلالنا على النظريات الكبيرة
+
+266
+00:21:41,850 --> 00:21:45,750
+الضخمة في حاجات صغيرة زي هيك في حاجات صغيرة زي هيك
+
+267
+00:21:45,750 --> 00:21:52,330
+طيب إذا كانت P and Q is true معناه ذلك أن P is
+
+268
+00:21:52,330 --> 00:22:01,670
+true و Q is true صح تمام P is trueلحالها ال Q is
+
+269
+00:22:01,670 --> 00:22:04,430
+true معناه ذلك ال conjunction تبعهم is true
+
+270
+00:22:04,430 --> 00:22:08,410
+ملاحظين كده بسيطة مفاهيمنا بس هاد بنبني عليها شغل
+
+271
+00:22:08,410 --> 00:22:15,790
+كتير كبير من حاجات بسيطة فمبدأيا عملية الإثبات
+
+272
+00:22:15,790 --> 00:22:22,050
+بسيطة مبنية على حاجات biologic انت عارفها لكن خلاص
+
+273
+00:22:22,050 --> 00:22:26,620
+ماجدتش على بالك لحظة ما بدت تعمل إثباتكطيب إذا
+
+274
+00:22:26,620 --> 00:22:31,140
+كانت P و هنا بدنا عشان هي كتبتلكوا هذه إذا كانت P
+
+275
+00:22:31,140 --> 00:22:38,040
+is true لاحظ و P implies Q is true يعني هذه true
+
+276
+00:22:38,040 --> 00:22:45,120
+وهذه true طلعليها على الجدول ال Q لابد تطلع true
+
+277
+00:22:45,120 --> 00:22:53,590
+لاحظ العمود الأول و التالت في الجدول true trueوين
+
+278
+00:22:53,590 --> 00:23:00,650
+فيه بيكونوا true true؟ فش للأخيرة صح؟ فإذا بنتكلم
+
+279
+00:23:00,650 --> 00:23:10,310
+عن q لازم تطلع true okay طيب هذه اللي هي ال
+
+280
+00:23:10,310 --> 00:23:13,590
+affirming أو التأكيد affirming اللي هي التأكيد
+
+281
+00:23:13,590 --> 00:23:20,530
+لأنه أكدنا قيمة q طيب في الdenying او الانكار
+
+282
+00:23:20,530 --> 00:23:25,530
+الانكار اني انكر قيمة او اقول false ل P ان هي ال
+
+283
+00:23:25,530 --> 00:23:29,330
+false هو التأكيد تبعها لو كانت negation ال Q is
+
+284
+00:23:29,330 --> 00:23:34,530
+true يعني ال Q false طيب و ال implication is true
+
+285
+00:23:34,530 --> 00:23:40,170
+برضه تطلع هيك على ال column التاني و التالت ال
+
+286
+00:23:40,170 --> 00:23:45,850
+column التاني لازم يكون false و التالت true ايه
+
+287
+00:23:45,850 --> 00:23:52,000
+انت بتحقق هذا الكلام؟فقط فإذا هذا بيأكد أن P is
+
+288
+00:23:52,000 --> 00:23:58,740
+false يعني negation P هي ال true negation P تمام
+
+289
+00:23:58,740 --> 00:24:02,040
+عشان كنت قلتلكوا هذا بدنا .. بدنا .. خلاص مافيش
+
+290
+00:24:02,040 --> 00:24:06,440
+مجال هذا معظم المصاق مبني على الجدول هذا معظم
+
+291
+00:24:06,440 --> 00:24:09,460
+مصاقنا مبني على الجدول هذا تمام فإذا حتى الآن
+
+292
+00:24:09,460 --> 00:24:13,320
+استدلالات بسيطة جدا استدلالات بسيطة جدا طيب كمان
+
+293
+00:24:13,320 --> 00:24:21,320
+استدلالإذا كانت P implies Q is true and قلنا مدام
+
+294
+00:24:21,320 --> 00:24:26,740
+الاتنين ال premises معناته and بينهم Q implies R
+
+295
+00:24:26,740 --> 00:24:34,300
+is true فهذا بضمن لمدام الاتنتين هدول صحيحين is
+
+296
+00:24:34,300 --> 00:24:42,960
+true معناته إذا كانت P is true إذا R is true تمام؟
+
+297
+00:24:42,960 --> 00:24:47,490
+تمامالسيلوجيزم هذه هذه نظرية السيلوجيزم او
+
+298
+00:24:47,490 --> 00:24:53,290
+المنطقية الاستدالة المنطقية او الاسترشادي مدام P
+
+299
+00:24:53,290 --> 00:24:58,190
+تضمن ل Q و Q تضمن ل R فإذا من الأساس P تضمن ل R
+
+300
+00:24:58,190 --> 00:25:04,810
+تضمن R كويس كمان واحدة P this junction Q is true
+
+301
+00:25:04,810 --> 00:25:12,830
+تمام واحدة منهم falseفأكيد التانية حتما .. حتما is
+
+302
+00:25:12,830 --> 00:25:18,550
+true صح؟ أكيد فإذا negation P is true يعني Q is
+
+303
+00:25:18,550 --> 00:25:24,610
+true حتى الآن أنا عارف بسيطة جدا وسهلة جدا ومع ذلك
+
+304
+00:25:24,610 --> 00:25:29,310
+ماشي معاك بشويش لإنه بعدين هنستخدمها في أكبر من
+
+305
+00:25:29,310 --> 00:25:33,840
+هيك تمام؟كمان revision سريع عليها أخدنا معظم
+
+306
+00:25:33,840 --> 00:25:37,760
+الحالات هنا إذا كانت P is true معناه ذلك أن P or
+
+307
+00:25:37,760 --> 00:25:43,400
+أي شيء هتطلع برضه true P and Q is true معناته كل
+
+308
+00:25:43,400 --> 00:25:49,480
+كل من هما لحاله منفرد هو is true تمام P true Q
+
+309
+00:25:49,480 --> 00:25:52,120
+true فإذا الإتنين مع بعض conjunction او
+
+310
+00:25:52,120 --> 00:25:58,190
+conjunction هي trueOkay أخدنا برضه ال denying إذا
+
+311
+00:25:58,190 --> 00:26:03,090
+كانت negation Q هي ال true و ال implication Q فإذا
+
+312
+00:26:03,090 --> 00:26:07,830
+negation P هي ال true بعدين أخدنا ال .. ال fearing
+
+313
+00:26:07,830 --> 00:26:12,570
+اللي هي ال .. ال .. ال syllogism اللي هي P
+
+314
+00:26:13,540 --> 00:26:17,860
+employees Q is true و Q employees R is true فإذا
+
+315
+00:26:17,860 --> 00:26:23,020
+automatically by default أو by logic P employees R
+
+316
+00:26:23,020 --> 00:26:30,480
+برضه is true جيد فإذا الأن مبدأيا خلصنا مجموعة
+
+317
+00:26:30,480 --> 00:26:35,360
+استدلالات هنشتغل فيها في الأمثلة اللي جاينة بس
+
+318
+00:26:35,360 --> 00:26:42,130
+بدنا نعرف أنه الأن كل اللي واضح لناإنه ال proof
+
+319
+00:26:42,130 --> 00:26:47,210
+نفسه ك rule هو المفروض إنه relation .. relation ال
+
+320
+00:26:47,210 --> 00:26:51,430
+proof هو relation يعني demonstrates بوضّح لنا إذا
+
+321
+00:26:51,430 --> 00:26:55,370
+كانت مجموعة ال premises اللي سمنها antecedents تو
+
+322
+00:26:55,370 --> 00:27:00,210
+مجموعة ال premises المعطيات كلهم is true كل واحدة
+
+323
+00:27:00,210 --> 00:27:04,790
+لحالها هي true فإذا كلهم مجموعة are true كلهم معنى
+
+324
+00:27:04,790 --> 00:27:09,860
+ذلك إن ال conclusion C is trueفإذن هذه بشكل أساسي
+
+325
+00:27:09,860 --> 00:27:13,980
+النظرية العامة لأي فكرة إثبات بدك تبدأ بدك تشوف
+
+326
+00:27:13,980 --> 00:27:16,600
+مجموعة ال premises إيش المعطيات وهذه اللي كنتوا
+
+327
+00:27:16,600 --> 00:27:19,320
+تاخدوها في كل إثباتها اللي كانت سابقة في أي مرحلة
+
+328
+00:27:19,320 --> 00:27:22,160
+من مراحل تعليمكوا كنتوا إيش بتدوره على المعطيات في
+
+329
+00:27:22,160 --> 00:27:27,020
+البداية ومن المعطيات بتحاولوا تروحوا لل conclusion
+
+330
+00:27:27,020 --> 00:27:34,210
+أو للاستنتاج للاستنتاج فإذن أي proof هوهي
+
+331
+00:27:34,210 --> 00:27:37,530
+استراتيجيته الأساسية مش هنطلع عن نفس الاستراتيجية
+
+332
+00:27:37,530 --> 00:27:44,410
+هي هي okay ناخد مثال هالوقت it's not sunny and
+
+333
+00:27:44,410 --> 00:27:52,150
+it's cold هي الدنيا مش مشمسة والجو بارد هي نعبة
+
+334
+00:27:52,150 --> 00:27:57,970
+هذه مجموعة premises خلي هذه بدنياها أو خليني نقول
+
+335
+00:27:57,970 --> 00:28:03,230
+على الأقل انتوا هتحتاجوهاو انا بشرح دايما اذا
+
+336
+00:28:03,230 --> 00:28:08,930
+التبس عندك هو صح و ارجعله ساحسبلك اياه هنا طبعا
+
+337
+00:28:08,930 --> 00:28:12,970
+فهذا مبدأيا هاي اول مجموعة premises لو في عندى
+
+338
+00:28:12,970 --> 00:28:17,710
+premises واحدة اتنين تلاتة اربعة مطلوب بدنا نثبت
+
+339
+00:28:17,710 --> 00:28:21,490
+ال conclusion الأخيرة مطلوب نثبت ال conclusion
+
+340
+00:28:21,490 --> 00:28:25,670
+الأخيرة بشوية خطوات الخطوات كلها لن تخرج عن مجموعة
+
+341
+00:28:25,670 --> 00:28:30,980
+ال rule of inference او ال ruleال rules اللي
+
+342
+00:28:30,980 --> 00:28:35,660
+أخدناهم قبل شوية فقط لا أكثر ولا أقل هيجنولك طريقة
+
+343
+00:28:35,660 --> 00:28:41,720
+نظرية واضحة و متسلسلة خلينا نبدأ الأولى it's not
+
+344
+00:28:41,720 --> 00:28:46,260
+sunny معناه ذلك انه معطى انه فعليا فش شمس اليوم و
+
+345
+00:28:46,260 --> 00:28:52,900
+كذلك and cold الجو فيه برد we will swim only if
+
+346
+00:28:52,900 --> 00:28:58,480
+it's sunny احنا هنسبح اذا كانت فقط sunnyإذا كانت
+
+347
+00:28:58,480 --> 00:29:02,880
+الدنيا مشمسة طيب if we don't swim إذا احنا
+
+348
+00:29:02,880 --> 00:29:06,420
+ماسبحناش إذا we will play volley هنلعب معاناة و
+
+349
+00:29:06,420 --> 00:29:09,840
+مافيش داعي نسبح على البحر خليني على الشط نلعب كرة
+
+350
+00:29:09,840 --> 00:29:14,740
+طائرة نحطها الشبك و نلعب طائرة و خلاص طيب if we
+
+351
+00:29:14,740 --> 00:29:19,960
+play volley then we will be home early معناته
+
+352
+00:29:19,960 --> 00:29:23,660
+هنروح بدري هنروح بدري بدنا نثبت أنه احنا فعلا
+
+353
+00:29:23,660 --> 00:29:27,220
+هنروح بدريهي طبعا بيولوجيا منطقية شايفينها انتوا
+
+354
+00:29:27,220 --> 00:29:30,820
+لحالها هي باينة هي باينة انا عارف ان هي باينة بس
+
+355
+00:29:30,820 --> 00:29:34,600
+الهدف الرئيسي منها كيف استخدام ال rules عليها بس
+
+356
+00:29:34,600 --> 00:29:41,060
+الان اول شغلة بدنا نعمل ال notationأول حاجة
+
+357
+00:29:41,060 --> 00:29:45,060
+أخدناها بتذاكرين في أول حصة في المصاق قولنا إن
+
+358
+00:29:45,060 --> 00:29:47,340
+الخطوات بتاعتنا بدنا نفهم ال language concise
+
+359
+00:29:47,340 --> 00:29:50,840
+language مش هيك و بعدين بدنا نعملها نعمل notations
+
+360
+00:29:50,840 --> 00:29:54,480
+لإلها و بعدين نبدأ في الاستدلالات بتاعتها أو نبدأ
+
+361
+00:29:54,480 --> 00:29:56,900
+في ال logic اللي إحنا شغالين عليه ك mathematical
+
+362
+00:29:56,900 --> 00:30:01,620
+logic فإحنا لان في نقطة ال notations بدنا نختصر
+
+363
+00:30:01,620 --> 00:30:04,660
+اللغة مش معجولة بدي أقعد كل شوية أكتب الجملة كاملة
+
+364
+00:30:04,660 --> 00:30:07,960
+فبدنا نختصرها نقول sunny خلاص هذا بدي أفترضها كإني
+
+365
+00:30:07,960 --> 00:30:13,050
+بقول PP it's sunny لأ بدي أسميها sunny و خلاص
+
+366
+00:30:13,050 --> 00:30:15,430
+what's cool فبتعامل معاها إنه هذي هيك على بعضها
+
+367
+00:30:15,430 --> 00:30:22,220
+أصبحت إيش هذي المتغير هذي Pال .. ال proposition
+
+368
+00:30:22,220 --> 00:30:26,660
+هذه ال proposition تمام اللي هي it's sunny طيب
+
+369
+00:30:26,660 --> 00:30:31,340
+cold خلصنا swim اختصرناهم بس عشان نستخدم ال
+
+370
+00:30:31,340 --> 00:30:34,620
+notations هذه كمختصرات و خلصناها اللي كان ال
+
+371
+00:30:34,620 --> 00:30:37,560
+premises اللي كانت موجودة بدنا نحولها ل
+
+372
+00:30:37,560 --> 00:30:43,120
+mathematical forms عشان نبدأ نحط عليها ال rules
+
+373
+00:30:43,120 --> 00:30:46,680
+اللي اتكلمنا عنها قبل شوية تمام فإذا أول rule كانت
+
+374
+00:30:46,680 --> 00:30:52,550
+إيش متذكرين it's not sunny and it's coldnegation
+
+375
+00:30:52,550 --> 00:31:00,890
+sunny and cold تمام التانية swim if only if sunny
+
+376
+00:31:00,890 --> 00:31:05,930
+وهذه واحدة لو رجعتوا لمحاضرة ال implication و
+
+377
+00:31:05,930 --> 00:31:10,170
+حطيتكم مجموعة forms كانت if في الحالة هذه اللي هي
+
+378
+00:31:10,170 --> 00:31:16,170
+only if only if معناته اللي في الأول هي ال P و في
+
+379
+00:31:16,170 --> 00:31:21,920
+ال A و بعدها ال Qده و متذكرين لإن only هذه هتنفيل
+
+380
+00:31:21,920 --> 00:31:28,300
+الحالة هذه فمعنى ذلك أنه ماينفعش تفهموها إنها
+
+381
+00:31:28,300 --> 00:31:32,860
+معكوسة هذه يمكن واحدة من الحالات اللي إذا مادجتش
+
+382
+00:31:32,860 --> 00:31:36,940
+كويس فيها ك language ممكن تتخربط فكتير كويس إنك
+
+383
+00:31:36,940 --> 00:31:40,460
+ترجعوا لمحاضرة ال implication و تشوف مجموعة ال
+
+384
+00:31:40,460 --> 00:31:46,300
+forms وهذه تحديدا اتركز فيها كويس لإن by logic
+
+385
+00:31:47,260 --> 00:31:51,180
+المنطق ممكن الكل يفهمها هنا لاحظلي اجربها كمان مرة
+
+386
+00:31:51,180 --> 00:31:54,540
+هتقول
+
+387
+00:31:54,540 --> 00:32:02,440
+يا ايه if معناته if sunny then we will swim غلط
+
+388
+00:32:02,440 --> 00:32:12,740
+غلط هيكون غلط بالظبط only هذه هتنفيلك حالة ال
+
+389
+00:32:12,740 --> 00:32:13,460
+false هنا
+
+390
+00:32:16,540 --> 00:32:20,660
+هتنفي حالة ال false اللي هنا انه طب لو false ال
+
+391
+00:32:20,660 --> 00:32:23,580
+conclusion ممكن يكون true لأ هنا ربطلك إياهم،
+
+392
+00:32:23,580 --> 00:32:27,540
+بينفعش، بالظبط، بالظبط، فإذا أنتم أخدين بالكم إن
+
+393
+00:32:27,540 --> 00:32:30,460
+الجزئية هذه خلاص، أحنا ماشيين، أنا حاببت بس
+
+394
+00:32:30,460 --> 00:32:33,260
+أوضحلكوا إياها، مش الكل ممكن ناخد باله، فاخدوا
+
+395
+00:32:33,260 --> 00:32:38,840
+بالكم إنه التركيبة هنا، هذه هي ال P وهذه هي ال Q
+
+396
+00:32:38,840 --> 00:32:42,360
+اه
+
+397
+00:32:42,360 --> 00:32:45,120
+if and only if هذا by conditional لسه، هذه ايش؟
+
+398
+00:32:46,020 --> 00:32:50,920
+only if بدون ال F الأولى، لاحظ، هذه حالة و هذه
+
+399
+00:32:50,920 --> 00:32:56,840
+حالة و بدون only حالة تالتة كمان، يعني لاحظ هنا
+
+400
+00:32:56,840 --> 00:33:07,740
+بدون هذه، هذه P وهذه Qطيب الان لأ only بطلت هيك
+
+401
+00:33:07,740 --> 00:33:11,900
+صارت هذه هي ال P و هذه هي ال Q اخدوا بالكوا مهم
+
+402
+00:33:11,900 --> 00:33:14,000
+جدا ان تكونوا عارفين مين ال P و من ال Q لأنه بده
+
+403
+00:33:14,000 --> 00:33:17,340
+يتغير مع ال two columns الأول و التاني هذا معناته
+
+404
+00:33:17,340 --> 00:33:23,580
+ان النتيجة كلها تتغير معاكم طيب لكن لو مولنا if
+
+405
+00:33:23,580 --> 00:33:32,060
+andonly if لأ أصلح أصبحت كلها مختلفة ك operator ال
+
+406
+00:33:32,060 --> 00:33:36,020
+operator كله بطل بطل ال if then أصلا صارت حاجة
+
+407
+00:33:36,020 --> 00:33:42,200
+تاني مختلفة تمام okay خلاص
+
+408
+00:33:42,200 --> 00:33:44,940
+هي ده اللي كنت بدأ أوضحها أركز عليها فصارت هنا
+
+409
+00:33:44,940 --> 00:33:50,240
+swim employs sunnyو بعد هيك خلاص اذا احنا ماسبحناش
+
+410
+00:33:50,240 --> 00:33:53,880
+اذا هنلعب volley ماسبحناش هنا negation swim
+
+411
+00:33:53,880 --> 00:33:57,800
+negation swim اذا volley طيب و اذا احنا volley اذا
+
+412
+00:33:57,800 --> 00:34:02,660
+early هنروح بدري طيب بسيط اذا كان هذه الموقعات
+
+413
+00:34:02,660 --> 00:34:06,800
+نبدأ فيهم واحدة واحدة اول موقع هي ال premise
+
+414
+00:34:06,800 --> 00:34:12,060
+number one negation sunny and cold معناته هذه
+
+415
+00:34:12,060 --> 00:34:17,400
+لحالها بحثتها true وهذه لحالها trueخلاص معناته هي
+
+416
+00:34:17,400 --> 00:34:23,600
+فعلا not sunny فإذا not sunny لحالها is true طيب
+
+417
+00:34:23,600 --> 00:34:29,560
+في اندرامس تانية كانت بتقول ليه swim if sunny only
+
+418
+00:34:29,560 --> 00:34:33,660
+if sunny تمام فإذا كانت swim employees sunny طيب
+
+419
+00:34:33,660 --> 00:34:39,200
+لاحظوا هنا negation sunny الحالة
+
+420
+00:34:39,200 --> 00:34:44,480
+بتاعة ال denying او الانكار معناه ذلك انهnegation
+
+421
+00:34:44,480 --> 00:34:47,960
+swim هتطلع negation swim هاي واحدة من ال rules
+
+422
+00:34:47,960 --> 00:34:50,500
+اللي كنا بتكلم عنها واحدة من ال rules اللي حكينا
+
+423
+00:34:50,500 --> 00:34:55,200
+عنهم قبل شوية فإذا negation swim is true طيب برضه
+
+424
+00:34:55,200 --> 00:34:57,560
+في عندى premise رقم تلاتة كانت بتقول ال negation
+
+425
+00:34:57,560 --> 00:35:07,420
+swim هي بيضمن ليه او predicate volley تمام هنا
+
+426
+00:35:07,420 --> 00:35:14,210
+التأكيد لإن فعلا هذه true هذه trueفإذا هذه true
+
+427
+00:35:14,210 --> 00:35:19,930
+لاحظته ال negation swim هي اللي true مش ال swim هي
+
+428
+00:35:19,930 --> 00:35:24,410
+اللي true صح فإذا هذه كاملة هيك على بعضها is true
+
+429
+00:35:24,410 --> 00:35:27,810
+طيب ما هذه هي كاملة بال negation جاي نازلة كاملة
+
+430
+00:35:27,810 --> 00:35:31,550
+على بعضها لو مافيش كنا نقولك اه دي false لكن كاملة
+
+431
+00:35:31,550 --> 00:35:34,530
+زيها زي باقا هيهم هذه true فإذا هذه كاملة على
+
+432
+00:35:34,530 --> 00:35:39,300
+بعضها negation swim is trueو هذا بضمنلي إذا كان ال
+
+433
+00:35:39,300 --> 00:35:43,180
+relation بتاعة ال implication كاملة هي true أكيد
+
+434
+00:35:43,180 --> 00:35:49,300
+معناته ال Q بتاعتها برضه true تمام volley is true
+
+435
+00:35:49,300 --> 00:35:52,980
+استنتجناها طيب في أن دي في الآخر كان آخر premise
+
+436
+00:35:52,980 --> 00:35:57,540
+موجودة أو معضة موجود volley إذا برضه نفس قانون
+
+437
+00:35:57,540 --> 00:36:02,640
+اللي جابلها اللي هو التأكيد ال what is affirming
+
+438
+00:36:03,440 --> 00:36:07,860
+firming خلاص مدام true و اللي true employees ال
+
+439
+00:36:07,860 --> 00:36:11,300
+true كلها على بعض true فإذا التاني لاجد تكون true
+
+440
+00:36:11,300 --> 00:36:15,560
+خلاص فإذا early وهذا معناه أننا فعلا هنروح بدري
+
+441
+00:36:15,560 --> 00:36:19,400
+معناه هنروح بدري بس كلها استدلالناها مش هي
+
+442
+00:36:19,400 --> 00:36:24,000
+biological فروحنا للحدث احنا الآن عارفين انه okay
+
+443
+00:36:24,000 --> 00:36:30,250
+باينة من شكلها انه هنروح بدري بس بدنانرتبها بشكل
+
+444
+00:36:30,250 --> 00:36:34,530
+رياضي و نثبتها واقعيا بشكل رياضي حتى لو كانت very
+
+445
+00:36:34,530 --> 00:36:40,570
+modest الاثبات المهم انك تثبتها okay نصل لحاجة
+
+446
+00:36:40,570 --> 00:36:44,510
+مهمة هي ال rules او ال inference rules لل
+
+447
+00:36:44,510 --> 00:36:48,790
+quantifiers ليش؟ لل quantifiers في عندي مجموعة
+
+448
+00:36:48,790 --> 00:36:54,150
+quantifiers أخدناهم المرة الماضية كان في عنديإذا
+
+449
+00:36:54,150 --> 00:36:56,850
+متذكرين ال for all و there exist طب هدول لما
+
+450
+00:36:56,850 --> 00:36:59,730
+يكونوا موجودين هل فيهم استدلالات؟ أه فيهم
+
+451
+00:36:59,730 --> 00:37:05,410
+استدلالات بقدر استدل منهم على بعض الأمور زي if for
+
+452
+00:37:05,410 --> 00:37:11,070
+all x P of X is true معناته كل عنصر داخل ال
+
+453
+00:37:11,070 --> 00:37:15,170
+universe of discourse تاعة X هو true صح معناته دلك
+
+454
+00:37:15,170 --> 00:37:18,530
+أن P of O و O هذا أي واحد داخل ال universe of
+
+455
+00:37:18,530 --> 00:37:22,590
+discourseالتالة المنطقية و مافيها غلبة هذه .. هذه
+
+456
+00:37:22,590 --> 00:37:27,570
+مافيها غلبة universal instant .. instant ..
+
+457
+00:37:27,570 --> 00:37:33,170
+instantational كويس فإذا أي واحدة هي true خلصنا
+
+458
+00:37:33,170 --> 00:37:40,450
+طيب هذه اللي شوية بدها تركزوا معايا طيب if P of G
+
+459
+00:37:40,450 --> 00:37:49,460
+is true اذا for all X P of X is trueبالشكل هذا و
+
+460
+00:37:49,460 --> 00:37:53,880
+بدون ما اوضح الشيال جي الكلام مش صح الكلام مش صح
+
+461
+00:37:53,880 --> 00:38:00,380
+صحيح لكن لما اقول جي arbitrary element from
+
+462
+00:38:00,380 --> 00:38:04,860
+universe of discourse arbitrary
+
+463
+00:38:04,860 --> 00:38:13,380
+بمعنى بشكل اعتباطي بشكل عشوائي أخدناها بمعنى ان جي
+
+464
+00:38:13,380 --> 00:38:16,880
+ممكن تكون اي element داخل universe of discourse
+
+465
+00:38:19,450 --> 00:38:23,610
+هقول طلاب كلهم هينجحوا امتى الكلام هذا؟ الكلام هذا
+
+466
+00:38:23,610 --> 00:38:26,510
+إذا كان على الغمضي شاورت على أي واحد و قلت هذا
+
+467
+00:38:26,510 --> 00:38:31,430
+هينجح true طيب هذا هينجح true هذا هينجح true طب ع
+
+468
+00:38:31,430 --> 00:38:35,170
+مين هيجي تيجي؟ هذا هينجح true و أنا مغمض و عارف ..
+
+469
+00:38:35,170 --> 00:38:37,930
+هيقولي غمض هناك و شاور على أي واحد و بدنا نخربطهم
+
+470
+00:38:37,930 --> 00:38:41,250
+إذا أنا عارف إن كله هينجح و هنجحوا .. هنجحكوا
+
+471
+00:38:41,250 --> 00:38:44,610
+كلكوا مش هيفرق معايا وين هشاور صح؟ arbitrarily
+
+472
+00:38:45,780 --> 00:38:49,380
+arbitrary بشكل عشوائي مش فارقة معايا وين أصبعي
+
+473
+00:38:49,380 --> 00:38:54,200
+هيروح فإذا هاختار أي حد و الأصبح هيجي على أي حد مش
+
+474
+00:38:54,200 --> 00:39:00,640
+مشكلة و هقول is it true إذا فعلا تحقق هذا ال
+
+475
+00:39:00,640 --> 00:39:06,020
+condition فإذا for all is true واضحيت؟ فإذا
+
+476
+00:39:06,020 --> 00:39:10,300
+بالمطلق لأ هو كلام مش صح لكن لما أقول جي arbitrary
+
+477
+00:39:10,300 --> 00:39:15,500
+elementأه بتصيرك صحيحة ليش؟ لإن أنا ماخده بدون
+
+478
+00:39:15,500 --> 00:39:19,620
+تعيين أنا مش محدد واحد معين قلت عليه أه هذا هينجح
+
+479
+00:39:19,620 --> 00:39:24,440
+أنا أي واحد هيجي قدامي هقولله أه هينجح من ال
+
+480
+00:39:24,440 --> 00:39:27,100
+universe of discourse فهذا automatically هيقودني
+
+481
+00:39:27,100 --> 00:39:30,680
+لفكرة أن معناته أنا مش فارقة معاك كلهم هينجحوا أنا
+
+482
+00:39:30,680 --> 00:39:33,200
+عامل fast seven كلهم هينجحوا مدام مش فارقة عند مين
+
+483
+00:39:33,200 --> 00:39:39,140
+هيجي أصبعي فوضحة الآن إذا كانت arbitrary هينجح ان
+
+484
+00:39:39,140 --> 00:39:47,770
+شاء اللهإذا بتصير for all x P of X طيب في ال exist
+
+485
+00:39:47,770 --> 00:39:53,490
+there exist x P of X إذا
+
+486
+00:39:53,490 --> 00:40:00,150
+هذه true على طول معناته P of C is true برضه
+
+487
+00:40:00,150 --> 00:40:07,290
+بالمطلق هيكي مش منطقية كتير مش معناه C يعنيلكن
+
+488
+00:40:07,290 --> 00:40:13,130
+لاحظ لما أقول هذه c الخصوصية هذه a new constant c
+
+489
+00:40:13,130 --> 00:40:21,230
+a new constant c فإذن هقول there exist أن في حد
+
+490
+00:40:21,230 --> 00:40:26,610
+هينجح لين عكسناها للأسف أن والله في حد هينجح طب
+
+491
+00:40:26,610 --> 00:40:30,330
+أمش مضرور لكل في الحالة هذه ويمكن واحد بس طيب لما
+
+492
+00:40:30,330 --> 00:40:34,010
+أقول في حد هينجح و أقول في الآخر اللي هينجح هذا x
+
+493
+00:40:34,010 --> 00:40:38,680
+بس أنا ماحددتش xأنا قلت إنه في ال new constant ال
+
+494
+00:40:38,680 --> 00:40:42,580
+new constant هذا اسمه X و X هينجح X هذا هيطلع في
+
+495
+00:40:42,580 --> 00:40:46,320
+الآخر محمد هيطلع أحمد هيطلع عمر المهم إنه هيطلع
+
+496
+00:40:46,320 --> 00:40:49,660
+حدا من مين من ال universe of discourse من فضاء
+
+497
+00:40:49,660 --> 00:40:54,080
+العينة أنا حاططله new constant عشان مايكونش حدا
+
+498
+00:40:54,080 --> 00:41:01,040
+تحديدا من العينة محدده شخصا لأ أنا قلت هو X و هو
+
+499
+00:41:01,040 --> 00:41:06,500
+موجود في العينة أنت حاطضلك الآن مين X مش فاهمكويس
+
+500
+00:41:06,500 --> 00:41:13,200
+واضحت فإذا كمان مرة C هذه ال new constant مش
+
+501
+00:41:13,200 --> 00:41:16,960
+بالضروري أن هو موجود من ال elements بتاعة مين؟
+
+502
+00:41:16,960 --> 00:41:20,560
+بتاعة ال universe of discourse أنا بقول C هو
+
+503
+00:41:20,560 --> 00:41:25,800
+constant موجود و بيحقق مادام there exist بس مين؟
+
+504
+00:41:25,800 --> 00:41:31,640
+أي واحد ممكن يكون C أي واحد فيكم ممكن يكون C من ال
+
+505
+00:41:31,640 --> 00:41:35,710
+universe of discourseكويس؟ وهذا ممكن يكون منطبق
+
+506
+00:41:35,710 --> 00:41:39,630
+عادي، C هذا ممكن يكون أكتر من واحد، ممكن يكون أكتر
+
+507
+00:41:39,630 --> 00:41:44,990
+من واحد، لكن في النهاية في حد هيحقق ال constant C،
+
+508
+00:41:44,990 --> 00:41:49,950
+واضحيت؟ ماقدرش أحدد تحديدًا C هو، أقول والله P of
+
+509
+00:41:49,950 --> 00:41:54,470
+Ahmed، بس Ahmed، لأ هي غلط، هي غلط، there exist
+
+510
+00:41:54,470 --> 00:41:57,550
+معناته بضمانليش تحديدًا Ahmed، ال there exist اللي
+
+511
+00:41:57,550 --> 00:42:00,490
+is a true، لأ ماحدش جال إنه Ahmed تحديدًا، يمكن
+
+512
+00:42:00,490 --> 00:42:04,980
+محمد، يمكن عمرو، يمكن خالدصحيح فإذا بقول C و C هدا
+
+513
+00:42:04,980 --> 00:42:11,660
+ممكن يكون أي حد بس أنا ضامن إنه في حد هيكون حقق ال
+
+514
+00:42:11,660 --> 00:42:17,540
+P of X في حدصحيح؟ تمام فحطنا له a new constant
+
+515
+00:42:17,540 --> 00:42:22,940
+عشان نطلع من مطب أنه هيك حددته لأ أنا محددتش هذا
+
+516
+00:42:22,940 --> 00:42:28,540
+new constant طيب هذا بتهيألي واضحة object داخل ال
+
+517
+00:42:28,540 --> 00:42:31,700
+universe of discourse إذا هو true فمعناته there
+
+518
+00:42:31,700 --> 00:42:36,780
+exist خلاص في معاه حدا فليكن إذا هو لحاله فليكن في
+
+519
+00:42:36,780 --> 00:42:39,640
+الحالتين اتحققت there exist there exist في
+
+520
+00:42:39,640 --> 00:42:44,080
+الحالتين حتى اتحققت خلاص مش هندا مشكلةمش هيكون فيه
+
+521
+00:42:44,080 --> 00:42:51,120
+مشكلة okay بيظهر لنا مشكلة كبيرة من ورا عدم فهمنا
+
+522
+00:42:51,120 --> 00:42:55,760
+لل implication هذه الشيء اللي هي ال fallacy
+
+523
+00:42:55,760 --> 00:43:01,480
+المغالطة او ال fallacies المغلطات احيانا المغلطات
+
+524
+00:43:01,480 --> 00:43:06,480
+هذه اما بتصير في عملية التأكيدأو في عملية الإنكار،
+
+525
+00:43:06,480 --> 00:43:09,920
+احنا أخدناها مرتين ال implication في الـ F بذات
+
+526
+00:43:09,920 --> 00:43:14,220
+توي صح؟ أخدناها مرة لما قلنا affirming إن والله
+
+527
+00:43:14,220 --> 00:43:18,840
+بدنا نأكد فيها ال consequence اللي هو ال
+
+528
+00:43:18,840 --> 00:43:23,900
+conclusion أو denying ل ال premise ل ال P لما
+
+529
+00:43:23,900 --> 00:43:29,620
+نفهنا ال P وقلنا بناستنتج negation P من negation Q
+
+530
+00:43:30,320 --> 00:43:35,180
+كويس فإذا في عندي كانوا حالتين بس هل الحالتين هدول
+
+531
+00:43:35,180 --> 00:43:38,320
+واضحين جدا لأ ممكن نصفيهم مغلطات أحيانا من ورا
+
+532
+00:43:38,320 --> 00:43:43,580
+حالتين هنتكلم عنهم ممكن جدا الفلس الأولى اللي هي
+
+533
+00:43:43,580 --> 00:43:47,900
+لل affirming أني أؤكد ال conclusion بينما هو مش
+
+534
+00:43:47,900 --> 00:43:51,360
+بالضروري يكون مؤكد زي لما أقول إذا كان ظهر عندي P
+
+535
+00:43:51,360 --> 00:43:57,160
+implies Q is true هذا true خلاص مية لمية و Q is
+
+536
+00:43:57,160 --> 00:44:01,800
+trueتروح تأكد ال premise التأكيد بيجي على ال
+
+537
+00:44:01,800 --> 00:44:06,620
+conclusion مش على ال premise توي النظرية اللي
+
+538
+00:44:06,620 --> 00:44:09,940
+أخدناها ال rule اللي أخدناها كانت تأكيد لل
+
+539
+00:44:09,940 --> 00:44:16,640
+conclusion و denying ل ال premiseخدوا بالكوا طيب
+
+540
+00:44:16,640 --> 00:44:22,500
+بمعنى انه هنا لما يقول لي P of P implication
+
+541
+00:44:22,500 --> 00:44:26,920
+او employs Q is true و Q is true ماحدش يجي يقول
+
+542
+00:44:26,920 --> 00:44:32,120
+ليه معناته P is true العكس صح بس هذه لأ اذا كان
+
+543
+00:44:32,120 --> 00:44:36,440
+هنا P is true بقولك اه Q is true اما Q is true
+
+544
+00:44:36,440 --> 00:44:37,500
+شوفولي
+
+545
+00:44:41,910 --> 00:44:47,890
+الـ Q اللي هو العمود التاني والتالت، الاتنين true
+
+546
+00:44:47,890 --> 00:44:53,390
+true شوفوا ليه ايش لازم تكون P يعني انت بتحتمل
+
+547
+00:44:53,390 --> 00:44:56,190
+الحالتين، ليش انت روح اتقررت ان هي لازم تكون true
+
+548
+00:44:56,190 --> 00:45:03,950
+خطأ فال affirming هادي لل conclusionمش لل premise
+
+549
+00:45:03,950 --> 00:45:07,410
+..مش لل premise طيب و العكس صحيح لما نيجي نتكلم عن
+
+550
+00:45:07,410 --> 00:45:10,650
+ال premise اللي هو في عملية ال denying اللي هو
+
+551
+00:45:10,650 --> 00:45:15,670
+الانكار او اللي هو الفلسي ان اقول الله دي false زي
+
+552
+00:45:15,670 --> 00:45:21,250
+حالة ان اقول P implies Q is true تمام اتفجنا ال
+
+553
+00:45:21,250 --> 00:45:27,010
+column التالت and P is false اما انت هيك قولت يا
+
+554
+00:45:27,010 --> 00:45:31,070
+دكتور لأ استنى انا ماقولتش هيكأنا قلت إذا تم إنكار
+
+555
+00:45:31,070 --> 00:45:35,950
+ال conclusion استنتج انه ال premise منكرة بس اللي
+
+556
+00:45:35,950 --> 00:45:40,530
+هنا تم إنكار ال premise ماتقدرش بناء عليها أنكر ال
+
+557
+00:45:40,530 --> 00:45:44,710
+conclusion تروح تقول ال Q معناته false شوف العمودي
+
+558
+00:45:44,710 --> 00:45:49,730
+الأول والتالت false true شوف ليه false true
+
+559
+00:45:49,730 --> 00:45:54,230
+العمودي الأول والتالت ال Q لها الحالتين فانت بناء
+
+560
+00:45:54,230 --> 00:45:59,340
+عليش روحت حكمتإذن هذه مغلطة بتصير و الواحد بدرش
+
+561
+00:45:59,340 --> 00:46:05,300
+فيها بيفكر أنه لأ هي منطقي بيفكر أنه لأ أنا صح ليش
+
+562
+00:46:05,300 --> 00:46:09,640
+هتقول غلط لأنه بتكون حالة من الحالتين هذول في
+
+563
+00:46:09,640 --> 00:46:13,080
+الغالب في الغالب هذه معظم الحالات اللي بتصير فيها
+
+564
+00:46:13,080 --> 00:46:18,680
+fallacy أو مغلطة بتكون من الحالتين طيب ننهي بمثال
+
+565
+00:46:21,500 --> 00:46:28,280
+ننهي بالمثال هذا و نشوف وين الخلص في الموضوع بدا
+
+566
+00:46:28,280 --> 00:46:33,780
+أقول أن a و b هي positive integers a تساوي b تمام؟
+
+567
+00:46:33,780 --> 00:46:38,680
+هضرب الأتنين في a كلاهما هضربوا في a a تربيع و a
+
+568
+00:46:38,680 --> 00:46:42,640
+في b و بعدين كلاهما طرحنا منه b تربيع على الطرفين
+
+569
+00:46:42,640 --> 00:46:46,620
+طرحنا من ال .. هي b تربيع و b تربيع كلاهما أخدنا
+
+570
+00:46:46,620 --> 00:46:53,610
+منهم common ال a ناقص bأخدناها common طبعا هنا
+
+571
+00:46:53,610 --> 00:46:59,990
+لاحظوا أن هذه طرح مربعين فلما بناخد ال a ناقص b
+
+572
+00:46:59,990 --> 00:47:03,590
+بتصير مضروبة في a زائد b هدول لو ضربتهم في بعض
+
+573
+00:47:03,590 --> 00:47:08,130
+هيرجعوا بالثاني تمام هنا ناخد ال a ناقص b فبتضل ال
+
+574
+00:47:08,130 --> 00:47:12,110
+b برا لحالها بعدين اختصر تنتين هدول مع بعض
+
+575
+00:47:12,110 --> 00:47:20,070
+اختصرناهم و اتكمل a ناقص b صارت هنا a هي نفسها b2A
+
+576
+00:47:20,070 --> 00:47:26,190
+2E مين الرجال اللي بتظبطش؟ ليش
+
+577
+00:47:26,190 --> 00:47:32,090
+بتظبطش؟ تجسم على صفر؟ ليش بدك تجسم على صفر؟
+
+578
+00:47:32,090 --> 00:47:37,070
+اختصرتهم اختصار مع بعض انا بس اختصرتهم اختصار
+
+579
+00:47:37,070 --> 00:47:41,850
+واحدة على اليمين واحدة على الشمال واختصرتهم احسنت
+
+580
+00:47:41,850 --> 00:47:45,150
+احسنت الاختصار مش معناه زي ما أنا جاعد بقول اختصر
+
+581
+00:47:45,150 --> 00:47:48,990
+و خلصنا ضياناهم مع بعض الاختصار معناه قسمةهي
+
+582
+00:47:48,990 --> 00:47:52,650
+policy واضحة جدا وكتير ممكن تصير معانا ليش؟ لإن
+
+583
+00:47:52,650 --> 00:47:57,110
+أنا بتدلوي الإثبات غصب عنه بدي أمشي فبتصير معاكم
+
+584
+00:47:57,110 --> 00:48:00,210
+إنك بدك تلوي غصب عنه، بدك تمشي، بدك تطلع إن لا
+
+585
+00:48:00,210 --> 00:48:04,450
+وصلت لنتيجة، بينما أنت عارف إن هي مش مقنعة وقد
+
+586
+00:48:04,450 --> 00:48:07,690
+تكون مش عارف، يعني أنا مثلا هنا قاعدة قدامك وطلعت
+
+587
+00:48:07,690 --> 00:48:12,720
+مش عارفروحت ايش سويت اختصرتهم مع بعض لأ فيش حاجة
+
+588
+00:48:12,720 --> 00:48:17,020
+اسمها اختصرتهم مع بعض في حاجة اسمها قسمت كل كلا
+
+589
+00:48:17,020 --> 00:48:20,700
+الطرفين على نفس ال term مافيش حاجة اقول اختصر مع
+
+590
+00:48:20,700 --> 00:48:24,020
+بعض مافيش حاجة هيك اسمها في ان هذه لحالها انا روحت
+
+591
+00:48:24,020 --> 00:48:27,080
+قسمتها على a ناقص واحد وانا من الأول قاعد بقول a
+
+592
+00:48:27,080 --> 00:48:33,640
+تساوي b فإذا قسمت على term ناقص نفسه يعني صار
+
+593
+00:48:33,640 --> 00:48:36,120
+كأنني بقسم على صفر undefined
+
+594
+00:48:37,960 --> 00:48:42,480
+إن هاتش هيطلع Undefined غير معرف معنا ذلك إنه اللي
+
+595
+00:48:42,480 --> 00:48:47,020
+طلع في الآخر Undefined يسوى Undefined وليس زي ما
+
+596
+00:48:47,020 --> 00:48:53,720
+أنا قلت هيك A زائد B تسوى B هاد Undefinedتمام
+
+597
+00:48:53,720 --> 00:48:58,120
+واضحت؟ الكل واضحت معاه؟ ماتيجيش تقتصر لاختصارات؟
+
+598
+00:48:58,120 --> 00:49:03,160
+الاختصارات دي هي زي ما اقوله احنا بنعمل اختصار
+
+599
+00:49:03,160 --> 00:49:07,460
+للعملية .. لعملية قسمة .. لعملية قسمة يلا يعطيك
+
+600
+00:49:07,460 --> 00:49:08,500
+الله عفا شباب خلصنا هي
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6ba2a03b415427856cc5f77e537fcc78058201d8
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0.srt
@@ -0,0 +1,1866 @@
+
+1
+00:00:05,230 --> 00:00:09,650
+السلام عليكم، يعطيكم العفو يا شباب، اليوم نستكمل
+
+2
+00:00:09,650 --> 00:00:14,070
+جزئية الـ proofs اللي كنا بنتكلم فيها، فاليوم إن
+
+3
+00:00:14,070 --> 00:00:17,850
+شاء الله هناخد مجموعة أمثلة محلولة، أو solve the
+
+4
+00:00:17,850 --> 00:00:23,590
+problems لما تم أخذه خلال هذا الأسبوع، وهذا شيء
+
+5
+00:00:23,590 --> 00:00:26,970
+كتير كويس أنه بيظل معانا في مجال هذا الأسبوع و
+
+6
+00:00:26,970 --> 00:00:30,690
+يمكن أنا أركز كتير على المحاضرات المصورة، فكتير
+
+7
+00:00:30,690 --> 00:00:33,430
+كويس أن أنتم تكونوا حاضرين المحاضرة المصورة، عشان
+
+8
+00:00:33,430 --> 00:00:38,350
+فعلا بتساعدني أن أكون ماشي بشكل كتير أفضل خلال
+
+9
+00:00:38,350 --> 00:00:42,910
+الأسبوع، وهذا بيوفر لنا وقت أن نحنا نعرف نحل أسئلة، و
+
+10
+00:00:42,910 --> 00:00:46,970
+يمكن هذه هي الأهم بالنسبة لكم، لأنه أمثلة في المعظم
+
+11
+00:00:46,970 --> 00:00:50,170
+هي أمثلة امتحانات، في المعظم هتلاقي أن هي أمثلة
+
+12
+00:00:50,170 --> 00:00:54,630
+امتحانات، فاليوم نبدأ نأخذ نأخذ الـ second set of
+
+13
+00:00:54,630 --> 00:00:58,090
+problems، المرة اللي فاتت، الأسبوع اللي فات أخذنا أول
+
+14
+00:00:58,090 --> 00:01:02,370
+set، أو أول مجموعة من الـ problems، اليوم نكمل مجموعة
+
+15
+00:01:02,370 --> 00:01:04,710
+ثانية، وهذا السؤال كان جاي في امتحان من الامتحانات
+
+16
+00:01:04,710 --> 00:01:09,890
+كان في أحد الامتحانات جاي سابقا أيضا، لـ discrete
+
+17
+00:01:09,890 --> 00:01:16,250
+mathematics، تمام، كان let f x y، و هذه تمثل
+
+18
+00:01:16,250 --> 00:01:21,610
+statement، x can help y، X can help Y، والمطلوب الآن
+
+19
+00:01:21,610 --> 00:01:25,610
+بالنسبة للـ domain اللي بيحتوي على كل الـ people in
+
+20
+00:01:25,610 --> 00:01:28,730
+the world، نفترض أنه الـ domain، الـ universal domain
+
+21
+00:01:28,730 --> 00:01:33,450
+طبعا هو كل سكان العالم، أو كل الناس في العالم، بدنا
+
+22
+00:01:33,450 --> 00:01:37,170
+نستخدم quantifiers and logical operators to
+
+23
+00:01:37,170 --> 00:01:41,350
+express each of the statements، و نبدا بمجموعة
+
+24
+00:01:41,350 --> 00:01:46,600
+statements، كويس، everyone can help Ali، everyone أكيد
+
+25
+00:01:46,600 --> 00:01:51,460
+بنقول for all، كويس، و هنكتب الـ for all، هذه كلمة X
+
+26
+00:01:51,460 --> 00:01:58,100
+فإذا هتبدأ بـ X، أو الـ F of X، لأن X احنا عملنا..
+
+27
+00:01:58,100 --> 00:02:03,240
+عملنا الـ quantification في الأول، for all X and Ali
+
+28
+00:02:03,240 --> 00:02:10,310
+why هنا Ali؟ صحيح؟ why، لأ هي بقت why، هي أصبحت help
+
+29
+00:02:10,310 --> 00:02:16,610
+علي، فأصبحت علي تحديدا علي، كويس، فهي هذه طريقة حلها
+
+30
+00:02:16,610 --> 00:02:20,830
+بكل بساطة، عرفنا جميع الـ limits اللي عندك في بعضهم
+
+31
+00:02:20,830 --> 00:02:24,030
+بعض الـ variables، اتعرفت من خلال الـ quantifier
+
+32
+00:02:24,030 --> 00:02:28,780
+وبعضهم اتعرف بشكل direct، مباشر، علي أنا قلت علي
+
+33
+00:02:28,780 --> 00:02:33,020
+مباشرة، فإذا بدي أعرفه علي على طول، صحيح؟ مش هحطه
+
+34
+00:02:33,020 --> 00:02:36,120
+why، ولا هقول there exist، ولا لأن هم there exist
+
+35
+00:02:36,120 --> 00:02:40,360
+أنا عارفه تحديدا، هو علي، كويس، نفس الكلام سارة
+
+36
+00:02:40,360 --> 00:02:45,080
+can help someone، there exist، ايش؟ why بالظبط،
+
+37
+00:02:45,080 --> 00:02:50,080
+هنفتح أقواس سارة و why، تمام جدا، هي واضحة الأمور
+
+38
+00:02:50,080 --> 00:02:53,720
+و سهلة، بسيطة جدا، صحيح؟ سؤال زي هذا، كتير كانوا
+
+39
+00:02:53,720 --> 00:02:58,750
+بيغلطوا فيه، تخيلوا سؤال بسيط بهذا الشكل، كتير كانوا
+
+40
+00:02:58,750 --> 00:03:03,790
+بيغلطوا فيه، بيجيبوا فيه علامة، تمام، just one، just
+
+41
+00:03:03,790 --> 00:03:08,390
+one، there exist، exclamation، مش متذكرينه، طيب، just
+
+42
+00:03:08,390 --> 00:03:14,610
+one man can help both Ali and Omar، فمعنى ذلك هنا
+
+43
+00:03:15,680 --> 00:03:20,620
+there exist، فنكتبها there exist with exclamation x
+
+44
+00:03:20,620 --> 00:03:24,320
+لأنه هو اللي بده يقدم الخدمة، هو الـ subject، و بدنا
+
+45
+00:03:24,320 --> 00:03:31,500
+نعمل x، و هنفتح أقواس عشان أقول أحمد and علي، عشان
+
+46
+00:03:31,500 --> 00:03:36,320
+نقول أحمد أو علي، إذا بدنا نكون جسمنا الـ four كلها،
+
+47
+00:03:36,320 --> 00:03:41,120
+تمام؟ فإذا يوجد شخص واحد، الشخص هذا بساعد أحمد
+
+48
+00:03:41,120 --> 00:03:44,760
+والشخص هذا بساعد عمر أو علي؟ أنا عمر
+
+49
+00:03:53,460 --> 00:03:59,040
+ممكن، بس مش هتكون كتير واضحة، مش هتوضح كتير الـ and
+
+50
+00:03:59,040 --> 00:04:03,240
+في هذه المشكلة، الـ and، كيف بدك تعملها؟ أنت بتقول كم
+
+51
+00:04:03,240 --> 00:04:10,240
+أنت بدك تحطها يعني هنا، هذه كله هذا بدون الأقواس
+
+52
+00:04:10,240 --> 00:04:12,960
+الأقواس هذه و هذه بس بدها تكون and واضحة
+
+53
+00:04:16,350 --> 00:04:23,950
+no one can help himself، no
+
+54
+00:04:23,950 --> 00:04:32,570
+one، negation for all، لا يوجد ولا واحد، لكن لو قلنا
+
+55
+00:04:32,570 --> 00:04:38,370
+there exist، معناته أنه لا يوجد بعضهم، تمام؟ لا يوجد
+
+56
+00:04:38,370 --> 00:04:41,830
+بعضهم، طيب، no one can.. بس أنا مش عليها، دي بتطلع
+
+57
+00:04:41,830 --> 00:04:43,550
+بتطلع علي كيف تكون ترجمة himself
+
+58
+00:04:46,420 --> 00:04:51,180
+هل بتحطه x؟ x و x، تمام، himself، لأن بدي أحطه
+
+59
+00:04:51,180 --> 00:04:54,400
+x و y، معناته قد يختلفوا x و y مع بعض، لكن أنا
+
+60
+00:04:54,400 --> 00:04:59,260
+بقول مش هيقدر يساعد نفسه، مش هيقدر يساعد نفسه، فمعنى
+
+61
+00:04:59,260 --> 00:05:04,920
+ذلك أنه أنا بتكلم عن عن هو x
+
+62
+00:05:04,920 --> 00:05:10,860
+x عن نفسه، تمام، هدول مهمين لأنه بتكلم وينها
+
+63
+00:05:10,860 --> 00:05:14,980
+أولا اللي هو x نفسه، اللي عرفنا himself
+
+64
+00:05:19,970 --> 00:05:27,810
+just one.. no one.. no one can.. اه there exist
+
+65
+00:05:27,810 --> 00:05:31,350
+هنا لا يوجد أحد.. اه لا يوجد أحد، هنا أن أنت
+
+66
+00:05:31,350 --> 00:05:35,770
+بتتكلم هنا لا يوجد أحد، إن بدك تعملها no one، معناته
+
+67
+00:05:35,770 --> 00:05:43,570
+بدك تحط for all، و جوا negation، فش
+
+68
+00:05:43,570 --> 00:05:48,240
+بعض، هنا أنا بتكلم عن نفس الشخص، هو نفس الشخص يعني
+
+69
+00:05:48,240 --> 00:05:54,600
+هنا بقول لا يوجد أي واحد بساعد نفسه، أنا ما تكلمتش عن
+
+70
+00:05:54,600 --> 00:06:00,540
+الثاني قد يساعد الثاني، و قد لا يساعد الثاني، بقى
+
+71
+00:06:00,540 --> 00:06:04,660
+بعرفش، ممكن يساعد غيره، و ممكن لأ، يساعدش غيره، و أيضا
+
+72
+00:06:04,660 --> 00:06:09,940
+ما يساعدش نفسه، ما احنا قلنا ممكن أو ممكن لأ في
+
+73
+00:06:09,940 --> 00:06:14,180
+الحالة هذه، إذا قلنا for all، معناته أنه لا الكل
+
+74
+00:06:14,180 --> 00:06:23,450
+الكل مش هيساعده، أو ليس الكل، معناها صح؟ لازم نعملها
+
+75
+00:06:23,450 --> 00:06:28,310
+for all، لأ، خلينا نكتبهم، كلامكم صح، خلينا نكمل مع
+
+76
+00:06:28,310 --> 00:06:30,490
+بعض، كويس، خلينا نفكر مع بعض، مش المشكلة، ما احنا
+
+77
+00:06:30,490 --> 00:06:36,570
+قلنا نراجع، نكتبها، و نحلل، مش صح أني أقول لك زي ما
+
+78
+00:06:36,570 --> 00:06:39,510
+أقول لك إيه غلط، و ينفع، و أحفظها هيك، خلينا نفهمها
+
+79
+00:06:39,510 --> 00:06:47,000
+لا يوجد كل، مش هيك، معناته أنه قد يكون بعضهم، ركزوا
+
+80
+00:06:47,000 --> 00:06:53,260
+معايا، شوفوها هيك، ظابطة معاكم، there is no all، على
+
+81
+00:06:53,260 --> 00:06:56,420
+اللي احنا كاتبينه، معناته أن ممكن يكونوا كلهم
+
+82
+00:06:56,420 --> 00:07:04,340
+بيحققوها، إلا واحد، مش هيك؟ صح؟ في شيء مش واضح؟ هيها
+
+83
+00:07:04,340 --> 00:07:08,380
+منطقية، طيب، العكس تبع، أو خلينا نقول الحالة اللي
+
+84
+00:07:08,380 --> 00:07:13,940
+احنا كاتبينها، و نفهمها، نحاول أن نحللها هنا
+
+85
+00:07:15,020 --> 00:07:18,800
+there exist، هذه حالتها، يعني على الأقل في واحد، طب
+
+86
+00:07:18,800 --> 00:07:24,940
+نقول ما فيش ولا واحد، لا يوجد
+
+87
+00:07:24,940 --> 00:07:29,860
+ولا واحد، هنا قد يكون في واحد، لكن اللي أكيد أنه مش
+
+88
+00:07:29,860 --> 00:07:35,020
+الكل، اللي فوق هذه معناته أنه مش الكل، ممكن يكون كل
+
+89
+00:07:35,020 --> 00:07:39,380
+واحد، الواحد هذا نفى الـ for all، الواحد نفى الـ for
+
+90
+00:07:39,380 --> 00:07:43,200
+all، أما هنا لأ، هذه يمكن تكون أكثر واقعية، واضحة، no
+
+91
+00:07:43,200 --> 00:07:48,450
+one، خلاص، الـ function بيظبط كلامك منطقي، فهنا بتصير
+
+92
+00:07:48,450 --> 00:07:55,050
+for all negation if، كلامك مية المية، تظبط هيك
+
+93
+00:07:55,050 --> 00:08:00,250
+معناته كأني بقول للكل، ولا واحد بيساعد حاله، بس في
+
+94
+00:08:00,250 --> 00:08:05,030
+الحالة هذه، أنت كل شيء عملت له دي، دي Morgan، صح، كلامك
+
+95
+00:08:05,030 --> 00:08:09,170
+ينطبق معي، أصبح مع الـ negation، there exist، طلعت
+
+96
+00:08:09,170 --> 00:08:14,050
+الـ negation برة، و اتحولت عندك بدل ما هي for all
+
+97
+00:08:14,050 --> 00:08:15,230
+اتحولت لـ there exist
+
+98
+00:08:18,340 --> 00:08:24,160
+تمام، الأخيرة، not everyone، ليس الكل، هذا  pathology
+
+99
+00:08:24,160 --> 00:08:27,980
+مع مين؟ مع مفهومنا، اعتوي، ليس الكل بساعد someone
+
+100
+00:08:27,980 --> 00:08:32,060
+فهنا هتكون ليس الكل، هنا بتظبط معانا، ليس الكل بمعنى
+
+101
+00:08:32,060 --> 00:08:37,800
+أن في بعض هيساعد، بس مش الكل، البعض هيساعد، اه بس ليس
+
+102
+00:08:37,800 --> 00:08:46,500
+الكل، بحظينا هنا، not everyone، negation for all، وطبعا
+
+103
+00:08:46,500 --> 00:08:49,080
+can help someone، someone، بنخليها زي ما هي
+
+104
+00:08:49,080 --> 00:08:57,400
+someone، there exist y، اللي هي someone، تمام، طيب هذا
+
+105
+00:08:57,400 --> 00:09:01,160
+حاسب لكم يا، برضه هنزل لكم الملف، تقرأوا، لأن اليوم
+
+106
+00:09:01,160 --> 00:09:07,590
+شوية مزود لكم حجم الـ، هدول مجرد بس العكس لهناك
+
+107
+00:09:07,590 --> 00:09:11,670
+هيكون في عندي الـ negations، أفوان الـ notations
+
+108
+00:09:11,670 --> 00:09:15,650
+موجودة للـ quantifiers، و المقلوب تكتب منها الجملة
+
+109
+00:09:15,650 --> 00:09:20,290
+الجملة بسيطة جدا، مجرد لغة، مجرد تركيب لغات، مجرد
+
+110
+00:09:20,290 --> 00:09:27,210
+تركيب لغة عشان نحاول نصل لـ الـ proving strategies
+
+111
+00:09:27,210 --> 00:09:29,790
+لأن أنا عامل مجموعة أسئلة في أخرها في الـ proving
+
+112
+00:09:29,790 --> 00:09:34,470
+strategies، معنى أنه نصلها، بتقرؤوها، إذا في واحدة
+
+113
+00:09:34,470 --> 00:09:38,230
+منهم مش واضحة معاكم، ترجعوا هنا
+
+114
+00:09:42,030 --> 00:09:45,170
+هذه مثلا واحدة من الأسئلة اللي شفتها في واحد من
+
+115
+00:09:45,170 --> 00:09:49,050
+الامتحانات على الـ net مثلا، All problems، طبعا أنتم
+
+116
+00:09:49,050 --> 00:09:52,470
+بتعرفوا الـ questions، في بعضها problems، و بعضها
+
+117
+00:09:52,470 --> 00:09:57,070
+true و false، و بعضها multiple choice، بس في منهم
+
+118
+00:09:57,070 --> 00:10:00,350
+problems، اللي هو بدأ حل، خطوات، فهنا لو قلنا كل
+
+119
+00:10:00,350 --> 00:10:05,030
+problems، اللي هي نوع من أنواع الـ questions، are
+
+120
+00:10:05,030 --> 00:10:10,810
+difficult and frustrating، difficult، معروفة صعبة
+
+121
+00:10:10,810 --> 00:10:18,670
+frustrating، محبطة، كويس، هذه premise، هيعطيكوا إياها
+
+122
+00:10:18,670 --> 00:10:22,070
+على طول، هيكون في عندكم مجموعة questions، الـ exam
+
+123
+00:10:22,070 --> 00:10:26,150
+تبعكم، في multiple choice، و في true و false، و في
+
+124
+00:10:26,150 --> 00:10:30,490
+problems، و بعدين أقول لكم دي، و بعدين كل الـ problems
+
+125
+00:10:30,490 --> 00:10:35,220
+صعبة و محبطة، فبتكونوا تذاكروا كويس، تمام، and some
+
+126
+00:10:35,220 --> 00:10:40,580
+problems are challenging، بعض المشاكل، أو بعض الـ
+
+127
+00:10:40,580 --> 00:10:46,060
+problems، هذه فيها تحدي، يعني هتكون فيها أفكار، كذا
+
+128
+00:10:46,060 --> 00:10:51,200
+فكرة، في بعض، كذا شيء، فيها تحدي، الآن، hence، المقلوب
+
+129
+00:10:51,200 --> 00:10:54,760
+إيش بتكون تثبته؟ أنه some problems are frustrating
+
+130
+00:10:54,760 --> 00:10:58,900
+and challenging، بتكون تثبته أن بعضها هو مش بس
+
+131
+00:10:58,900 --> 00:11:05,410
+challenging، لأ، كمان محبطة، بعضها ليس فقط فيه تحدي
+
+132
+00:11:05,410 --> 00:11:11,810
+وإنما كمان محبطة، تمام، بطريقة.. كيف؟ بطريقة تقليدية
+
+133
+00:11:11,810 --> 00:11:16,030
+بدنا نحط من الـ universe of discourse، اللي هي
+
+134
+00:11:16,030 --> 00:11:18,950
+مجموعة الـ questions كلها، عشان نبدأ نقول الـ
+
+135
+00:11:18,950 --> 00:11:22,950
+definitions اللي كانت عندي، لمجموعة الـ premises، و
+
+136
+00:11:22,950 --> 00:11:26,110
+الـ conclusion، هنعرفها بهذا الشكل، الـ P، هقول أن هي
+
+137
+00:11:26,110 --> 00:11:30,190
+problem، من كل questions، مين الـ problem؟ فكل problem
+
+138
+00:11:30,190 --> 00:11:37,790
+هو محبط أو أو صعب، مش هيك؟ هاي أول حالة من الحلقة دي
+
+139
+00:11:37,790 --> 00:11:41,390
+بالظبط، هتكون for all، هي all دي هقول هي لـ difficult
+
+140
+00:11:41,390 --> 00:11:48,290
+الـ F لـ frustrating، و الـ C لـ challenging، عشان نبدأ
+
+141
+00:11:48,290 --> 00:11:52,990
+نكتب الـ premises، كيف هيكون شكلها؟ for all x، يعني
+
+142
+00:11:52,990 --> 00:11:58,050
+لكل الـ questions، إذا كانت الـ question هي problem
+
+143
+00:11:58,050 --> 00:12:05,480
+إذا هي difficult و frustrating، تمام، التانية some
+
+144
+00:12:05,480 --> 00:12:11,100
+problems are، فعلا there exist x، some، بعض الـ
+
+145
+00:12:11,100 --> 00:12:15,360
+questions هي problems، و challenging، هي فعلا
+
+146
+00:12:15,360 --> 00:12:18,040
+problem، و في نفس الوقت، مدام هي problem، برضه هتكون
+
+147
+00:12:18,040 --> 00:12:22,000
+challenging، لأن and، معناته الإثنين، هي problem، و هي
+
+148
+00:12:22,000 --> 00:12:24,800
+challenging، في نفس الوقت، طيب، إيش اللي بدنا نثبته؟
+
+149
+00:12:24,800 --> 00:12:31,010
+بدنا نثبت some problems، there exist x، problem هي
+
+150
+00:12:31,010 --> 00:12:38,530
+some problem، frustrating و challenging، تمام، كبنث
+
+151
+00:12:38,530 --> 00:12:42,330
+بتهادي من هادي، فبتهادي بسيطة، يمكن احنا أخذنا المرة
+
+152
+00:12:42,330 --> 00:12:46,170
+اللي فاتت بعض أمثلة عليها، نحاول نطلعهم كلهم true
+
+153
+00:12:46,170 --> 00:12:49,290
+بالظبط
+
+154
+00:12:49,290 --> 00:12:53,930
+إذا وصلنا لمرحلة نطلعهم كلهم true، خلصت الـ proof
+
+155
+00:12:53,930 --> 00:12:57,070
+تبعنا، هنبدأ بالـ premise الأولى، الـ premise الأولى for all
+
+156
+00:12:57,070 --> 00:13:00,590
+معناته أكيد، من الـ for all هدول، هفترض أنه في عنصر
+
+157
+00:13:00,590 --> 00:13:06,110
+اسمه A، شاك، معناته من كل الـ problems اللي موجودة
+
+158
+00:13:06,110 --> 00:13:09,390
+هتكون الـ problem A و B و C و D و.. جد ما بدك، الـ
+
+159
+00:13:09,390 --> 00:13:13,030
+problems، بس واحدة منهم A، و هذه A واحدة من الـ
+
+160
+00:13:13,030 --> 00:13:16,430
+universal discourse، أكيد بدون for all، يعني كلهم
+
+161
+00:13:16,430 --> 00:13:21,050
+شاك، بيقولوا أن في واحدة منهم هي A، فإذا
+
+162
+00:13:21,050 --> 00:13:24,950
+automatically، كأنه P of A، عملنا الـ universal
+
+163
+00:13:24,950 --> 00:13:29,570
+specification، اللي أخدناها برضه المحاضرة مش السابقة
+
+164
+00:13:29,570 --> 00:13:35,650
+اللي جبناها، P of A implies D and F، okay، بس لمين؟
+
+165
+00:13:35,650 --> 00:13:40,590
+مش للعنصر X و I go for all، لأ، حددنا واحد منهم، حددنا
+
+166
+00:13:40,590 --> 00:13:45,990
+واحد منهم A، و A هذا لازم يكون طبعا أكيد، belong to
+
+167
+00:13:45,990 --> 00:13:55,170
+لـ X، belong لمين؟ لـ X، أو لست X، اللي هي الـ questions
+
+168
+00:13:55,170 --> 00:13:59,610
+اللي هي الـ questions، تمام، التانية اللي هو الـ
+
+169
+00:13:59,610 --> 00:14:02,270
+premise التاني، المقصود فيها اللي هو there exist X،
+
+170
+00:14:02,550 --> 00:14:06,450
+B of X and C of X، معناته أنا ايش بقول؟ بقول يوجد
+
+171
+00:14:06,450 --> 00:14:10,430
+مشكلة من الـ universe of discourse.. من مجموعة
+
+172
+00:14:10,430 --> 00:14:13,930
+الم
+
+223
+00:18:22,280 --> 00:18:27,480
+الconclusion بسيطة جدا سهلة وسلسة ومافي مشكلة بس
+
+224
+00:18:27,480 --> 00:18:31,200
+سلاستها وبساطتها جاية من الimplication فهمنا اللي
+
+225
+00:18:31,200 --> 00:18:33,860
+الimplication الimplication هو اللي بيحلها تمام
+
+226
+00:18:34,900 --> 00:18:37,840
+هي كمان سؤال طبعا واضح من الخربشة اللي عليه أنه هذا
+
+227
+00:18:37,840 --> 00:18:41,760
+سؤال امتحان كنا جايبينه في امتحان سابق، السؤال هذا
+
+228
+00:18:41,760 --> 00:18:46,980
+كان سؤال اتنين في وجهته في ترتيب الأسئلة المهم
+
+229
+00:18:48,780 --> 00:18:53,800
+ميعطيني، بيقول لي إذا كان all animals with scales
+
+230
+00:18:53,800 --> 00:18:59,280
+are dragons، كل الحيوانات بحراشيف أو لها حراشف، و
+
+231
+00:18:59,280 --> 00:19:03,640
+جسمها هي dragons، هي اللي هي سحال التنين هذه
+
+232
+00:19:03,640 --> 00:19:09,460
+التنانين، كويس، كومة أو نقطة حتى dot، some animals
+
+233
+00:19:09,460 --> 00:19:14,620
+with scales are not dragons، بعض الحيوانات التي ليست
+
+234
+00:19:14,620 --> 00:19:21,550
+dragons have sharp claws، ليست دراغونس ولها مخالب
+
+235
+00:19:21,550 --> 00:19:27,930
+حادة، بعض الحيوانات ليست دراغونس ولها مخالب حادة،
+
+236
+00:19:27,930 --> 00:19:33,810
+كويس، هاي ال two premises، so إذا إيش there are
+
+237
+00:19:33,810 --> 00:19:39,810
+animals without scales which have sharp claws،
+
+238
+00:19:39,810 --> 00:19:45,330
+معناه ذلك إنه يوجد بعض الحيوانات اللي ليست لها
+
+239
+00:19:45,330 --> 00:19:53,470
+حراشف على ظهرها أو على جسمها ولها مخالب حادة، من
+
+240
+00:19:53,470 --> 00:19:58,050
+الpremises بدنا نثبت أو نprove الconclusion،
+
+241
+00:19:58,050 --> 00:20:04,010
+الطبيعي طبعا بدنا نقول إنه في الآخر في عند ال S هي
+
+242
+00:20:04,010 --> 00:20:06,990
+بده ارمزهم عشان ما نكوش نكتب الكلمات كاملة بس
+
+243
+00:20:06,990 --> 00:20:10,530
+نرمزهم هيك، نختصرها، أقول إن ال S هذي لأنها scales،
+
+244
+00:20:10,530 --> 00:20:13,770
+فناخد الحرف الأول منها فأقول إن ال S of X هذي اللي
+
+245
+00:20:13,770 --> 00:20:19,570
+هي معناته إنها لها scales أو لها حراشف، ال D هي
+
+246
+00:20:19,570 --> 00:20:25,830
+dragon، وال C sharp claws، كويس، عشان نبدأ نحط ال
+
+247
+00:20:25,830 --> 00:20:29,230
+premise الأولى، ال premise الأولى for all animals
+
+248
+00:20:29,230 --> 00:20:32,990
+with scales، معناته إذا كانت ال
+
+249
+00:20:32,990 --> 00:20:36,710
+animals هذه with scales فهي dragon، حيها إذا كانت
+
+250
+00:20:36,710 --> 00:20:42,450
+ال animals هذه لها scales إذن هي dragon، for all
+
+251
+00:20:42,450 --> 00:20:48,470
+scales implies D، التانية ال premise التانية some
+
+252
+00:20:48,470 --> 00:20:53,960
+animals، بعض .. there .. معناه تكتب أول شي there
+
+253
+00:20:53,960 --> 00:21:04,640
+exist، ولا إيش negation D and C، فإذا
+
+254
+00:21:04,640 --> 00:21:13,660
+يوجد animals ليست dragons ولها مخالب، يوجد هي لها
+
+255
+00:21:13,660 --> 00:21:17,640
+ليست dragons لكن في نفس الوقت لها مخالب، لها مخالب هذه
+
+256
+00:21:17,640 --> 00:21:20,960
+مش implication، خدوا بالكم اتكلمنا فيها سابقا،
+
+257
+00:21:20,960 --> 00:21:25,180
+وشرحناها وهنا بنرجع وبنؤكد على الموضوع، تمام، ال
+
+258
+00:21:25,180 --> 00:21:31,400
+conclusion المطلوب there exist أنه ليس لها scales،
+
+259
+00:21:31,400 --> 00:21:37,120
+negation scales، و claws لها claws، فإذا there
+
+260
+00:21:37,120 --> 00:21:39,380
+exist، و there exist زي ما قلت لكم دائما بتاخد
+
+261
+00:21:39,380 --> 00:21:48,490
+معها and، for all implication، okay، بدنا نبدأ نشتغل
+
+262
+00:21:48,490 --> 00:21:52,530
+فهنطلع هدول فوق عشان نبدأ نشتغل تحتهم وننطلق منهم،
+
+263
+00:21:52,530 --> 00:21:56,230
+هننطلق من الأولى وبرضه هفترض إنه في عندي ايه
+
+264
+00:21:56,230 --> 00:22:01,250
+animals، احنا بتقول for all و there exist تحت،
+
+265
+00:22:01,250 --> 00:22:04,490
+معناته there exist اللي تحت هذا واللي هفترضه ايه
+
+266
+00:22:04,490 --> 00:22:09,010
+ينطبق عليه ما ينطبق على ال all لأنه واحد منهم، هو
+
+267
+00:22:09,010 --> 00:22:12,090
+واحد منهم، فإذا عشان أحقق ال two premises مع بعض
+
+268
+00:22:12,090 --> 00:22:15,910
+يوجد على الأقل answer بيحققهم مع بعض، check there
+
+269
+00:22:15,910 --> 00:22:20,490
+exist، يعني يكفيني واحد، الواحد هذا بتفترضه هو ايه
+
+270
+00:22:20,490 --> 00:22:26,270
+طب هو نفسه ايه من ال for all، من ال for all، فإذا
+
+271
+00:22:26,270 --> 00:22:31,290
+ما تبلجوش إنه والله أحط a وأتوعّود مكانه ب a خلاص،
+
+272
+00:22:31,290 --> 00:22:35,370
+هاي بدأنا بال there exist، ال there exist هذه هتصبح
+
+273
+00:22:35,370 --> 00:22:42,740
+negation D of a، ف dragon هو ال a، وله clause
+
+274
+00:22:42,740 --> 00:22:48,260
+sharp claws، برضه هو نفسه ال animal a، الآن التانية
+
+275
+00:22:48,260 --> 00:22:53,120
+برضه منها بنقدر نجيب S of A implies that أو
+
+276
+00:22:53,120 --> 00:22:57,740
+implies D of A، أتوقع من اللي فوق بنقدر نقول إن
+
+277
+00:22:57,740 --> 00:23:02,840
+negation D is true لحالها، و C is true لحالها، طيب،
+
+278
+00:23:02,840 --> 00:23:08,160
+نبدأ بال D هاي،
+
+279
+00:23:08,160 --> 00:23:15,440
+D negation دي false، فإذن وين بتكون ال implies أو
+
+280
+00:23:15,440 --> 00:23:22,780
+ال implication كلها true، و ال q false، ال true وال
+
+281
+00:23:22,780 --> 00:23:28,460
+q false هذه بتصحّش، هيها، فإذن محكوم أكيد، هذا معناه
+
+282
+00:23:28,460 --> 00:23:34,240
+أن ال P false، يعني بقدر أقول negation S، check
+
+283
+00:23:34,240 --> 00:23:42,600
+negation S، تمام، negation S، خلصت المسألة، انتهت
+
+284
+00:23:42,600 --> 00:23:50,240
+الجثة، لأن C من الخطوة الرقم 3 أكيد هتكون true، فإذا
+
+285
+00:23:50,240 --> 00:23:56,320
+negation S and C برضه true مع بعض، وال A مدام هي
+
+286
+00:23:56,320 --> 00:24:00,220
+متحققة وأنا مش ضامن غيرها، أنا مش ضامن غيرها، أنا
+
+287
+00:24:00,220 --> 00:24:02,820
+بعرف إن ال A تحديدا اه هو يحقق ال premises اللي
+
+288
+00:24:02,820 --> 00:24:07,820
+بالأساس، لكن غيره مضمنش، عشان هيك there exist، وبشيل
+
+289
+00:24:07,820 --> 00:24:13,180
+ال a وبقول قد يكون في معاها، لكن على الأقل هو ال
+
+290
+00:24:13,180 --> 00:24:19,360
+a موجود، حققنا إنه ليس له scales وفي نفس الوقت
+
+291
+00:24:19,360 --> 00:24:21,540
+له sharp claws،
+
+292
+00:24:28,650 --> 00:24:31,930
+Okay، هنا في مجموعة arguments هتكون موجودة عندنا،
+
+293
+00:24:31,930 --> 00:24:35,830
+محتاجين بس نعرف هل هي صحيحة ولا خاطئة، إذا كانت
+
+294
+00:24:35,830 --> 00:24:39,250
+صحيحة ضمن أي rule أو وين اتعلمناها، وين أخذناها
+
+295
+00:24:39,250 --> 00:24:43,990
+بالضبط في المحاضرات .. المحاضرتين السابقتين أو ..
+
+296
+00:24:43,990 --> 00:24:48,890
+أو هي خطأ فإيش تصحيحها .. فإيش تصحيحها، أعطاني
+
+297
+00:24:48,890 --> 00:24:51,690
+theorem بهذا الشكل أو معلومة بهذا الشكل، نبدأ ..
+
+298
+00:24:51,690 --> 00:24:56,170
+نبدأ نفهم هي صح ولا غلط، صح ولا .. خلوا عينكم هنا، هي
+
+299
+00:24:56,170 --> 00:25:00,710
+نص الحل، نص الحل، إن عينك على الجدول هذا أنتم
+
+300
+00:25:00,710 --> 00:25:07,130
+ملاحظين كده، الجدول مهم معانا؟ مهم جدا، طيب، if n is
+
+301
+00:25:07,130 --> 00:25:14,530
+a real number such that n أكبر من واحد، إذا n تربيع
+
+302
+00:25:14,530 --> 00:25:20,390
+أكبر من واحد، هذا معناته بيقودني لفرضية إن n تربيع
+
+303
+00:25:20,390 --> 00:25:27,390
+أكبر من واحد، إذا n أكبر من واحد، وين المشكلة؟ مفروض
+
+304
+00:25:27,390 --> 00:25:31,810
+أنت مقتنع فيها الجملة ولا مش مقتنع فيها؟ هذا هو
+
+305
+00:25:31,810 --> 00:25:34,530
+السؤال، أنت هل مبدأيا مقتنع بالموضوع ولا مش مقتنع
+
+306
+00:25:34,530 --> 00:25:37,910
+بالموضوع؟ وليه؟
+
+307
+00:25:45,550 --> 00:25:49,190
+أكبر من واحد، كيف ده تصير سالبة؟ أكبر من واحد يعني
+
+308
+00:25:49,190 --> 00:25:54,270
+خلاص، من واحد في أقل، بكل السالب تبعه مش موجود، أنت
+
+309
+00:25:54,270 --> 00:25:58,070
+بتكلم من واحد to positive infinity، من واحد to
+
+310
+00:25:58,070 --> 00:26:02,270
+positive infinity، مفيهاش مشكلة، فكروا بغيرها،
+
+311
+00:26:02,270 --> 00:26:05,270
+مفيهاش مشكلة، هي كحد .. بحاجة .. هتفضل شوية
+
+312
+00:26:05,270 --> 00:26:10,050
+ناسي؟ بيجيب واحدة تم في هذا الشيء اللي هو مثلا
+
+313
+00:26:10,050 --> 00:26:14,290
+أربعة، سالب اتنين تانية وهي مش أكبر من واحد،
+
+314
+00:26:18,540 --> 00:26:21,860
+طيب ما احنا قاعدين بنقول من الأساس تعريفك إنه هو
+
+315
+00:26:21,860 --> 00:26:28,720
+أكبر من، هنا سالب، مش هيك، معناته أنت ما حققتش إن هي
+
+316
+00:26:28,720 --> 00:26:32,820
+أكبر من واحد، هي معناته هذه false، أنت بدأتها في
+
+317
+00:26:32,820 --> 00:26:36,160
+false وهذه برضه راحت false، فأنت فعلا ما حققتش
+
+318
+00:26:36,160 --> 00:26:42,860
+الموضوع، طيب، هنرجع لنفس فكرة ال implication تبعتنا،
+
+319
+00:26:42,860 --> 00:26:46,660
+مبدأيا هذه فيه policy في ال affirming اللي احنا
+
+320
+00:26:46,660 --> 00:26:50,920
+افترضنا إنه حدث، ليه؟ لأن أنت بتتكلم عن
+
+321
+00:26:50,920 --> 00:26:54,640
+implication، المفروض إنها true، ال implication هذا
+
+322
+00:26:54,640 --> 00:27:00,260
+الأصل إنه يكون true، مش هيك، المفروض P هي اللي تكون
+
+323
+00:27:00,260 --> 00:27:06,040
+ال true، عشان زي ما أقوله أستنتج منها Q وليس العكس،
+
+324
+00:27:06,040 --> 00:27:16,480
+بس ما تنتجش P من Q، صحة P من صحة Q احنا عادة بنستنتج
+
+325
+00:27:16,480 --> 00:27:21,760
+صحة Q من صحة P، إذا كان ال implies كله أو ال
+
+326
+00:27:21,760 --> 00:27:26,800
+implication كله على بعضه هو فعلا true، تمام؟ الكلام
+
+327
+00:27:26,800 --> 00:27:31,760
+هذا هل ينطبق عندنا هنا؟ هنشوف، هنا بنتكلم عن if n is
+
+328
+00:27:31,760 --> 00:27:36,340
+a real number which is such that n أكبر من واحد، هذه
+
+329
+00:27:36,340 --> 00:27:39,800
+إذا n تربيع أكبر من واحد، هذه كلها ال implication،
+
+330
+00:27:41,360 --> 00:27:44,700
+هذه هي ال implication، الكلمة العربية بتعطيني جملة
+
+331
+00:27:44,700 --> 00:27:51,280
+كاملة وبيقولها this is true، فأنت منها افترضت إنه
+
+332
+00:27:51,280 --> 00:27:58,780
+إن تربيع أكبر من واحد، يعني
+
+333
+00:27:58,780 --> 00:28:05,520
+هذه إيش Q، هذه كلها
+
+334
+00:28:07,900 --> 00:28:15,520
+P implies Q، بالضبط، P implies Q، صح؟
+
+335
+00:28:15,520 --> 00:28:21,380
+تمام، هيها rule، يعطيك إيها كاملة، إذا إذا خلصناها و
+
+336
+00:28:21,380 --> 00:28:25,820
+بعدين بيقول لك suppose that، إذا كانت n تربيع أكبر
+
+337
+00:28:25,820 --> 00:28:37,060
+من واحد، هذه Q، فإذا كأنه جا لك Q and P implies Q، و
+
+338
+00:28:37,060 --> 00:28:42,560
+راح جا لك إذا P is true، وهذا خطأ .. هذا خطأ، لو
+
+339
+00:28:42,560 --> 00:28:45,800
+رجعتوا لمحاضرة ال policy لما اتكلمنا عنها، ال policy
+
+340
+00:28:45,800 --> 00:28:51,980
+قلنا إذا كان ال implication is true و P is true،
+
+341
+00:28:51,980 --> 00:28:56,140
+إذا Q is true، مفيش مشكلة، لكن ال implication is
+
+342
+00:28:56,140 --> 00:29:00,880
+true و Q is true، ما أقدرش أقول من دون إن P is true،
+
+343
+00:29:00,880 --> 00:29:07,720
+صحيح، ال implication is true و Q is true، هي في عندي
+
+344
+00:29:07,720 --> 00:29:12,080
+حالتين، Q is true، ما أقدرش أقول إن P is true، لأن في
+
+345
+00:29:12,080 --> 00:29:16,540
+الحالتين ممكن تكون false، ممكن تكون true، فما يركبش
+
+346
+00:29:16,540 --> 00:29:23,300
+أقول true، صح، هيها الحالة التانية والحالة الرابعة،
+
+347
+00:29:23,300 --> 00:29:29,460
+خلوا عينكم معانا ونترجمهم هنا، إذا كانت n هي عدد
+
+348
+00:29:29,460 --> 00:29:35,350
+حقيقي أكبر من واحد، إذا n تربيع زاد .. n تربيع
+
+349
+00:29:35,350 --> 00:29:38,030
+أكبر من واحد، هذه ال implication كلها على بعضها هذه
+
+350
+00:29:38,030 --> 00:29:41,990
+true، أنا شاكة إنها true، صحيحة، فإذا أنا بتكلم في
+
+351
+00:29:41,990 --> 00:29:48,370
+الحالة اتنين وأربعة، تمام، طيب جا لي هنا إيه سبب ده؟
+
+352
+00:29:48,370 --> 00:29:54,690
+n تربيع أكبر من واحد، هذه Q حسب ال .. ال
+
+353
+00:29:54,690 --> 00:29:58,290
+implication، هذه هي Q، تمام، فإذا وين ال Q بتكون true،
+
+354
+00:29:58,290 --> 00:30:06,140
+هاي true، راح على طول، هو استنتج، حطي ال event واستنتج
+
+355
+00:30:06,140 --> 00:30:10,460
+إنه معناته إن أكبر من واحد، وهذا مش صحيح، مش صحيح،
+
+356
+00:30:10,460 --> 00:30:14,100
+لأنه لأ، فيه ممكن تكون false في ال column التاني في
+
+357
+00:30:14,100 --> 00:30:18,940
+ال row التاني، مش هيك، أو تكون true في ال row الرابع،
+
+358
+00:30:18,940 --> 00:30:22,620
+فإذن لأ، ما أقدرش أستنتج الاستنتاج اللي حكى لنا إياه،
+
+359
+00:30:22,620 --> 00:30:28,980
+فإذن false، false، ليه عرفنا، ليه، تمام، طيب هي التانية،
+
+360
+00:30:32,440 --> 00:30:38,400
+برضه إنكم هنا if n is
+
+361
+00:30:38,400 --> 00:30:43,280
+a real number أو عدد حقيقي أكبر من تلاتة، إذا n
+
+362
+00:30:43,280 --> 00:30:47,860
+تربيع أكبر من تسعة، كلام حلو، suppose that n تربيع
+
+363
+00:30:47,860 --> 00:30:55,240
+أقل أو يساوي تسعة، إذا n أقل أو يساوي تلاتة، لعند
+
+364
+00:30:55,240 --> 00:31:02,570
+هنا ونقطع، شوف الجملة اللي قبلها، هذه كلها أحسنت،
+
+365
+00:31:02,570 --> 00:31:10,250
+هذه كلها إيش؟ P implies Q، وهذه negation
+
+366
+00:31:11,150 --> 00:31:16,710
+ال Q، فهل أقدر أقول إنه إذا negation ال Q و P
+
+367
+00:31:16,710 --> 00:31:21,090
+implies ال Q، فهل أقدر أستنتج إن هناك، هل أقدر
+
+368
+00:31:21,090 --> 00:31:26,630
+أستنتج إنه فعلا في شيء مميز لل P هنا، حقيقة فيه ال
+
+369
+00:31:26,630 --> 00:31:29,970
+true، ال implies بمعنى إن العمود التالت لازم يكون
+
+370
+00:31:29,970 --> 00:31:35,770
+true، و ال Q بده يكون false، هذا لا ينطبق إلا على ال
+
+371
+00:31:35,770 --> 00:31:40,090
+row الأول، فإذا أقدر أستنتج إنه لازم يطلع negation
+
+372
+00:31:40,090 --> 00:31:44,400
+P، إيش، راح يطلع negation P؟ طيب، هل فعلا اللي
+
+373
+00:31:44,400 --> 00:31:48,160
+أعطاني إياه هو negation P؟ آه فعلا negation P، كانت
+
+374
+00:31:48,160 --> 00:31:51,120
+هنا أكبر من تلاتة، نصر أقل أو يساوي تلاتة، هي ال
+
+375
+00:31:51,120 --> 00:31:57,660
+negation بتاعتها؟ صح، valid، صارت المفعول منطقي صحيح
+
+376
+00:31:57,660 --> 00:32:01,140
+ومافيش أي مشكلة إطلاقا، كلامك مائة بالمائة، مش قادر
+
+377
+00:32:01,140 --> 00:32:03,920
+أقول عنه حاجة، صح، دكتور، احنا بنشوف ال validity
+
+378
+00:32:03,920 --> 00:32:08,760
+للجملة التانية؟ آه، لهذه الجزئية، الجزء الأول هذا
+
+379
+00:32:08,760 --> 00:32:13,020
+كله اللي أعطاك ال implication، صيغة ال implication
+
+380
+00:32:13,020 --> 00:32:18,400
+اللي هو صيغة P implies Q، ثم بعد ذلك هو فرض لك
+
+381
+00:32:18,400 --> 00:32:23,700
+negation Q وحط نقطة، وبعدين جا لك إنه أنا بستنتج
+
+382
+00:32:23,700 --> 00:32:28,520
+بناء على ذلك كذا، هل الكذا اللي استنتج صح ولا غلط؟ و
+
+383
+00:32:28,520 --> 00:32:30,600
+نفس الكلام هنا، هذا الاستنتاج صح ولا غلط؟ هذا
+
+384
+00:32:30,600 --> 00:32:37,100
+الاستنتاج صح ولا غلط؟ طيب، خلاص، قلنا valid وانتهينا،
+
+385
+00:32:37,100 --> 00:32:44,580
+التالتة، التقسيم،
+
+386
+00:32:44,580 --> 00:32:45,400
+نفسها هي هي،
+
+387
+00:32:50,910 --> 00:32:56,210
+نفس التانية يعني true، كيف نفس التانية؟ طب التانية
+
+388
+00:32:56,210 --> 00:33:00,550
+كانت true، أيوة،
+
+389
+00:33:00,550 --> 00:33:07,830
+في عندك مشكلة، إشكالية هنا، هذه نشوفهم هدول هيك زي
+
+390
+00:33:07,830 --> 00:33:15,110
+ما قلنا كلها P implies Q، P implies Q، هنا يعطيك
+
+391
+00:33:15,110 --> 00:33:22,820
+إيش negation P، يعني كأنه قال لك هنا negation P، و
+
+392
+00:33:22,820 --> 00:33:26,140
+بدنا نشوف هل بيطلع إيش هنا ولا لأ، طب شوف لي negation
+
+393
+00:33:26,140 --> 00:33:31,800
+P، يعني false أول two rows أو صفين، أول صفين، و true، طب هم
+
+3
+
+445
+00:37:55,320 --> 00:38:02,840
+اللي أتانياهنستخدم k و k زائد واحد عشان نثبت أن هي
+
+446
+00:38:02,840 --> 00:38:07,320
+نفسهم، الـ difference لـ الـ square تبعهم هيعطيني نفس
+
+447
+00:38:07,320 --> 00:38:12,980
+الـ هل فعلاً الكلام هذا منطقي ولا لأ؟ هنشوف k زائد
+
+448
+00:38:12,980 --> 00:38:20,260
+واحد تربيع ناقص k تربيع. فك أقواس عشان تصبح الأولى
+
+449
+00:38:21,360 --> 00:38:26,480
+k تربيع زائد اتنين k زائد واحد، كله ناقص k تربيع. شيل
+
+450
+00:38:26,480 --> 00:38:32,270
+الـ k تربيع مع الـ k تربيع. نفس الـ thing، نفس اللي فوق. فإذا
+
+451
+00:38:32,270 --> 00:38:34,930
+فعلاً الـ two terms بتساوي بعض، اللي هي اتنين زائد
+
+452
+00:38:34,930 --> 00:38:38,470
+واحد بتساوي n، اللي هو الـ odd number أصلاً، اللي هو
+
+453
+00:38:38,470 --> 00:38:43,490
+الـ odd number. طريقة بسيطة جداً. آه، طريقة... من
+
+454
+00:38:43,490 --> 00:38:47,150
+الأول كانت مش بسيطة... من الأول مش بسيطة، لكن عاد
+
+455
+00:38:47,150 --> 00:38:50,210
+سحر الأرقام هو اللي خلها تصير بسيطة. بالمناسبة، في
+
+456
+00:38:50,210 --> 00:38:54,290
+كتير relations هيك حلوة في الرياضيات. الأرقام كيف
+
+457
+00:38:54,290 --> 00:38:57,730
+مرتبطة مع بعضها بشكل كتير. هذه مش الأولى ولا
+
+458
+00:38:57,730 --> 00:39:02,670
+الأخيرة. هتكون اللي هتشوفوها. طيب، so that if N is
+
+459
+00:39:02,670 --> 00:39:11,130
+an integer and N تكعيب plus five is odd, then N is
+
+460
+00:39:11,130 --> 00:39:15,910
+even. لاحظتوا؟
+
+461
+00:39:15,910 --> 00:39:23,790
+بدنا نثبت إذا كانت N integer و N تكعيب زائد خمسة
+
+462
+00:39:23,790 --> 00:39:30,130
+odd. بدنا نثبت منها أن N is even باستخدام كل مرة
+
+463
+00:39:30,130 --> 00:39:36,530
+حالة. مرة باستخدام الـ proof by contraposition. نبدأ
+
+464
+00:39:36,530 --> 00:39:40,270
+بالـ contraposition، ثم بالـ contradiction، والفرق
+
+465
+00:39:40,270 --> 00:39:43,990
+شاسع بين التنتين. طيب، بتهيألي بالـ contraposition
+
+466
+00:39:43,990 --> 00:39:50,810
+ما فيها مشكلة. هنفرض عكس الـ equation يعني هبدأ من هنا وأفرض
+
+467
+00:39:50,810 --> 00:39:57,280
+أن هذه odd ونحسب. هذه مش هيك يعني مش كتير صعبة...
+
+468
+00:39:57,280 --> 00:40:02,360
+مش كتير صعبة. فـ assume n is odd، اللي هي عكس
+
+469
+00:40:02,360 --> 00:40:07,500
+تمام. بسطت الأمور وخلصت. معناه ذلك أنه بقدر أحطها بـ
+
+470
+00:40:07,500 --> 00:40:11,560
+2k plus 1 وانتهى الموضوع، وأنعوض في الـ n تكعيب
+
+471
+00:40:11,560 --> 00:40:17,400
+زائد خمسة. عوضنا في n تكعيب زائد خمسة. بنفككها n
+
+472
+00:40:17,400 --> 00:40:20,860
+تكعيب زائد واحد تربيعها، وبعدين أضربه كمان مرة في
+
+473
+00:40:20,860 --> 00:40:25,300
+اتنين k زائد واحد، عشان يظهر معانا term بهذا الشكل.
+
+474
+00:40:25,300 --> 00:40:29,660
+طيب، الـ term اللي بهذا الشكل لو فكّيناها،  حالياً أن في
+
+475
+00:40:29,660 --> 00:40:33,040
+عندي خمسة زائد واحد ستة، وبعدين بناخد عامل مشترك
+
+476
+00:40:33,040 --> 00:40:37,280
+عشان نجد أن الخمسة زائد ستة... خمسة زائد واحد، بـتصير
+
+477
+00:40:37,280 --> 00:40:40,980
+ستة. الستة even، يعني بنفع آخد منه اتنين عامل مشترك.
+
+478
+00:40:42,200 --> 00:40:44,840
+هنا بقدر آخد منها عامل مشترك اتنين، وهنا بقدر آخد
+
+479
+00:40:44,840 --> 00:40:46,960
+اتنين عامل مشترك، وهنا بقدر آخد اتنين عامل مشترك، و
+
+480
+00:40:46,960 --> 00:40:50,360
+مجموع الاتنين هدول برضه بقدر آخد عامل مشترك. ما دام
+
+481
+00:40:50,360 --> 00:40:56,860
+ذلك ممكن أحطّه بصورة اتنين في some k. أصبحت إيش؟ even.
+
+482
+00:40:56,860 --> 00:41:01,480
+أنا بدأت بـ odd، طلعت even. هنا كان بدري يعني أبدأ بـ
+
+483
+00:41:01,480 --> 00:41:07,480
+odd وأروح لـ even. عكسناها، عكسناها. لما بدأنا بـ
+
+484
+00:41:07,480 --> 00:41:12,740
+negation q، طلع لنا negation p. بالـ contrapositive
+
+485
+00:41:12,740 --> 00:41:18,920
+أكيد is true. فإذا خلصنا منها الآن باستخدام الـ
+
+486
+00:41:18,920 --> 00:41:21,860
+contradiction. باستخدام الـ contradiction الموضوع
+
+487
+00:41:21,860 --> 00:41:28,660
+هِيختلف. هنشتغل على إنه n plus واحد is odd، and n is
+
+488
+00:41:28,660 --> 00:41:32,940
+عكسناها
+
+489
+00:41:32,940 --> 00:41:37,420
+خالص. بدي أفرض عكسها... مش بدنا نفرض عكسها. نجي للـ
+
+490
+00:41:37,420 --> 00:41:39,680
+contradiction. كلنا بنقول إنّا بدنا نفرضها العكس.
+
+491
+00:41:39,680 --> 00:41:45,040
+Okay، هي العكس. العكس. بدل ما كنت بقول if n تكعيب زائد
+
+492
+00:41:45,040 --> 00:41:51,300
+خمسة is odd، then n is even. لأ، بدأ أقول if n is odd،
+
+493
+00:41:51,300 --> 00:41:59,960
+okay. بدأنا بالـ odd، ومنها n is odd، وكلنا عارفين
+
+494
+00:41:59,960 --> 00:42:10,620
+أنّه الـ... is odd. وكلنا عارفين أنّه odd في odd، odd هي
+
+495
+00:42:10,620 --> 00:42:20,120
+عبارة عن odd في odd، فهي ساوي odd. طيب، n تكعيب ما
+
+496
+00:42:20,120 --> 00:42:26,140
+هي عبارة عن n تربيع في n، يعني نفس الكلام. odd في
+
+497
+00:42:26,140 --> 00:42:32,470
+odd، يعني n تكعيب برضه هتطلع odd. برضه هتكون عبارة
+
+498
+00:42:32,470 --> 00:42:39,630
+عن odd، صح؟ فيها and
+
+499
+00:42:39,630 --> 00:42:47,550
+n is odd. طيب، odd تكعيب، خلاص odd. طيب، odd زائد odd
+
+500
+00:42:47,550 --> 00:42:55,050
+even. even هتطلع، وليس زي فرضيتنا أن هي odd، وليست
+
+501
+00:42:55,050 --> 00:43:00,250
+كما افترضنا أن هي odd. فإذا هذا معناه أن تربيعها is
+
+502
+00:43:00,250 --> 00:43:03,250
+odd، وهذا معناه أن تكعيبها برضه is odd. خليني نمحي
+
+503
+00:43:03,250 --> 00:43:09,830
+الكتاب اللي وضحنا فيه وهذا
+
+504
+00:43:09,830 --> 00:43:13,790
+معناه أن خمسة is odd، أساساً هي بحد ذاتها، وصار odd
+
+505
+00:43:13,790 --> 00:43:19,010
+زائد odd، even. عكس فرضيتنا اللي افترضناها، وهذا
+
+506
+00:43:19,010 --> 00:43:24,630
+معناه أن الفرضية اللي احنا suppose that n تكعيب
+
+507
+00:43:24,630 --> 00:43:28,830
+زائد خمسة is odd، and n is odd، اللي كانت المفروض
+
+508
+00:43:28,830 --> 00:43:32,910
+even، حسب
+
+509
+00:43:32,910 --> 00:43:36,710
+النظرية الأصلية. احنا فرضنا عكسها، طلع عكسها false.
+
+510
+00:43:36,710 --> 00:43:42,960
+إذاً هي true. أخذنا هذا المثال، مش هيك بس، كان لقّاش
+
+511
+00:43:42,960 --> 00:43:49,180
+جذر تربيعي، تكعيبه مش هيفرق كتير، بس فكرته أنه كان
+
+512
+00:43:49,180 --> 00:43:53,500
+سؤال في امتحان. طبعاً الطلاب شافوا أنه تكعيبي، وقفوا
+
+513
+00:43:53,500 --> 00:43:58,220
+حالهم، ووقفوا حالهم. زي ما بقوله لأ، بصد ولا برد
+
+514
+00:43:58,220 --> 00:44:02,200
+صاروا. ليش؟ ما فيش فيها شيء. طب ما هي نفس اللي حلينا في
+
+515
+00:44:02,200 --> 00:44:05,700
+الـ slides. هو هو. اعملوا بنفس خطواته، إيش هيتغير
+
+516
+00:44:05,700 --> 00:44:10,140
+معاكم رقمين؟ بس الـ process هي هي. ليش ما
+
+517
+00:44:10,140 --> 00:44:13,360
+تجرأتو يا طلاب مثلاً تعملوها؟ الـ process اعمل الـ
+
+518
+00:44:13,360 --> 00:44:15,500
+process. خليه يطلع الأقل. بطبيعي مش كل الأسئلة
+
+519
+00:44:15,500 --> 00:44:18,920
+بتجيك زي ما هي. الـ coffee class هيها، عملنا نفس
+
+520
+00:44:18,920 --> 00:44:24,440
+الفكرة. يقول لنا أن هي rational، ومعناه ذلك أنه بقدر
+
+521
+00:44:24,440 --> 00:44:28,900
+أحطها بصيغة... طيب تمام، وهذا معناه أنه بدل ما أجيب
+
+522
+00:44:28,900 --> 00:44:35,310
+تربيع، أجيب تكعيب للطرفين. بس جبنا تكعيب للطرفين، منها
+
+523
+00:44:35,310 --> 00:44:39,070
+بيطلع إنه بدل ما كانت A تربيع هي اللي even، طب هي
+
+524
+00:44:39,070 --> 00:44:43,050
+نفس الـ A تكعيب هي اللي even، والاستنتاج هو هو
+
+525
+00:44:43,050 --> 00:44:47,770
+هيطلع. ما احنا طول لسه مش طول. كنا حالين N تكعيب، إذا
+
+526
+00:44:47,770 --> 00:44:52,730
+كان odd، N، الـ N تكعيب برضه هيطلع odd. طيب ما هي نفس
+
+527
+00:44:52,730 --> 00:44:56,610
+الفكرة. نفس الفكرة. إيش اختلفت بالله هالوجه عن اللي
+
+528
+00:44:56,610 --> 00:45:01,300
+كانت في الـ slides؟ ولا شيء ولا حاجة. بس عشان ظهر
+
+529
+00:45:01,300 --> 00:45:06,860
+التكعيب. خلّصنا. بتفعل الباقي نفس المحاضرة. الباقي نفس
+
+530
+00:45:06,860 --> 00:45:10,260
+المحاضرة تماماً. فـ is even، وهذا معناه أن A بقدر
+
+531
+00:45:10,260 --> 00:45:13,360
+أحطها بـ اتنين K. وفي الحالة هذه بنكملها، بدل ما كان
+
+532
+00:45:13,360 --> 00:45:17,520
+هيطلع أربعة في K تربيع، هتصير ثمانية في K تكعيب، وفي
+
+533
+00:45:17,520 --> 00:45:20,360
+جميع الأحوال الثمانية هتختصر مع الاتنين، وهتظل
+
+534
+00:45:20,360 --> 00:45:23,380
+برضه even. هناك كانت أربعة بتظل even، هنا ثمانية
+
+535
+00:45:23,380 --> 00:45:29,540
+بتظل even. برضه نفس القصة... نفس القصة، ف... بالضبط
+
+536
+00:45:29,540 --> 00:45:32,840
+even على even، معناته في common، وانتهى الكلام، و
+
+537
+00:45:32,840 --> 00:45:35,120
+خلصت. هيك طريقة حلها.
+
+538
+00:45:42,420 --> 00:45:46,360
+طيب، بتهيألي هذه كتير برضه بسيط حلها، أنه لو N is
+
+539
+00:45:46,360 --> 00:45:56,220
+positive، then N is odd if and only if... if... if
+
+540
+00:45:56,220 --> 00:46:03,060
+and only if five N plus six is odd. بدي شغالة أحلها.
+
+541
+00:46:03,060 --> 00:46:06,640
+بدنا نشوف فكرة الحل، إيش ممكن نعمل فيها؟ فكرة
+
+542
+00:46:06,640 --> 00:46:07,180
+الحل؟
+
+543
+00:46:12,950 --> 00:46:20,330
+n is positive، يعني إيش؟ أكبر من صفر، إذا أو أكبر
+
+544
+00:46:20,330 --> 00:46:27,410
+من صفر، إذا n
+
+545
+00:46:27,410 --> 00:46:40,210
+is odd if and only if five n plus six is odd.
+
+546
+00:46:49,610 --> 00:46:58,590
+طيب بس بس بس لأ مظبوط، بس خلصت الجثة، ههه. هنعملها
+
+547
+00:46:58,590 --> 00:47:05,250
+أخذنا هذه الـ if and only if. هي عبارة عن n is odd، إذا
+
+548
+00:47:05,250 --> 00:47:11,110
+five n plus six is odd، and
+
+549
+00:47:14,260 --> 00:47:24,480
+five n plus six is odd، even if n is odd. اعمل هذه
+
+550
+00:47:24,480 --> 00:47:30,300
+الحالة، اعمل هذه الحالة وخلصناها. بس الأولى ما فيش
+
+551
+00:47:30,300 --> 00:47:34,320
+فيها مشكلة إطلاقاً، لأن أنت direct، هتفرض أن n فعلاً
+
+552
+00:47:34,320 --> 00:47:38,880
+هي is odd، وبتعوض بـ 2k plus 1 في هذا الـ term.
+
+553
+00:47:38,880 --> 00:47:44,520
+هيطلع أن الـ term هذا odd. انتهى. هنا مش هتقدر تتعامل
+
+554
+00:47:44,520 --> 00:47:51,360
+معاها. اعمل indirect، افرض n is even، وأثبت منها أن
+
+555
+00:47:51,360 --> 00:47:57,800
+خمسة n plus six even. معنى ذلك بالـ contrapositive
+
+556
+00:47:57,800 --> 00:48:04,880
+بتصير الـ relation هذه صحيحة. صحيح
+
+557
+00:48:04,880 --> 00:48:08,940
+صحيح. لاحظتوا كيف انتهى؟ بدك تعملها direct، اعملها
+
+558
+00:48:08,940 --> 00:48:12,440
+direct. هذه بدك تعملها direct، اعملها direct. بس بدك
+
+559
+00:48:12,440 --> 00:48:16,520
+تكون فاهم أنك هذه إذا كان هذه odd، odd في odd، odd
+
+560
+00:48:16,520 --> 00:48:21,020
+plus even، خلاص. نعم، بدك تعمل direct، اعمل direct.
+
+561
+00:48:21,020 --> 00:48:23,640
+ما فيش مشكلة، بس فاهمين فكرة أنّه بده اعمل
+
+562
+00:48:23,640 --> 00:48:27,830
+duplication. الآن، الـ if and only if، معناته f في
+
+563
+00:48:27,830 --> 00:48:33,710
+اتجاه p to q، وبرضه implication في اتجاه q to p.
+
+564
+00:48:33,710 --> 00:48:38,130
+تمام، خلصناها. بتنزل معاكم هذه محلولة، بس أخذنا
+
+565
+00:48:38,130 --> 00:48:41,370
+الفكرة، الـ concept بتاعتها بسيطة جداً، فتاخد على
+
+566
+00:48:41,370 --> 00:48:45,090
+الحالتين، عشان تكون خلصنا جزئيتنا لهذا اليوم.
+
+567
+00:48:45,090 --> 00:48:49,870
+الأسبوع الجاي بنبدأ درس جديد إن شاء الله تعالى.
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..95dfdead4cf52ac8d36f9eaaea72b54c4c0da141
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0_postprocess.srt
@@ -0,0 +1,2268 @@
+1
+00:00:05,230 --> 00:00:09,650
+السلام عليكم، يعطيكم العفو يا شباب، اليوم نستكمل
+
+2
+00:00:09,650 --> 00:00:14,070
+جزئية ال proofs اللي كنا بنتكلم فيها، فاليوم ان
+
+3
+00:00:14,070 --> 00:00:17,850
+شاء الله هناخد مجموعة أمثلة محلولة أو solve the
+
+4
+00:00:17,850 --> 00:00:23,590
+problem لما تم أخذه خلال هذا الأسبوع، وهذا اشي
+
+5
+00:00:23,590 --> 00:00:26,970
+كتير كويس انه بيظل معانا في مجالفي الأسبوع هذا و
+
+6
+00:00:26,970 --> 00:00:30,690
+يمكن انا مراكن كتير على المحاضرات المصورة فكتير
+
+7
+00:00:30,690 --> 00:00:33,430
+كويس ان انتوا تكونوا حاضرين المحاضرة المصورة عشان
+
+8
+00:00:33,430 --> 00:00:38,350
+فعلا بتساعدني ان اكون ماشي بشكل كتير افضل خلال
+
+9
+00:00:38,350 --> 00:00:42,910
+الأسبوع و هذا بوفرلنا وقت ان احنا نعرف نحل أسئلة و
+
+10
+00:00:42,910 --> 00:00:46,970
+يمكن هذه هي الأهم بالنسبالكوا لأنه أمثلة في المعظم
+
+11
+00:00:46,970 --> 00:00:50,170
+هي أمثلة امتحاناتفي المعظم هتلاقي ان هي أمثلة
+
+12
+00:00:50,170 --> 00:00:54,630
+امتحانات فاليوم نبدأ ناخد ناخد ال second set of
+
+13
+00:00:54,630 --> 00:00:58,090
+problems المرة اللي فات الأسبوع اللي فات أخدنا أول
+
+14
+00:00:58,090 --> 00:01:02,370
+set أو أول مجموعة من ال problems اليوم نكمل مجموعة
+
+15
+00:01:02,370 --> 00:01:04,710
+تانية وهذا السؤال كان جاي في امتحان من الامتحانات
+
+16
+00:01:04,710 --> 00:01:09,890
+كان في أحد الامتحانات جاي سابقا برضه ل discrete
+
+17
+00:01:09,890 --> 00:01:16,250
+mathematics تمام كان let f x y و هذه تمثل
+
+18
+00:01:16,250 --> 00:01:21,610
+statement x can help yX can help Y والمطلوب الآن
+
+19
+00:01:21,610 --> 00:01:25,610
+بالنسبة لل domain اللي بيحتوي على كل ال people in
+
+20
+00:01:25,610 --> 00:01:28,730
+the world نفترض أنه ال domain ال universal domain
+
+21
+00:01:28,730 --> 00:01:33,450
+طبعا هو كل سكان العالم أو كل الناس في العالم بدنا
+
+22
+00:01:33,450 --> 00:01:37,170
+نستخدم quantifiers and logical operators to
+
+23
+00:01:37,170 --> 00:01:41,350
+express each of the statements و بحنبدأ بمجموعة
+
+24
+00:01:41,350 --> 00:01:46,600
+statementsكويس everyone can help Ali everyone أكيد
+
+25
+00:01:46,600 --> 00:01:51,460
+بنقول for all كويس و هنكتب ال for all هذه لملة X
+
+26
+00:01:51,460 --> 00:01:58,100
+فإذا هتبدأ ب X او ال F of X لأن X احنا عملنا ..
+
+27
+00:01:58,100 --> 00:02:03,240
+عملنا ال quantification في الأول for all X and Ali
+
+28
+00:02:03,240 --> 00:02:10,310
+why هنا Ali؟ صحيح؟why لأ هي بطلت why هي أصبحت help
+
+29
+00:02:10,310 --> 00:02:16,610
+علي فأصبحت علي تحديدا علي كويس فهي هذه طريقة حلها
+
+30
+00:02:16,610 --> 00:02:20,830
+بكل بساطة أعرفت جميع ال limits اللي عندك في بعضهم
+
+31
+00:02:20,830 --> 00:02:24,030
+بعض ال variables اتعرفت من خلال ال quantifier
+
+32
+00:02:24,030 --> 00:02:28,780
+وبعضهم اتعرف بشكل direct مباشرعالي أنا قولت عالي
+
+33
+00:02:28,780 --> 00:02:33,020
+مباشرة فإذا بدي أعرفه عالي على طول صحيح؟ مش هحطه
+
+34
+00:02:33,020 --> 00:02:36,120
+why ولا هقول there exist ولا لإن هم there exist
+
+35
+00:02:36,120 --> 00:02:40,360
+أنا عارفه تحديدا، هو عالي كويس، نفس الكلام سارة
+
+36
+00:02:40,360 --> 00:02:45,080
+can help someone there exist ايش؟ why بالظبط،
+
+37
+00:02:45,080 --> 00:02:50,080
+هنفتح أقواز سارة و why تمام جدا، هي واضحة الأمور
+
+38
+00:02:50,080 --> 00:02:53,720
+وسهلة بسيطة جدا، صحيح؟ سؤال زي هذا، كتير كانوا
+
+39
+00:02:53,720 --> 00:02:58,750
+بغلطوا فيهتخيلوا سؤال بسيط بهذا الشكل كتير كانوا
+
+40
+00:02:58,750 --> 00:03:03,790
+بيغلطوا فيه بيجيبوش في علامته تمام just one just
+
+41
+00:03:03,790 --> 00:03:08,390
+one there exist exclamation مش متذكرينه طيب just
+
+42
+00:03:08,390 --> 00:03:14,610
+one man can help both Ali and Omar فمعنى ذلك هنا
+
+43
+00:03:15,680 --> 00:03:20,620
+there exist فنكتبها there exist with exclamation x
+
+44
+00:03:20,620 --> 00:03:24,320
+لإن هو اللي بده يقدّم الخدمة هو ال subject و بدنا
+
+45
+00:03:24,320 --> 00:03:31,500
+نعمل x و هنفتح أقواص عشان أقول أحمد and علي عشان
+
+46
+00:03:31,500 --> 00:03:36,320
+نقول أحمد او علي إذا بدنا نكون جسمنا ال four كلها،
+
+47
+00:03:36,320 --> 00:03:41,120
+تمام؟ فإذا يوجد شخص واحد الشخص هذا بساعد أحمد
+
+48
+00:03:41,120 --> 00:03:44,760
+والشخص هذا بساعد عمر ولا علي؟ أنا عمر
+
+49
+00:03:53,460 --> 00:03:59,040
+ممكن بس مش هتكون كتير واضحة مش هتوضح كتير ال and
+
+50
+00:03:59,040 --> 00:04:03,240
+في هذه المشكلة ال and كيف بدك تعملها انت بتقول كمه
+
+51
+00:04:03,240 --> 00:04:10,240
+انت بدك تحطها يعني هنا هذه كله هذا بدون القسين
+
+52
+00:04:10,240 --> 00:04:12,960
+الأقواص هذه و هذه بس بدها تكون and واضحة
+
+53
+00:04:16,350 --> 00:04:23,950
+no one can help himself no
+
+54
+00:04:23,950 --> 00:04:32,570
+one negation for all لا يوجد ولا واحد لكن لو قلنا
+
+55
+00:04:32,570 --> 00:04:38,370
+there exist معناته انه لا يوجد بعضهم تمام؟ لاوجد
+
+56
+00:04:38,370 --> 00:04:41,830
+بعضهم طيب no one can .. بس انا مش عليها دي بتطلع
+
+57
+00:04:41,830 --> 00:04:43,550
+بتطلع علي كيف تكون ترجمه himself
+
+58
+00:04:46,420 --> 00:04:51,180
+هل بتحطه اكس؟ اكس و اكس تمام himself لإن بدي احطه
+
+59
+00:04:51,180 --> 00:04:54,400
+اكس و اي معناته قد يختلفوا اكس و اي مع بعض لكن انا
+
+60
+00:04:54,400 --> 00:04:59,260
+بقول مش هيقدر يساعد نفسه مش هيقدر يساعد نفسه فمعنى
+
+61
+00:04:59,260 --> 00:05:04,920
+ذلك انه انا بتكلم عن عن هو اكس
+
+62
+00:05:04,920 --> 00:05:10,860
+اكس عن نفسه تمام هدولة مهمين لإنه بتتكلم وينها
+
+63
+00:05:10,860 --> 00:05:14,980
+اولا اللي هو اكس نفسه اللي عرفنا himself
+
+64
+00:05:19,970 --> 00:05:27,810
+just one .. no one .. no one can .. اه there exist
+
+65
+00:05:27,810 --> 00:05:31,350
+هنا لا يوجد احد .. اه لا يوجد احد هنا ان انت
+
+66
+00:05:31,350 --> 00:05:35,770
+بتتكلم هنا لا يوجد احد ان بدك تعملها no one معناته
+
+67
+00:05:35,770 --> 00:05:43,570
+بدك تحط for all و جوا negation فش
+
+68
+00:05:43,570 --> 00:05:48,240
+بعض هنا انا بتكلم عن نفس الشخصهو نفس الشخص يعني
+
+69
+00:05:48,240 --> 00:05:54,600
+هنا بقول لاوجد اي واحد بساعد نفسه انا ماتكلمتش عن
+
+70
+00:05:54,600 --> 00:06:00,540
+التاني قد يساعد التاني و قد لا يساعد التاني بقى
+
+71
+00:06:00,540 --> 00:06:04,660
+بعرفش ممكن بساعد غيره و ممكن لأ بساعدش غيره و برضه
+
+72
+00:06:04,660 --> 00:06:09,940
+بساعدش نفسه ما احنا قولنا ممكن او ممكن لأ في
+
+73
+00:06:09,940 --> 00:06:14,180
+الحالة هذه اذا قلنا for all معناته انه لا الكل
+
+74
+00:06:14,180 --> 00:06:23,450
+الكل مش هيساعدهأو ليس الكل معناها صح؟ لازم نعملها
+
+75
+00:06:23,450 --> 00:06:28,310
+for all لأ خلينا نكتبهم كلامكم صح خلينا نكمل مع
+
+76
+00:06:28,310 --> 00:06:30,490
+بعض كويس خلينا نفكر مع بعض مش المشكلة ما احنا
+
+77
+00:06:30,490 --> 00:06:36,570
+قالين نراجع نكتبها و نحلل مش صح اني أقولك زي ما
+
+78
+00:06:36,570 --> 00:06:39,510
+أقولك ألا غلط و بنفع و أحفظها هيك خلينا نفهمها
+
+79
+00:06:39,510 --> 00:06:47,000
+لاوجد كل مش هيك معناته أنه قد يكون بعضهمركزوا
+
+80
+00:06:47,000 --> 00:06:53,260
+معايا شوفوها هيك زابطة معاكم there is no all على
+
+81
+00:06:53,260 --> 00:06:56,420
+اللي احنا كاتبينه معناته ان ممكن يكونوا كلهم
+
+82
+00:06:56,420 --> 00:07:04,340
+بيحققوها الا واحد مش هيك؟ صح؟ في اشي مش واضح؟ هيها
+
+83
+00:07:04,340 --> 00:07:08,380
+منطقية طيب العكس تبع او خلينا نقول الحالة اللي
+
+84
+00:07:08,380 --> 00:07:13,940
+احنا كاتبينها و نفهمها نحاول ان نحللها هنا
+
+85
+00:07:15,020 --> 00:07:18,800
+there exist هذه الحالها يعني على الأقل في واحد طب
+
+86
+00:07:18,800 --> 00:07:24,940
+نقول مافيش ولا واحد لاوجد
+
+87
+00:07:24,940 --> 00:07:29,860
+ولا واحد هنا قد يكون في واحد لكن اللي أكيد أنه مش
+
+88
+00:07:29,860 --> 00:07:35,020
+الكل اللي فوق هذه معناته أنه مش الكل ممكن يكون كل
+
+89
+00:07:35,020 --> 00:07:39,380
+واحد الواحد هذا نفع ال for all الواحد نفع ال for
+
+90
+00:07:39,380 --> 00:07:43,200
+all أما هنا لأ هذه يمكن تكون أكثر وقعية واضحة no
+
+91
+00:07:43,200 --> 00:07:48,450
+one خلاصلل function بيظبط كلامك منطقي فهنا بتصير
+
+92
+00:07:48,450 --> 00:07:55,050
+for all negation if كلامك مية المية تظبط هيك
+
+93
+00:07:55,050 --> 00:08:00,250
+معناته كإني بقول للكل ولا واحد بيساعد حاله بس في
+
+94
+00:08:00,250 --> 00:08:05,030
+الحالة هد انت كلش عملت لها دي دي Morgan صح فكلامك
+
+95
+00:08:05,030 --> 00:08:09,170
+ينطبق مع حدي أصبح مع ال negation there exist طلعت
+
+96
+00:08:09,170 --> 00:08:14,050
+ال ال negation برا و اتحولت عندك بدل ما هي for all
+
+97
+00:08:14,050 --> 00:08:15,230
+اتحولت ل there exist
+
+98
+00:08:18,340 --> 00:08:24,160
+تمام الأخيرة not everyone ليس الكل هدرك pathology
+
+99
+00:08:24,160 --> 00:08:27,980
+مع مين مع مفهومنا تعتوي ليس الكل بساعد someone
+
+100
+00:08:27,980 --> 00:08:32,060
+فهنا هتكون ليس الكل هنا بتظبط معانا ليس الكل بمعنى
+
+101
+00:08:32,060 --> 00:08:37,800
+أن في بعض هيساعد بس مش الكل البعض هيساعد أه بس ليس
+
+102
+00:08:37,800 --> 00:08:46,500
+الكل بحظين هنا not everyone negation for allوطبعا
+
+103
+00:08:46,500 --> 00:08:49,080
+can help someone, someone بنتخليها زي ما هي
+
+104
+00:08:49,080 --> 00:08:57,400
+someone there exist y اللي هي someone تمام طيب هذا
+
+105
+00:08:57,400 --> 00:09:01,160
+حاسبلكوا يا برضه هنزلكوا الملف تقرأوا لإن اليوم
+
+106
+00:09:01,160 --> 00:09:07,590
+شوية مزودلكوا حجم الالهدول هذا مجرد بس العكس لهناك
+
+107
+00:09:07,590 --> 00:09:11,670
+هيكون في عندى ال negations .. أفوان ال notations
+
+108
+00:09:11,670 --> 00:09:15,650
+موجودة لل quantifiers و المقلوب تكتب منها الجملة
+
+109
+00:09:15,650 --> 00:09:20,290
+الجملة بسيطة جدا مجرد لغة مجرد تركيب لغات مجرد
+
+110
+00:09:20,290 --> 00:09:27,210
+تركيب لغة عشان نحاول نصل ل ال proving strategies
+
+111
+00:09:27,210 --> 00:09:29,790
+لإن انا عامل مجموعة أسئلة في أخرها في ال proving
+
+112
+00:09:29,790 --> 00:09:34,470
+strategies معنى أنه نصلهابتقرؤوها إذا في واحدة
+
+113
+00:09:34,470 --> 00:09:38,230
+منهم مش واضحة معاكم ترجعوا هنا
+
+114
+00:09:42,030 --> 00:09:45,170
+هذه مثلا واحدة من الأسئلة اللي شفتها في واحد من
+
+115
+00:09:45,170 --> 00:09:49,050
+الامتحانات على ال net مثلا All problems طبعا أنتوا
+
+116
+00:09:49,050 --> 00:09:52,470
+بتعرفين ال questions في بعضها problems و بعضها
+
+117
+00:09:52,470 --> 00:09:57,070
+true و false و بعضها multiple choice بس في منهم
+
+118
+00:09:57,070 --> 00:10:00,350
+problems اللي هو بدأ حل خطوات فهنا لو قلنا كل
+
+119
+00:10:00,350 --> 00:10:05,030
+problems اللي هي نوع من أنواع ال questions are
+
+120
+00:10:05,030 --> 00:10:10,810
+difficult and frustratingdifficult معروفة صعبة
+
+121
+00:10:10,810 --> 00:10:18,670
+frustrating محبطة كويس هذه premise هيعطيكوا إياها
+
+122
+00:10:18,670 --> 00:10:22,070
+على طول هيكون في عندكوا مجموعة questions ال exam
+
+123
+00:10:22,070 --> 00:10:26,150
+تبعكم في multiple choice و في true و false و في
+
+124
+00:10:26,150 --> 00:10:30,490
+problems و بعدين أقولكوا دي و بعدين كل ال problems
+
+125
+00:10:30,490 --> 00:10:35,220
+صعبة و محبطة فبتكونوا تذاكروا كويستمام and some
+
+126
+00:10:35,220 --> 00:10:40,580
+problems are challenging بعض المشاكل أو بعض ال
+
+127
+00:10:40,580 --> 00:10:46,060
+problems هذه فيها تحدي يعني هتكون فيها أفكار كذا
+
+128
+00:10:46,060 --> 00:10:51,200
+فكرة في بعض كذا إشي فيها تحدي الآن hence المقلوب
+
+129
+00:10:51,200 --> 00:10:54,760
+إيش بتكون تثبته أنه some problems are frustrating
+
+130
+00:10:54,760 --> 00:10:58,900
+and challenging بتكون تثبته أن بعضها هو مش بس
+
+131
+00:10:58,900 --> 00:11:05,410
+challenging لأ كمان محبطبعضها ليس فقط فيه تحدي
+
+132
+00:11:05,410 --> 00:11:11,810
+وإنما كمان محبط تمام بطريقة .. كيف؟ بطريقة تقليدية
+
+133
+00:11:11,810 --> 00:11:16,030
+بدنا نحط من ال universe of discourse اللي هي
+
+134
+00:11:16,030 --> 00:11:18,950
+مجموعة ال questions كلها عشان نبدأ نقول ال
+
+135
+00:11:18,950 --> 00:11:22,950
+definitions اللي كانت عندى لمجموعة ال premises و
+
+136
+00:11:22,950 --> 00:11:26,110
+ال conclusion هنعرفها بهذا الشكل ال P هقول ان هي
+
+137
+00:11:26,110 --> 00:11:30,190
+problem من كل questions مين ال problem فكل problem
+
+138
+00:11:30,190 --> 00:11:37,790
+هو محبط اوأو صعب مش هيك هاي أول حالة من الحلقة دي
+
+139
+00:11:37,790 --> 00:11:41,390
+بالظبط هتكون for all هي all دي هقول هي ل difficult
+
+140
+00:11:41,390 --> 00:11:48,290
+ال F ل frustrating و ال C ل challenging عشان نبدأ
+
+141
+00:11:48,290 --> 00:11:52,990
+نكتب ال premises كيف هيكون شكلها for all x يعني
+
+142
+00:11:52,990 --> 00:11:58,050
+لكل ال questions إذا كانت ال question هي problem
+
+143
+00:11:58,050 --> 00:12:05,480
+إذا هي difficult وfrustrating تمام التانية some
+
+144
+00:12:05,480 --> 00:12:11,100
+problems are فعلا there exist x some بعض ال
+
+145
+00:12:11,100 --> 00:12:15,360
+questions هي problems و challenging هي فعلا
+
+146
+00:12:15,360 --> 00:12:18,040
+problem و في نفس الوقت مدام هي problem برضه هتكون
+
+147
+00:12:18,040 --> 00:12:22,000
+challenging لأن and معناته لاتنين هي problem و هي
+
+148
+00:12:22,000 --> 00:12:24,800
+challenging في نفس الوقت طيب إيش اللي بدنا نثبته
+
+149
+00:12:24,800 --> 00:12:31,010
+بدنا نثبت some problems there exist xproblem هي
+
+150
+00:12:31,010 --> 00:12:38,530
+some problem frustrating و challenging تمام كبنث
+
+151
+00:12:38,530 --> 00:12:42,330
+بتهادي من هادي فبتهاد بسيطة يمكن احنا أخدنا المرة
+
+152
+00:12:42,330 --> 00:12:46,170
+اللي فاتت بعض أمثل عليها نحاول نطلعهم كلهم true
+
+153
+00:12:46,170 --> 00:12:49,290
+بالظبط
+
+154
+00:12:49,290 --> 00:12:53,930
+إذا وصلنا لمرحلة نطلعهم كلهم true خلصت فال proof
+
+155
+00:12:53,930 --> 00:12:57,070
+تبعنا هنبدأ بالبرميز الأولى البرميز الأولى for all
+
+156
+00:12:57,070 --> 00:13:00,590
+معناته أكيدمن ال for all هدول هفترض أنه في عنصر
+
+157
+00:13:00,590 --> 00:13:06,110
+اسمه A شاك معناته من كل ال problems اللي موجودة
+
+158
+00:13:06,110 --> 00:13:09,390
+هتكون ال problem A وB وC وD و .. جد ما بدك ال
+
+159
+00:13:09,390 --> 00:13:13,030
+problems بس واحدة منهم A وهدي A واحدة من ال
+
+160
+00:13:13,030 --> 00:13:16,430
+universive discourse أكيد بدون for all يعني كلهم
+
+161
+00:13:16,430 --> 00:13:21,050
+شاك بيقولوا أن في واحدة منهم هي A فإذا
+
+162
+00:13:21,050 --> 00:13:24,950
+automatically كأنه P of Aأعملنا ال universal
+
+163
+00:13:24,950 --> 00:13:29,570
+specification اللي أخدمها برضه المحاضرة مش السابقة
+
+164
+00:13:29,570 --> 00:13:35,650
+اللي جابلها P of A implies D and F okay بس لمين؟
+
+165
+00:13:35,650 --> 00:13:40,590
+مش للعنصر X و I go for all لأ حددت واحد منهم حددنا
+
+166
+00:13:40,590 --> 00:13:45,990
+واحد منهم A و A هذا لازم يكون طبعا أكيد belong to
+
+167
+00:13:45,990 --> 00:13:55,170
+ل X belong لمين؟ ل Xأو لست X اللي هي ال questions
+
+168
+00:13:55,170 --> 00:13:59,610
+اللي هي ال questions تمام التانية اللي هو ال
+
+169
+00:13:59,610 --> 00:14:02,270
+premise التاني المقصود فيها اللي هو there exist X,
+
+170
+00:14:02,550 --> 00:14:06,450
+B of X and C of X معناته انا ايش بقول؟ بقول يوجد
+
+171
+00:14:06,450 --> 00:14:10,430
+مشكلة من ال universe of discourse .. من مجموعة
+
+172
+00:14:10,430 --> 00:14:13,930
+المشاكل اللي جبتلكيها في الامتحان يوجد مشكلة هي
+
+173
+00:14:13,930 --> 00:14:19,800
+problem و challenging في نفس الوقتواحدة من المسائل
+
+174
+00:14:19,800 --> 00:14:23,500
+اللي جبتهم كانت في جزئية ال problems اللي هي بدأ
+
+175
+00:14:23,500 --> 00:14:27,080
+حلول يعني مش مجرد صح و غلط و true or false بدأ حل
+
+176
+00:14:27,080 --> 00:14:30,780
+و في نفس الوقت هي فيها تحدي واحدة منهم على الأقل
+
+177
+00:14:30,780 --> 00:14:34,240
+there exist طيب بدي افترض ان الواحدة ده هي اللي
+
+178
+00:14:34,240 --> 00:14:43,830
+ايه؟ في مشكلة؟فيش مشكلة هي .. هذه بدي اقولهنا بهذا
+
+179
+00:14:43,830 --> 00:14:48,190
+الشكل يعني كأنني بإذن الله أقدر أقول P of A and C
+
+180
+00:14:48,190 --> 00:14:53,870
+of A في عنكم أي مشكلة قبل ما نعديها احنا قولنا إيش
+
+181
+00:14:53,870 --> 00:14:59,860
+في واحدة من المشاكلوحدة من المشاكل هي problem أو
+
+182
+00:14:59,860 --> 00:15:04,300
+من الأسئلة هي problem و challenging صح؟ وقلنا أن
+
+183
+00:15:04,300 --> 00:15:08,200
+هذي بدأ افترض أنها a واحدة منهم و هي ال a بس بدأ
+
+184
+00:15:08,200 --> 00:15:11,800
+أقول كمان مدام واحدة يعني at least في واحد هي ال a
+
+185
+00:15:11,800 --> 00:15:16,160
+طيب في نفس الوقت ال a هذه ماهي واحدة من الفرقول
+
+186
+00:15:16,160 --> 00:15:23,200
+صح؟ يعني معنى ذلك أن a تحديدا كحالة خاصة ممكن
+
+187
+00:15:23,200 --> 00:15:29,150
+ينطبق عليها ال two quantifiersالـ two premises
+
+188
+00:15:29,150 --> 00:15:33,650
+فهنقول برضه هي ال A at least ال A يمكن يكون في
+
+189
+00:15:33,650 --> 00:15:36,850
+غيرها بس على الأقل ال A هذه واحدة منهم على الأقل
+
+190
+00:15:36,850 --> 00:15:42,590
+ال A هذه محققة ال two premises okay بتهيألي بعد
+
+191
+00:15:42,590 --> 00:15:46,090
+هيك الأمور صارت بسيطة جدا لأنه معناه ذلك أن P
+
+192
+00:15:46,090 --> 00:15:49,450
+problem أه هي problem فإذا مجرد أن هي problem
+
+193
+00:15:49,450 --> 00:15:54,900
+السؤال AA هذه أول شغلة هي problem هي ليست true or
+
+194
+00:15:54,900 --> 00:15:59,000
+false ولا multiple choice هي problem بدها حل كويس
+
+195
+00:15:59,000 --> 00:16:06,160
+و C بالبرضه بالمقابل أكيد true مدام أنت و هذه كلها
+
+196
+00:16:06,160 --> 00:16:11,020
+true فأكيد ال atomic proposition الأول true ال
+
+197
+00:16:11,020 --> 00:16:13,460
+atomic proposition التاني برضه true خلصنا منها
+
+198
+00:16:13,460 --> 00:16:17,580
+كويس الآن الأثنين هذه الموجودين عندك و هذه true
+
+199
+00:16:17,580 --> 00:16:20,020
+طيب و ال implication هذا true
+
+200
+00:16:25,990 --> 00:16:38,170
+نرجع نكتب الجدول نرجع نكتب الجدول ال
+
+201
+00:16:38,170 --> 00:16:46,590
+implication
+
+202
+00:16:46,590 --> 00:16:52,970
+true كله على بعضال P true ال implication true وال
+
+203
+00:16:52,970 --> 00:16:58,770
+P true بس الحالة الوحيدة مش شايف فإذن أكيد Q true
+
+204
+00:16:58,770 --> 00:17:05,210
+فإذن في الحالة هذه أكيد D and F true صح؟
+
+205
+00:17:05,210 --> 00:17:10,250
+تمام okay هاي روسم كده و أحطلك ال chat board في
+
+206
+00:17:10,250 --> 00:17:15,950
+هيك حالة مدام هذه and معناه دي لحالهافلحالها true
+
+207
+00:17:15,950 --> 00:17:20,130
+وانتوا قلته قبل شوية يعني معناته كأنه بدنا نثبت ان
+
+208
+00:17:20,130 --> 00:17:24,510
+كلهم ال true هي كلهم ال true بتهيألي سهل جدا مادام
+
+209
+00:17:24,510 --> 00:17:29,130
+كله طلع true في بعضه ان رتب رتب اللي بدكية and
+
+210
+00:17:29,130 --> 00:17:33,930
+هيطلع true مادام كلهم ال true كل atomic لحاله هو
+
+211
+00:17:33,930 --> 00:17:38,350
+true خلاصبتصفتهم مين اللي بدك إياه، بدك P مع F مع
+
+212
+00:17:38,350 --> 00:17:43,930
+C، هم كلهم اتروح، هاي P مع F مع C، خلاص، بدك تحط
+
+213
+00:17:43,930 --> 00:17:48,990
+دي كمان حط دي، ما هي برضه ظابط معاهم، فبترتب حسب
+
+214
+00:17:48,990 --> 00:17:52,870
+ال conclusion اللي بدك إياه، رتبناهم مع بعض، تمام،
+
+215
+00:17:52,870 --> 00:17:56,270
+هاد F لحالها مظبوطة، رتبناهم مع بعض، و بتهيألي
+
+216
+00:17:56,270 --> 00:18:00,250
+مدام A ينطبق عليها هذا ال condition فهو there
+
+217
+00:18:00,250 --> 00:18:03,210
+exist، لأنه من الأساس احنا نقول إن هو واحد من
+
+218
+00:18:03,210 --> 00:18:07,620
+مجموعات ال questionsهو واحد من مجموعات ال
+
+219
+00:18:07,620 --> 00:18:10,920
+questions داخل ال universive discourse صح فإذا
+
+220
+00:18:10,920 --> 00:18:15,500
+بينطبق عليه كلمة where exist تنطبق عليه فكرة where
+
+221
+00:18:15,500 --> 00:18:19,000
+exist فإذا ممكن أشيله و أحط X و أقول where exist
+
+222
+00:18:19,000 --> 00:18:22,280
+نفس
+
+223
+00:18:22,280 --> 00:18:27,480
+ال conclusion بسيطة جدا سهلة وسلسة و مافي مشكلة بس
+
+224
+00:18:27,480 --> 00:18:31,200
+سلستها و بساطتها جاية من ال implication فهمنا اللي
+
+225
+00:18:31,200 --> 00:18:33,860
+ال implication ال implication هو اللي بيحلها تمام
+
+226
+00:18:34,900 --> 00:18:37,840
+هي كمان سؤال طبعا واضح من الخربش اللي عليه أنه هذا
+
+227
+00:18:37,840 --> 00:18:41,760
+سؤال امتحان كنا جايبينه في امتحان سابق السؤال هذا
+
+228
+00:18:41,760 --> 00:18:46,980
+كان سؤال اتنين في وجهتها في ترتيب الأسئلة المهم
+
+229
+00:18:48,780 --> 00:18:53,800
+ميعطيني بيقول لي إذا كان all animals with scales
+
+230
+00:18:53,800 --> 00:18:59,280
+are dragons كل الحيوانات بحراشيف أو إلها حراشف و
+
+231
+00:18:59,280 --> 00:19:03,640
+جسمها هي dragons هي اللي هي سحال التنين هذه
+
+232
+00:19:03,640 --> 00:19:09,460
+التنانين كويس كومة أو نقطة حتى dot some animals
+
+233
+00:19:09,460 --> 00:19:14,620
+with are not dragons بعض الحيوانات اللتي ليست
+
+234
+00:19:14,620 --> 00:19:21,550
+dragons have sharp clawsليست دراجونس ولها مخالب
+
+235
+00:19:21,550 --> 00:19:27,930
+حادة بعض الحيوانات ليست دراجونس ولها مخالب حادة
+
+236
+00:19:27,930 --> 00:19:33,810
+كويس هاي ال two premises so إذا إيش there are
+
+237
+00:19:33,810 --> 00:19:39,810
+animals without scales which have sharp claws
+
+238
+00:19:39,810 --> 00:19:45,330
+معناه ذلك إنه بعض يوجد بعض الحيوانات اللي ليست لها
+
+239
+00:19:45,330 --> 00:19:53,470
+حراشفعلى ظهرها أو على جسمها ولها مخالب حدكويس من
+
+240
+00:19:53,470 --> 00:19:58,050
+ال premises بدنا نثبت او prove the conclusion
+
+241
+00:19:58,050 --> 00:20:04,010
+الطبيعي طبعا بدنا نقول انه في الآخر في عند ال S هي
+
+242
+00:20:04,010 --> 00:20:06,990
+بده ارمزهم عشان مانكوش نكتب الكلمات كاملة بس
+
+243
+00:20:06,990 --> 00:20:10,530
+نرمزهم هيك نختصرها اقول ان ال S هذي لأنه scales
+
+244
+00:20:10,530 --> 00:20:13,770
+فناخد الحرف الأول منها فاجول ان ال S of X هذي اللي
+
+245
+00:20:13,770 --> 00:20:19,570
+هي معناته انه إش إله scales أو إله حراشف ال D هي
+
+246
+00:20:19,570 --> 00:20:25,830
+dragonو ال c sharp clouds كويس عشان نبدأ نحط ال
+
+247
+00:20:25,830 --> 00:20:29,230
+premise الأولى ال premise الأولى for all animals
+
+248
+00:20:29,230 --> 00:20:32,990
+for all animals with skills معناته إذا كانت ال
+
+249
+00:20:32,990 --> 00:20:36,710
+animals هذه with skills فهي dragon حيها إذا كانت
+
+250
+00:20:36,710 --> 00:20:42,450
+ال animals هذه هي skills إذن هي dragon for all
+
+251
+00:20:42,450 --> 00:20:48,470
+skills employs D التانية ال premise التانية some
+
+252
+00:20:48,470 --> 00:20:53,960
+animalsبعض .. there .. معناه تكتب أول شي there
+
+253
+00:20:53,960 --> 00:21:04,640
+exist و لا إيش negation D and C فإذا
+
+254
+00:21:04,640 --> 00:21:13,660
+يوجد animals ليست dragons ولها مخالب يوجد هي لها
+
+255
+00:21:13,660 --> 00:21:17,640
+دراجون لكن في نفس الوجود لها مخالب لها مخالب هذه
+
+256
+00:21:17,640 --> 00:21:20,960
+مش implicationخدوا بالكوا اتكلمنا فيها سابقًا
+
+257
+00:21:20,960 --> 00:21:25,180
+وشرحناها وهنا بنرجع و بنأكد عن الموضوع تمام ال
+
+258
+00:21:25,180 --> 00:21:31,400
+conclusion المطلوب there exist أنه ليس لها skills
+
+259
+00:21:31,400 --> 00:21:37,120
+negation skills و claws إلها claws فإذا there
+
+260
+00:21:37,120 --> 00:21:39,380
+exist و there exist زي ما قلتلكوا دايما بتاخد
+
+261
+00:21:39,380 --> 00:21:48,490
+معاها and for all implication okay بدنا نبدأنشتغل
+
+262
+00:21:48,490 --> 00:21:52,530
+فهنطلع هدول فوق عشان نبدأ نشتغل تحتهم و ننطلق منهم
+
+263
+00:21:52,530 --> 00:21:56,230
+هننطلق من الأولى و برضه هفترض أنه في عندى ايه
+
+264
+00:21:56,230 --> 00:22:01,250
+animals احنا بتقول for all و there exist تحت
+
+265
+00:22:01,250 --> 00:22:04,490
+معناته there exist اللي تحت هذا و اللي هفترضه ايه
+
+266
+00:22:04,490 --> 00:22:09,010
+ينطبق عليه ما ينطبق على ال all لأن هو واحد منهم هو
+
+267
+00:22:09,010 --> 00:22:12,090
+واحد منهم فإذا عشان أحقق ال two premises مع بعض
+
+268
+00:22:12,090 --> 00:22:15,910
+يوجد على الأقل answer بيحققهم مع بعضcheck there
+
+269
+00:22:15,910 --> 00:22:20,490
+exist يعني يكفيني واحد الواحد هذا بتفترضه هو ايه
+
+270
+00:22:20,490 --> 00:22:26,270
+طب هو نفسه ايه من ال for all من ال for all فإذا
+
+271
+00:22:26,270 --> 00:22:31,290
+ماتبلجوش أنه والله أحط a و أتوعود مكانه ب a خلاص
+
+272
+00:22:31,290 --> 00:22:35,370
+هاي بدأنا بال there exist ال there exist هذه هتصبح
+
+273
+00:22:35,370 --> 00:22:42,740
+negation d of a ف dragon هو ال aand له clause
+
+274
+00:22:42,740 --> 00:22:48,260
+sharp clause برضه هو نفسه ال animal a الان التانية
+
+275
+00:22:48,260 --> 00:22:53,120
+برضه منها بنقدر نجيب S of A employs that او
+
+276
+00:22:53,120 --> 00:22:57,740
+employs D of A اتوقع من اللي فوق بنقدر نقول ان
+
+277
+00:22:57,740 --> 00:23:02,840
+negation D is true لحالها و C is true لحالها طيب
+
+278
+00:23:02,840 --> 00:23:08,160
+نبدأ بال D هاي
+
+279
+00:23:08,160 --> 00:23:15,440
+Dnegation دي false فإذن وين بتكون ال employees أو
+
+280
+00:23:15,440 --> 00:23:22,780
+ال implication كلها true و ال q false ال true و ال
+
+281
+00:23:22,780 --> 00:23:28,460
+q false هذه بتصبتش هيها فإذن محكوم أكيد هذا معناه
+
+282
+00:23:28,460 --> 00:23:34,240
+أن ال P false يعني بقدر أقول negation S check
+
+283
+00:23:34,240 --> 00:23:42,600
+negation S تمامnegation S خلصت المسألة انتهت
+
+284
+00:23:42,600 --> 00:23:50,240
+الجثة لأن C من الخطوة الرقم 3 اكيد هتكون true فإذا
+
+285
+00:23:50,240 --> 00:23:56,320
+negation S and C برضه true مع بعض وال A مدام هي
+
+286
+00:23:56,320 --> 00:24:00,220
+متحققة وانا مش ضامن غيرها انا مش ضامن غيرها انا
+
+287
+00:24:00,220 --> 00:24:02,820
+بعرف ان ال A تحديدا اه هو يحقق ال premises اللي
+
+288
+00:24:02,820 --> 00:24:07,820
+بالاساس لكن غيره مضمنش عشان هيك there existوبشيل
+
+289
+00:24:07,820 --> 00:24:13,180
+ال a و بقول قد يكون في معائشة لكن على الأقل هو ال
+
+290
+00:24:13,180 --> 00:24:19,360
+a موجود حققنا ان هو ليس له skills و في نفس الوقت
+
+291
+00:24:19,360 --> 00:24:21,540
+له sharp claws
+
+292
+00:24:28,650 --> 00:24:31,930
+Okay هنا في مجموعة arguments هتكون موجودة عندنا
+
+293
+00:24:31,930 --> 00:24:35,830
+محتاجين بس نعرف هل هي صحيحة ولا خاطئة إذا كانت
+
+294
+00:24:35,830 --> 00:24:39,250
+صحيحة ضمن أي rule أو وين اتعلمناها وين أخدناها
+
+295
+00:24:39,250 --> 00:24:43,990
+بالظبط في المحاضرات .. المحاضرتين السابقتين او ..
+
+296
+00:24:43,990 --> 00:24:48,890
+او هي خطأ فإيش تصحيحها .. فإيش تصحيحها اعطاني
+
+297
+00:24:48,890 --> 00:24:51,690
+theorem بهذا الشكل أو معلومة بهذا الشكل بدأش ..
+
+298
+00:24:51,690 --> 00:24:56,170
+بدأ افهم هي صح ولا غلط صح ولا .. خلوا عينكوا هناهي
+
+299
+00:24:56,170 --> 00:25:00,710
+نص الحل نص الحل ان عينك على الجدول هذا انتوا
+
+300
+00:25:00,710 --> 00:25:07,130
+ملاحظين كده الجدول مهم معانا؟ مهم جدا طيب if n is
+
+301
+00:25:07,130 --> 00:25:14,530
+a real number such that n أكبر من واحد اذا n تربيع
+
+302
+00:25:14,530 --> 00:25:20,390
+أكبر من واحد هذا معناته بيقودني لفرضية ان n تربيع
+
+303
+00:25:20,390 --> 00:25:27,390
+أكبر من واحد اذا n أكبر من واحدوين المشكلة؟ مفروض
+
+304
+00:25:27,390 --> 00:25:31,810
+انت مقتنع فيها الجملة ولا مش مقتنع فيها؟ هذا هو
+
+305
+00:25:31,810 --> 00:25:34,530
+السؤال انت هل مبدأيا مقتنع بالموضوع ولا مش مقتنع
+
+306
+00:25:34,530 --> 00:25:37,910
+بالموضوع؟ وليش؟
+
+307
+00:25:45,550 --> 00:25:49,190
+أكبر من واحد كيف ده تصير سالبة؟ أكبر من واحد يعني
+
+308
+00:25:49,190 --> 00:25:54,270
+خلاص من واحد في أقل بكل السالب تبعه مش موجود انت
+
+309
+00:25:54,270 --> 00:25:58,070
+بتكلم من واحد to positive infinity من واحد to
+
+310
+00:25:58,070 --> 00:26:02,270
+positive infinity هدفش فيها مشكلة فكروا بغيرها
+
+311
+00:26:02,270 --> 00:26:05,270
+هدفش فيها مشكلة هي كحد .. بحاجة .. هتفضل شوية
+
+312
+00:26:05,270 --> 00:26:10,050
+ناسي؟ بيجيب واحدة تم في هذا الاشي اللي هو مثلا
+
+313
+00:26:10,050 --> 00:26:14,290
+أربعة سالب اتنين تانية وهي مش أكبر من واحد
+
+314
+00:26:18,540 --> 00:26:21,860
+طيب ما احنا قاعدين بنقول من الاساس تعريفك ان هو
+
+315
+00:26:21,860 --> 00:26:28,720
+اكبر من هنا سالب مش هيك معناته انت محققتش ان هي
+
+316
+00:26:28,720 --> 00:26:32,820
+اكبر من واحد هي معناته هذه false انت بدأتها في
+
+317
+00:26:32,820 --> 00:26:36,160
+false وهذه برضه راحت false فانت فعلا ماحققش
+
+318
+00:26:36,160 --> 00:26:42,860
+الموضوع طيب هنرجع لنفس فكرةالـ implication تبعتنا
+
+319
+00:26:42,860 --> 00:26:46,660
+مبدأيا هذه فيه policy في ال affirming اللي احنا
+
+320
+00:26:46,660 --> 00:26:50,920
+افترضنا ان هو حدث ليش؟ لأن انت بتتكلم عن
+
+321
+00:26:50,920 --> 00:26:54,640
+implication المفروض ان هي true ال implication هدا
+
+322
+00:26:54,640 --> 00:27:00,260
+الاصل انه يكون true مش هيك المفروض P هي اللي تكون
+
+323
+00:27:00,260 --> 00:27:06,040
+ال true عشان زي ما أقوله أستنتج منها Q وليس العكس
+
+324
+00:27:06,040 --> 00:27:16,480
+بس تنتجش P من Qصحة P من صحة Q احنا عادة بنستنتج
+
+325
+00:27:16,480 --> 00:27:21,760
+صحة Q من صحة P إذا كان ال employees كله أو ال
+
+326
+00:27:21,760 --> 00:27:26,800
+implication كله على بعض هو فعلا true تمام؟ الكلام
+
+327
+00:27:26,800 --> 00:27:31,760
+هذا هل ينطبق عند هنا؟ هنشوف هنا بنتكلم عن in is
+
+328
+00:27:31,760 --> 00:27:36,340
+real number which is such that in أكبر من واحد هذه
+
+329
+00:27:36,340 --> 00:27:39,800
+إذا in تربيع أكبر من واحد هذه كلها ال implication
+
+330
+00:27:41,360 --> 00:27:44,700
+هذه هي ال implication كلمة العربة بتعطيني جملة
+
+331
+00:27:44,700 --> 00:27:51,280
+كاملة و بيقولها this is true فانت منها افترضت انه
+
+332
+00:27:51,280 --> 00:27:58,780
+ان تربيع اكبر من واحد يعني
+
+333
+00:27:58,780 --> 00:28:05,520
+هذه ايش Q هذه كلها
+
+334
+00:28:07,900 --> 00:28:15,520
+P implies Q بالظبط P implies Q صح؟
+
+335
+00:28:15,520 --> 00:28:21,380
+تمام هيها rule يعطيك إيها كاملة إذا إذا خلصناها و
+
+336
+00:28:21,380 --> 00:28:25,820
+بعدين بيقولك suppose that إذا كانت إم تربية أكبر
+
+337
+00:28:25,820 --> 00:28:37,060
+من واحد هذه Q فإذا كأنه جالك Q and P implies Qو
+
+338
+00:28:37,060 --> 00:28:42,560
+راح جالك اذا P is true و هذا خطأ .. هذا خطأ لو
+
+339
+00:28:42,560 --> 00:28:45,800
+رجعتوا محاضرة ال policy لما اتكلمنا عنها ال policy
+
+340
+00:28:45,800 --> 00:28:51,980
+قلنا اذا كان ال implication is true و P is true
+
+341
+00:28:51,980 --> 00:28:56,140
+اذا Q is true مافيش مشكلة لكن ال implication is
+
+342
+00:28:56,140 --> 00:29:00,880
+true و Q is true بقدرش اقول من دون ان P is true
+
+343
+00:29:00,880 --> 00:29:07,720
+صحيح ال implication is trueو Q is true هي في عندي
+
+344
+00:29:07,720 --> 00:29:12,080
+حالتين Q is true ما بقدر اقول ان P is true لان في
+
+345
+00:29:12,080 --> 00:29:16,540
+الحالتين ممكن تكون false ممكن تكون true فما بيركب
+
+346
+00:29:16,540 --> 00:29:23,300
+اقول true صح هيها الحالة التانية والحالة الرابعة
+
+347
+00:29:23,300 --> 00:29:29,460
+خلوا عينكم معانا ونترجمهم هنا اذا كانت N هي عدد
+
+348
+00:29:29,460 --> 00:29:35,350
+حقيقي اكبر من واحد اذاإن تربية زاد .. إن تربية
+
+349
+00:29:35,350 --> 00:29:38,030
+أكبر من واحد هذه ال implication كلها على بعض هذه
+
+350
+00:29:38,030 --> 00:29:41,990
+true أنا شاك فيها هذه true صحيحة فإذا أنا بتكلم في
+
+351
+00:29:41,990 --> 00:29:48,370
+الحالة اتنين و أربعة تمام طيب جالي هنا إيه سبب ده
+
+352
+00:29:48,370 --> 00:29:54,690
+إن تربية أكبر من واحد هذه Q حسب ال .. ال
+
+353
+00:29:54,690 --> 00:29:58,290
+implication هذه هي Q تمام فإذا وين ال Q بتكون true
+
+354
+00:29:58,290 --> 00:30:06,140
+هاي true راح على طول هو استنتجحطي ال event واستنتج
+
+355
+00:30:06,140 --> 00:30:10,460
+انه معناته ان اكبر من واحد وهذا مش صحيح مش صحيح
+
+356
+00:30:10,460 --> 00:30:14,100
+لأنه لأ فيه ممكن تكون false في ال column التاني في
+
+357
+00:30:14,100 --> 00:30:18,940
+ال row التاني مش هيك او تكون true في ال row الرابع
+
+358
+00:30:18,940 --> 00:30:22,620
+فإذن لأ بقدرش استنتج الاستنتاج اللي حكي لنا هي
+
+359
+00:30:22,620 --> 00:30:28,980
+فإذن false false ليش عرفنا ليش تمام طيب هي التانية
+
+360
+00:30:32,440 --> 00:30:38,400
+برضه انكوا هنا in
+
+361
+00:30:38,400 --> 00:30:43,280
+real number او عدد حقيقي اكبر من تلاتة اذا in
+
+362
+00:30:43,280 --> 00:30:47,860
+تربية اكبر من تسعة كلام حلو suppose that in تربية
+
+363
+00:30:47,860 --> 00:30:55,240
+اقل او يساوي تسعة اذا in اقل او يساوي تلاتة لعند
+
+364
+00:30:55,240 --> 00:31:02,570
+هنا و اقطعشوف الجملة اللي قبلها، هذه كلها أحسنت،
+
+365
+00:31:02,570 --> 00:31:10,250
+هذه كلها إيش؟ P employs Q، و هذه negation
+
+366
+00:31:11,150 --> 00:31:16,710
+الـ Q فهل بقدر أقول إنه إذا negation الـ Q و P
+
+367
+00:31:16,710 --> 00:31:21,090
+implies الـ Q فهل بقدر أستنتج إن هناك هل بقدر
+
+368
+00:31:21,090 --> 00:31:26,630
+أستنتج إنه فعلا في إشي مميز لل P هنا حقيقة فيه ال
+
+369
+00:31:26,630 --> 00:31:29,970
+true ال employees بمعنى إن العمود التالت لازم يكون
+
+370
+00:31:29,970 --> 00:31:35,770
+true و ال Q بده يكون false هذا لا ينطبق إلا على ال
+
+371
+00:31:35,770 --> 00:31:40,090
+role أول فإذا بقدر أستنتج إنه لازم هيطلع negation
+
+372
+00:31:40,090 --> 00:31:44,400
+Pأيش بارح هيطلع Negation P؟ طيب، هل فعلا اللي
+
+373
+00:31:44,400 --> 00:31:48,160
+أعطاني يهو Negation P؟ أه فعلا Negation P، كانت
+
+374
+00:31:48,160 --> 00:31:51,120
+هنا أكبر من تلاتة نصر أقل أو يساوي تلاتة، هي ال
+
+375
+00:31:51,120 --> 00:31:57,660
+Negation بتاعتها؟ صحvalid صارت المفعول منطقي صحيح
+
+376
+00:31:57,660 --> 00:32:01,140
+ومافيش اي مشكلة اطلاقا كلامك مائة بالمائة مش قادر
+
+377
+00:32:01,140 --> 00:32:03,920
+اقول عنه حاجة صح دكتور احنا بتشوف ال validity
+
+378
+00:32:03,920 --> 00:32:08,760
+للجملة التانية؟ اه لهذه الجزئية الجزء الاول هذا
+
+379
+00:32:08,760 --> 00:32:13,020
+كله اللي اعطاك ال implication صيغة ال implication
+
+380
+00:32:13,020 --> 00:32:18,400
+اللي هو صيغة P implies Q ثم بعد ذلك هو فرض لك
+
+381
+00:32:18,400 --> 00:32:23,700
+negation Qو حط نقطة و بعدين جالك انه انا بستنتج
+
+382
+00:32:23,700 --> 00:32:28,520
+بناء على ذلك كذا هل الكذا ال استنتج صح ولا غلط؟ و
+
+383
+00:32:28,520 --> 00:32:30,600
+نفس الكلام هنا هذا الاستنتج صح ولا غلط؟ هذا
+
+384
+00:32:30,600 --> 00:32:37,100
+الاستنتج صح ولا غلط؟ طيب خلاص قلنا valid و انتهينا
+
+385
+00:32:37,100 --> 00:32:44,580
+التالتة التقسيم
+
+386
+00:32:44,580 --> 00:32:45,400
+نفسها هي هي
+
+387
+00:32:50,910 --> 00:32:56,210
+نفس التانية يعني true هكيف نفس التانية طب التانية
+
+388
+00:32:56,210 --> 00:33:00,550
+كانت true ايوة
+
+389
+00:33:00,550 --> 00:33:07,830
+في عندك مشكلة إشكالية هنا هذه نشوفهم هدول هيك زي
+
+390
+00:33:07,830 --> 00:33:15,110
+ما قولنا كلها P implies Q P implies Q هنا يعطيك
+
+391
+00:33:15,110 --> 00:33:22,820
+إيش Negation Pيعني كأنه قال لك هنا negation P و
+
+392
+00:33:22,820 --> 00:33:26,140
+بدنا نشوف هل بطلع إش هنا ولا لأ طب شوف لي negation
+
+393
+00:33:26,140 --> 00:33:31,800
+P يعني false أول two أو صفين أول صفين و true طب هم
+
+394
+00:33:31,800 --> 00:33:35,160
+ال true برضه في الحالتين هل هذا بيستنتجلي قيمة ل
+
+395
+00:33:35,160 --> 00:33:39,560
+Q؟ لأ الحقيقة هو راح هنا استنتجلي قيمة ل Q أكيد
+
+396
+00:33:39,560 --> 00:33:44,090
+خطأ لأنه مابقدر استنتج قيمة هنا ل Qهو هنا بدل ما
+
+397
+00:33:44,090 --> 00:33:48,870
+يستعمل Negation في ال support تبعه Negation Q
+
+398
+00:33:48,870 --> 00:33:53,510
+استعمل Negation P Negation P لا تؤدي ل Negation Q
+
+399
+00:33:53,510 --> 00:34:01,910
+P تؤدي ل Q ال Q لا تؤدي ل P Negation Q تؤدي ل
+
+400
+00:34:01,910 --> 00:34:05,990
+Negation P Negation P لا تؤدي ل Negation Q الجدول
+
+401
+00:34:05,990 --> 00:34:08,370
+اللي بيحكي الكلام هذا okay
+
+402
+00:34:11,120 --> 00:34:17,860
+تمام هي هيك مجموعة كويسة في .. ناخدلنا كمان جزئية
+
+403
+00:34:17,860 --> 00:34:23,720
+في الاثبات
+
+404
+00:34:23,720 --> 00:34:29,080
+نبدأ ناخد ال direct و ال .. و ال contradiction
+
+405
+00:34:29,080 --> 00:34:32,920
+ناخدلنا سؤال هيك و سؤال هيك هي في عندي سؤال ايش
+
+406
+00:34:32,920 --> 00:34:35,840
+بيقولك استخدم ال direct على طول يعني هو بيحددلك في
+
+407
+00:34:35,840 --> 00:34:37,520
+السؤال مباشرة ايش اللي تستخدمه
+
+408
+00:34:44,960 --> 00:34:50,400
+عشان تظهر التالي every odd integer is the
+
+409
+00:34:50,400 --> 00:34:56,620
+difference of two squares و بس تخيل لو مافيش ال
+
+410
+00:34:56,620 --> 00:35:03,860
+hint هذه بدك تقيش بس معها الجملة يقولك اثبتلي ان
+
+411
+00:35:03,860 --> 00:35:07,100
+كل odd integer هو عبارة عن difference of two
+
+412
+00:35:07,100 --> 00:35:10,710
+squaresهو فرق رقمين مربعين
+
+413
+00:35:16,620 --> 00:35:20,900
+direct مبدأيا بدنا نفهم إيش يعني difference دى
+
+414
+00:35:20,900 --> 00:35:24,740
+عشانك على الهامش بتعملك شوية تجربة اتجرب تشوف إيه
+
+415
+00:35:24,740 --> 00:35:29,160
+إيش اللي بتتكلم عنه فعشانك أطلق ال hint find the
+
+416
+00:35:29,160 --> 00:35:34,200
+difference of two squares k plus واحد and k where
+
+417
+00:35:34,200 --> 00:35:36,900
+k is a positive integer و نشوف إيش اللي بتطلع معنا
+
+418
+00:35:36,900 --> 00:35:40,280
+مثلا عند التلاتة بالمناسبة حتى عند الواحد اللي هو
+
+419
+00:35:40,280 --> 00:35:44,360
+أول odd برضه بظبطعند التلاتة التلاتة احنا كلنا
+
+420
+00:35:44,360 --> 00:35:47,940
+عارفين ان هي مادام قد بنقدر نحطها بصورة 2 في some
+
+421
+00:35:47,940 --> 00:35:52,520
+k plus 1 مش كلنا عارفين الكلام هذا 2 في some
+
+422
+00:35:52,520 --> 00:36:02,340
+integer plus 1 فهي 2 في some integer plus 1 تمام
+
+423
+00:36:02,340 --> 00:36:07,580
+طيب هي نفس التلاتة بقدر احطها برضه بنفس القالية ال
+
+424
+00:36:07,580 --> 00:36:16,060
+k اللي استخدمتها هنا هيهامع زائد واحد K زائد واحد
+
+425
+00:36:16,060 --> 00:36:23,120
+وK هي اتنين اللي هي K زائد واحد تربيأ ناقص ال K
+
+426
+00:36:23,120 --> 00:36:28,260
+تربيأ difference of two squares برضه بيساوي تلاتة
+
+427
+00:36:28,260 --> 00:36:35,130
+برضه بيساوي تلاتةالرياضيات فيها سحر مش طبيعي في
+
+428
+00:36:35,130 --> 00:36:39,130
+بعض ال relations بين الأرقام هذه واحدة منهم
+
+429
+00:36:39,130 --> 00:36:43,970
+الخامسة نفس الجثة صح بقدر أحطها بصيغة اتنين في
+
+430
+00:36:43,970 --> 00:36:50,010
+some k plus واحد بقدر اه نقدر طيب ال k هناك بحثت
+
+431
+00:36:50,010 --> 00:36:55,870
+اتنين اتنين في اتنين زائد واحد فالk باتنين هحط هنا
+
+432
+00:36:55,870 --> 00:37:00,550
+برضه k زائد تلاتة تربيع ناقص k تربيع برضه هتطلع
+
+433
+00:37:00,550 --> 00:37:06,780
+خمسةنفس اليسة ال K هنا هنستخدمها تلاتة للرقم سبعة
+
+434
+00:37:06,780 --> 00:37:10,040
+طب ما هى نفسها K زايد واحد اللى هى أربعة تربيع
+
+435
+00:37:10,040 --> 00:37:14,280
+ناقص التلاتة تربيع and so on افهمنها ال logic ايش
+
+436
+00:37:14,280 --> 00:37:16,780
+اللى بدويانا نثبته بدويانا نثبت ان هذا العلاقة
+
+437
+00:37:16,780 --> 00:37:21,620
+الصحيحة direct بدويانا نثبت ان هذا العلاقة الصحيحة
+
+438
+00:37:21,620 --> 00:37:27,980
+okay فإذا direct هنبدأ من مين every odd integer
+
+439
+00:37:27,980 --> 00:37:32,680
+فهنبدأ من ال odd integerعشان نكون direct ثم بده من
+
+440
+00:37:32,680 --> 00:37:36,600
+هذا الكلام نثبت انه is the difference بعدين هنشوف
+
+441
+00:37:36,600 --> 00:37:41,040
+حكاية ال difference هذه فمبدأيا هنبدأ ان n is odd
+
+442
+00:37:41,040 --> 00:37:45,800
+حسب الفرضية هو بيقول ليه إذا كانت odd هي odd معناه
+
+443
+00:37:45,800 --> 00:37:49,480
+ذلك ان بقدر اكتبها بصيغة اتنين كزائد واحد for some
+
+444
+00:37:49,480 --> 00:37:55,320
+integer k صح؟ ثم خلصنا هاي بداية طيب من ال hint
+
+445
+00:37:55,320 --> 00:38:02,840
+اللي أتانياهنستخدم k وk زائد واحد عشان نثبت ان هي
+
+446
+00:38:02,840 --> 00:38:07,320
+نفسهم ال difference ل ال square تبعهم هيعطيني نفس
+
+447
+00:38:07,320 --> 00:38:12,980
+ان هل فعلا الكلام هذا منطقي ولا لأ هنشوف k زائد
+
+448
+00:38:12,980 --> 00:38:20,260
+واحد تربيع ناقص k تربيع فك أقواص عشان تصبح الأولى
+
+449
+00:38:21,360 --> 00:38:26,480
+كتربيع زائد اتنين ك زائد واحد كله ناقص كتربيع شيل
+
+450
+00:38:26,480 --> 00:38:32,270
+الكتربيع مع الكتربيع نفس الفجرنفس اللي فوق فإذا
+
+451
+00:38:32,270 --> 00:38:34,930
+فعلا ال two terms بتساوي بعض اللي هي اتنين زائد
+
+452
+00:38:34,930 --> 00:38:38,470
+واحد بتساوي n اللي هو ال odd number اصلا اللي هو
+
+453
+00:38:38,470 --> 00:38:43,490
+الاش ال odd number طريقة بسيطة جدا اه طريقة .. من
+
+454
+00:38:43,490 --> 00:38:47,150
+الأول كانت مش بسيطة .. من الأول مش بسيطة لكن عاد
+
+455
+00:38:47,150 --> 00:38:50,210
+سحر الأرقام هو اللي خلها تصير بسيطة بالمناسبة في
+
+456
+00:38:50,210 --> 00:38:54,290
+كتير relations هيك حلوة في الرياضيات الأرقام كيف
+
+457
+00:38:54,290 --> 00:38:57,730
+مرتبطة مع بعضها بشكل كتير هذه مش الأولة ولا
+
+458
+00:38:57,730 --> 00:39:02,670
+الأخيرة هتكون اللي هتشوفوهاطيب so that if N is
+
+459
+00:39:02,670 --> 00:39:11,130
+integer and N تكعيب plus five is odd then N is
+
+460
+00:39:11,130 --> 00:39:15,910
+even لاحظته؟
+
+461
+00:39:15,910 --> 00:39:23,790
+بدنا نثبت إذا كانت N integer و N تكعيب زائد خمسة
+
+462
+00:39:23,790 --> 00:39:30,130
+oddبدنا نثبت منها ان N is even باستخدام كل مرة
+
+463
+00:39:30,130 --> 00:39:36,530
+حالة مرة باستخدام ال proof by contraposition نبدأ
+
+464
+00:39:36,530 --> 00:39:40,270
+بالcontraposition ثم بال contradiction و الفرق
+
+465
+00:39:40,270 --> 00:39:43,990
+شاسع بين التنتين طيب بتهيألي بالcontraposition
+
+466
+00:39:43,990 --> 00:39:50,810
+مافيها مشكلة هنفرض عكس EQ يعني هبدأ من هنا و افرض
+
+467
+00:39:50,810 --> 00:39:57,280
+ان هذه odd و نحسب هذهمش هيك يعني مش كتير جثتها ..
+
+468
+00:39:57,280 --> 00:40:02,360
+مش كتير جثتها صعبة ف assume n is odd اللي هي عكس
+
+469
+00:40:02,360 --> 00:40:07,500
+تمام بسطت الأمور و خلصت معناه ذلك أنه بقدر أحطها ب
+
+470
+00:40:07,500 --> 00:40:11,560
+2k plus 1 و انتهى الموضوع و انعوض في ال n تكعيب
+
+471
+00:40:11,560 --> 00:40:17,400
+زائد خمسةعوضنا في إنتك عيب زائد خمسة بنفكفكها إنتك
+
+472
+00:40:17,400 --> 00:40:20,860
+عيب زائد واحد تربيحها و بعدين أضربه كمان مرة في
+
+473
+00:40:20,860 --> 00:40:25,300
+اتنين K زائد واحد عشان يظهر معانا term بهذا الشكل
+
+474
+00:40:25,300 --> 00:40:29,660
+طيب ال term اللي بهذا الشكل لو فكناه حالج أن في
+
+475
+00:40:29,660 --> 00:40:33,040
+عندي خمسة زائد واحد ستة و بعدين بناخد عامل مشترك
+
+476
+00:40:33,040 --> 00:40:37,280
+عشان نجد أن الخمسة زائد ستة .. خمسة زائد واحد بسوء
+
+477
+00:40:37,280 --> 00:40:40,980
+ستة الستة even يعني بنفع أخد منه اتنين عامل مشترك
+
+478
+00:40:42,200 --> 00:40:44,840
+هنا بقدر اخد منها عامل مشترك اتنين و هنا بقدر اخد
+
+479
+00:40:44,840 --> 00:40:46,960
+اتنين عامل مشترك و هنا بقدر اخد اتنين عامل مشترك و
+
+480
+00:40:46,960 --> 00:40:50,360
+مجموع الاتنين هدول برضه بقدر اخد عامل مشترك مانا
+
+481
+00:40:50,360 --> 00:40:56,860
+ذلك ممكن احطه بصورة اتنين في some k اصبحت ايش even
+
+482
+00:40:56,860 --> 00:41:01,480
+انا بدأت ب odd طلعت even هنا كان بدري يعني ابدأ ب
+
+483
+00:41:01,480 --> 00:41:07,480
+odd و اروح ل even عكسناها عكسناهالما بدأنا ب
+
+484
+00:41:07,480 --> 00:41:12,740
+negation q طلق ليه negation p بالcontrapositive
+
+485
+00:41:12,740 --> 00:41:18,920
+أكيد is true فإذا خلصنا منها الآن باستخدام ال
+
+486
+00:41:18,920 --> 00:41:21,860
+contradiction باستخدام ال contradiction الموضوع
+
+487
+00:41:21,860 --> 00:41:28,660
+هيختلف هنشتغل على إنه n plus واحد is odd and n is
+
+488
+00:41:28,660 --> 00:41:32,940
+عكسناها
+
+489
+00:41:32,940 --> 00:41:37,420
+خالص بدي أفرض عكسهامش بدنا نفرض عكسها نجي ال
+
+490
+00:41:37,420 --> 00:41:39,680
+contradiction كلنا بنقول اننا بدنا نفرضها العكس
+
+491
+00:41:39,680 --> 00:41:45,040
+okay هي العكس العكس بدل ما كنت بقول if تكييف زائد
+
+492
+00:41:45,040 --> 00:41:51,300
+خمسة is odd then n is even لأ بدأ أقول if n is odd
+
+493
+00:41:51,300 --> 00:41:59,960
+okay بدأنا بال odd و منها n is odd و كلنا عارفين
+
+494
+00:41:59,960 --> 00:42:10,620
+انه ال ..is odd وكلنا عارفين انه odd في odd odd هي
+
+495
+00:42:10,620 --> 00:42:20,120
+عبارة عن odd في odd فهي ساوي odd طيب ان تكعيب ما
+
+496
+00:42:20,120 --> 00:42:26,140
+هي عبارة عن ان تربيع في ان يعني نفس الكلام odd في
+
+497
+00:42:26,140 --> 00:42:32,470
+odd يعني حتى تكعيب برضه هتطلع oddبرضه هتكون عبارة
+
+498
+00:42:32,470 --> 00:42:39,630
+عن odd صح؟ فيها and
+
+499
+00:42:39,630 --> 00:42:47,550
+in is odd طيب odd تكعيب خلاص odd طيب odd زائد odd
+
+500
+00:42:47,550 --> 00:42:55,050
+even even هتطلع و ليس زي فرضيتنا أن هي oddوليست
+
+501
+00:42:55,050 --> 00:43:00,250
+كما افترضنا ان هي odd فإذا هذا معناه ان تربيه is
+
+502
+00:43:00,250 --> 00:43:03,250
+odd وهذا معناه ان تكيب برضه is odd خليني نمحي
+
+503
+00:43:03,250 --> 00:43:09,830
+الكتاب اللي وضحنا فيه وهذا
+
+504
+00:43:09,830 --> 00:43:13,790
+معناه أن خمسة is odd أساسا هي بحد ذاتها وصار odd
+
+505
+00:43:13,790 --> 00:43:19,010
+زائد odd even عكس فرضيتنا اللي افترضناها وهذا
+
+506
+00:43:19,010 --> 00:43:24,630
+معناه أن الفرضية اللي احنا suppose thatإن تكعيب
+
+507
+00:43:24,630 --> 00:43:28,830
+زائد خمسة is odd and in is odd اللي كانت المفروض
+
+508
+00:43:28,830 --> 00:43:32,910
+even حسب
+
+509
+00:43:32,910 --> 00:43:36,710
+النظرية الأصلية احنا فرضنا عكسها طلع عكسها false
+
+510
+00:43:36,710 --> 00:43:42,960
+إذا ان هي trueأخدنا هذا المثال مش هيك بس كان لقاش
+
+511
+00:43:42,960 --> 00:43:49,180
+جدر تربيعي تكعيبه مش هيفرج كتير بس فكرته أنه كان
+
+512
+00:43:49,180 --> 00:43:53,500
+سؤال في امتحان طبعا الطلاب شافوا أنه تكعيبي وقفوا
+
+513
+00:43:53,500 --> 00:43:58,220
+حالهم ووقفت مالهم زي ما بقوله لأ بصد و لا برد
+
+514
+00:43:58,220 --> 00:44:02,200
+صاروا ليش؟ مافيش فيها إشي طب ماهي نفس اللي حلنا في
+
+515
+00:44:02,200 --> 00:44:05,700
+ال slides هو هو اعملوا بنفس خطواته إيش هيتغير
+
+516
+00:44:05,700 --> 00:44:10,140
+معاكوا رقم رقمين؟بس ال process هي هي ليش ما
+
+517
+00:44:10,140 --> 00:44:13,360
+تجرأتوش يا طلاب مثلا تعملوها ال process اعمل ال
+
+518
+00:44:13,360 --> 00:44:15,500
+process خلّيه يطلع الأقل بطبيعي مش كل الأسئلة
+
+519
+00:44:15,500 --> 00:44:18,920
+بتجيك زي ما هي ال coffee class هيها اعملنا نفس
+
+520
+00:44:18,920 --> 00:44:24,440
+الفكرة يقولنا ان هي rational و معناه ذلك أنه بقدر
+
+521
+00:44:24,440 --> 00:44:28,900
+أحطها بصيغة طيب تمام و هذا معناه أنه بدل ما أجيب
+
+522
+00:44:28,900 --> 00:44:35,310
+تربية أجيب تكريب للطرفين بس جبنا تكريب للطرفينمنها
+
+523
+00:44:35,310 --> 00:44:39,070
+بطلع إنه بدل ما كانت A تربية هي اللي even طب هي
+
+524
+00:44:39,070 --> 00:44:43,050
+نفس ال A تكعيب هي اللي even و الاستنتاج هو هو
+
+525
+00:44:43,050 --> 00:44:47,770
+هيطلع ماحنا طوي لسه مش طوي كنا حالين N تكعيب إذا
+
+526
+00:44:47,770 --> 00:44:52,730
+كان odd N ال N تكعيب برضه هيطلع odd طيب ما هي نفس
+
+527
+00:44:52,730 --> 00:44:56,610
+الفكرة نفس الفكرة إيش اختلفت بالله هالوجة عن اللي
+
+528
+00:44:56,610 --> 00:45:01,300
+كانت في ال slides؟ولا اشي ولا حاجة بس عشان ظهر
+
+529
+00:45:01,300 --> 00:45:06,860
+التكعيب خلصنا بتفعل الباقي نفس المحاضرة الباقي نفس
+
+530
+00:45:06,860 --> 00:45:10,260
+المحاضرة تماما ف is even وهذا معناه ان ايه بقدر
+
+531
+00:45:10,260 --> 00:45:13,360
+أحطها باتنين K وفي الحالة هذه بنكملها بدل ما كان
+
+532
+00:45:13,360 --> 00:45:17,520
+هيطلع أربعة في K تربية هتصيب تمانية في K تكعيب وفي
+
+533
+00:45:17,520 --> 00:45:20,360
+جميع الأحوال التمانية هتختصر مع الأتنين و هتظل
+
+534
+00:45:20,360 --> 00:45:23,380
+برضه even هناك كانت أربعة بتظل even هنا تمانية
+
+535
+00:45:23,380 --> 00:45:29,540
+بتظل even برضهنفس القصة .. نفس القصة ف .. بالضبط
+
+536
+00:45:29,540 --> 00:45:32,840
+even على even معناته في common و انتهى الكلام و
+
+537
+00:45:32,840 --> 00:45:35,120
+خلصت هيكي طريقة حلها
+
+538
+00:45:42,420 --> 00:45:46,360
+طيب بتهيأليها دي كتير برضه بسيط حلها أنه لو N is
+
+539
+00:45:46,360 --> 00:45:56,220
+positive then N is odd if and only if .. if .. if
+
+540
+00:45:56,220 --> 00:46:03,060
+and only if five N plus six is odd بدي شغالة أحلها
+
+541
+00:46:03,060 --> 00:46:06,640
+بدنا نشوف الفكرة الحل إيش ممكن نعمل فيها فكرة
+
+542
+00:46:06,640 --> 00:46:07,180
+الحل؟
+
+543
+00:46:12,950 --> 00:46:20,330
+in is positive يعني ايش؟ اكبر من صفر اذا او اكبر
+
+544
+00:46:20,330 --> 00:46:27,410
+من صفر اذا in
+
+545
+00:46:27,410 --> 00:46:40,210
+is odd if and only if five in plus six is odd
+
+546
+00:46:49,610 --> 00:46:58,590
+طيب بس بس بس لأ مظبوط بس خلصت الجثة هه هنعملها
+
+547
+00:46:58,590 --> 00:47:05,250
+أخدنا هذه ال F and only F هي عبارة عن N is odd اذا
+
+548
+00:47:05,250 --> 00:47:11,110
+five N plus six is odd and
+
+549
+00:47:14,260 --> 00:47:24,480
+five n plus six is odd even if n is odd اعمل هذه
+
+550
+00:47:24,480 --> 00:47:30,300
+الحالة اعمل هذه الحالة و خلصناهابس الاولى مافيش
+
+551
+00:47:30,300 --> 00:47:34,320
+فيها مشكلة اطلاقا لان انت direct هتفرض ان ان فعلا
+
+552
+00:47:34,320 --> 00:47:38,880
+هي is odd و بتعود بال 2k plus 1 في هذا ال term
+
+553
+00:47:38,880 --> 00:47:44,520
+هيطلع ان ال term هذا odd انتهى هنا مش هتقدر تتعامل
+
+554
+00:47:44,520 --> 00:47:51,360
+معاها اعمل indirect افرض in is even و اثبت منها ان
+
+555
+00:47:51,360 --> 00:47:57,800
+خمسة in plus six evenمعنى ذلك بال contrapositive
+
+556
+00:47:57,800 --> 00:48:04,880
+بتصير ال relation هذه صحيحة صحيح
+
+557
+00:48:04,880 --> 00:48:08,940
+صحيح لاحظته كيف انتهى بدك تعملها direct اعملها
+
+558
+00:48:08,940 --> 00:48:12,440
+direct هذي بدك تعملها direct اعملها direct بس بدك
+
+559
+00:48:12,440 --> 00:48:16,520
+تكون فاهم انك هذي اذا كان هذي odd odd في odd odd
+
+560
+00:48:16,520 --> 00:48:21,020
+plus even خلاص نعم بدك تعمل direct اعمل direct
+
+561
+00:48:21,020 --> 00:48:23,640
+مافيش مشكلة بس فاهمين فكرة انه بده اعمل
+
+562
+00:48:23,640 --> 00:48:27,830
+duplication هنالأن ال F and only F معناته F في
+
+563
+00:48:27,830 --> 00:48:33,710
+اتجاه P to Q و برضه implication في اتجاه Q to P
+
+564
+00:48:33,710 --> 00:48:38,130
+تمام خلصناها بتنزل معاكوا هذه محلولة بس أخدنا
+
+565
+00:48:38,130 --> 00:48:41,370
+الفكرة ال concept بتاعة بسيط جدا فتاخد على
+
+566
+00:48:41,370 --> 00:48:45,090
+الحالتين عشان تكون خلصنا جزئيتنا لهذا اليوم
+
+567
+00:48:45,090 --> 00:48:49,870
+الأسبوع الجاي بنبدأ درس جديد ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..8ef2c81fe797ecb556baf729f85e71b7db948971
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0_raw.json
@@ -0,0 +1 @@
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{"id": 19, "seek": 52400, "start": 498.34, "end": 524.0, "text": "تمام الأخيرة not everyone ليس الكل هدرك pathology مع مين مع مفهومنا تعتوي ليس الكل بساعد someone فهنا هتكون ليس الكل هنا بتظبط معانا ليس الكل بمعنى أن في بعض هيساعد بس مش الكل البعض هيساعد أه بس ليس الكل بحظين هنا not everyone negation for all", "tokens": [39237, 10943, 16247, 9778, 48923, 406, 1518, 32239, 3794, 2423, 28820, 8032, 3215, 2288, 4117, 3100, 1793, 20449, 3714, 9957, 20449, 3714, 5172, 3224, 20498, 8315, 6055, 34268, 45865, 32239, 3794, 2423, 28820, 4724, 3794, 995, 22488, 1580, 6156, 3224, 8315, 8032, 2655, 30544, 32239, 3794, 2423, 28820, 34105, 39894, 19913, 3555, 9566, 20449, 7649, 995, 32239, 3794, 2423, 28820, 4724, 2304, 3615, 1863, 7578, 14739, 8978, 45030, 11242, 39896, 3794, 995, 22488, 4724, 3794, 37893, 2423, 28820, 29739, 3615, 11242, 39896, 3794, 995, 22488, 5551, 3224, 4724, 3794, 32239, 3794, 2423, 28820, 4724, 5016, 19913, 9957, 34105, 406, 1518, 2485, 399, 337, 439], "avg_logprob": 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1636.48, "word": " بنستنتج", "probability": 0.9307861328125}, {"start": 1636.48, "end": 1637.14, "word": " صحة", "probability": 0.9845377604166666}, {"start": 1637.14, "end": 1637.6, "word": " Q", "probability": 0.8671875}, {"start": 1637.6, "end": 1638.2, "word": " من", "probability": 0.984375}, {"start": 1638.2, "end": 1638.86, "word": " صحة", "probability": 0.9874674479166666}, {"start": 1638.86, "end": 1639.4, "word": " P", "probability": 0.9921875}, {"start": 1639.4, "end": 1639.96, "word": " إذا", "probability": 0.674560546875}, {"start": 1639.96, "end": 1640.22, "word": " كان", "probability": 0.98193359375}, {"start": 1640.22, "end": 1640.36, "word": " ال", "probability": 0.96435546875}, {"start": 1640.36, "end": 1641.06, "word": " employees", "probability": 0.6962890625}, {"start": 1641.06, "end": 1641.56, "word": " كله", "probability": 0.95068359375}, {"start": 1641.56, "end": 1641.66, "word": " أو", "probability": 0.61083984375}, {"start": 1641.66, "end": 1641.76, "word": " ال", "probability": 0.962890625}, {"start": 1641.76, "end": 1642.1, "word": " implication", "probability": 0.92236328125}, {"start": 1642.1, "end": 1642.5, "word": " كله", "probability": 0.958251953125}, {"start": 1642.5, "end": 1642.64, "word": " على", "probability": 0.81396484375}, {"start": 1642.64, "end": 1642.88, "word": " بعض", "probability": 0.986083984375}, {"start": 1642.88, "end": 1643.0, "word": " هو", "probability": 0.91357421875}, {"start": 1643.0, "end": 1643.3, "word": " فعلا", "probability": 0.9108072916666666}, {"start": 1643.3, "end": 1643.58, "word": " true", "probability": 0.72265625}, {"start": 1643.58, "end": 1646.06, "word": " تمام؟", "probability": 0.5836588541666666}, {"start": 1646.06, "end": 1646.8, "word": " الكلام", "probability": 0.9366861979166666}, {"start": 1646.8, "end": 1647.02, "word": " هذا", "probability": 0.83203125}, {"start": 1647.02, "end": 1647.16, "word": " هل", "probability": 0.845947265625}, {"start": 1647.16, "end": 1647.52, "word": " ينطبق", "probability": 0.89130859375}, {"start": 1647.52, "end": 1647.7, "word": " عند", "probability": 0.73779296875}, {"start": 1647.7, "end": 1648.72, "word": " هنا؟", "probability": 0.74462890625}, {"start": 1648.72, "end": 1649.18, "word": " هنشوف", "probability": 0.9302978515625}, {"start": 1649.18, "end": 1649.8, "word": " هنا", "probability": 0.82861328125}, {"start": 1649.8, "end": 1650.48, "word": " بنتكلم", "probability": 0.73583984375}, {"start": 1650.48, "end": 1650.82, "word": " عن", "probability": 0.96923828125}, {"start": 1650.82, "end": 1651.12, "word": " in", "probability": 0.234375}, {"start": 1651.12, "end": 1651.76, "word": " is", "probability": 0.82177734375}, {"start": 1651.76, "end": 1652.06, "word": " real", "probability": 0.62744140625}, {"start": 1652.06, "end": 1652.42, "word": " number", "probability": 0.96728515625}, {"start": 1652.42, "end": 1652.78, "word": " which", "probability": 0.85107421875}, {"start": 1652.78, "end": 1653.34, "word": " is", "probability": 0.96875}, {"start": 1653.34, "end": 1654.0, "word": " such", "probability": 0.447998046875}, {"start": 1654.0, "end": 1654.4, "word": " that", "probability": 0.94482421875}, {"start": 1654.4, "end": 1654.72, "word": " in", "probability": 0.8046875}, {"start": 1654.72, "end": 1655.02, "word": " أكبر", "probability": 0.9552408854166666}, {"start": 1655.02, "end": 1655.18, "word": " من", "probability": 0.9921875}, {"start": 1655.18, "end": 1655.66, "word": " واحد", "probability": 0.861572265625}, {"start": 1655.66, "end": 1656.34, "word": " هذه", "probability": 0.297607421875}, {"start": 1656.34, "end": 1657.04, "word": " إذا", "probability": 0.70654296875}, {"start": 1657.04, "end": 1657.5, "word": " in", "probability": 0.77099609375}, {"start": 1657.5, "end": 1658.18, "word": " تربيع", "probability": 0.91455078125}, {"start": 1658.18, "end": 1658.58, "word": " أكبر", "probability": 0.9710286458333334}, {"start": 1658.58, "end": 1658.74, "word": " من", "probability": 0.99560546875}, {"start": 1658.74, "end": 1658.96, "word": " واحد", "probability": 0.966796875}, {"start": 1658.96, "end": 1659.14, "word": " هذه", "probability": 0.85986328125}, {"start": 1659.14, "end": 1659.42, "word": " كلها", "probability": 0.990966796875}, {"start": 1659.42, "end": 1659.48, "word": " ال", "probability": 0.97314453125}, {"start": 1659.48, "end": 1659.8, "word": " implication", "probability": 0.982421875}], "temperature": 1.0}, {"id": 64, "seek": 168552, "start": 1661.36, "end": 1685.52, "text": "هذه هي ال implication كلمة العربة بتعطيني جملة كاملة و بيقولها this is true فانت منها افترضت انه ان تربيع اكبر من واحد يعني هذه ايش Q هذه كلها", "tokens": [3224, 24192, 39896, 2423, 37814, 9122, 19528, 3660, 18863, 25513, 3660, 39894, 3615, 9566, 9957, 1829, 10874, 2304, 37977, 9122, 10943, 37977, 4032, 4724, 1829, 39648, 11296, 341, 307, 2074, 6156, 7649, 2655, 9154, 11296, 1975, 5172, 2655, 43042, 2655, 16472, 3224, 16472, 6055, 2288, 21292, 3615, 1975, 4117, 26890, 9154, 36764, 24401, 37495, 22653, 29538, 1975, 1829, 8592, 1249, 29538, 28242, 11296], "avg_logprob": -0.29736329102888703, "compression_ratio": 1.4625, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1661.36, "end": 1661.68, "word": "هذه", "probability": 0.778564453125}, {"start": 1661.68, "end": 1661.88, "word": " هي", "probability": 0.98974609375}, {"start": 1661.88, "end": 1662.12, "word": " ال", "probability": 0.9521484375}, {"start": 1662.12, "end": 1662.66, "word": " implication", "probability": 0.96630859375}, {"start": 1662.66, "end": 1663.18, "word": " كلمة", "probability": 0.64794921875}, {"start": 1663.18, "end": 1663.52, "word": " العربة", "probability": 0.5592447916666666}, {"start": 1663.52, "end": 1664.06, "word": " بتعطيني", "probability": 0.632421875}, {"start": 1664.06, "end": 1664.7, "word": " جملة", "probability": 0.96533203125}, {"start": 1664.7, "end": 1664.98, "word": " كاملة", "probability": 0.9677734375}, {"start": 1664.98, "end": 1665.1, "word": " و", "probability": 0.2548828125}, {"start": 1665.1, "end": 1665.28, "word": " بيقولها", "probability": 0.822998046875}, {"start": 1665.28, "end": 1665.42, "word": " this", "probability": 0.4873046875}, {"start": 1665.42, "end": 1665.58, "word": " is", "probability": 0.90576171875}, {"start": 1665.58, "end": 1665.88, "word": " true", "probability": 0.97705078125}, {"start": 1665.88, "end": 1667.06, "word": " فانت", "probability": 0.8590494791666666}, {"start": 1667.06, "end": 1667.34, "word": " منها", "probability": 0.9912109375}, {"start": 1667.34, "end": 1668.1, "word": " افترضت", "probability": 0.98505859375}, {"start": 1668.1, "end": 1671.28, "word": " انه", "probability": 0.6611328125}, {"start": 1671.28, "end": 1671.54, "word": " ان", "probability": 0.66552734375}, {"start": 1671.54, "end": 1672.22, "word": " تربيع", "probability": 0.842041015625}, {"start": 1672.22, "end": 1672.76, "word": " اكبر", "probability": 0.9080403645833334}, {"start": 1672.76, "end": 1673.28, "word": " من", "probability": 0.9892578125}, {"start": 1673.28, "end": 1674.14, "word": " واحد", "probability": 0.988525390625}, {"start": 1674.14, "end": 1678.78, "word": " يعني", "probability": 0.89501953125}, {"start": 1678.78, "end": 1679.06, "word": " هذه", "probability": 0.6435546875}, {"start": 1679.06, "end": 1679.52, "word": " ايش", "probability": 0.6787109375}, {"start": 1679.52, "end": 1681.04, "word": " Q", "probability": 0.185302734375}, {"start": 1681.04, "end": 1682.18, "word": " هذه", "probability": 0.6552734375}, {"start": 1682.18, "end": 1685.52, "word": " كلها", "probability": 0.72021484375}], "temperature": 1.0}, {"id": 65, "seek": 171536, "start": 1687.9, "end": 1715.36, "text": "P implies Q بالظبط P implies Q صح؟ تمام هيها rule يعطيك إيها كاملة إذا إذا خلصناها و بعدين بيقولك suppose that إذا كانت إم تربية أكبر من واحد هذه Q فإذا كأنه جالك Q and P implies Q", "tokens": [47, 18779, 1249, 20666, 19913, 3555, 9566, 430, 18779, 1249, 20328, 5016, 22807, 46811, 10943, 39896, 11296, 4978, 7251, 3615, 9566, 1829, 4117, 11933, 1829, 11296, 9122, 10943, 37977, 11933, 15730, 11933, 15730, 16490, 1211, 9381, 8315, 11296, 4032, 39182, 9957, 4724, 1829, 39648, 4117, 7297, 300, 11933, 15730, 25961, 2655, 11933, 2304, 6055, 25513, 10632, 5551, 4117, 26890, 9154, 36764, 24401, 29538, 1249, 6156, 28814, 15730, 9122, 33456, 3224, 10874, 6027, 4117, 1249, 293, 430, 18779, 1249], "avg_logprob": -0.25830695674389226, "compression_ratio": 1.5193370165745856, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1687.9, "end": 1688.12, "word": "P", "probability": 0.1795654296875}, {"start": 1688.12, "end": 1688.48, "word": " implies", "probability": 0.479248046875}, {"start": 1688.48, "end": 1688.86, "word": " Q", "probability": 0.9140625}, {"start": 1688.86, "end": 1689.86, "word": " بالظبط", "probability": 0.82647705078125}, {"start": 1689.86, "end": 1690.4, "word": " P", "probability": 0.53857421875}, {"start": 1690.4, "end": 1691.28, "word": " implies", "probability": 0.9306640625}, {"start": 1691.28, "end": 1691.92, "word": " Q", "probability": 0.9716796875}, {"start": 1691.92, "end": 1695.52, "word": " صح؟", "probability": 0.6490071614583334}, {"start": 1695.52, "end": 1696.2, "word": " تمام", "probability": 0.970703125}, {"start": 1696.2, "end": 1696.78, "word": " هيها", "probability": 0.63427734375}, {"start": 1696.78, "end": 1697.32, "word": " rule", "probability": 0.861328125}, {"start": 1697.32, "end": 1697.84, "word": " يعطيك", "probability": 0.737451171875}, {"start": 1697.84, "end": 1698.02, "word": " إيها", "probability": 0.743408203125}, {"start": 1698.02, "end": 1698.54, "word": " كاملة", "probability": 0.97509765625}, {"start": 1698.54, "end": 1699.18, "word": " إذا", "probability": 0.95068359375}, {"start": 1699.18, "end": 1699.96, "word": " إذا", "probability": 0.6002197265625}, {"start": 1699.96, "end": 1701.16, "word": " خلصناها", "probability": 0.85126953125}, {"start": 1701.16, "end": 1701.38, "word": " و", "probability": 0.58935546875}, {"start": 1701.38, "end": 1701.64, "word": " بعدين", "probability": 0.908935546875}, {"start": 1701.64, "end": 1702.24, "word": " بيقولك", "probability": 0.915771484375}, {"start": 1702.24, "end": 1702.76, "word": " suppose", "probability": 0.9423828125}, {"start": 1702.76, "end": 1703.26, "word": " that", "probability": 0.93896484375}, {"start": 1703.26, "end": 1704.04, "word": " إذا", "probability": 0.953857421875}, {"start": 1704.04, "end": 1704.5, "word": " كانت", "probability": 0.98876953125}, {"start": 1704.5, "end": 1704.76, "word": " إم", "probability": 0.5294189453125}, {"start": 1704.76, "end": 1705.42, "word": " تربية", "probability": 0.9108072916666666}, {"start": 1705.42, "end": 1705.82, "word": " أكبر", "probability": 0.9609375}, {"start": 1705.82, "end": 1706.0, "word": " من", "probability": 0.98974609375}, {"start": 1706.0, "end": 1706.58, "word": " واحد", "probability": 0.979248046875}, {"start": 1706.58, "end": 1707.04, "word": " هذه", "probability": 0.321044921875}, {"start": 1707.04, "end": 1707.42, "word": " Q", "probability": 0.875}, {"start": 1707.42, "end": 1708.62, "word": " فإذا", "probability": 0.8592122395833334}, {"start": 1708.62, "end": 1709.72, "word": " كأنه", "probability": 0.9451497395833334}, {"start": 1709.72, "end": 1710.1, "word": " جالك", "probability": 0.7430013020833334}, {"start": 1710.1, "end": 1710.62, "word": " Q", "probability": 0.293701171875}, {"start": 1710.62, "end": 1712.88, "word": " and", "probability": 0.931640625}, {"start": 1712.88, "end": 1713.38, "word": " P", "probability": 0.9873046875}, {"start": 1713.38, "end": 1714.36, "word": " implies", "probability": 0.84716796875}, {"start": 1714.36, "end": 1715.36, "word": " Q", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 66, "seek": 174504, "start": 1716.84, "end": 1745.04, "text": "و راح جالك اذا P is true و هذا خطأ .. هذا خطأ لو رجعتوا محاضرة ال policy لما اتكلمنا عنها ال policy قلنا اذا كان ال implication is true و P is true اذا Q is true مافيش مشكلة لكن ال implication is true و Q is true بقدرش اقول من دون ان P is true صحيح ال implication is true", "tokens": [2407, 12602, 39319, 10874, 6027, 4117, 1975, 15730, 430, 307, 2074, 4032, 23758, 16490, 9566, 10721, 4386, 23758, 16490, 9566, 10721, 45164, 12602, 7435, 34268, 14407, 3714, 5016, 46958, 25720, 2423, 3897, 5296, 15042, 1975, 2655, 4117, 19528, 8315, 18871, 11296, 2423, 3897, 12174, 1211, 8315, 1975, 15730, 25961, 2423, 37814, 307, 2074, 4032, 430, 307, 2074, 1975, 15730, 1249, 307, 2074, 19446, 41185, 8592, 37893, 28820, 3660, 44381, 2423, 37814, 307, 2074, 4032, 1249, 307, 2074, 4724, 28543, 2288, 8592, 1975, 39648, 9154, 11778, 11536, 16472, 430, 307, 2074, 20328, 5016, 1829, 5016, 2423, 37814, 307, 2074], "avg_logprob": -0.20864898628658718, "compression_ratio": 1.9639175257731958, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1716.84, "end": 1717.06, "word": "و", "probability": 0.83740234375}, {"start": 1717.06, "end": 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"word": " plus", "probability": 0.921875}, {"start": 2347.73, "end": 2348.49, "word": " five", "probability": 0.5556640625}, {"start": 2348.49, "end": 2348.77, "word": " is", "probability": 0.9599609375}, {"start": 2348.77, "end": 2349.07, "word": " odd", "probability": 0.9384765625}, {"start": 2349.07, "end": 2349.73, "word": " then", "probability": 0.66748046875}, {"start": 2349.73, "end": 2350.75, "word": " N", "probability": 0.96728515625}, {"start": 2350.75, "end": 2351.13, "word": " is", "probability": 0.96923828125}, {"start": 2351.13, "end": 2352.21, "word": " even", "probability": 0.91162109375}, {"start": 2352.21, "end": 2355.91, "word": " لاحظته؟", "probability": 0.8091796875}, {"start": 2355.91, "end": 2356.29, "word": " بدنا", "probability": 0.96630859375}, {"start": 2356.29, "end": 2356.81, "word": " نثبت", "probability": 0.995361328125}, {"start": 2356.81, "end": 2357.25, "word": " إذا", "probability": 0.781005859375}, {"start": 2357.25, "end": 2357.69, "word": " كانت", 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هنا و افرض ان هذه odd و نحسب هذه", "tokens": [44510, 8315, 8717, 12984, 3555, 2655, 9154, 11296, 16472, 426, 307, 754, 4724, 995, 14851, 9778, 3215, 10943, 28242, 3714, 25720, 11331, 6027, 3660, 3714, 25720, 4724, 995, 14851, 9778, 3215, 10943, 2423, 8177, 538, 660, 4007, 5830, 8717, 44510, 10721, 20666, 9000, 4007, 5830, 38637, 2304, 20666, 34937, 4032, 27188, 2288, 4587, 13412, 32277, 3615, 49374, 16712, 29399, 9957, 23032, 1829, 3555, 39894, 3224, 1829, 10721, 20292, 20666, 9000, 4007, 5830, 19446, 41185, 11296, 37893, 28820, 3660, 8032, 1863, 5172, 43042, 6225, 4117, 3794, 33580, 37495, 22653, 8032, 44510, 10721, 9154, 34105, 4032, 1975, 5172, 43042, 16472, 29538, 7401, 4032, 8717, 5016, 35457, 29538], "avg_logprob": -0.19251179020359832, "compression_ratio": 1.737991266375546, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2365.91, "end": 2366.31, "word": "بدنا", "probability": 0.60650634765625}, {"start": 2366.31, "end": 2366.63, "word": " نثبت", "probability": 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"probability": 0.8369140625}, {"start": 2371.99, "end": 2372.37, "word": " proof", "probability": 0.931640625}, {"start": 2372.37, "end": 2373.33, "word": " by", "probability": 0.78515625}, {"start": 2373.33, "end": 2375.79, "word": " contraposition", "probability": 0.75927734375}, {"start": 2375.79, "end": 2376.53, "word": " نبدأ", "probability": 0.8396809895833334}, {"start": 2376.53, "end": 2377.31, "word": " بالcontraposition", "probability": 0.8470458984375}, {"start": 2377.31, "end": 2378.05, "word": " ثم", "probability": 0.978271484375}, {"start": 2378.05, "end": 2378.27, "word": " بال", "probability": 0.97412109375}, {"start": 2378.27, "end": 2378.79, "word": " contradiction", "probability": 0.68359375}, {"start": 2378.79, "end": 2380.01, "word": " و", "probability": 0.44287109375}, {"start": 2380.01, "end": 2380.27, "word": " الفرق", "probability": 0.9677734375}, {"start": 2380.27, "end": 2380.57, "word": " شاسع", "probability": 0.9710286458333334}, {"start": 2380.57, "end": 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"end": 2389.79, "word": " من", "probability": 0.98486328125}, {"start": 2389.79, "end": 2390.07, "word": " هنا", "probability": 0.9970703125}, {"start": 2390.07, "end": 2390.57, "word": " و", "probability": 0.9169921875}, {"start": 2390.57, "end": 2390.81, "word": " افرض", "probability": 0.8499348958333334}, {"start": 2390.81, "end": 2390.97, "word": " ان", "probability": 0.7158203125}, {"start": 2390.97, "end": 2391.27, "word": " هذه", "probability": 0.30712890625}, {"start": 2391.27, "end": 2391.75, "word": " odd", "probability": 0.65966796875}, {"start": 2391.75, "end": 2392.55, "word": " و", "probability": 0.95947265625}, {"start": 2392.55, "end": 2392.91, "word": " نحسب", "probability": 0.9606119791666666}, {"start": 2392.91, "end": 2393.21, "word": " هذه", "probability": 0.85888671875}], "temperature": 1.0}, {"id": 93, "seek": 241234, "start": 2394.04, "end": 2412.34, "text": "مش هيك يعني مش كتير جثتها .. مش كتير جثتها صعبة ف assume n is odd اللي هي عكس تمام بسطت الأمور و خلصت معناه ذلك أنه بقدر أحطها ب 2k plus 1 و انتهى الموضوع و انعوض في ال n تكعيب زائد خمسة", "tokens": [2304, 8592, 39896, 4117, 37495, 22653, 37893, 9122, 2655, 13546, 10874, 12984, 2655, 11296, 4386, 37893, 9122, 2655, 13546, 10874, 12984, 2655, 11296, 20328, 3615, 49401, 6156, 6552, 297, 307, 7401, 13672, 1829, 39896, 6225, 4117, 3794, 46811, 10943, 4724, 3794, 9566, 2655, 16247, 2304, 13063, 4032, 16490, 1211, 9381, 2655, 20449, 8315, 3224, 29910, 23275, 14739, 3224, 4724, 28543, 2288, 5551, 5016, 9566, 11296, 4724, 568, 74, 1804, 502, 4032, 16472, 47395, 7578, 9673, 2407, 11242, 45367, 4032, 16472, 3615, 2407, 11242, 8978, 2423, 297, 6055, 4117, 3615, 1829, 3555, 30767, 16373, 3215, 16490, 2304, 3794, 3660], "avg_logprob": -0.15246211489041647, "compression_ratio": 1.566326530612245, "no_speech_prob": 5.900859832763672e-06, "words": [{"start": 2394.04, "end": 2394.36, "word": "مش", "probability": 0.83056640625}, {"start": 2394.36, "end": 2394.68, "word": " هيك", "probability": 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99, "seek": 257361, "start": 2551.09, "end": 2573.61, "text": "برضه هتكون عبارة عن odd صح؟ فيها and in is odd طيب odd تكعيب خلاص odd طيب odd زائد odd even even هتطلع و ليس زي فرضيتنا أن هي odd", "tokens": [26890, 11242, 3224, 8032, 2655, 30544, 6225, 3555, 9640, 3660, 18871, 7401, 20328, 5016, 22807, 8978, 11296, 293, 294, 307, 7401, 23032, 1829, 3555, 7401, 6055, 4117, 3615, 1829, 3555, 16490, 1211, 33546, 7401, 23032, 1829, 3555, 7401, 30767, 16373, 3215, 7401, 754, 754, 8032, 2655, 9566, 1211, 3615, 4032, 32239, 3794, 30767, 1829, 6156, 43042, 36081, 8315, 14739, 39896, 7401], "avg_logprob": -0.17615928044242243, "compression_ratio": 1.3884892086330936, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2551.09, "end": 2551.65, "word": "برضه", "probability": 0.8955078125}, {"start": 2551.65, "end": 2552.21, "word": " هتكون", "probability": 0.9384765625}, {"start": 2552.21, "end": 2552.47, "word": " عبارة", "probability": 0.9449462890625}, {"start": 2552.47, "end": 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"إن تكعيب زائد خمسة is odd and in is odd اللي كانت المفروض even حسب النظرية الأصلية احنا فرضنا عكسها طلع عكسها false إذا ان هي true", "tokens": [28814, 1863, 6055, 4117, 3615, 1829, 3555, 30767, 16373, 3215, 16490, 2304, 3794, 3660, 307, 7401, 293, 294, 307, 7401, 13672, 1829, 25961, 2655, 9673, 5172, 32887, 11242, 754, 11331, 35457, 28239, 19913, 2288, 10632, 16247, 36520, 10632, 1975, 5016, 8315, 6156, 43042, 8315, 6225, 4117, 3794, 11296, 23032, 1211, 3615, 6225, 4117, 3794, 11296, 7908, 11933, 15730, 16472, 39896, 2074], "avg_logprob": -0.23084677755832672, "compression_ratio": 1.3825503355704698, "no_speech_prob": 5.304813385009766e-06, "words": [{"start": 2603.15, "end": 2603.57, "word": "إن", "probability": 0.622314453125}, {"start": 2603.57, "end": 2604.63, "word": " تكعيب", "probability": 0.809375}, {"start": 2604.63, "end": 2605.11, "word": " زائد", "probability": 0.7462565104166666}, {"start": 2605.11, "end": 2605.61, "word": " خمسة", "probability": 0.9588623046875}, 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"text": "أخدنا هذا المثال مش هيك بس كان لقاش جدر تربيعي تكعيبه مش هيفرج كتير بس فكرته أنه كان سؤال في امتحان طبعا الطلاب شافوا أنه تكعيبي وقفوا حالهم ووقفت مالهم زي ما بقوله لأ بصد و لا برد صاروا ليش؟ مافيش فيها إشي طب ماهي نفس اللي حلنا في ال slides هو هو اعملوا بنفس خطواته إيش هيتغير معاكوا رقم رقمين؟", "tokens": [10721, 9778, 3215, 8315, 23758, 9673, 12984, 6027, 37893, 39896, 4117, 4724, 3794, 25961, 5296, 4587, 33599, 10874, 3215, 2288, 6055, 2288, 21292, 3615, 1829, 6055, 4117, 3615, 1829, 3555, 3224, 37893, 39896, 5172, 47341, 9122, 2655, 13546, 4724, 3794, 6156, 4117, 43500, 3224, 14739, 3224, 25961, 8608, 33604, 6027, 8978, 1975, 2304, 2655, 5016, 7649, 23032, 3555, 3615, 995, 41950, 15040, 3555, 13412, 31845, 14407, 14739, 3224, 6055, 4117, 3615, 1829, 21292, 4032, 4587, 5172, 14407, 11331, 6027, 16095, 4032, 30543, 5172, 2655, 3714, 6027, 16095, 30767, 1829, 19446, 4724, 39648, 3224, 5296, 10721, 4724, 9381, 3215, 4032, 20193, 4724, 2288, 3215, 20328, 9640, 14407, 32239, 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{"start": 2890.06, "end": 2890.32, "word": " تعملها", "probability": 0.970458984375}, {"start": 2890.32, "end": 2890.58, "word": " direct", "probability": 0.9677734375}, {"start": 2890.58, "end": 2890.88, "word": " اعملها", "probability": 0.9427490234375}, {"start": 2890.88, "end": 2891.26, "word": " direct", "probability": 0.95849609375}, {"start": 2891.26, "end": 2892.28, "word": " بس", "probability": 0.978515625}, {"start": 2892.28, "end": 2892.44, "word": " بدك", "probability": 0.931640625}, {"start": 2892.44, "end": 2892.64, "word": " تكون", "probability": 0.985595703125}, {"start": 2892.64, "end": 2892.88, "word": " فاهم", "probability": 0.92529296875}, {"start": 2892.88, "end": 2893.06, "word": " انك", "probability": 0.7587890625}, {"start": 2893.06, "end": 2893.28, "word": " هذي", "probability": 0.8255208333333334}, {"start": 2893.28, "end": 2893.44, "word": " اذا", "probability": 0.822509765625}, {"start": 2893.44, "end": 2893.64, "word": " كان", "probability": 0.98828125}, {"start": 2893.64, "end": 2893.84, "word": " هذي", "probability": 0.9142252604166666}, {"start": 2893.84, "end": 2894.2, "word": " odd", "probability": 0.873046875}, {"start": 2894.2, "end": 2894.72, "word": " odd", "probability": 0.53515625}, {"start": 2894.72, "end": 2894.86, "word": " في", "probability": 0.81201171875}, {"start": 2894.86, "end": 2895.22, "word": " odd", "probability": 0.9599609375}, {"start": 2895.22, "end": 2896.52, "word": " odd", "probability": 0.8017578125}, {"start": 2896.52, "end": 2897.3, "word": " plus", "probability": 0.89697265625}, {"start": 2897.3, "end": 2898.06, "word": " even", "probability": 0.92138671875}, {"start": 2898.06, "end": 2899.1, "word": " خلاص", "probability": 0.8785807291666666}, {"start": 2899.1, "end": 2899.46, "word": " نعم", "probability": 0.937255859375}, {"start": 2899.46, "end": 2900.18, "word": " بدك", "probability": 0.97314453125}, {"start": 2900.18, "end": 2900.36, "word": " تعمل", "probability": 0.9845377604166666}, {"start": 2900.36, "end": 2900.56, "word": " direct", "probability": 0.94677734375}, {"start": 2900.56, "end": 2900.86, "word": " اعمل", "probability": 0.7784830729166666}, {"start": 2900.86, "end": 2901.02, "word": " direct", "probability": 0.908203125}, {"start": 2901.02, "end": 2901.22, "word": " مافيش", "probability": 0.7074381510416666}, {"start": 2901.22, "end": 2901.82, "word": " مشكلة", "probability": 0.9833984375}, {"start": 2901.82, "end": 2902.28, "word": " بس", "probability": 0.98046875}, {"start": 2902.28, "end": 2902.66, "word": " فاهمين", "probability": 0.9674072265625}, {"start": 2902.66, "end": 2903.0, "word": " فكرة", "probability": 0.9742838541666666}, {"start": 2903.0, "end": 2903.3, "word": " انه", "probability": 0.814697265625}, {"start": 2903.3, "end": 2903.48, "word": " بده", "probability": 0.486572265625}, {"start": 2903.48, "end": 2903.64, "word": " اعمل", "probability": 0.8821614583333334}, {"start": 2903.64, "end": 2904.16, "word": " duplication", "probability": 0.916015625}, {"start": 2904.16, "end": 2904.34, "word": " هنا", "probability": 0.99365234375}], "temperature": 1.0}, {"id": 113, "seek": 292987, "start": 2905.05, "end": 2929.87, "text": "لأن ال F and only F معناته F في اتجاه P to Q و برضه implication في اتجاه Q to P تمام خلصناها بتنزل معاكوا هذه محلولة بس أخدنا الفكرة ال concept بتاعة بسيط جدا فتاخد على الحالتين عشان تكون خلصنا جزئيتنا لهذا اليوم الأسبوع الجاي بنبدأ درس جديد ان شاء الله تعالى", "tokens": [1211, 33456, 2423, 479, 293, 787, 479, 20449, 8315, 47395, 479, 8978, 1975, 2655, 7435, 40294, 430, 281, 1249, 4032, 4724, 43042, 3224, 37814, 8978, 1975, 2655, 7435, 40294, 1249, 281, 430, 46811, 10943, 16490, 1211, 9381, 8315, 11296, 39894, 1863, 11622, 1211, 20449, 995, 4117, 14407, 29538, 3714, 5016, 1211, 12610, 3660, 4724, 3794, 5551, 9778, 3215, 8315, 27188, 4117, 25720, 2423, 3410, 39894, 995, 27884, 4724, 3794, 1829, 9566, 10874, 28259, 6156, 2655, 47283, 3215, 15844, 21542, 6027, 2655, 9957, 6225, 8592, 7649, 6055, 30544, 16490, 1211, 9381, 8315, 10874, 11622, 19986, 36081, 8315, 46740, 15730, 45595, 20498, 16247, 35457, 45367, 25724, 47302, 44945, 44510, 10721, 11778, 2288, 3794, 10874, 16254, 3215, 16472, 13412, 16606, 21984, 37279, 6027, 7578], "avg_logprob": -0.1379354509418128, "compression_ratio": 1.6412213740458015, "no_speech_prob": 3.933906555175781e-06, "words": [{"start": 2905.05, "end": 2905.41, "word": "لأن", "probability": 0.770263671875}, {"start": 2905.41, "end": 2905.75, "word": " ال", "probability": 0.52685546875}, {"start": 2905.75, "end": 2905.99, "word": " F", "probability": 0.256103515625}, {"start": 2905.99, "end": 2906.17, "word": " and", "probability": 0.8759765625}, {"start": 2906.17, "end": 2906.41, "word": " only", "probability": 0.83544921875}, {"start": 2906.41, "end": 2906.59, "word": " F", "probability": 0.90380859375}, {"start": 2906.59, "end": 2907.01, "word": " معناته", "probability": 0.9080403645833334}, {"start": 2907.01, "end": 2907.71, "word": " F", "probability": 0.78271484375}, {"start": 2907.71, "end": 2907.83, "word": " في", "probability": 0.40283203125}, {"start": 2907.83, "end": 2908.29, "word": " اتجاه", "probability": 0.9727783203125}, {"start": 2908.29, "end": 2908.75, "word": " P", "probability": 0.92626953125}, {"start": 2908.75, "end": 2908.99, "word": " to", "probability": 0.95361328125}, {"start": 2908.99, "end": 2909.39, "word": " Q", "probability": 0.96923828125}, {"start": 2909.39, "end": 2910.21, "word": " و", "probability": 0.8623046875}, {"start": 2910.21, "end": 2911.59, "word": " برضه", "probability": 0.709228515625}, {"start": 2911.59, "end": 2911.97, "word": " implication", "probability": 0.814453125}, {"start": 2911.97, "end": 2912.21, "word": " في", "probability": 0.9296875}, {"start": 2912.21, "end": 2912.55, "word": " اتجاه", "probability": 0.9825439453125}, {"start": 2912.55, "end": 2913.07, "word": " Q", "probability": 0.80712890625}, {"start": 2913.07, "end": 2913.49, "word": " to", "probability": 0.95703125}, {"start": 2913.49, "end": 2913.71, "word": " P", "probability": 0.9677734375}, {"start": 2913.71, "end": 2914.45, "word": " تمام", "probability": 0.7369384765625}, {"start": 2914.45, "end": 2915.71, "word": " خلصناها", "probability": 0.9587890625}, {"start": 2915.71, "end": 2916.63, "word": " بتنزل", "probability": 0.9176025390625}, {"start": 2916.63, "end": 2916.97, "word": " معاكوا", "probability": 0.89794921875}, {"start": 2916.97, "end": 2917.15, "word": " هذه", "probability": 0.5791015625}, {"start": 2917.15, "end": 2917.55, "word": " محلولة", "probability": 0.908984375}, {"start": 2917.55, "end": 2917.75, "word": " بس", "probability": 0.95654296875}, {"start": 2917.75, "end": 2918.13, "word": " أخدنا", "probability": 0.918212890625}, {"start": 2918.13, "end": 2918.49, "word": " الفكرة", "probability": 0.9934895833333334}, {"start": 2918.49, "end": 2918.79, "word": " ال", "probability": 0.923828125}, {"start": 2918.79, "end": 2919.09, "word": " concept", "probability": 0.89013671875}, {"start": 2919.09, "end": 2919.35, "word": " بتاعة", "probability": 0.64453125}, {"start": 2919.35, "end": 2919.69, "word": " بسيط", "probability": 0.987548828125}, {"start": 2919.69, "end": 2919.97, "word": " جدا", "probability": 0.99169921875}, {"start": 2919.97, "end": 2921.27, "word": " فتاخد", "probability": 0.86279296875}, {"start": 2921.27, "end": 2921.37, "word": " على", "probability": 0.72998046875}, {"start": 2921.37, "end": 2921.87, "word": " الحالتين", "probability": 0.8419189453125}, {"start": 2921.87, "end": 2922.45, "word": " عشان", "probability": 0.9835611979166666}, {"start": 2922.45, "end": 2922.69, "word": " تكون", "probability": 0.964111328125}, {"start": 2922.69, "end": 2923.33, "word": " خلصنا", "probability": 0.9925537109375}, {"start": 2923.33, "end": 2924.45, "word": " جزئيتنا", "probability": 0.8734375}, {"start": 2924.45, "end": 2924.71, "word": " لهذا", "probability": 0.93994140625}, {"start": 2924.71, "end": 2925.09, "word": " اليوم", "probability": 0.974365234375}, {"start": 2925.09, "end": 2926.61, "word": " الأسبوع", "probability": 0.9571940104166666}, {"start": 2926.61, "end": 2927.09, "word": " الجاي", "probability": 0.762939453125}, {"start": 2927.09, "end": 2927.97, "word": " بنبدأ", "probability": 0.9207356770833334}, {"start": 2927.97, "end": 2928.83, "word": " درس", "probability": 0.9861653645833334}, {"start": 2928.83, "end": 2929.15, "word": " جديد", "probability": 0.9908854166666666}, {"start": 2929.15, "end": 2929.27, "word": " ان", "probability": 0.81396484375}, {"start": 2929.27, "end": 2929.41, "word": " شاء", "probability": 0.9404296875}, {"start": 2929.41, "end": 2929.47, "word": " الله", "probability": 0.94482421875}, {"start": 2929.47, "end": 2929.87, "word": " تعالى", "probability": 0.9817708333333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2930.0564375, "duration_after_vad": 2819.3268749999897}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..95dfdead4cf52ac8d36f9eaaea72b54c4c0da141
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/h_1_ZeRMZk0_raw.srt
@@ -0,0 +1,2268 @@
+1
+00:00:05,230 --> 00:00:09,650
+السلام عليكم، يعطيكم العفو يا شباب، اليوم نستكمل
+
+2
+00:00:09,650 --> 00:00:14,070
+جزئية ال proofs اللي كنا بنتكلم فيها، فاليوم ان
+
+3
+00:00:14,070 --> 00:00:17,850
+شاء الله هناخد مجموعة أمثلة محلولة أو solve the
+
+4
+00:00:17,850 --> 00:00:23,590
+problem لما تم أخذه خلال هذا الأسبوع، وهذا اشي
+
+5
+00:00:23,590 --> 00:00:26,970
+كتير كويس انه بيظل معانا في مجالفي الأسبوع هذا و
+
+6
+00:00:26,970 --> 00:00:30,690
+يمكن انا مراكن كتير على المحاضرات المصورة فكتير
+
+7
+00:00:30,690 --> 00:00:33,430
+كويس ان انتوا تكونوا حاضرين المحاضرة المصورة عشان
+
+8
+00:00:33,430 --> 00:00:38,350
+فعلا بتساعدني ان اكون ماشي بشكل كتير افضل خلال
+
+9
+00:00:38,350 --> 00:00:42,910
+الأسبوع و هذا بوفرلنا وقت ان احنا نعرف نحل أسئلة و
+
+10
+00:00:42,910 --> 00:00:46,970
+يمكن هذه هي الأهم بالنسبالكوا لأنه أمثلة في المعظم
+
+11
+00:00:46,970 --> 00:00:50,170
+هي أمثلة امتحاناتفي المعظم هتلاقي ان هي أمثلة
+
+12
+00:00:50,170 --> 00:00:54,630
+امتحانات فاليوم نبدأ ناخد ناخد ال second set of
+
+13
+00:00:54,630 --> 00:00:58,090
+problems المرة اللي فات الأسبوع اللي فات أخدنا أول
+
+14
+00:00:58,090 --> 00:01:02,370
+set أو أول مجموعة من ال problems اليوم نكمل مجموعة
+
+15
+00:01:02,370 --> 00:01:04,710
+تانية وهذا السؤال كان جاي في امتحان من الامتحانات
+
+16
+00:01:04,710 --> 00:01:09,890
+كان في أحد الامتحانات جاي سابقا برضه ل discrete
+
+17
+00:01:09,890 --> 00:01:16,250
+mathematics تمام كان let f x y و هذه تمثل
+
+18
+00:01:16,250 --> 00:01:21,610
+statement x can help yX can help Y والمطلوب الآن
+
+19
+00:01:21,610 --> 00:01:25,610
+بالنسبة لل domain اللي بيحتوي على كل ال people in
+
+20
+00:01:25,610 --> 00:01:28,730
+the world نفترض أنه ال domain ال universal domain
+
+21
+00:01:28,730 --> 00:01:33,450
+طبعا هو كل سكان العالم أو كل الناس في العالم بدنا
+
+22
+00:01:33,450 --> 00:01:37,170
+نستخدم quantifiers and logical operators to
+
+23
+00:01:37,170 --> 00:01:41,350
+express each of the statements و بحنبدأ بمجموعة
+
+24
+00:01:41,350 --> 00:01:46,600
+statementsكويس everyone can help Ali everyone أكيد
+
+25
+00:01:46,600 --> 00:01:51,460
+بنقول for all كويس و هنكتب ال for all هذه لملة X
+
+26
+00:01:51,460 --> 00:01:58,100
+فإذا هتبدأ ب X او ال F of X لأن X احنا عملنا ..
+
+27
+00:01:58,100 --> 00:02:03,240
+عملنا ال quantification في الأول for all X and Ali
+
+28
+00:02:03,240 --> 00:02:10,310
+why هنا Ali؟ صحيح؟why لأ هي بطلت why هي أصبحت help
+
+29
+00:02:10,310 --> 00:02:16,610
+علي فأصبحت علي تحديدا علي كويس فهي هذه طريقة حلها
+
+30
+00:02:16,610 --> 00:02:20,830
+بكل بساطة أعرفت جميع ال limits اللي عندك في بعضهم
+
+31
+00:02:20,830 --> 00:02:24,030
+بعض ال variables اتعرفت من خلال ال quantifier
+
+32
+00:02:24,030 --> 00:02:28,780
+وبعضهم اتعرف بشكل direct مباشرعالي أنا قولت عالي
+
+33
+00:02:28,780 --> 00:02:33,020
+مباشرة فإذا بدي أعرفه عالي على طول صحيح؟ مش هحطه
+
+34
+00:02:33,020 --> 00:02:36,120
+why ولا هقول there exist ولا لإن هم there exist
+
+35
+00:02:36,120 --> 00:02:40,360
+أنا عارفه تحديدا، هو عالي كويس، نفس الكلام سارة
+
+36
+00:02:40,360 --> 00:02:45,080
+can help someone there exist ايش؟ why بالظبط،
+
+37
+00:02:45,080 --> 00:02:50,080
+هنفتح أقواز سارة و why تمام جدا، هي واضحة الأمور
+
+38
+00:02:50,080 --> 00:02:53,720
+وسهلة بسيطة جدا، صحيح؟ سؤال زي هذا، كتير كانوا
+
+39
+00:02:53,720 --> 00:02:58,750
+بغلطوا فيهتخيلوا سؤال بسيط بهذا الشكل كتير كانوا
+
+40
+00:02:58,750 --> 00:03:03,790
+بيغلطوا فيه بيجيبوش في علامته تمام just one just
+
+41
+00:03:03,790 --> 00:03:08,390
+one there exist exclamation مش متذكرينه طيب just
+
+42
+00:03:08,390 --> 00:03:14,610
+one man can help both Ali and Omar فمعنى ذلك هنا
+
+43
+00:03:15,680 --> 00:03:20,620
+there exist فنكتبها there exist with exclamation x
+
+44
+00:03:20,620 --> 00:03:24,320
+لإن هو اللي بده يقدّم الخدمة هو ال subject و بدنا
+
+45
+00:03:24,320 --> 00:03:31,500
+نعمل x و هنفتح أقواص عشان أقول أحمد and علي عشان
+
+46
+00:03:31,500 --> 00:03:36,320
+نقول أحمد او علي إذا بدنا نكون جسمنا ال four كلها،
+
+47
+00:03:36,320 --> 00:03:41,120
+تمام؟ فإذا يوجد شخص واحد الشخص هذا بساعد أحمد
+
+48
+00:03:41,120 --> 00:03:44,760
+والشخص هذا بساعد عمر ولا علي؟ أنا عمر
+
+49
+00:03:53,460 --> 00:03:59,040
+ممكن بس مش هتكون كتير واضحة مش هتوضح كتير ال and
+
+50
+00:03:59,040 --> 00:04:03,240
+في هذه المشكلة ال and كيف بدك تعملها انت بتقول كمه
+
+51
+00:04:03,240 --> 00:04:10,240
+انت بدك تحطها يعني هنا هذه كله هذا بدون القسين
+
+52
+00:04:10,240 --> 00:04:12,960
+الأقواص هذه و هذه بس بدها تكون and واضحة
+
+53
+00:04:16,350 --> 00:04:23,950
+no one can help himself no
+
+54
+00:04:23,950 --> 00:04:32,570
+one negation for all لا يوجد ولا واحد لكن لو قلنا
+
+55
+00:04:32,570 --> 00:04:38,370
+there exist معناته انه لا يوجد بعضهم تمام؟ لاوجد
+
+56
+00:04:38,370 --> 00:04:41,830
+بعضهم طيب no one can .. بس انا مش عليها دي بتطلع
+
+57
+00:04:41,830 --> 00:04:43,550
+بتطلع علي كيف تكون ترجمه himself
+
+58
+00:04:46,420 --> 00:04:51,180
+هل بتحطه اكس؟ اكس و اكس تمام himself لإن بدي احطه
+
+59
+00:04:51,180 --> 00:04:54,400
+اكس و اي معناته قد يختلفوا اكس و اي مع بعض لكن انا
+
+60
+00:04:54,400 --> 00:04:59,260
+بقول مش هيقدر يساعد نفسه مش هيقدر يساعد نفسه فمعنى
+
+61
+00:04:59,260 --> 00:05:04,920
+ذلك انه انا بتكلم عن عن هو اكس
+
+62
+00:05:04,920 --> 00:05:10,860
+اكس عن نفسه تمام هدولة مهمين لإنه بتتكلم وينها
+
+63
+00:05:10,860 --> 00:05:14,980
+اولا اللي هو اكس نفسه اللي عرفنا himself
+
+64
+00:05:19,970 --> 00:05:27,810
+just one .. no one .. no one can .. اه there exist
+
+65
+00:05:27,810 --> 00:05:31,350
+هنا لا يوجد احد .. اه لا يوجد احد هنا ان انت
+
+66
+00:05:31,350 --> 00:05:35,770
+بتتكلم هنا لا يوجد احد ان بدك تعملها no one معناته
+
+67
+00:05:35,770 --> 00:05:43,570
+بدك تحط for all و جوا negation فش
+
+68
+00:05:43,570 --> 00:05:48,240
+بعض هنا انا بتكلم عن نفس الشخصهو نفس الشخص يعني
+
+69
+00:05:48,240 --> 00:05:54,600
+هنا بقول لاوجد اي واحد بساعد نفسه انا ماتكلمتش عن
+
+70
+00:05:54,600 --> 00:06:00,540
+التاني قد يساعد التاني و قد لا يساعد التاني بقى
+
+71
+00:06:00,540 --> 00:06:04,660
+بعرفش ممكن بساعد غيره و ممكن لأ بساعدش غيره و برضه
+
+72
+00:06:04,660 --> 00:06:09,940
+بساعدش نفسه ما احنا قولنا ممكن او ممكن لأ في
+
+73
+00:06:09,940 --> 00:06:14,180
+الحالة هذه اذا قلنا for all معناته انه لا الكل
+
+74
+00:06:14,180 --> 00:06:23,450
+الكل مش هيساعدهأو ليس الكل معناها صح؟ لازم نعملها
+
+75
+00:06:23,450 --> 00:06:28,310
+for all لأ خلينا نكتبهم كلامكم صح خلينا نكمل مع
+
+76
+00:06:28,310 --> 00:06:30,490
+بعض كويس خلينا نفكر مع بعض مش المشكلة ما احنا
+
+77
+00:06:30,490 --> 00:06:36,570
+قالين نراجع نكتبها و نحلل مش صح اني أقولك زي ما
+
+78
+00:06:36,570 --> 00:06:39,510
+أقولك ألا غلط و بنفع و أحفظها هيك خلينا نفهمها
+
+79
+00:06:39,510 --> 00:06:47,000
+لاوجد كل مش هيك معناته أنه قد يكون بعضهمركزوا
+
+80
+00:06:47,000 --> 00:06:53,260
+معايا شوفوها هيك زابطة معاكم there is no all على
+
+81
+00:06:53,260 --> 00:06:56,420
+اللي احنا كاتبينه معناته ان ممكن يكونوا كلهم
+
+82
+00:06:56,420 --> 00:07:04,340
+بيحققوها الا واحد مش هيك؟ صح؟ في اشي مش واضح؟ هيها
+
+83
+00:07:04,340 --> 00:07:08,380
+منطقية طيب العكس تبع او خلينا نقول الحالة اللي
+
+84
+00:07:08,380 --> 00:07:13,940
+احنا كاتبينها و نفهمها نحاول ان نحللها هنا
+
+85
+00:07:15,020 --> 00:07:18,800
+there exist هذه الحالها يعني على الأقل في واحد طب
+
+86
+00:07:18,800 --> 00:07:24,940
+نقول مافيش ولا واحد لاوجد
+
+87
+00:07:24,940 --> 00:07:29,860
+ولا واحد هنا قد يكون في واحد لكن اللي أكيد أنه مش
+
+88
+00:07:29,860 --> 00:07:35,020
+الكل اللي فوق هذه معناته أنه مش الكل ممكن يكون كل
+
+89
+00:07:35,020 --> 00:07:39,380
+واحد الواحد هذا نفع ال for all الواحد نفع ال for
+
+90
+00:07:39,380 --> 00:07:43,200
+all أما هنا لأ هذه يمكن تكون أكثر وقعية واضحة no
+
+91
+00:07:43,200 --> 00:07:48,450
+one خلاصلل function بيظبط كلامك منطقي فهنا بتصير
+
+92
+00:07:48,450 --> 00:07:55,050
+for all negation if كلامك مية المية تظبط هيك
+
+93
+00:07:55,050 --> 00:08:00,250
+معناته كإني بقول للكل ولا واحد بيساعد حاله بس في
+
+94
+00:08:00,250 --> 00:08:05,030
+الحالة هد انت كلش عملت لها دي دي Morgan صح فكلامك
+
+95
+00:08:05,030 --> 00:08:09,170
+ينطبق مع حدي أصبح مع ال negation there exist طلعت
+
+96
+00:08:09,170 --> 00:08:14,050
+ال ال negation برا و اتحولت عندك بدل ما هي for all
+
+97
+00:08:14,050 --> 00:08:15,230
+اتحولت ل there exist
+
+98
+00:08:18,340 --> 00:08:24,160
+تمام الأخيرة not everyone ليس الكل هدرك pathology
+
+99
+00:08:24,160 --> 00:08:27,980
+مع مين مع مفهومنا تعتوي ليس الكل بساعد someone
+
+100
+00:08:27,980 --> 00:08:32,060
+فهنا هتكون ليس الكل هنا بتظبط معانا ليس الكل بمعنى
+
+101
+00:08:32,060 --> 00:08:37,800
+أن في بعض هيساعد بس مش الكل البعض هيساعد أه بس ليس
+
+102
+00:08:37,800 --> 00:08:46,500
+الكل بحظين هنا not everyone negation for allوطبعا
+
+103
+00:08:46,500 --> 00:08:49,080
+can help someone, someone بنتخليها زي ما هي
+
+104
+00:08:49,080 --> 00:08:57,400
+someone there exist y اللي هي someone تمام طيب هذا
+
+105
+00:08:57,400 --> 00:09:01,160
+حاسبلكوا يا برضه هنزلكوا الملف تقرأوا لإن اليوم
+
+106
+00:09:01,160 --> 00:09:07,590
+شوية مزودلكوا حجم الالهدول هذا مجرد بس العكس لهناك
+
+107
+00:09:07,590 --> 00:09:11,670
+هيكون في عندى ال negations .. أفوان ال notations
+
+108
+00:09:11,670 --> 00:09:15,650
+موجودة لل quantifiers و المقلوب تكتب منها الجملة
+
+109
+00:09:15,650 --> 00:09:20,290
+الجملة بسيطة جدا مجرد لغة مجرد تركيب لغات مجرد
+
+110
+00:09:20,290 --> 00:09:27,210
+تركيب لغة عشان نحاول نصل ل ال proving strategies
+
+111
+00:09:27,210 --> 00:09:29,790
+لإن انا عامل مجموعة أسئلة في أخرها في ال proving
+
+112
+00:09:29,790 --> 00:09:34,470
+strategies معنى أنه نصلهابتقرؤوها إذا في واحدة
+
+113
+00:09:34,470 --> 00:09:38,230
+منهم مش واضحة معاكم ترجعوا هنا
+
+114
+00:09:42,030 --> 00:09:45,170
+هذه مثلا واحدة من الأسئلة اللي شفتها في واحد من
+
+115
+00:09:45,170 --> 00:09:49,050
+الامتحانات على ال net مثلا All problems طبعا أنتوا
+
+116
+00:09:49,050 --> 00:09:52,470
+بتعرفين ال questions في بعضها problems و بعضها
+
+117
+00:09:52,470 --> 00:09:57,070
+true و false و بعضها multiple choice بس في منهم
+
+118
+00:09:57,070 --> 00:10:00,350
+problems اللي هو بدأ حل خطوات فهنا لو قلنا كل
+
+119
+00:10:00,350 --> 00:10:05,030
+problems اللي هي نوع من أنواع ال questions are
+
+120
+00:10:05,030 --> 00:10:10,810
+difficult and frustratingdifficult معروفة صعبة
+
+121
+00:10:10,810 --> 00:10:18,670
+frustrating محبطة كويس هذه premise هيعطيكوا إياها
+
+122
+00:10:18,670 --> 00:10:22,070
+على طول هيكون في عندكوا مجموعة questions ال exam
+
+123
+00:10:22,070 --> 00:10:26,150
+تبعكم في multiple choice و في true و false و في
+
+124
+00:10:26,150 --> 00:10:30,490
+problems و بعدين أقولكوا دي و بعدين كل ال problems
+
+125
+00:10:30,490 --> 00:10:35,220
+صعبة و محبطة فبتكونوا تذاكروا كويستمام and some
+
+126
+00:10:35,220 --> 00:10:40,580
+problems are challenging بعض المشاكل أو بعض ال
+
+127
+00:10:40,580 --> 00:10:46,060
+problems هذه فيها تحدي يعني هتكون فيها أفكار كذا
+
+128
+00:10:46,060 --> 00:10:51,200
+فكرة في بعض كذا إشي فيها تحدي الآن hence المقلوب
+
+129
+00:10:51,200 --> 00:10:54,760
+إيش بتكون تثبته أنه some problems are frustrating
+
+130
+00:10:54,760 --> 00:10:58,900
+and challenging بتكون تثبته أن بعضها هو مش بس
+
+131
+00:10:58,900 --> 00:11:05,410
+challenging لأ كمان محبطبعضها ليس فقط فيه تحدي
+
+132
+00:11:05,410 --> 00:11:11,810
+وإنما كمان محبط تمام بطريقة .. كيف؟ بطريقة تقليدية
+
+133
+00:11:11,810 --> 00:11:16,030
+بدنا نحط من ال universe of discourse اللي هي
+
+134
+00:11:16,030 --> 00:11:18,950
+مجموعة ال questions كلها عشان نبدأ نقول ال
+
+135
+00:11:18,950 --> 00:11:22,950
+definitions اللي كانت عندى لمجموعة ال premises و
+
+136
+00:11:22,950 --> 00:11:26,110
+ال conclusion هنعرفها بهذا الشكل ال P هقول ان هي
+
+137
+00:11:26,110 --> 00:11:30,190
+problem من كل questions مين ال problem فكل problem
+
+138
+00:11:30,190 --> 00:11:37,790
+هو محبط اوأو صعب مش هيك هاي أول حالة من الحلقة دي
+
+139
+00:11:37,790 --> 00:11:41,390
+بالظبط هتكون for all هي all دي هقول هي ل difficult
+
+140
+00:11:41,390 --> 00:11:48,290
+ال F ل frustrating و ال C ل challenging عشان نبدأ
+
+141
+00:11:48,290 --> 00:11:52,990
+نكتب ال premises كيف هيكون شكلها for all x يعني
+
+142
+00:11:52,990 --> 00:11:58,050
+لكل ال questions إذا كانت ال question هي problem
+
+143
+00:11:58,050 --> 00:12:05,480
+إذا هي difficult وfrustrating تمام التانية some
+
+144
+00:12:05,480 --> 00:12:11,100
+problems are فعلا there exist x some بعض ال
+
+145
+00:12:11,100 --> 00:12:15,360
+questions هي problems و challenging هي فعلا
+
+146
+00:12:15,360 --> 00:12:18,040
+problem و في نفس الوقت مدام هي problem برضه هتكون
+
+147
+00:12:18,040 --> 00:12:22,000
+challenging لأن and معناته لاتنين هي problem و هي
+
+148
+00:12:22,000 --> 00:12:24,800
+challenging في نفس الوقت طيب إيش اللي بدنا نثبته
+
+149
+00:12:24,800 --> 00:12:31,010
+بدنا نثبت some problems there exist xproblem هي
+
+150
+00:12:31,010 --> 00:12:38,530
+some problem frustrating و challenging تمام كبنث
+
+151
+00:12:38,530 --> 00:12:42,330
+بتهادي من هادي فبتهاد بسيطة يمكن احنا أخدنا المرة
+
+152
+00:12:42,330 --> 00:12:46,170
+اللي فاتت بعض أمثل عليها نحاول نطلعهم كلهم true
+
+153
+00:12:46,170 --> 00:12:49,290
+بالظبط
+
+154
+00:12:49,290 --> 00:12:53,930
+إذا وصلنا لمرحلة نطلعهم كلهم true خلصت فال proof
+
+155
+00:12:53,930 --> 00:12:57,070
+تبعنا هنبدأ بالبرميز الأولى البرميز الأولى for all
+
+156
+00:12:57,070 --> 00:13:00,590
+معناته أكيدمن ال for all هدول هفترض أنه في عنصر
+
+157
+00:13:00,590 --> 00:13:06,110
+اسمه A شاك معناته من كل ال problems اللي موجودة
+
+158
+00:13:06,110 --> 00:13:09,390
+هتكون ال problem A وB وC وD و .. جد ما بدك ال
+
+159
+00:13:09,390 --> 00:13:13,030
+problems بس واحدة منهم A وهدي A واحدة من ال
+
+160
+00:13:13,030 --> 00:13:16,430
+universive discourse أكيد بدون for all يعني كلهم
+
+161
+00:13:16,430 --> 00:13:21,050
+شاك بيقولوا أن في واحدة منهم هي A فإذا
+
+162
+00:13:21,050 --> 00:13:24,950
+automatically كأنه P of Aأعملنا ال universal
+
+163
+00:13:24,950 --> 00:13:29,570
+specification اللي أخدمها برضه المحاضرة مش السابقة
+
+164
+00:13:29,570 --> 00:13:35,650
+اللي جابلها P of A implies D and F okay بس لمين؟
+
+165
+00:13:35,650 --> 00:13:40,590
+مش للعنصر X و I go for all لأ حددت واحد منهم حددنا
+
+166
+00:13:40,590 --> 00:13:45,990
+واحد منهم A و A هذا لازم يكون طبعا أكيد belong to
+
+167
+00:13:45,990 --> 00:13:55,170
+ل X belong لمين؟ ل Xأو لست X اللي هي ال questions
+
+168
+00:13:55,170 --> 00:13:59,610
+اللي هي ال questions تمام التانية اللي هو ال
+
+169
+00:13:59,610 --> 00:14:02,270
+premise التاني المقصود فيها اللي هو there exist X,
+
+170
+00:14:02,550 --> 00:14:06,450
+B of X and C of X معناته انا ايش بقول؟ بقول يوجد
+
+171
+00:14:06,450 --> 00:14:10,430
+مشكلة من ال universe of discourse .. من مجموعة
+
+172
+00:14:10,430 --> 00:14:13,930
+المشاكل اللي جبتلكيها في الامتحان يوجد مشكلة هي
+
+173
+00:14:13,930 --> 00:14:19,800
+problem و challenging في نفس الوقتواحدة من المسائل
+
+174
+00:14:19,800 --> 00:14:23,500
+اللي جبتهم كانت في جزئية ال problems اللي هي بدأ
+
+175
+00:14:23,500 --> 00:14:27,080
+حلول يعني مش مجرد صح و غلط و true or false بدأ حل
+
+176
+00:14:27,080 --> 00:14:30,780
+و في نفس الوقت هي فيها تحدي واحدة منهم على الأقل
+
+177
+00:14:30,780 --> 00:14:34,240
+there exist طيب بدي افترض ان الواحدة ده هي اللي
+
+178
+00:14:34,240 --> 00:14:43,830
+ايه؟ في مشكلة؟فيش مشكلة هي .. هذه بدي اقولهنا بهذا
+
+179
+00:14:43,830 --> 00:14:48,190
+الشكل يعني كأنني بإذن الله أقدر أقول P of A and C
+
+180
+00:14:48,190 --> 00:14:53,870
+of A في عنكم أي مشكلة قبل ما نعديها احنا قولنا إيش
+
+181
+00:14:53,870 --> 00:14:59,860
+في واحدة من المشاكلوحدة من المشاكل هي problem أو
+
+182
+00:14:59,860 --> 00:15:04,300
+من الأسئلة هي problem و challenging صح؟ وقلنا أن
+
+183
+00:15:04,300 --> 00:15:08,200
+هذي بدأ افترض أنها a واحدة منهم و هي ال a بس بدأ
+
+184
+00:15:08,200 --> 00:15:11,800
+أقول كمان مدام واحدة يعني at least في واحد هي ال a
+
+185
+00:15:11,800 --> 00:15:16,160
+طيب في نفس الوقت ال a هذه ماهي واحدة من الفرقول
+
+186
+00:15:16,160 --> 00:15:23,200
+صح؟ يعني معنى ذلك أن a تحديدا كحالة خاصة ممكن
+
+187
+00:15:23,200 --> 00:15:29,150
+ينطبق عليها ال two quantifiersالـ two premises
+
+188
+00:15:29,150 --> 00:15:33,650
+فهنقول برضه هي ال A at least ال A يمكن يكون في
+
+189
+00:15:33,650 --> 00:15:36,850
+غيرها بس على الأقل ال A هذه واحدة منهم على الأقل
+
+190
+00:15:36,850 --> 00:15:42,590
+ال A هذه محققة ال two premises okay بتهيألي بعد
+
+191
+00:15:42,590 --> 00:15:46,090
+هيك الأمور صارت بسيطة جدا لأنه معناه ذلك أن P
+
+192
+00:15:46,090 --> 00:15:49,450
+problem أه هي problem فإذا مجرد أن هي problem
+
+193
+00:15:49,450 --> 00:15:54,900
+السؤال AA هذه أول شغلة هي problem هي ليست true or
+
+194
+00:15:54,900 --> 00:15:59,000
+false ولا multiple choice هي problem بدها حل كويس
+
+195
+00:15:59,000 --> 00:16:06,160
+و C بالبرضه بالمقابل أكيد true مدام أنت و هذه كلها
+
+196
+00:16:06,160 --> 00:16:11,020
+true فأكيد ال atomic proposition الأول true ال
+
+197
+00:16:11,020 --> 00:16:13,460
+atomic proposition التاني برضه true خلصنا منها
+
+198
+00:16:13,460 --> 00:16:17,580
+كويس الآن الأثنين هذه الموجودين عندك و هذه true
+
+199
+00:16:17,580 --> 00:16:20,020
+طيب و ال implication هذا true
+
+200
+00:16:25,990 --> 00:16:38,170
+نرجع نكتب الجدول نرجع نكتب الجدول ال
+
+201
+00:16:38,170 --> 00:16:46,590
+implication
+
+202
+00:16:46,590 --> 00:16:52,970
+true كله على بعضال P true ال implication true وال
+
+203
+00:16:52,970 --> 00:16:58,770
+P true بس الحالة الوحيدة مش شايف فإذن أكيد Q true
+
+204
+00:16:58,770 --> 00:17:05,210
+فإذن في الحالة هذه أكيد D and F true صح؟
+
+205
+00:17:05,210 --> 00:17:10,250
+تمام okay هاي روسم كده و أحطلك ال chat board في
+
+206
+00:17:10,250 --> 00:17:15,950
+هيك حالة مدام هذه and معناه دي لحالهافلحالها true
+
+207
+00:17:15,950 --> 00:17:20,130
+وانتوا قلته قبل شوية يعني معناته كأنه بدنا نثبت ان
+
+208
+00:17:20,130 --> 00:17:24,510
+كلهم ال true هي كلهم ال true بتهيألي سهل جدا مادام
+
+209
+00:17:24,510 --> 00:17:29,130
+كله طلع true في بعضه ان رتب رتب اللي بدكية and
+
+210
+00:17:29,130 --> 00:17:33,930
+هيطلع true مادام كلهم ال true كل atomic لحاله هو
+
+211
+00:17:33,930 --> 00:17:38,350
+true خلاصبتصفتهم مين اللي بدك إياه، بدك P مع F مع
+
+212
+00:17:38,350 --> 00:17:43,930
+C، هم كلهم اتروح، هاي P مع F مع C، خلاص، بدك تحط
+
+213
+00:17:43,930 --> 00:17:48,990
+دي كمان حط دي، ما هي برضه ظابط معاهم، فبترتب حسب
+
+214
+00:17:48,990 --> 00:17:52,870
+ال conclusion اللي بدك إياه، رتبناهم مع بعض، تمام،
+
+215
+00:17:52,870 --> 00:17:56,270
+هاد F لحالها مظبوطة، رتبناهم مع بعض، و بتهيألي
+
+216
+00:17:56,270 --> 00:18:00,250
+مدام A ينطبق عليها هذا ال condition فهو there
+
+217
+00:18:00,250 --> 00:18:03,210
+exist، لأنه من الأساس احنا نقول إن هو واحد من
+
+218
+00:18:03,210 --> 00:18:07,620
+مجموعات ال questionsهو واحد من مجموعات ال
+
+219
+00:18:07,620 --> 00:18:10,920
+questions داخل ال universive discourse صح فإذا
+
+220
+00:18:10,920 --> 00:18:15,500
+بينطبق عليه كلمة where exist تنطبق عليه فكرة where
+
+221
+00:18:15,500 --> 00:18:19,000
+exist فإذا ممكن أشيله و أحط X و أقول where exist
+
+222
+00:18:19,000 --> 00:18:22,280
+نفس
+
+223
+00:18:22,280 --> 00:18:27,480
+ال conclusion بسيطة جدا سهلة وسلسة و مافي مشكلة بس
+
+224
+00:18:27,480 --> 00:18:31,200
+سلستها و بساطتها جاية من ال implication فهمنا اللي
+
+225
+00:18:31,200 --> 00:18:33,860
+ال implication ال implication هو اللي بيحلها تمام
+
+226
+00:18:34,900 --> 00:18:37,840
+هي كمان سؤال طبعا واضح من الخربش اللي عليه أنه هذا
+
+227
+00:18:37,840 --> 00:18:41,760
+سؤال امتحان كنا جايبينه في امتحان سابق السؤال هذا
+
+228
+00:18:41,760 --> 00:18:46,980
+كان سؤال اتنين في وجهتها في ترتيب الأسئلة المهم
+
+229
+00:18:48,780 --> 00:18:53,800
+ميعطيني بيقول لي إذا كان all animals with scales
+
+230
+00:18:53,800 --> 00:18:59,280
+are dragons كل الحيوانات بحراشيف أو إلها حراشف و
+
+231
+00:18:59,280 --> 00:19:03,640
+جسمها هي dragons هي اللي هي سحال التنين هذه
+
+232
+00:19:03,640 --> 00:19:09,460
+التنانين كويس كومة أو نقطة حتى dot some animals
+
+233
+00:19:09,460 --> 00:19:14,620
+with are not dragons بعض الحيوانات اللتي ليست
+
+234
+00:19:14,620 --> 00:19:21,550
+dragons have sharp clawsليست دراجونس ولها مخالب
+
+235
+00:19:21,550 --> 00:19:27,930
+حادة بعض الحيوانات ليست دراجونس ولها مخالب حادة
+
+236
+00:19:27,930 --> 00:19:33,810
+كويس هاي ال two premises so إذا إيش there are
+
+237
+00:19:33,810 --> 00:19:39,810
+animals without scales which have sharp claws
+
+238
+00:19:39,810 --> 00:19:45,330
+معناه ذلك إنه بعض يوجد بعض الحيوانات اللي ليست لها
+
+239
+00:19:45,330 --> 00:19:53,470
+حراشفعلى ظهرها أو على جسمها ولها مخالب حدكويس من
+
+240
+00:19:53,470 --> 00:19:58,050
+ال premises بدنا نثبت او prove the conclusion
+
+241
+00:19:58,050 --> 00:20:04,010
+الطبيعي طبعا بدنا نقول انه في الآخر في عند ال S هي
+
+242
+00:20:04,010 --> 00:20:06,990
+بده ارمزهم عشان مانكوش نكتب الكلمات كاملة بس
+
+243
+00:20:06,990 --> 00:20:10,530
+نرمزهم هيك نختصرها اقول ان ال S هذي لأنه scales
+
+244
+00:20:10,530 --> 00:20:13,770
+فناخد الحرف الأول منها فاجول ان ال S of X هذي اللي
+
+245
+00:20:13,770 --> 00:20:19,570
+هي معناته انه إش إله scales أو إله حراشف ال D هي
+
+246
+00:20:19,570 --> 00:20:25,830
+dragonو ال c sharp clouds كويس عشان نبدأ نحط ال
+
+247
+00:20:25,830 --> 00:20:29,230
+premise الأولى ال premise الأولى for all animals
+
+248
+00:20:29,230 --> 00:20:32,990
+for all animals with skills معناته إذا كانت ال
+
+249
+00:20:32,990 --> 00:20:36,710
+animals هذه with skills فهي dragon حيها إذا كانت
+
+250
+00:20:36,710 --> 00:20:42,450
+ال animals هذه هي skills إذن هي dragon for all
+
+251
+00:20:42,450 --> 00:20:48,470
+skills employs D التانية ال premise التانية some
+
+252
+00:20:48,470 --> 00:20:53,960
+animalsبعض .. there .. معناه تكتب أول شي there
+
+253
+00:20:53,960 --> 00:21:04,640
+exist و لا إيش negation D and C فإذا
+
+254
+00:21:04,640 --> 00:21:13,660
+يوجد animals ليست dragons ولها مخالب يوجد هي لها
+
+255
+00:21:13,660 --> 00:21:17,640
+دراجون لكن في نفس الوجود لها مخالب لها مخالب هذه
+
+256
+00:21:17,640 --> 00:21:20,960
+مش implicationخدوا بالكوا اتكلمنا فيها سابقًا
+
+257
+00:21:20,960 --> 00:21:25,180
+وشرحناها وهنا بنرجع و بنأكد عن الموضوع تمام ال
+
+258
+00:21:25,180 --> 00:21:31,400
+conclusion المطلوب there exist أنه ليس لها skills
+
+259
+00:21:31,400 --> 00:21:37,120
+negation skills و claws إلها claws فإذا there
+
+260
+00:21:37,120 --> 00:21:39,380
+exist و there exist زي ما قلتلكوا دايما بتاخد
+
+261
+00:21:39,380 --> 00:21:48,490
+معاها and for all implication okay بدنا نبدأنشتغل
+
+262
+00:21:48,490 --> 00:21:52,530
+فهنطلع هدول فوق عشان نبدأ نشتغل تحتهم و ننطلق منهم
+
+263
+00:21:52,530 --> 00:21:56,230
+هننطلق من الأولى و برضه هفترض أنه في عندى ايه
+
+264
+00:21:56,230 --> 00:22:01,250
+animals احنا بتقول for all و there exist تحت
+
+265
+00:22:01,250 --> 00:22:04,490
+معناته there exist اللي تحت هذا و اللي هفترضه ايه
+
+266
+00:22:04,490 --> 00:22:09,010
+ينطبق عليه ما ينطبق على ال all لأن هو واحد منهم هو
+
+267
+00:22:09,010 --> 00:22:12,090
+واحد منهم فإذا عشان أحقق ال two premises مع بعض
+
+268
+00:22:12,090 --> 00:22:15,910
+يوجد على الأقل answer بيحققهم مع بعضcheck there
+
+269
+00:22:15,910 --> 00:22:20,490
+exist يعني يكفيني واحد الواحد هذا بتفترضه هو ايه
+
+270
+00:22:20,490 --> 00:22:26,270
+طب هو نفسه ايه من ال for all من ال for all فإذا
+
+271
+00:22:26,270 --> 00:22:31,290
+ماتبلجوش أنه والله أحط a و أتوعود مكانه ب a خلاص
+
+272
+00:22:31,290 --> 00:22:35,370
+هاي بدأنا بال there exist ال there exist هذه هتصبح
+
+273
+00:22:35,370 --> 00:22:42,740
+negation d of a ف dragon هو ال aand له clause
+
+274
+00:22:42,740 --> 00:22:48,260
+sharp clause برضه هو نفسه ال animal a الان التانية
+
+275
+00:22:48,260 --> 00:22:53,120
+برضه منها بنقدر نجيب S of A employs that او
+
+276
+00:22:53,120 --> 00:22:57,740
+employs D of A اتوقع من اللي فوق بنقدر نقول ان
+
+277
+00:22:57,740 --> 00:23:02,840
+negation D is true لحالها و C is true لحالها طيب
+
+278
+00:23:02,840 --> 00:23:08,160
+نبدأ بال D هاي
+
+279
+00:23:08,160 --> 00:23:15,440
+Dnegation دي false فإذن وين بتكون ال employees أو
+
+280
+00:23:15,440 --> 00:23:22,780
+ال implication كلها true و ال q false ال true و ال
+
+281
+00:23:22,780 --> 00:23:28,460
+q false هذه بتصبتش هيها فإذن محكوم أكيد هذا معناه
+
+282
+00:23:28,460 --> 00:23:34,240
+أن ال P false يعني بقدر أقول negation S check
+
+283
+00:23:34,240 --> 00:23:42,600
+negation S تمامnegation S خلصت المسألة انتهت
+
+284
+00:23:42,600 --> 00:23:50,240
+الجثة لأن C من الخطوة الرقم 3 اكيد هتكون true فإذا
+
+285
+00:23:50,240 --> 00:23:56,320
+negation S and C برضه true مع بعض وال A مدام هي
+
+286
+00:23:56,320 --> 00:24:00,220
+متحققة وانا مش ضامن غيرها انا مش ضامن غيرها انا
+
+287
+00:24:00,220 --> 00:24:02,820
+بعرف ان ال A تحديدا اه هو يحقق ال premises اللي
+
+288
+00:24:02,820 --> 00:24:07,820
+بالاساس لكن غيره مضمنش عشان هيك there existوبشيل
+
+289
+00:24:07,820 --> 00:24:13,180
+ال a و بقول قد يكون في معائشة لكن على الأقل هو ال
+
+290
+00:24:13,180 --> 00:24:19,360
+a موجود حققنا ان هو ليس له skills و في نفس الوقت
+
+291
+00:24:19,360 --> 00:24:21,540
+له sharp claws
+
+292
+00:24:28,650 --> 00:24:31,930
+Okay هنا في مجموعة arguments هتكون موجودة عندنا
+
+293
+00:24:31,930 --> 00:24:35,830
+محتاجين بس نعرف هل هي صحيحة ولا خاطئة إذا كانت
+
+294
+00:24:35,830 --> 00:24:39,250
+صحيحة ضمن أي rule أو وين اتعلمناها وين أخدناها
+
+295
+00:24:39,250 --> 00:24:43,990
+بالظبط في المحاضرات .. المحاضرتين السابقتين او ..
+
+296
+00:24:43,990 --> 00:24:48,890
+او هي خطأ فإيش تصحيحها .. فإيش تصحيحها اعطاني
+
+297
+00:24:48,890 --> 00:24:51,690
+theorem بهذا الشكل أو معلومة بهذا الشكل بدأش ..
+
+298
+00:24:51,690 --> 00:24:56,170
+بدأ افهم هي صح ولا غلط صح ولا .. خلوا عينكوا هناهي
+
+299
+00:24:56,170 --> 00:25:00,710
+نص الحل نص الحل ان عينك على الجدول هذا انتوا
+
+300
+00:25:00,710 --> 00:25:07,130
+ملاحظين كده الجدول مهم معانا؟ مهم جدا طيب if n is
+
+301
+00:25:07,130 --> 00:25:14,530
+a real number such that n أكبر من واحد اذا n تربيع
+
+302
+00:25:14,530 --> 00:25:20,390
+أكبر من واحد هذا معناته بيقودني لفرضية ان n تربيع
+
+303
+00:25:20,390 --> 00:25:27,390
+أكبر من واحد اذا n أكبر من واحدوين المشكلة؟ مفروض
+
+304
+00:25:27,390 --> 00:25:31,810
+انت مقتنع فيها الجملة ولا مش مقتنع فيها؟ هذا هو
+
+305
+00:25:31,810 --> 00:25:34,530
+السؤال انت هل مبدأيا مقتنع بالموضوع ولا مش مقتنع
+
+306
+00:25:34,530 --> 00:25:37,910
+بالموضوع؟ وليش؟
+
+307
+00:25:45,550 --> 00:25:49,190
+أكبر من واحد كيف ده تصير سالبة؟ أكبر من واحد يعني
+
+308
+00:25:49,190 --> 00:25:54,270
+خلاص من واحد في أقل بكل السالب تبعه مش موجود انت
+
+309
+00:25:54,270 --> 00:25:58,070
+بتكلم من واحد to positive infinity من واحد to
+
+310
+00:25:58,070 --> 00:26:02,270
+positive infinity هدفش فيها مشكلة فكروا بغيرها
+
+311
+00:26:02,270 --> 00:26:05,270
+هدفش فيها مشكلة هي كحد .. بحاجة .. هتفضل شوية
+
+312
+00:26:05,270 --> 00:26:10,050
+ناسي؟ بيجيب واحدة تم في هذا الاشي اللي هو مثلا
+
+313
+00:26:10,050 --> 00:26:14,290
+أربعة سالب اتنين تانية وهي مش أكبر من واحد
+
+314
+00:26:18,540 --> 00:26:21,860
+طيب ما احنا قاعدين بنقول من الاساس تعريفك ان هو
+
+315
+00:26:21,860 --> 00:26:28,720
+اكبر من هنا سالب مش هيك معناته انت محققتش ان هي
+
+316
+00:26:28,720 --> 00:26:32,820
+اكبر من واحد هي معناته هذه false انت بدأتها في
+
+317
+00:26:32,820 --> 00:26:36,160
+false وهذه برضه راحت false فانت فعلا ماحققش
+
+318
+00:26:36,160 --> 00:26:42,860
+الموضوع طيب هنرجع لنفس فكرةالـ implication تبعتنا
+
+319
+00:26:42,860 --> 00:26:46,660
+مبدأيا هذه فيه policy في ال affirming اللي احنا
+
+320
+00:26:46,660 --> 00:26:50,920
+افترضنا ان هو حدث ليش؟ لأن انت بتتكلم عن
+
+321
+00:26:50,920 --> 00:26:54,640
+implication المفروض ان هي true ال implication هدا
+
+322
+00:26:54,640 --> 00:27:00,260
+الاصل انه يكون true مش هيك المفروض P هي اللي تكون
+
+323
+00:27:00,260 --> 00:27:06,040
+ال true عشان زي ما أقوله أستنتج منها Q وليس العكس
+
+324
+00:27:06,040 --> 00:27:16,480
+بس تنتجش P من Qصحة P من صحة Q احنا عادة بنستنتج
+
+325
+00:27:16,480 --> 00:27:21,760
+صحة Q من صحة P إذا كان ال employees كله أو ال
+
+326
+00:27:21,760 --> 00:27:26,800
+implication كله على بعض هو فعلا true تمام؟ الكلام
+
+327
+00:27:26,800 --> 00:27:31,760
+هذا هل ينطبق عند هنا؟ هنشوف هنا بنتكلم عن in is
+
+328
+00:27:31,760 --> 00:27:36,340
+real number which is such that in أكبر من واحد هذه
+
+329
+00:27:36,340 --> 00:27:39,800
+إذا in تربيع أكبر من واحد هذه كلها ال implication
+
+330
+00:27:41,360 --> 00:27:44,700
+هذه هي ال implication كلمة العربة بتعطيني جملة
+
+331
+00:27:44,700 --> 00:27:51,280
+كاملة و بيقولها this is true فانت منها افترضت انه
+
+332
+00:27:51,280 --> 00:27:58,780
+ان تربيع اكبر من واحد يعني
+
+333
+00:27:58,780 --> 00:28:05,520
+هذه ايش Q هذه كلها
+
+334
+00:28:07,900 --> 00:28:15,520
+P implies Q بالظبط P implies Q صح؟
+
+335
+00:28:15,520 --> 00:28:21,380
+تمام هيها rule يعطيك إيها كاملة إذا إذا خلصناها و
+
+336
+00:28:21,380 --> 00:28:25,820
+بعدين بيقولك suppose that إذا كانت إم تربية أكبر
+
+337
+00:28:25,820 --> 00:28:37,060
+من واحد هذه Q فإذا كأنه جالك Q and P implies Qو
+
+338
+00:28:37,060 --> 00:28:42,560
+راح جالك اذا P is true و هذا خطأ .. هذا خطأ لو
+
+339
+00:28:42,560 --> 00:28:45,800
+رجعتوا محاضرة ال policy لما اتكلمنا عنها ال policy
+
+340
+00:28:45,800 --> 00:28:51,980
+قلنا اذا كان ال implication is true و P is true
+
+341
+00:28:51,980 --> 00:28:56,140
+اذا Q is true مافيش مشكلة لكن ال implication is
+
+342
+00:28:56,140 --> 00:29:00,880
+true و Q is true بقدرش اقول من دون ان P is true
+
+343
+00:29:00,880 --> 00:29:07,720
+صحيح ال implication is trueو Q is true هي في عندي
+
+344
+00:29:07,720 --> 00:29:12,080
+حالتين Q is true ما بقدر اقول ان P is true لان في
+
+345
+00:29:12,080 --> 00:29:16,540
+الحالتين ممكن تكون false ممكن تكون true فما بيركب
+
+346
+00:29:16,540 --> 00:29:23,300
+اقول true صح هيها الحالة التانية والحالة الرابعة
+
+347
+00:29:23,300 --> 00:29:29,460
+خلوا عينكم معانا ونترجمهم هنا اذا كانت N هي عدد
+
+348
+00:29:29,460 --> 00:29:35,350
+حقيقي اكبر من واحد اذاإن تربية زاد .. إن تربية
+
+349
+00:29:35,350 --> 00:29:38,030
+أكبر من واحد هذه ال implication كلها على بعض هذه
+
+350
+00:29:38,030 --> 00:29:41,990
+true أنا شاك فيها هذه true صحيحة فإذا أنا بتكلم في
+
+351
+00:29:41,990 --> 00:29:48,370
+الحالة اتنين و أربعة تمام طيب جالي هنا إيه سبب ده
+
+352
+00:29:48,370 --> 00:29:54,690
+إن تربية أكبر من واحد هذه Q حسب ال .. ال
+
+353
+00:29:54,690 --> 00:29:58,290
+implication هذه هي Q تمام فإذا وين ال Q بتكون true
+
+354
+00:29:58,290 --> 00:30:06,140
+هاي true راح على طول هو استنتجحطي ال event واستنتج
+
+355
+00:30:06,140 --> 00:30:10,460
+انه معناته ان اكبر من واحد وهذا مش صحيح مش صحيح
+
+356
+00:30:10,460 --> 00:30:14,100
+لأنه لأ فيه ممكن تكون false في ال column التاني في
+
+357
+00:30:14,100 --> 00:30:18,940
+ال row التاني مش هيك او تكون true في ال row الرابع
+
+358
+00:30:18,940 --> 00:30:22,620
+فإذن لأ بقدرش استنتج الاستنتاج اللي حكي لنا هي
+
+359
+00:30:22,620 --> 00:30:28,980
+فإذن false false ليش عرفنا ليش تمام طيب هي التانية
+
+360
+00:30:32,440 --> 00:30:38,400
+برضه انكوا هنا in
+
+361
+00:30:38,400 --> 00:30:43,280
+real number او عدد حقيقي اكبر من تلاتة اذا in
+
+362
+00:30:43,280 --> 00:30:47,860
+تربية اكبر من تسعة كلام حلو suppose that in تربية
+
+363
+00:30:47,860 --> 00:30:55,240
+اقل او يساوي تسعة اذا in اقل او يساوي تلاتة لعند
+
+364
+00:30:55,240 --> 00:31:02,570
+هنا و اقطعشوف الجملة اللي قبلها، هذه كلها أحسنت،
+
+365
+00:31:02,570 --> 00:31:10,250
+هذه كلها إيش؟ P employs Q، و هذه negation
+
+366
+00:31:11,150 --> 00:31:16,710
+الـ Q فهل بقدر أقول إنه إذا negation الـ Q و P
+
+367
+00:31:16,710 --> 00:31:21,090
+implies الـ Q فهل بقدر أستنتج إن هناك هل بقدر
+
+368
+00:31:21,090 --> 00:31:26,630
+أستنتج إنه فعلا في إشي مميز لل P هنا حقيقة فيه ال
+
+369
+00:31:26,630 --> 00:31:29,970
+true ال employees بمعنى إن العمود التالت لازم يكون
+
+370
+00:31:29,970 --> 00:31:35,770
+true و ال Q بده يكون false هذا لا ينطبق إلا على ال
+
+371
+00:31:35,770 --> 00:31:40,090
+role أول فإذا بقدر أستنتج إنه لازم هيطلع negation
+
+372
+00:31:40,090 --> 00:31:44,400
+Pأيش بارح هيطلع Negation P؟ طيب، هل فعلا اللي
+
+373
+00:31:44,400 --> 00:31:48,160
+أعطاني يهو Negation P؟ أه فعلا Negation P، كانت
+
+374
+00:31:48,160 --> 00:31:51,120
+هنا أكبر من تلاتة نصر أقل أو يساوي تلاتة، هي ال
+
+375
+00:31:51,120 --> 00:31:57,660
+Negation بتاعتها؟ صحvalid صارت المفعول منطقي صحيح
+
+376
+00:31:57,660 --> 00:32:01,140
+ومافيش اي مشكلة اطلاقا كلامك مائة بالمائة مش قادر
+
+377
+00:32:01,140 --> 00:32:03,920
+اقول عنه حاجة صح دكتور احنا بتشوف ال validity
+
+378
+00:32:03,920 --> 00:32:08,760
+للجملة التانية؟ اه لهذه الجزئية الجزء الاول هذا
+
+379
+00:32:08,760 --> 00:32:13,020
+كله اللي اعطاك ال implication صيغة ال implication
+
+380
+00:32:13,020 --> 00:32:18,400
+اللي هو صيغة P implies Q ثم بعد ذلك هو فرض لك
+
+381
+00:32:18,400 --> 00:32:23,700
+negation Qو حط نقطة و بعدين جالك انه انا بستنتج
+
+382
+00:32:23,700 --> 00:32:28,520
+بناء على ذلك كذا هل الكذا ال استنتج صح ولا غلط؟ و
+
+383
+00:32:28,520 --> 00:32:30,600
+نفس الكلام هنا هذا الاستنتج صح ولا غلط؟ هذا
+
+384
+00:32:30,600 --> 00:32:37,100
+الاستنتج صح ولا غلط؟ طيب خلاص قلنا valid و انتهينا
+
+385
+00:32:37,100 --> 00:32:44,580
+التالتة التقسيم
+
+386
+00:32:44,580 --> 00:32:45,400
+نفسها هي هي
+
+387
+00:32:50,910 --> 00:32:56,210
+نفس التانية يعني true هكيف نفس التانية طب التانية
+
+388
+00:32:56,210 --> 00:33:00,550
+كانت true ايوة
+
+389
+00:33:00,550 --> 00:33:07,830
+في عندك مشكلة إشكالية هنا هذه نشوفهم هدول هيك زي
+
+390
+00:33:07,830 --> 00:33:15,110
+ما قولنا كلها P implies Q P implies Q هنا يعطيك
+
+391
+00:33:15,110 --> 00:33:22,820
+إيش Negation Pيعني كأنه قال لك هنا negation P و
+
+392
+00:33:22,820 --> 00:33:26,140
+بدنا نشوف هل بطلع إش هنا ولا لأ طب شوف لي negation
+
+393
+00:33:26,140 --> 00:33:31,800
+P يعني false أول two أو صفين أول صفين و true طب هم
+
+394
+00:33:31,800 --> 00:33:35,160
+ال true برضه في الحالتين هل هذا بيستنتجلي قيمة ل
+
+395
+00:33:35,160 --> 00:33:39,560
+Q؟ لأ الحقيقة هو راح هنا استنتجلي قيمة ل Q أكيد
+
+396
+00:33:39,560 --> 00:33:44,090
+خطأ لأنه مابقدر استنتج قيمة هنا ل Qهو هنا بدل ما
+
+397
+00:33:44,090 --> 00:33:48,870
+يستعمل Negation في ال support تبعه Negation Q
+
+398
+00:33:48,870 --> 00:33:53,510
+استعمل Negation P Negation P لا تؤدي ل Negation Q
+
+399
+00:33:53,510 --> 00:34:01,910
+P تؤدي ل Q ال Q لا تؤدي ل P Negation Q تؤدي ل
+
+400
+00:34:01,910 --> 00:34:05,990
+Negation P Negation P لا تؤدي ل Negation Q الجدول
+
+401
+00:34:05,990 --> 00:34:08,370
+اللي بيحكي الكلام هذا okay
+
+402
+00:34:11,120 --> 00:34:17,860
+تمام هي هيك مجموعة كويسة في .. ناخدلنا كمان جزئية
+
+403
+00:34:17,860 --> 00:34:23,720
+في الاثبات
+
+404
+00:34:23,720 --> 00:34:29,080
+نبدأ ناخد ال direct و ال .. و ال contradiction
+
+405
+00:34:29,080 --> 00:34:32,920
+ناخدلنا سؤال هيك و سؤال هيك هي في عندي سؤال ايش
+
+406
+00:34:32,920 --> 00:34:35,840
+بيقولك استخدم ال direct على طول يعني هو بيحددلك في
+
+407
+00:34:35,840 --> 00:34:37,520
+السؤال مباشرة ايش اللي تستخدمه
+
+408
+00:34:44,960 --> 00:34:50,400
+عشان تظهر التالي every odd integer is the
+
+409
+00:34:50,400 --> 00:34:56,620
+difference of two squares و بس تخيل لو مافيش ال
+
+410
+00:34:56,620 --> 00:35:03,860
+hint هذه بدك تقيش بس معها الجملة يقولك اثبتلي ان
+
+411
+00:35:03,860 --> 00:35:07,100
+كل odd integer هو عبارة عن difference of two
+
+412
+00:35:07,100 --> 00:35:10,710
+squaresهو فرق رقمين مربعين
+
+413
+00:35:16,620 --> 00:35:20,900
+direct مبدأيا بدنا نفهم إيش يعني difference دى
+
+414
+00:35:20,900 --> 00:35:24,740
+عشانك على الهامش بتعملك شوية تجربة اتجرب تشوف إيه
+
+415
+00:35:24,740 --> 00:35:29,160
+إيش اللي بتتكلم عنه فعشانك أطلق ال hint find the
+
+416
+00:35:29,160 --> 00:35:34,200
+difference of two squares k plus واحد and k where
+
+417
+00:35:34,200 --> 00:35:36,900
+k is a positive integer و نشوف إيش اللي بتطلع معنا
+
+418
+00:35:36,900 --> 00:35:40,280
+مثلا عند التلاتة بالمناسبة حتى عند الواحد اللي هو
+
+419
+00:35:40,280 --> 00:35:44,360
+أول odd برضه بظبطعند التلاتة التلاتة احنا كلنا
+
+420
+00:35:44,360 --> 00:35:47,940
+عارفين ان هي مادام قد بنقدر نحطها بصورة 2 في some
+
+421
+00:35:47,940 --> 00:35:52,520
+k plus 1 مش كلنا عارفين الكلام هذا 2 في some
+
+422
+00:35:52,520 --> 00:36:02,340
+integer plus 1 فهي 2 في some integer plus 1 تمام
+
+423
+00:36:02,340 --> 00:36:07,580
+طيب هي نفس التلاتة بقدر احطها برضه بنفس القالية ال
+
+424
+00:36:07,580 --> 00:36:16,060
+k اللي استخدمتها هنا هيهامع زائد واحد K زائد واحد
+
+425
+00:36:16,060 --> 00:36:23,120
+وK هي اتنين اللي هي K زائد واحد تربيأ ناقص ال K
+
+426
+00:36:23,120 --> 00:36:28,260
+تربيأ difference of two squares برضه بيساوي تلاتة
+
+427
+00:36:28,260 --> 00:36:35,130
+برضه بيساوي تلاتةالرياضيات فيها سحر مش طبيعي في
+
+428
+00:36:35,130 --> 00:36:39,130
+بعض ال relations بين الأرقام هذه واحدة منهم
+
+429
+00:36:39,130 --> 00:36:43,970
+الخامسة نفس الجثة صح بقدر أحطها بصيغة اتنين في
+
+430
+00:36:43,970 --> 00:36:50,010
+some k plus واحد بقدر اه نقدر طيب ال k هناك بحثت
+
+431
+00:36:50,010 --> 00:36:55,870
+اتنين اتنين في اتنين زائد واحد فالk باتنين هحط هنا
+
+432
+00:36:55,870 --> 00:37:00,550
+برضه k زائد تلاتة تربيع ناقص k تربيع برضه هتطلع
+
+433
+00:37:00,550 --> 00:37:06,780
+خمسةنفس اليسة ال K هنا هنستخدمها تلاتة للرقم سبعة
+
+434
+00:37:06,780 --> 00:37:10,040
+طب ما هى نفسها K زايد واحد اللى هى أربعة تربيع
+
+435
+00:37:10,040 --> 00:37:14,280
+ناقص التلاتة تربيع and so on افهمنها ال logic ايش
+
+436
+00:37:14,280 --> 00:37:16,780
+اللى بدويانا نثبته بدويانا نثبت ان هذا العلاقة
+
+437
+00:37:16,780 --> 00:37:21,620
+الصحيحة direct بدويانا نثبت ان هذا العلاقة الصحيحة
+
+438
+00:37:21,620 --> 00:37:27,980
+okay فإذا direct هنبدأ من مين every odd integer
+
+439
+00:37:27,980 --> 00:37:32,680
+فهنبدأ من ال odd integerعشان نكون direct ثم بده من
+
+440
+00:37:32,680 --> 00:37:36,600
+هذا الكلام نثبت انه is the difference بعدين هنشوف
+
+441
+00:37:36,600 --> 00:37:41,040
+حكاية ال difference هذه فمبدأيا هنبدأ ان n is odd
+
+442
+00:37:41,040 --> 00:37:45,800
+حسب الفرضية هو بيقول ليه إذا كانت odd هي odd معناه
+
+443
+00:37:45,800 --> 00:37:49,480
+ذلك ان بقدر اكتبها بصيغة اتنين كزائد واحد for some
+
+444
+00:37:49,480 --> 00:37:55,320
+integer k صح؟ ثم خلصنا هاي بداية طيب من ال hint
+
+445
+00:37:55,320 --> 00:38:02,840
+اللي أتانياهنستخدم k وk زائد واحد عشان نثبت ان هي
+
+446
+00:38:02,840 --> 00:38:07,320
+نفسهم ال difference ل ال square تبعهم هيعطيني نفس
+
+447
+00:38:07,320 --> 00:38:12,980
+ان هل فعلا الكلام هذا منطقي ولا لأ هنشوف k زائد
+
+448
+00:38:12,980 --> 00:38:20,260
+واحد تربيع ناقص k تربيع فك أقواص عشان تصبح الأولى
+
+449
+00:38:21,360 --> 00:38:26,480
+كتربيع زائد اتنين ك زائد واحد كله ناقص كتربيع شيل
+
+450
+00:38:26,480 --> 00:38:32,270
+الكتربيع مع الكتربيع نفس الفجرنفس اللي فوق فإذا
+
+451
+00:38:32,270 --> 00:38:34,930
+فعلا ال two terms بتساوي بعض اللي هي اتنين زائد
+
+452
+00:38:34,930 --> 00:38:38,470
+واحد بتساوي n اللي هو ال odd number اصلا اللي هو
+
+453
+00:38:38,470 --> 00:38:43,490
+الاش ال odd number طريقة بسيطة جدا اه طريقة .. من
+
+454
+00:38:43,490 --> 00:38:47,150
+الأول كانت مش بسيطة .. من الأول مش بسيطة لكن عاد
+
+455
+00:38:47,150 --> 00:38:50,210
+سحر الأرقام هو اللي خلها تصير بسيطة بالمناسبة في
+
+456
+00:38:50,210 --> 00:38:54,290
+كتير relations هيك حلوة في الرياضيات الأرقام كيف
+
+457
+00:38:54,290 --> 00:38:57,730
+مرتبطة مع بعضها بشكل كتير هذه مش الأولة ولا
+
+458
+00:38:57,730 --> 00:39:02,670
+الأخيرة هتكون اللي هتشوفوهاطيب so that if N is
+
+459
+00:39:02,670 --> 00:39:11,130
+integer and N تكعيب plus five is odd then N is
+
+460
+00:39:11,130 --> 00:39:15,910
+even لاحظته؟
+
+461
+00:39:15,910 --> 00:39:23,790
+بدنا نثبت إذا كانت N integer و N تكعيب زائد خمسة
+
+462
+00:39:23,790 --> 00:39:30,130
+oddبدنا نثبت منها ان N is even باستخدام كل مرة
+
+463
+00:39:30,130 --> 00:39:36,530
+حالة مرة باستخدام ال proof by contraposition نبدأ
+
+464
+00:39:36,530 --> 00:39:40,270
+بالcontraposition ثم بال contradiction و الفرق
+
+465
+00:39:40,270 --> 00:39:43,990
+شاسع بين التنتين طيب بتهيألي بالcontraposition
+
+466
+00:39:43,990 --> 00:39:50,810
+مافيها مشكلة هنفرض عكس EQ يعني هبدأ من هنا و افرض
+
+467
+00:39:50,810 --> 00:39:57,280
+ان هذه odd و نحسب هذهمش هيك يعني مش كتير جثتها ..
+
+468
+00:39:57,280 --> 00:40:02,360
+مش كتير جثتها صعبة ف assume n is odd اللي هي عكس
+
+469
+00:40:02,360 --> 00:40:07,500
+تمام بسطت الأمور و خلصت معناه ذلك أنه بقدر أحطها ب
+
+470
+00:40:07,500 --> 00:40:11,560
+2k plus 1 و انتهى الموضوع و انعوض في ال n تكعيب
+
+471
+00:40:11,560 --> 00:40:17,400
+زائد خمسةعوضنا في إنتك عيب زائد خمسة بنفكفكها إنتك
+
+472
+00:40:17,400 --> 00:40:20,860
+عيب زائد واحد تربيحها و بعدين أضربه كمان مرة في
+
+473
+00:40:20,860 --> 00:40:25,300
+اتنين K زائد واحد عشان يظهر معانا term بهذا الشكل
+
+474
+00:40:25,300 --> 00:40:29,660
+طيب ال term اللي بهذا الشكل لو فكناه حالج أن في
+
+475
+00:40:29,660 --> 00:40:33,040
+عندي خمسة زائد واحد ستة و بعدين بناخد عامل مشترك
+
+476
+00:40:33,040 --> 00:40:37,280
+عشان نجد أن الخمسة زائد ستة .. خمسة زائد واحد بسوء
+
+477
+00:40:37,280 --> 00:40:40,980
+ستة الستة even يعني بنفع أخد منه اتنين عامل مشترك
+
+478
+00:40:42,200 --> 00:40:44,840
+هنا بقدر اخد منها عامل مشترك اتنين و هنا بقدر اخد
+
+479
+00:40:44,840 --> 00:40:46,960
+اتنين عامل مشترك و هنا بقدر اخد اتنين عامل مشترك و
+
+480
+00:40:46,960 --> 00:40:50,360
+مجموع الاتنين هدول برضه بقدر اخد عامل مشترك مانا
+
+481
+00:40:50,360 --> 00:40:56,860
+ذلك ممكن احطه بصورة اتنين في some k اصبحت ايش even
+
+482
+00:40:56,860 --> 00:41:01,480
+انا بدأت ب odd طلعت even هنا كان بدري يعني ابدأ ب
+
+483
+00:41:01,480 --> 00:41:07,480
+odd و اروح ل even عكسناها عكسناهالما بدأنا ب
+
+484
+00:41:07,480 --> 00:41:12,740
+negation q طلق ليه negation p بالcontrapositive
+
+485
+00:41:12,740 --> 00:41:18,920
+أكيد is true فإذا خلصنا منها الآن باستخدام ال
+
+486
+00:41:18,920 --> 00:41:21,860
+contradiction باستخدام ال contradiction الموضوع
+
+487
+00:41:21,860 --> 00:41:28,660
+هيختلف هنشتغل على إنه n plus واحد is odd and n is
+
+488
+00:41:28,660 --> 00:41:32,940
+عكسناها
+
+489
+00:41:32,940 --> 00:41:37,420
+خالص بدي أفرض عكسهامش بدنا نفرض عكسها نجي ال
+
+490
+00:41:37,420 --> 00:41:39,680
+contradiction كلنا بنقول اننا بدنا نفرضها العكس
+
+491
+00:41:39,680 --> 00:41:45,040
+okay هي العكس العكس بدل ما كنت بقول if تكييف زائد
+
+492
+00:41:45,040 --> 00:41:51,300
+خمسة is odd then n is even لأ بدأ أقول if n is odd
+
+493
+00:41:51,300 --> 00:41:59,960
+okay بدأنا بال odd و منها n is odd و كلنا عارفين
+
+494
+00:41:59,960 --> 00:42:10,620
+انه ال ..is odd وكلنا عارفين انه odd في odd odd هي
+
+495
+00:42:10,620 --> 00:42:20,120
+عبارة عن odd في odd فهي ساوي odd طيب ان تكعيب ما
+
+496
+00:42:20,120 --> 00:42:26,140
+هي عبارة عن ان تربيع في ان يعني نفس الكلام odd في
+
+497
+00:42:26,140 --> 00:42:32,470
+odd يعني حتى تكعيب برضه هتطلع oddبرضه هتكون عبارة
+
+498
+00:42:32,470 --> 00:42:39,630
+عن odd صح؟ فيها and
+
+499
+00:42:39,630 --> 00:42:47,550
+in is odd طيب odd تكعيب خلاص odd طيب odd زائد odd
+
+500
+00:42:47,550 --> 00:42:55,050
+even even هتطلع و ليس زي فرضيتنا أن هي oddوليست
+
+501
+00:42:55,050 --> 00:43:00,250
+كما افترضنا ان هي odd فإذا هذا معناه ان تربيه is
+
+502
+00:43:00,250 --> 00:43:03,250
+odd وهذا معناه ان تكيب برضه is odd خليني نمحي
+
+503
+00:43:03,250 --> 00:43:09,830
+الكتاب اللي وضحنا فيه وهذا
+
+504
+00:43:09,830 --> 00:43:13,790
+معناه أن خمسة is odd أساسا هي بحد ذاتها وصار odd
+
+505
+00:43:13,790 --> 00:43:19,010
+زائد odd even عكس فرضيتنا اللي افترضناها وهذا
+
+506
+00:43:19,010 --> 00:43:24,630
+معناه أن الفرضية اللي احنا suppose thatإن تكعيب
+
+507
+00:43:24,630 --> 00:43:28,830
+زائد خمسة is odd and in is odd اللي كانت المفروض
+
+508
+00:43:28,830 --> 00:43:32,910
+even حسب
+
+509
+00:43:32,910 --> 00:43:36,710
+النظرية الأصلية احنا فرضنا عكسها طلع عكسها false
+
+510
+00:43:36,710 --> 00:43:42,960
+إذا ان هي trueأخدنا هذا المثال مش هيك بس كان لقاش
+
+511
+00:43:42,960 --> 00:43:49,180
+جدر تربيعي تكعيبه مش هيفرج كتير بس فكرته أنه كان
+
+512
+00:43:49,180 --> 00:43:53,500
+سؤال في امتحان طبعا الطلاب شافوا أنه تكعيبي وقفوا
+
+513
+00:43:53,500 --> 00:43:58,220
+حالهم ووقفت مالهم زي ما بقوله لأ بصد و لا برد
+
+514
+00:43:58,220 --> 00:44:02,200
+صاروا ليش؟ مافيش فيها إشي طب ماهي نفس اللي حلنا في
+
+515
+00:44:02,200 --> 00:44:05,700
+ال slides هو هو اعملوا بنفس خطواته إيش هيتغير
+
+516
+00:44:05,700 --> 00:44:10,140
+معاكوا رقم رقمين؟بس ال process هي هي ليش ما
+
+517
+00:44:10,140 --> 00:44:13,360
+تجرأتوش يا طلاب مثلا تعملوها ال process اعمل ال
+
+518
+00:44:13,360 --> 00:44:15,500
+process خلّيه يطلع الأقل بطبيعي مش كل الأسئلة
+
+519
+00:44:15,500 --> 00:44:18,920
+بتجيك زي ما هي ال coffee class هيها اعملنا نفس
+
+520
+00:44:18,920 --> 00:44:24,440
+الفكرة يقولنا ان هي rational و معناه ذلك أنه بقدر
+
+521
+00:44:24,440 --> 00:44:28,900
+أحطها بصيغة طيب تمام و هذا معناه أنه بدل ما أجيب
+
+522
+00:44:28,900 --> 00:44:35,310
+تربية أجيب تكريب للطرفين بس جبنا تكريب للطرفينمنها
+
+523
+00:44:35,310 --> 00:44:39,070
+بطلع إنه بدل ما كانت A تربية هي اللي even طب هي
+
+524
+00:44:39,070 --> 00:44:43,050
+نفس ال A تكعيب هي اللي even و الاستنتاج هو هو
+
+525
+00:44:43,050 --> 00:44:47,770
+هيطلع ماحنا طوي لسه مش طوي كنا حالين N تكعيب إذا
+
+526
+00:44:47,770 --> 00:44:52,730
+كان odd N ال N تكعيب برضه هيطلع odd طيب ما هي نفس
+
+527
+00:44:52,730 --> 00:44:56,610
+الفكرة نفس الفكرة إيش اختلفت بالله هالوجة عن اللي
+
+528
+00:44:56,610 --> 00:45:01,300
+كانت في ال slides؟ولا اشي ولا حاجة بس عشان ظهر
+
+529
+00:45:01,300 --> 00:45:06,860
+التكعيب خلصنا بتفعل الباقي نفس المحاضرة الباقي نفس
+
+530
+00:45:06,860 --> 00:45:10,260
+المحاضرة تماما ف is even وهذا معناه ان ايه بقدر
+
+531
+00:45:10,260 --> 00:45:13,360
+أحطها باتنين K وفي الحالة هذه بنكملها بدل ما كان
+
+532
+00:45:13,360 --> 00:45:17,520
+هيطلع أربعة في K تربية هتصيب تمانية في K تكعيب وفي
+
+533
+00:45:17,520 --> 00:45:20,360
+جميع الأحوال التمانية هتختصر مع الأتنين و هتظل
+
+534
+00:45:20,360 --> 00:45:23,380
+برضه even هناك كانت أربعة بتظل even هنا تمانية
+
+535
+00:45:23,380 --> 00:45:29,540
+بتظل even برضهنفس القصة .. نفس القصة ف .. بالضبط
+
+536
+00:45:29,540 --> 00:45:32,840
+even على even معناته في common و انتهى الكلام و
+
+537
+00:45:32,840 --> 00:45:35,120
+خلصت هيكي طريقة حلها
+
+538
+00:45:42,420 --> 00:45:46,360
+طيب بتهيأليها دي كتير برضه بسيط حلها أنه لو N is
+
+539
+00:45:46,360 --> 00:45:56,220
+positive then N is odd if and only if .. if .. if
+
+540
+00:45:56,220 --> 00:46:03,060
+and only if five N plus six is odd بدي شغالة أحلها
+
+541
+00:46:03,060 --> 00:46:06,640
+بدنا نشوف الفكرة الحل إيش ممكن نعمل فيها فكرة
+
+542
+00:46:06,640 --> 00:46:07,180
+الحل؟
+
+543
+00:46:12,950 --> 00:46:20,330
+in is positive يعني ايش؟ اكبر من صفر اذا او اكبر
+
+544
+00:46:20,330 --> 00:46:27,410
+من صفر اذا in
+
+545
+00:46:27,410 --> 00:46:40,210
+is odd if and only if five in plus six is odd
+
+546
+00:46:49,610 --> 00:46:58,590
+طيب بس بس بس لأ مظبوط بس خلصت الجثة هه هنعملها
+
+547
+00:46:58,590 --> 00:47:05,250
+أخدنا هذه ال F and only F هي عبارة عن N is odd اذا
+
+548
+00:47:05,250 --> 00:47:11,110
+five N plus six is odd and
+
+549
+00:47:14,260 --> 00:47:24,480
+five n plus six is odd even if n is odd اعمل هذه
+
+550
+00:47:24,480 --> 00:47:30,300
+الحالة اعمل هذه الحالة و خلصناهابس الاولى مافيش
+
+551
+00:47:30,300 --> 00:47:34,320
+فيها مشكلة اطلاقا لان انت direct هتفرض ان ان فعلا
+
+552
+00:47:34,320 --> 00:47:38,880
+هي is odd و بتعود بال 2k plus 1 في هذا ال term
+
+553
+00:47:38,880 --> 00:47:44,520
+هيطلع ان ال term هذا odd انتهى هنا مش هتقدر تتعامل
+
+554
+00:47:44,520 --> 00:47:51,360
+معاها اعمل indirect افرض in is even و اثبت منها ان
+
+555
+00:47:51,360 --> 00:47:57,800
+خمسة in plus six evenمعنى ذلك بال contrapositive
+
+556
+00:47:57,800 --> 00:48:04,880
+بتصير ال relation هذه صحيحة صحيح
+
+557
+00:48:04,880 --> 00:48:08,940
+صحيح لاحظته كيف انتهى بدك تعملها direct اعملها
+
+558
+00:48:08,940 --> 00:48:12,440
+direct هذي بدك تعملها direct اعملها direct بس بدك
+
+559
+00:48:12,440 --> 00:48:16,520
+تكون فاهم انك هذي اذا كان هذي odd odd في odd odd
+
+560
+00:48:16,520 --> 00:48:21,020
+plus even خلاص نعم بدك تعمل direct اعمل direct
+
+561
+00:48:21,020 --> 00:48:23,640
+مافيش مشكلة بس فاهمين فكرة انه بده اعمل
+
+562
+00:48:23,640 --> 00:48:27,830
+duplication هنالأن ال F and only F معناته F في
+
+563
+00:48:27,830 --> 00:48:33,710
+اتجاه P to Q و برضه implication في اتجاه Q to P
+
+564
+00:48:33,710 --> 00:48:38,130
+تمام خلصناها بتنزل معاكوا هذه محلولة بس أخدنا
+
+565
+00:48:38,130 --> 00:48:41,370
+الفكرة ال concept بتاعة بسيط جدا فتاخد على
+
+566
+00:48:41,370 --> 00:48:45,090
+الحالتين عشان تكون خلصنا جزئيتنا لهذا اليوم
+
+567
+00:48:45,090 --> 00:48:49,870
+الأسبوع الجاي بنبدأ درس جديد ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/jCXELgNR1NU_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/jCXELgNR1NU_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5b75236faf76fb84b939c343eda7ec34f14fa49d
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/jCXELgNR1NU_raw.json
@@ -0,0 +1 @@
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83.85, "text": "السابقة عشان تكونوا هتلاقوا ان مافيش فيها اشي جديد يعني أصلا فخليني نبدأ اليوم في بعض الأسئلة أو بعض مسائل كانت موجودة في problems موجودة في امتحانات سابقة عن الأكام من الموضوع اللي أخدناهم سابقا", "tokens": [6027, 3794, 16758, 28671, 6225, 8592, 7649, 6055, 30544, 14407, 8032, 2655, 15040, 4587, 14407, 16472, 19446, 41185, 8592, 8978, 11296, 1975, 8592, 1829, 10874, 16254, 3215, 37495, 22653, 5551, 9381, 15040, 6156, 9778, 1211, 9957, 1829, 8717, 44510, 10721, 45595, 20498, 8978, 45030, 11242, 16247, 3794, 19986, 37977, 34051, 45030, 11242, 47524, 16373, 1211, 25961, 2655, 3714, 29245, 23328, 3660, 8978, 2740, 3714, 29245, 23328, 3660, 8978, 1975, 2304, 2655, 5016, 7649, 9307, 8608, 16758, 28671, 18871, 16247, 4117, 10943, 9154, 9673, 2407, 11242, 45367, 13672, 1829, 5551, 9778, 3215, 8315, 16095, 8608, 16758, 4587, 995], "avg_logprob": -0.1146364799719684, "compression_ratio": 1.7938144329896908, "no_speech_prob": 9.196996688842773e-05, "words": [{"start": 67.77, 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أكثر وضوحا هنا اللي بالأحمر هنا كانت أكثر وضوحا جالك والله بفضله culture was sport but not politics يعني هذه بتعطيك إرياحية أكتر من غيرها طيب بعدين في عندك تمانية بفضله ال politics and", "tokens": [2304, 43020, 4032, 46958, 5016, 3660, 9122, 33911, 16712, 2288, 16758, 9566, 2423, 20009, 1296, 552, 49374, 16712, 1211, 9307, 3660, 10479, 8032, 3215, 12610, 3660, 6156, 2304, 2655, 5172, 43042, 8592, 9154, 43242, 4117, 20449, 1211, 20498, 3660, 37893, 3714, 4117, 2655, 37746, 3660, 9122, 45865, 3794, 34105, 29538, 20449, 1211, 20498, 3660, 5551, 4117, 49115, 4032, 11242, 2407, 5016, 995, 34105, 13672, 1829, 20666, 10721, 5016, 29973, 34105, 25961, 2655, 5551, 4117, 49115, 4032, 11242, 2407, 5016, 995, 10874, 6027, 4117, 16070, 43761, 4724, 5172, 11242, 1211, 3224, 3713, 390, 7282, 457, 406, 7341, 37495, 22653, 29538, 39894, 3615, 9566, 1829, 4117, 11933, 16572, 39319, 10632, 5551, 4117, 2655, 2288, 9154, 32771, 13546, 11296, 23032, 1829, 3555, 39182, 9957, 8978, 43242, 4117, 46811, 7649, 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خلصناها اي تسعة الاولى خلصناها بعد هيك تمانية هذه عبارة عن ايش ال politics and sport but not culture برضه نقدر نشطبها و نخلصها", "tokens": [66, 8389, 39896, 3713, 4032, 7282, 457, 406, 16490, 1211, 33546, 44945, 1863, 11622, 1211, 8978, 11296, 6055, 3794, 27884, 47525, 4117, 6055, 5016, 9566, 25894, 11296, 6055, 3794, 27884, 16490, 1211, 9381, 8315, 11296, 1975, 1829, 6055, 3794, 27884, 42963, 12610, 7578, 16490, 1211, 9381, 8315, 11296, 39182, 39896, 4117, 46811, 7649, 10632, 29538, 6225, 3555, 9640, 3660, 18871, 1975, 1829, 8592, 2423, 7341, 293, 7282, 457, 406, 3713, 4724, 43042, 3224, 8717, 28543, 2288, 8717, 8592, 9566, 3555, 11296, 4032, 8717, 9778, 1211, 9381, 11296], "avg_logprob": -0.13423295657743106, "compression_ratio": 1.6756756756756757, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1027.1, "end": 1027.78, "word": "culture", "probability": 0.68896484375}, {"start": 1027.78, "end": 1028.54, "word": " هي", "probability": 0.366943359375}, {"start": 1028.54, 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1211, 8032, 1863, 9778, 20292, 3714, 7435, 2304, 2407, 27884, 6055, 7649, 10632, 4724, 43042, 3224, 20449, 2423, 32284, 5296, 19528, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 16247, 35457, 45367, 25062, 18513, 2304, 8032, 1863, 47283, 3215, 2423, 32284, 4032, 8032, 1863, 44510, 10721, 8978, 2423, 14642, 8032, 1863, 44510, 10721, 8717, 2655, 3615, 19528, 3089, 10874, 16254, 3215, 13672, 1829, 31439, 2423, 25505, 532, 905, 1429], "avg_logprob": -0.11233836224024323, "compression_ratio": 1.6898395721925135, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 2503.44, "end": 2504.1, "word": "هيك", "probability": 0.642822265625}, {"start": 2504.1, "end": 2504.42, "word": " أخدنا", "probability": 0.8963623046875}, {"start": 2504.42, "end": 2504.8, "word": " مجموعة", "probability": 0.9546875}, {"start": 2504.8, "end": 2505.68, "word": " مسائل", "probability": 0.9591471354166666}, {"start": 2505.68, "end": 2506.3, "word": " هنخلي", "probability": 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"word": " نتعلم", "probability": 0.9901123046875}, {"start": 2517.52, "end": 2518.02, "word": " code", "probability": 0.89599609375}, {"start": 2518.02, "end": 2518.56, "word": " جديد", "probability": 0.9879557291666666}, {"start": 2518.56, "end": 2518.72, "word": " اللي", "probability": 0.920166015625}, {"start": 2518.72, "end": 2518.88, "word": " هو", "probability": 0.994140625}, {"start": 2518.88, "end": 2518.98, "word": " ال", "probability": 0.88916015625}, {"start": 2518.98, "end": 2519.52, "word": " pseudocode", "probability": 0.8486328125}], "temperature": 1.0}, {"id": 102, "seek": 254426, "start": 2520.06, "end": 2544.26, "text": "ال code المتعرف عليه كلكم بتعرفوا انه انت ممكن تشتغل Java انا اشتغل C++ بس في النهاية المفروض نفهم بعض المفروض ان نفهم بعض في ال pseudocode كويس فلازم يكون في code وصفي اللي هو ال pseudocode و اللي المفروض تشتغله عليه الاصل هي تشتغله عليه في ال data structure بالظبط فهنتكلم عنه يلا يعطيكوا العفو", "tokens": [6027, 3089, 9673, 2655, 3615, 28480, 47356, 28242, 24793, 39894, 3615, 28480, 14407, 16472, 3224, 16472, 2655, 3714, 43020, 6055, 8592, 2655, 17082, 1211, 10745, 1975, 8315, 1975, 8592, 2655, 17082, 1211, 383, 25472, 4724, 3794, 8978, 28239, 11296, 10632, 9673, 5172, 32887, 11242, 8717, 5172, 16095, 45030, 11242, 9673, 5172, 32887, 11242, 16472, 8717, 5172, 16095, 45030, 11242, 8978, 2423, 25505, 532, 905, 1429, 9122, 45865, 3794, 6156, 1211, 31377, 2304, 7251, 30544, 8978, 3089, 4032, 9381, 41185, 13672, 1829, 31439, 2423, 25505, 532, 905, 1429, 4032, 13672, 1829, 9673, 5172, 32887, 11242, 6055, 8592, 2655, 17082, 43761, 47356, 2423, 33546, 1211, 39896, 6055, 8592, 2655, 17082, 43761, 47356, 8978, 2423, 1412, 3877, 20666, 19913, 3555, 9566, 6156, 3224, 1863, 2655, 4117, 19528, 18871, 3224, 7251, 15040, 37495, 9566, 1829, 4117, 14407, 18863, 5172, 2407], "avg_logprob": -0.1677691597138008, "compression_ratio": 2.0632911392405062, "no_speech_prob": 2.008676528930664e-05, "words": [{"start": 2520.06, "end": 2520.24, "word": "ال", "probability": 0.9599609375}, {"start": 2520.24, "end": 2520.44, "word": " code", "probability": 0.85595703125}, {"start": 2520.44, "end": 2520.94, "word": " المتعرف", "probability": 0.874755859375}, {"start": 2520.94, "end": 2521.18, "word": " عليه", "probability": 0.81640625}, {"start": 2521.18, "end": 2521.5, "word": " كلكم", "probability": 0.707763671875}, {"start": 2521.5, "end": 2522.04, "word": " بتعرفوا", "probability": 0.929931640625}, {"start": 2522.04, "end": 2523.38, "word": " انه", "probability": 0.6787109375}, {"start": 2523.38, "end": 2524.1, "word": " انت", "probability": 0.843017578125}, {"start": 2524.1, "end": 2524.36, "word": " ممكن", "probability": 0.994384765625}, {"start": 2524.36, "end": 2525.36, "word": " تشتغل", "probability": 0.99384765625}, {"start": 2525.36, "end": 2525.94, "word": " Java", "probability": 0.599609375}, {"start": 2525.94, "end": 2526.6, "word": " انا", "probability": 0.725830078125}, {"start": 2526.6, "end": 2526.88, "word": " اشتغل", 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" pseudocode", "probability": 0.9498291015625}, {"start": 2536.5, "end": 2536.66, "word": " و", "probability": 0.60498046875}, {"start": 2536.66, "end": 2536.76, "word": " اللي", "probability": 0.947998046875}, {"start": 2536.76, "end": 2537.04, "word": " المفروض", "probability": 0.9837646484375}, {"start": 2537.04, "end": 2537.48, "word": " تشتغله", "probability": 0.94013671875}, {"start": 2537.48, "end": 2537.82, "word": " عليه", "probability": 0.97900390625}, {"start": 2537.82, "end": 2538.66, "word": " الاصل", "probability": 0.6904296875}, {"start": 2538.66, "end": 2538.78, "word": " هي", "probability": 0.986328125}, {"start": 2538.78, "end": 2539.16, "word": " تشتغله", "probability": 0.91181640625}, {"start": 2539.16, "end": 2539.28, "word": " عليه", "probability": 0.9853515625}, {"start": 2539.28, "end": 2539.42, "word": " في", "probability": 0.84130859375}, {"start": 2539.42, "end": 2539.44, "word": " ال", "probability": 0.88330078125}, {"start": 2539.44, "end": 2539.56, "word": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/jCXELgNR1NU_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/jCXELgNR1NU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bf51b8efcf36eabff3e8b4bd4a8aa17a46963b36
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/jCXELgNR1NU_raw.srt
@@ -0,0 +1,2084 @@
+1
+00:00:05,130 --> 00:00:09,090
+طيب السلام عليكم هعطيكوا العفو يا شباب خلصنا يمكن
+
+2
+00:00:09,090 --> 00:00:12,810
+احنا ال functions و بعدها ال sequence و ال
+
+3
+00:00:12,810 --> 00:00:16,810
+summation كان دايلة اللي يمكن جزئية كتير صغيرة
+
+4
+00:00:16,810 --> 00:00:20,890
+دايلة في السياق اللي احنا بنتكلمه اللي هي ال
+
+5
+00:00:20,890 --> 00:00:26,590
+matrices و باعتبار ان ال matrices يعني مش كتيرأشي
+
+6
+00:00:26,590 --> 00:00:29,870
+جديد بالنسبالكم فحنأجله للمرة القادمة ان شاء الله
+
+7
+00:00:29,870 --> 00:00:33,510
+نحاول نعدي عليه بسرعة معظمها نفس ال matrices أو
+
+8
+00:00:33,510 --> 00:00:36,610
+المصفوفات اللي انتوا أخدتوها سابقا كمعلومات عن
+
+9
+00:00:36,610 --> 00:00:40,090
+المصفوفات فنخليها للأسبوع الجاي بحيث انه جابل ما
+
+10
+00:00:40,090 --> 00:00:43,910
+ننسى جزء اللي عد علينا بعض الأجزاء اللي عدت علينا
+
+11
+00:00:43,910 --> 00:00:46,710
+خلينا ناخدوا ناكم من سؤال عليهم من أسئلة
+
+12
+00:00:46,710 --> 00:00:51,740
+الامتحانات السابقة خلينا نشوف كيف تيجي عليهمأسئلة
+
+13
+00:00:51,740 --> 00:00:54,300
+جابل ما نكون انسيناهم و أجلناهم لسه للأسبوع اللي
+
+14
+00:00:54,300 --> 00:00:58,460
+ورا فبنخل ال matrices للأسبوع القادم ان شاء الله
+
+15
+00:00:58,460 --> 00:01:03,520
+تعالى ماعتقدش انه هتكون صعب عليكوا يعني فكتير كويس
+
+16
+00:01:03,520 --> 00:01:07,480
+انه برضه لو طلعتوا على المحاضرة تاعت المصففات
+
+17
+00:01:07,770 --> 00:01:12,230
+السابقة عشان تكونوا هتلاقوا ان مافيش فيها اشي جديد
+
+18
+00:01:12,230 --> 00:01:17,270
+يعني أصلا فخليني نبدأ اليوم في بعض الأسئلة أو بعض
+
+19
+00:01:17,270 --> 00:01:20,630
+مسائل كانت موجودة في problems موجودة في امتحانات
+
+20
+00:01:20,630 --> 00:01:24,840
+سابقة عن الأكام من الموضوع اللي أخدناهم سابقاو
+
+21
+00:01:24,840 --> 00:01:29,040
+نشوفهم هل ال issues صعب فعلا؟ هل الامتحانات كانت
+
+22
+00:01:29,040 --> 00:01:31,740
+صعبة كتير يعني لهذا الدرجة؟ هل فعلا فيها مشكلة؟
+
+23
+00:01:31,740 --> 00:01:34,380
+ماكنش فيه مشكلة؟ و لو فيه مشكلة تعرفوا والله كيف
+
+24
+00:01:34,380 --> 00:01:39,500
+تحلوا هالمشكلة فنشوف هاي مثلا واحد من الأسئلة اللي
+
+25
+00:01:39,500 --> 00:01:43,880
+كانت موجودة على ال sets على ال sets و واضح انه
+
+26
+00:01:43,880 --> 00:01:48,700
+مطلوب ايش بده منها؟ بده منها اثبات ان ال two terms
+
+27
+00:01:48,700 --> 00:01:53,370
+هدولةمتساوين او equivalent لبعض بيساووا بعض او
+
+28
+00:01:53,370 --> 00:01:56,790
+equivalent لبعض حدد انها بدواش بال set builder
+
+29
+00:01:56,790 --> 00:02:00,210
+notation بال set builder notation اذا كانت انت
+
+30
+00:02:00,210 --> 00:02:04,490
+متذكرين احنا اخدنا عدة طرق صحيح اخدنا بال mutual
+
+31
+00:02:04,490 --> 00:02:09,050
+subsetمتذكرينها؟ بدي أفترض كل واحدة هي subset من
+
+32
+00:02:09,050 --> 00:02:11,750
+التانية ولا لأ؟ وإذا أثبتنا إن كل واحدة منهم
+
+33
+00:02:11,750 --> 00:02:15,270
+subset من التانية فمعناه ذلك إن هم equivalent لبعض
+
+34
+00:02:15,270 --> 00:02:18,450
+الطريقة التانية كانت اللي هي ال set builder
+
+35
+00:02:18,450 --> 00:02:21,170
+notation اللي هنشوفها الوجد اللي هنستخدم فيها
+
+36
+00:02:21,170 --> 00:02:23,790
+مجموعة ال rules اللي احنا أخدناهم و اللي كانوا
+
+37
+00:02:23,790 --> 00:02:28,930
+تمثل فيها .. بنمثل فيها ال intersection بال and و
+
+38
+00:02:28,930 --> 00:02:34,310
+ال union بالorمتذكرينه الكلام هذا؟ تمام و ال .. ال
+
+39
+00:02:34,310 --> 00:02:38,650
+compliment بال negation فقط و بنستخدم كنا مجموعة
+
+40
+00:02:38,650 --> 00:02:41,150
+ال rules اللي متعرف عليها في ال logic أو في ال
+
+41
+00:02:41,150 --> 00:02:44,470
+sets و بتمشي الأمور تمام هذه اللي هي كانت النوع
+
+42
+00:02:44,470 --> 00:02:47,010
+التاني، النوع التالت كانت ال membership tables
+
+43
+00:02:47,010 --> 00:02:51,570
+متذكرينه؟اللي هي زي ال truth table بالظبط بس
+
+44
+00:02:51,570 --> 00:02:54,930
+membership اللي هي ينتمي او لا ينتمي فلأ السؤال
+
+45
+00:02:54,930 --> 00:02:59,050
+هنا محددنا تحديدا من خلال معرفتك في ال sets
+
+46
+00:02:59,050 --> 00:03:02,170
+اثبتلنا ال two terms هدولة equivalent لبعض
+
+47
+00:03:02,170 --> 00:03:06,470
+باستخدامه محددتنا تحديدا ايش الاستخدام المطلوب لان
+
+48
+00:03:06,470 --> 00:03:09,310
+الامور بسيطة مافيش فيها مشكلة كل اللي بنعمله بس
+
+49
+00:03:09,310 --> 00:03:13,640
+بنمسك طرف من الأطرافالطرف اللى موجود عندنا هنا
+
+50
+00:03:13,640 --> 00:03:18,020
+الطرف الشمال عشان نحطه بصيغة ال builder notation
+
+51
+00:03:18,020 --> 00:03:24,320
+هنقول ان هى ال term هو عبارة عن set هو احنا اصلا
+
+52
+00:03:24,320 --> 00:03:30,640
+كل كلامنا عن set اصلا set of x بحيث انه x و بنكتب
+
+53
+00:03:30,640 --> 00:03:34,540
+تنتمي و بنكتب كل الكلام هذا بعد ما نكون حولنا زى
+
+54
+00:03:34,540 --> 00:03:39,100
+ما قلنا ال complement ل negationال .. ال
+
+55
+00:03:39,100 --> 00:03:43,880
+intersection and و ال union لأور بس هي كل اللي
+
+56
+00:03:43,880 --> 00:03:48,300
+هنعمله بعد هيك نتعامل معاها باستخدام القوانين
+
+57
+00:03:48,300 --> 00:03:53,800
+المعروفة اللي كانت موجودة عندك الآن أول شغلة واضحة
+
+58
+00:03:53,800 --> 00:04:01,660
+جدا هنا ان في عندك andor وفي قص، إيش بدك تسوي؟
+
+59
+00:04:01,660 --> 00:04:05,600
+distribution، distributive rule، خلاص هاي
+
+60
+00:04:05,600 --> 00:04:09,860
+distributive rule وزّع ال negation إيه؟ وزّعنا
+
+61
+00:04:09,860 --> 00:04:13,870
+negation إيه؟مافيش فيها إيش نهائي السؤال طلع فاضي
+
+62
+00:04:13,870 --> 00:04:16,210
+الواجهة اللي بيّنها الواجهة انه خلاص فضى السؤال
+
+63
+00:04:16,210 --> 00:04:20,750
+السؤال فضى فتخيل ان السؤال زي هذا يكون نص الطلاب
+
+64
+00:04:20,750 --> 00:04:24,410
+مش عارفين يحلوه هل المشكلة في السؤال هاي قدامك
+
+65
+00:04:24,410 --> 00:04:28,290
+السؤال لاحظتوا كيف خلصنا السؤال بتالي هنا انتهى
+
+66
+00:04:28,290 --> 00:04:30,810
+انتهى يعني حتى لو قلتلكوا خلينا نشوف السؤال اللي
+
+67
+00:04:30,810 --> 00:04:34,350
+بعده مش هكون جالجانين ان انتوا هتجفوا فيه خلصت
+
+68
+00:04:34,350 --> 00:04:37,170
+لأنه مش ضالش في إشي كل اللي انتوا عارفين أنه هذي
+
+69
+00:04:37,170 --> 00:04:45,100
+falseو false أو أي شيء .. أي شيء خلصناها فلاحظوا
+
+70
+00:04:45,100 --> 00:04:48,860
+أن أي شيء هذا بصورة أو باخرة هو فعلا نفس ال term
+
+71
+00:04:48,860 --> 00:04:53,200
+هذا لا ينتمي و ينتمي يعني هيوا يوجد في بي ولا يوجد
+
+72
+00:04:53,200 --> 00:04:58,000
+في اي بس بدها ترتيبة رتبها عمللي الترتيب مش اكتر
+
+73
+00:04:58,000 --> 00:05:05,800
+من هيك طيب فصارت ينتمي ل بي و لا ينتمي ل اي تماما
+
+74
+00:05:05,800 --> 00:05:08,320
+هذا معناه انه
+
+75
+00:05:13,430 --> 00:05:18,550
+سؤال مش عارف يمكن .. أنا أعتقد أنه بسيط، أعتقد أنه
+
+76
+00:05:18,550 --> 00:05:23,250
+كتير بسيط ك .. ك .. كسؤال امتحان أصلا كيف؟
+
+77
+00:05:27,810 --> 00:05:31,290
+لأ هينزل .. هينزل عندكم بس احنا قولنا المحلولة هذه
+
+78
+00:05:31,290 --> 00:05:36,070
+هتنزل بعد ما نخلص .. ما نحلها مالهاش معناه نزلكيا
+
+79
+00:05:36,070 --> 00:05:39,490
+من الأول ليش نقعد نحلها؟ مانت هتقراها لحالك يعني
+
+80
+00:05:39,490 --> 00:05:43,630
+كأنك اعطيت .. اعطيتك ال mood of answer و خلصنا طيب
+
+81
+00:05:43,630 --> 00:05:47,490
+هاي الفرق بيه كان من نفس السؤال و اللي كان بناء
+
+82
+00:05:47,490 --> 00:05:53,630
+على our knowledge about set كان بكل بساطة معطيني
+
+83
+00:05:53,630 --> 00:06:02,370
+ايهاشها دي؟ Cartesian product بيه، ايه؟ Cartesian
+
+84
+00:06:02,370 --> 00:06:07,220
+product بيههذه من أول السؤال، إذا أنت قريقها صح،
+
+85
+00:06:07,220 --> 00:06:10,660
+نحل السؤال، مش قريقها صح، مش هتحل، مش هتصل معاك
+
+86
+00:06:10,660 --> 00:06:14,300
+لعيشها، ليش؟ لأن أنت بدأت تكون عارف أن ال set اللي
+
+87
+00:06:14,300 --> 00:06:18,380
+ماعطيكيها هي ال Cartesian product ل A و B طيب، إيش
+
+88
+00:06:18,380 --> 00:06:21,020
+يعني ال Cartesian product ل A و لا B؟ معناته هي
+
+89
+00:06:21,020 --> 00:06:24,800
+عبارة عن pairs، ال pairs هذه العنصر الأول من ال ..
+
+90
+00:06:24,800 --> 00:06:27,700
+من ال set الأولى و العنصر التاني من ال set التاني
+
+91
+00:06:28,810 --> 00:06:32,450
+بس a و b بتقدر تجيب ال two in two بقرية حية
+
+92
+00:06:32,450 --> 00:06:35,810
+ماعنكاش اي مشكلة اما انت اذا كان انت بدك تروح تكمل
+
+93
+00:06:35,810 --> 00:06:40,190
+السؤال fine ل b خلاص جيب ل b تمام وصلت الأمور
+
+94
+00:06:40,190 --> 00:06:43,810
+بتفعلي مافيش اكتر من هيك في حل الموضوع هذا فانت
+
+95
+00:06:43,810 --> 00:06:51,190
+بتجيب ال a واضحة هي واحد اتنين تلاتة كرة خلصناها
+
+96
+00:06:51,190 --> 00:06:56,740
+طيب بيإيش بيه؟ اتنين عندك الاتنين و عندك الواحد و
+
+97
+00:06:56,740 --> 00:07:00,700
+عندك أربعة يعني واحد اتنين أربعة مش هيك؟ واحد
+
+98
+00:07:00,700 --> 00:07:05,060
+اتنين أربعة طيب ال bar بدك تجيب كل ال subsets من
+
+99
+00:07:05,060 --> 00:07:09,900
+واحد اتنين أربعة يعني الفاي ماحدش ينسى الفاي و
+
+100
+00:07:09,900 --> 00:07:18,640
+نفسها و بعدين ابدأ أحط ال parts تبعتهاواحد لحالها
+
+101
+00:07:18,640 --> 00:07:22,960
+اتنين لحالها اربعة لحالها واحد اتنين واحد اربعة
+
+102
+00:07:22,960 --> 00:07:27,460
+اتنين اربعة و ال file طبعا هذه مسبقا اول حاجة
+
+103
+00:07:27,460 --> 00:07:32,200
+بتحطها اول اشي اول اشي على طول بتحط ال file هاي
+
+104
+00:07:32,200 --> 00:07:35,600
+السؤال خلص السؤال هاي السؤال كامل بالفرعين تابعونه
+
+105
+00:07:35,600 --> 00:07:39,100
+المفروض ان درجته درجتها كانت الاصل كانت مضمونة عند
+
+106
+00:07:39,100 --> 00:07:44,320
+الطلاب صحيحهيه هيه أنا قاعد بحلمها نصفة هدى اه
+
+107
+00:07:44,320 --> 00:07:46,640
+نصفة هدى هيه انا ماكنش ألاقاه هدى كانت في امتحان
+
+108
+00:07:46,640 --> 00:07:55,040
+نصفي طيب كمان سؤال مقلوب هنا في امتحان اخر يعني في
+
+109
+00:07:55,040 --> 00:07:58,880
+C بس في كندا ماكنتش في نفس الامتحان كانت في امتحان
+
+110
+00:07:58,880 --> 00:08:02,920
+تاني كان المقلوب برضه نفس الفكرة بدنا نمثل بال
+
+111
+00:08:02,920 --> 00:08:08,100
+Venn diagram مجموعة ال relations لل sets واحد و
+
+112
+00:08:08,100 --> 00:08:13,270
+اتنينبدنا نرسمهم Venn diagram بس بخيّر مش أكتر من
+
+113
+00:08:13,270 --> 00:08:18,450
+هيك فكل اللي بدنا نعمله بدنا نرسم هاي ال A و B و C
+
+114
+00:08:18,450 --> 00:08:25,390
+مدام A و B و C A و B و C خدوا بالكم لازم تعملوهم
+
+115
+00:08:25,390 --> 00:08:29,170
+بالشكل هذا ليش؟ بمعنى أنتوا حطيتوا كل التقطعات
+
+116
+00:08:29,170 --> 00:08:33,950
+الممكنة بعد هيك بنقول موجودة ولا مش موجودة بس ما
+
+117
+00:08:33,950 --> 00:08:40,360
+تسيبليش يا واحد يعمليها بهذا الشكل مثلاواحد يعمل
+
+118
+00:08:40,360 --> 00:08:47,920
+ليههم هيك أنا بتكلم عن نماذج كانت إجابات يعني بهذا
+
+119
+00:08:47,920 --> 00:08:52,860
+الشكل طب لو طلبنا نجيب تقاطع .. هي تقاطع أصلا وين
+
+120
+00:08:52,860 --> 00:08:57,400
+بينت هنا؟ مافيش تقاطع .. مافيش تقاطع فلأ بدك
+
+121
+00:08:57,400 --> 00:09:01,260
+ترسمهم بالشكل هذا مبدئيا على طول تبدأ شغلك بالشكل
+
+122
+00:09:01,260 --> 00:09:07,580
+هذا إلا إذا السؤال أعطاك إشي تانيزي ايش؟ disjoint
+
+123
+00:09:07,580 --> 00:09:11,440
+مثلا خلاص اذا قالك disjoint خلاص okay افصلهم
+
+124
+00:09:11,440 --> 00:09:14,480
+ابعدهم عنهم انت عارف انه مافيش اصلا تقاطع تمام
+
+125
+00:09:14,480 --> 00:09:20,800
+فهنا بقى نكتب بهذا الشكل عشان نبدأ نشوف مين موجود
+
+126
+00:09:20,800 --> 00:09:25,240
+في ايه و غير موجود في مين في التقاطع طب وين
+
+127
+00:09:25,240 --> 00:09:30,420
+التقاطع بيه C؟
+
+128
+00:09:30,420 --> 00:09:36,500
+هى التقاطع بيه Cبالضبط طيب لما نقول ايه موجود في
+
+129
+00:09:36,500 --> 00:09:40,820
+ايه و غير موجود في التقاطع، يعني انا بتكلم، بغير
+
+130
+00:09:40,820 --> 00:09:46,180
+اللون، بتكلم عن هذا
+
+131
+00:09:46,180 --> 00:09:49,880
+الجزء صحيح؟
+
+132
+00:09:49,880 --> 00:09:56,480
+خلص هاي السؤال، انتهت السؤال السؤال انتهى هاي
+
+133
+00:09:56,480 --> 00:10:03,350
+تقاطع زي ما قلنابعد ما حلناها نشوف كده هاي التقاطع
+
+134
+00:10:03,350 --> 00:10:09,130
+وهي المطلوب في
+
+135
+00:10:09,130 --> 00:10:13,070
+أسهل من هيك سؤال؟ مافيش طيب التاني نفس الفكرة بدك
+
+136
+00:10:13,070 --> 00:10:18,830
+تبدأ من التلات دوائر و كل المشكلة كانت سابقا في
+
+137
+00:10:18,830 --> 00:10:23,110
+بداية التلات دوائر هدول لأنك انت لازم تحط كل ال
+
+138
+00:10:23,110 --> 00:10:26,890
+possibilities الممكنةما لهاش معنى تعملهم disjoint
+
+139
+00:10:26,890 --> 00:10:29,010
+طب انا قلتلك disjoint السؤال جال في disjoint
+
+140
+00:10:29,010 --> 00:10:33,070
+ماجالش طب ليش افترضت من عندك انه في disjoint مافيش
+
+141
+00:10:33,070 --> 00:10:37,890
+disjoint اه بس بدك تحدد disjoint لمين مع مين
+
+142
+00:10:37,890 --> 00:10:41,110
+بالظبط
+
+143
+00:10:41,110 --> 00:10:44,270
+اه فبدك تاخد .. بقالك ان مين مع مين بدك تفصلهم مع
+
+144
+00:10:44,270 --> 00:10:50,500
+بعض طيب فهي هي الفكرة بدك تبدأ تجيب ايهdifference
+
+145
+00:10:50,500 --> 00:10:55,660
+B A difference B اللي هو بدك تبدأ بهذا الشكل A وهي
+
+146
+00:10:55,660 --> 00:11:01,820
+B مش هي A وB فهي A difference B طيب
+
+147
+00:11:01,820 --> 00:11:08,340
+A difference C هي A difference C فانت بتتكلم عن
+
+148
+00:11:08,340 --> 00:11:10,720
+هذا الجزء
+
+149
+00:11:13,580 --> 00:11:18,300
+اللي بالأحمر مطلوب ايش اتحاد ولا تقاطع اتحاد خلاص
+
+150
+00:11:18,300 --> 00:11:23,420
+بتعمل اتحاد لبتنتين بتعمل اتحاد لبتنتين فهنا هاي
+
+151
+00:11:23,420 --> 00:11:29,820
+بدنا ناخد كل واحدة لحال يعني
+
+152
+00:11:29,820 --> 00:11:33,220
+كان ممكن السؤال ييجي اغيره في امتحان تاني اقول
+
+153
+00:11:33,220 --> 00:11:34,660
+اثبت ان الاتنين بيساوي بعض
+
+154
+00:11:38,930 --> 00:11:41,750
+صح ولا مش صح؟ يعني معناه ذلك أن هو نفس السؤال أنا
+
+155
+00:11:41,750 --> 00:11:45,290
+في عندي flexibility لإن أنا في امتحان تاني أجيبهم
+
+156
+00:11:45,290 --> 00:11:49,670
+نفسهم لكن صيغة السؤال أغيرها ليش أقولك أرسمها في
+
+157
+00:11:49,670 --> 00:11:54,790
+دياجرام و أسكت؟ هقولك اثبتلي إن هما بيسووا بعض لإن
+
+158
+00:11:54,790 --> 00:11:57,350
+هين بيبيني إن هما بيسووا بعض، صحيح؟ بيبيني إن هما
+
+159
+00:11:57,350 --> 00:12:03,070
+بيسووا بعض، تمام طيب، كمان مثال ممكن ييجي على ال
+
+160
+00:12:03,070 --> 00:12:09,400
+sitsعلى ال sets زي مثلا الأمثلة المقالية اللي زي
+
+161
+00:12:09,400 --> 00:12:14,020
+هيك ممكن تيجي وهذه مالية ال net مليانة وموجودة
+
+162
+00:12:14,020 --> 00:12:18,360
+كأسئلة كتير بتيجيخلّينا نشوف في مطلوب newspaper
+
+163
+00:12:18,360 --> 00:12:23,200
+runs a survey في واحدة من الجرايد عملت survey عملت
+
+164
+00:12:23,200 --> 00:12:27,160
+اللي هي يعني مسح و استبانة الاستبانة هذه بدأت تعمل
+
+165
+00:12:27,160 --> 00:12:30,680
+collection لبعض الحقائق اللي عندها فوجدوا بعض
+
+166
+00:12:30,680 --> 00:12:35,760
+النتائج زهرت عندهم زهر عندهم انه واحد واربعين شخص
+
+167
+00:12:36,590 --> 00:12:40,450
+من الناس اللي اتوزعت عليهم الاستبانة بفضلوا
+
+168
+00:12:40,450 --> 00:12:44,510
+المقالات ال politics السياسية بفضلوا السياسية
+
+169
+00:12:44,510 --> 00:12:48,370
+تلاتة و تلاتين من الناس بفضلوا ال cultures ثقافية
+
+170
+00:12:48,370 --> 00:12:53,710
+أما في الآخر في ستة و تلاتين بفضلوا ال sport ده هم
+
+171
+00:12:53,710 --> 00:12:56,670
+أصلا شاروا الجريدة كلها على بعض عشان يتدوروا على
+
+172
+00:12:56,670 --> 00:13:00,230
+آخر تلت أربع صفحات في الآخر اللي هم عادة بيكونوا
+
+173
+00:13:00,230 --> 00:13:04,960
+لا إيش لل sport تمامفهيك هي ال survey الأولى طيب
+
+174
+00:13:04,960 --> 00:13:08,940
+اجوا حلله وجدوا انه فيه أربع تاشر people likes
+
+175
+00:13:08,940 --> 00:13:16,520
+politics and sport واجدوا من الست و تلاتين و
+
+176
+00:13:16,520 --> 00:13:20,640
+الواحد و أربعين في تقاطع بينهم أربع تاشر واحد بيحب
+
+177
+00:13:20,640 --> 00:13:25,650
+هادي و هادي بفضل يقرأ التنتين مع بعضأول ما ببدأ
+
+178
+00:13:25,650 --> 00:13:29,230
+ببدأ بال politics في بداية الصفحات و بعدين بنجل
+
+179
+00:13:29,230 --> 00:13:34,630
+على آخر صفحتين تلاتة بقرأ ال sport تسعة culture
+
+180
+00:13:34,630 --> 00:13:41,070
+and sport but not the politics هنا حدد culture and
+
+181
+00:13:41,070 --> 00:13:47,270
+sport و سكت ماجالش أي معلومة عنالطرف التالت عن ال
+
+182
+00:13:47,270 --> 00:13:51,850
+politics فعشان هيك هنا ماتكلمش عن مين عن ال
+
+183
+00:13:51,850 --> 00:13:57,110
+culture لما قال في 14 بفضله politics و sport فما
+
+184
+00:13:57,110 --> 00:14:00,810
+تفترضش أنت من عندك فرضية أنا ماتكلمتش عنها ولا هي
+
+185
+00:14:00,810 --> 00:14:04,550
+موجودة أن معناته مالهمش في ال culture يمكن يكون في
+
+186
+00:14:04,550 --> 00:14:11,610
+منهم جزء بفضل ال culture كمانممكن واضحة كيف
+
+187
+00:14:11,610 --> 00:14:16,990
+الترابط ال correlation between them بين التلاتة
+
+188
+00:14:16,990 --> 00:14:20,970
+categories هدولة فمتفرضش من عندك معلومة مش مكتوبة
+
+189
+00:14:20,970 --> 00:14:25,370
+كويس هنا هذه معلومة أكثر وضوحا هنا اللي بالأحمر
+
+190
+00:14:25,370 --> 00:14:28,990
+هنا كانت أكثر وضوحا جالك والله بفضله culture was
+
+191
+00:14:28,990 --> 00:14:33,110
+sport but not politics يعني هذه بتعطيك إرياحية
+
+192
+00:14:33,110 --> 00:14:36,630
+أكتر من غيرها طيب بعدين في عندك تمانية بفضله ال
+
+193
+00:14:36,630 --> 00:14:42,260
+politics andSport but not cultures تمام، اتناشر
+
+194
+00:14:42,260 --> 00:14:50,320
+واحد بيفضله politics and وليس ال .. ال other two
+
+195
+00:14:50,320 --> 00:14:55,820
+conversions يعني بيفضل فقط politics و فقط politics
+
+196
+00:14:55,820 --> 00:15:02,740
+طيب، حد يقول ليه؟ إيش الفرق بالاتنعاش هذه؟ و إيه؟
+
+197
+00:15:02,740 --> 00:15:09,070
+الواحد و ربعين؟ بالظبط و تحت؟طبعا هذا الكلام لما
+
+198
+00:15:09,070 --> 00:15:12,790
+اعتقد مع ضغط الامتحان مابيانش مع الطلاب انه فاهمين
+
+199
+00:15:12,790 --> 00:15:17,950
+الكلام هذا فصار في لبس بين هذه وبين هذه بتهيألي
+
+200
+00:15:17,950 --> 00:15:20,970
+واضح الفرق بينهم شاسع الفرق بينهم هذه الواحد
+
+201
+00:15:20,970 --> 00:15:23,570
+واربعين انا قلت ان هو بفضله politics بس ماقلتش
+
+202
+00:15:23,570 --> 00:15:27,030
+بفضله .. بفضلوش اشي تانيممكن بفضل ال politics و
+
+203
+00:15:27,030 --> 00:15:30,790
+بفضل كمان ال culture، بفضل ال politics و بفضل كمان
+
+204
+00:15:30,790 --> 00:15:34,270
+ال sport، بفضل ال politics و بفضلهم التلتة على
+
+205
+00:15:34,270 --> 00:15:37,250
+بعض، كلهم بحبهم، بحب يقراها، بمسكها الجريدة من
+
+206
+00:15:37,250 --> 00:15:43,800
+أولها لأخرهاOkay لكن هدول لأ هو تحديدا بقرا أول
+
+207
+00:15:43,800 --> 00:15:47,700
+مقالين تلاتة عن ال politics و خلاص و بسكرها تماما
+
+208
+00:15:47,700 --> 00:15:53,160
+بقرأش لا culture ولا بقرأ sport واضحة فتماما واضحة
+
+209
+00:15:53,160 --> 00:15:55,840
+الأمور الآن عشان نحل هذا الكلام و قبل ما نشوف إيش
+
+210
+00:15:55,840 --> 00:15:59,880
+بدنا .. بدنا نرسم التلات دوائر تعونا هذه التلات
+
+211
+00:15:59,880 --> 00:16:01,820
+دوائر تعونا بدنا نحط ال university discourse و
+
+212
+00:16:01,820 --> 00:16:04,420
+بعدين هذه التلات دوائر واحدة politics واحدة
+
+213
+00:16:04,420 --> 00:16:11,160
+culturesو واحدة لمن لل sport تمام هاي رسمناهم و
+
+214
+00:16:11,160 --> 00:16:16,880
+حددنا كل المساحات او كل التقطعات اللي ممكنها اول
+
+215
+00:16:16,880 --> 00:16:23,300
+شغلة ال 41 هذه .. هذه هنا موجودة لكن مجلش توزيحها
+
+216
+00:16:23,300 --> 00:16:27,220
+جدش هنا .. جدش هنا .. جدش هنا .. ماتكلمش فبسيبها
+
+217
+00:16:27,220 --> 00:16:30,920
+أكيد هسيبها لأنه مش هستفيد منها في الوقت الحالي
+
+218
+00:16:30,920 --> 00:16:33,640
+طيب مين اللي هقدر استفيد منها في الوقت الحالي
+
+219
+00:16:33,640 --> 00:16:34,680
+واضحة تماما
+
+220
+00:16:38,610 --> 00:16:43,310
+الاطمعاش ممكن تكون بصورة و باخرة اه واضحة طيب
+
+221
+00:16:43,310 --> 00:16:49,830
+ناخدها هيك بس تقديمها ناخدها تسلسلي عندك الاربع
+
+222
+00:16:49,830 --> 00:16:54,250
+عشر هنا إيش بفضل؟ politics لا مش هنستفيد منها
+
+223
+00:16:54,250 --> 00:16:59,670
+التسعة إيش بفضل؟ culture sport but not politics
+
+224
+00:16:59,670 --> 00:17:04,430
+تمام معناته هي هذه بنقدر نشطبها لإن بنقدر نستفيد
+
+225
+00:17:04,430 --> 00:17:16,440
+منهاculture هي culture و sport but not خلاص
+
+226
+00:17:16,440 --> 00:17:21,620
+بننزل فيها تسعة بدك
+
+227
+00:17:21,620 --> 00:17:25,260
+تحط عليها تسعة خلصناها اي تسعة الاولى خلصناها بعد
+
+228
+00:17:25,260 --> 00:17:29,560
+هيك تمانية هذه عبارة عن ايش ال politics and sport
+
+229
+00:17:29,560 --> 00:17:36,170
+but not culture برضه نقدر نشطبها و نخلصهاهد مين مع
+
+230
+00:17:36,170 --> 00:17:39,070
+مين بقولنا احنا politics و sport هاي الجزء هنا
+
+231
+00:17:39,070 --> 00:17:44,670
+صحيح؟ فإذا عندك هنا تمانية بتكتب التمانية حطينا
+
+232
+00:17:44,670 --> 00:17:50,890
+التمانية إيش كمان ضال عندى؟ الاطنعش الاطنعش اللي
+
+233
+00:17:50,890 --> 00:17:55,410
+ممكن نتكلم عنها مش فيها مشكلة برضه خلينا نشطبها
+
+234
+00:17:55,410 --> 00:18:03,350
+وفي عندك عشرين don't like any coward فإذا هد بدها
+
+235
+00:18:03,350 --> 00:18:09,130
+تكونبرة حطناها خارجية هي من ال universe of
+
+236
+00:18:09,130 --> 00:18:12,730
+discourse لكن بفضلش ولا نوع من المقالات التلاتة
+
+237
+00:18:12,730 --> 00:18:16,810
+okay حطناها هنا طلعناها لبرة الآن بنرجع أرجو عشان
+
+238
+00:18:16,810 --> 00:18:20,450
+نكمل لسه ماخدنهاش بتهيألي الآن الأربع تاش صار ..
+
+239
+00:18:20,450 --> 00:18:25,150
+في إمكاني أن نتعامل معها؟ عندك أربع تاش أو .. okay
+
+240
+00:18:25,150 --> 00:18:29,930
+أربع تاش و اتطلع .. و هدولة كياش واحدة؟Okay هذه
+
+241
+00:18:29,930 --> 00:18:32,890
+كويسة يمكن لأن فيها تشابهات فدائما ابدأ باللي
+
+242
+00:18:32,890 --> 00:18:36,910
+بيكون تقاطعات فيها لإنه بتكون مساحتها أضيق فبتقدر
+
+243
+00:18:36,910 --> 00:18:40,910
+تتعامل معاها أسرع أربعة عاش هدولة بفضله politics
+
+244
+00:18:40,910 --> 00:18:46,250
+and sport politics and sport تقاطع الأتنين بيعطيني
+
+245
+00:18:46,250 --> 00:18:53,030
+كل هذا في منهم تمانية بالظبط ودحت؟ خلصت فكل هذه
+
+246
+00:18:53,030 --> 00:18:56,670
+المفروض أربعة عاش طب أنا في عندي تمانية منهم بيضل
+
+247
+00:18:56,670 --> 00:19:07,270
+ستة بيضلجزء الستة كويس خلصنا هيك مين الجزء هذا تحت
+
+248
+00:19:07,270 --> 00:19:11,350
+احنا خلصنا هذه برضه ماضلش الا بس نعرف كل واحدة
+
+249
+00:19:11,350 --> 00:19:15,350
+total جديش مع بعضها فممكن ال politics الآن اللي هي
+
+250
+00:19:15,350 --> 00:19:20,190
+واحد و أربعين نتجس منهم التلتة هدولة لأنه ماضلش
+
+251
+00:19:20,190 --> 00:19:23,710
+الا خانة واحدة فخانة واحدة خلاص المتبقي هو علي
+
+252
+00:19:23,710 --> 00:19:29,410
+إلها بطلع عندك جديش واحد و أربعين خمستاشر
+
+253
+00:19:31,930 --> 00:19:35,990
+أه ماشي بتفرجش المهم ان التلاتة كلهم هرجت بتصفوا
+
+254
+00:19:35,990 --> 00:19:41,050
+كلهم ايش بتصفوا واضحت ان كله هيبين خلصناهم الان
+
+255
+00:19:41,050 --> 00:19:45,250
+تبدأ تشوف ايش بده و هيك خلصت الحل اصلا يعني هيك
+
+256
+00:19:45,250 --> 00:19:52,250
+خلص الحل أساسا الحل انتهى تمام هذه خليني أقولكم
+
+257
+00:19:52,250 --> 00:19:55,850
+عدد
+
+258
+00:19:55,850 --> 00:19:57,530
+قليل جدا من الطلاب اللي كان بيحلها
+
+259
+00:20:01,050 --> 00:20:05,660
+كيف؟ ما هي حسب بقى الامتحانحسب بجي الامتحان يعني
+
+260
+00:20:05,660 --> 00:20:09,340
+انت جداش ال weight تبع الامتحان بياخد درجة بياخد
+
+261
+00:20:09,340 --> 00:20:13,680
+درجة بس بتكون عادة درجة كويسة محرزة يعني بتستاهل
+
+262
+00:20:13,680 --> 00:20:19,900
+انك انت تقعد ترسم .. تستاهل ترسم كويسة فالنتائج
+
+263
+00:20:19,900 --> 00:20:23,760
+الآن بعدين انت حققها براحتك okay حققها براحتك مش
+
+264
+00:20:23,760 --> 00:20:26,680
+مشكلة مدام انت وصلت للنقطة هذه كل واحدة بتمسكها و
+
+265
+00:20:26,680 --> 00:20:28,900
+بتقراها أيش اللي بدويا بالظبط و بت .. بتجيب
+
+266
+00:20:28,900 --> 00:20:34,030
+المجموع بتجيب ال totals تبعتهمخمسين اه الاولى هدى
+
+267
+00:20:34,030 --> 00:20:39,550
+او ماني ال people don't like sports بيفضلوش sport
+
+268
+00:20:39,550 --> 00:20:44,050
+هى ال sport مش هيك يعني شيل خد هدوله و اجمع الباقي
+
+269
+00:20:44,050 --> 00:20:50,110
+خمس ايوه خمسين ولا مش خمسين هى هى هى هى دى معها دى
+
+270
+00:20:50,110 --> 00:20:54,130
+خمستاشه مع خمستاشه هى تلاتين و عشرين برا خلاص هى
+
+271
+00:20:54,130 --> 00:20:58,370
+الخمسين و قص على ذلك طيب
+
+272
+00:21:05,640 --> 00:21:10,000
+تمام هى كمان مثال من الأمثلة بتاعة امتحانات كان
+
+273
+00:21:10,000 --> 00:21:12,200
+عليها خمس درجات حتى ينجيبلكوا إياها بالدرجة
+
+274
+00:21:12,200 --> 00:21:21,000
+بتاعتها كيف؟
+
+275
+00:21:21,000 --> 00:21:24,640
+لأ
+
+276
+00:21:24,640 --> 00:21:32,240
+لأ ماكناش من هال .. طب ما هى كل .. كل امتحانات أنا
+
+277
+00:21:32,240 --> 00:21:35,880
+مش جايبلك بس من السنة اللي فاتت من اللي جابليطيب
+
+278
+00:21:35,880 --> 00:21:44,080
+لت a و هي بيعطيك a a b c d e b ال 6b برضه بيعطينها
+
+279
+00:21:44,080 --> 00:21:48,120
+ال 6c given برضه الان كل المطلوب مثلا لما نيجي
+
+280
+00:21:48,120 --> 00:21:53,920
+نطلب a union b طيب هذه إيه علاقة بامتحان سابق
+
+281
+00:21:53,920 --> 00:21:59,520
+وامتحان لاحق السؤال هذه محتاجة صعوبة لهذا الدرجة
+
+282
+00:21:59,520 --> 00:22:02,040
+أنه في امتحان ما تنحلش؟
+
+283
+00:22:04,730 --> 00:22:08,550
+يعني انا .. المنطق أصلا أن هذا مش سؤال أجي أحله
+
+284
+00:22:08,550 --> 00:22:13,970
+هنا على ال .. لكن لأن سؤال امتحان جاي بالكوية أما
+
+285
+00:22:13,970 --> 00:22:16,910
+هو مش منطق أصلا في المحاضرة دلوقت ناني ينحله لأنه
+
+286
+00:22:16,910 --> 00:22:20,030
+أبسط من أنه ينحل مش هيك و رغم ذلك كان جاي في
+
+287
+00:22:20,030 --> 00:22:27,710
+امتحان .. كان جاي في امتحان طيب ايه؟difference B
+
+288
+00:22:27,710 --> 00:22:32,770
+intersection C بدك تجيب B intersection C ماعتقدش
+
+289
+00:22:32,770 --> 00:22:36,830
+كتير صعبة الجثة عشان في الآخر تترحى من ال A فهتقول
+
+290
+00:22:36,830 --> 00:22:45,210
+A وهيلاقي ال B intersection C وخلصنا بتكمل الشغل
+
+291
+00:22:45,210 --> 00:22:49,370
+في اشي تاني كمان اه هنا مثلا في رقم تلاتة في رقم
+
+292
+00:22:49,370 --> 00:22:55,350
+تلاتة مطلوب A intersection CCartesian product C
+
+293
+00:22:55,350 --> 00:22:59,850
+difference B بتجيب هدى لحال هدى لحال وبعدين تعمل
+
+294
+00:22:59,850 --> 00:23:07,050
+أزواج مرتبة من الأولى مع التانية خلصناها من الأولى
+
+295
+00:23:07,050 --> 00:23:13,430
+مع التانية فهدى فعليا تطلع A وC بتكملها بتكملها
+
+296
+00:23:13,430 --> 00:23:21,270
+طيب مطلوب ال cardinality ل ال power of Aاتنين؟ بس
+
+297
+00:23:21,270 --> 00:23:26,370
+خلصنا .. ليش اشخاص خمسة؟ عساس انه ال cardinality
+
+298
+00:23:26,370 --> 00:23:30,230
+لإيه؟ اتنين تتباور ال cardinality لإيه؟ قانون كان
+
+299
+00:23:30,230 --> 00:23:36,550
+موجود و مباشر يعني .. مباشر خلصناها طيب مطلوب ال
+
+300
+00:23:36,550 --> 00:23:43,140
+cardinality لإيه؟ Cartesian product Cعدد العناصر
+
+301
+00:23:43,140 --> 00:23:49,120
+مضروبة في بعض فال cardinality ل A مضروب
+
+302
+00:23:49,120 --> 00:23:57,500
+في عدد ال cardinality ل B ل C A جداش خمسة و C خمسة
+
+303
+00:23:57,500 --> 00:24:01,780
+أه شايفين فيه F هنا على السيف الصبورة على حد
+
+304
+00:24:01,780 --> 00:24:06,080
+الصبورة طيب فإذا خمسة في خمسة المفروض عشان نطلع
+
+305
+00:24:06,080 --> 00:24:10,000
+هنا خمسة و عشرينهذه السؤال كل فرقية بدرجة درجة
+
+306
+00:24:10,000 --> 00:24:13,860
+درجة هي خمس درجات هدول هيك المفروض انه كانوا بس
+
+307
+00:24:13,860 --> 00:24:21,540
+خمس درجات طيب بال functionsال functions قولتلكوا
+
+308
+00:24:21,540 --> 00:24:25,400
+قبل هيك انا نبهتكوا ديروا بالكم هذه مش عملية
+
+309
+00:24:25,400 --> 00:24:30,520
+تبدلية ال composition فعشان نوضح هذا الكلام كنا
+
+310
+00:24:30,520 --> 00:24:37,220
+جايبين هنا مرتين مرة مطلوب g compose f و مرة
+
+311
+00:24:37,220 --> 00:24:43,620
+طالبين f compose gفهذه الحال و هذه لحالها تماما لا
+
+312
+00:24:43,620 --> 00:24:47,460
+هذه لها علاقة بهذه ولا هذه لها علاقة بهذه فبدناش
+
+313
+00:24:47,460 --> 00:24:51,180
+حد يخربطهم عن بعض على بعض يفكر جاب صيغة صيغة معينة
+
+314
+00:24:51,180 --> 00:24:55,480
+أو معادلة معينة ك composition للتنتين و يعوض فيهم
+
+315
+00:24:55,480 --> 00:24:59,220
+مرة بالاتنين و مرة بالتلاتة ويريح راسه لأ نبدأ
+
+316
+00:24:59,220 --> 00:25:04,760
+بحالة حالة الأولى اللي هي G compose Fof اتنين كأنك
+
+317
+00:25:04,760 --> 00:25:11,340
+بتقول G of F of اتنين طريقة بدك تحل فيها اتوكل على
+
+318
+00:25:11,340 --> 00:25:16,020
+الله حل فيها مافيش مشكلة لكن الطريقة اللي اشيك من
+
+319
+00:25:16,020 --> 00:25:20,620
+هيك انك انت تطلعها بصيغة تطلعها صيغة واضحة قدامك ف
+
+320
+00:25:20,620 --> 00:25:28,770
+.. او تكتبها بهذا الشكل فانت هتبدأ منالـ G هي الـ
+
+321
+00:25:28,770 --> 00:25:33,390
+G X تربيع زائد واحد، طب انت عارف ان ال X تربيع
+
+322
+00:25:33,390 --> 00:25:35,470
+اللي هي ال input بتاعة ال G المفروض هي ال output
+
+323
+00:25:35,470 --> 00:25:40,950
+بتاعة F فبتمسك ال F هذه كاملة بتحطها مكان ال X
+
+324
+00:25:40,950 --> 00:25:45,990
+اللي هنا ليش؟
+
+325
+00:25:45,990 --> 00:25:49,770
+لأنه هذه X ال input، F of X ال output، طب ال
+
+326
+00:25:49,770 --> 00:25:52,930
+output إيش بيساوي؟ كل هذا، هذا outputعلى بعضه كامل
+
+327
+00:25:52,930 --> 00:25:56,230
+ال term كله على بعض هو ال output هو output F
+
+328
+00:25:56,230 --> 00:26:03,670
+فبتحطه مكان input G حطناها مكانه و حلها افتحها
+
+329
+00:26:03,670 --> 00:26:07,610
+خلاص لو عوضت في التلاتة المفروض يطلع نفس النتج
+
+330
+00:26:07,610 --> 00:26:15,310
+المفروض يطلع نفس النتج جيد طيب التانية برضه نفس
+
+331
+00:26:15,310 --> 00:26:18,210
+الفكرة بدك تعملها بالطريقة السريعة هيك تعوض على
+
+332
+00:26:18,210 --> 00:26:22,900
+مرحلتين عوض مش هقولك لأبس الطريقة زي ما قلته كل
+
+333
+00:26:22,900 --> 00:26:26,640
+أشياء كل أحسن ليش؟ لأنه بدك تدرب حالك على أساس أن
+
+334
+00:26:26,640 --> 00:26:30,580
+انت بالظبط بدك تبرمج فهدولة يطلعوا معادلة لو انطلب
+
+335
+00:26:30,580 --> 00:26:35,480
+منك أرقام أخرى، ماتقعدش تعود كل مرة في معادلتين،
+
+336
+00:26:35,480 --> 00:26:43,090
+فنفس الفكرة بتعملها في شكل ..F الأول و مكان ال X
+
+337
+00:26:43,090 --> 00:26:48,810
+بتاعة ال F بتحط قيمة G قيمة ال G مكانها و بتفكفك
+
+338
+00:26:48,810 --> 00:26:51,990
+بس المعادلة تبعتك و انتهت لو عوضت فيها ده الكلام
+
+339
+00:26:51,990 --> 00:26:59,510
+هيطلع برضه نفس ال .. الناتج كنتج جيد نتصعد شوية
+
+340
+00:26:59,510 --> 00:27:04,830
+بالأسئلة هاي كمان سؤال كان موجود مطلوب decision
+
+341
+00:27:04,830 --> 00:27:09,130
+منك هل ال F of X تساوي
+
+342
+00:27:10,380 --> 00:27:23,000
+x plus one over x plus two بيجيكشن و لا لأ ليش؟
+
+343
+00:27:23,000 --> 00:27:26,540
+بيجيكشن
+
+344
+00:27:26,540 --> 00:27:32,140
+يعني one to one و one to one طيب هيك فكر فيها one
+
+345
+00:27:32,140 --> 00:27:35,020
+to one و one to one في السؤال الاتنين موجود في
+
+346
+00:27:35,020 --> 00:27:41,540
+الفردان لما نعكس مش هيكون في الدميةصحيح انت لو
+
+347
+00:27:41,540 --> 00:27:43,420
+ماتيش ترسمها حتى لو ماتيش تتطلع على ال behavior
+
+348
+00:27:43,420 --> 00:27:48,120
+تبعها هتلاقيها فعليا تصعودية و بعدين تصعودية
+
+349
+00:27:48,120 --> 00:27:54,440
+المشكلة عند سالب اتنين عند
+
+350
+00:27:54,440 --> 00:28:02,840
+سالب اتنين ايش المشكلة هنا ان هي لها قيمتين يعني
+
+351
+00:28:02,840 --> 00:28:06,740
+هي مش function اصلا يعني عند سالب اتنين هي ليست
+
+352
+00:28:06,740 --> 00:28:11,160
+function فكيف بده اقول ان هي bijection functionوهي
+
+353
+00:28:11,160 --> 00:28:16,220
+اصلا عند سالب اتنين ماهياش function احنا لما
+
+354
+00:28:16,220 --> 00:28:19,520
+اتكلمنا المرة السابقة قولنا ان لأ هي مش function
+
+355
+00:28:19,520 --> 00:28:24,640
+بتنفعش لكن باستثناء سالب اتنين هي تصعودية هنا اه
+
+356
+00:28:24,640 --> 00:28:28,420
+هذه تصعودية هناك كان الواحد على اكس تنازلية تنقصية
+
+357
+00:28:28,420 --> 00:28:33,820
+باستثناء عند صفرلكن لأ إذا بدناش نستثن صفر معناه
+
+358
+00:28:33,820 --> 00:28:38,740
+تقولها بتنفعش أصلا لأن هي مش function أساسا في
+
+359
+00:28:38,740 --> 00:28:43,080
+السالب اتنين هنا فإذا لأ هي مش bijection هي ليست
+
+360
+00:28:43,080 --> 00:28:47,600
+bijection السؤال التاني كان فرع معاها برضه نفس
+
+361
+00:28:47,600 --> 00:28:49,900
+الفكرة عن ال functions اللي كنا نتكلم فكان فرع بيه
+
+362
+00:28:49,900 --> 00:28:54,220
+من نفس السؤال قريب من السؤال اللي جابله بس هذا كان
+
+363
+00:28:54,220 --> 00:28:57,390
+في امتحان و هذا امتحان تانيكل واحد في امتحان نفس
+
+364
+00:28:57,390 --> 00:29:01,530
+الشغل G of X given عندك F of X given عندك ومطلوب F
+
+365
+00:29:01,530 --> 00:29:07,850
+compose G of 2 نفس القالية بدك تعمل مباشر اعمل بدك
+
+366
+00:29:07,850 --> 00:29:12,930
+تعمل معادلة معادلة ال composition اعمل تنتين بظبط
+
+367
+00:29:12,930 --> 00:29:18,190
+132
+
+368
+00:29:18,190 --> 00:29:23,520
+بدك تعود في الاتنين هنا و هنا هتبدأ تعوضك وينفي ال
+
+369
+00:29:23,520 --> 00:29:28,140
+G هتبدأ في G الأول فخدوا بالكم في بعض الطلاب
+
+370
+00:29:28,140 --> 00:29:31,740
+أحيانا تبتغ بغلطه في الجزئية هذه انه ببدأ تعويضه
+
+371
+00:29:31,740 --> 00:29:42,640
+في F فتاخد بالك هي مين ال function لمين تمام نفس
+
+372
+00:29:42,640 --> 00:29:51,000
+الجثة هي في عندنا Ffrom positive real to positive
+
+373
+00:29:51,000 --> 00:29:57,380
+real for f of x three x squared plus two هل هي one
+
+374
+00:29:57,380 --> 00:30:02,940
+to one؟ هل هي on two؟ justify your answer يعني ما
+
+375
+00:30:02,940 --> 00:30:08,800
+تقوليش one to one، تسكت، ليش one to one؟ ما تقوليش
+
+376
+00:30:08,800 --> 00:30:11,930
+لا لا هي مش on two، طب ليش مش on two؟ولا هي بس
+
+377
+00:30:11,930 --> 00:30:15,030
+عينك جابتها مع الورقة اللي جنبك انتوا فخلص هي
+
+378
+00:30:15,030 --> 00:30:20,830
+انتوا خلصنا احكيلي بس ليش؟ كويس نبدأ شوية شوية yes
+
+379
+00:30:20,830 --> 00:30:28,910
+or no yes or no مبدأيا خلينا .. اه اللي هي بدأنا
+
+380
+00:30:28,910 --> 00:30:35,650
+احنا .. هي yes or no هذه شكلها اول شي linear عفوا
+
+381
+00:30:35,650 --> 00:30:36,230
+اللي لأ مش linear
+
+382
+00:30:45,180 --> 00:30:57,840
+بادية من عند اتنين من عند اتنين هي
+
+383
+00:30:57,840 --> 00:31:09,120
+شكلها بس فهي تصاع عودية تصاع عودية صح؟واضح اني
+
+384
+00:31:09,120 --> 00:31:12,700
+مالكاش علاقة بتربيع انا ال domain محدده من الأول
+
+385
+00:31:12,700 --> 00:31:19,620
+positive ال domain من الأساس positive
+
+386
+00:31:19,620 --> 00:31:25,640
+كان اه كان قولت لأ معناته هاني هيك هي ليس
+
+387
+00:31:25,640 --> 00:31:28,540
+التساعدية و بس هي تناقصية في البداية و بعدين
+
+388
+00:31:28,540 --> 00:31:33,180
+تساعدية فإذا ماتنفعش لأ فعليا احنا حددنا من الأول
+
+389
+00:31:33,180 --> 00:31:37,660
+ال function from
+
+390
+00:31:39,950 --> 00:31:44,810
+positive real numbers to positive real numbers
+
+391
+00:31:44,810 --> 00:31:50,250
+كويس، فإذا one to one؟ one to one طيب و on to
+
+392
+00:31:50,250 --> 00:31:55,990
+كمان، ليش on to كمان؟
+
+393
+00:31:55,990 --> 00:32:03,930
+ال code منين؟ من صفر، from R positive فهي من صفر
+
+394
+00:32:03,930 --> 00:32:11,310
+to infinity فعليا actually بتبدأ من اتنينفإذن كل
+
+395
+00:32:11,310 --> 00:32:17,490
+الأجزاء هذه من صفر لإتنين هذه مش موجودة في ال
+
+396
+00:32:17,490 --> 00:32:20,990
+range موجودة في ال code domain أه بس مش موجودة في
+
+397
+00:32:20,990 --> 00:32:26,770
+ال range واضحة؟ احنا من الأساس السؤال يعطيك ال
+
+398
+00:32:26,770 --> 00:32:31,530
+domain و ال code domain يعطيك يهيومين إلى فاحنا
+
+399
+00:32:31,530 --> 00:32:33,910
+ملتزمين بال code domain تعالي تطلع عن ال range لأ
+
+400
+00:32:33,910 --> 00:32:37,880
+ال range مش بدي من صفرال range بيبدأش من الصفر
+
+401
+00:32:37,880 --> 00:32:42,720
+ليش؟ عشان الاتنين المضافة هذه الاتنين الإضافية
+
+402
+00:32:42,720 --> 00:32:49,440
+اللي هنا هذه بس هي اللي عملت الإشكال تمام فإذا كل
+
+403
+00:32:49,440 --> 00:32:54,700
+image هذا بالنسبة لل one to one عشان نقول كل image
+
+404
+00:32:54,700 --> 00:32:57,440
+هنا له pre image واحدة
+
+405
+00:33:00,500 --> 00:33:04,640
+أكيد طبعا مش onto لإن ال domain فعليا positive
+
+406
+00:33:04,640 --> 00:33:12,180
+أكبر من صفر في حين إنه ال rangeأقل من ال code
+
+407
+00:33:12,180 --> 00:33:15,120
+domain أقل من ال code domain ليش لأنه بيبدأ من
+
+408
+00:33:15,120 --> 00:33:18,340
+اتنين كمعادلة كاملة على بعض ال function كلها على
+
+409
+00:33:18,340 --> 00:33:21,440
+بعض لإن بتبدأ من الأتنين فهي من أكبر من الأتنين
+
+410
+00:33:21,440 --> 00:33:27,580
+اتنين فأكبر تمام هاي كمان مثال show that يعني
+
+411
+00:33:27,580 --> 00:33:32,740
+المفروض اثبت اثبت أنه خمسة x plus eight هي
+
+412
+00:33:32,740 --> 00:33:37,340
+bijection وجيبلنا ال inverse تبعها جيب ال inverse
+
+413
+00:33:37,340 --> 00:33:42,700
+تبعهامبدأيا عشان تقول هي فعلا بيجيكشن بدنا نثبت ان
+
+414
+00:33:42,700 --> 00:33:47,460
+هي one to one وبدنا نثبت ان هي one to one فإذا one
+
+415
+00:33:47,460 --> 00:33:51,540
+to one باين لأنه linear انتوا ملاحظين ان هي
+
+416
+00:33:51,540 --> 00:33:56,080
+linear؟ اه عفوا باين
+
+417
+00:33:56,080 --> 00:34:02,260
+ان هي عيش linear هي خطية خطية معناته هي ايات
+
+418
+00:34:02,260 --> 00:34:08,270
+السعودية التنازلية بس هي خطخطو بس تمام واضح ان هي
+
+419
+00:34:08,270 --> 00:34:14,070
+تصعدي لأن كلها positive فالمال تبعها موجب مالها
+
+420
+00:34:14,070 --> 00:34:24,770
+موجب هتكون
+
+421
+00:34:24,770 --> 00:34:36,520
+عند الصفر مثلا هتيجي تمانية و عندf of x بتساوى صفر
+
+422
+00:34:36,520 --> 00:34:42,460
+بتشوف قيمة x هتكون تمانية على خمسة
+
+423
+00:34:42,460 --> 00:34:47,080
+تمانية على خمسة سالب تمانية هتيجي هنا سالب تمانية
+
+424
+00:34:47,080 --> 00:34:53,620
+على خمسة ورسم خط بين التنتين فإذا one to one او
+
+425
+00:34:53,620 --> 00:34:59,180
+one to one one to one one to one ليش؟ لأنه ممتدة
+
+426
+00:34:59,180 --> 00:35:05,560
+من minus infinity to positive infinityكويس فهي
+
+427
+00:35:05,560 --> 00:35:09,940
+مافيش مشكلة في هذا الجزء تماما اطلاقا كل من الرسم
+
+428
+00:35:09,940 --> 00:35:15,040
+باين ان كل image هي جاية من one preimage من one
+
+429
+00:35:15,040 --> 00:35:19,160
+preimage وهذا الكلام ينطبق على كل ال linears كل
+
+430
+00:35:19,160 --> 00:35:22,260
+المعادلات الخطية ينطبق عليه نفس الكلمة لان هي خط
+
+431
+00:35:22,260 --> 00:35:29,460
+خلاص الان كل preimage من ال domain له قيمة في ال
+
+432
+00:35:29,460 --> 00:35:34,720
+code domain يعني معناه ذلك انه في ال rangeكله له
+
+433
+00:35:34,720 --> 00:35:42,440
+range كل قيمة على ال X axis لها صورة على ال Y axis
+
+434
+00:35:42,440 --> 00:35:48,500
+معناه ذلك ان ال range مغطي كل ال code domain ال
+
+435
+00:35:48,500 --> 00:35:51,280
+code domain او ال Y axis خلاص نبحث عن هذه هي
+
+436
+00:35:51,280 --> 00:35:58,160
+موجودة تمام الان ال inverse كيف نجيب ال inverse
+
+437
+00:35:58,160 --> 00:35:58,580
+تبعها
+
+438
+00:36:07,930 --> 00:36:11,390
+جيب هذه مكانها دي جيب هذه مكانها دي فبتصير X
+
+439
+00:36:11,390 --> 00:36:17,630
+بتساوي خمسة Y خلّيني أقول زائد تمانية بدك تجيب Y
+
+440
+00:36:17,630 --> 00:36:22,110
+بدك تجيب Y فهي ده هتنجوله على ناحية التانية على
+
+441
+00:36:22,110 --> 00:36:31,950
+خمسة فبتصير F of Y بهذا الشكل يعني F of هنا Y خلاص
+
+442
+00:36:31,950 --> 00:36:35,210
+بتصير X بتصير inverse
+
+443
+00:36:37,880 --> 00:36:41,960
+ال inverse طبعا طيب كيف تعمل check اعمل
+
+444
+00:36:41,960 --> 00:36:49,960
+composition مش المفروض if compose يساوي واحد اللي
+
+445
+00:36:49,960 --> 00:36:55,300
+هي ال identity ايه كان المفروض و نفس الكلام if to
+
+446
+00:36:55,300 --> 00:36:57,480
+the power minus one compose if المفروض برضه
+
+447
+00:36:57,480 --> 00:37:01,820
+identity نفس الجثة طيب بنفس اللي اللي طبعا عملناها
+
+448
+00:37:01,820 --> 00:37:05,940
+لو عملنا نفس الكلام هل فعلا مظبط هذا ال term هذا
+
+449
+00:37:05,940 --> 00:37:07,320
+يكون مكان x
+
+450
+00:37:10,550 --> 00:37:13,550
+خمسة مع الخمسة و minus تمانية مع تمانية فبطلع واحد
+
+451
+00:37:13,550 --> 00:37:17,930
+و العكس صحيح لو هذه ك term هو اللي حطته مكان x
+
+452
+00:37:17,930 --> 00:37:21,190
+تمانية
+
+453
+00:37:21,190 --> 00:37:23,270
+هتروح مع التمانية و الخمسة مع الخمسة و بعدين بتضل
+
+454
+00:37:23,270 --> 00:37:30,610
+x فبضل برضه one لواحد فإذن مظبوط فإذن خلاص صح فإذن
+
+455
+00:37:30,610 --> 00:37:35,270
+صحيح طيب من الحاجات المهمة اللي شفناها في هذا
+
+456
+00:37:35,270 --> 00:37:36,590
+الموضوع أنه
+
+457
+00:37:39,040 --> 00:37:45,860
+هنا اعتبروا هي نفسها inverse و خلاص انا مافهمتش
+
+458
+00:37:45,860 --> 00:37:49,920
+طبعا كيف ممكن حدا يفكر ان هي نفسها تكون inverse
+
+459
+00:37:49,920 --> 00:37:53,460
+لنفسها و خلاص ماعرفتش كيف المهم انه اكيد هتكون غلط
+
+460
+00:37:53,460 --> 00:37:57,440
+ال inverse بتعمله بهذا الشكل بتعكس X مع Y و بتشوف
+
+461
+00:37:57,440 --> 00:38:01,560
+بدلالة X نفس الأشياء تمام
+
+462
+00:38:04,850 --> 00:38:15,630
+Okay فهي قيمة ال term اللي قلنا عكس
+
+463
+00:38:15,630 --> 00:38:21,510
+عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس
+
+464
+00:38:21,510 --> 00:38:21,750
+عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس
+
+465
+00:38:21,750 --> 00:38:21,910
+عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس
+
+466
+00:38:21,910 --> 00:38:22,130
+عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس
+
+467
+00:38:22,130 --> 00:38:25,630
+عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس عكس
+
+468
+00:38:25,630 --> 00:38:32,310
+عكس عكس عكس عكس عكس عكس عكس عكس عكس
+
+469
+00:38:37,370 --> 00:38:41,870
+عوض النقاط عرفك شوف
+
+470
+00:38:41,870 --> 00:38:44,790
+بده يعوض النقاط يعوض النقاط بس الطريقة الأشياء ان
+
+471
+00:38:44,790 --> 00:38:47,070
+احنا نستخدم ال composition و أريح انت بده زي ما
+
+472
+00:38:47,070 --> 00:38:52,390
+قلتلكوا تقومش يقولنا عوض بنقطة انت حر عوض عوض في
+
+473
+00:38:52,390 --> 00:38:54,850
+النهاية انا ايش اللي بهمني انا اللي طالب منك ال
+
+474
+00:38:54,850 --> 00:39:01,170
+inverse انت كيف عملت check انه صح هذه سغلك انت كيف
+
+475
+00:39:01,170 --> 00:39:06,170
+تتأكد ان إجابتك صح شوف الطريقة اللي بتناسبكأما
+
+476
+00:39:06,170 --> 00:39:10,190
+السؤال كان طالب inverse okay جبنا ال inverse الآن
+
+477
+00:39:10,190 --> 00:39:13,830
+ماكملاش احنا بعد هيك لكن قلنا عشان تعمل check تكون
+
+478
+00:39:13,830 --> 00:39:17,450
+مطمن بدك تعمل composition للمعادلة هذه مع المعادلة
+
+479
+00:39:17,450 --> 00:39:21,030
+الأصلية المفروض يطلع واحد أو الأصلية معاها يطلع
+
+480
+00:39:21,030 --> 00:39:24,130
+برضه واحد ليش؟ لأنه إذا كان في إلها inverse فمعنى
+
+481
+00:39:24,130 --> 00:39:29,180
+ذلك إنه ال composition بصير تبادل فيش مشكلةمين جاب
+
+482
+00:39:29,180 --> 00:39:33,240
+المين مش هتفرج، هيعطيني identity في النهاية ال
+
+483
+00:39:33,240 --> 00:39:36,400
+identity انت بدك تعمل لأ و الله بتعمل check هنا
+
+484
+00:39:36,400 --> 00:39:40,680
+على المعادلات فهيكوا يعني مش إشكال مش إشكال طيب
+
+485
+00:39:40,680 --> 00:39:43,300
+السؤال هنا أنا شايف بس عرف ليش هو ال one two عرف
+
+486
+00:39:43,300 --> 00:39:47,140
+ال one to one طيب بس يعني هذا بالذات يعتبر طيب
+
+487
+00:39:47,140 --> 00:39:54,470
+صحيح انت مش رسمتها الرسمة واضحة ولا مش واضحة؟واضح
+
+488
+00:39:54,470 --> 00:39:57,890
+جدا انت بدك تزيد اكتر تقول والله اتفهم انك انت
+
+489
+00:39:57,890 --> 00:40:01,250
+فاهم رياضية اكتر تقولي والله معروفة ان كل ال
+
+490
+00:40:01,250 --> 00:40:07,650
+linear هي one to one هقولك ما مظبوط yes كل ال
+
+491
+00:40:07,650 --> 00:40:13,550
+linear مدام هي linear بهذا الشكل فهي بتغطي اذا
+
+492
+00:40:13,550 --> 00:40:17,490
+كانت ليست constant لان ال constant الوحيد اللي
+
+493
+00:40:17,490 --> 00:40:22,700
+ساعتها بتقدرش تقول انه هيغطي ال code mainصحيح؟
+
+494
+00:40:22,700 --> 00:40:26,960
+فإلها mail ال mail لا يساوي صفر، مدام ال mail لا
+
+495
+00:40:26,960 --> 00:40:30,620
+يساوي صفر فأكيد هيصل من minus infinity to infinity
+
+496
+00:40:30,620 --> 00:40:34,600
+الحالة الوحيدة أنه يكون linear ويكون بهذا الشكل
+
+497
+00:40:34,600 --> 00:40:42,060
+فهو مغطاش من minus infinity to infinity أما إذا
+
+498
+00:40:42,060 --> 00:40:48,040
+كان ال mail تبعه موجب أو سالب، بغض النظر جديش يعني
+
+499
+00:40:48,040 --> 00:40:52,530
+أقولك حتى لو افترضنا أن ال mail يدوبميل بسيط جدا
+
+500
+00:40:52,530 --> 00:40:58,530
+بهذا الشكل مثلا صحيح في ال infinity هيكون وصل هنا
+
+501
+00:40:58,530 --> 00:41:01,870
+ال infinity في ال minus infinity هيكون وصل معاك
+
+502
+00:41:01,870 --> 00:41:07,430
+هنا ال minus infinity فغطالك ال ال code main ك
+
+503
+00:41:07,430 --> 00:41:11,450
+range غطى ال code main تمام فال linear سهلة ال
+
+504
+00:41:11,450 --> 00:41:14,670
+linear سهلة الأهم أنها بس ما تكونش الميل تبقى 0
+
+505
+00:41:15,750 --> 00:41:19,090
+الميل تبقى حزيره لأ هنا فيه مشكلة لأنه مش .. لأ
+
+506
+00:41:19,090 --> 00:41:21,230
+function عادي function لأ لأ function عادية جدا
+
+507
+00:41:21,230 --> 00:41:25,850
+انت هيك معناته لغاية ان كل ال DC power ال DC power
+
+508
+00:41:25,850 --> 00:41:30,870
+طب ما هي function DC مش هيك مش ال generator اللي
+
+509
+00:41:30,870 --> 00:41:34,670
+بيطلعلك DC البطارية البطارية العادية هذه البطارية
+
+510
+00:41:34,670 --> 00:41:37,930
+الأصبع طب ما هي ال DC هذه المشكلة معناته انت طلعت
+
+511
+00:41:37,930 --> 00:41:45,680
+خارج العلم بتاعتنا تمام ف ..هيك أخدنا مجموعة مسائل
+
+512
+00:41:45,680 --> 00:41:50,440
+هنخلي مجموعة تانية برضه مع ال matrices للمرة
+
+513
+00:41:50,440 --> 00:41:53,320
+القادمة ان شاء الله تعالى الأسبوع القادم هناخد ال
+
+514
+00:41:53,320 --> 00:41:58,020
+matrices و هنبدأ في ال algorithms هنبدأ نتعلم code
+
+515
+00:41:58,020 --> 00:42:01,180
+جديد اللي هو ال pseudocodeال code المتعرف عليه
+
+516
+00:42:01,180 --> 00:42:07,380
+كلكم بتعرفوا انه انت ممكن تشتغل Java انا اشتغل C++
+
+517
+00:42:07,380 --> 00:42:11,800
+بس في النهاية المفروض نفهم بعض المفروض ان نفهم بعض
+
+518
+00:42:11,800 --> 00:42:15,740
+في ال pseudocode كويس فلازم يكون في code وصفي اللي
+
+519
+00:42:15,740 --> 00:42:18,660
+هو ال pseudocode و اللي المفروض تشتغله عليه الاصل
+
+520
+00:42:18,660 --> 00:42:22,120
+هي تشتغله عليه في ال data structure بالظبط فهنتكلم
+
+521
+00:42:22,120 --> 00:42:24,260
+عنه يلا يعطيكوا العفو
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a2aca5ff7adca659539fa52373ea2964ee98e537
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM.srt
@@ -0,0 +1,1974 @@
+1
+00:00:04,880 --> 00:00:07,360
+بسم الله الرحمن الرحيم. هنبدأ اليوم يا شباب إن شاء
+
+2
+00:00:07,360 --> 00:00:11,160
+الله تعالى. نكمل الجزء المتبقي في الـ graph في موضوع
+
+3
+00:00:11,160 --> 00:00:14,080
+الـ graph واللي اتكلمنا فيه المرة الماضية يمكن
+
+4
+00:00:14,080 --> 00:00:17,900
+أشرنا إلى بعض أنواع الـ graphs، واتكلمنا عن degrees و
+
+5
+00:00:17,900 --> 00:00:20,680
+عرفنا شيئًا عن degrees، وشوية terminology تعرّفنا
+
+6
+00:00:20,680 --> 00:00:24,840
+عنها المرة الماضية. اليوم هنتكلم عن الـ
+
+7
+00:00:24,840 --> 00:00:28,180
+representation للـ graph. كيف أنا بقدر أمثل الـ graph
+
+8
+00:00:28,180 --> 00:00:34,120
+والـ isomorphism. الـ isomorphism ببساطة أن هو أنك
+
+9
+00:00:34,120 --> 00:00:36,580
+يكون في عندك two graphs بغض النظر أن هم
+
+10
+00:00:36,580 --> 00:00:43,060
+identical شكلاً، كأنهم زي بعض، لكن هم فعلياً تماماً زي
+
+11
+00:00:43,060 --> 00:00:46,300
+بعض، لكن يمكن أنت بتكون الـ nodes مغير أماكنهم، مش
+
+12
+00:00:46,300 --> 00:00:49,500
+أكثر من هيك. عملية تغيير أماكن، لا أكثر ولا أقل
+
+13
+00:00:49,500 --> 00:00:52,140
+وبتيجي أسئلة كتير الحقيقة في الـ IQ test على
+
+14
+00:00:52,140 --> 00:00:55,580
+الحاجات هذه، على الحاجات تلك، اللي هو two graphs
+
+15
+00:00:55,580 --> 00:00:59,050
+وبيقول لك: هل هما اتنين identical ولا لأ؟ هم بيكونوا
+
+16
+00:00:59,050 --> 00:01:02,070
+فعلاً identical، بس المظهر اللي عامله يغيّر ذلك.
+
+17
+00:01:02,070 --> 00:01:05,390
+طب كيف نعمل test على الـ isomorphism هذه؟ أو أن
+
+18
+00:01:05,390 --> 00:01:08,870
+واحدة منهم isomorphic للتانية؟ هنتكلم عنها في
+
+19
+00:01:08,870 --> 00:01:11,730
+موضوعنا اليوم في الـ representation، الـ adjacency
+
+20
+00:01:11,730 --> 00:01:16,870
+lists، الـ adjacency matrices، والـ incidence
+
+21
+00:01:16,870 --> 00:01:19,790
+matrices. هم هدول الثلاث أنواع اللي هنتكلم عنهم
+
+22
+00:01:19,790 --> 00:01:23,430
+اليوم في تمثيل أي graph. فبالنسبة للـ adjacency
+
+23
+00:01:23,430 --> 00:01:29,240
+lists فهي واضحة: قائمة المجاورات أو المتجاورات. بكل
+
+24
+00:01:29,240 --> 00:01:34,400
+بساطة، كل واحدة من الـ vertices تبعتك بتحطهم في
+
+25
+00:01:34,400 --> 00:01:40,280
+column. أولها قدام كل واحدة منهم، هيصبح الـ adjacent
+
+26
+00:01:40,280 --> 00:01:47,180
+vertices اللي خاصة في كل vertex منهم. فتتكلم عن A
+
+27
+00:01:47,180 --> 00:01:52,480
+مثلاً، هي مجاورة لـ B وC، فبتحط قدامها B وC. انتهى. B
+
+28
+00:01:52,480 --> 00:02:01,840
+لـ A وC وE وF، وهكذا. خلّيني أشوف D مثلاً، isolated.
+
+29
+00:02:01,840 --> 00:02:05,660
+isolated معناته zero في الشاشة قدامها، أو هي مش
+
+30
+00:02:05,660 --> 00:02:09,860
+مجاورة لأي vertex أخرى. فالـ adjacency هنا مش
+
+31
+00:02:09,860 --> 00:02:14,000
+متحققة لها، فهي فعلياً zero. وهكذا. هذا تمثيل أولي
+
+32
+00:02:14,000 --> 00:02:18,360
+بحيث أنك أنت بتقدر من الجدول هذا، لو الرسم الـ graph
+
+33
+00:02:18,360 --> 00:02:22,700
+نفسه مش موجود، أنت بتقدر ترسمه تاني. تقدر بكل بساطة
+
+34
+00:02:22,700 --> 00:02:27,420
+ترسمه من خلال الـ adjacency lists اللي قدامك، اللي
+
+35
+00:02:27,420 --> 00:02:31,340
+عندك قدامك. طيب، بالنسبة للـ directed، في الـ directed
+
+36
+00:02:31,340 --> 00:02:34,620
+الأمور بتختلف شوية. في الـ directed، إحنا هنصير نتكلم عن
+
+37
+00:02:34,620 --> 00:02:40,980
+إيش الـ edges، الـ edges، أو اللي طالعة من الـ vertex
+
+38
+00:02:40,980 --> 00:02:43,700
+اللي بنتكلم عنها. فإذا برضه بالنسبة للـ adjacency
+
+39
+00:02:43,700 --> 00:02:51,360
+lists، بنحطها زي ما هي. إيه هاي إيه متصلة بمين، مش مين
+
+40
+00:02:51,360 --> 00:02:56,460
+متصل فيها. هي متصلة مع مين؟ فهي adjacent to مين؟
+
+41
+00:02:59,190 --> 00:03:04,530
+ما هي بتصير للعنصر الثاني، يعني هيها B هنا هي مش
+
+42
+00:03:04,530 --> 00:03:10,430
+متصلة بـ A. لاحظ A هي اللي متصلة بـ B. B غير متصلة في
+
+43
+00:03:10,430 --> 00:03:15,470
+A. فلاحظ، تعالَ هنا A هي متصلة في B، لكن B مش متصلة
+
+44
+00:03:15,470 --> 00:03:22,110
+مع A بالظبط. فأنت هنا بتتكلم عن بدايات، البدايات هي
+
+45
+00:03:22,110 --> 00:03:26,450
+دائماً الـ vertex اللي بتمثل بالنسبة لها. فلو مش موجود
+
+46
+00:03:26,450 --> 00:03:29,970
+الرسم هذا، بتقدر ترجع تستنتج الرسم نفسه من مجموعة
+
+47
+00:03:29,970 --> 00:03:35,450
+أو من الـ adjacency lists اللي قدامك. تمام؟ فهي بكل
+
+48
+00:03:35,450 --> 00:03:41,070
+بكل بساطة، تعالَ تطلع، هتلاقي أن مثلاً حاجة زي الـ C، C
+
+49
+00:03:41,070 --> 00:03:46,330
+مع C، فأنت بتعرف أن هذه self loop. هذه نعرفها على طول
+
+50
+00:03:46,330 --> 00:03:50,710
+أنه معناته فيها مثل self-loop. الـ B نفس الكلام، ففي
+
+51
+00:03:50,710 --> 00:03:54,850
+عندك فعلاً self-loop لكل vertex من الـ two vertices
+
+52
+00:03:54,850 --> 00:03:59,650
+هذول، تمام؟ فهذه بطريقة مبسطة، كيف ممكن تعمل
+
+53
+00:03:59,650 --> 00:04:04,690
+التمثيل الـ adjacency. اتفضل. تختلف self-loop يعني
+
+54
+00:04:04,690 --> 00:04:06,870
+أنا للجمهور الفاضل، ما حكيت لك أنه مش هتفرق من
+
+55
+00:04:06,870 --> 00:04:09,690
+اتجاه، هتنقطع من نفسه وترجع لنفسه، بس أنا لو أصبح
+
+56
+00:04:09,690 --> 00:04:13,950
+تعاكسه، الجدول مش هيديني اتجاه، ليش؟ مش هيعطيك
+
+57
+00:04:13,950 --> 00:04:17,210
+الاتجاه. أنت هالوقت تفرق معاك هي أي C اللي ميعطي
+
+58
+00:04:17,210 --> 00:04:22,530
+للتانية، يعني أنا رسمته هيك ولا أنا رسمته هيك؟ لأ
+
+59
+00:04:22,530 --> 00:04:26,710
+اتجاه في الـ different vertices، لـ different
+
+60
+00:04:26,710 --> 00:04:30,470
+vertices بختلف الاتجاه، اه. يعني بمعنى هذا اتجاه A
+
+61
+00:04:30,470 --> 00:04:35,750
+وB هو اتجاه واحد. فهذه في الاتجاه العكس مش موجودة.
+
+62
+00:04:35,750 --> 00:04:42,770
+لكن من B لنفسها، ما هي من B لنفسها. عرفت؟ فأنا هنا
+
+63
+00:04:42,770 --> 00:04:45,170
+مافيش multigraph، لأ، أنا ما أعرفش... ما... ما أعتقدش
+
+64
+00:04:45,170 --> 00:04:47,890
+أنه ليه الموضوع علاقة بالـ multigraph، لأ، مالوش
+
+65
+00:04:47,890 --> 00:04:49,870
+علاقة بالـ multigraph. هنا أنت في عندك هنا
+
+66
+00:04:49,870 --> 00:04:53,630
+multigraph فيه... فيه mult... فيه المفروض أنه هنا
+
+67
+00:04:53,630 --> 00:04:58,330
+لو في multigraph، بتمثل، بس في الحالة هذه بده يكتب
+
+68
+00:04:58,330 --> 00:05:01,850
+اتنين بيه، بده يكتب قدامك اتنين بيه، لو في
+
+69
+00:05:01,850 --> 00:05:05,450
+multigraph. لو في عندك الـ... جثة الـ multigraph هنا
+
+70
+00:05:05,450 --> 00:05:06,710
+متهيئة مش متمثلة في الرسم.
+
+71
+00:05:09,540 --> 00:05:13,840
+عارف، اه، بس بدك توضّح أنه جدّيش، يعني ممكن ساعتها لو
+
+72
+00:05:13,840 --> 00:05:16,940
+افترضنا، خلينا نحن نحط من هنا افتراضية، هاي حطّ
+
+73
+00:05:16,940 --> 00:05:23,140
+بتقول فيها، هاي كمان بهذا الشكل، فبينطلع لمين؟ لـ E، لـ E
+
+74
+00:05:23,140 --> 00:05:29,100
+فإذا هنا يا بكتب E، يا بنكتب اتنين E. كويس؟
+
+75
+00:05:29,100 --> 00:05:33,440
+أنت يعني فتحتَ موضوع، عشان يبين معانا أن والله في
+
+76
+00:05:33,440 --> 00:05:35,940
+multi-graph. إذا في multi-graph، لأن فعلاً المثال
+
+77
+00:05:35,940 --> 00:05:38,660
+ما فيهوش multi-graph. إذا في multi-graph، يا أما بتعمل
+
+78
+00:05:38,660 --> 00:05:44,960
+كمان E تانية، أو بتعمل اتنين E، حسب جدّيش عدد الـ
+
+79
+00:05:44,960 --> 00:05:51,680
+edges اللي رايحة من A لـ E، من A لـ E. تمام؟ طيب، الـ
+
+80
+00:05:51,680 --> 00:05:55,980
+adjacency matrices، هو مصفوفات المجاورة، مصفوفات
+
+81
+00:05:55,980 --> 00:05:59,400
+المجاورة كتير أبسط، كتير كتير أبسط. كل ما أنا
+
+82
+00:05:59,400 --> 00:06:03,600
+محتاجه أن أعمل matrix، الـ matrix هذا، الـ rows
+
+83
+00:06:03,600 --> 00:06:08,860
+تبعتها، أو الـ columns نفسهم، هي مجموعة الـ vertices،
+
+84
+00:06:08,860 --> 00:06:12,180
+مجموعة الـ vertices. هنقول والله الـ node الأولى
+
+85
+00:06:12,180 --> 00:06:15,120
+الثانية، الثالثة، وهكذا. الأول، الـ node الأولى
+
+86
+00:06:15,120 --> 00:06:18,640
+الثانية، الثالثة، وهكذا. إذا كان في connection
+
+87
+00:06:18,640 --> 00:06:23,600
+between من الثانية للأولى، بنحط قدامها هنا واحد.
+
+88
+00:06:23,600 --> 00:06:29,480
+مافيش، صفر، zero، أو صفر. خلاص بكل بساطة. فإذا أن هي
+
+89
+00:06:29,480 --> 00:06:35,900
+عبارة عن matrix. الـ matrix ها دي، العنصر I وJ بيكون
+
+90
+00:06:35,900 --> 00:06:39,620
+واحد، إذا في فعلاً في connection between الـ vertex I
+
+91
+00:06:39,620 --> 00:06:45,040
+to vertex J. طبعاً في الـ undirected، كلاهما في نفس
+
+92
+00:06:45,040 --> 00:06:51,720
+الاتجاه. فمن I لـ J، ومن J لـ I، فكلاهما بيمشي الحالة.
+
+93
+00:06:51,720 --> 00:06:53,900
+في الـ directed شوية بتختلف الأمور. في الـ directed
+
+94
+00:06:53,900 --> 00:06:57,580
+زي ما هتشوف، هتختلف معانا شوية. otherwise، بنحطها
+
+95
+00:06:57,580 --> 00:07:02,500
+zero، معناته مافيش أصلاً edge between them. هاي مثال
+
+96
+00:07:05,750 --> 00:07:11,030
+هي عندك مثل A، B، C، وD بهذا الشكل، وبدنا نرسم أو
+
+97
+00:07:11,030 --> 00:07:15,290
+نمثل الشكل اللي قدامنا، أو بعد ما نرسمه، بعد ما ناخد
+
+98
+00:07:15,290 --> 00:07:18,410
+الـ matrix تبعتنا. من الـ matrix بدي ارجع اخذ الرسم.
+
+99
+00:07:18,410 --> 00:07:22,570
+فالمفروض representation، يعني المفروض العكس صحيح: من
+
+100
+00:07:22,570 --> 00:07:27,930
+الـ matrix أقدر ارجع ارسم الـ graph نفسه. تمام؟ فالآن
+
+101
+00:07:27,930 --> 00:07:29,610
+بكل بساطة، هنعمل نفس القايمة.
+
+102
+00:07:36,480 --> 00:07:41,420
+from A to A، مافيش self loop، فإذا zero. طيب، A متصلة
+
+103
+00:07:41,420 --> 00:07:46,120
+بالباقي، فإذا متصلة مع B واحد، مع C واحد، مع D واحد.
+
+104
+00:07:46,120 --> 00:07:50,120
+بهذا الشكل، تمام؟ الـ B نفس الجثة، الـ B متصلة مع مين؟
+
+105
+00:07:50,120 --> 00:07:54,580
+مع A وD، نفس
+
+106
+00:07:54,580 --> 00:08:01,080
+الكلام. D متصلة مع الكل، أما مع نفسها لأ. بعد ما
+
+107
+00:08:01,080 --> 00:08:01,660
+ترسمها.
+
+108
+00:08:05,480 --> 00:08:09,400
+لأ، هذه بتصير symmetric، اه، symmetric. فهذه أول
+
+109
+00:08:09,400 --> 00:08:15,960
+ملاحظة، أن في الـ adjacency matrices بتكون دائماً
+
+110
+00:08:15,960 --> 00:08:22,080
+symmetric، مادام undirected. بالظبط، مادام undirected.
+
+111
+00:08:22,080 --> 00:08:25,840
+فهي دائماً symmetric، بس أهم شغلة أن هي تكون
+
+112
+00:08:25,840 --> 00:08:32,290
+undirected، وبفرق undirected. إذا كان عندي multi
+
+113
+00:08:32,290 --> 00:08:35,110
+-path ولا لأ، أو multi-graph ولا لأ. حتى في الـ multi
+
+114
+00:08:35,110 --> 00:08:38,790
+-graph مش هتفرق. المهم إن هي undirected، ليش؟ لأنه
+
+115
+00:08:38,790 --> 00:08:42,130
+إذا كان بدي أقول والله بين الـ C والـ B فيه اتنين
+
+116
+00:08:42,130 --> 00:08:48,470
+نفترض، معناته هي نفسها بين الـ B والـ C هتكون برضه
+
+117
+00:08:48,470 --> 00:08:52,210
+اتنين. هذه undirected. فإذا الشرط هنا، عشان أقول إن
+
+118
+00:08:52,210 --> 00:08:57,670
+هي symmetric، هي جزئية الـ undirected. تمام؟ بتقلي
+
+119
+00:08:57,670 --> 00:09:04,670
+واضح، حتى ما فيهوش كتير غلبة التنفيذ هذا. okay.
+
+120
+00:09:04,670 --> 00:09:07,790
+الآن في الـ multigraph، لما يكون في عندك multigraph
+
+121
+00:09:07,790 --> 00:09:12,050
+زي ما قلنا بقى، الـ one بنستعيض عن الـ one، zero لأ،
+
+122
+00:09:12,050 --> 00:09:14,590
+بنستعيض عنه بالـ natural number، الـ natural number
+
+123
+00:09:14,590 --> 00:09:18,910
+هذه، أو بنحط مكانها قيمة، بالظبط عدد الـ edges.
+
+124
+00:09:19,890 --> 00:09:23,670
+فبنحط قيمة الـ edges نفسها، بدل ما نحط واحد، لمجرد أن
+
+125
+00:09:23,670 --> 00:09:27,070
+الواحد دي دلالة على وجود relation، أو دلالة على
+
+126
+00:09:27,070 --> 00:09:31,270
+وجود edge، لأ، بنحطها كـ natural number. زي المثال
+
+127
+00:09:31,270 --> 00:09:35,870
+برضه اللي هنعدّل عليه بهذا الشكل، عشان يصبح عندي
+
+128
+00:09:35,870 --> 00:09:44,550
+برضه نفس الشيء، a, b, c, d، a, b, c, d. خليني أنا آخذ مثلاً
+
+129
+00:09:44,550 --> 00:09:46,850
+C وD.
+
+130
+00:09:49,240 --> 00:09:56,040
+بين C وD فيه ثلاثة. طيب، بين D وC برضه ثلاثة. فهي D، C
+
+131
+00:09:56,040 --> 00:10:04,640
+وهي C، D. طيب، حافظنا برضه على نفس الـ symmetric، على
+
+132
+00:10:04,640 --> 00:10:07,960
+نفس الـ symmetric، رغم أنه موجود عندك مثلاً B وB
+
+133
+00:10:10,330 --> 00:10:14,410
+self loop، بس مش هتفرق معاك، ليش؟ لإنه لما تعكس
+
+134
+00:10:14,410 --> 00:10:18,430
+الصفوف أعمدة، أو لاعمدة، الصفوف، هتظل الـ matrix زي ما
+
+135
+00:10:18,430 --> 00:10:23,090
+هي. فإذا هي symmetric فعلياً كـ matrix، مادام
+
+136
+00:10:23,090 --> 00:10:29,130
+undirected. مفروض يكون كاتب لك اه، undirected. مادام
+
+137
+00:10:29,130 --> 00:10:34,570
+إيش؟ undirected. تمام؟ بسيطة
+
+138
+00:10:34,570 --> 00:10:41,190
+الفكرة. طيب، الآن في الـ incidence matrix، في الـ
+
+139
+00:10:41,190 --> 00:10:45,970
+incidence matrix، بكل بساطة أنا بحطّش vertices مع
+
+140
+00:10:45,970 --> 00:10:52,730
+vertices، بنحط الـ vertices كـ rows، والـ edges بنحطهم
+
+141
+00:10:52,730 --> 00:11:01,130
+columns. بحيث أن العلاقة بينهم، مين منهم بيسقط هذا الـ
+
+142
+00:11:01,130 --> 00:11:04,410
+edge من الـ vertices اللي موجودة قدامنا، مين منهم
+
+143
+00:11:05,740 --> 00:11:10,280
+بيطلع الـ edge اللي قدامه. فالـ relation الآن هي مش
+
+144
+00:11:10,280 --> 00:11:13,780
+adjacency. adjacency. لما كنت بتكلم عن vertices
+
+145
+00:11:13,780 --> 00:11:16,860
+موجودة، بمعنى أن عندي vertex هنا وvertex هنا.
+
+146
+00:11:16,860 --> 00:11:20,560
+فالعلاقة بينهم كانت مين اللي بيجاور الثاني؟ لكن لما
+
+147
+00:11:20,560 --> 00:11:25,900
+بقول العلاقة الآن بين vertex وخط، link، فهو معنى
+
+148
+00:11:25,900 --> 00:11:29,860
+ذلك، أنه مين من الـ vertices هدول بيطلع الـ link هذا؟
+
+149
+00:11:31,210 --> 00:11:35,450
+فـ incidence، مين هو اللي بيسقط الـ... الـ... الـ edge
+
+150
+00:11:35,450 --> 00:11:40,570
+هذه؟ فأصبحت الـ relation هنا incidence matrix. فصرت
+
+151
+00:11:40,570 --> 00:11:43,430
+الـ incidence هي العلاقة، هي الـ relation اللي بدي
+
+152
+00:11:43,430 --> 00:11:47,950
+أحسبها، موجودة ولا غير موجودة. إذا كانوا موجودة، فإذا
+
+153
+00:11:47,950 --> 00:11:54,970
+العنصر داخل الـ matrix، والعنصر I vertex، الـ vertex I
+
+154
+00:11:54,970 --> 00:12:00,450
+والـ edge J. إذا فعلاً هم مرتبطين في بعض، بمعنى أن الـ
+
+155
+00:12:00,450 --> 00:12:07,960
+edge J هو صادر من الـ vertex I، فبنحط مقابلهم 1، على
+
+156
+00:12:07,960 --> 00:12:11,000
+تقاطعهم في الـ matrix، نقطة تقاطعهم في الـ matrix
+
+157
+00:12:11,000 --> 00:12:13,800
+بنحط عليها واحد، زي ما هنشوف في المثال. otherwise،
+
+158
+00:12:13,800 --> 00:12:16,720
+إذا ما هم مش علاقة ببعض، لأ، الـ edge هذه مالهاش
+
+159
+00:12:16,720 --> 00:12:24,340
+علاقة بالـ... بالـ vertex، بنحطها zero. complement، إيش
+
+160
+00:12:24,340 --> 00:12:27,440
+دخل complement هنا؟ مع عدد الـ edges اللي مش موجودة؟
+
+161
+00:12:28,710 --> 00:12:32,330
+لأ، إحنا ما نعنيش في اللي مش موجودة، هنا الـ... الـ...
+
+162
+00:12:32,330 --> 00:12:35,130
+الـ complement هي الـ zeros. بحطّ، أصبح، إحنا هي kick.
+
+163
+00:12:35,130 --> 00:12:37,790
+بنحطها zero. يعني بمعنى، إذا كان مش موجود فهو zero،
+
+164
+00:12:37,790 --> 00:12:43,370
+بس الفكرة مش موجودة ولا غير موجودة. الفكرة الـ edge
+
+165
+00:12:43,370 --> 00:12:48,240
+هي موجودة، والـ vertex موجودة، بس هل الـ vertex هذه
+
+166
+00:12:48,240 --> 00:12:50,780
+هي اللي شايلة هذا الـ edge؟ يعني طالعة منها الـ edge
+
+167
+00:12:50,780 --> 00:12:54,840
+هذا؟ يمكن ما يكونش طالعة منها. هو الـ edge موجود، لكن
+
+168
+00:12:54,840 --> 00:12:58,960
+مش طالعة من الـ vertex اللي قدامنا. ببساطة جداً، هي
+
+169
+00:12:58,960 --> 00:13:04,280
+هذا مثلاً، هي هذه edge، هل الـ edge هذه لها علاقة
+
+170
+00:13
+
+223
+00:17:49,860 --> 00:17:54,420
+لواحد out degree بالنسبة لواحد لأ طيب هو لمين out
+
+224
+00:17:54,420 --> 00:18:01,360
+degree لاتنين فإذا بتيجي هنا صفر واحد in degree
+
+225
+00:18:01,360 --> 00:18:05,780
+out degree others هو مالش أي علاقة لا in ولا out
+
+226
+00:18:05,780 --> 00:18:09,800
+others مش هتكون له لا in ولا out في الحالة هذه
+
+227
+00:18:09,800 --> 00:18:14,500
+فبتكتبها بهذا الشكل اتنين
+
+228
+00:18:16,760 --> 00:18:21,960
+بمين؟ مع مين هي العلاقة؟ مع اتنين واربعة فإذا هنا
+
+229
+00:18:21,960 --> 00:18:28,760
+00 و هنا 00 إحنا إلنا هنا و هنا أيوة إن لمين؟ وإن
+
+230
+00:18:28,760 --> 00:18:33,940
+هي اتنين لأربعة فإذا أربعة هي اللي هتبدأ بالواحد و
+
+231
+00:18:33,940 --> 00:18:40,720
+Zero و هنا Zero و واحد Zero و واحد تمام هنكمل بهذا
+
+232
+00:18:40,720 --> 00:18:41,080
+الشكل
+
+233
+00:18:46,150 --> 00:18:55,740
+Okay تلاتة، وين تلاتة؟ V1 و V4 ف2 و 3 على طول zeros
+
+234
+00:18:55,740 --> 00:19:00,020
+بتصفرهم مباشرة من غير ما تفكر كتير فيهم و بس بتشوف
+
+235
+00:19:00,020 --> 00:19:03,620
+مين ال in و مين ال out مين ال in و مين ال out ف ال
+
+236
+00:19:03,620 --> 00:19:09,360
+in هو V1 لإنه رايح ل V1 فإذن هو اللي بياخد ال واحد
+
+237
+00:19:09,360 --> 00:19:12,440
+الأول الواحد الأول في عندنا self loop اه هي إجت
+
+238
+00:19:12,440 --> 00:19:18,140
+عند مين؟ عند 7 لما نصل ل7 بنشوف كيف بنتمثلها هذه
+
+239
+00:19:18,140 --> 00:19:25,100
+التالتة وهذه الخمسة وهذه السادسة الآن بكل بساطة
+
+240
+00:19:25,100 --> 00:19:29,680
+لما بدك تيجي ترسم directed graph بالعكس يعني انت
+
+241
+00:19:29,680 --> 00:19:32,940
+هتمسك مين السهم يعني بما أن أنا عندك فيه واحد
+
+242
+00:19:32,940 --> 00:19:35,740
+اتنين تلاتة اربعة على طول بتروح تعمل الأربعة أنا
+
+243
+00:19:35,740 --> 00:19:42,300
+عندي أربعة ارتبهم زي ما بدك أقولك ارتبهم كما يحلوا
+
+244
+00:19:42,300 --> 00:19:48,110
+لك خليني أقول مثلا بدي أحط هذه عطوني خربطة خربطولي
+
+245
+00:19:48,110 --> 00:19:55,190
+الدنيا هنا بدنا نحط إيش V2 ماشي هنا V3 تحاضر هنا
+
+246
+00:19:55,190 --> 00:19:59,190
+V1 الشجل اللي بيسيه ما بدك تحطه أربعة مش مشكلة هاي
+
+247
+00:19:59,190 --> 00:20:07,470
+واحد إيش ضل V4 لأ
+
+248
+00:20:07,470 --> 00:20:13,270
+لأ لأ هدولة اتخربطوا اتخربطوا هدولة بس هيك اتعكست
+
+249
+00:20:13,270 --> 00:20:17,390
+يمكن بدل ما كنا ماشيين هيك مشينا؟ لأ لأ لأ اتخربطت
+
+250
+00:20:17,390 --> 00:20:21,870
+اه لأ اتخربطونا إياها يا جماعة اتخربطت اتخربطت
+
+251
+00:20:21,870 --> 00:20:25,430
+أيوة هيك اتخربطت هي اللي صح اه اتخربطت هي اللي
+
+252
+00:20:25,430 --> 00:20:29,510
+كانت خلاص خلاص صحيح أنا اتخربطت طيب عشان بس أنا أش
+
+253
+00:20:29,510 --> 00:20:35,410
+اللي بدي أسلق من الخربطة هذه بعد ما نرسمها الخربطة
+
+254
+00:20:35,410 --> 00:20:39,770
+اللي هتطلع هي اللي هتتدالب الموضوع اللي ورا إيش
+
+255
+00:20:39,770 --> 00:20:43,490
+بدك إيش بدك عشان اتخربطها طيب إيش بدك عشان
+
+256
+00:20:43,490 --> 00:20:49,630
+اتخربطها حاضر هاي تلاتة و واحد حاضرين ها هاي واحد
+
+257
+00:20:49,630 --> 00:20:58,150
+وهاي تلاتة خلاص شوي شوي خلينا نمسك أول أول
+
+258
+00:20:58,150 --> 00:21:03,130
+edge ال edge الأولى من مين لمين؟ من إلى كيف
+
+259
+00:21:03,130 --> 00:21:13,010
+تحسبها؟ لأ أيوة out ل in out ل in من اتنين ل واحد
+
+260
+00:21:17,960 --> 00:21:28,100
+طيب الثانية out ل in اتنين لاربعة طيب
+
+261
+00:21:28,100 --> 00:21:38,400
+هي خلصنا هذا و خلصنا هذا طيب هتكون من أربعة لواحد
+
+262
+00:21:38,400 --> 00:21:45,550
+هي أربعة وهي واحد الثالثة أو الرقم أربعة إحنا على
+
+263
+00:21:45,550 --> 00:21:49,690
+فكرة المفروض كتبناهم هنا الأول هذه E واحد E اتنين
+
+264
+00:21:49,690 --> 00:21:57,330
+و E تلاتة E أربعة من أربعة اه اه إحنا خلصنا هذا من
+
+265
+00:21:57,330 --> 00:22:02,830
+تلاتة لاتنين هي تلاتة لاتنين وهي E أربعة اللي
+
+266
+00:22:02,830 --> 00:22:11,270
+وراها من اتنين لتلاتة اتنين لتلاتة هي E خمسة
+
+267
+00:22:12,780 --> 00:22:19,400
+الأخيرة عندنا هنا أو قبل الأخيرة أربعة لتلاتة، فهي
+
+268
+00:22:19,400 --> 00:22:25,060
+أربعة لتلاتة طيب، الآن اللي ضلت أخيرة هذه لما
+
+269
+00:22:25,060 --> 00:22:28,920
+بدنا نمثلها من إلى، هذه من وين لوين؟ من أربعة
+
+270
+00:22:28,920 --> 00:22:32,280
+لأربعة، يعني معناه ذلك هي two ones قدام الأربعة
+
+271
+00:22:32,280 --> 00:22:41,360
+فقط، فهي من إلى من و لنفسه هذه الواضحة هي مش two
+
+272
+00:22:41,360 --> 00:22:45,180
+vertices مع بعض هي نفس ال vertex مع نفسها فبرضه
+
+273
+00:22:45,180 --> 00:22:49,520
+هذه بتسهل جدا لما ترجع تمثلها باينة واحد واحد
+
+274
+00:22:49,520 --> 00:22:56,960
+معناته من أربعة لأربعة هاي من أربعة لأربعة طيب
+
+275
+00:22:56,960 --> 00:23:02,420
+تعالى تطلع على الاتنين هدولة للواحدة الأولى بتحس
+
+276
+00:23:02,420 --> 00:23:06,730
+إنه في إشي غلط صحيح؟ ال Symmetric هدولة كانوا
+
+277
+00:23:06,730 --> 00:23:10,330
+جايين في النص .. هدول صاروا فوق .. مكانهم ..
+
+278
+00:23:10,330 --> 00:23:13,470
+ماكانش في إيش مكانهم هنا .. صاروا هدول بالعكس ..
+
+279
+00:23:13,470 --> 00:23:17,450
+بتحس إن هي اتشجلبت هيك .. اتشجلبت .. بس رغم ذلك
+
+280
+00:23:17,450 --> 00:23:21,650
+إحنا عارفين إن هما واحد .. صح؟ إحنا مسبقا عارفين
+
+281
+00:23:21,650 --> 00:23:26,610
+إن هو واحد .. لو قدرنا الآن هدولة خيوط عادي .. أنت
+
+282
+00:23:26,610 --> 00:23:31,530
+رابطهم بخيط أو بسلك .. بس ال nodes هدولة عبارة عن
+
+283
+00:23:31,530 --> 00:23:36,970
+دبابيس أنت حاططهم في الخشبة فال kid ده بوس بخطانه و
+
+284
+00:23:36,970 --> 00:23:43,530
+لفته قعدت الترتيب هذه هترجع نفس الشكل كما هو هيرجع
+
+285
+00:23:43,530 --> 00:23:48,650
+الشكل هذا كما هو الاتنين isomorphic لبعض الاتنين
+
+286
+00:23:48,650 --> 00:23:53,730
+isomorphic لبعض فهو ال isomorphism تحققت المشابهة
+
+287
+00:23:53,730 --> 00:23:56,590
+بينهم المكافئة بينهم تحققت هم الاتنين متكافئين رغم
+
+288
+00:23:56,590 --> 00:24:02,390
+أنه ظاهريا شكلهم مختلف لكن هم نفس الشيء هم الاتنين
+
+289
+00:24:02,390 --> 00:24:07,180
+نفس الأشياء تمام فهذه هتقودنا ل isomorphism معناه
+
+290
+00:24:07,180 --> 00:24:10,560
+ذلك أن لأ كلمة isomorphism مش بالضروري أنه أجي
+
+291
+00:24:10,560 --> 00:24:12,400
+أطلع عليهم أباين واضحة
+
+292
+00:24:14,760 --> 00:24:18,960
+لو عدد ال vertices جليل يمكن بمجرد النظر تظبط معاك
+
+293
+00:24:18,960 --> 00:24:21,620
+تحاول تتخيلها لو النقطة هذه شيلناها هنا طبال
+
+294
+00:24:21,620 --> 00:24:24,660
+النقطة هذه شيلناها هنا اوه برجع نفس الأشياء ممكن
+
+295
+00:24:24,660 --> 00:24:29,900
+كويس لكن عشان نبعد عن التخيولات الكتير ومش كلنا
+
+296
+00:24:29,900 --> 00:24:33,440
+بنعرف نتخيل خليني نقول زي ما كنتوا في الهندسة
+
+297
+00:24:33,440 --> 00:24:37,140
+الفراغية مش كلكوا هتقدروا تتخيلوا كيف الـ .. الشكل
+
+298
+00:24:37,140 --> 00:24:42,240
+المجسم قدامكوا عشان تتخيلوا تحلوا فبنلجأ لمجموعة
+
+299
+00:24:42,240 --> 00:24:47,550
+خطوات لازم نعملها عشان نعمل ال check هل فعلا ال two
+
+300
+00:24:47,550 --> 00:24:53,410
+graphs اللي قدامنا هم isomorphic لبعض ولا لأ؟ أو
+
+301
+00:24:53,410 --> 00:24:56,830
+تحققت ال isomorphism ولا لأ؟ فهذه بكل بساطة أن
+
+302
+00:24:56,830 --> 00:25:00,630
+يكون في عندك زي ما شوفنا طوى G1 و G2، G1 اللي كان
+
+303
+00:25:00,630 --> 00:25:04,530
+فوق و G2 اللي إحنا عملنا له reconstruction من ال
+
+304
+00:25:04,530 --> 00:25:08,770
+matrix كلهما هل هما isomorphic لبعض؟ فهذا بيكون
+
+305
+00:25:08,770 --> 00:25:12,410
+إمتى if and only if في علاقة bijection between
+
+306
+00:25:12,410 --> 00:25:18,230
+them one to one لازم يكون لأن كل node هنا معناته في
+
+307
+00:25:18,230 --> 00:25:22,350
+إيها node هنا و on to بمعنى إنه ماجيش أعمل علاقة
+
+308
+00:25:22,350 --> 00:25:26,370
+بين two vertices هنا ألا جئت طلعت علاقة مختلفة عن
+
+309
+00:25:26,370 --> 00:25:30,350
+اللي هنا فال edges نفسها نفس الشيء ال edges هي هي
+
+310
+00:25:30,350 --> 00:25:33,230
+لأن ال edges المفروض هي العلاقة هي ال relation
+
+311
+00:25:33,230 --> 00:25:37,530
+تمام فمعنى ذلك بنقدر نقول إن isomorphic إذا فعلا
+
+312
+00:25:37,530 --> 00:25:40,950
+انتحقت يوجد bijection between them بين كل V واحد
+
+313
+00:25:40,950 --> 00:25:46,720
+من هنا مع V من هنا بنكون vertex من الرسمة الأولى مع
+
+314
+00:25:46,720 --> 00:25:49,720
+كل .. مع أي vertex من الرسمة الثانية المهم إنه
+
+315
+00:25:49,720 --> 00:25:52,540
+خلاص هدول مرتبطين إيش الفرق الوحيد؟ هي في الإسم
+
+316
+00:25:52,540 --> 00:25:59,150
+أنا هنا كنت مسميه E5 هنا سميته 7 عملية الترتيب مش
+
+317
+00:25:59,150 --> 00:26:01,710
+أكثر من هيك .. عملية الترتيب مش أكثر من هيك .. تمام
+
+318
+00:26:01,710 --> 00:26:05,270
+هذا الكلام كيف نقدر نحصل عليه إذا الرسمة بسيطة
+
+319
+00:26:05,270 --> 00:26:08,830
+صغيرة زي ما قلت لكم بإمكانك بمجرد الرسم بس مش كلنا
+
+320
+00:26:08,830 --> 00:26:12,470
+بنقدر برضه على نقعد نجهد دماغنا عشان والله أقعد
+
+321
+00:26:12,470 --> 00:26:16,290
+أتخيل هذه و بعدين تظلك تتخيل أن أنت قددت هذه و
+
+322
+00:26:16,290 --> 00:26:18,750
+تجيب هذه و تقعد تتخيل أنه اتنين تان مع بعض تتبدلوا
+
+323
+00:26:18,750 --> 00:26:22,430
+فتحاول تجيب .. هل إحنا مش هنقعد نعمل كلام هذا؟ بدنا
+
+324
+00:26:22,430 --> 00:26:27,110
+نعرف إنه أول شغلة ل G1 و G2 أهم شغلة بدنا نعمل
+
+325
+00:26:27,110 --> 00:26:32,190
+check عليها إنه ال cardinality لل vertices set
+
+326
+00:26:32,190 --> 00:26:36,250
+متساوية بمعنى عدد ال vertices في الأول هو يساوي
+
+327
+00:26:36,250 --> 00:26:39,330
+عدد ال vertices للثاني لل graph طبعا عدد ال edges
+
+328
+00:26:39,330 --> 00:26:42,690
+في الأول يساوي عدد ال edges للثاني برضه شرط ضروري
+
+329
+00:26:42,690 --> 00:26:47,270
+جدا، كويس؟ الآن عدد ال vertices with degree a
+
+330
+00:26:47,270 --> 00:26:51,030
+certain degree with degree n معينة المفروض أنه
+
+331
+00:26:51,030 --> 00:26:54,930
+متساويين بين هنا و هنا لما أجي أ مسك degree two
+
+332
+00:26:54,930 --> 00:26:59,630
+degree two معناته كل node هو طالع منها اتنين two
+
+333
+00:26:59,630 --> 00:27:02,670
+edges كم واحدة طالع منها اتنين edges في ال graph
+
+334
+00:27:02,670 --> 00:27:05,730
+الأول خمسة طب بشوف ال graph الثاني كم واحدة برضه
+
+335
+00:27:05,730 --> 00:27:08,750
+طالع منها two edges يعني ال degree بتاعتها برضه
+
+336
+00:27:08,750 --> 00:27:12,690
+اتنين خمسة خلاص بشوف ال degree تلاتة degree أربعة
+
+337
+00:27:12,690 --> 00:27:18,180
+degree خمسة لازم يظل دائما متساويين دائما متساويين إذا
+
+338
+00:27:18,180 --> 00:27:21,700
+قدرنا نعمل هذا الكلام بيصير الآن الجزء الثالث شوية
+
+339
+00:27:21,700 --> 00:27:26,660
+صعب هذه لكن شرط من الشروط أنه أي sub graph آخذه
+
+340
+00:27:26,660 --> 00:27:36,240
+من G1 من G1 لازم يكون sub graph من 2 أكيد لازم
+
+341
+00:27:36,240 --> 00:27:41,590
+يكون sub graph من 2 أو isomorphic لجزء من 2 Okay
+
+342
+00:27:41,590 --> 00:27:45,750
+نبدأ نمثل الكلام هذا نبدأ نشطر على تمثيله، الآن
+
+343
+00:27:45,750 --> 00:27:48,650
+إذا كان في isomorphic بين ال two graphs اللي
+
+344
+00:27:48,650 --> 00:27:51,990
+موجودين قدامنا، إذا في، يعني إحنا بدنا نعمل check
+
+345
+00:27:51,990 --> 00:27:55,970
+هل يوجد isomorphic ولا لأ، وإذا يوجد عملنا rename
+
+346
+00:27:55,970 --> 00:28:01,760
+لهالأسماء ال vertices هذه كل vertex وين صارت هنا
+
+347
+00:28:01,760 --> 00:28:05,960
+طبعا يبدو هيك للشكل اللي له لأنه مخربطين عن بعض
+
+348
+00:28:05,960 --> 00:28:09,560
+لكن فعليا لأ إحنا ما نقدر أقول هيك مباشرة مخربطين
+
+349
+00:28:09,560 --> 00:28:15,020
+مع بعض لأ بدك تفحص خليني أشوف أول شغلة ال number
+
+350
+00:28:15,020 --> 00:28:19,860
+of vertices في الجراف الأول أو في الجراف الثاني
+
+351
+00:28:22,720 --> 00:28:26,000
+فأنت فيه عندك ستة و ستة okay هاي أول شرط خلصناها
+
+352
+00:28:26,000 --> 00:28:33,080
+هنا ستة و هنا ستة طيب ال numbers of edges هاي فيه
+
+353
+00:28:33,080 --> 00:28:37,080
+عندك واحد اتنين تلاتة أربعة خمسة ستة سبعة تمانية
+
+354
+00:28:37,080 --> 00:28:42,360
+تسعة هاي فيه عندك تسعة فيه جيه اتنين مش مشكلة هاي
+
+355
+00:28:42,360 --> 00:28:46,260
+واحد اتنين تلاتة أربعة خمسة ستة سبعة تمانية تسعة
+
+356
+00:28:46,260 --> 00:28:51,840
+طيب نبدأ degree two
+
+357
+00:28:53,520 --> 00:28:59,020
+degree two هاي degree two صحيح؟ و هاي degree two
+
+358
+00:28:59,020 --> 00:29:02,980
+فاتنين في عند degree two طب نفس الكلام موجود هنا
+
+359
+00:29:02,980 --> 00:29:08,080
+degree two هاي degree two و هاي degree two في
+
+360
+00:29:08,080 --> 00:29:15,720
+غيرهم؟ معناته حتى الآن اتنين و اتنين degree three
+
+361
+00:29:15,720 --> 00:29:21,040
+three هاي واحدة و هاي اتنين
+
+362
+00:29:24,890 --> 00:29:31,230
+هي اتنين هنا degree three هي واحدة وهي
+
+363
+00:29:31,230 --> 00:29:35,990
+اتنين، في غيرهم؟ مافيش غيرهم، فإذا اتنين و اتنين
+
+364
+00:29:35,990 --> 00:29:39,270
+degree four
+
+365
+00:29:45,420 --> 00:29:50,980
+هذه دقيقة واحدة وهذه دقيقة اتنين وهذه دقيقة واحدة
+
+366
+00:29:50,980 --> 00:29:54,340
+وهذه دقيقة اتنين وهذه دقيقة اتنين وهذه دقيقة اتنين
+
+367
+00:29:54,340 --> 00:29:55,180
+وهذه دقيقة اتنين وهذه دقيقة اتنين وهذه دقيقة اتنين
+
+368
+00:29:55,180 --> 00:29:57,440
+وهذه دقيقة اتنين وهذه دقيقة اتنين وهذه دقيقة اتنين
+
+369
+00:29:57,440 --> 00:29:58,540
+وهذه دقيقة اتنين وهذه دقيقة اتنين وهذه دقيقة اتنين
+
+370
+00:29:58,540 --> 00:30:01,320
+وهذه دقيقة اتنين وهذه دقيقة اتنين وهذه دقيقة اتنين
+
+371
+00:30:01,320 --> 00:30:04,180
+وهذه دقيقة اتنين وهذه دقيقة اتنين وهذه دقيقة اتنين
+
+372
+00:30:04,180 --> 00:30:11,460
+وهذه دقيقة اتنين وهذه دقيقة اتنين
+
+373
+00:30:11,460 --> 00:30:17,700
+ولكن ليست كافية مبدأ يمكن نركن عليها شوية لو
+
+374
+00:30:17,700 --> 00:30:22,280
+إجينا طلعنا بدنا نعمل إعادة تسمية عشان أن نشوف هي
+
+375
+00:30:22,280 --> 00:30:26,680
+وين اتغيرت الـ .. الدبابيس هذه فخلينا نبدأ مثلا
+
+376
+00:30:26,680 --> 00:30:30,660
+بالاتنين في عندي يا هادي يا هادي و هنا يا هادي يا
+
+377
+00:30:30,660 --> 00:30:35,360
+هادي فإذا خلينا نحط .. بدك تحط F بيمشي F على فكرة
+
+378
+00:30:39,960 --> 00:30:42,840
+دي أحسن عشان موجودة عندكوا في الـ .. في الورق أنا
+
+379
+00:30:42,840 --> 00:30:46,240
+بدي آخذ F لأ يعني قصد في المحاضرة في نازلة في الـ
+
+380
+00:30:46,240 --> 00:30:49,460
+slides هيك في الـ slides نازلة هيك بس الحاجة اللي
+
+381
+00:30:49,460 --> 00:30:52,960
+أنت مش عارفها أن هو هذا symmetric لو تغير هيمشي
+
+382
+00:30:52,960 --> 00:30:56,560
+حالة مين اللي جالك؟
+
+383
+00:30:56,560 --> 00:31:01,320
+كله اتنينات اتنينات اتنينات ال degrees بتاعتك كلها
+
+384
+00:31:01,320 --> 00:31:06,860
+اتنينات فأنت .. براحتك بتبدأ تغيرها و تشوف و يمكن
+
+385
+00:31:06,860 --> 00:31:09,800
+في الآخر تلاقي أنه لأ هو الصح كنت أنت تشجلبهم مع
+
+386
+00:31:09,800 --> 00:31:13,780
+بعض اللي بدي أقول هي D فعلا زي ما هيحلها الوجه الـ
+
+387
+00:31:13,780 --> 00:31:18,400
+D بس أنا بدي أقول و بدي أعملها F okay معنى ذلك أنه
+
+388
+00:31:18,400 --> 00:31:25,100
+الثانية هي ال D تمام؟ خلاص الآن D متصلة ب node
+
+389
+00:31:25,100 --> 00:31:28,500
+تلاتة و node أربعة طب هتشوف مين التلاتة و مين
+
+390
+00:31:28,500 --> 00:31:37,700
+الأربعة التلاتة هي ال A و الأربعة هي ال B طيب ال F
+
+391
+00:31:37,700 --> 00:31:41,520
+برضه مربوطة بأربعة و بتلاتة التلاتة هي ال C
+
+392
+00:31:41,520 --> 00:31:51,140
+و الأربعة هي ال E الحل بيمشي الحل بيمشي الحل إيه حل و
+
+393
+00:31:51,140 --> 00:31:54,400
+خلاص مشي .. ليش
+
+445
+00:36:11,660 --> 00:36:15,880
+كل شيء عملناه طلع صح، كل شيء عملناه طلع صح، معناته فيه
+
+446
+00:36:15,880 --> 00:36:20,980
+شيء محتاجين كمان شوية نتعلموا زيادة، لأ، في حاجات
+
+447
+00:36:20,980 --> 00:36:25,160
+كمان أكتر شرط محتاجين نروح لهم، لأن هذا مثل اللغة
+
+448
+00:36:25,160 --> 00:36:27,920
+واضح لكم، قاعدين بتطلعوا، و كلكم شايفين قاعدين
+
+449
+00:36:27,920 --> 00:36:32,120
+بتتخيلوا و بتعدوا و بتحسبوا مظبوط، كل شيء مظبوط
+
+450
+00:36:32,120 --> 00:36:36,200
+فيه حتى الـ degrees بتاعتهم كلهم مظبوطة، الـ degree
+
+451
+00:36:36,200 --> 00:36:39,160
+اتنين عددهم كامل، الـ degree تلاتة مافيش degree
+
+452
+00:36:39,160 --> 00:36:41,560
+تلاتة لأ، الله، في degree تلاتة، هيهم... هم كلهم
+
+453
+00:36:41,560 --> 00:36:45,360
+تلاتة أصلا، أربعة degree تلاتة، و خلاص، هاي كل الـ
+
+454
+00:36:45,360 --> 00:36:51,380
+graph على بعضه تمام، كله متحقق، لكن أنا بقول لك زي ما
+
+455
+00:36:51,380 --> 00:36:57,780
+قلت لك، حطهم على لوح خشب بدبابيس، هذه خطان أو سلك
+
+456
+00:36:57,780 --> 00:37:01,060
+بينهم، و قعد تغيروا شكله، هل بتطلع معاك الشكل هذا، أو
+
+457
+00:37:01,060 --> 00:37:07,560
+لأ، هاي السؤال، بس مش تطلع الدبوس ينفك منه الخطان و
+
+458
+00:37:07,560 --> 00:37:10,640
+تخرب كل اللي بنقوله و تقول هاه، الدكتور قال لنا ما هي
+
+459
+00:37:10,640 --> 00:37:15,740
+... و ده تبقى مربوطة بخطّاتها، تمام، فإذا في شيء
+
+460
+00:37:15,740 --> 00:37:19,440
+محتاجين نرجع للشكل هذا و نأكد منه، هل هو فعلا
+
+461
+00:37:19,440 --> 00:37:22,920
+isomorphic ولا لأ، هذا الشيء هو الـ connectivity هو
+
+462
+00:37:22,920 --> 00:37:27,800
+الـ connectivity، احنا ما أخدنا transitive عبثا، أخدنا
+
+463
+00:37:27,800 --> 00:37:30,600
+الـ transitive لإني عارف إنه أنا في النهاية باطلع
+
+464
+00:37:30,600 --> 00:37:36,000
+من مكان بروح لمكان، معناته هذه relation أولى، طيب من
+
+465
+00:37:36,000 --> 00:37:39,880
+نفس المكان ببدأ منه رحلة تانية، بس هي نفس اللي كانت
+
+466
+00:37:39,880 --> 00:37:44,060
+نهاية الرحلة الأولى، فإذا نهاية الـ relation الأولى
+
+467
+00:37:44,060 --> 00:37:46,920
+المفروض تتفق مع بداية الـ relation التانية، عشان إيه؟
+
+468
+00:37:46,920 --> 00:37:49,860
+كانت الـ transitive، عشان في الآخر أقول أنا طلعت من
+
+469
+00:37:49,860 --> 00:37:56,130
+واحد لتلاتة من خلال اتنين، طيب كويس، الوقت لو عملنا
+
+470
+00:37:56,130 --> 00:38:01,110
+هذا الكلام، الـ path هذا مشيناه ورجعنا لواحد، إيش
+
+471
+00:38:01,110 --> 00:38:06,690
+سميناها الـ circuit، تمام، بالضبط، هذا اللي بدنا نبدأ
+
+472
+00:38:06,690 --> 00:38:12,750
+نتكلم عنه، هل عدد الـ circuits بـ degree معينة هو
+
+473
+00:38:12,750 --> 00:38:16,590
+نفسه هنا وهنا، بمعنى أنا في نفس النقطة موجود في
+
+474
+00:38:16,590 --> 00:38:20,890
+نقطة عشان أعمل أي loop و أرجع لنفس النقطة، قد إيش عدد
+
+475
+00:38:20,890 --> 00:38:26,060
+الـ in الـ edges اللي مرت فيها، معناها كده عدد الـ
+
+476
+00:38:26,060 --> 00:38:28,560
+relations اللي عدت فيها، كم مرة عملت composition
+
+477
+00:38:30,790 --> 00:38:35,430
+لاحظت كيف؟ فإذا بدور على الـ closed loop أو الـ
+
+478
+00:38:35,430 --> 00:38:39,150
+circuits، خلينا نبدأ، الفكرة بيكون عندك path of
+
+479
+00:38:39,150 --> 00:38:42,770
+length N from U to V، عارفين هي sequence of
+
+480
+00:38:42,770 --> 00:38:48,690
+adjacent edges بحيث أني أذهب من U لـ V، وإذا كان عندك
+
+481
+00:38:48,690 --> 00:38:52,510
+U تساوي V، معناته رجعت لنفس النقطة، بنسميها circuit
+
+482
+00:38:52,510 --> 00:38:57,550
+أو cycle، circuit أو cycle، فالـ path ببساطة أن يكون
+
+483
+00:38:57,550 --> 00:39:02,090
+فيه أكتر من one edge، بمعنى إنه يكون في عندك loop
+
+484
+00:39:02,090 --> 00:39:05,990
+معين، في عندك حركة بتتحرك فيها، loop معين، و بدك تشوف
+
+485
+00:39:05,990 --> 00:39:10,750
+قد إيش عدد الـ edges اللي مريت فيها عشان ترجع لنفس
+
+486
+00:39:10,750 --> 00:39:13,530
+النقطة، طيب هذا هيقوّينا لحاجة برضه في الـ
+
+487
+00:39:13,530 --> 00:39:17,970
+connectivity، إنه أنا لازم أكون مستمر،
+
+488
+00:39:17,970 --> 00:39:21,070
+مش ينقطع في النص، مش ينقطع في النص، معناه ذلك أنه
+
+489
+00:39:21,070 --> 00:39:24,870
+بدي أقول أمثلة واضحة عشان ناخد بالنا أنه
+
+490
+00:39:24,870 --> 00:39:29,290
+لازم يكون الـ connection كاملة، الـ connectivity كاملة
+
+491
+00:39:29,290 --> 00:39:33,630
+مثال زي هذا، هذا بقدر أقول عنه connected graph ولا
+
+492
+00:39:33,630 --> 00:39:38,350
+لأ؟ هذا أول yes، التاني لغة ده؟ أكيد لأ، فما في حد
+
+493
+00:39:38,350 --> 00:39:42,700
+شيء يقول لي والله هاي path، فلازم تكون في
+
+494
+00:39:42,700 --> 00:39:46,480
+connectivity واضحة، مستمرة، عشان نعمل الـ check تبعنا
+
+495
+00:39:46,480 --> 00:39:54,840
+هذه أكيد no، التالتة تحت، بكل
+
+496
+00:39:54,840 --> 00:39:59,660
+بساطة، بتقدر من أي نقطة تروح لأي نقطة، من أي نقطة
+
+497
+00:39:59,660 --> 00:40:03,320
+بتقدر تروح لأي نقطة، صح، الـ connectivity إنك أنت
+
+498
+00:40:03,320 --> 00:40:05,820
+موجود في أي نقطة، بتقدر تروح لأي نقطة على الـ graph
+
+499
+00:40:06,810 --> 00:40:14,010
+بس هنا وصلنا لـ E، من E تصل لـ B، من B موصلين كلهم، ما
+
+500
+00:40:14,010 --> 00:40:17,550
+هو، فأنت بتقدر تتحرك من أي vertex لأي vertex ثاني
+
+501
+00:40:17,550 --> 00:40:21,450
+بكل بساطة، هناك ما كنتش بتقدر، لأنك بدك تروح مثلا من
+
+502
+00:40:21,450 --> 00:40:26,650
+C لـ A، isolated بالنسبة لبعض، فبنسميهم هنا مش
+
+503
+00:40:26,650 --> 00:40:30,950
+isolated node، بسميهم components، في عندك two
+
+504
+00:40:30,950 --> 00:40:34,390
+components للـ graph، مش one component، مش one
+
+505
+00:40:34,390 --> 00:40:39,290
+component، طيب الأخيرة No، بالضبط، لأن هدول مش nodes،
+
+506
+00:40:39,290 --> 00:40:44,010
+مش nodes، هدول مش nodes، كويس؟ فإذا هتلاقي في عندك
+
+507
+00:40:44,010 --> 00:40:46,650
+three nodes لحال، و three other... و other three
+
+508
+00:40:46,650 --> 00:40:50,630
+nodes لحال، هدول two components، في الحالة اللي
+
+509
+00:40:50,630 --> 00:40:56,060
+عندنا، بالظبط، النص الأول ما بيصلش مع النص الثاني، فالـ
+
+510
+00:40:56,060 --> 00:40:59,360
+components هذه، زي graph بهذا الشكل، هي graph كامل
+
+511
+00:40:59,360 --> 00:41:04,240
+الـ graph هذا، بقدر أقول أن هو مكون من أربعة
+
+512
+00:41:04,240 --> 00:41:10,700
+components، الأربع components هذه a, b, c, d، هذه set
+
+513
+00:41:10,700 --> 00:41:15,540
+of components لحال، ثم في عندك الـ E لحال، ثم الـ F
+
+514
+00:41:15,540 --> 00:41:22,760
+لحال، و أخيرا I, H, G, J لحال، هدول لحالهم، فعندك في
+
+515
+00:41:22,760 --> 00:41:27,120
+أربعة components، طيب في أي graph... أي graph كامل
+
+516
+00:41:27,120 --> 00:41:32,680
+one component، في بعض الـ edges و الـ vertices اللي
+
+517
+00:41:32,680 --> 00:41:38,920
+هم خصوصية، بنقدر نسميهم cut vertex أو cut edge، هذا
+
+518
+00:41:38,920 --> 00:41:43,820
+إذا كان عملنا له remove، بيفصل الـ graph لـ two
+
+519
+00:41:43,820 --> 00:41:50,720
+components at least، كويس؟ يعني مثلا زي هنا مثلا، و
+
+520
+00:41:50,720 --> 00:41:55,640
+بدي أفترض أن هذا لحاله graph لحاله، كويس؟
+
+521
+00:41:55,640 --> 00:42:03,260
+لو شلنا a، إيش المتبقي؟ هاي المتبقي، صح؟ بيضل قطعة
+
+522
+00:42:03,260 --> 00:42:08,580
+واحدة، فهذا ليس cut vertex، هذا مش cut vertex، تمام؟
+
+523
+00:42:08,580 --> 00:42:12,640
+لأنه لما يروح مش هيتغير معانا، إيش، هتضل برضه
+
+524
+00:42:12,640 --> 00:42:18,170
+component واحدة للـ graph، لكن لو شلت b، بيصبح الشكل
+
+525
+00:42:18,170 --> 00:42:23,830
+عندك بهذا الشكل، و نقطة هنا اللي هي لـ D و C، و هنا A
+
+526
+00:42:23,830 --> 00:42:29,110
+لأن هذه راحت خلاص، فمعنى ذلك أن هذه cut vertex، هذه
+
+527
+00:42:29,110 --> 00:42:35,130
+cut vertex، تمام، okay، نفس الكلام للـ edges، هل وجد لو
+
+528
+00:42:35,130 --> 00:42:41,290
+قلنا الـ edge هذه شيلناها، و أنا بتكلم عن هذا الشكل
+
+529
+00:42:41,290 --> 00:42:50,180
+بس، شلنا الـ edge اللي عليها الـ X، مش هيؤثر، هيظل
+
+530
+00:42:50,180 --> 00:42:53,920
+عبارة عن one component برضه لـ graph، فهذه ليست cut
+
+531
+00:42:53,920 --> 00:43:01,120
+edge، طيب، شلنا الـ edge هنا، مش هتفرق معانا في شيء،
+
+532
+00:43:01,120 --> 00:43:06,960
+لأ، لو شلت هذه، صح،
+
+533
+00:43:06,960 --> 00:43:13,020
+هتظل J لحالها، isolated vertex، هتصير isolated
+
+534
+00:43:13,020 --> 00:43:17,160
+vertex، فهتصير هنا two parts، two components زي ما
+
+535
+00:43:17,160 --> 00:43:20,320
+أخدناه كله، وسمينا هذه لحالها component، وهي
+
+536
+00:43:20,320 --> 00:43:25,060
+isolated، معناه ذلك أنه الـ edge هذه لو انشالت، to be
+
+537
+00:43:25,060 --> 00:43:32,220
+removed، حيضل عندي J isolated، هتضل
+
+538
+00:43:32,220 --> 00:43:36,760
+لحالها node، فقط node لحالها، فإذا هذه بسميها cut
+
+539
+00:43:36,760 --> 00:43:39,920
+edge، cut edge، تمام
+
+540
+00:43:44,150 --> 00:43:48,190
+الآن، الـ connectivity، برضه في حاجة اسمها، و أنتم
+
+541
+00:43:48,190 --> 00:43:51,030
+كنتم بتسألوا عن الـ strong، فبرضه الـ strong معانا
+
+542
+00:43:51,030 --> 00:43:54,310
+حتى في مين، في الـ connectivity، ففي عندي weakly و في
+
+543
+00:43:54,310 --> 00:44:00,790
+strongly connection، و هذه المصطلحين، هدول بنستخدمهم
+
+544
+00:44:00,790 --> 00:44:04,470
+أكتر لما يكون في عندي directed graph، في directed
+
+545
+00:44:04,470 --> 00:44:10,370
+graph، بسمي weak إذا كان فعلا هم بيتصل جميع النقاط
+
+546
+00:44:10,370 --> 00:44:15,280
+مع بعضها، في حال أهملت الاتجاه، لكن في حال أخذت
+
+547
+00:44:15,280 --> 00:44:18,560
+الاتجاه بعين الاعتبار، هتلاجي أنه في نقاط مش هتصل
+
+548
+00:44:18,560 --> 00:44:24,400
+بعض، يعني أنا بدي أحترم أن الشارع هذا هو رايح مش
+
+549
+00:44:24,400 --> 00:44:28,720
+جاي، غير لأ، ممكن ألاقيه جاي في وجهي، كويس؟ فهنا
+
+550
+00:44:28,720 --> 00:44:32,240
+weak أو strong، هل وجد... لما نيجي نتكلم عن الـ curve
+
+551
+00:44:32,240 --> 00:44:41,580
+الأول، في البداية، هل وجد، بتطلع مثلا من B لـ D، هل
+
+552
+00:44:41,580 --> 00:44:46,770
+بتقدر تطلع بدون ما تخالف الإشارة؟ طيب لو بدك تطلع
+
+553
+00:44:46,770 --> 00:44:51,450
+من C لـ D، إلا
+
+554
+00:44:51,450 --> 00:44:58,030
+إذا خلفت الاتجاه، فإذا، إذا خلفت الاتجاه بأصل، بنصل
+
+555
+00:44:58,030 --> 00:45:00,990
+okay، معناه ذلك إن الـ connectivity هنا weakly
+
+556
+00:45:00,990 --> 00:45:07,230
+connectivity، هنا الاتصال ضعيف، اتصال ضعيف، لأنه لازم
+
+557
+00:45:07,230 --> 00:45:10,790
+ألتزم بالاتجاه، طبعا لو ما فيش أصلا، هو ما فيش أصلا
+
+558
+00:45:10,790 --> 00:45:14,430
+connection، يعني حتى weakly ما بقدرش أقول عنه weakly
+
+559
+00:45:14,430 --> 00:45:17,690
+connected، weekly connected، ما بقدرش أقولها، طيب في
+
+560
+00:45:17,690 --> 00:45:22,670
+الحالة التانية، أي نقطة بتصل لأي نقطة، وأنت ملتزم
+
+561
+00:45:22,670 --> 00:45:27,190
+بالاتجاه، من أي نقطة بتقدر تروح لأي نقطة، ببساطة جدا
+
+562
+00:45:27,190 --> 00:45:30,950
+لأنه عمل لك cycle خارجي للكل، يعني أنت بتقدر تتحرك
+
+563
+00:45:30,950 --> 00:45:35,150
+بسهولة جدا من خلال الـ ring هذا، من أي نقطة للتانية
+
+564
+00:45:35,150 --> 00:45:41,310
+من أي نقطة للتانية، هي، فأنت على الدوار بتقدر تمر
+
+565
+00:45:41,310 --> 00:45:44,510
+على أي طرف من أطراف الدوار، صحيح؟ لأن أنت ماشي في
+
+566
+00:45:44,510 --> 00:45:52,350
+اتجاه الصح، تمام، في أي دوار تماما، okay، نرجع لمثالنا
+
+567
+00:45:52,350 --> 00:45:55,850
+بعد هالـ connectivity اللي اتعلمناها، هل بقدر أحل
+
+568
+00:45:55,850 --> 00:45:58,990
+الموضوع الآن، بقدر أقول هي فعلا isomorphic ونخلص
+
+569
+00:45:58,990 --> 00:46:03,510
+ولا لأ، مبدئيا مش هنجد، نحسب قد إيش عدد، لأنه عارفين
+
+570
+00:46:03,510 --> 00:46:08,350
+عارفين، صحيح؟ طيب الـ connectivity الآن، الكون اكتفيت
+
+571
+00:46:08,350 --> 00:46:13,030
+هيني، بدي أطلع من نقطة وأرجع لها، والـ degree تلاتة
+
+572
+00:46:13,030 --> 00:46:16,470
+طبعا
+
+573
+00:46:16,470 --> 00:46:21,610
+خليني اسميها يعني cycle، تلاتة degree تلاتة مثلا
+
+574
+00:46:21,610 --> 00:46:28,630
+cycle تلاتة، هاي جي اتنين، في عندي واحدة، و هاي في
+
+575
+00:46:28,630 --> 00:46:34,050
+التانية، بتلاتة، في غيرهم بتلاتة، برجع لنفس النقطة
+
+576
+00:46:34,050 --> 00:46:37,790
+يعني هل في عندي أي cycle، الـ degree بتاعتها تلاتة
+
+577
+00:46:37,790 --> 00:46:42,610
+أو الـ circuit، ما فيش، هما الاتنين، طيب بالنسبة لـ G
+
+578
+00:46:42,610 --> 00:46:51,850
+واحد، ما فيش، ما فيش تلاتات، أقل شيء أربعة، هي أربعة، وهي
+
+579
+00:46:51,850 --> 00:46:55,770
+أربعة، وهي أربعة، وهي أربعة
+
+580
+00:46:58,750 --> 00:47:05,370
+أيوا، تلاتة فش، خلاص، مش isomorphic، انتهى، خلص، رغم أنه
+
+581
+00:47:05,370 --> 00:47:11,370
+حسب الـ necessary condition، كله متحقق، لكن فعليا حسب
+
+582
+00:47:11,370 --> 00:47:15,510
+الـ connectivity الآن، وضحت أنه لأ، أنا مش هقدر أصل لـ
+
+583
+00:47:15,510 --> 00:47:18,930
+loop بنفس الـ degree في الحالتين، فإذا not
+
+584
+00:47:18,930 --> 00:47:22,290
+isomorphic، في الحالة اللي عندنا، أكيد مش هيكونوا
+
+585
+00:47:22,290 --> 00:47:26,710
+isomorphic، في الحالة اللي موجودة عندنا، تمام، يكفي أن
+
+586
+00:47:26,710 --> 00:47:29,910
+شرط واحد يتم نفيه، أو واحدة من الـ conditions تم
+
+587
+00:47:29,910 --> 00:47:33,090
+نفيها، عشان تقول لأ، خلاص، ما اتحققتش... ما اتحققتش
+
+588
+00:47:33,090 --> 00:47:37,850
+تمام؟ هيك بنكون خلصنا الجزئية بتاعت الـ graphs
+
+589
+00:47:37,850 --> 00:47:40,550
+بيضّل لنا موضوع واحد أعتقد خلال الأسبوع هذا، ان شاء الله
+
+590
+00:47:40,550 --> 00:47:45,150
+بنخلصه، واللي هو الـ tree، و هذه حالة خاصة جدا من الـ
+
+591
+00:47:45,150 --> 00:47:49,510
+graph، زي ما احنا انطلقنا من الـ relation و قلنا في
+
+592
+00:47:49,510 --> 00:47:53,240
+حالة خاصة منه هي الـ graph، كويس، برضه الـ graph في
+
+593
+00:47:53,240 --> 00:47:56,580
+حالة خاصة جدا منه اسمها tree، هنعرف لإيش ممكن
+
+594
+00:47:56,580 --> 00:48:01,360
+نستخدم الـ tree هذه، كويس، وممكن نحل فيها أسئلة، أو
+
+595
+00:48:01,360 --> 00:48:06,200
+ممكن نحل فيها أسئلة، وممكن تستخدم كبداية
+
+596
+00:48:06,200 --> 00:48:10,840
+التفكير في الذكاء الاصطناعي، الـ AI، الـ tree يعطيكم
+
+597
+00:48:10,840 --> 00:48:11,980
+ألف عافية، و بارك الله فيكم
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f4c395f324be90f4e41235ff26b88426649c4a63
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM_postprocess.srt
@@ -0,0 +1,2388 @@
+1
+00:00:04,880 --> 00:00:07,360
+بسم الله الرحمن الرحيم هنبدأ اليوم يا شباب ان شاء
+
+2
+00:00:07,360 --> 00:00:11,160
+الله تعالى نكمل الجزء المتبقي في ال graph في موضوع
+
+3
+00:00:11,160 --> 00:00:14,080
+ال graph و اللي اتكلمنا فيه المرة الماضية يمكن
+
+4
+00:00:14,080 --> 00:00:17,900
+أخرش عن بعض أنواع ال graphs و اتكلمنا عن degrees و
+
+5
+00:00:17,900 --> 00:00:20,680
+عرفنا اشي عن degrees و شوية terminology اتعرفنا
+
+6
+00:00:20,680 --> 00:00:24,840
+عنهاالمرة الماضية اليوم هنتكلم عن ال
+
+7
+00:00:24,840 --> 00:00:28,180
+representation لل graph كيف انا بقدر امثل ال graph
+
+8
+00:00:28,180 --> 00:00:34,120
+و ال isomorphism ال isomorphism ببساطة ان هو انك
+
+9
+00:00:34,120 --> 00:00:36,580
+انت يكون في عندك two graphs بغض النظر ان هم
+
+10
+00:00:36,580 --> 00:00:43,060
+identical شكلا كأنهم زي بعض لكن هم فعلياتماما زى
+
+11
+00:00:43,060 --> 00:00:46,300
+بعض لكن يمكن انت بتكون ال nodes مغير اماكنهم مش
+
+12
+00:00:46,300 --> 00:00:49,500
+اكتر من هيك عملية تغيير اماكن لا اكتر ولا اقل
+
+13
+00:00:49,500 --> 00:00:52,140
+وبتيجى اسئلة كتير الحقيقة فى ال IQ test على
+
+14
+00:00:52,140 --> 00:00:55,580
+الحاجات هذه على الحاجات لذاك اللي هو two graphs
+
+15
+00:00:55,580 --> 00:00:59,050
+وبيقولك هل هما اتنين identical ولا لأهم بيكونوا
+
+16
+00:00:59,050 --> 00:01:02,070
+فعلا identical بس انت المظهر اللي عامله يروحي بذلك
+
+17
+00:01:02,070 --> 00:01:05,390
+طب كيف نعمل test على ال isomorphism هذي أو ان
+
+18
+00:01:05,390 --> 00:01:08,870
+واحدة منهم isomorphic للتانية؟ هنتكلم عنها في
+
+19
+00:01:08,870 --> 00:01:11,730
+موضوعنا لليوم في ال representation ال adjacency
+
+20
+00:01:11,730 --> 00:01:16,870
+lists ال adjacency matrices و ال incidence
+
+21
+00:01:16,870 --> 00:01:19,790
+matrices هم هدولة التلت أنواع اللي هنتكلم عنهم
+
+22
+00:01:19,790 --> 00:01:23,430
+اليوم في تمثيل أي graph فبالنسبة لل adjacency
+
+23
+00:01:23,430 --> 00:01:29,240
+listsفهي واضحة قائمة المجاورات أو المتجاورات بكل
+
+24
+00:01:29,240 --> 00:01:34,400
+بساطة كل واحدة من ال vertices تبعتك بتحطهم في
+
+25
+00:01:34,400 --> 00:01:40,280
+column أولو قدام كل واحدة منهم هيصبح ال adjacent
+
+26
+00:01:40,280 --> 00:01:47,180
+vertices اللي خاصة في كل vertex منهم فتتكلم عن A
+
+27
+00:01:47,180 --> 00:01:52,480
+مثلا هي مجاورة ل B و C فبتحط قدامها B و C انتهى B
+
+28
+00:01:52,480 --> 00:02:01,840
+ل A و C و E و F و هكذا خلّيني أشوف D مثلاisolated
+
+29
+00:02:01,840 --> 00:02:05,660
+isolated معناته zero في الشاشة قدامها أو هي مش
+
+30
+00:02:05,660 --> 00:02:09,860
+مجاورة لأي vertex أخرى فال adjacency هنا مش
+
+31
+00:02:09,860 --> 00:02:14,000
+متحققالها فهي فعليا zero وهكذا هذا تمثيلة أولى
+
+32
+00:02:14,000 --> 00:02:18,360
+بحيث أنك انت بتقدر من الجدول هذا لو الرسم ال graph
+
+33
+00:02:18,360 --> 00:02:22,700
+نفسه مش موجود انت بتقدر ترسمه تاني تقدر بكل بساطة
+
+34
+00:02:22,700 --> 00:02:27,420
+ترسمه من خلال ال adjacency lists اللي قدامك اللي
+
+35
+00:02:27,420 --> 00:02:31,340
+عاجيها دهقدامك طيب بالنسبة لل direct في ال direct
+
+36
+00:02:31,340 --> 00:02:34,620
+الأمور بتختلف شوية في ال direct احنا مصير نتكلم عن
+
+37
+00:02:34,620 --> 00:02:40,980
+ايش ال edges ال edges او اللي طالعة من ال vertex
+
+38
+00:02:40,980 --> 00:02:43,700
+اللي بنتكلم عنها فإذا برضه بالنسبة لل adjacency
+
+39
+00:02:43,700 --> 00:02:51,360
+less بنحطها زي ما هي ايه هاي ايه متصلة بمين مش مين
+
+40
+00:02:51,360 --> 00:02:56,460
+متصل فيها هي متصلة مع مين فهي adjacent to مين
+
+41
+00:02:59,190 --> 00:03:04,530
+ما هي بتصير للعنصر التاني، يعني هيها B هنا هي مش
+
+42
+00:03:04,530 --> 00:03:10,430
+متصلة بA، لاحظ A هي اللي متصلة بB، B غير متصلة في
+
+43
+00:03:10,430 --> 00:03:15,470
+A، فلاحظ تعالي هنا A هي متصلة في B، لكن B مش متصلة
+
+44
+00:03:15,470 --> 00:03:22,110
+مع Aبالظبط فانت هنا بتتكلم عن بدايات البدايات هي
+
+45
+00:03:22,110 --> 00:03:26,450
+دايما ال vertex اللي بتمثل بالنسبالها فلو مش موجود
+
+46
+00:03:26,450 --> 00:03:29,970
+الرسم هذا بتقدر ترجع تستنتج الرسم نفسه من مجموعة
+
+47
+00:03:29,970 --> 00:03:35,450
+او من ال adjacency last اللي قدامك تمام فهي بكل
+
+48
+00:03:35,450 --> 00:03:41,070
+بكل بساطة تعالي تطلع هتلاقي ان مثلا حاجة زي ال C C
+
+49
+00:03:41,070 --> 00:03:46,330
+مع C فانت بتعرف ان هذه self loopهذه نعرفها على طول
+
+50
+00:03:46,330 --> 00:03:50,710
+أنه معناته فيها مثل self-loop ال B نفس الكلام ففي
+
+51
+00:03:50,710 --> 00:03:54,850
+عندك فعلا self-loop لكل vertex من ال two vertices
+
+52
+00:03:54,850 --> 00:03:59,650
+هدول، تمام؟ فهذه بطريقة مبسطة كيف ممكن تعمل
+
+53
+00:03:59,650 --> 00:04:04,690
+التمثيل ال adjacency، اتفضل تختلف self-loop يعني
+
+54
+00:04:04,690 --> 00:04:06,870
+أنا الجمهور الفاتنة ما حكيتلك أنه مش هتفرج من
+
+55
+00:04:06,870 --> 00:04:09,690
+اتجاه، هتنقطع من نفسه و ترجع لنفسه، بس أنا لو أصبح
+
+56
+00:04:09,690 --> 00:04:13,950
+تعاكسه الجدول مش هيديني اتجاهلأ ليش مش هيعطيك
+
+57
+00:04:13,950 --> 00:04:17,210
+الاتجاه انت هالوقت تفرج معاك هي اي C اللي ميعطي
+
+58
+00:04:17,210 --> 00:04:22,530
+للتانية يعني انا رسمته هيك ولا انا رسمته هيك لأ
+
+59
+00:04:22,530 --> 00:04:26,710
+اتجاه في ال different vertices ل different
+
+60
+00:04:26,710 --> 00:04:30,470
+vertices بختلف الاتجاه اه يعني بمعنى هذا اتجاه A
+
+61
+00:04:30,470 --> 00:04:35,750
+وB هو اتجاه واحد فهذه في الاتجاه العكس مش موجودة
+
+62
+00:04:35,750 --> 00:04:42,770
+لكن من B لنفسها ما هي من B لنفسهاعرفت؟ فأنا هنا
+
+63
+00:04:42,770 --> 00:04:45,170
+مافيش multigraph لأ أنا ماعرفش .. ما .. ماعتقدش
+
+64
+00:04:45,170 --> 00:04:47,890
+أنه ليه الموضوع علاقة بال multigraph لأ مالوش
+
+65
+00:04:47,890 --> 00:04:49,870
+علاقة بال multigraph هنا أنت في عندك هنا
+
+66
+00:04:49,870 --> 00:04:53,630
+multigraph فيه .. فيه mult .. فيه المفروض أنه هنا
+
+67
+00:04:53,630 --> 00:04:58,330
+لو في multigraph بتمثل بس في الحالة هذه بده يكتب
+
+68
+00:04:58,330 --> 00:05:01,850
+اتنين بيه بده يكتب جدامك اتنين بيه لو في
+
+69
+00:05:01,850 --> 00:05:05,450
+multigraph لو في عندك ال .. جثة ال multigraph هنا
+
+70
+00:05:05,450 --> 00:05:06,710
+متهيأرة مش متمثلة في الرسم
+
+71
+00:05:09,540 --> 00:05:13,840
+عارف اه بس بدك توضح انه جديش يعني ممكن ساعتها لو
+
+72
+00:05:13,840 --> 00:05:16,940
+افترضنا خلينا نحنا نحط من هنا افتراضية هاي حط
+
+73
+00:05:16,940 --> 00:05:23,140
+بتقول فيهاي كمان بهذا الشكل فبينطلع لمين ل E ل E
+
+74
+00:05:23,140 --> 00:05:29,100
+فإذا هنا يا بكتب E يا بنكتب اتنين E كويس
+
+75
+00:05:29,100 --> 00:05:33,440
+انت يعني فتحتيك موضوععشان يبين معانا ان و الله في
+
+76
+00:05:33,440 --> 00:05:35,940
+multi-graph اذا في multi-graph لان فعلا المثال
+
+77
+00:05:35,940 --> 00:05:38,660
+مافيش في multi-graph اذا في multi-graph ياما بتعمل
+
+78
+00:05:38,660 --> 00:05:44,960
+كمان E تانية او بتعمل اتنين E حسب جداش عدد ال
+
+79
+00:05:44,960 --> 00:05:51,680
+edges اللي رايحة من A لE من A لE تمام طيب ال
+
+80
+00:05:51,680 --> 00:05:55,980
+adjacency matricesهو مصفوفات المجاورة، مصفوفات
+
+81
+00:05:55,980 --> 00:05:59,400
+المجاورة كتير أبسط، كتير كتير أبسط، كل ما أنا
+
+82
+00:05:59,400 --> 00:06:03,600
+محتاجه أن أعمل matrix، ال matrix هذا ال rows
+
+83
+00:06:03,600 --> 00:06:08,860
+تبعتها أو ال columns نفسهم هي مجموعة ال vertices،
+
+84
+00:06:08,860 --> 00:06:12,180
+مجموعة ال verticesهنقول والله ال node الأولى
+
+85
+00:06:12,180 --> 00:06:15,120
+التانية التالتة و هكذا الأول ال node الأولى
+
+86
+00:06:15,120 --> 00:06:18,640
+التانية التالتة و هكذا إذا كان في connection
+
+87
+00:06:18,640 --> 00:06:23,600
+between من التانية للأولى بنحط قدامها هنا واحد
+
+88
+00:06:23,600 --> 00:06:29,480
+مافيش صفر zero أو صفر خلاص بكل بساطة فإذا ان هي
+
+89
+00:06:29,480 --> 00:06:35,900
+عبارة عن matrix ال matrix ها دي العنصرI و J بيكون
+
+90
+00:06:35,900 --> 00:06:39,620
+واحد إذا في فعل في connection between ال vertex I
+
+91
+00:06:39,620 --> 00:06:45,040
+to vertex J طبعا في ال undirected كلاهما في نفس
+
+92
+00:06:45,040 --> 00:06:51,720
+الاتجاه فمن I ل J و من J ل I فكلاهما بيمشي الحالة
+
+93
+00:06:51,720 --> 00:06:53,900
+في ال directed شوية بتختلف الأمور في ال directed
+
+94
+00:06:53,900 --> 00:06:57,580
+زي ما هتشوف هتختلف معانا شوية otherwise بنحطها
+
+95
+00:06:57,580 --> 00:07:02,500
+zero معناته مافيش أصلا edge between them هاي مثال
+
+96
+00:07:05,750 --> 00:07:11,030
+هي عندك مثل A B C و D بهذا الشكل و بدنا نرسم او
+
+97
+00:07:11,030 --> 00:07:15,290
+نمثل الشكل اللي قدامنا او بعد ما نرسمه بعد ما ناخد
+
+98
+00:07:15,290 --> 00:07:18,410
+ال matrix تبعتنا من ال matrix بدي ارجع اخد الرسم
+
+99
+00:07:18,410 --> 00:07:22,570
+فالمفروض representation يعني المفروض العكس صحيح من
+
+100
+00:07:22,570 --> 00:07:27,930
+ال matrix اقدر ارجع ارسم ال graph نفسه تمام فالان
+
+101
+00:07:27,930 --> 00:07:29,610
+بكل بساطة هنعمل نفس القالية
+
+102
+00:07:36,480 --> 00:07:41,420
+from A to A مافيش self loop فإذا zero طيب A متصلة
+
+103
+00:07:41,420 --> 00:07:46,120
+بالباجي فإذا متصلة مع B واحد مع C واحد مع D واحد
+
+104
+00:07:46,120 --> 00:07:50,120
+بهذا الشكل تمام ال B نفس الجثة ال B متصلة مع مين
+
+105
+00:07:50,120 --> 00:07:54,580
+مع A و D نفس
+
+106
+00:07:54,580 --> 00:08:01,080
+الكلام D متصلة مع الكل أما مع نفسها لأ بعد ما
+
+107
+00:08:01,080 --> 00:08:01,660
+ترسمها
+
+108
+00:08:05,480 --> 00:08:09,400
+لأ هذه بتصير symmetric اه symmetric فهذه اول
+
+109
+00:08:09,400 --> 00:08:15,960
+ملاحظة انه في ال adjacency matrices بتكون دايما
+
+110
+00:08:15,960 --> 00:08:22,080
+symmetric مادام undirected بالظبط مادام undirected
+
+111
+00:08:22,080 --> 00:08:25,840
+فهي دايما symmetric بس اهم شغلة ان هي تكون
+
+112
+00:08:25,840 --> 00:08:32,290
+undirectedو بفرجش undirected إذا كان عندي multi
+
+113
+00:08:32,290 --> 00:08:35,110
+-path ولا لأ أو multi-graph ولا لأ حتى في ال multi
+
+114
+00:08:35,110 --> 00:08:38,790
+-graph مش هتفرج المهم إن هي undirected ليش؟ لأنه
+
+115
+00:08:38,790 --> 00:08:42,130
+إذا كان بدي أقول و الله بين ال C و ال B فيه اتنين
+
+116
+00:08:42,130 --> 00:08:48,470
+نفترض معناته هي نفسها بين ال B و ال C هتكون برضه
+
+117
+00:08:48,470 --> 00:08:52,210
+اتنين هذه undirected فإذا الشرط هنا عشان أقول إن
+
+118
+00:08:52,210 --> 00:08:57,670
+هي symmetric هي جزئية ال undirectedتمام بتقليه
+
+119
+00:08:57,670 --> 00:09:04,670
+واضح حتى مافيش فيه كتير غلبة التنفيذ هذا okay
+
+120
+00:09:04,670 --> 00:09:07,790
+الان في ال multigraph لما يكون في عندك multigraph
+
+121
+00:09:07,790 --> 00:09:12,050
+زي ما قلنا بقى ال one بنستعيد عن ال one zero لأ
+
+122
+00:09:12,050 --> 00:09:14,590
+بنستعيد عنه ال natural number ال natural number
+
+123
+00:09:14,590 --> 00:09:18,910
+هذه تعود او بنحط مكانها قيمة بالظبط عدد ال edges
+
+124
+00:09:19,890 --> 00:09:23,670
+فمنحط قيمة ال edges نفسها بدل منحط واحد لمجرد ان
+
+125
+00:09:23,670 --> 00:09:27,070
+الواحد دي دلالة على وجود relation او دلالة على
+
+126
+00:09:27,070 --> 00:09:31,270
+وجود edge لأ منحطها ك natural number زي المثال
+
+127
+00:09:31,270 --> 00:09:35,870
+برضه اللي هنعدل عليه بهذا الشكل عشان يصبح عندى
+
+128
+00:09:35,870 --> 00:09:44,550
+برضه نفس الاشي a,b,c,d a,b,c,d خليني انا اخد مثلا
+
+129
+00:09:44,550 --> 00:09:46,850
+c و d
+
+130
+00:09:49,240 --> 00:09:56,040
+بين C وD فيه تلاتة طيب بين D وC برضه تلاتة فهي D C
+
+131
+00:09:56,040 --> 00:10:04,640
+وهي C D طيب حافظنا برضه على نفس ال symmetric على
+
+132
+00:10:04,640 --> 00:10:07,960
+نفس ال symmetric رغم انه موجود عندك مثلا B وB
+
+133
+00:10:10,330 --> 00:10:14,410
+self loop بس مش هيفرج معاك ليش لإنه لما تعكس
+
+134
+00:10:14,410 --> 00:10:18,430
+الصفوف أعمد أو لاعمد الصفوف هتظل ال matrix زي ما
+
+135
+00:10:18,430 --> 00:10:23,090
+هي فإذا هي symmetric فعليا ك matrix مدام
+
+136
+00:10:23,090 --> 00:10:29,130
+undirected مفروض يكون كاتبلك اه undirected مدام
+
+137
+00:10:29,130 --> 00:10:34,570
+إيش undirected تمام بسيطة
+
+138
+00:10:34,570 --> 00:10:41,190
+الفكرةطيب الآن في ال incidence matrix في ال
+
+139
+00:10:41,190 --> 00:10:45,970
+incidence matrix بكل بساطة انا بحطش vertices مع
+
+140
+00:10:45,970 --> 00:10:52,730
+vertices بنحط ال vertices ك raw و ال edges بنحطهم
+
+141
+00:10:52,730 --> 00:11:01,130
+column بحيث ان العلاقة بينهم مين منهم بيسقط هذا ال
+
+142
+00:11:01,130 --> 00:11:04,410
+edge من ال vertices اللي موجودة قدامنا مين منهم
+
+143
+00:11:05,740 --> 00:11:10,280
+بيطلّع ال edge اللي قدّامه فال relation الآن هي مش
+
+144
+00:11:10,280 --> 00:11:13,780
+adjacency adjacency لما كنت بتكلم عن vertices
+
+145
+00:11:13,780 --> 00:11:16,860
+موجودة بمعنى ان عندي vertex هنا و vertex هنا
+
+146
+00:11:16,860 --> 00:11:20,560
+فالعلاقة بينهم كان مين اللي بيجاور التاني لكن لما
+
+147
+00:11:20,560 --> 00:11:25,900
+بقول العلاقة الآن بين vertex و خط link فهو معنى
+
+148
+00:11:25,900 --> 00:11:29,860
+ذلك انه مين من ال vertices هدول بيطلّع ال link هذا
+
+149
+00:11:31,210 --> 00:11:35,450
+فincidence مين هو اللي بيسقط ال .. ال .. ال edge
+
+150
+00:11:35,450 --> 00:11:40,570
+هذه فأصبحت ال relation هنا incidence matrix فصرت
+
+151
+00:11:40,570 --> 00:11:43,430
+ال incidence هي العلاقة هي ال relation اللي بدي
+
+152
+00:11:43,430 --> 00:11:47,950
+أحسبها موجودة ولا غير موجودةإذا كانوا موجودة فإذا
+
+153
+00:11:47,950 --> 00:11:54,970
+العنصر داخل ال matrix والعنصر I vertex ال vertex I
+
+154
+00:11:54,970 --> 00:12:00,450
+و ال edge J إذا فعلا هم مرتبطين في بعض بمعنى إن ال
+
+155
+00:12:00,450 --> 00:12:07,960
+edge J هو صادر من ال vertex I فبنحط مقابلهم 1على
+
+156
+00:12:07,960 --> 00:12:11,000
+تقاطعهم في ال matrix نقطة تقاطعهم في ال matrix
+
+157
+00:12:11,000 --> 00:12:13,800
+بنحط عليها واحد زي ما هنشوف في المثال otherwise
+
+158
+00:12:13,800 --> 00:12:16,720
+إذا ما هم مش علاقة ببعض لأ ال edge هذه مالهاش
+
+159
+00:12:16,720 --> 00:12:24,340
+علاقة بال بال vertex بنحطها zero complement ايش
+
+160
+00:12:24,340 --> 00:12:27,440
+دخل compliment هنا مع عدد ال edges اللي مش موجودة
+
+161
+00:12:28,710 --> 00:12:32,330
+لأ احنا مانعش في اللي مش موجودة، هنا ال .. ال ..
+
+162
+00:12:32,330 --> 00:12:35,130
+ال compliment هي ال zeros، بحط أصبح، احنا هي kick
+
+163
+00:12:35,130 --> 00:12:37,790
+بنحطها zero، يعني بمعنى إذا كان مش موجود فهو zero،
+
+164
+00:12:37,790 --> 00:12:43,370
+بس الفكرة مش موجودة ولا غير موجود، الفكرة ال edge
+
+165
+00:12:43,370 --> 00:12:48,240
+هي موجودة، و ال vertex موجودةبس هل ال vertex هذه
+
+166
+00:12:48,240 --> 00:12:50,780
+هي اللي تشيع هذا ال edge؟ يعني طالع منها ال edge
+
+167
+00:12:50,780 --> 00:12:54,840
+هذا؟ يمكن مايكونش طالع منها، هو ال edge موجود، لكن
+
+168
+00:12:54,840 --> 00:12:58,960
+مش طالع من ال vertex اللي قدامنا، ببساطة جدا، هي
+
+169
+00:12:58,960 --> 00:13:04,280
+هذا مثلا، هي هذه edge، هل ال edge هذه لها علاقة
+
+170
+00:13:04,280 --> 00:13:08,400
+بال إيه؟ كلا هما موجود، فانا مابقدر أقول
+
+171
+00:13:08,400 --> 00:13:11,860
+compliment، compliment معناته بكمل، هنا الأثنين
+
+172
+00:13:11,860 --> 00:13:14,580
+موجودين، لكن فعليا مافيش علاقة بينهم، فلما بدأ
+
+173
+00:13:14,580 --> 00:13:20,930
+أقولفرضًا هذا ال A و هذا ال H هذا بتسميها E1 مثلًا
+
+174
+00:13:20,930 --> 00:13:25,930
+معنى ذلك لما أقول A و E1 المفروض هنا يطلع Zero
+
+175
+00:13:25,930 --> 00:13:36,130
+مقابلهم يطلع Zero لأنهم مش علاقة ببعض طيب هل واجد
+
+176
+00:13:36,130 --> 00:13:43,030
+حنشوف هاي مثل هاي مثل برضه نفس الجثة هي في عندكالـ
+
+177
+00:13:43,030 --> 00:13:47,110
+graph هو هو لكن انطلب بال incidence matrix
+
+178
+00:13:47,110 --> 00:13:51,070
+incidence matrix انت عارف مسبقا انه لازم تكون عامل
+
+179
+00:13:51,070 --> 00:13:55,110
+naming او labeling لمين لل edges فبتحط لهم
+
+180
+00:13:55,110 --> 00:13:59,770
+labeling هذا الأول هذا التاني هذا الخامس بتحط لهم
+
+181
+00:13:59,770 --> 00:14:06,170
+أرقام عشان تيجي تحط الأرقام هنا فتحط E1 E2 E3 ال
+
+182
+00:14:06,170 --> 00:14:11,390
+edge الرابعال edge الخامسة و ال edge السادسة و هنا
+
+183
+00:14:11,390 --> 00:14:19,690
+هتعمل a,b,c و D طيب E one هاي one إله علاقة بال A
+
+184
+00:14:19,690 --> 00:14:25,770
+إله علاقة معناته واحد طيب هو نفسه إله علاقة بمين
+
+185
+00:14:25,770 --> 00:14:31,250
+كمان بال B معناته مع ال B فلما تيشي تتطلع عليه ك
+
+186
+00:14:31,250 --> 00:14:36,740
+column بتقدر تعرف هو بين مين و مين بين ال onesبين
+
+187
+00:14:36,740 --> 00:14:42,000
+ال ones فهو بين a و b طيب ال edge التانية التانية
+
+188
+00:14:42,000 --> 00:14:47,500
+بين a و d بين
+
+189
+00:14:47,500 --> 00:14:56,160
+a و d تمام التالت b و d متحت
+
+190
+00:14:56,160 --> 00:15:05,340
+بسيطة كتير كتير بسيطة طيب E4 ب C و D هي C وهي D
+
+191
+00:15:07,130 --> 00:15:09,830
+يعني بمعنى انت مش مضطر تعملهم element by element
+
+192
+00:15:09,830 --> 00:15:14,590
+اتطلع على كل edge ال two terminals تبعونه وحط
+
+193
+00:15:14,590 --> 00:15:18,550
+قدامهم محايد و الباقي zeros فالجثة سريعة يعني مش
+
+194
+00:15:18,550 --> 00:15:22,350
+هتاخد منك كتير وجهة لما نتكلم عن خمسة بالمرة
+
+195
+00:15:22,350 --> 00:15:29,610
+نكملهم a و c ف a و c و others zero الستة اه ستة
+
+196
+00:15:29,610 --> 00:15:36,820
+واحد تعالي تطلع هناهتلاقي ان هو واحد لحاله فلو بدي
+
+197
+00:15:36,820 --> 00:15:43,480
+ارجع ارسمه هو لحاله ال E دي خاصة بمين بال C فقط
+
+198
+00:15:43,480 --> 00:15:47,300
+ومش غيرها وماحدش غيرها معناته هي self loop معناته
+
+199
+00:15:47,300 --> 00:15:53,040
+هي ماطلعتش من الواحد طيب
+
+200
+00:15:53,040 --> 00:15:53,540
+بال direct
+
+201
+00:15:57,200 --> 00:15:59,880
+لأنه ممكن ييجي direct او ممكن ييجي direct بييجي
+
+202
+00:15:59,880 --> 00:16:03,180
+direct بكل بساطة هنا بتكلم عنها بشكل سريع هنا بال
+
+203
+00:16:03,180 --> 00:16:06,940
+directed بال directed graph معناته هنعمل زي ما
+
+204
+00:16:06,940 --> 00:16:11,700
+عملنا في ال adjacency list انه مين اللي طالع؟ طيب
+
+205
+00:16:11,700 --> 00:16:15,660
+مين اللي طالع؟ بس انا هنا بهمني كمان وين رايح؟
+
+206
+00:16:15,950 --> 00:16:20,930
+فعشان هيك هيكون كل element هو عبارة عن زوج مرتب او
+
+207
+00:16:20,930 --> 00:16:26,270
+two ones يمثل two ones هيكون عبارة عن two ones زي
+
+208
+00:16:26,270 --> 00:16:30,590
+ما هو كاتب هنا كاتب لك two ones و عامل one اخر لل
+
+209
+00:16:30,590 --> 00:16:34,270
+loop بس مالوش داعي يعني احنا ممكن نختزله مش
+
+210
+00:16:34,270 --> 00:16:38,070
+محتاجين ال one التالتة في التمثيل يكفي اتنين بس
+
+211
+00:16:38,070 --> 00:16:41,810
+كيف هنستخدم الاتنين هدولة و كيف منهم نعرف انه في
+
+212
+00:16:41,810 --> 00:16:49,820
+loop ببساطة هي graphرسمة من الرسومات أسئلة الكتاب
+
+213
+00:16:49,820 --> 00:16:53,500
+مثلا أخدتها زي ما هي و حلناها نشوف كيف نحلها بكل
+
+214
+00:16:53,500 --> 00:16:58,000
+بساطة أول ما هنبدأ نعمل ال matrix ساعتنا و نحدد
+
+215
+00:16:58,000 --> 00:17:03,200
+أسماء لل edges عشان نعرف نرتبها و ال vertices
+
+216
+00:17:03,200 --> 00:17:06,600
+تبعتنا كلها موجودة أحد أتنين أكام أحد أتلاتة أربعة
+
+217
+00:17:06,600 --> 00:17:12,340
+أربعة نبدأ بالأول E1 E1
+
+218
+00:17:17,390 --> 00:17:24,350
+فإذا هو من اتنين لواحد فإذا بدي أعرف انه in لمين؟
+
+219
+00:17:24,350 --> 00:17:30,070
+in degree و out degree هنبدأ ال two elements هنا
+
+220
+00:17:30,070 --> 00:17:37,210
+الأول in degree والتاني out degree طيب هذا بالنسبة
+
+221
+00:17:37,210 --> 00:17:42,030
+لل in degree لمين in degree ل V واحد فإذا جدا V
+
+222
+00:17:42,030 --> 00:17:49,860
+واحد بحط هنا واحد و zeroلأن هو in degree بالنسبة
+
+223
+00:17:49,860 --> 00:17:54,420
+لواحد out degree بالنسبة لواحد لأ طيب هو لمين out
+
+224
+00:17:54,420 --> 00:18:01,360
+degree لاتنين فإذا بتيجي هنا صفر واحد in degree
+
+225
+00:18:01,360 --> 00:18:05,780
+out degree others هو مالش أي علاقة لا in ولا out
+
+226
+00:18:05,780 --> 00:18:09,800
+others مش هتكون له لا in ولا out في الحالة هذه
+
+227
+00:18:09,800 --> 00:18:14,500
+فبتكتبها بهذا الشكل اتنين
+
+228
+00:18:16,760 --> 00:18:21,960
+بمين؟ مع مين هي العلاقة؟ مع اتنين واربعة فإذا هنا
+
+229
+00:18:21,960 --> 00:18:28,760
+00 و هنا 00 إحنا إلنا هنا و هنا أيوة إن لمين؟ وإن
+
+230
+00:18:28,760 --> 00:18:33,940
+هي اتنين لأربعة فإذا أربعة هي اللي هتبدأ بالواحد و
+
+231
+00:18:33,940 --> 00:18:40,720
+Zero و هنا Zero و واحد Zero و واحد تمام هنكمل بهذا
+
+232
+00:18:40,720 --> 00:18:41,080
+الشكل
+
+233
+00:18:46,150 --> 00:18:55,740
+Okay تلاتة، وين تلاتة؟V1 و V4 ف2 و 3 على طول zeros
+
+234
+00:18:55,740 --> 00:19:00,020
+بتصفرهم مباشرة من غير ما تفكر كتير فيهم و بس بتشوف
+
+235
+00:19:00,020 --> 00:19:03,620
+مين ال in و مين ال out مين ال in و مين ال out ف ال
+
+236
+00:19:03,620 --> 00:19:09,360
+in هو V1 لإنه رايح ل V1 فإذن هو اللي بياخد ال واحد
+
+237
+00:19:09,360 --> 00:19:12,440
+الأول الواحد الأول في عندنا self loop اه هي إجت
+
+238
+00:19:12,440 --> 00:19:18,140
+عند مين؟ عند 7 لما نصل ل7 بنشوف كيف بنتمثلهاهذه
+
+239
+00:19:18,140 --> 00:19:25,100
+التالتة وهذه الخمسة وهذه السادسة الآن بكل بساطة
+
+240
+00:19:25,100 --> 00:19:29,680
+لما بدك تيجي ترسم directed graph بالعكس يعني انت
+
+241
+00:19:29,680 --> 00:19:32,940
+هتمسك مين السهم يعني بما ان انا عندك فيه واحد
+
+242
+00:19:32,940 --> 00:19:35,740
+اتنين تلاتة اربعة على طول بتروح تعمل الأربعة انا
+
+243
+00:19:35,740 --> 00:19:42,300
+عندي أربعة ارتبهم زي ما بدك اقولك ارتبهم كما يحلوا
+
+244
+00:19:42,300 --> 00:19:48,110
+لك خليني اقول مثلا بدي احط هذهعطوني خربطة خربطولي
+
+245
+00:19:48,110 --> 00:19:55,190
+الدنيا هنا بدنا نحط ايش V2 ماشي هنا V3 تحاضر هنا
+
+246
+00:19:55,190 --> 00:19:59,190
+V1 الشجل اللي بيسيه ما بدك تحطه اربعة مش مشكلة هاي
+
+247
+00:19:59,190 --> 00:20:07,470
+واحد ايش ضل V4 لأ
+
+248
+00:20:07,470 --> 00:20:13,270
+لأ لأ هدولة اتخربطوا اتخربطوا هدولة بس هيك اتعكست
+
+249
+00:20:13,270 --> 00:20:17,390
+يمكن بدل ما كنا ماشيين هيكمشينا؟ لأ لأ لأ اتخربطت
+
+250
+00:20:17,390 --> 00:20:21,870
+اه لأ اتخربطونا اياها يا جماعة اتخربطت اتخربطت
+
+251
+00:20:21,870 --> 00:20:25,430
+ايوة هيك اتخربطت هي اللي صح اه اتخربطت هي اللي
+
+252
+00:20:25,430 --> 00:20:29,510
+كانت خلاص خلاص صحيح انا اتخربطت طيب عشان بس انا اش
+
+253
+00:20:29,510 --> 00:20:35,410
+اللي بدي اسلق من الخربطة هذه بعد ما نرسمها الخربطة
+
+254
+00:20:35,410 --> 00:20:39,770
+اللي هتطلع هي اللي هتتدالب الموضوع اللي ورا ايش
+
+255
+00:20:39,770 --> 00:20:43,490
+بدك ايش بدك عشان اتخربطها طيب ايش بدك عشان
+
+256
+00:20:43,490 --> 00:20:49,630
+اتخربطهاحاضر هاي تلاتة و واحد حاضرين ها هاي واحد
+
+257
+00:20:49,630 --> 00:20:58,150
+وهاي تلاتة خلاص شوي شوي خلينا نمسك أول أول
+
+258
+00:20:58,150 --> 00:21:03,130
+edge ال edge الأولى من مين لمين؟ من إلى كيف
+
+259
+00:21:03,130 --> 00:21:13,010
+تحسبها؟ لأ ايوة out ل in out ل in من اتنين ل واحد
+
+260
+00:21:17,960 --> 00:21:28,100
+طيب التانية out ل in اتنين لاربعة طيب
+
+261
+00:21:28,100 --> 00:21:38,400
+هي خلصنا هذا و خلصنا هذا طيب هتكون من اربعة لواحد
+
+262
+00:21:38,400 --> 00:21:45,550
+هي اربعة وهي واحدالتالتة او الرقم اربعة احنا على
+
+263
+00:21:45,550 --> 00:21:49,690
+فكرة المفروض كتبناهم هنا الأول هذه E واحد E اتنين
+
+264
+00:21:49,690 --> 00:21:57,330
+و E تلاتة E اربعة من اربع اه اه احنا خلصنا هذا من
+
+265
+00:21:57,330 --> 00:22:02,830
+تلاتة لاتنين هي تلاتة لاتنين وهي E اربعة اللي
+
+266
+00:22:02,830 --> 00:22:11,270
+وراها من اتنين لتلاتة اتنين لتلاتة هي E خمسة
+
+267
+00:22:12,780 --> 00:22:19,400
+الأخيرة عندنا هنا أو قبل الأخيرة أربعة لتلاتة، فهي
+
+268
+00:22:19,400 --> 00:22:25,060
+أربعة لتلاتة طيب، الآن اللي ضالت أخيرة هذه لما
+
+269
+00:22:25,060 --> 00:22:28,920
+بدنا نمثلها من إلى، هذه من وين لوين؟ من أربعة
+
+270
+00:22:28,920 --> 00:22:32,280
+لأربعة، يعني معناه ذلك هي two ones قدام الأربعة
+
+271
+00:22:32,280 --> 00:22:41,360
+فقط، فهي من إلىمن و لنفسه هذه الواضحة هي مش two
+
+272
+00:22:41,360 --> 00:22:45,180
+vertices مع بعض هي نفس ال vertex مع نفسها فبرضه
+
+273
+00:22:45,180 --> 00:22:49,520
+هذه بتسهل جدا لما ترجع تمثلها باينة واحد واحد
+
+274
+00:22:49,520 --> 00:22:56,960
+معناته من اربعة لاربعة هاي من اربعة لاربعة طيب
+
+275
+00:22:56,960 --> 00:23:02,420
+تعالى تطلع على الاتنين هدولة للواحدة الأولى بتحس
+
+276
+00:23:02,420 --> 00:23:06,730
+انه في اشي غلط صحيح؟الـ Symmetric هدولة كانوا
+
+277
+00:23:06,730 --> 00:23:10,330
+جايين في النص .. هدول صاروا فوق .. مكانهم ..
+
+278
+00:23:10,330 --> 00:23:13,470
+ماكانش في إيش مكانهم هنا .. صاروا هدول بالعكس ..
+
+279
+00:23:13,470 --> 00:23:17,450
+بتحس إن هي اتشجلبت هيك .. اتشجلبت .. بس رغم ذلك
+
+280
+00:23:17,450 --> 00:23:21,650
+احنا عارفين إن هما واحد .. صح؟ احنا مسبقا عارفين
+
+281
+00:23:21,650 --> 00:23:26,610
+إن هو واحد .. لو قدرنا الآن هدولة خيوط عادي .. انت
+
+282
+00:23:26,610 --> 00:23:31,530
+رابطهم بخيط أو بسلك .. بس ال nodes هدولة عبارة عن
+
+283
+00:23:31,530 --> 00:23:36,970
+دبابيس انت حاططهم في الخشبةفال kid ده بوس بخطانه و
+
+284
+00:23:36,970 --> 00:23:43,530
+لفته قعدت الترتيب هذه هترجع نفس الشكل كما هو هيرجع
+
+285
+00:23:43,530 --> 00:23:48,650
+الشكل هذا كما هو الاتنين isomorphic لبعض الاتنين
+
+286
+00:23:48,650 --> 00:23:53,730
+isomorphic لبعض فهو ال isomorphism تحققت المشابهة
+
+287
+00:23:53,730 --> 00:23:56,590
+بينهم المكافئة بينهم تحققت هم الاتنين متكافئين رغم
+
+288
+00:23:56,590 --> 00:24:02,390
+انه ظاهريا شكلهم مختلف لكن هم نفس الشيء هم الاتنين
+
+289
+00:24:02,390 --> 00:24:07,180
+نفس الاشياءتمام فهذه هتقودنا ل isomorphism معناه
+
+290
+00:24:07,180 --> 00:24:10,560
+ذلك ان لأ كلمة isomorphism مش بالضروري انه أجي
+
+291
+00:24:10,560 --> 00:24:12,400
+أطلع عليهم أباين واضحة
+
+292
+00:24:14,760 --> 00:24:18,960
+لو عدد ال vertices جليل يمكن بمجرد النظر تظبط معاك
+
+293
+00:24:18,960 --> 00:24:21,620
+تحاول تتخيلها لو النقطة هده شيلناها هنا طبال
+
+294
+00:24:21,620 --> 00:24:24,660
+النقطة هده شيلناها هنا اوه برجع نفس الاشياء ممكن
+
+295
+00:24:24,660 --> 00:24:29,900
+كويس لكن عشان نبعد عن التخيولات الكتير ومش كلنا
+
+296
+00:24:29,900 --> 00:24:33,440
+بنعرف نتخيل خليني نقول زي ايا ما كنتوا في الهندسة
+
+297
+00:24:33,440 --> 00:24:37,140
+الفراغية مش كلكوا هتقدروا تتخيلوا كيف ال ..الشكل
+
+298
+00:24:37,140 --> 00:24:42,240
+المجسم قدامكوا عشان تتخيلوا تحلوا فبنلجأ لمجموعة
+
+299
+00:24:42,240 --> 00:24:47,550
+خطوات لازم نعملها عشان نعمل ال check هل فعلاال two
+
+300
+00:24:47,550 --> 00:24:53,410
+graphs اللي قدامنا هم isomorphic لبعض ولا لأ؟ او
+
+301
+00:24:53,410 --> 00:24:56,830
+تحققت ال isomorphism ولا لأ؟ فهذه بكل بساطة ان
+
+302
+00:24:56,830 --> 00:25:00,630
+يكون في عندك زي ما شوفنا طوى G1 و G2، G1 اللي كان
+
+303
+00:25:00,630 --> 00:25:04,530
+فوق و G2 اللي احنا عملنا له reconstruction من ال
+
+304
+00:25:04,530 --> 00:25:08,770
+matrix كلهما هل هما isomorphic لبعض؟ فهذا بيكون
+
+305
+00:25:08,770 --> 00:25:12,410
+امتى if and only if في علاقة bijection between
+
+306
+00:25:12,410 --> 00:25:18,230
+themone to one لازم يكون لأن كل node هنا معناته في
+
+307
+00:25:18,230 --> 00:25:22,350
+إيها node هنا و on to بمعنى إنه ماجيش أعمل علاقة
+
+308
+00:25:22,350 --> 00:25:26,370
+بين two vertices هنا ألاجئ طلعت علاقة مختلفة عن
+
+309
+00:25:26,370 --> 00:25:30,350
+اللي هنا فال edges نفسها نفس الاشي ال edges هي هي
+
+310
+00:25:30,350 --> 00:25:33,230
+لإن ال edges المفروض هي العلاقة هي ال relation
+
+311
+00:25:33,230 --> 00:25:37,530
+تمام فمعنى ذلك بنقدر نقول إن isomorphic إذا فعلا
+
+312
+00:25:37,530 --> 00:25:40,950
+انتحقت يوجد bijection between them بين كل V واحد
+
+313
+00:25:40,950 --> 00:25:46,720
+من هنا مع Vمن هنا بنكون vertex من الرسمة الأولى مع
+
+314
+00:25:46,720 --> 00:25:49,720
+كل .. مع أي vertex من الرسمة التانية المهم إنه
+
+315
+00:25:49,720 --> 00:25:52,540
+خلاص هدول مرتبطين إيش الفرق الوحيد؟ هي في الإسم
+
+316
+00:25:52,540 --> 00:25:59,150
+أنا هنا كنت مسميه E5 هنا سميته 7عملية الترتيب مش
+
+317
+00:25:59,150 --> 00:26:01,710
+اكتر من هيك ..عملية الترتيب مش اكتر من هيك .. تمام
+
+318
+00:26:01,710 --> 00:26:05,270
+هذا الكلام كيف نقدر نحصل عليه إذا الرسمة بسيطة
+
+319
+00:26:05,270 --> 00:26:08,830
+صغيرة زي ما قلتلكم بإمكانك بمجرد الرسم بس مش كلنا
+
+320
+00:26:08,830 --> 00:26:12,470
+بنقدر برضه على نقعد نجهد دماغنا عشان والله أقعد
+
+321
+00:26:12,470 --> 00:26:16,290
+أتخيل هذي و بعدين تظلك تتخيل أن انت قددت هذي و
+
+322
+00:26:16,290 --> 00:26:18,750
+تجيب هذي و تقعد تتخيل أنه اتن تان مع بعض تتبدلوا
+
+323
+00:26:18,750 --> 00:26:22,430
+فتحاول تجيب .. هل احنا مش هنقعد نعمل كلام هذا؟بدنا
+
+324
+00:26:22,430 --> 00:26:27,110
+نعرف إنه أول شغلة ل G1 و G2 أهم شغلة بدنا نعمل
+
+325
+00:26:27,110 --> 00:26:32,190
+check عليها إنه ال cardinality لل vertices set
+
+326
+00:26:32,190 --> 00:26:36,250
+متساوية بمعنى عدد ال vertices في الأول هو يساوي
+
+327
+00:26:36,250 --> 00:26:39,330
+عدد ال vertices للتاني لل graph طبعا عدد ال edges
+
+328
+00:26:39,330 --> 00:26:42,690
+في الأول يساوي عدد ال edges للتاني برضه شرط ضروري
+
+329
+00:26:42,690 --> 00:26:47,270
+جدا، كويس؟ الآن عدد ال vertices with degree a
+
+330
+00:26:47,270 --> 00:26:51,030
+certain degreewith degree n معينة المفروض انه
+
+331
+00:26:51,030 --> 00:26:54,930
+متسوين بين هنا و هنا لما اجى امسك degree two
+
+332
+00:26:54,930 --> 00:26:59,630
+degree two معناته كل node هو طالع منها اتنين two
+
+333
+00:26:59,630 --> 00:27:02,670
+edges اكم واحدة طالع منها اتنين edges في ال graph
+
+334
+00:27:02,670 --> 00:27:05,730
+الأول خمسة طب بشوف ال graph التاني اكم واحدة برضه
+
+335
+00:27:05,730 --> 00:27:08,750
+طالع منها two edges يعني ال degree بتاعتها برضه
+
+336
+00:27:08,750 --> 00:27:12,690
+اتنين خمسة خلاص بشوف ال degree تلاتة degree أربعة
+
+337
+00:27:12,690 --> 00:27:18,180
+degree خمسة لازم يظل دائما متسوين دائما متسوينوإذا
+
+338
+00:27:18,180 --> 00:27:21,700
+قدرنا نعمل هذا الكلام بصير الان جزء التالت شوية
+
+339
+00:27:21,700 --> 00:27:26,660
+صعب هذه لكن شرط من الشروط أنه أي sub graph باخده
+
+340
+00:27:26,660 --> 00:27:36,240
+من G1 من G1 لازم يكون sub graph من 2 أكيد لازم
+
+341
+00:27:36,240 --> 00:27:41,590
+يكون sub graph من 2 أو isomorphic لجزء من 2Okay
+
+342
+00:27:41,590 --> 00:27:45,750
+نبدأ نمثل الكلام هذا نبدأ نشطر على تمثيله، الآن
+
+343
+00:27:45,750 --> 00:27:48,650
+إذا كان في isomorphic بين ال two graphs اللي
+
+344
+00:27:48,650 --> 00:27:51,990
+موجودين قدامنا، إذا في، يعني احنا بدنا نعمل check
+
+345
+00:27:51,990 --> 00:27:55,970
+هل يوجد isomorphic ولا لأ، وإذا يوجد عملنا rename
+
+346
+00:27:55,970 --> 00:28:01,760
+لهالأسماء ال vertices هذه كل vertex وين صارت هنا
+
+347
+00:28:01,760 --> 00:28:05,960
+طبعا يبدو هيك للشكل اللي له لأنه مخربطين عن بعض
+
+348
+00:28:05,960 --> 00:28:09,560
+لكن فعليا لأ احنا مابقدر أقول هيك مباشرة مخربطين
+
+349
+00:28:09,560 --> 00:28:15,020
+مع بعض لأ بدك تفحص خليني أشوف أول شغلة ال number
+
+350
+00:28:15,020 --> 00:28:19,860
+of vertices في الجراف الأول أو في الجراف التاني
+
+351
+00:28:22,720 --> 00:28:26,000
+فانت فيه عندك ستة و ستة okay هاي أول شرط خلصناها
+
+352
+00:28:26,000 --> 00:28:33,080
+هنا ستة و هنا ستة طيب ال numbers of edges هاي فيه
+
+353
+00:28:33,080 --> 00:28:37,080
+عندك واحد اتنين تلاتة أربعة خمسة ستة سبعة تمانية
+
+354
+00:28:37,080 --> 00:28:42,360
+تسعة هاي فيه عندك تسعة فيه جيه اتنين مش مشكلة هاي
+
+355
+00:28:42,360 --> 00:28:46,260
+واحد اتنين تلاتة أربعة خمسة ستة سبعة تمانية تسعة
+
+356
+00:28:46,260 --> 00:28:51,840
+طيب نبدأ degree two
+
+357
+00:28:53,520 --> 00:28:59,020
+degree two هاي degree two صحيح؟ و هاي degree two
+
+358
+00:28:59,020 --> 00:29:02,980
+فاتنين في عند degree two طب نفس الكلام موجود هنا
+
+359
+00:29:02,980 --> 00:29:08,080
+degree two هاي degree two و هاي degree two في
+
+360
+00:29:08,080 --> 00:29:15,720
+غيرهم؟ معناته حتى الآن اتنين و اتنين degree three
+
+361
+00:29:15,720 --> 00:29:21,040
+three هاي واحدة و هاي اتنين
+
+362
+00:29:24,890 --> 00:29:31,230
+هي اتنين هنا degree three هي واحدة وهي
+
+363
+00:29:31,230 --> 00:29:35,990
+اتنين، في غيرهم؟ مافيش غيرهم، فإذا اتنين و اتنين
+
+364
+00:29:35,990 --> 00:29:39,270
+degree four
+
+365
+00:29:45,420 --> 00:29:50,980
+هذه دقيقة واحدة وهذه دقيقة اتنين وهذه دقيقة واحدة
+
+366
+00:29:50,980 --> 00:29:54,340
+وهذه دقيقة اتنين وهذه دقيقة اتنين وهذه دقيقة اتنين
+
+367
+00:29:54,340 --> 00:29:55,180
+وهذه دقيقة اتنين وهذه دقيقة اتنين وهذه دقيقة اتنين
+
+368
+00:29:55,180 --> 00:29:57,440
+وهذه دقيقة أتنين وهذه دقيقة أتنين وهذه دقيقة أتنين
+
+369
+00:29:57,440 --> 00:29:58,540
+وهذه دقيقة أتنين وهذه دقيقة أتنين وهذه دقيقة أتنين
+
+370
+00:29:58,540 --> 00:30:01,320
+وهذه دقيقة أتنين وهذه دقيقة أتنين وهذه دقيقة أتنين
+
+371
+00:30:01,320 --> 00:30:04,180
+وهذه دقيقة أتنين وهذه دقيقة أتنين وهذه دقيقة أتنين
+
+372
+00:30:04,180 --> 00:30:11,460
+وهذه دقيقة أتنين وهذه دقيقة أتنين
+
+373
+00:30:11,460 --> 00:30:17,700
+ولكن ليست كافية مبدأ يانمكن نركن عليها شوية لو
+
+374
+00:30:17,700 --> 00:30:22,280
+إجينا اطلعنا بدنا نعمل إعادة تسمية عساس ان نشوف هي
+
+375
+00:30:22,280 --> 00:30:26,680
+وين اتغيرت ال .. الدبابيس هذه فخلينا نبدأ مثلا
+
+376
+00:30:26,680 --> 00:30:30,660
+بالاتنين في عندي يا هادي يا هادي و هنا يا هادي يا
+
+377
+00:30:30,660 --> 00:30:35,360
+هادي فإذا خلينا نحط .. بدك تحط F بمشي F على فكرة
+
+378
+00:30:39,960 --> 00:30:42,840
+دي أحسن عشان موجودة عندكوا في ال .. في الورق أنا
+
+379
+00:30:42,840 --> 00:30:46,240
+بدي أخد F لأ يعني قصد في المحاضرة في نازلة في ال
+
+380
+00:30:46,240 --> 00:30:49,460
+slides هيك في ال slides نازلة هيك بس الحاجة اللي
+
+381
+00:30:49,460 --> 00:30:52,960
+أنت مش عارفها أن هو هذا symmetric لو تغير هيمشي
+
+382
+00:30:52,960 --> 00:30:56,560
+حاله مين اللي جالك؟
+
+383
+00:30:56,560 --> 00:31:01,320
+كله اتنينات اتنينات اتنينات ال degrees بتاعتك كلها
+
+384
+00:31:01,320 --> 00:31:06,860
+اتنينات فانت ..براحتك بتبدأ تغيرها و تشوف و يمكن
+
+385
+00:31:06,860 --> 00:31:09,800
+في الآخر تلاقي انه لأ هو الصح كنت انت تشجلبهم مع
+
+386
+00:31:09,800 --> 00:31:13,780
+بعض اللي بدي اقول هي D فعلا زي ما هيحلها الوجه ال
+
+387
+00:31:13,780 --> 00:31:18,400
+D بس انا بدي اقول و بدي اعملها F okay معنى ذلك انه
+
+388
+00:31:18,400 --> 00:31:25,100
+التانية هي ال D تمام؟ خلاص الآن D متصلة ب node
+
+389
+00:31:25,100 --> 00:31:28,500
+تلاتة و node أربعة طب هتشوف مين التلاتة و مين
+
+390
+00:31:28,500 --> 00:31:37,700
+الأربعة التلاتة هي ال Aوالاربعة هي ال B طيب ال F
+
+391
+00:31:37,700 --> 00:31:41,520
+برضه مربوطة باربعة و بتلاتة التلاتة هي ال C
+
+392
+00:31:41,520 --> 00:31:51,140
+والاربعة هي ال E حل بمشي الحل بمشي الحل ايه حل و
+
+393
+00:31:51,140 --> 00:31:54,400
+خلاص مشي .. ليش؟ لأن هو symmetric كأنه رسمة لو
+
+394
+00:31:54,400 --> 00:31:58,940
+جلبتها هتطلع نفسهاو هذه صدفت بالصدفة ان طلعت لو
+
+395
+00:31:58,940 --> 00:32:03,640
+جلبت بتطلع نفسها تطلع نفسها ضالت مظبوطة كاملة بدك
+
+396
+00:32:03,640 --> 00:32:06,500
+تحط ال D فوق معناته كل العناصر اللي هنا كانت بتصير
+
+397
+00:32:06,500 --> 00:32:09,220
+هنا و اللي هنا بتصير هنا بس يعني كأنك إيش مسكته
+
+398
+00:32:09,220 --> 00:32:17,240
+جلبته بس على هاي 8 حلوة اللي هيتم فيها ليش؟ لأنه
+
+399
+00:32:17,240 --> 00:32:22,340
+احنا في كل خطوة كان عندنا خيارين لأ انت بتبدأ بأول
+
+400
+00:32:22,340 --> 00:32:26,500
+خيارين بس لأ لل initial اللي بدك تحطهابقى ديك
+
+401
+00:32:26,500 --> 00:32:31,060
+الباقي مربوط فيها لأ
+
+402
+00:32:31,060 --> 00:32:38,520
+لأ لأ مابتقدر هالواجهة دي D D صح بالظبط هم خيارين
+
+403
+00:32:38,520 --> 00:32:41,760
+و احنا فعلا توح لنا بخيار و هالواجهة دي فيها خيار
+
+404
+00:32:41,760 --> 00:32:45,900
+تاني ماعنكاش غيره ال D بتظبطش إلا مع ال A و ال B
+
+405
+00:32:45,900 --> 00:32:49,180
+مابتقدر تقول أربعة معناته بقدر أحط مكانها ال E
+
+406
+00:32:54,340 --> 00:32:57,260
+لأ هذا لو كانوا نفس ال degree بس هو فعلا لأ
+
+407
+00:32:57,260 --> 00:33:02,430
+المختلفة ال degrees تبعتهم هذه تلاتة وهذه أربعةفي
+
+408
+00:33:02,430 --> 00:33:07,450
+معنى ذلك أن هذه تلاتة هذه A وهذه B هل بتقدر
+
+409
+00:33:07,450 --> 00:33:12,030
+تغيرهم؟ لأ بتقدرش فإذا أنت ملزم بالحل لآخره ملزم
+
+410
+00:33:12,030 --> 00:33:14,890
+بالحل لآخره ال option الوحيد اللي كان عندك في
+
+411
+00:33:14,890 --> 00:33:19,570
+البداية تحط هذه D ولا F بس بعد هيك بمجرد ما حطيتها
+
+412
+00:33:19,570 --> 00:33:23,230
+انتهى بدك تكمل الحل مافيش فيه احتمالات بصير بعد
+
+413
+00:33:23,230 --> 00:33:25,770
+هيك أو possibilities بدك تكمله زي ما هو
+
+414
+00:33:30,790 --> 00:33:36,510
+تمام غيره هاي كمان مثال تاني هاي كمان مثال تاني
+
+415
+00:33:36,510 --> 00:33:43,450
+نبدأ نعمل نفس الفكرة number of vertices وهذا G1
+
+416
+00:33:43,450 --> 00:33:48,450
+وهي G2
+
+417
+00:33:48,450 --> 00:33:53,110
+مابينمش؟
+
+418
+00:33:53,110 --> 00:33:58,970
+طب ليه؟ هاي واحد اتنين تلاتة أربعة خمسة وهي واحد
+
+419
+00:33:58,970 --> 00:34:05,110
+اتنين تلاتة أربعة خمسةال number of edges هاي واحد
+
+420
+00:34:05,110 --> 00:34:08,930
+اتنين تلاتة اربعة خمسة ستة سبعة هاي واحد اتنين
+
+421
+00:34:08,930 --> 00:34:16,190
+تلاتة اربعة خمسة ستة سبعة degree اتنين ايش اللي
+
+422
+00:34:16,190 --> 00:34:26,530
+مغلبك انت ايش اللي ايش هي ال degree بس
+
+423
+00:34:31,660 --> 00:34:36,840
+بس امسك فيها دي مافيش داعي ان اكمل خلاص انت بيكفي
+
+424
+00:34:36,840 --> 00:34:40,180
+واحدة ليش لأن احنا كمان مرة هنرجع نقول هذا
+
+425
+00:34:40,180 --> 00:34:44,100
+necessary condition في necessary condition ماعرفش
+
+426
+00:34:44,100 --> 00:34:46,380
+اذا كتوا في ال calculus او لا في حاجة اسمها
+
+427
+00:34:46,380 --> 00:34:49,440
+necessary condition وفي حاجة اسمها sufficient
+
+428
+00:34:49,440 --> 00:34:54,340
+condition او sufficiency فال necessity و ال
+
+429
+00:34:54,340 --> 00:34:57,580
+sufficiency هل بتحقق ولا لأ لما بتكلم عن necessary
+
+430
+00:34:57,580 --> 00:35:01,910
+condition بمعنى انه شرط ضروريولكن غير كافي زي
+
+431
+00:35:01,910 --> 00:35:06,170
+بالظبط لما كنت اتقول والله هدول شروط ضرورية هيهم
+
+432
+00:35:06,170 --> 00:35:11,670
+الشروط هدول ضرورية بمعنى إن هم إذا انتفى واحد منهم
+
+433
+00:35:11,670 --> 00:35:16,130
+بقول هدول مش isomorphic بس إذا تحققوا بقول يمكن
+
+434
+00:35:16,130 --> 00:35:20,510
+isomorphic لكن أيوة أما إذا كان بتكلم عن ال
+
+435
+00:35:20,510 --> 00:35:24,270
+sufficiency بمعنى إنه هدى شروط كافية لو تحققت
+
+436
+00:35:24,270 --> 00:35:28,730
+فكافي جدا إن أقول أه هدول اتنين isomorphicبقدر
+
+437
+00:35:28,730 --> 00:35:32,350
+أقول مباشرة اه isomorphic طيب من وين بيجيني هذا ال
+
+438
+00:35:32,350 --> 00:35:37,850
+.. طبعا احنا هنا اتكلمنا عن التلات حالات مين اللي
+
+439
+00:35:37,850 --> 00:35:41,490
+هيقولي الكلام هذا و مين اللي مضح ليه المثال هذا
+
+440
+00:35:41,490 --> 00:35:48,350
+طلع المثال هذا شايفين
+
+441
+00:35:48,350 --> 00:35:52,570
+المثال شوفوا قدش عدد ال edges
+
+442
+00:35:56,760 --> 00:36:01,280
+كل شي بتحقق كل شي بتحقق معناه ذلك ان ال sufficient
+
+443
+00:36:01,280 --> 00:36:07,260
+condition كلها متحققة بالظبط معناته كيف اعرف ان هم
+
+444
+00:36:07,260 --> 00:36:11,660
+مش isomorphic ليش .. ليش ماطلعوش isomorphic مدام
+
+445
+00:36:11,660 --> 00:36:15,880
+كل شي عملناه طلع صح كل شي عملناه طلع صح معناته في
+
+446
+00:36:15,880 --> 00:36:20,980
+شي محتاجين كمان شوية نتعلموا زيادة لأ في حاجات
+
+447
+00:36:20,980 --> 00:36:25,160
+كمان أكمن شرط محتاجين نروحلهم لأن هذا مثل اللغة
+
+448
+00:36:25,160 --> 00:36:27,920
+واضحكلكوا قاعدين بتبتطلع و كلكوا شايفكوا قاعدين
+
+449
+00:36:27,920 --> 00:36:32,120
+بتتخيلوا و بتعدوا و بتحسبوا مظبوط كل إشي مظبوطة
+
+450
+00:36:32,120 --> 00:36:36,200
+فيه حتى ال degrees بتاعتهم كلهم مظبوطة ال degree
+
+451
+00:36:36,200 --> 00:36:39,160
+اتنين عددهم كامل ال degree تلاتة مافيش degree
+
+452
+00:36:39,160 --> 00:36:41,560
+تلاتة لأ الله في degree تلاتة هيهم .. هم كلهم
+
+453
+00:36:41,560 --> 00:36:45,360
+تلاتة أصلا أربعة degree تلاتة و خلاص هاي كل ل
+
+454
+00:36:45,360 --> 00:36:51,380
+graph على بعضه تمام كله متحقق لكن أنا بقولك زي ما
+
+455
+00:36:51,380 --> 00:36:57,780
+قلتلك حطهم على لوح خشب بدبابيسو هذه خطان او سلك
+
+456
+00:36:57,780 --> 00:37:01,060
+بينهم و قعد تغيروا شكله هل بتطلع معاك الشكل هذا او
+
+457
+00:37:01,060 --> 00:37:07,560
+لأ هاي السؤال بس مش تطلع الدبوس ينفق منه الخطان و
+
+458
+00:37:07,560 --> 00:37:10,640
+تخرب كل اللي بنقوله و تقول هاه الدكتور جالنا ما هي
+
+459
+00:37:10,640 --> 00:37:15,740
+.. و ده تبقى مربوطة بخطانها تمام فإذا في إشي
+
+460
+00:37:15,740 --> 00:37:19,440
+محتاجين نرجع للشكل هذا و نأكد منه هل هو فعلا
+
+461
+00:37:19,440 --> 00:37:22,920
+isomorphic ولا لأ هذا الإشي هو ال connectivity هو
+
+462
+00:37:22,920 --> 00:37:27,800
+ال connectivity احنا ما أخدنا transitiveعبثا أخدنا
+
+463
+00:37:27,800 --> 00:37:30,600
+ال transitive لإني عارف إنه أنا في النهاية باطلع
+
+464
+00:37:30,600 --> 00:37:36,000
+من مكان بروح لمكان معناته هذه relation أولى طيب من
+
+465
+00:37:36,000 --> 00:37:39,880
+نفس المكان ببدأ منه رحلة تانية بس هي نفس اللي كانت
+
+466
+00:37:39,880 --> 00:37:44,060
+نهاية الرحلة الأولى فإذا نهاية ال relation الأولى
+
+467
+00:37:44,060 --> 00:37:46,920
+المفروض تتفق مع بداية ال relation التانية عشان إيه
+
+468
+00:37:46,920 --> 00:37:49,860
+كانت ال transitive عشان في الآخر أقول أنا طلعت من
+
+469
+00:37:49,860 --> 00:37:56,130
+واحد لتلاتة من خلال اتنين طيب كويسالوقت لو عملنا
+
+470
+00:37:56,130 --> 00:38:01,110
+هذا الكلام ال path هذا امشيناه و رجعنا لواحد ايش
+
+471
+00:38:01,110 --> 00:38:06,690
+سمناها ال circuit تمام بالضبط هذا اللي بدنا نبدأ
+
+472
+00:38:06,690 --> 00:38:12,750
+نتكلم عنه هل عدد ال circuits ب degree معينة هو
+
+473
+00:38:12,750 --> 00:38:16,590
+نفسه هنا و هنا بمعنى انا في نفس النقطة موجود في
+
+474
+00:38:16,590 --> 00:38:20,890
+نقطة عشان اعمل اي loop و ارجع لنفس النقطة جدش عدد
+
+475
+00:38:20,890 --> 00:38:26,060
+ال inال edges اللي مرت فيها معناها كده عدد ال
+
+476
+00:38:26,060 --> 00:38:28,560
+relations اللي عدت فيها كم مرة عملت composition
+
+477
+00:38:30,790 --> 00:38:35,430
+لاحظت كيف؟ فإذا بدور على ال closed loop أو ال
+
+478
+00:38:35,430 --> 00:38:39,150
+circuits خلّيني نبدأ الفكرة بيكون عندك path of
+
+479
+00:38:39,150 --> 00:38:42,770
+length N from U to V عارفين هي sequence of
+
+480
+00:38:42,770 --> 00:38:48,690
+adjacent edges بحيث أني أذهب من U لV وإذا كان عندك
+
+481
+00:38:48,690 --> 00:38:52,510
+U تسوي V معناته رجعت لنفس النقطة بنسميها circuit
+
+482
+00:38:52,510 --> 00:38:57,550
+أو cycle circuit أو cycle فال path ببساطة أن يكون
+
+483
+00:38:57,550 --> 00:39:02,090
+فيه أكتر من oneedge بمعنى إنه يكون في عندك loop
+
+484
+00:39:02,090 --> 00:39:05,990
+معين في عندك حركة بتتحرك فيها loop معين و بدك تشوف
+
+485
+00:39:05,990 --> 00:39:10,750
+قداش عدد ال edges اللي مريت فيها عشان ترجع لنفس
+
+486
+00:39:10,750 --> 00:39:13,530
+النقطة طيب هذا هيقوتنا لحاجة برضه في ال
+
+487
+00:39:13,530 --> 00:39:17,970
+connectivity إنه أنا مستمريعني المفروض أكون مستمر،
+
+488
+00:39:17,970 --> 00:39:21,070
+مش ينقطع في النص، مش ينقطع في النص، معناه ذلك أنه
+
+489
+00:39:21,070 --> 00:39:24,870
+بدي أقول أمثلة على الصريحة عشان ناخد بالنا أنه
+
+490
+00:39:24,870 --> 00:39:29,290
+لازم يكون ال connection كامل ال connectivity كاملة
+
+491
+00:39:29,290 --> 00:39:33,630
+مثال زي هذا، هذا بقدر أقول عنه connected graph ولا
+
+492
+00:39:33,630 --> 00:39:38,350
+لأ؟ هذا أول yes، التاني لغة ده؟ أكيد لأ، فمافي حد
+
+493
+00:39:38,350 --> 00:39:42,700
+شيشي يقولي والله هاي pathفلازم تكون في
+
+494
+00:39:42,700 --> 00:39:46,480
+connectivity واضحة مستمرة عشان نعمل ال check تبعنا
+
+495
+00:39:46,480 --> 00:39:54,840
+هذه أكيد no التالتة تحت بكل
+
+496
+00:39:54,840 --> 00:39:59,660
+بساطة بتقدر من أي نقطة تروح لأي نقطة من أي نقطة
+
+497
+00:39:59,660 --> 00:40:03,320
+بتقدر تروح لأي نقطة صح ال connectivity إنك أنت
+
+498
+00:40:03,320 --> 00:40:05,820
+موجود في أي نقطة بتقدر تروح لأي نقطة على ال graph
+
+499
+00:40:06,810 --> 00:40:14,010
+بس هنا وصلنا ل E من E تصل ل B من B موصلين كلهم ما
+
+500
+00:40:14,010 --> 00:40:17,550
+هو فانت بتقدر تتحرك من أي vertex ل أي vertex تاني
+
+501
+00:40:17,550 --> 00:40:21,450
+بكل بساطة هناك ماكنتش بتقدر لإنك بدك تروح مثلا من
+
+502
+00:40:21,450 --> 00:40:26,650
+C ل A isolated بالنسبة لبعض فبنسميهم هنا مش
+
+503
+00:40:26,650 --> 00:40:30,950
+isolated node بسميهم components فى عندك two
+
+504
+00:40:30,950 --> 00:40:34,390
+components لل graph مش one component مش one
+
+505
+00:40:34,390 --> 00:40:39,290
+component طيب الأخيرةNo، بالظبط لأن هدول مش nodes،
+
+506
+00:40:39,290 --> 00:40:44,010
+مش nodes، هدول مش nodes، كويس؟ فإذا هتلاقي في عندك
+
+507
+00:40:44,010 --> 00:40:46,650
+three nodes لحال و three other .. و other three
+
+508
+00:40:46,650 --> 00:40:50,630
+nodes لحال، هدول two components في الحالة اللي
+
+509
+00:40:50,630 --> 00:40:56,060
+عندنافبالظبط النص الأول بصالش مع النص التانى فال
+
+510
+00:40:56,060 --> 00:40:59,360
+components هذه زى graph بهذا الشكل هى graph كامل
+
+511
+00:40:59,360 --> 00:41:04,240
+ال graph هذا بقدر أقول أن هو مكون من أربعة
+
+512
+00:41:04,240 --> 00:41:10,700
+components الاربعة components هذه a,b,c,d هذه set
+
+513
+00:41:10,700 --> 00:41:15,540
+of components لحال ثم في عندك ال E لحال ثم ال F
+
+514
+00:41:15,540 --> 00:41:22,760
+لحال و أخيرا I,H,G,J لحالهدولة لحالهم فعندك في
+
+515
+00:41:22,760 --> 00:41:27,120
+أربع components طيب في أي graph .. أي graph كامل
+
+516
+00:41:27,120 --> 00:41:32,680
+one component في بعض ال edges و ال vertices اللي
+
+517
+00:41:32,680 --> 00:41:38,920
+هم خصوصية بنقدر نسميهم cut vertex أو cut edge هذا
+
+518
+00:41:38,920 --> 00:41:43,820
+إذا كان عملنا له remove بيفصل ل graph ل two
+
+519
+00:41:43,820 --> 00:41:50,720
+components at least كويس؟ يعني مثلًا زي هنا مثلًاو
+
+520
+00:41:50,720 --> 00:41:55,640
+بدى افترض ان هذا لحاله graph لحاله كويس؟
+
+521
+00:41:55,640 --> 00:42:03,260
+لو شيلنا a ايش المتبقي؟ هاي المتبقي صح؟ بيضل جطعة
+
+522
+00:42:03,260 --> 00:42:08,580
+واحدة فهذا ليس cut vertex هذا مش cut vertex تمام؟
+
+523
+00:42:08,580 --> 00:42:12,640
+لأنه لما يروح مش هيتغير معانا ايش هتضل برضه
+
+524
+00:42:12,640 --> 00:42:18,170
+component واحدة لل graph لكن لو شيلت bبيصبح الشكل
+
+525
+00:42:18,170 --> 00:42:23,830
+عندك بهذا الشكل و نقطة هنا اللي هي ل D و C و هنا A
+
+526
+00:42:23,830 --> 00:42:29,110
+لأن هذه راحت خلاص فمعنى ذلك أن هذه cut vertex هذه
+
+527
+00:42:29,110 --> 00:42:35,130
+cut vertex تمام okay نفس الكلام لل edges هلوجد لو
+
+528
+00:42:35,130 --> 00:42:41,290
+قلنا ال edge هذه شيلناها و أنا بتكلم عن هذا الشكل
+
+529
+00:42:41,290 --> 00:42:50,180
+بس شيلنا ال edge اللي عليهاالـ X مش هيؤثر، هيظل
+
+530
+00:42:50,180 --> 00:42:53,920
+عبارة عن one component برضه لـ graph فهذه ليست cut
+
+531
+00:42:53,920 --> 00:43:01,120
+edge طيب، شيلنا ال edge هنا مش هتفرج معانا في شيء،
+
+532
+00:43:01,120 --> 00:43:06,960
+لأ، لو شيلت هذه صح،
+
+533
+00:43:06,960 --> 00:43:13,020
+هتظل J لحالها isolated vertex هتصير isolated
+
+534
+00:43:13,020 --> 00:43:17,160
+vertex، فهتصير هنا two partsتو components زي ما
+
+535
+00:43:17,160 --> 00:43:20,320
+أخدناه كله وسمينا هذه لحالها component وهي
+
+536
+00:43:20,320 --> 00:43:25,060
+isolated معناه ذلك انه ال edge هذه لو انشالت to be
+
+537
+00:43:25,060 --> 00:43:32,220
+removed حيضل عندي j isolated هتضل
+
+538
+00:43:32,220 --> 00:43:36,760
+لحالها node فقط node لحالها فإذا هذه بسميها cut
+
+539
+00:43:36,760 --> 00:43:39,920
+edge cut edge تمام
+
+540
+00:43:44,150 --> 00:43:48,190
+الان ال connectivity برضه في حاجة اسمها و أنتوا
+
+541
+00:43:48,190 --> 00:43:51,030
+كنتوا بتسألوا عن ال strong فبرضه ال strong معانا
+
+542
+00:43:51,030 --> 00:43:54,310
+حتى في مين في ال connectivity ففي عندي weakly و في
+
+543
+00:43:54,310 --> 00:44:00,790
+strongly connection و هذه المصطلحين هدول بنستخدمهم
+
+544
+00:44:00,790 --> 00:44:04,470
+أكتر لما يكون في عندي directed graph في directed
+
+545
+00:44:04,470 --> 00:44:10,370
+graph بسمي weak إذا كان فعلا هم بيتصل جميع النقاط
+
+546
+00:44:10,370 --> 00:44:15,280
+مع بعضها في حال أهملت الاتجاهلكن في حال أخذت
+
+547
+00:44:15,280 --> 00:44:18,560
+الاتجاه بعين الاعتبار هلاجي أنه في نقاط مش هتصلى
+
+548
+00:44:18,560 --> 00:44:24,400
+بعض يعني أنا بدي أحترم أن الشارع هذا هو رايح مش
+
+549
+00:44:24,400 --> 00:44:28,720
+جاي غير لأ ممكن ألاجيه جاي في وجهي، كويس؟ فهنا
+
+550
+00:44:28,720 --> 00:44:32,240
+weak أو strong هل وجد .. لما نجي نتكلم عن ال curve
+
+551
+00:44:32,240 --> 00:44:41,580
+الأول في البداية هل وجد بتطلع مثلا من B لD هل
+
+552
+00:44:41,580 --> 00:44:46,770
+بتقدر تطلع بدون ما تخالف الإشارة؟طيب لو بدك تطلع
+
+553
+00:44:46,770 --> 00:44:51,450
+من C ل D إلا
+
+554
+00:44:51,450 --> 00:44:58,030
+إذا خلفت الاتجاه فإذا إذا خلفت الاتجاه بأصل بنصل
+
+555
+00:44:58,030 --> 00:45:00,990
+okay معناه ذلك إن ال connectivity هنا weekly
+
+556
+00:45:00,990 --> 00:45:07,230
+connectivity هنا الاتصال ضعيف اتصال hash لأنه لازم
+
+557
+00:45:07,230 --> 00:45:10,790
+ألتزم بالاتجاه طبعا لو مافيش أصلا هو مافيش أصلا
+
+558
+00:45:10,790 --> 00:45:14,430
+connectionيعني حتى weekly بقدرش أقول عنه weekly
+
+559
+00:45:14,430 --> 00:45:17,690
+connected weekly connected بقدرش أقولها طيب في
+
+560
+00:45:17,690 --> 00:45:22,670
+الحالة التانية أي نقطة بتصل لأي نقطة و أنت ملتزم
+
+561
+00:45:22,670 --> 00:45:27,190
+بالاتجاه من أي نقطة بتقدر تروح لأي نقطة ببساطة جدا
+
+562
+00:45:27,190 --> 00:45:30,950
+لإن هو عملك cycle خارجي للكل يعني أنت بتقدر تتحرك
+
+563
+00:45:30,950 --> 00:45:35,150
+بسهولة جدا من خلال ال ring هذا من أي نقطة للتانية
+
+564
+00:45:35,150 --> 00:45:41,310
+من أي نقطة للتانية هيومفانت على الدوار بتقدر تمر
+
+565
+00:45:41,310 --> 00:45:44,510
+على أي طرف من أطراف الدوار صحيح؟ لأن انت ماشي في
+
+566
+00:45:44,510 --> 00:45:52,350
+اتجاه الصح تمام في أي دوار تماما okay نرجع لمثالنا
+
+567
+00:45:52,350 --> 00:45:55,850
+بعد هال connectivity اللي اتعلمناها هل بقدر أحل
+
+568
+00:45:55,850 --> 00:45:58,990
+الموضوع الآن بقدر أقول هي فعلا isomorphic ونخلص
+
+569
+00:45:58,990 --> 00:46:03,510
+ولا لأ مبدأيا مش هنجد نحسب قداش عدد لأنه عارفين
+
+570
+00:46:03,510 --> 00:46:08,350
+عارفين صحيح؟ طيب ال connectivity الآنالكون اكتفتي
+
+571
+00:46:08,350 --> 00:46:13,030
+هيني بدي اطلع من نقطة و ارجعلها و ال degree تلاتة
+
+572
+00:46:13,030 --> 00:46:16,470
+طبعا
+
+573
+00:46:16,470 --> 00:46:21,610
+خليني اسميها يعني cycle تلاتة degree تلاتة مثلا
+
+574
+00:46:21,610 --> 00:46:28,630
+cycle تلاتة هاي جي اتنين في عندى واحدة و هاي في
+
+575
+00:46:28,630 --> 00:46:34,050
+التانيةبتلاتة فى غيرهم بتلاتة برجع لنفس النقطة
+
+576
+00:46:34,050 --> 00:46:37,790
+يعني هل فى عندى اي cycle ال degree بتاعتها تلاتة
+
+577
+00:46:37,790 --> 00:46:42,610
+او ال circuit مافيش فهما تنتين طيب بالنسبة ل G
+
+578
+00:46:42,610 --> 00:46:51,850
+واحد مافيش مافيش تلاتات اقل اشي اربعة هى اربعة وهى
+
+579
+00:46:51,850 --> 00:46:55,770
+اربعة وهى اربعة وهى اربعة
+
+580
+00:46:58,750 --> 00:47:05,370
+أيوة تلاتة فش خلاص مش isomorphic انتهى خلص رغم أنه
+
+581
+00:47:05,370 --> 00:47:11,370
+حسب ال necessary condition كله متحقق لكن فعليا حسب
+
+582
+00:47:11,370 --> 00:47:15,510
+ال connectivity الأن وضحت أنه لأ أنا مش هقدر أصل ل
+
+583
+00:47:15,510 --> 00:47:18,930
+loop بنفس ال degree في الحالتين فإذا not
+
+584
+00:47:18,930 --> 00:47:22,290
+isomorphic في الحالة اللي عندنا أكيد مش هيكونوا
+
+585
+00:47:22,290 --> 00:47:26,710
+isomorphic في الحالة اللي موجودة عندنا تماميكفي ان
+
+586
+00:47:26,710 --> 00:47:29,910
+شرط واحد يتم نفيه او واحدة من ال conditions تم
+
+587
+00:47:29,910 --> 00:47:33,090
+نفيها عشان تقول لأ خلاص مااتحققتش .. مااتحققتش
+
+588
+00:47:33,090 --> 00:47:37,850
+تمام؟ هيك بنكون خلصنا الجزئية تبعت ال graphs
+
+589
+00:47:37,850 --> 00:47:40,550
+بيضللنا موضوع واحد اعتقد خلال الأسبوع هاد انشارة
+
+590
+00:47:40,550 --> 00:47:45,150
+بنخلصه و اللي هو ال tree و هذه حالة خاصة جدا من ال
+
+591
+00:47:45,150 --> 00:47:49,510
+graph زي ما احنا انطلقنا من ال relation و قلنا في
+
+592
+00:47:49,510 --> 00:47:53,240
+حالة خاصة منه هي ال graphكويس برضه ال graph في
+
+593
+00:47:53,240 --> 00:47:56,580
+حالة خاصة جدا منه اسمها tree هنعرف لايش ممكن
+
+594
+00:47:56,580 --> 00:48:01,360
+نستخدم ال tree هذه كويس و ممكن نحل فيها أسئلة او
+
+595
+00:48:01,360 --> 00:48:06,200
+ممكن نحل فيها أسئلة و ممكن تستخدم كبداية
+
+596
+00:48:06,200 --> 00:48:10,840
+التفكير في الذكاء الاصطناعي ال AI ال tree يعطيكوا
+
+597
+00:48:10,840 --> 00:48:11,980
+ألف عافية و برك الله فيكم
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..2123b78ed6d1de2966a9e9b10727641ac38b765d
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM_raw.json
@@ -0,0 +1 @@
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"word": " الجدول", "probability": 0.95947265625}, {"start": 135.66, "end": 136.08, "word": " هذا", "probability": 0.87890625}, {"start": 136.08, "end": 137.44, "word": " لو", "probability": 0.9189453125}, {"start": 137.44, "end": 137.92, "word": " الرسم", "probability": 0.7149658203125}, {"start": 137.92, "end": 138.12, "word": " ال", "probability": 0.60693359375}, {"start": 138.12, "end": 138.36, "word": " graph", "probability": 0.7548828125}, {"start": 138.36, "end": 138.76, "word": " نفسه", "probability": 0.99072265625}, {"start": 138.76, "end": 138.92, "word": " مش", "probability": 0.9619140625}, {"start": 138.92, "end": 139.42, "word": " موجود", "probability": 0.9892578125}, {"start": 139.42, "end": 139.9, "word": " انت", "probability": 0.838134765625}, {"start": 139.9, "end": 140.24, "word": " بتقدر", "probability": 0.9449869791666666}, {"start": 140.24, "end": 140.66, "word": " ترسمه", "probability": 0.9959716796875}, {"start": 140.66, "end": 140.96, "word": " تاني", 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"probability": 0.53173828125}, {"start": 470.28, "end": 470.62, "word": " A", "probability": 0.97216796875}, {"start": 470.62, "end": 471.14, "word": " و", "probability": 0.9521484375}, {"start": 471.14, "end": 471.52, "word": " D", "probability": 0.50390625}, {"start": 471.52, "end": 474.58, "word": " نفس", "probability": 0.686279296875}, {"start": 474.58, "end": 474.96, "word": " الكلام", "probability": 0.9391276041666666}, {"start": 474.96, "end": 475.24, "word": " D", "probability": 0.9609375}, {"start": 475.24, "end": 476.26, "word": " متصلة", "probability": 0.9716796875}, {"start": 476.26, "end": 476.62, "word": " مع", "probability": 0.994140625}, {"start": 476.62, "end": 477.04, "word": " الكل", "probability": 0.896484375}, {"start": 477.04, "end": 479.32, "word": " أما", "probability": 0.907958984375}, {"start": 479.32, "end": 479.46, "word": " مع", "probability": 0.98876953125}, {"start": 479.46, "end": 479.82, "word": " نفسها", "probability": 0.9973958333333334}, {"start": 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multi-graph ولا لأ حتى في ال multi-graph مش هتفرج المهم إن هي undirected ليش؟ لأنه إذا كان بدي أقول و الله بين ال C و ال B فيه اتنين نفترض معناته هي نفسها بين ال B و ال C هتكون برضه اتنين هذه undirected فإذا الشرط هنا عشان أقول إن هي symmetric هي جزئية ال undirected", "tokens": [2407, 4724, 5172, 47341, 8592, 674, 11890, 292, 11933, 15730, 25961, 18871, 16254, 4825, 12, 31852, 49429, 5296, 10721, 34051, 4825, 12, 34091, 49429, 5296, 10721, 11331, 49975, 8978, 2423, 4825, 12, 34091, 37893, 8032, 2655, 5172, 47341, 9673, 16095, 36145, 39896, 674, 11890, 292, 32239, 8592, 22807, 5296, 33456, 3224, 11933, 15730, 25961, 4724, 16254, 5551, 39648, 4032, 21984, 49374, 2423, 383, 4032, 2423, 363, 8978, 3224, 1975, 2655, 1863, 9957, 8717, 5172, 2655, 43042, 20449, 8315, 47395, 39896, 8717, 36178, 11296, 49374, 2423, 363, 4032, 2423, 383, 8032, 2655, 30544, 4724, 43042, 3224, 1975, 2655, 1863, 9957, 29538, 674, 11890, 292, 6156, 28814, 15730, 25124, 2288, 9566, 34105, 6225, 8592, 7649, 5551, 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{"start": 525.65, "end": 526.27, "word": " ال", "probability": 0.96923828125}, {"start": 526.27, "end": 526.55, "word": " B", "probability": 0.48876953125}, {"start": 526.55, "end": 527.15, "word": " و", "probability": 0.75927734375}, {"start": 527.15, "end": 527.27, "word": " ال", "probability": 0.8515625}, {"start": 527.27, "end": 527.43, "word": " C", "probability": 0.96484375}, {"start": 527.43, "end": 528.23, "word": " هتكون", "probability": 0.8538411458333334}, {"start": 528.23, "end": 528.47, "word": " برضه", "probability": 0.9861653645833334}, {"start": 528.47, "end": 529.21, "word": " اتنين", "probability": 0.9776611328125}, {"start": 529.21, "end": 529.59, "word": " هذه", "probability": 0.30859375}, {"start": 529.59, "end": 530.45, "word": " undirected", "probability": 0.9733072916666666}, {"start": 530.45, "end": 530.85, "word": " فإذا", "probability": 0.88671875}, {"start": 530.85, "end": 531.31, "word": " الشرط", "probability": 0.94970703125}, {"start": 531.31, "end": 531.53, "word": " هنا", "probability": 0.9921875}, {"start": 531.53, "end": 531.97, "word": " عشان", "probability": 0.9817708333333334}, {"start": 531.97, "end": 532.13, "word": " أقول", "probability": 0.87451171875}, {"start": 532.13, "end": 532.21, "word": " إن", "probability": 0.9326171875}, {"start": 532.21, "end": 532.33, "word": " هي", "probability": 0.77001953125}, {"start": 532.33, "end": 532.81, "word": " symmetric", "probability": 0.72314453125}, {"start": 532.81, "end": 533.35, "word": " هي", "probability": 0.943359375}, {"start": 533.35, "end": 533.87, "word": " جزئية", "probability": 0.91162109375}, {"start": 533.87, "end": 534.03, "word": " ال", "probability": 0.9912109375}, {"start": 534.03, "end": 534.85, "word": " undirected", "probability": 0.8733723958333334}], "temperature": 1.0}, {"id": 23, "seek": 55891, "start": 536.59, "end": 558.91, "text": "تمام بتقليه واضح حتى مافيش فيه كتير غلبة التنفيذ هذا okay الان في ال multigraph لما يكون في عندك multigraph زي ما قلنا بقى ال one بنستعيد عن ال one zero لأ بنستعيد عنه ال natural number ال natural number هذه تعود او بنحط مكانها قيمة بالظبط عدد ال edges", "tokens": [39237, 10943, 39894, 4587, 20292, 3224, 4032, 46958, 5016, 11331, 49975, 19446, 41185, 8592, 8978, 3224, 9122, 2655, 13546, 32771, 46152, 3660, 16712, 1863, 41185, 8848, 23758, 1392, 2423, 7649, 8978, 2423, 2120, 42034, 5296, 15042, 7251, 30544, 8978, 43242, 4117, 2120, 42034, 30767, 1829, 19446, 12174, 1211, 8315, 4724, 4587, 7578, 2423, 472, 44945, 14851, 3615, 25708, 18871, 2423, 472, 4018, 5296, 10721, 44945, 14851, 3615, 25708, 18871, 3224, 2423, 3303, 1230, 2423, 3303, 1230, 29538, 37279, 23328, 1975, 2407, 44945, 5016, 9566, 3714, 41361, 11296, 12174, 32640, 3660, 20666, 19913, 3555, 9566, 6225, 3215, 3215, 2423, 8819], "avg_logprob": -0.17484374552965165, "compression_ratio": 1.703056768558952, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 536.59, "end": 537.03, "word": "تمام", "probability": 0.7166748046875}, 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"word": " one", "probability": 0.85546875}, {"start": 549.89, "end": 550.87, "word": " بنستعيد", "probability": 0.9261474609375}, {"start": 550.87, "end": 551.01, "word": " عن", "probability": 0.91357421875}, {"start": 551.01, "end": 551.13, "word": " ال", "probability": 0.9580078125}, {"start": 551.13, "end": 551.27, "word": " one", "probability": 0.919921875}, {"start": 551.27, "end": 551.61, "word": " zero", "probability": 0.83642578125}, {"start": 551.61, "end": 552.05, "word": " لأ", "probability": 0.942626953125}, {"start": 552.05, "end": 552.45, "word": " بنستعيد", "probability": 0.9649658203125}, {"start": 552.45, "end": 552.69, "word": " عنه", "probability": 0.902587890625}, {"start": 552.69, "end": 552.89, "word": " ال", "probability": 0.351806640625}, {"start": 552.89, "end": 553.21, "word": " natural", "probability": 0.93310546875}, {"start": 553.21, "end": 553.57, "word": " number", "probability": 0.98486328125}, {"start": 553.57, "end": 553.95, "word": " ال", "probability": 0.96875}, {"start": 553.95, "end": 554.25, "word": " natural", "probability": 0.9423828125}, {"start": 554.25, "end": 554.59, "word": " number", "probability": 0.9833984375}, {"start": 554.59, "end": 554.83, "word": " هذه", "probability": 0.489990234375}, {"start": 554.83, "end": 555.45, "word": " تعود", "probability": 0.824462890625}, {"start": 555.45, "end": 555.69, "word": " او", "probability": 0.794189453125}, {"start": 555.69, "end": 556.07, "word": " بنحط", "probability": 0.9630533854166666}, {"start": 556.07, "end": 556.63, "word": " مكانها", "probability": 0.9895833333333334}, {"start": 556.63, "end": 557.27, "word": " قيمة", "probability": 0.99462890625}, {"start": 557.27, "end": 557.75, "word": " بالظبط", "probability": 0.9716796875}, {"start": 557.75, "end": 558.27, "word": " عدد", "probability": 0.9921875}, {"start": 558.27, "end": 558.65, "word": " ال", "probability": 0.98193359375}, {"start": 558.65, "end": 558.91, "word": " edges", "probability": 0.96533203125}], "temperature": 1.0}, {"id": 24, "seek": 58685, "start": 559.89, "end": 586.85, "text": "فمنحط قيمة ال edges نفسها بدل منحط واحد لمجرد ان الواحد دي دلالة على وجود relation او دلالة على وجود edge لأ منحطها ك natural number زي المثال برضه اللي هنعدل عليه بهذا الشكل عشان يصبح عندى برضه نفس الاشي a,b,c,d a,b,c,d خليني انا اخد مثلا c و d", "tokens": [5172, 27842, 5016, 9566, 12174, 32640, 3660, 2423, 8819, 8717, 36178, 11296, 47525, 1211, 9154, 5016, 9566, 36764, 24401, 32767, 7435, 2288, 3215, 16472, 2423, 14407, 24401, 11778, 1829, 11778, 1211, 6027, 3660, 15844, 49610, 23328, 9721, 1975, 2407, 11778, 1211, 6027, 3660, 15844, 49610, 23328, 4691, 5296, 10721, 9154, 5016, 9566, 11296, 9122, 3303, 1230, 30767, 1829, 9673, 12984, 6027, 4724, 43042, 3224, 13672, 1829, 8032, 1863, 22488, 1211, 47356, 39627, 15730, 25124, 28820, 6225, 8592, 7649, 7251, 9381, 49628, 43242, 7578, 4724, 43042, 3224, 8717, 36178, 2423, 33599, 1829, 257, 11, 65, 11, 66, 11, 67, 257, 11, 65, 11, 66, 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" بين", "probability": 0.900390625}, {"start": 592.04, "end": 592.22, "word": " D", "probability": 0.9638671875}, {"start": 592.22, "end": 592.74, "word": " وC", "probability": 0.821533203125}, {"start": 592.74, "end": 593.78, "word": " برضه", "probability": 0.9191080729166666}, {"start": 593.78, "end": 594.26, "word": " تلاتة", "probability": 0.9873046875}, {"start": 594.26, "end": 594.84, "word": " فهي", "probability": 0.9005533854166666}, {"start": 594.84, "end": 595.1, "word": " D", "probability": 0.60888671875}, {"start": 595.1, "end": 596.04, "word": " C", "probability": 0.58935546875}, {"start": 596.04, "end": 597.52, "word": " وهي", "probability": 0.796142578125}, {"start": 597.52, "end": 598.02, "word": " C", "probability": 0.72998046875}, {"start": 598.02, "end": 599.02, "word": " D", "probability": 0.97802734375}, {"start": 599.02, "end": 600.48, "word": " طيب", "probability": 0.8544921875}, {"start": 600.48, "end": 601.06, "word": " حافظنا", "probability": 0.8988037109375}, 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"word": " عندك", "probability": 0.998291015625}, {"start": 606.6, "end": 606.92, "word": " مثلا", "probability": 0.95068359375}, {"start": 606.92, "end": 607.26, "word": " B", "probability": 0.60009765625}, {"start": 607.26, "end": 607.96, "word": " وB", "probability": 0.8056640625}], "temperature": 1.0}, {"id": 26, "seek": 63501, "start": 610.33, "end": 635.01, "text": "self loop بس مش هيفرج معاك ليش لإنه لما تعكس الصفوف أعمد أو لاعمد الصفوف هتظل ال matrix زي ما هي فإذا هي symmetric فعليا ك matrix مدام undirected مفروض يكون كاتبلك اه undirected مدام إيش undirected تمام بسيطة الفكرة", "tokens": [927, 6367, 4724, 3794, 37893, 39896, 5172, 47341, 20449, 995, 4117, 32239, 8592, 5296, 28814, 1863, 3224, 5296, 15042, 6055, 3615, 4117, 3794, 31767, 5172, 38688, 5551, 25957, 3215, 34051, 20193, 25957, 3215, 31767, 5172, 38688, 8032, 2655, 19913, 1211, 2423, 8141, 30767, 1829, 19446, 39896, 6156, 28814, 15730, 39896, 32330, 6156, 3615, 20292, 995, 9122, 8141, 3714, 3215, 10943, 674, 11890, 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613.51, "end": 613.89, "word": " لما", "probability": 0.96875}, {"start": 613.89, "end": 614.41, "word": " تعكس", "probability": 0.8548583984375}, {"start": 614.41, "end": 615.59, "word": " الصفوف", "probability": 0.8155924479166666}, {"start": 615.59, "end": 615.85, "word": " أعمد", "probability": 0.78759765625}, {"start": 615.85, "end": 615.93, "word": " أو", "probability": 0.390869140625}, {"start": 615.93, "end": 616.19, "word": " لاعمد", "probability": 0.7913411458333334}, {"start": 616.19, "end": 616.47, "word": " الصفوف", "probability": 0.8953450520833334}, {"start": 616.47, "end": 616.97, "word": " هتظل", "probability": 0.8314208984375}, {"start": 616.97, "end": 617.49, "word": " ال", "probability": 0.95556640625}, {"start": 617.49, "end": 617.91, "word": " matrix", "probability": 0.95947265625}, {"start": 617.91, "end": 618.33, "word": " زي", "probability": 0.98095703125}, {"start": 618.33, "end": 618.43, "word": " ما", "probability": 0.951171875}, {"start": 618.43, "end": 618.67, "word": " هي", "probability": 0.8828125}, {"start": 618.67, "end": 619.27, "word": " فإذا", "probability": 0.90185546875}, {"start": 619.27, "end": 619.55, "word": " هي", "probability": 0.203369140625}, {"start": 619.55, "end": 620.33, "word": " symmetric", "probability": 0.58642578125}, {"start": 620.33, "end": 620.93, "word": " فعليا", "probability": 0.8748779296875}, {"start": 620.93, "end": 622.05, "word": " ك", "probability": 0.93212890625}, {"start": 622.05, "end": 622.45, "word": " matrix", "probability": 0.93310546875}, {"start": 622.45, "end": 623.09, "word": " مدام", "probability": 0.7561848958333334}, {"start": 623.09, "end": 624.35, "word": " undirected", "probability": 0.8873697916666666}, {"start": 624.35, "end": 626.03, "word": " مفروض", "probability": 0.8277587890625}, {"start": 626.03, "end": 626.21, "word": " يكون", "probability": 0.98828125}, {"start": 626.21, "end": 626.67, "word": " كاتبلك", "probability": 0.80938720703125}, {"start": 626.67, "end": 626.99, "word": " اه", "probability": 0.708251953125}, {"start": 626.99, "end": 628.39, "word": " undirected", "probability": 0.8240559895833334}, {"start": 628.39, "end": 629.13, "word": " مدام", "probability": 0.8660481770833334}, {"start": 629.13, "end": 629.39, "word": " إيش", "probability": 0.740966796875}, {"start": 629.39, "end": 630.07, "word": " undirected", "probability": 0.8297526041666666}, {"start": 630.07, "end": 631.49, "word": " تمام", "probability": 0.97412109375}, {"start": 631.49, "end": 634.57, "word": " بسيطة", "probability": 0.98740234375}, {"start": 634.57, "end": 635.01, "word": " الفكرة", "probability": 0.9925130208333334}], "temperature": 1.0}, {"id": 27, "seek": 66441, "start": 637.01, "end": 664.41, "text": "طيب الآن في ال incidence matrix في ال incidence matrix بكل بساطة انا بحطش vertices مع vertices بنحط ال vertices ك raw و ال edges بنحطهم column بحيث ان العلاقة بينهم مين منهم بيسقط هذا ال edge من ال vertices اللي موجودة قدامنا مين منهم", "tokens": [9566, 1829, 3555, 6024, 48506, 8978, 2423, 41726, 8141, 8978, 2423, 41726, 8141, 4724, 28820, 4724, 3794, 41193, 3660, 1975, 8315, 4724, 5016, 9566, 8592, 32053, 20449, 32053, 44945, 5016, 9566, 2423, 32053, 9122, 8936, 4032, 2423, 8819, 44945, 5016, 9566, 16095, 7738, 4724, 5016, 1829, 12984, 16472, 18863, 15040, 28671, 49374, 16095, 3714, 9957, 9154, 16095, 4724, 1829, 3794, 47432, 23758, 2423, 4691, 9154, 2423, 32053, 13672, 1829, 3714, 29245, 23328, 3660, 12174, 3215, 10943, 8315, 3714, 9957, 9154, 16095], "avg_logprob": -0.14072027239130763, "compression_ratio": 1.82010582010582, "no_speech_prob": 0.0, "words": [{"start": 637.01, "end": 637.37, "word": "طيب", "probability": 0.91064453125}, {"start": 637.37, "end": 637.95, "word": " الآن", "probability": 0.57244873046875}, {"start": 637.95, "end": 638.43, "word": " في", "probability": 0.7744140625}, {"start": 638.43, "end": 638.69, "word": " ال", "probability": 0.97705078125}, {"start": 638.69, "end": 639.65, "word": " incidence", 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0.9794921875}, {"start": 646.43, "end": 647.21, "word": " بنحط", "probability": 0.9127604166666666}, {"start": 647.21, "end": 647.95, "word": " ال", "probability": 0.98486328125}, {"start": 647.95, "end": 648.39, "word": " vertices", "probability": 0.982421875}, {"start": 648.39, "end": 649.37, "word": " ك", "probability": 0.96435546875}, {"start": 649.37, "end": 649.97, "word": " raw", "probability": 0.49560546875}, {"start": 649.97, "end": 651.11, "word": " و", "probability": 0.84521484375}, {"start": 651.11, "end": 651.35, "word": " ال", "probability": 0.97607421875}, {"start": 651.35, "end": 651.83, "word": " edges", "probability": 0.9482421875}, {"start": 651.83, "end": 652.73, "word": " بنحطهم", "probability": 0.926025390625}, {"start": 652.73, "end": 653.07, "word": " column", "probability": 0.89697265625}, {"start": 653.07, "end": 655.51, "word": " بحيث", "probability": 0.85357666015625}, {"start": 655.51, "end": 655.67, "word": " ان", "probability": 0.78759765625}, {"start": 655.67, "end": 656.21, "word": " العلاقة", "probability": 0.9676106770833334}, {"start": 656.21, "end": 657.03, "word": " بينهم", "probability": 0.984619140625}, {"start": 657.03, "end": 658.31, "word": " مين", "probability": 0.901123046875}, {"start": 658.31, "end": 658.77, "word": " منهم", "probability": 0.99365234375}, {"start": 658.77, "end": 660.11, "word": " بيسقط", "probability": 0.977783203125}, {"start": 660.11, "end": 660.83, "word": " هذا", "probability": 0.953125}, {"start": 660.83, "end": 661.13, "word": " ال", "probability": 0.98974609375}, {"start": 661.13, "end": 661.45, "word": " edge", "probability": 0.95947265625}, {"start": 661.45, "end": 662.01, "word": " من", "probability": 0.94677734375}, {"start": 662.01, "end": 662.11, "word": " ال", "probability": 0.98583984375}, {"start": 662.11, "end": 662.41, "word": " vertices", "probability": 0.994140625}, {"start": 662.41, "end": 662.63, "word": " اللي", "probability": 0.852783203125}, {"start": 662.63, "end": 662.93, "word": " موجودة", "probability": 0.982421875}, {"start": 662.93, "end": 663.41, "word": " قدامنا", "probability": 0.9407958984375}, {"start": 663.41, "end": 664.01, "word": " مين", "probability": 0.81591796875}, {"start": 664.01, "end": 664.41, "word": " منهم", "probability": 0.99169921875}], "temperature": 1.0}, {"id": 28, "seek": 68986, "start": 665.74, "end": 689.86, "text": "بيطلّع ال edge اللي قدّامه فال relation الآن هي مش adjacency adjacency لما كنت بتكلم عن vertices موجودة بمعنى ان عندي vertex هنا و vertex هنا فالعلاقة بينهم كان مين اللي بيجاور التاني لكن لما بقول العلاقة الآن بين vertex و خط link فهو معنى ذلك انه مين من ال vertices هدول بيطلّع ال link هذا", "tokens": [21292, 9566, 1211, 11703, 3615, 2423, 4691, 13672, 1829, 12174, 3215, 11703, 10943, 3224, 6156, 6027, 9721, 6024, 48506, 39896, 37893, 22940, 3020, 22940, 3020, 5296, 15042, 9122, 29399, 39894, 4117, 19528, 18871, 32053, 3714, 29245, 23328, 3660, 4724, 2304, 3615, 1863, 7578, 16472, 18871, 16254, 28162, 34105, 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فال", "probability": 0.840087890625}, {"start": 668.52, "end": 668.9, "word": " relation", "probability": 0.994140625}, {"start": 668.9, "end": 669.44, "word": " الآن", "probability": 0.606689453125}, {"start": 669.44, "end": 670.06, "word": " هي", "probability": 0.828125}, {"start": 670.06, "end": 670.28, "word": " مش", "probability": 0.982421875}, {"start": 670.28, "end": 671.08, "word": " adjacency", "probability": 0.992919921875}, {"start": 671.08, "end": 672.04, "word": " adjacency", "probability": 0.9638671875}, {"start": 672.04, "end": 672.24, "word": " لما", "probability": 0.892822265625}, {"start": 672.24, "end": 672.42, "word": " كنت", "probability": 0.98779296875}, {"start": 672.42, "end": 672.82, "word": " بتكلم", "probability": 0.9178059895833334}, {"start": 672.82, "end": 673.1, "word": " عن", "probability": 0.99609375}, {"start": 673.1, "end": 673.78, "word": " vertices", "probability": 0.97802734375}, {"start": 673.78, "end": 674.3, "word": " موجودة", "probability": 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"end": 678.6, "word": " اللي", "probability": 0.95947265625}, {"start": 678.6, "end": 679.18, "word": " بيجاور", "probability": 0.96513671875}, {"start": 679.18, "end": 679.8, "word": " التاني", "probability": 0.9581705729166666}, {"start": 679.8, "end": 680.38, "word": " لكن", "probability": 0.8017578125}, {"start": 680.38, "end": 680.56, "word": " لما", "probability": 0.980712890625}, {"start": 680.56, "end": 680.84, "word": " بقول", "probability": 0.968017578125}, {"start": 680.84, "end": 681.3, "word": " العلاقة", "probability": 0.94677734375}, {"start": 681.3, "end": 681.56, "word": " الآن", "probability": 0.7376708984375}, {"start": 681.56, "end": 681.82, "word": " بين", "probability": 0.92431640625}, {"start": 681.82, "end": 682.42, "word": " vertex", "probability": 0.88525390625}, {"start": 682.42, "end": 683.36, "word": " و", "probability": 0.98193359375}, {"start": 683.36, "end": 684.04, "word": " خط", "probability": 0.94384765625}, {"start": 684.04, "end": 684.58, "word": " link", "probability": 0.81640625}, {"start": 684.58, "end": 685.62, "word": " فهو", "probability": 0.9850260416666666}, {"start": 685.62, "end": 685.9, "word": " معنى", "probability": 0.9412434895833334}, {"start": 685.9, "end": 686.14, "word": " ذلك", "probability": 0.990478515625}, {"start": 686.14, "end": 686.46, "word": " انه", "probability": 0.5244140625}, {"start": 686.46, "end": 687.04, "word": " مين", "probability": 0.984619140625}, {"start": 687.04, "end": 687.24, "word": " من", "probability": 0.99560546875}, {"start": 687.24, "end": 687.38, "word": " ال", "probability": 0.9912109375}, {"start": 687.38, "end": 687.82, "word": " vertices", "probability": 0.978515625}, {"start": 687.82, "end": 688.24, "word": " هدول", "probability": 0.9612630208333334}, {"start": 688.24, "end": 689.22, "word": " بيطلّع", "probability": 0.9485677083333334}, {"start": 689.22, "end": 689.34, "word": " ال", "probability": 0.9853515625}, {"start": 689.34, "end": 689.6, "word": " link", "probability": 0.990234375}, {"start": 689.6, "end": 689.86, "word": " هذا", "probability": 0.78515625}], "temperature": 1.0}, {"id": 29, "seek": 70547, "start": 691.21, "end": 705.47, "text": "فincidence مين هو اللي بيسقط ال .. ال .. ال edge هذه فأصبحت ال relation هنا incidence matrix فصرت ال incidence هي العلاقة هي ال relation اللي بدي أحسبها موجودة ولا غير موجودة", "tokens": [5172, 4647, 2778, 3714, 9957, 31439, 13672, 1829, 4724, 1829, 3794, 47432, 2423, 4386, 2423, 4386, 2423, 4691, 29538, 6156, 10721, 9381, 3555, 33753, 2423, 9721, 34105, 41726, 8141, 6156, 9381, 43500, 2423, 41726, 39896, 18863, 15040, 28671, 39896, 2423, 9721, 13672, 1829, 4724, 16254, 5551, 5016, 35457, 11296, 3714, 29245, 23328, 3660, 49429, 32771, 13546, 3714, 29245, 23328, 3660], "avg_logprob": -0.17507684035379378, "compression_ratio": 1.61875, "no_speech_prob": 0.0, "words": [{"start": 691.2099999999999, "end": 691.91, "word": "فincidence", "probability": 0.6866861979166666}, {"start": 691.91, "end": 692.51, "word": " 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{"start": 696.57, "end": 696.89, "word": " relation", "probability": 0.99169921875}, {"start": 696.89, "end": 697.29, "word": " هنا", "probability": 0.9853515625}, {"start": 697.29, "end": 698.19, "word": " incidence", "probability": 0.9443359375}, {"start": 698.19, "end": 699.59, "word": " matrix", "probability": 0.96337890625}, {"start": 699.59, "end": 700.57, "word": " فصرت", "probability": 0.8512369791666666}, {"start": 700.57, "end": 700.71, "word": " ال", "probability": 0.99072265625}, {"start": 700.71, "end": 701.21, "word": " incidence", "probability": 0.8935546875}, {"start": 701.21, "end": 701.59, "word": " هي", "probability": 0.9580078125}, {"start": 701.59, "end": 702.29, "word": " العلاقة", "probability": 0.98828125}, {"start": 702.29, "end": 702.69, "word": " هي", "probability": 0.78466796875}, {"start": 702.69, "end": 702.83, "word": " ال", "probability": 0.94775390625}, {"start": 702.83, "end": 703.15, "word": " relation", "probability": 0.99560546875}, {"start": 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"word": " موضوع", "probability": 0.9947509765625}, {"start": 2858.71, "end": 2859.09, "word": " واحد", "probability": 0.9912109375}, {"start": 2859.09, "end": 2859.57, "word": " اعتقد", "probability": 0.8610026041666666}, {"start": 2859.57, "end": 2859.79, "word": " خلال", "probability": 0.9646809895833334}, {"start": 2859.79, "end": 2860.13, "word": " الأسبوع", "probability": 0.9588216145833334}, {"start": 2860.13, "end": 2860.27, "word": " هاد", "probability": 0.3162841796875}, {"start": 2860.27, "end": 2860.55, "word": " انشارة", "probability": 0.70953369140625}, {"start": 2860.55, "end": 2861.05, "word": " بنخلصه", "probability": 0.96201171875}, {"start": 2861.05, "end": 2861.37, "word": " و", "probability": 0.465576171875}, {"start": 2861.37, "end": 2861.45, "word": " اللي", "probability": 0.82373046875}, {"start": 2861.45, "end": 2861.61, "word": " هو", "probability": 0.98974609375}, {"start": 2861.61, "end": 2861.73, "word": " ال", "probability": 0.95068359375}, {"start": 2861.73, "end": 2861.99, "word": " tree", "probability": 0.8095703125}, {"start": 2861.99, "end": 2862.97, "word": " و", "probability": 0.35498046875}, {"start": 2862.97, "end": 2863.09, "word": " هذه", "probability": 0.333740234375}, {"start": 2863.09, "end": 2863.41, "word": " حالة", "probability": 0.9889322916666666}, {"start": 2863.41, "end": 2864.13, "word": " خاصة", "probability": 0.98095703125}, {"start": 2864.13, "end": 2864.79, "word": " جدا", "probability": 0.99169921875}, {"start": 2864.79, "end": 2864.99, "word": " من", "probability": 0.978515625}, {"start": 2864.99, "end": 2865.15, "word": " ال", "probability": 0.95751953125}, {"start": 2865.15, "end": 2865.47, "word": " graph", "probability": 0.97314453125}, {"start": 2865.47, "end": 2865.93, "word": " زي", "probability": 0.937744140625}, {"start": 2865.93, "end": 2866.01, "word": " ما", "probability": 0.9501953125}, {"start": 2866.01, "end": 2866.15, "word": " احنا", "probability": 0.8883463541666666}, {"start": 2866.15, "end": 2866.65, "word": " انطلقنا", "probability": 0.95166015625}, {"start": 2866.65, "end": 2866.85, "word": " من", "probability": 0.99658203125}, {"start": 2866.85, "end": 2867.59, "word": " ال", "probability": 0.98779296875}, {"start": 2867.59, "end": 2868.85, "word": " relation", "probability": 0.96875}, {"start": 2868.85, "end": 2869.19, "word": " و", "probability": 0.9560546875}, {"start": 2869.19, "end": 2869.39, "word": " قلنا", "probability": 0.7841796875}, {"start": 2869.39, "end": 2869.51, "word": " في", "probability": 0.8525390625}, {"start": 2869.51, "end": 2869.83, "word": " حالة", "probability": 0.9895833333333334}, {"start": 2869.83, "end": 2870.15, "word": " خاصة", "probability": 0.9840494791666666}, {"start": 2870.15, "end": 2870.37, "word": " منه", "probability": 0.984130859375}, {"start": 2870.37, "end": 2870.53, "word": " هي", "probability": 0.7802734375}, {"start": 2870.53, "end": 2870.67, "word": " ال", "probability": 0.9326171875}, {"start": 2870.67, "end": 2871.01, "word": " graph", "probability": 0.9716796875}], "temperature": 1.0}, {"id": 114, "seek": 289198, "start": 2871.84, "end": 2891.98, "text": "كويس برضه ال graph في حالة خاصة جدا منه اسمها tree هنعرف لايش ممكن نستخدم ال tree هذه كويس و ممكن نحل فيها أسئلة او ممكن نحل فيها أسئلة و ممكن تستخدم كبداية التفكير في الذكاء الاصطناعي ال AI ال tree يعطيكوا ألف عافية و برك الله فيكم", "tokens": [4117, 45865, 3794, 4724, 43042, 3224, 2423, 4295, 8978, 11331, 6027, 3660, 16490, 33546, 3660, 10874, 28259, 9154, 3224, 24525, 2304, 11296, 4230, 8032, 1863, 3615, 28480, 20193, 1829, 8592, 3714, 43020, 8717, 14851, 9778, 40448, 2423, 4230, 29538, 9122, 45865, 3794, 4032, 3714, 43020, 8717, 5016, 1211, 8978, 11296, 5551, 3794, 19986, 37977, 1975, 2407, 3714, 43020, 8717, 5016, 1211, 8978, 11296, 5551, 3794, 19986, 37977, 4032, 3714, 43020, 6055, 14851, 9778, 40448, 9122, 3555, 28259, 10632, 16712, 5172, 4117, 13546, 8978, 32545, 4117, 16606, 2423, 33546, 9566, 8315, 3615, 1829, 2423, 7318, 2423, 4230, 37495, 9566, 1829, 4117, 14407, 5551, 46538, 6225, 31845, 10632, 4032, 4724, 31747, 21984, 8978, 24793], "avg_logprob": -0.1894358343782678, "compression_ratio": 1.8952380952380952, "no_speech_prob": 9.715557098388672e-06, "words": [{"start": 2871.84, "end": 2872.3, "word": "كويس", "probability": 0.716064453125}, {"start": 2872.3, "end": 2872.68, "word": " برضه", "probability": 0.787841796875}, {"start": 2872.68, "end": 2872.76, "word": " ال", "probability": 0.28955078125}, {"start": 2872.76, "end": 2873.08, "word": " graph", "probability": 0.9326171875}, {"start": 2873.08, "end": 2873.24, "word": " في", "probability": 0.640625}, {"start": 2873.24, "end": 2873.52, "word": " حالة", "probability": 0.9637044270833334}, {"start": 2873.52, "end": 2873.9, "word": " خاصة", "probability": 0.9226888020833334}, {"start": 2873.9, "end": 2874.22, "word": " جدا", "probability": 0.989013671875}, {"start": 2874.22, "end": 2874.64, "word": " منه", "probability": 0.9580078125}, {"start": 2874.64, "end": 2875.04, "word": " اسمها", "probability": 0.95556640625}, {"start": 2875.04, "end": 2875.34, "word": " tree", "probability": 0.447021484375}, {"start": 2875.34, "end": 2876.12, "word": " هنعرف", "probability": 0.8814697265625}, {"start": 2876.12, "end": 2876.38, "word": " لايش", "probability": 0.5506184895833334}, {"start": 2876.38, "end": 2876.58, "word": " ممكن", "probability": 0.972412109375}, {"start": 2876.58, "end": 2877.04, "word": " نستخدم", "probability": 0.98779296875}, {"start": 2877.04, "end": 2877.14, "word": " ال", "probability": 0.361083984375}, {"start": 2877.14, "end": 2877.36, "word": " tree", "probability": 0.888671875}, {"start": 2877.36, "end": 2877.68, "word": " هذه", "probability": 0.61181640625}, {"start": 2877.68, "end": 2878.56, "word": " كويس", "probability": 0.7775065104166666}, {"start": 2878.56, "end": 2879.06, "word": " و", "probability": 0.9775390625}, {"start": 2879.06, "end": 2880.38, "word": " ممكن", "probability": 0.911376953125}, {"start": 2880.38, "end": 2880.68, "word": " نحل", "probability": 0.93896484375}, {"start": 2880.68, "end": 2880.9, "word": " فيها", "probability": 0.978759765625}, {"start": 2880.9, "end": 2881.18, "word": " أسئلة", "probability": 0.922607421875}, {"start": 2881.18, "end": 2881.36, "word": " او", "probability": 0.6407470703125}, {"start": 2881.36, "end": 2881.54, "word": " ممكن", "probability": 0.927978515625}, {"start": 2881.54, "end": 2881.74, "word": " نحل", "probability": 0.85791015625}, {"start": 2881.74, "end": 2881.88, "word": " فيها", "probability": 0.98779296875}, {"start": 2881.88, "end": 2882.06, "word": " أسئلة", "probability": 0.9639892578125}, {"start": 2882.06, "end": 2882.14, "word": " و", "probability": 0.4296875}, {"start": 2882.14, "end": 2882.32, "word": " ممكن", "probability": 0.955078125}, {"start": 2882.32, "end": 2883.14, "word": " تستخدم", "probability": 0.9876708984375}, {"start": 2883.14, "end": 2886.2, "word": " كبداية", "probability": 0.79547119140625}, {"start": 2886.2, "end": 2887.06, "word": " التفكير", "probability": 0.99609375}, {"start": 2887.06, "end": 2887.3, "word": " في", "probability": 0.97998046875}, {"start": 2887.3, "end": 2887.68, "word": " الذكاء", "probability": 0.9775390625}, {"start": 2887.68, "end": 2888.28, "word": " الاصطناعي", "probability": 0.8876139322916666}, {"start": 2888.28, "end": 2888.62, "word": " ال", "probability": 0.95263671875}, {"start": 2888.62, "end": 2888.92, "word": " AI", "probability": 0.8408203125}, {"start": 2888.92, "end": 2889.34, "word": " ال", "probability": 0.564453125}, {"start": 2889.34, "end": 2890.28, "word": " tree", "probability": 0.7685546875}, {"start": 2890.28, "end": 2890.84, "word": " يعطيكوا", "probability": 0.88076171875}, {"start": 2890.84, "end": 2891.0, "word": " ألف", "probability": 0.736572265625}, {"start": 2891.0, "end": 2891.24, "word": " عافية", "probability": 0.86767578125}, {"start": 2891.24, "end": 2891.32, "word": " و", "probability": 0.91552734375}, {"start": 2891.32, "end": 2891.5, "word": " برك", "probability": 0.77294921875}, {"start": 2891.5, "end": 2891.64, "word": " الله", "probability": 0.9580078125}, {"start": 2891.64, "end": 2891.98, "word": " فيكم", "probability": 0.978271484375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2892.13825, "duration_after_vad": 2757.701249999984}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f4c395f324be90f4e41235ff26b88426649c4a63
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/pBcetAq7DGM_raw.srt
@@ -0,0 +1,2388 @@
+1
+00:00:04,880 --> 00:00:07,360
+بسم الله الرحمن الرحيم هنبدأ اليوم يا شباب ان شاء
+
+2
+00:00:07,360 --> 00:00:11,160
+الله تعالى نكمل الجزء المتبقي في ال graph في موضوع
+
+3
+00:00:11,160 --> 00:00:14,080
+ال graph و اللي اتكلمنا فيه المرة الماضية يمكن
+
+4
+00:00:14,080 --> 00:00:17,900
+أخرش عن بعض أنواع ال graphs و اتكلمنا عن degrees و
+
+5
+00:00:17,900 --> 00:00:20,680
+عرفنا اشي عن degrees و شوية terminology اتعرفنا
+
+6
+00:00:20,680 --> 00:00:24,840
+عنهاالمرة الماضية اليوم هنتكلم عن ال
+
+7
+00:00:24,840 --> 00:00:28,180
+representation لل graph كيف انا بقدر امثل ال graph
+
+8
+00:00:28,180 --> 00:00:34,120
+و ال isomorphism ال isomorphism ببساطة ان هو انك
+
+9
+00:00:34,120 --> 00:00:36,580
+انت يكون في عندك two graphs بغض النظر ان هم
+
+10
+00:00:36,580 --> 00:00:43,060
+identical شكلا كأنهم زي بعض لكن هم فعلياتماما زى
+
+11
+00:00:43,060 --> 00:00:46,300
+بعض لكن يمكن انت بتكون ال nodes مغير اماكنهم مش
+
+12
+00:00:46,300 --> 00:00:49,500
+اكتر من هيك عملية تغيير اماكن لا اكتر ولا اقل
+
+13
+00:00:49,500 --> 00:00:52,140
+وبتيجى اسئلة كتير الحقيقة فى ال IQ test على
+
+14
+00:00:52,140 --> 00:00:55,580
+الحاجات هذه على الحاجات لذاك اللي هو two graphs
+
+15
+00:00:55,580 --> 00:00:59,050
+وبيقولك هل هما اتنين identical ولا لأهم بيكونوا
+
+16
+00:00:59,050 --> 00:01:02,070
+فعلا identical بس انت المظهر اللي عامله يروحي بذلك
+
+17
+00:01:02,070 --> 00:01:05,390
+طب كيف نعمل test على ال isomorphism هذي أو ان
+
+18
+00:01:05,390 --> 00:01:08,870
+واحدة منهم isomorphic للتانية؟ هنتكلم عنها في
+
+19
+00:01:08,870 --> 00:01:11,730
+موضوعنا لليوم في ال representation ال adjacency
+
+20
+00:01:11,730 --> 00:01:16,870
+lists ال adjacency matrices و ال incidence
+
+21
+00:01:16,870 --> 00:01:19,790
+matrices هم هدولة التلت أنواع اللي هنتكلم عنهم
+
+22
+00:01:19,790 --> 00:01:23,430
+اليوم في تمثيل أي graph فبالنسبة لل adjacency
+
+23
+00:01:23,430 --> 00:01:29,240
+listsفهي واضحة قائمة المجاورات أو المتجاورات بكل
+
+24
+00:01:29,240 --> 00:01:34,400
+بساطة كل واحدة من ال vertices تبعتك بتحطهم في
+
+25
+00:01:34,400 --> 00:01:40,280
+column أولو قدام كل واحدة منهم هيصبح ال adjacent
+
+26
+00:01:40,280 --> 00:01:47,180
+vertices اللي خاصة في كل vertex منهم فتتكلم عن A
+
+27
+00:01:47,180 --> 00:01:52,480
+مثلا هي مجاورة ل B و C فبتحط قدامها B و C انتهى B
+
+28
+00:01:52,480 --> 00:02:01,840
+ل A و C و E و F و هكذا خلّيني أشوف D مثلاisolated
+
+29
+00:02:01,840 --> 00:02:05,660
+isolated معناته zero في الشاشة قدامها أو هي مش
+
+30
+00:02:05,660 --> 00:02:09,860
+مجاورة لأي vertex أخرى فال adjacency هنا مش
+
+31
+00:02:09,860 --> 00:02:14,000
+متحققالها فهي فعليا zero وهكذا هذا تمثيلة أولى
+
+32
+00:02:14,000 --> 00:02:18,360
+بحيث أنك انت بتقدر من الجدول هذا لو الرسم ال graph
+
+33
+00:02:18,360 --> 00:02:22,700
+نفسه مش موجود انت بتقدر ترسمه تاني تقدر بكل بساطة
+
+34
+00:02:22,700 --> 00:02:27,420
+ترسمه من خلال ال adjacency lists اللي قدامك اللي
+
+35
+00:02:27,420 --> 00:02:31,340
+عاجيها دهقدامك طيب بالنسبة لل direct في ال direct
+
+36
+00:02:31,340 --> 00:02:34,620
+الأمور بتختلف شوية في ال direct احنا مصير نتكلم عن
+
+37
+00:02:34,620 --> 00:02:40,980
+ايش ال edges ال edges او اللي طالعة من ال vertex
+
+38
+00:02:40,980 --> 00:02:43,700
+اللي بنتكلم عنها فإذا برضه بالنسبة لل adjacency
+
+39
+00:02:43,700 --> 00:02:51,360
+less بنحطها زي ما هي ايه هاي ايه متصلة بمين مش مين
+
+40
+00:02:51,360 --> 00:02:56,460
+متصل فيها هي متصلة مع مين فهي adjacent to مين
+
+41
+00:02:59,190 --> 00:03:04,530
+ما هي بتصير للعنصر التاني، يعني هيها B هنا هي مش
+
+42
+00:03:04,530 --> 00:03:10,430
+متصلة بA، لاحظ A هي اللي متصلة بB، B غير متصلة في
+
+43
+00:03:10,430 --> 00:03:15,470
+A، فلاحظ تعالي هنا A هي متصلة في B، لكن B مش متصلة
+
+44
+00:03:15,470 --> 00:03:22,110
+مع Aبالظبط فانت هنا بتتكلم عن بدايات البدايات هي
+
+45
+00:03:22,110 --> 00:03:26,450
+دايما ال vertex اللي بتمثل بالنسبالها فلو مش موجود
+
+46
+00:03:26,450 --> 00:03:29,970
+الرسم هذا بتقدر ترجع تستنتج الرسم نفسه من مجموعة
+
+47
+00:03:29,970 --> 00:03:35,450
+او من ال adjacency last اللي قدامك تمام فهي بكل
+
+48
+00:03:35,450 --> 00:03:41,070
+بكل بساطة تعالي تطلع هتلاقي ان مثلا حاجة زي ال C C
+
+49
+00:03:41,070 --> 00:03:46,330
+مع C فانت بتعرف ان هذه self loopهذه نعرفها على طول
+
+50
+00:03:46,330 --> 00:03:50,710
+أنه معناته فيها مثل self-loop ال B نفس الكلام ففي
+
+51
+00:03:50,710 --> 00:03:54,850
+عندك فعلا self-loop لكل vertex من ال two vertices
+
+52
+00:03:54,850 --> 00:03:59,650
+هدول، تمام؟ فهذه بطريقة مبسطة كيف ممكن تعمل
+
+53
+00:03:59,650 --> 00:04:04,690
+التمثيل ال adjacency، اتفضل تختلف self-loop يعني
+
+54
+00:04:04,690 --> 00:04:06,870
+أنا الجمهور الفاتنة ما حكيتلك أنه مش هتفرج من
+
+55
+00:04:06,870 --> 00:04:09,690
+اتجاه، هتنقطع من نفسه و ترجع لنفسه، بس أنا لو أصبح
+
+56
+00:04:09,690 --> 00:04:13,950
+تعاكسه الجدول مش هيديني اتجاهلأ ليش مش هيعطيك
+
+57
+00:04:13,950 --> 00:04:17,210
+الاتجاه انت هالوقت تفرج معاك هي اي C اللي ميعطي
+
+58
+00:04:17,210 --> 00:04:22,530
+للتانية يعني انا رسمته هيك ولا انا رسمته هيك لأ
+
+59
+00:04:22,530 --> 00:04:26,710
+اتجاه في ال different vertices ل different
+
+60
+00:04:26,710 --> 00:04:30,470
+vertices بختلف الاتجاه اه يعني بمعنى هذا اتجاه A
+
+61
+00:04:30,470 --> 00:04:35,750
+وB هو اتجاه واحد فهذه في الاتجاه العكس مش موجودة
+
+62
+00:04:35,750 --> 00:04:42,770
+لكن من B لنفسها ما هي من B لنفسهاعرفت؟ فأنا هنا
+
+63
+00:04:42,770 --> 00:04:45,170
+مافيش multigraph لأ أنا ماعرفش .. ما .. ماعتقدش
+
+64
+00:04:45,170 --> 00:04:47,890
+أنه ليه الموضوع علاقة بال multigraph لأ مالوش
+
+65
+00:04:47,890 --> 00:04:49,870
+علاقة بال multigraph هنا أنت في عندك هنا
+
+66
+00:04:49,870 --> 00:04:53,630
+multigraph فيه .. فيه mult .. فيه المفروض أنه هنا
+
+67
+00:04:53,630 --> 00:04:58,330
+لو في multigraph بتمثل بس في الحالة هذه بده يكتب
+
+68
+00:04:58,330 --> 00:05:01,850
+اتنين بيه بده يكتب جدامك اتنين بيه لو في
+
+69
+00:05:01,850 --> 00:05:05,450
+multigraph لو في عندك ال .. جثة ال multigraph هنا
+
+70
+00:05:05,450 --> 00:05:06,710
+متهيأرة مش متمثلة في الرسم
+
+71
+00:05:09,540 --> 00:05:13,840
+عارف اه بس بدك توضح انه جديش يعني ممكن ساعتها لو
+
+72
+00:05:13,840 --> 00:05:16,940
+افترضنا خلينا نحنا نحط من هنا افتراضية هاي حط
+
+73
+00:05:16,940 --> 00:05:23,140
+بتقول فيهاي كمان بهذا الشكل فبينطلع لمين ل E ل E
+
+74
+00:05:23,140 --> 00:05:29,100
+فإذا هنا يا بكتب E يا بنكتب اتنين E كويس
+
+75
+00:05:29,100 --> 00:05:33,440
+انت يعني فتحتيك موضوععشان يبين معانا ان و الله في
+
+76
+00:05:33,440 --> 00:05:35,940
+multi-graph اذا في multi-graph لان فعلا المثال
+
+77
+00:05:35,940 --> 00:05:38,660
+مافيش في multi-graph اذا في multi-graph ياما بتعمل
+
+78
+00:05:38,660 --> 00:05:44,960
+كمان E تانية او بتعمل اتنين E حسب جداش عدد ال
+
+79
+00:05:44,960 --> 00:05:51,680
+edges اللي رايحة من A لE من A لE تمام طيب ال
+
+80
+00:05:51,680 --> 00:05:55,980
+adjacency matricesهو مصفوفات المجاورة، مصفوفات
+
+81
+00:05:55,980 --> 00:05:59,400
+المجاورة كتير أبسط، كتير كتير أبسط، كل ما أنا
+
+82
+00:05:59,400 --> 00:06:03,600
+محتاجه أن أعمل matrix، ال matrix هذا ال rows
+
+83
+00:06:03,600 --> 00:06:08,860
+تبعتها أو ال columns نفسهم هي مجموعة ال vertices،
+
+84
+00:06:08,860 --> 00:06:12,180
+مجموعة ال verticesهنقول والله ال node الأولى
+
+85
+00:06:12,180 --> 00:06:15,120
+التانية التالتة و هكذا الأول ال node الأولى
+
+86
+00:06:15,120 --> 00:06:18,640
+التانية التالتة و هكذا إذا كان في connection
+
+87
+00:06:18,640 --> 00:06:23,600
+between من التانية للأولى بنحط قدامها هنا واحد
+
+88
+00:06:23,600 --> 00:06:29,480
+مافيش صفر zero أو صفر خلاص بكل بساطة فإذا ان هي
+
+89
+00:06:29,480 --> 00:06:35,900
+عبارة عن matrix ال matrix ها دي العنصرI و J بيكون
+
+90
+00:06:35,900 --> 00:06:39,620
+واحد إذا في فعل في connection between ال vertex I
+
+91
+00:06:39,620 --> 00:06:45,040
+to vertex J طبعا في ال undirected كلاهما في نفس
+
+92
+00:06:45,040 --> 00:06:51,720
+الاتجاه فمن I ل J و من J ل I فكلاهما بيمشي الحالة
+
+93
+00:06:51,720 --> 00:06:53,900
+في ال directed شوية بتختلف الأمور في ال directed
+
+94
+00:06:53,900 --> 00:06:57,580
+زي ما هتشوف هتختلف معانا شوية otherwise بنحطها
+
+95
+00:06:57,580 --> 00:07:02,500
+zero معناته مافيش أصلا edge between them هاي مثال
+
+96
+00:07:05,750 --> 00:07:11,030
+هي عندك مثل A B C و D بهذا الشكل و بدنا نرسم او
+
+97
+00:07:11,030 --> 00:07:15,290
+نمثل الشكل اللي قدامنا او بعد ما نرسمه بعد ما ناخد
+
+98
+00:07:15,290 --> 00:07:18,410
+ال matrix تبعتنا من ال matrix بدي ارجع اخد الرسم
+
+99
+00:07:18,410 --> 00:07:22,570
+فالمفروض representation يعني المفروض العكس صحيح من
+
+100
+00:07:22,570 --> 00:07:27,930
+ال matrix اقدر ارجع ارسم ال graph نفسه تمام فالان
+
+101
+00:07:27,930 --> 00:07:29,610
+بكل بساطة هنعمل نفس القالية
+
+102
+00:07:36,480 --> 00:07:41,420
+from A to A مافيش self loop فإذا zero طيب A متصلة
+
+103
+00:07:41,420 --> 00:07:46,120
+بالباجي فإذا متصلة مع B واحد مع C واحد مع D واحد
+
+104
+00:07:46,120 --> 00:07:50,120
+بهذا الشكل تمام ال B نفس الجثة ال B متصلة مع مين
+
+105
+00:07:50,120 --> 00:07:54,580
+مع A و D نفس
+
+106
+00:07:54,580 --> 00:08:01,080
+الكلام D متصلة مع الكل أما مع نفسها لأ بعد ما
+
+107
+00:08:01,080 --> 00:08:01,660
+ترسمها
+
+108
+00:08:05,480 --> 00:08:09,400
+لأ هذه بتصير symmetric اه symmetric فهذه اول
+
+109
+00:08:09,400 --> 00:08:15,960
+ملاحظة انه في ال adjacency matrices بتكون دايما
+
+110
+00:08:15,960 --> 00:08:22,080
+symmetric مادام undirected بالظبط مادام undirected
+
+111
+00:08:22,080 --> 00:08:25,840
+فهي دايما symmetric بس اهم شغلة ان هي تكون
+
+112
+00:08:25,840 --> 00:08:32,290
+undirectedو بفرجش undirected إذا كان عندي multi
+
+113
+00:08:32,290 --> 00:08:35,110
+-path ولا لأ أو multi-graph ولا لأ حتى في ال multi
+
+114
+00:08:35,110 --> 00:08:38,790
+-graph مش هتفرج المهم إن هي undirected ليش؟ لأنه
+
+115
+00:08:38,790 --> 00:08:42,130
+إذا كان بدي أقول و الله بين ال C و ال B فيه اتنين
+
+116
+00:08:42,130 --> 00:08:48,470
+نفترض معناته هي نفسها بين ال B و ال C هتكون برضه
+
+117
+00:08:48,470 --> 00:08:52,210
+اتنين هذه undirected فإذا الشرط هنا عشان أقول إن
+
+118
+00:08:52,210 --> 00:08:57,670
+هي symmetric هي جزئية ال undirectedتمام بتقليه
+
+119
+00:08:57,670 --> 00:09:04,670
+واضح حتى مافيش فيه كتير غلبة التنفيذ هذا okay
+
+120
+00:09:04,670 --> 00:09:07,790
+الان في ال multigraph لما يكون في عندك multigraph
+
+121
+00:09:07,790 --> 00:09:12,050
+زي ما قلنا بقى ال one بنستعيد عن ال one zero لأ
+
+122
+00:09:12,050 --> 00:09:14,590
+بنستعيد عنه ال natural number ال natural number
+
+123
+00:09:14,590 --> 00:09:18,910
+هذه تعود او بنحط مكانها قيمة بالظبط عدد ال edges
+
+124
+00:09:19,890 --> 00:09:23,670
+فمنحط قيمة ال edges نفسها بدل منحط واحد لمجرد ان
+
+125
+00:09:23,670 --> 00:09:27,070
+الواحد دي دلالة على وجود relation او دلالة على
+
+126
+00:09:27,070 --> 00:09:31,270
+وجود edge لأ منحطها ك natural number زي المثال
+
+127
+00:09:31,270 --> 00:09:35,870
+برضه اللي هنعدل عليه بهذا الشكل عشان يصبح عندى
+
+128
+00:09:35,870 --> 00:09:44,550
+برضه نفس الاشي a,b,c,d a,b,c,d خليني انا اخد مثلا
+
+129
+00:09:44,550 --> 00:09:46,850
+c و d
+
+130
+00:09:49,240 --> 00:09:56,040
+بين C وD فيه تلاتة طيب بين D وC برضه تلاتة فهي D C
+
+131
+00:09:56,040 --> 00:10:04,640
+وهي C D طيب حافظنا برضه على نفس ال symmetric على
+
+132
+00:10:04,640 --> 00:10:07,960
+نفس ال symmetric رغم انه موجود عندك مثلا B وB
+
+133
+00:10:10,330 --> 00:10:14,410
+self loop بس مش هيفرج معاك ليش لإنه لما تعكس
+
+134
+00:10:14,410 --> 00:10:18,430
+الصفوف أعمد أو لاعمد الصفوف هتظل ال matrix زي ما
+
+135
+00:10:18,430 --> 00:10:23,090
+هي فإذا هي symmetric فعليا ك matrix مدام
+
+136
+00:10:23,090 --> 00:10:29,130
+undirected مفروض يكون كاتبلك اه undirected مدام
+
+137
+00:10:29,130 --> 00:10:34,570
+إيش undirected تمام بسيطة
+
+138
+00:10:34,570 --> 00:10:41,190
+الفكرةطيب الآن في ال incidence matrix في ال
+
+139
+00:10:41,190 --> 00:10:45,970
+incidence matrix بكل بساطة انا بحطش vertices مع
+
+140
+00:10:45,970 --> 00:10:52,730
+vertices بنحط ال vertices ك raw و ال edges بنحطهم
+
+141
+00:10:52,730 --> 00:11:01,130
+column بحيث ان العلاقة بينهم مين منهم بيسقط هذا ال
+
+142
+00:11:01,130 --> 00:11:04,410
+edge من ال vertices اللي موجودة قدامنا مين منهم
+
+143
+00:11:05,740 --> 00:11:10,280
+بيطلّع ال edge اللي قدّامه فال relation الآن هي مش
+
+144
+00:11:10,280 --> 00:11:13,780
+adjacency adjacency لما كنت بتكلم عن vertices
+
+145
+00:11:13,780 --> 00:11:16,860
+موجودة بمعنى ان عندي vertex هنا و vertex هنا
+
+146
+00:11:16,860 --> 00:11:20,560
+فالعلاقة بينهم كان مين اللي بيجاور التاني لكن لما
+
+147
+00:11:20,560 --> 00:11:25,900
+بقول العلاقة الآن بين vertex و خط link فهو معنى
+
+148
+00:11:25,900 --> 00:11:29,860
+ذلك انه مين من ال vertices هدول بيطلّع ال link هذا
+
+149
+00:11:31,210 --> 00:11:35,450
+فincidence مين هو اللي بيسقط ال .. ال .. ال edge
+
+150
+00:11:35,450 --> 00:11:40,570
+هذه فأصبحت ال relation هنا incidence matrix فصرت
+
+151
+00:11:40,570 --> 00:11:43,430
+ال incidence هي العلاقة هي ال relation اللي بدي
+
+152
+00:11:43,430 --> 00:11:47,950
+أحسبها موجودة ولا غير موجودةإذا كانوا موجودة فإذا
+
+153
+00:11:47,950 --> 00:11:54,970
+العنصر داخل ال matrix والعنصر I vertex ال vertex I
+
+154
+00:11:54,970 --> 00:12:00,450
+و ال edge J إذا فعلا هم مرتبطين في بعض بمعنى إن ال
+
+155
+00:12:00,450 --> 00:12:07,960
+edge J هو صادر من ال vertex I فبنحط مقابلهم 1على
+
+156
+00:12:07,960 --> 00:12:11,000
+تقاطعهم في ال matrix نقطة تقاطعهم في ال matrix
+
+157
+00:12:11,000 --> 00:12:13,800
+بنحط عليها واحد زي ما هنشوف في المثال otherwise
+
+158
+00:12:13,800 --> 00:12:16,720
+إذا ما هم مش علاقة ببعض لأ ال edge هذه مالهاش
+
+159
+00:12:16,720 --> 00:12:24,340
+علاقة بال بال vertex بنحطها zero complement ايش
+
+160
+00:12:24,340 --> 00:12:27,440
+دخل compliment هنا مع عدد ال edges اللي مش موجودة
+
+161
+00:12:28,710 --> 00:12:32,330
+لأ احنا مانعش في اللي مش موجودة، هنا ال .. ال ..
+
+162
+00:12:32,330 --> 00:12:35,130
+ال compliment هي ال zeros، بحط أصبح، احنا هي kick
+
+163
+00:12:35,130 --> 00:12:37,790
+بنحطها zero، يعني بمعنى إذا كان مش موجود فهو zero،
+
+164
+00:12:37,790 --> 00:12:43,370
+بس الفكرة مش موجودة ولا غير موجود، الفكرة ال edge
+
+165
+00:12:43,370 --> 00:12:48,240
+هي موجودة، و ال vertex موجودةبس هل ال vertex هذه
+
+166
+00:12:48,240 --> 00:12:50,780
+هي اللي تشيع هذا ال edge؟ يعني طالع منها ال edge
+
+167
+00:12:50,780 --> 00:12:54,840
+هذا؟ يمكن مايكونش طالع منها، هو ال edge موجود، لكن
+
+168
+00:12:54,840 --> 00:12:58,960
+مش طالع من ال vertex اللي قدامنا، ببساطة جدا، هي
+
+169
+00:12:58,960 --> 00:13:04,280
+هذا مثلا، هي هذه edge، هل ال edge هذه لها علاقة
+
+170
+00:13:04,280 --> 00:13:08,400
+بال إيه؟ كلا هما موجود، فانا مابقدر أقول
+
+171
+00:13:08,400 --> 00:13:11,860
+compliment، compliment معناته بكمل، هنا الأثنين
+
+172
+00:13:11,860 --> 00:13:14,580
+موجودين، لكن فعليا مافيش علاقة بينهم، فلما بدأ
+
+173
+00:13:14,580 --> 00:13:20,930
+أقولفرضًا هذا ال A و هذا ال H هذا بتسميها E1 مثلًا
+
+174
+00:13:20,930 --> 00:13:25,930
+معنى ذلك لما أقول A و E1 المفروض هنا يطلع Zero
+
+175
+00:13:25,930 --> 00:13:36,130
+مقابلهم يطلع Zero لأنهم مش علاقة ببعض طيب هل واجد
+
+176
+00:13:36,130 --> 00:13:43,030
+حنشوف هاي مثل هاي مثل برضه نفس الجثة هي في عندكالـ
+
+177
+00:13:43,030 --> 00:13:47,110
+graph هو هو لكن انطلب بال incidence matrix
+
+178
+00:13:47,110 --> 00:13:51,070
+incidence matrix انت عارف مسبقا انه لازم تكون عامل
+
+179
+00:13:51,070 --> 00:13:55,110
+naming او labeling لمين لل edges فبتحط لهم
+
+180
+00:13:55,110 --> 00:13:59,770
+labeling هذا الأول هذا التاني هذا الخامس بتحط لهم
+
+181
+00:13:59,770 --> 00:14:06,170
+أرقام عشان تيجي تحط الأرقام هنا فتحط E1 E2 E3 ال
+
+182
+00:14:06,170 --> 00:14:11,390
+edge الرابعال edge الخامسة و ال edge السادسة و هنا
+
+183
+00:14:11,390 --> 00:14:19,690
+هتعمل a,b,c و D طيب E one هاي one إله علاقة بال A
+
+184
+00:14:19,690 --> 00:14:25,770
+إله علاقة معناته واحد طيب هو نفسه إله علاقة بمين
+
+185
+00:14:25,770 --> 00:14:31,250
+كمان بال B معناته مع ال B فلما تيشي تتطلع عليه ك
+
+186
+00:14:31,250 --> 00:14:36,740
+column بتقدر تعرف هو بين مين و مين بين ال onesبين
+
+187
+00:14:36,740 --> 00:14:42,000
+ال ones فهو بين a و b طيب ال edge التانية التانية
+
+188
+00:14:42,000 --> 00:14:47,500
+بين a و d بين
+
+189
+00:14:47,500 --> 00:14:56,160
+a و d تمام التالت b و d متحت
+
+190
+00:14:56,160 --> 00:15:05,340
+بسيطة كتير كتير بسيطة طيب E4 ب C و D هي C وهي D
+
+191
+00:15:07,130 --> 00:15:09,830
+يعني بمعنى انت مش مضطر تعملهم element by element
+
+192
+00:15:09,830 --> 00:15:14,590
+اتطلع على كل edge ال two terminals تبعونه وحط
+
+193
+00:15:14,590 --> 00:15:18,550
+قدامهم محايد و الباقي zeros فالجثة سريعة يعني مش
+
+194
+00:15:18,550 --> 00:15:22,350
+هتاخد منك كتير وجهة لما نتكلم عن خمسة بالمرة
+
+195
+00:15:22,350 --> 00:15:29,610
+نكملهم a و c ف a و c و others zero الستة اه ستة
+
+196
+00:15:29,610 --> 00:15:36,820
+واحد تعالي تطلع هناهتلاقي ان هو واحد لحاله فلو بدي
+
+197
+00:15:36,820 --> 00:15:43,480
+ارجع ارسمه هو لحاله ال E دي خاصة بمين بال C فقط
+
+198
+00:15:43,480 --> 00:15:47,300
+ومش غيرها وماحدش غيرها معناته هي self loop معناته
+
+199
+00:15:47,300 --> 00:15:53,040
+هي ماطلعتش من الواحد طيب
+
+200
+00:15:53,040 --> 00:15:53,540
+بال direct
+
+201
+00:15:57,200 --> 00:15:59,880
+لأنه ممكن ييجي direct او ممكن ييجي direct بييجي
+
+202
+00:15:59,880 --> 00:16:03,180
+direct بكل بساطة هنا بتكلم عنها بشكل سريع هنا بال
+
+203
+00:16:03,180 --> 00:16:06,940
+directed بال directed graph معناته هنعمل زي ما
+
+204
+00:16:06,940 --> 00:16:11,700
+عملنا في ال adjacency list انه مين اللي طالع؟ طيب
+
+205
+00:16:11,700 --> 00:16:15,660
+مين اللي طالع؟ بس انا هنا بهمني كمان وين رايح؟
+
+206
+00:16:15,950 --> 00:16:20,930
+فعشان هيك هيكون كل element هو عبارة عن زوج مرتب او
+
+207
+00:16:20,930 --> 00:16:26,270
+two ones يمثل two ones هيكون عبارة عن two ones زي
+
+208
+00:16:26,270 --> 00:16:30,590
+ما هو كاتب هنا كاتب لك two ones و عامل one اخر لل
+
+209
+00:16:30,590 --> 00:16:34,270
+loop بس مالوش داعي يعني احنا ممكن نختزله مش
+
+210
+00:16:34,270 --> 00:16:38,070
+محتاجين ال one التالتة في التمثيل يكفي اتنين بس
+
+211
+00:16:38,070 --> 00:16:41,810
+كيف هنستخدم الاتنين هدولة و كيف منهم نعرف انه في
+
+212
+00:16:41,810 --> 00:16:49,820
+loop ببساطة هي graphرسمة من الرسومات أسئلة الكتاب
+
+213
+00:16:49,820 --> 00:16:53,500
+مثلا أخدتها زي ما هي و حلناها نشوف كيف نحلها بكل
+
+214
+00:16:53,500 --> 00:16:58,000
+بساطة أول ما هنبدأ نعمل ال matrix ساعتنا و نحدد
+
+215
+00:16:58,000 --> 00:17:03,200
+أسماء لل edges عشان نعرف نرتبها و ال vertices
+
+216
+00:17:03,200 --> 00:17:06,600
+تبعتنا كلها موجودة أحد أتنين أكام أحد أتلاتة أربعة
+
+217
+00:17:06,600 --> 00:17:12,340
+أربعة نبدأ بالأول E1 E1
+
+218
+00:17:17,390 --> 00:17:24,350
+فإذا هو من اتنين لواحد فإذا بدي أعرف انه in لمين؟
+
+219
+00:17:24,350 --> 00:17:30,070
+in degree و out degree هنبدأ ال two elements هنا
+
+220
+00:17:30,070 --> 00:17:37,210
+الأول in degree والتاني out degree طيب هذا بالنسبة
+
+221
+00:17:37,210 --> 00:17:42,030
+لل in degree لمين in degree ل V واحد فإذا جدا V
+
+222
+00:17:42,030 --> 00:17:49,860
+واحد بحط هنا واحد و zeroلأن هو in degree بالنسبة
+
+223
+00:17:49,860 --> 00:17:54,420
+لواحد out degree بالنسبة لواحد لأ طيب هو لمين out
+
+224
+00:17:54,420 --> 00:18:01,360
+degree لاتنين فإذا بتيجي هنا صفر واحد in degree
+
+225
+00:18:01,360 --> 00:18:05,780
+out degree others هو مالش أي علاقة لا in ولا out
+
+226
+00:18:05,780 --> 00:18:09,800
+others مش هتكون له لا in ولا out في الحالة هذه
+
+227
+00:18:09,800 --> 00:18:14,500
+فبتكتبها بهذا الشكل اتنين
+
+228
+00:18:16,760 --> 00:18:21,960
+بمين؟ مع مين هي العلاقة؟ مع اتنين واربعة فإذا هنا
+
+229
+00:18:21,960 --> 00:18:28,760
+00 و هنا 00 إحنا إلنا هنا و هنا أيوة إن لمين؟ وإن
+
+230
+00:18:28,760 --> 00:18:33,940
+هي اتنين لأربعة فإذا أربعة هي اللي هتبدأ بالواحد و
+
+231
+00:18:33,940 --> 00:18:40,720
+Zero و هنا Zero و واحد Zero و واحد تمام هنكمل بهذا
+
+232
+00:18:40,720 --> 00:18:41,080
+الشكل
+
+233
+00:18:46,150 --> 00:18:55,740
+Okay تلاتة، وين تلاتة؟V1 و V4 ف2 و 3 على طول zeros
+
+234
+00:18:55,740 --> 00:19:00,020
+بتصفرهم مباشرة من غير ما تفكر كتير فيهم و بس بتشوف
+
+235
+00:19:00,020 --> 00:19:03,620
+مين ال in و مين ال out مين ال in و مين ال out ف ال
+
+236
+00:19:03,620 --> 00:19:09,360
+in هو V1 لإنه رايح ل V1 فإذن هو اللي بياخد ال واحد
+
+237
+00:19:09,360 --> 00:19:12,440
+الأول الواحد الأول في عندنا self loop اه هي إجت
+
+238
+00:19:12,440 --> 00:19:18,140
+عند مين؟ عند 7 لما نصل ل7 بنشوف كيف بنتمثلهاهذه
+
+239
+00:19:18,140 --> 00:19:25,100
+التالتة وهذه الخمسة وهذه السادسة الآن بكل بساطة
+
+240
+00:19:25,100 --> 00:19:29,680
+لما بدك تيجي ترسم directed graph بالعكس يعني انت
+
+241
+00:19:29,680 --> 00:19:32,940
+هتمسك مين السهم يعني بما ان انا عندك فيه واحد
+
+242
+00:19:32,940 --> 00:19:35,740
+اتنين تلاتة اربعة على طول بتروح تعمل الأربعة انا
+
+243
+00:19:35,740 --> 00:19:42,300
+عندي أربعة ارتبهم زي ما بدك اقولك ارتبهم كما يحلوا
+
+244
+00:19:42,300 --> 00:19:48,110
+لك خليني اقول مثلا بدي احط هذهعطوني خربطة خربطولي
+
+245
+00:19:48,110 --> 00:19:55,190
+الدنيا هنا بدنا نحط ايش V2 ماشي هنا V3 تحاضر هنا
+
+246
+00:19:55,190 --> 00:19:59,190
+V1 الشجل اللي بيسيه ما بدك تحطه اربعة مش مشكلة هاي
+
+247
+00:19:59,190 --> 00:20:07,470
+واحد ايش ضل V4 لأ
+
+248
+00:20:07,470 --> 00:20:13,270
+لأ لأ هدولة اتخربطوا اتخربطوا هدولة بس هيك اتعكست
+
+249
+00:20:13,270 --> 00:20:17,390
+يمكن بدل ما كنا ماشيين هيكمشينا؟ لأ لأ لأ اتخربطت
+
+250
+00:20:17,390 --> 00:20:21,870
+اه لأ اتخربطونا اياها يا جماعة اتخربطت اتخربطت
+
+251
+00:20:21,870 --> 00:20:25,430
+ايوة هيك اتخربطت هي اللي صح اه اتخربطت هي اللي
+
+252
+00:20:25,430 --> 00:20:29,510
+كانت خلاص خلاص صحيح انا اتخربطت طيب عشان بس انا اش
+
+253
+00:20:29,510 --> 00:20:35,410
+اللي بدي اسلق من الخربطة هذه بعد ما نرسمها الخربطة
+
+254
+00:20:35,410 --> 00:20:39,770
+اللي هتطلع هي اللي هتتدالب الموضوع اللي ورا ايش
+
+255
+00:20:39,770 --> 00:20:43,490
+بدك ايش بدك عشان اتخربطها طيب ايش بدك عشان
+
+256
+00:20:43,490 --> 00:20:49,630
+اتخربطهاحاضر هاي تلاتة و واحد حاضرين ها هاي واحد
+
+257
+00:20:49,630 --> 00:20:58,150
+وهاي تلاتة خلاص شوي شوي خلينا نمسك أول أول
+
+258
+00:20:58,150 --> 00:21:03,130
+edge ال edge الأولى من مين لمين؟ من إلى كيف
+
+259
+00:21:03,130 --> 00:21:13,010
+تحسبها؟ لأ ايوة out ل in out ل in من اتنين ل واحد
+
+260
+00:21:17,960 --> 00:21:28,100
+طيب التانية out ل in اتنين لاربعة طيب
+
+261
+00:21:28,100 --> 00:21:38,400
+هي خلصنا هذا و خلصنا هذا طيب هتكون من اربعة لواحد
+
+262
+00:21:38,400 --> 00:21:45,550
+هي اربعة وهي واحدالتالتة او الرقم اربعة احنا على
+
+263
+00:21:45,550 --> 00:21:49,690
+فكرة المفروض كتبناهم هنا الأول هذه E واحد E اتنين
+
+264
+00:21:49,690 --> 00:21:57,330
+و E تلاتة E اربعة من اربع اه اه احنا خلصنا هذا من
+
+265
+00:21:57,330 --> 00:22:02,830
+تلاتة لاتنين هي تلاتة لاتنين وهي E اربعة اللي
+
+266
+00:22:02,830 --> 00:22:11,270
+وراها من اتنين لتلاتة اتنين لتلاتة هي E خمسة
+
+267
+00:22:12,780 --> 00:22:19,400
+الأخيرة عندنا هنا أو قبل الأخيرة أربعة لتلاتة، فهي
+
+268
+00:22:19,400 --> 00:22:25,060
+أربعة لتلاتة طيب، الآن اللي ضالت أخيرة هذه لما
+
+269
+00:22:25,060 --> 00:22:28,920
+بدنا نمثلها من إلى، هذه من وين لوين؟ من أربعة
+
+270
+00:22:28,920 --> 00:22:32,280
+لأربعة، يعني معناه ذلك هي two ones قدام الأربعة
+
+271
+00:22:32,280 --> 00:22:41,360
+فقط، فهي من إلىمن و لنفسه هذه الواضحة هي مش two
+
+272
+00:22:41,360 --> 00:22:45,180
+vertices مع بعض هي نفس ال vertex مع نفسها فبرضه
+
+273
+00:22:45,180 --> 00:22:49,520
+هذه بتسهل جدا لما ترجع تمثلها باينة واحد واحد
+
+274
+00:22:49,520 --> 00:22:56,960
+معناته من اربعة لاربعة هاي من اربعة لاربعة طيب
+
+275
+00:22:56,960 --> 00:23:02,420
+تعالى تطلع على الاتنين هدولة للواحدة الأولى بتحس
+
+276
+00:23:02,420 --> 00:23:06,730
+انه في اشي غلط صحيح؟الـ Symmetric هدولة كانوا
+
+277
+00:23:06,730 --> 00:23:10,330
+جايين في النص .. هدول صاروا فوق .. مكانهم ..
+
+278
+00:23:10,330 --> 00:23:13,470
+ماكانش في إيش مكانهم هنا .. صاروا هدول بالعكس ..
+
+279
+00:23:13,470 --> 00:23:17,450
+بتحس إن هي اتشجلبت هيك .. اتشجلبت .. بس رغم ذلك
+
+280
+00:23:17,450 --> 00:23:21,650
+احنا عارفين إن هما واحد .. صح؟ احنا مسبقا عارفين
+
+281
+00:23:21,650 --> 00:23:26,610
+إن هو واحد .. لو قدرنا الآن هدولة خيوط عادي .. انت
+
+282
+00:23:26,610 --> 00:23:31,530
+رابطهم بخيط أو بسلك .. بس ال nodes هدولة عبارة عن
+
+283
+00:23:31,530 --> 00:23:36,970
+دبابيس انت حاططهم في الخشبةفال kid ده بوس بخطانه و
+
+284
+00:23:36,970 --> 00:23:43,530
+لفته قعدت الترتيب هذه هترجع نفس الشكل كما هو هيرجع
+
+285
+00:23:43,530 --> 00:23:48,650
+الشكل هذا كما هو الاتنين isomorphic لبعض الاتنين
+
+286
+00:23:48,650 --> 00:23:53,730
+isomorphic لبعض فهو ال isomorphism تحققت المشابهة
+
+287
+00:23:53,730 --> 00:23:56,590
+بينهم المكافئة بينهم تحققت هم الاتنين متكافئين رغم
+
+288
+00:23:56,590 --> 00:24:02,390
+انه ظاهريا شكلهم مختلف لكن هم نفس الشيء هم الاتنين
+
+289
+00:24:02,390 --> 00:24:07,180
+نفس الاشياءتمام فهذه هتقودنا ل isomorphism معناه
+
+290
+00:24:07,180 --> 00:24:10,560
+ذلك ان لأ كلمة isomorphism مش بالضروري انه أجي
+
+291
+00:24:10,560 --> 00:24:12,400
+أطلع عليهم أباين واضحة
+
+292
+00:24:14,760 --> 00:24:18,960
+لو عدد ال vertices جليل يمكن بمجرد النظر تظبط معاك
+
+293
+00:24:18,960 --> 00:24:21,620
+تحاول تتخيلها لو النقطة هده شيلناها هنا طبال
+
+294
+00:24:21,620 --> 00:24:24,660
+النقطة هده شيلناها هنا اوه برجع نفس الاشياء ممكن
+
+295
+00:24:24,660 --> 00:24:29,900
+كويس لكن عشان نبعد عن التخيولات الكتير ومش كلنا
+
+296
+00:24:29,900 --> 00:24:33,440
+بنعرف نتخيل خليني نقول زي ايا ما كنتوا في الهندسة
+
+297
+00:24:33,440 --> 00:24:37,140
+الفراغية مش كلكوا هتقدروا تتخيلوا كيف ال ..الشكل
+
+298
+00:24:37,140 --> 00:24:42,240
+المجسم قدامكوا عشان تتخيلوا تحلوا فبنلجأ لمجموعة
+
+299
+00:24:42,240 --> 00:24:47,550
+خطوات لازم نعملها عشان نعمل ال check هل فعلاال two
+
+300
+00:24:47,550 --> 00:24:53,410
+graphs اللي قدامنا هم isomorphic لبعض ولا لأ؟ او
+
+301
+00:24:53,410 --> 00:24:56,830
+تحققت ال isomorphism ولا لأ؟ فهذه بكل بساطة ان
+
+302
+00:24:56,830 --> 00:25:00,630
+يكون في عندك زي ما شوفنا طوى G1 و G2، G1 اللي كان
+
+303
+00:25:00,630 --> 00:25:04,530
+فوق و G2 اللي احنا عملنا له reconstruction من ال
+
+304
+00:25:04,530 --> 00:25:08,770
+matrix كلهما هل هما isomorphic لبعض؟ فهذا بيكون
+
+305
+00:25:08,770 --> 00:25:12,410
+امتى if and only if في علاقة bijection between
+
+306
+00:25:12,410 --> 00:25:18,230
+themone to one لازم يكون لأن كل node هنا معناته في
+
+307
+00:25:18,230 --> 00:25:22,350
+إيها node هنا و on to بمعنى إنه ماجيش أعمل علاقة
+
+308
+00:25:22,350 --> 00:25:26,370
+بين two vertices هنا ألاجئ طلعت علاقة مختلفة عن
+
+309
+00:25:26,370 --> 00:25:30,350
+اللي هنا فال edges نفسها نفس الاشي ال edges هي هي
+
+310
+00:25:30,350 --> 00:25:33,230
+لإن ال edges المفروض هي العلاقة هي ال relation
+
+311
+00:25:33,230 --> 00:25:37,530
+تمام فمعنى ذلك بنقدر نقول إن isomorphic إذا فعلا
+
+312
+00:25:37,530 --> 00:25:40,950
+انتحقت يوجد bijection between them بين كل V واحد
+
+313
+00:25:40,950 --> 00:25:46,720
+من هنا مع Vمن هنا بنكون vertex من الرسمة الأولى مع
+
+314
+00:25:46,720 --> 00:25:49,720
+كل .. مع أي vertex من الرسمة التانية المهم إنه
+
+315
+00:25:49,720 --> 00:25:52,540
+خلاص هدول مرتبطين إيش الفرق الوحيد؟ هي في الإسم
+
+316
+00:25:52,540 --> 00:25:59,150
+أنا هنا كنت مسميه E5 هنا سميته 7عملية الترتيب مش
+
+317
+00:25:59,150 --> 00:26:01,710
+اكتر من هيك ..عملية الترتيب مش اكتر من هيك .. تمام
+
+318
+00:26:01,710 --> 00:26:05,270
+هذا الكلام كيف نقدر نحصل عليه إذا الرسمة بسيطة
+
+319
+00:26:05,270 --> 00:26:08,830
+صغيرة زي ما قلتلكم بإمكانك بمجرد الرسم بس مش كلنا
+
+320
+00:26:08,830 --> 00:26:12,470
+بنقدر برضه على نقعد نجهد دماغنا عشان والله أقعد
+
+321
+00:26:12,470 --> 00:26:16,290
+أتخيل هذي و بعدين تظلك تتخيل أن انت قددت هذي و
+
+322
+00:26:16,290 --> 00:26:18,750
+تجيب هذي و تقعد تتخيل أنه اتن تان مع بعض تتبدلوا
+
+323
+00:26:18,750 --> 00:26:22,430
+فتحاول تجيب .. هل احنا مش هنقعد نعمل كلام هذا؟بدنا
+
+324
+00:26:22,430 --> 00:26:27,110
+نعرف إنه أول شغلة ل G1 و G2 أهم شغلة بدنا نعمل
+
+325
+00:26:27,110 --> 00:26:32,190
+check عليها إنه ال cardinality لل vertices set
+
+326
+00:26:32,190 --> 00:26:36,250
+متساوية بمعنى عدد ال vertices في الأول هو يساوي
+
+327
+00:26:36,250 --> 00:26:39,330
+عدد ال vertices للتاني لل graph طبعا عدد ال edges
+
+328
+00:26:39,330 --> 00:26:42,690
+في الأول يساوي عدد ال edges للتاني برضه شرط ضروري
+
+329
+00:26:42,690 --> 00:26:47,270
+جدا، كويس؟ الآن عدد ال vertices with degree a
+
+330
+00:26:47,270 --> 00:26:51,030
+certain degreewith degree n معينة المفروض انه
+
+331
+00:26:51,030 --> 00:26:54,930
+متسوين بين هنا و هنا لما اجى امسك degree two
+
+332
+00:26:54,930 --> 00:26:59,630
+degree two معناته كل node هو طالع منها اتنين two
+
+333
+00:26:59,630 --> 00:27:02,670
+edges اكم واحدة طالع منها اتنين edges في ال graph
+
+334
+00:27:02,670 --> 00:27:05,730
+الأول خمسة طب بشوف ال graph التاني اكم واحدة برضه
+
+335
+00:27:05,730 --> 00:27:08,750
+طالع منها two edges يعني ال degree بتاعتها برضه
+
+336
+00:27:08,750 --> 00:27:12,690
+اتنين خمسة خلاص بشوف ال degree تلاتة degree أربعة
+
+337
+00:27:12,690 --> 00:27:18,180
+degree خمسة لازم يظل دائما متسوين دائما متسوينوإذا
+
+338
+00:27:18,180 --> 00:27:21,700
+قدرنا نعمل هذا الكلام بصير الان جزء التالت شوية
+
+339
+00:27:21,700 --> 00:27:26,660
+صعب هذه لكن شرط من الشروط أنه أي sub graph باخده
+
+340
+00:27:26,660 --> 00:27:36,240
+من G1 من G1 لازم يكون sub graph من 2 أكيد لازم
+
+341
+00:27:36,240 --> 00:27:41,590
+يكون sub graph من 2 أو isomorphic لجزء من 2Okay
+
+342
+00:27:41,590 --> 00:27:45,750
+نبدأ نمثل الكلام هذا نبدأ نشطر على تمثيله، الآن
+
+343
+00:27:45,750 --> 00:27:48,650
+إذا كان في isomorphic بين ال two graphs اللي
+
+344
+00:27:48,650 --> 00:27:51,990
+موجودين قدامنا، إذا في، يعني احنا بدنا نعمل check
+
+345
+00:27:51,990 --> 00:27:55,970
+هل يوجد isomorphic ولا لأ، وإذا يوجد عملنا rename
+
+346
+00:27:55,970 --> 00:28:01,760
+لهالأسماء ال vertices هذه كل vertex وين صارت هنا
+
+347
+00:28:01,760 --> 00:28:05,960
+طبعا يبدو هيك للشكل اللي له لأنه مخربطين عن بعض
+
+348
+00:28:05,960 --> 00:28:09,560
+لكن فعليا لأ احنا مابقدر أقول هيك مباشرة مخربطين
+
+349
+00:28:09,560 --> 00:28:15,020
+مع بعض لأ بدك تفحص خليني أشوف أول شغلة ال number
+
+350
+00:28:15,020 --> 00:28:19,860
+of vertices في الجراف الأول أو في الجراف التاني
+
+351
+00:28:22,720 --> 00:28:26,000
+فانت فيه عندك ستة و ستة okay هاي أول شرط خلصناها
+
+352
+00:28:26,000 --> 00:28:33,080
+هنا ستة و هنا ستة طيب ال numbers of edges هاي فيه
+
+353
+00:28:33,080 --> 00:28:37,080
+عندك واحد اتنين تلاتة أربعة خمسة ستة سبعة تمانية
+
+354
+00:28:37,080 --> 00:28:42,360
+تسعة هاي فيه عندك تسعة فيه جيه اتنين مش مشكلة هاي
+
+355
+00:28:42,360 --> 00:28:46,260
+واحد اتنين تلاتة أربعة خمسة ستة سبعة تمانية تسعة
+
+356
+00:28:46,260 --> 00:28:51,840
+طيب نبدأ degree two
+
+357
+00:28:53,520 --> 00:28:59,020
+degree two هاي degree two صحيح؟ و هاي degree two
+
+358
+00:28:59,020 --> 00:29:02,980
+فاتنين في عند degree two طب نفس الكلام موجود هنا
+
+359
+00:29:02,980 --> 00:29:08,080
+degree two هاي degree two و هاي degree two في
+
+360
+00:29:08,080 --> 00:29:15,720
+غيرهم؟ معناته حتى الآن اتنين و اتنين degree three
+
+361
+00:29:15,720 --> 00:29:21,040
+three هاي واحدة و هاي اتنين
+
+362
+00:29:24,890 --> 00:29:31,230
+هي اتنين هنا degree three هي واحدة وهي
+
+363
+00:29:31,230 --> 00:29:35,990
+اتنين، في غيرهم؟ مافيش غيرهم، فإذا اتنين و اتنين
+
+364
+00:29:35,990 --> 00:29:39,270
+degree four
+
+365
+00:29:45,420 --> 00:29:50,980
+هذه دقيقة واحدة وهذه دقيقة اتنين وهذه دقيقة واحدة
+
+366
+00:29:50,980 --> 00:29:54,340
+وهذه دقيقة اتنين وهذه دقيقة اتنين وهذه دقيقة اتنين
+
+367
+00:29:54,340 --> 00:29:55,180
+وهذه دقيقة اتنين وهذه دقيقة اتنين وهذه دقيقة اتنين
+
+368
+00:29:55,180 --> 00:29:57,440
+وهذه دقيقة أتنين وهذه دقيقة أتنين وهذه دقيقة أتنين
+
+369
+00:29:57,440 --> 00:29:58,540
+وهذه دقيقة أتنين وهذه دقيقة أتنين وهذه دقيقة أتنين
+
+370
+00:29:58,540 --> 00:30:01,320
+وهذه دقيقة أتنين وهذه دقيقة أتنين وهذه دقيقة أتنين
+
+371
+00:30:01,320 --> 00:30:04,180
+وهذه دقيقة أتنين وهذه دقيقة أتنين وهذه دقيقة أتنين
+
+372
+00:30:04,180 --> 00:30:11,460
+وهذه دقيقة أتنين وهذه دقيقة أتنين
+
+373
+00:30:11,460 --> 00:30:17,700
+ولكن ليست كافية مبدأ يانمكن نركن عليها شوية لو
+
+374
+00:30:17,700 --> 00:30:22,280
+إجينا اطلعنا بدنا نعمل إعادة تسمية عساس ان نشوف هي
+
+375
+00:30:22,280 --> 00:30:26,680
+وين اتغيرت ال .. الدبابيس هذه فخلينا نبدأ مثلا
+
+376
+00:30:26,680 --> 00:30:30,660
+بالاتنين في عندي يا هادي يا هادي و هنا يا هادي يا
+
+377
+00:30:30,660 --> 00:30:35,360
+هادي فإذا خلينا نحط .. بدك تحط F بمشي F على فكرة
+
+378
+00:30:39,960 --> 00:30:42,840
+دي أحسن عشان موجودة عندكوا في ال .. في الورق أنا
+
+379
+00:30:42,840 --> 00:30:46,240
+بدي أخد F لأ يعني قصد في المحاضرة في نازلة في ال
+
+380
+00:30:46,240 --> 00:30:49,460
+slides هيك في ال slides نازلة هيك بس الحاجة اللي
+
+381
+00:30:49,460 --> 00:30:52,960
+أنت مش عارفها أن هو هذا symmetric لو تغير هيمشي
+
+382
+00:30:52,960 --> 00:30:56,560
+حاله مين اللي جالك؟
+
+383
+00:30:56,560 --> 00:31:01,320
+كله اتنينات اتنينات اتنينات ال degrees بتاعتك كلها
+
+384
+00:31:01,320 --> 00:31:06,860
+اتنينات فانت ..براحتك بتبدأ تغيرها و تشوف و يمكن
+
+385
+00:31:06,860 --> 00:31:09,800
+في الآخر تلاقي انه لأ هو الصح كنت انت تشجلبهم مع
+
+386
+00:31:09,800 --> 00:31:13,780
+بعض اللي بدي اقول هي D فعلا زي ما هيحلها الوجه ال
+
+387
+00:31:13,780 --> 00:31:18,400
+D بس انا بدي اقول و بدي اعملها F okay معنى ذلك انه
+
+388
+00:31:18,400 --> 00:31:25,100
+التانية هي ال D تمام؟ خلاص الآن D متصلة ب node
+
+389
+00:31:25,100 --> 00:31:28,500
+تلاتة و node أربعة طب هتشوف مين التلاتة و مين
+
+390
+00:31:28,500 --> 00:31:37,700
+الأربعة التلاتة هي ال Aوالاربعة هي ال B طيب ال F
+
+391
+00:31:37,700 --> 00:31:41,520
+برضه مربوطة باربعة و بتلاتة التلاتة هي ال C
+
+392
+00:31:41,520 --> 00:31:51,140
+والاربعة هي ال E حل بمشي الحل بمشي الحل ايه حل و
+
+393
+00:31:51,140 --> 00:31:54,400
+خلاص مشي .. ليش؟ لأن هو symmetric كأنه رسمة لو
+
+394
+00:31:54,400 --> 00:31:58,940
+جلبتها هتطلع نفسهاو هذه صدفت بالصدفة ان طلعت لو
+
+395
+00:31:58,940 --> 00:32:03,640
+جلبت بتطلع نفسها تطلع نفسها ضالت مظبوطة كاملة بدك
+
+396
+00:32:03,640 --> 00:32:06,500
+تحط ال D فوق معناته كل العناصر اللي هنا كانت بتصير
+
+397
+00:32:06,500 --> 00:32:09,220
+هنا و اللي هنا بتصير هنا بس يعني كأنك إيش مسكته
+
+398
+00:32:09,220 --> 00:32:17,240
+جلبته بس على هاي 8 حلوة اللي هيتم فيها ليش؟ لأنه
+
+399
+00:32:17,240 --> 00:32:22,340
+احنا في كل خطوة كان عندنا خيارين لأ انت بتبدأ بأول
+
+400
+00:32:22,340 --> 00:32:26,500
+خيارين بس لأ لل initial اللي بدك تحطهابقى ديك
+
+401
+00:32:26,500 --> 00:32:31,060
+الباقي مربوط فيها لأ
+
+402
+00:32:31,060 --> 00:32:38,520
+لأ لأ مابتقدر هالواجهة دي D D صح بالظبط هم خيارين
+
+403
+00:32:38,520 --> 00:32:41,760
+و احنا فعلا توح لنا بخيار و هالواجهة دي فيها خيار
+
+404
+00:32:41,760 --> 00:32:45,900
+تاني ماعنكاش غيره ال D بتظبطش إلا مع ال A و ال B
+
+405
+00:32:45,900 --> 00:32:49,180
+مابتقدر تقول أربعة معناته بقدر أحط مكانها ال E
+
+406
+00:32:54,340 --> 00:32:57,260
+لأ هذا لو كانوا نفس ال degree بس هو فعلا لأ
+
+407
+00:32:57,260 --> 00:33:02,430
+المختلفة ال degrees تبعتهم هذه تلاتة وهذه أربعةفي
+
+408
+00:33:02,430 --> 00:33:07,450
+معنى ذلك أن هذه تلاتة هذه A وهذه B هل بتقدر
+
+409
+00:33:07,450 --> 00:33:12,030
+تغيرهم؟ لأ بتقدرش فإذا أنت ملزم بالحل لآخره ملزم
+
+410
+00:33:12,030 --> 00:33:14,890
+بالحل لآخره ال option الوحيد اللي كان عندك في
+
+411
+00:33:14,890 --> 00:33:19,570
+البداية تحط هذه D ولا F بس بعد هيك بمجرد ما حطيتها
+
+412
+00:33:19,570 --> 00:33:23,230
+انتهى بدك تكمل الحل مافيش فيه احتمالات بصير بعد
+
+413
+00:33:23,230 --> 00:33:25,770
+هيك أو possibilities بدك تكمله زي ما هو
+
+414
+00:33:30,790 --> 00:33:36,510
+تمام غيره هاي كمان مثال تاني هاي كمان مثال تاني
+
+415
+00:33:36,510 --> 00:33:43,450
+نبدأ نعمل نفس الفكرة number of vertices وهذا G1
+
+416
+00:33:43,450 --> 00:33:48,450
+وهي G2
+
+417
+00:33:48,450 --> 00:33:53,110
+مابينمش؟
+
+418
+00:33:53,110 --> 00:33:58,970
+طب ليه؟ هاي واحد اتنين تلاتة أربعة خمسة وهي واحد
+
+419
+00:33:58,970 --> 00:34:05,110
+اتنين تلاتة أربعة خمسةال number of edges هاي واحد
+
+420
+00:34:05,110 --> 00:34:08,930
+اتنين تلاتة اربعة خمسة ستة سبعة هاي واحد اتنين
+
+421
+00:34:08,930 --> 00:34:16,190
+تلاتة اربعة خمسة ستة سبعة degree اتنين ايش اللي
+
+422
+00:34:16,190 --> 00:34:26,530
+مغلبك انت ايش اللي ايش هي ال degree بس
+
+423
+00:34:31,660 --> 00:34:36,840
+بس امسك فيها دي مافيش داعي ان اكمل خلاص انت بيكفي
+
+424
+00:34:36,840 --> 00:34:40,180
+واحدة ليش لأن احنا كمان مرة هنرجع نقول هذا
+
+425
+00:34:40,180 --> 00:34:44,100
+necessary condition في necessary condition ماعرفش
+
+426
+00:34:44,100 --> 00:34:46,380
+اذا كتوا في ال calculus او لا في حاجة اسمها
+
+427
+00:34:46,380 --> 00:34:49,440
+necessary condition وفي حاجة اسمها sufficient
+
+428
+00:34:49,440 --> 00:34:54,340
+condition او sufficiency فال necessity و ال
+
+429
+00:34:54,340 --> 00:34:57,580
+sufficiency هل بتحقق ولا لأ لما بتكلم عن necessary
+
+430
+00:34:57,580 --> 00:35:01,910
+condition بمعنى انه شرط ضروريولكن غير كافي زي
+
+431
+00:35:01,910 --> 00:35:06,170
+بالظبط لما كنت اتقول والله هدول شروط ضرورية هيهم
+
+432
+00:35:06,170 --> 00:35:11,670
+الشروط هدول ضرورية بمعنى إن هم إذا انتفى واحد منهم
+
+433
+00:35:11,670 --> 00:35:16,130
+بقول هدول مش isomorphic بس إذا تحققوا بقول يمكن
+
+434
+00:35:16,130 --> 00:35:20,510
+isomorphic لكن أيوة أما إذا كان بتكلم عن ال
+
+435
+00:35:20,510 --> 00:35:24,270
+sufficiency بمعنى إنه هدى شروط كافية لو تحققت
+
+436
+00:35:24,270 --> 00:35:28,730
+فكافي جدا إن أقول أه هدول اتنين isomorphicبقدر
+
+437
+00:35:28,730 --> 00:35:32,350
+أقول مباشرة اه isomorphic طيب من وين بيجيني هذا ال
+
+438
+00:35:32,350 --> 00:35:37,850
+.. طبعا احنا هنا اتكلمنا عن التلات حالات مين اللي
+
+439
+00:35:37,850 --> 00:35:41,490
+هيقولي الكلام هذا و مين اللي مضح ليه المثال هذا
+
+440
+00:35:41,490 --> 00:35:48,350
+طلع المثال هذا شايفين
+
+441
+00:35:48,350 --> 00:35:52,570
+المثال شوفوا قدش عدد ال edges
+
+442
+00:35:56,760 --> 00:36:01,280
+كل شي بتحقق كل شي بتحقق معناه ذلك ان ال sufficient
+
+443
+00:36:01,280 --> 00:36:07,260
+condition كلها متحققة بالظبط معناته كيف اعرف ان هم
+
+444
+00:36:07,260 --> 00:36:11,660
+مش isomorphic ليش .. ليش ماطلعوش isomorphic مدام
+
+445
+00:36:11,660 --> 00:36:15,880
+كل شي عملناه طلع صح كل شي عملناه طلع صح معناته في
+
+446
+00:36:15,880 --> 00:36:20,980
+شي محتاجين كمان شوية نتعلموا زيادة لأ في حاجات
+
+447
+00:36:20,980 --> 00:36:25,160
+كمان أكمن شرط محتاجين نروحلهم لأن هذا مثل اللغة
+
+448
+00:36:25,160 --> 00:36:27,920
+واضحكلكوا قاعدين بتبتطلع و كلكوا شايفكوا قاعدين
+
+449
+00:36:27,920 --> 00:36:32,120
+بتتخيلوا و بتعدوا و بتحسبوا مظبوط كل إشي مظبوطة
+
+450
+00:36:32,120 --> 00:36:36,200
+فيه حتى ال degrees بتاعتهم كلهم مظبوطة ال degree
+
+451
+00:36:36,200 --> 00:36:39,160
+اتنين عددهم كامل ال degree تلاتة مافيش degree
+
+452
+00:36:39,160 --> 00:36:41,560
+تلاتة لأ الله في degree تلاتة هيهم .. هم كلهم
+
+453
+00:36:41,560 --> 00:36:45,360
+تلاتة أصلا أربعة degree تلاتة و خلاص هاي كل ل
+
+454
+00:36:45,360 --> 00:36:51,380
+graph على بعضه تمام كله متحقق لكن أنا بقولك زي ما
+
+455
+00:36:51,380 --> 00:36:57,780
+قلتلك حطهم على لوح خشب بدبابيسو هذه خطان او سلك
+
+456
+00:36:57,780 --> 00:37:01,060
+بينهم و قعد تغيروا شكله هل بتطلع معاك الشكل هذا او
+
+457
+00:37:01,060 --> 00:37:07,560
+لأ هاي السؤال بس مش تطلع الدبوس ينفق منه الخطان و
+
+458
+00:37:07,560 --> 00:37:10,640
+تخرب كل اللي بنقوله و تقول هاه الدكتور جالنا ما هي
+
+459
+00:37:10,640 --> 00:37:15,740
+.. و ده تبقى مربوطة بخطانها تمام فإذا في إشي
+
+460
+00:37:15,740 --> 00:37:19,440
+محتاجين نرجع للشكل هذا و نأكد منه هل هو فعلا
+
+461
+00:37:19,440 --> 00:37:22,920
+isomorphic ولا لأ هذا الإشي هو ال connectivity هو
+
+462
+00:37:22,920 --> 00:37:27,800
+ال connectivity احنا ما أخدنا transitiveعبثا أخدنا
+
+463
+00:37:27,800 --> 00:37:30,600
+ال transitive لإني عارف إنه أنا في النهاية باطلع
+
+464
+00:37:30,600 --> 00:37:36,000
+من مكان بروح لمكان معناته هذه relation أولى طيب من
+
+465
+00:37:36,000 --> 00:37:39,880
+نفس المكان ببدأ منه رحلة تانية بس هي نفس اللي كانت
+
+466
+00:37:39,880 --> 00:37:44,060
+نهاية الرحلة الأولى فإذا نهاية ال relation الأولى
+
+467
+00:37:44,060 --> 00:37:46,920
+المفروض تتفق مع بداية ال relation التانية عشان إيه
+
+468
+00:37:46,920 --> 00:37:49,860
+كانت ال transitive عشان في الآخر أقول أنا طلعت من
+
+469
+00:37:49,860 --> 00:37:56,130
+واحد لتلاتة من خلال اتنين طيب كويسالوقت لو عملنا
+
+470
+00:37:56,130 --> 00:38:01,110
+هذا الكلام ال path هذا امشيناه و رجعنا لواحد ايش
+
+471
+00:38:01,110 --> 00:38:06,690
+سمناها ال circuit تمام بالضبط هذا اللي بدنا نبدأ
+
+472
+00:38:06,690 --> 00:38:12,750
+نتكلم عنه هل عدد ال circuits ب degree معينة هو
+
+473
+00:38:12,750 --> 00:38:16,590
+نفسه هنا و هنا بمعنى انا في نفس النقطة موجود في
+
+474
+00:38:16,590 --> 00:38:20,890
+نقطة عشان اعمل اي loop و ارجع لنفس النقطة جدش عدد
+
+475
+00:38:20,890 --> 00:38:26,060
+ال inال edges اللي مرت فيها معناها كده عدد ال
+
+476
+00:38:26,060 --> 00:38:28,560
+relations اللي عدت فيها كم مرة عملت composition
+
+477
+00:38:30,790 --> 00:38:35,430
+لاحظت كيف؟ فإذا بدور على ال closed loop أو ال
+
+478
+00:38:35,430 --> 00:38:39,150
+circuits خلّيني نبدأ الفكرة بيكون عندك path of
+
+479
+00:38:39,150 --> 00:38:42,770
+length N from U to V عارفين هي sequence of
+
+480
+00:38:42,770 --> 00:38:48,690
+adjacent edges بحيث أني أذهب من U لV وإذا كان عندك
+
+481
+00:38:48,690 --> 00:38:52,510
+U تسوي V معناته رجعت لنفس النقطة بنسميها circuit
+
+482
+00:38:52,510 --> 00:38:57,550
+أو cycle circuit أو cycle فال path ببساطة أن يكون
+
+483
+00:38:57,550 --> 00:39:02,090
+فيه أكتر من oneedge بمعنى إنه يكون في عندك loop
+
+484
+00:39:02,090 --> 00:39:05,990
+معين في عندك حركة بتتحرك فيها loop معين و بدك تشوف
+
+485
+00:39:05,990 --> 00:39:10,750
+قداش عدد ال edges اللي مريت فيها عشان ترجع لنفس
+
+486
+00:39:10,750 --> 00:39:13,530
+النقطة طيب هذا هيقوتنا لحاجة برضه في ال
+
+487
+00:39:13,530 --> 00:39:17,970
+connectivity إنه أنا مستمريعني المفروض أكون مستمر،
+
+488
+00:39:17,970 --> 00:39:21,070
+مش ينقطع في النص، مش ينقطع في النص، معناه ذلك أنه
+
+489
+00:39:21,070 --> 00:39:24,870
+بدي أقول أمثلة على الصريحة عشان ناخد بالنا أنه
+
+490
+00:39:24,870 --> 00:39:29,290
+لازم يكون ال connection كامل ال connectivity كاملة
+
+491
+00:39:29,290 --> 00:39:33,630
+مثال زي هذا، هذا بقدر أقول عنه connected graph ولا
+
+492
+00:39:33,630 --> 00:39:38,350
+لأ؟ هذا أول yes، التاني لغة ده؟ أكيد لأ، فمافي حد
+
+493
+00:39:38,350 --> 00:39:42,700
+شيشي يقولي والله هاي pathفلازم تكون في
+
+494
+00:39:42,700 --> 00:39:46,480
+connectivity واضحة مستمرة عشان نعمل ال check تبعنا
+
+495
+00:39:46,480 --> 00:39:54,840
+هذه أكيد no التالتة تحت بكل
+
+496
+00:39:54,840 --> 00:39:59,660
+بساطة بتقدر من أي نقطة تروح لأي نقطة من أي نقطة
+
+497
+00:39:59,660 --> 00:40:03,320
+بتقدر تروح لأي نقطة صح ال connectivity إنك أنت
+
+498
+00:40:03,320 --> 00:40:05,820
+موجود في أي نقطة بتقدر تروح لأي نقطة على ال graph
+
+499
+00:40:06,810 --> 00:40:14,010
+بس هنا وصلنا ل E من E تصل ل B من B موصلين كلهم ما
+
+500
+00:40:14,010 --> 00:40:17,550
+هو فانت بتقدر تتحرك من أي vertex ل أي vertex تاني
+
+501
+00:40:17,550 --> 00:40:21,450
+بكل بساطة هناك ماكنتش بتقدر لإنك بدك تروح مثلا من
+
+502
+00:40:21,450 --> 00:40:26,650
+C ل A isolated بالنسبة لبعض فبنسميهم هنا مش
+
+503
+00:40:26,650 --> 00:40:30,950
+isolated node بسميهم components فى عندك two
+
+504
+00:40:30,950 --> 00:40:34,390
+components لل graph مش one component مش one
+
+505
+00:40:34,390 --> 00:40:39,290
+component طيب الأخيرةNo، بالظبط لأن هدول مش nodes،
+
+506
+00:40:39,290 --> 00:40:44,010
+مش nodes، هدول مش nodes، كويس؟ فإذا هتلاقي في عندك
+
+507
+00:40:44,010 --> 00:40:46,650
+three nodes لحال و three other .. و other three
+
+508
+00:40:46,650 --> 00:40:50,630
+nodes لحال، هدول two components في الحالة اللي
+
+509
+00:40:50,630 --> 00:40:56,060
+عندنافبالظبط النص الأول بصالش مع النص التانى فال
+
+510
+00:40:56,060 --> 00:40:59,360
+components هذه زى graph بهذا الشكل هى graph كامل
+
+511
+00:40:59,360 --> 00:41:04,240
+ال graph هذا بقدر أقول أن هو مكون من أربعة
+
+512
+00:41:04,240 --> 00:41:10,700
+components الاربعة components هذه a,b,c,d هذه set
+
+513
+00:41:10,700 --> 00:41:15,540
+of components لحال ثم في عندك ال E لحال ثم ال F
+
+514
+00:41:15,540 --> 00:41:22,760
+لحال و أخيرا I,H,G,J لحالهدولة لحالهم فعندك في
+
+515
+00:41:22,760 --> 00:41:27,120
+أربع components طيب في أي graph .. أي graph كامل
+
+516
+00:41:27,120 --> 00:41:32,680
+one component في بعض ال edges و ال vertices اللي
+
+517
+00:41:32,680 --> 00:41:38,920
+هم خصوصية بنقدر نسميهم cut vertex أو cut edge هذا
+
+518
+00:41:38,920 --> 00:41:43,820
+إذا كان عملنا له remove بيفصل ل graph ل two
+
+519
+00:41:43,820 --> 00:41:50,720
+components at least كويس؟ يعني مثلًا زي هنا مثلًاو
+
+520
+00:41:50,720 --> 00:41:55,640
+بدى افترض ان هذا لحاله graph لحاله كويس؟
+
+521
+00:41:55,640 --> 00:42:03,260
+لو شيلنا a ايش المتبقي؟ هاي المتبقي صح؟ بيضل جطعة
+
+522
+00:42:03,260 --> 00:42:08,580
+واحدة فهذا ليس cut vertex هذا مش cut vertex تمام؟
+
+523
+00:42:08,580 --> 00:42:12,640
+لأنه لما يروح مش هيتغير معانا ايش هتضل برضه
+
+524
+00:42:12,640 --> 00:42:18,170
+component واحدة لل graph لكن لو شيلت bبيصبح الشكل
+
+525
+00:42:18,170 --> 00:42:23,830
+عندك بهذا الشكل و نقطة هنا اللي هي ل D و C و هنا A
+
+526
+00:42:23,830 --> 00:42:29,110
+لأن هذه راحت خلاص فمعنى ذلك أن هذه cut vertex هذه
+
+527
+00:42:29,110 --> 00:42:35,130
+cut vertex تمام okay نفس الكلام لل edges هلوجد لو
+
+528
+00:42:35,130 --> 00:42:41,290
+قلنا ال edge هذه شيلناها و أنا بتكلم عن هذا الشكل
+
+529
+00:42:41,290 --> 00:42:50,180
+بس شيلنا ال edge اللي عليهاالـ X مش هيؤثر، هيظل
+
+530
+00:42:50,180 --> 00:42:53,920
+عبارة عن one component برضه لـ graph فهذه ليست cut
+
+531
+00:42:53,920 --> 00:43:01,120
+edge طيب، شيلنا ال edge هنا مش هتفرج معانا في شيء،
+
+532
+00:43:01,120 --> 00:43:06,960
+لأ، لو شيلت هذه صح،
+
+533
+00:43:06,960 --> 00:43:13,020
+هتظل J لحالها isolated vertex هتصير isolated
+
+534
+00:43:13,020 --> 00:43:17,160
+vertex، فهتصير هنا two partsتو components زي ما
+
+535
+00:43:17,160 --> 00:43:20,320
+أخدناه كله وسمينا هذه لحالها component وهي
+
+536
+00:43:20,320 --> 00:43:25,060
+isolated معناه ذلك انه ال edge هذه لو انشالت to be
+
+537
+00:43:25,060 --> 00:43:32,220
+removed حيضل عندي j isolated هتضل
+
+538
+00:43:32,220 --> 00:43:36,760
+لحالها node فقط node لحالها فإذا هذه بسميها cut
+
+539
+00:43:36,760 --> 00:43:39,920
+edge cut edge تمام
+
+540
+00:43:44,150 --> 00:43:48,190
+الان ال connectivity برضه في حاجة اسمها و أنتوا
+
+541
+00:43:48,190 --> 00:43:51,030
+كنتوا بتسألوا عن ال strong فبرضه ال strong معانا
+
+542
+00:43:51,030 --> 00:43:54,310
+حتى في مين في ال connectivity ففي عندي weakly و في
+
+543
+00:43:54,310 --> 00:44:00,790
+strongly connection و هذه المصطلحين هدول بنستخدمهم
+
+544
+00:44:00,790 --> 00:44:04,470
+أكتر لما يكون في عندي directed graph في directed
+
+545
+00:44:04,470 --> 00:44:10,370
+graph بسمي weak إذا كان فعلا هم بيتصل جميع النقاط
+
+546
+00:44:10,370 --> 00:44:15,280
+مع بعضها في حال أهملت الاتجاهلكن في حال أخذت
+
+547
+00:44:15,280 --> 00:44:18,560
+الاتجاه بعين الاعتبار هلاجي أنه في نقاط مش هتصلى
+
+548
+00:44:18,560 --> 00:44:24,400
+بعض يعني أنا بدي أحترم أن الشارع هذا هو رايح مش
+
+549
+00:44:24,400 --> 00:44:28,720
+جاي غير لأ ممكن ألاجيه جاي في وجهي، كويس؟ فهنا
+
+550
+00:44:28,720 --> 00:44:32,240
+weak أو strong هل وجد .. لما نجي نتكلم عن ال curve
+
+551
+00:44:32,240 --> 00:44:41,580
+الأول في البداية هل وجد بتطلع مثلا من B لD هل
+
+552
+00:44:41,580 --> 00:44:46,770
+بتقدر تطلع بدون ما تخالف الإشارة؟طيب لو بدك تطلع
+
+553
+00:44:46,770 --> 00:44:51,450
+من C ل D إلا
+
+554
+00:44:51,450 --> 00:44:58,030
+إذا خلفت الاتجاه فإذا إذا خلفت الاتجاه بأصل بنصل
+
+555
+00:44:58,030 --> 00:45:00,990
+okay معناه ذلك إن ال connectivity هنا weekly
+
+556
+00:45:00,990 --> 00:45:07,230
+connectivity هنا الاتصال ضعيف اتصال hash لأنه لازم
+
+557
+00:45:07,230 --> 00:45:10,790
+ألتزم بالاتجاه طبعا لو مافيش أصلا هو مافيش أصلا
+
+558
+00:45:10,790 --> 00:45:14,430
+connectionيعني حتى weekly بقدرش أقول عنه weekly
+
+559
+00:45:14,430 --> 00:45:17,690
+connected weekly connected بقدرش أقولها طيب في
+
+560
+00:45:17,690 --> 00:45:22,670
+الحالة التانية أي نقطة بتصل لأي نقطة و أنت ملتزم
+
+561
+00:45:22,670 --> 00:45:27,190
+بالاتجاه من أي نقطة بتقدر تروح لأي نقطة ببساطة جدا
+
+562
+00:45:27,190 --> 00:45:30,950
+لإن هو عملك cycle خارجي للكل يعني أنت بتقدر تتحرك
+
+563
+00:45:30,950 --> 00:45:35,150
+بسهولة جدا من خلال ال ring هذا من أي نقطة للتانية
+
+564
+00:45:35,150 --> 00:45:41,310
+من أي نقطة للتانية هيومفانت على الدوار بتقدر تمر
+
+565
+00:45:41,310 --> 00:45:44,510
+على أي طرف من أطراف الدوار صحيح؟ لأن انت ماشي في
+
+566
+00:45:44,510 --> 00:45:52,350
+اتجاه الصح تمام في أي دوار تماما okay نرجع لمثالنا
+
+567
+00:45:52,350 --> 00:45:55,850
+بعد هال connectivity اللي اتعلمناها هل بقدر أحل
+
+568
+00:45:55,850 --> 00:45:58,990
+الموضوع الآن بقدر أقول هي فعلا isomorphic ونخلص
+
+569
+00:45:58,990 --> 00:46:03,510
+ولا لأ مبدأيا مش هنجد نحسب قداش عدد لأنه عارفين
+
+570
+00:46:03,510 --> 00:46:08,350
+عارفين صحيح؟ طيب ال connectivity الآنالكون اكتفتي
+
+571
+00:46:08,350 --> 00:46:13,030
+هيني بدي اطلع من نقطة و ارجعلها و ال degree تلاتة
+
+572
+00:46:13,030 --> 00:46:16,470
+طبعا
+
+573
+00:46:16,470 --> 00:46:21,610
+خليني اسميها يعني cycle تلاتة degree تلاتة مثلا
+
+574
+00:46:21,610 --> 00:46:28,630
+cycle تلاتة هاي جي اتنين في عندى واحدة و هاي في
+
+575
+00:46:28,630 --> 00:46:34,050
+التانيةبتلاتة فى غيرهم بتلاتة برجع لنفس النقطة
+
+576
+00:46:34,050 --> 00:46:37,790
+يعني هل فى عندى اي cycle ال degree بتاعتها تلاتة
+
+577
+00:46:37,790 --> 00:46:42,610
+او ال circuit مافيش فهما تنتين طيب بالنسبة ل G
+
+578
+00:46:42,610 --> 00:46:51,850
+واحد مافيش مافيش تلاتات اقل اشي اربعة هى اربعة وهى
+
+579
+00:46:51,850 --> 00:46:55,770
+اربعة وهى اربعة وهى اربعة
+
+580
+00:46:58,750 --> 00:47:05,370
+أيوة تلاتة فش خلاص مش isomorphic انتهى خلص رغم أنه
+
+581
+00:47:05,370 --> 00:47:11,370
+حسب ال necessary condition كله متحقق لكن فعليا حسب
+
+582
+00:47:11,370 --> 00:47:15,510
+ال connectivity الأن وضحت أنه لأ أنا مش هقدر أصل ل
+
+583
+00:47:15,510 --> 00:47:18,930
+loop بنفس ال degree في الحالتين فإذا not
+
+584
+00:47:18,930 --> 00:47:22,290
+isomorphic في الحالة اللي عندنا أكيد مش هيكونوا
+
+585
+00:47:22,290 --> 00:47:26,710
+isomorphic في الحالة اللي موجودة عندنا تماميكفي ان
+
+586
+00:47:26,710 --> 00:47:29,910
+شرط واحد يتم نفيه او واحدة من ال conditions تم
+
+587
+00:47:29,910 --> 00:47:33,090
+نفيها عشان تقول لأ خلاص مااتحققتش .. مااتحققتش
+
+588
+00:47:33,090 --> 00:47:37,850
+تمام؟ هيك بنكون خلصنا الجزئية تبعت ال graphs
+
+589
+00:47:37,850 --> 00:47:40,550
+بيضللنا موضوع واحد اعتقد خلال الأسبوع هاد انشارة
+
+590
+00:47:40,550 --> 00:47:45,150
+بنخلصه و اللي هو ال tree و هذه حالة خاصة جدا من ال
+
+591
+00:47:45,150 --> 00:47:49,510
+graph زي ما احنا انطلقنا من ال relation و قلنا في
+
+592
+00:47:49,510 --> 00:47:53,240
+حالة خاصة منه هي ال graphكويس برضه ال graph في
+
+593
+00:47:53,240 --> 00:47:56,580
+حالة خاصة جدا منه اسمها tree هنعرف لايش ممكن
+
+594
+00:47:56,580 --> 00:48:01,360
+نستخدم ال tree هذه كويس و ممكن نحل فيها أسئلة او
+
+595
+00:48:01,360 --> 00:48:06,200
+ممكن نحل فيها أسئلة و ممكن تستخدم كبداية
+
+596
+00:48:06,200 --> 00:48:10,840
+التفكير في الذكاء الاصطناعي ال AI ال tree يعطيكوا
+
+597
+00:48:10,840 --> 00:48:11,980
+ألف عافية و برك الله فيكم
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/tfL57plaSsE_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/tfL57plaSsE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e6e22941e4393c59875f1d44cf6603f0097aa26d
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/tfL57plaSsE_postprocess.srt
@@ -0,0 +1,1888 @@
+1
+00:00:05,150 --> 00:00:07,510
+طيب بسم الله الرحمن الرحيم السلام عليكم يا شباب
+
+2
+00:00:07,510 --> 00:00:11,290
+نكمل اليوم في جزئية ال quantifiers اللي حكينا عنها
+
+3
+00:00:11,290 --> 00:00:15,450
+المرة الماضية نكمل الجزء اللي كان متبقيلنا و زي ما
+
+4
+00:00:15,450 --> 00:00:18,290
+وعدناكوا كل ما هنلاقي معانا وقت فاضي في أخر
+
+5
+00:00:18,290 --> 00:00:22,530
+الأسبوع و فيه واجت هنحل أسئلة هنحل مجموعة أسئلة
+
+6
+00:00:22,530 --> 00:00:25,490
+فاليوم إن شاء الله إذا كان أسعفنا الوقت مجهز
+
+7
+00:00:25,490 --> 00:00:29,050
+مجموعة أسئلة برضه على شوية مواضيع من المواضيع اللي
+
+8
+00:00:29,050 --> 00:00:33,750
+مروا عليناجد ما بنقدر ناخد ناخد و بنشوف بعدين
+
+9
+00:00:33,750 --> 00:00:37,570
+لباقي الأسئلة اللاحقة طيب في ال quantifiers
+
+10
+00:00:37,570 --> 00:00:44,470
+اتكلمنا انه there exist مع for all لنفس المتغير مش
+
+11
+00:00:44,470 --> 00:00:47,890
+هيظبطوا الإتنين مع بعض أخدناها المرة الماضية نفس
+
+12
+00:00:47,890 --> 00:00:54,850
+الكلام لما يكون في عندهfor all x p of x تمام و في
+
+13
+00:00:54,850 --> 00:00:58,370
+اقواس معناه ذلك ان ال quantifier هذا لل p of x فقط
+
+14
+00:00:58,370 --> 00:01:04,370
+و ليس لل q of x مدام غير مشمول الاقواس معها طيب
+
+15
+00:01:04,370 --> 00:01:08,530
+نفس الشغل قولنا لما يكون في عندي for all x p of x
+
+16
+00:01:09,860 --> 00:01:13,800
+مع بعض لحالها and there exist x q of x معناه ذلك
+
+17
+00:01:13,800 --> 00:01:17,380
+أن كل x من تنتين هدول مختلفة عن التانية كل واحدة
+
+18
+00:01:17,380 --> 00:01:21,420
+خاصة بال function أو بال predicate بتاعتها و ال
+
+19
+00:01:21,420 --> 00:01:23,860
+quantifier تبعها of course فهنا هيكون في end
+
+20
+00:01:23,860 --> 00:01:31,020
+different xحكينا عن ال quantifier equivalence laws
+
+21
+00:01:31,020 --> 00:01:35,300
+و شفنا ان for all معناته بتكلم عن مجموعة and و for
+
+22
+00:01:35,300 --> 00:01:40,660
+all there exist بتكلم عن مجموعة or تمام؟ و قلنا ال
+
+23
+00:01:40,660 --> 00:01:43,260
+two properties هدولة و أثبتناهم المرة الماضية
+
+24
+00:01:43,260 --> 00:01:47,560
+أثبتنا كيف ممكن فعلا انحقق التنتين هدولة من خلال
+
+25
+00:01:47,560 --> 00:01:54,060
+دي مورغانطيب لما تكون عندي for all x for all y مين
+
+26
+00:01:54,060 --> 00:01:58,600
+جاب للتاني مش هيفرج for all y for all x برضه مش
+
+27
+00:01:58,600 --> 00:02:02,020
+هتفرجزاه بالظبط لما تكون في ال language بحول من
+
+28
+00:02:02,020 --> 00:02:06,220
+direct ل ish ل n direct ل indirect نفس الكلام لل
+
+29
+00:02:06,220 --> 00:02:10,780
+there exist طيب لما تكون ال for all محكومة بأقواص
+
+30
+00:02:10,780 --> 00:02:15,240
+كاملة لمين لأ ال two predicatestwo predicates مع
+
+31
+00:02:15,240 --> 00:02:19,440
+بعض معناتهم الفرق لل predicate الأول و ال
+
+32
+00:02:19,440 --> 00:02:24,280
+quantifier برضه لل predicate التاني فنقدر نوزحها
+
+33
+00:02:24,280 --> 00:02:26,740
+مدام الأقواص حكمانة ال priority دايما هي اللي
+
+34
+00:02:26,740 --> 00:02:30,560
+بتحكمنا في توزياتنا نفس الكلام لمين الveer exist
+
+35
+00:02:30,560 --> 00:02:38,210
+okay برضهحالات تانية كتير ممكن تتعامل معها انك
+
+36
+00:02:38,210 --> 00:02:41,530
+تلاقي for all x for all y for all z كلهم for all
+
+37
+00:02:41,530 --> 00:02:43,670
+for all for all معناه ذلك ان انا ممكن احط for all
+
+38
+00:02:43,670 --> 00:02:49,530
+واحدة نكتبها for all x y z مع بعض تمام كومز او
+
+39
+00:02:49,530 --> 00:02:53,590
+بدون كومز على طول مباشرة كله بمشي الحال فبتفهم
+
+40
+00:02:53,590 --> 00:02:56,350
+مباشرة ان اذا جالك for all x y z معناته ان انا
+
+41
+00:02:56,350 --> 00:03:00,950
+بتكلم عن for all y for all x for all z صح كلهم
+
+42
+00:03:03,240 --> 00:03:07,560
+تمام نصل لبداية محاضرتنا لليوم اللي هي بدنا نتكلم
+
+43
+00:03:07,560 --> 00:03:10,840
+فيها عن بعد ما عملنا revision سريعة نتكلم فيها عن
+
+44
+00:03:10,840 --> 00:03:15,820
+a new quantifier إضافي غير ال there exist و ال for
+
+45
+00:03:15,820 --> 00:03:18,900
+all اللي أخدناهم المرة الماضية اللي هو there exist
+
+46
+00:03:18,900 --> 00:03:24,170
+exactly onethere exist كلنا عارفين ان هي one or
+
+47
+00:03:24,170 --> 00:03:30,990
+more بديش or هذه for one just one just one فبنعمل
+
+48
+00:03:30,990 --> 00:03:34,670
+there exist exclamation علامة التعجب هذه
+
+49
+00:03:34,670 --> 00:03:38,750
+exclamation x p of x فهذه بفهم منها ان يوجد
+
+50
+00:03:38,750 --> 00:03:44,370
+exactly one value for x such that p of x is true
+
+51
+00:03:44,370 --> 00:03:49,810
+فإذا يوجد قيمة واحدة ل x تحقق p of x وتحديدا واحدة
+
+52
+00:03:50,510 --> 00:03:55,830
+فهنا بتكون تحديدا exactly one تمام طيب هذه إيش
+
+53
+00:03:55,830 --> 00:04:00,150
+معناها؟ معناها لما بدي أجي أحللها ال .. ال new
+
+54
+00:04:00,150 --> 00:04:02,870
+quantifier هذه اللي هي there exist exclamation أو
+
+55
+00:04:02,870 --> 00:04:06,870
+exactly one X P of X هذه تكافئ لإيش؟ ل there exist
+
+56
+00:04:06,870 --> 00:04:14,610
+X تحقق P of X and لا يوجد غيرها يحقق صح؟ مش هيك
+
+57
+00:04:14,610 --> 00:04:20,210
+معناها؟هي لا يوجد Y تحقق P of X بشرط أن Y لا تسوى
+
+58
+00:04:20,210 --> 00:04:24,330
+X بمعنى أن Y هي أي شيء غير X لأن X يحقق
+
+59
+00:04:28,260 --> 00:04:32,620
+there exists exactly one P of X هذي مكافئة لإيش
+
+60
+00:04:32,620 --> 00:04:35,660
+يعني احنا اختزلنا عشان نحط الجملة بهذا الشكل لو
+
+61
+00:04:35,660 --> 00:04:38,920
+كنت فير بهذا الشكل هل كان له فائده ان احطه بهذا
+
+62
+00:04:38,920 --> 00:04:43,180
+الشكل اه كان له فائده لإن هو ده بيختزل ليه form
+
+63
+00:04:43,180 --> 00:04:48,310
+كتير ضخم و كتير كبير اللي هو إيش there exists XP
+
+64
+00:04:48,310 --> 00:04:53,090
+of X فإذا يوجد قيمة ل X تحقق P of X و غيرها لا
+
+65
+00:04:53,090 --> 00:04:56,970
+يحقق مش بدي أترجم كلمة و غيرها لا يحقق لأنها واحد
+
+66
+00:04:56,970 --> 00:05:03,050
+فقط X بس فإذا يحقق P of X and غيرها لا يحقق من
+
+67
+00:05:03,050 --> 00:05:10,750
+غيرها أي حاجة تانية Y معناته لا يوجد Y تحقق P of X
+
+68
+00:05:10,750 --> 00:05:15,550
+بس ناخد بالنا مش يطلعلي بالآخر Y هي نفسها Xأحنا
+
+69
+00:05:15,550 --> 00:05:19,330
+قلنا لو وجد غيرها، غيرها معناته بدي أحدد أن why لا
+
+70
+00:05:19,330 --> 00:05:24,570
+تسوى x لأنه غيرها عشان تكون فعلا غيرها فإذا هنا
+
+71
+00:05:24,570 --> 00:05:29,370
+أنا بكون بدقة كاملة عرفت التعريف بدون ما أنسى أو
+
+72
+00:05:29,370 --> 00:05:35,270
+أخفل أي case ممكن تضرب ليه تعريفي لو ما كتبناش
+
+73
+00:05:35,270 --> 00:05:39,090
+الأخيرة هذه هيجيك واحد يقولك طب ماشي why تسوى x هي
+
+74
+00:05:39,090 --> 00:05:45,810
+بتصبط وصار في عندكconfusion .. confusion واضح انه
+
+75
+00:05:45,810 --> 00:05:50,830
+في اختلاف في المعنيين هذه صارت غير هذه لأ مهمة جدا
+
+76
+00:05:50,830 --> 00:05:56,130
+حتى اخر حاجة انكتبت مهمة جدا فإذا كل كلمة بدنا
+
+77
+00:05:56,130 --> 00:06:00,910
+انعرفها او مهمة في التعريف لازم تكون واضحة في ال
+
+78
+00:06:00,910 --> 00:06:04,830
+expression اللي بتكتبه لابد تكون واضحة ما تختزلش
+
+79
+00:06:04,830 --> 00:06:07,550
+حاجة تقول ما هو معروفة مافيش حاجة ما هو معروفة
+
+80
+00:06:07,550 --> 00:06:11,740
+احنا الآن زي ما قلنا كمان مرةال discrete هذه عشان
+
+81
+00:06:11,740 --> 00:06:15,020
+هتفهم مع الحاسوب الحاسوب بيفهمش ما هي معروفة
+
+82
+00:06:15,020 --> 00:06:19,240
+الحاسوب بيعرفش شي الحاسوب في الآخر silicon رمل
+
+83
+00:06:19,240 --> 00:06:22,440
+يعني تقوله لأ ما هي معروفة انه انا بقول لا يوجد
+
+84
+00:06:22,440 --> 00:06:25,800
+غيرها هقول لك انا ماعرفتش ان انت ايش جصدك بغيرها
+
+85
+00:06:25,800 --> 00:06:30,140
+لازم تحطه ال y لا بساوة x انا عارف ان في حاجات انت
+
+86
+00:06:30,140 --> 00:06:32,920
+by default بتحس تا ماهي منطقة لأ مش فيش حاسوبة
+
+87
+00:06:32,920 --> 00:06:37,080
+منطقية كمان مرة الرمساق تبعنا مش عشاني انا وانت
+
+88
+00:06:37,910 --> 00:06:44,170
+عشان انت بدأت تتعامل مع هال machine هذه فإذا أصبح
+
+89
+00:06:44,170 --> 00:06:49,330
+تعريفنا there is an X such that P of X where is no
+
+90
+00:06:49,330 --> 00:06:56,590
+Y such that P of Y and Y other than X و Y هذي أي
+
+91
+00:06:56,590 --> 00:07:01,190
+شيء تاني غير X عشان مايجيش واحد يضرب للتعريف و
+
+92
+00:07:01,190 --> 00:07:03,770
+يقول طيب ماشي انت حطيت X و Y ما هو ما يمكن نفس
+
+93
+00:07:03,770 --> 00:07:07,730
+القيمة تنتهيX تساوي تلاتة و Y تساوي تلاتة هاي
+
+94
+00:07:07,730 --> 00:07:16,310
+طلعوا بيساوي بعض فمهم جدا Y is other than X تمام
+
+95
+00:07:16,310 --> 00:07:23,110
+ناخد مثلين لتعريفين من ال language أو من English
+
+96
+00:07:23,110 --> 00:07:28,050
+language بدنا نعرفها بشكل mathematical form لما
+
+97
+00:07:28,050 --> 00:07:32,430
+أقول الأعداد الزوجية
+
+98
+00:07:33,970 --> 00:07:37,170
+أعداد زوجية هفترض مبدأي ان انا بتعامل مع ال
+
+99
+00:07:37,170 --> 00:07:39,390
+natural numbers اللي هي من صفر واحد اتنين تلاتة to
+
+100
+00:07:39,390 --> 00:07:44,410
+infinity و بدنا نعرف اي رقم زوجي فبقول a number x
+
+101
+00:07:44,410 --> 00:07:49,290
+is even هي اول تعريف انا بدي اعرف رقم زوجي يعني E
+
+102
+00:07:49,290 --> 00:07:56,910
+of X و E هي اللي بتكلم X is even تمام هذا الكلام
+
+103
+00:07:56,910 --> 00:08:03,060
+صحيح if and only ifit's equal to two times some
+
+104
+00:08:03,060 --> 00:08:12,520
+other number عشان اقول ان X is even فإذا لابد ان X
+
+105
+00:08:12,520 --> 00:08:20,320
+هذي تكون اتنين في some other number Y مثلا وإلا
+
+106
+00:08:20,320 --> 00:08:24,550
+فهي ليست زوجيمعنى ذلك ان هي لسة زوجة التعريف هذا
+
+107
+00:08:24,550 --> 00:08:28,190
+بدنا ان ترجمه بشكل معادلة بس لا أكثر ولا أقل
+
+108
+00:08:28,190 --> 00:08:36,690
+فهنقول for all x لكل قيم x x هذا هيكون even x
+
+109
+00:08:36,690 --> 00:08:43,390
+هيكون even لكن بشرط even if and only if إذا وإذا
+
+110
+00:08:43,390 --> 00:08:49,910
+فقط بمعنى ان هنا ليست implication خد بالك ليست
+
+111
+00:08:49,910 --> 00:08:54,600
+implicationلنوضحها ليست implication ببساطة جدا
+
+112
+00:08:54,600 --> 00:09:00,160
+لأنه إذا كان even فإذا هو اتنين Y بس هل معناه ذلك
+
+113
+00:09:00,160 --> 00:09:03,740
+أنه يمكن يكون اتنين Y بينما هو مش even؟ ولا يمكن
+
+114
+00:09:03,740 --> 00:09:10,500
+صح؟ فإذا implication لن تصلح هنا لابد إنك أنت
+
+115
+00:09:10,500 --> 00:09:15,220
+تستخدم if and only if ال by conditional فإذا لكل
+
+116
+00:09:15,220 --> 00:09:23,400
+قيم X، X evenif and only if there exists y يوجد
+
+117
+00:09:23,400 --> 00:09:30,540
+رقم آخر اتنين تمثل ضعفه اللي هي عفوا x تمثل ضعفه
+
+118
+00:09:30,540 --> 00:09:37,820
+يوجد y اللي هو other than x يوجد y x تسوى اتنين y
+
+119
+00:09:37,820 --> 00:09:42,100
+طبعا هنا مالهاش معنى تقولي اه مسكت الكتابة كثير
+
+120
+00:09:42,100 --> 00:09:48,110
+لأن عادة و بدنا نحط y لا تسوى xمالهاش معنى ال gate
+
+121
+00:09:48,110 --> 00:09:51,810
+ليش لأن أنا جاوب أقولك تسوى 2Y فإذا هي اللي تسويها
+
+122
+00:09:51,810 --> 00:10:00,470
+أصلا صح ال صفر فقط الحالة الصفر الوحيدة تمام فإذا
+
+123
+00:10:00,470 --> 00:10:06,290
+لكل قيم X X is even خلاص if and only if there
+
+124
+00:10:06,290 --> 00:10:13,010
+exist YX تمثل ضعف Y أو تمثل اتنين من Y تمام هذه
+
+125
+00:10:13,010 --> 00:10:17,410
+تعريف لكل المصطلح أو ال definition اللي كنا كتبينه
+
+126
+00:10:17,410 --> 00:10:21,490
+طيب كمان definition و بدنا نحوله لمعادلة ايش ال
+
+127
+00:10:21,490 --> 00:10:26,130
+definition لمين لأرقام ال primes هقول a number is
+
+128
+00:10:26,130 --> 00:10:32,290
+prime الرقم أولي فبسميه P of X انت بيكون الرقم
+
+129
+00:10:32,290 --> 00:10:37,050
+أولي if and only if إذا وإذا فقطit's greater than
+
+130
+00:10:37,050 --> 00:10:42,010
+one ال one مش أولي اتفقنا ال one مش أولي فإذا هو
+
+131
+00:10:42,010 --> 00:10:49,070
+أكبر من واحد and it's not the product of two non
+
+132
+00:10:49,070 --> 00:10:54,690
+unity numbers وهو لا يمكن أن يكون حاصل ضرب رقمين
+
+133
+00:10:54,690 --> 00:11:01,140
+غير الواحدعشان ماتجيش تلغيلي إياها و تقولي ما هي
+
+134
+00:11:01,140 --> 00:11:05,520
+الواحد أو سبعة في واحد أو خلّيني أقول سبعة هي أصلا
+
+135
+00:11:05,520 --> 00:11:10,880
+prime تقولي مثلا أربعة في واحد لأ دير بالك
+
+136
+00:11:10,880 --> 00:11:15,100
+الرقامين اللي لاتصلح إنها ال prime يكون ضربهم
+
+137
+00:11:15,100 --> 00:11:20,400
+الرقامين لازم يكونوش واحد لا الأول واحد ولا التاني
+
+138
+00:11:20,400 --> 00:11:26,200
+واحد فهذه بينات في إيش non unityليس فيهم الواحد
+
+139
+00:11:26,200 --> 00:11:31,760
+تمام هذا الكلام كتعريف لغوي فاهمينه لأن احنا
+
+140
+00:11:31,760 --> 00:11:34,520
+عارفين ال primes من المسبق العداد الأولى عارفينها
+
+141
+00:11:34,520 --> 00:11:38,820
+المسبقات بدنا نترجمها الآن برضه هقول لكل الأرقام
+
+142
+00:11:38,820 --> 00:11:46,760
+او لكل for all X P of X فإذا لكل قيم X X is prime
+
+143
+00:11:46,760 --> 00:11:54,780
+بس if and only if إذا وإذا فقطX أكبر من واحد حسب
+
+144
+00:11:54,780 --> 00:11:58,900
+التعريف هيا بدأنا ب X أكبر من واحد طيب إيش كمان لا
+
+145
+00:11:58,900 --> 00:12:06,500
+يوجد رقمين ضربهم يسوى X لا يوجد خلصنا هذا and لا
+
+146
+00:12:06,500 --> 00:12:15,060
+يوجد مش هي لا يوجد there is no Y Z هاي رقمين لا
+
+147
+00:12:15,060 --> 00:12:22,910
+يوجد Y و Z ضربهم يسوى Xإيش ضال في الآخر؟ بس ناخد
+
+148
+00:12:22,910 --> 00:12:25,870
+بالنا من الواحد عشان الكمبيوتر بيفهمش لحاله
+
+149
+00:12:25,870 --> 00:12:29,870
+الكمبيوتر بيفهمش لحاله فبتجي تقوله and y لا تسوى
+
+150
+00:12:29,870 --> 00:12:34,130
+واحد وزيد لا تسوى واحد لأن زي ما قلنا احنا
+
+151
+00:12:34,130 --> 00:12:37,490
+ماتتعاملش مع بعض احنا متعامل مع الحسوب مع شوية
+
+152
+00:12:37,490 --> 00:12:42,150
+الرمل اللي اتصنعت silicone فصار يفهم وياخد ويعطي
+
+153
+00:12:42,150 --> 00:12:47,390
+معناه عشان هيك لما نكون دقيقين في هذا الكلاممش
+
+154
+00:12:47,390 --> 00:12:50,490
+لأنه بدك تقولي ما احنا فاهمين يا دكتور ماشي بس انت
+
+155
+00:12:50,490 --> 00:12:53,470
+مش بتفهمني شنا ولا بتفهم ازميك لكن انت بدك تفهم
+
+156
+00:12:53,470 --> 00:12:59,250
+الحاسوب تمام فهيها كتعريف تمام هيك احنا بنكون
+
+157
+00:12:59,250 --> 00:13:03,350
+خلينا نقول فيما يخص المادة اللي خاصة بهذا الأسبوع
+
+158
+00:13:03,350 --> 00:13:09,830
+خلصناها فبنقدر ناخد مرتاحين شوية أسئلة على محتوى
+
+159
+00:13:09,830 --> 00:13:13,330
+الأسبوع اللي احنا اشتغلنا فيه طبعا في أسئلة كتير
+
+160
+00:13:13,330 --> 00:13:18,850
+بسيطة انا كنت عاملحسابنا أنه مسبقا أنه فيه عدد
+
+161
+00:13:18,850 --> 00:13:24,990
+كويس فلو قولنا مثلا P of X هي عبارة عن the word X
+
+162
+00:13:24,990 --> 00:13:29,630
+contains the letter A لو افترضنا أنه ال predicate
+
+163
+00:13:29,630 --> 00:13:41,790
+P هي الكلمة X تحتوي على حرف A فلما أجي أقول P of
+
+164
+00:13:41,790 --> 00:13:43,110
+Orange
+
+165
+00:13:46,590 --> 00:13:53,070
+true ولا false؟ true proposition و true طيب P of
+
+166
+00:13:53,070 --> 00:13:56,930
+lemon؟ false فهي proposition و false
+
+167
+00:14:00,660 --> 00:14:05,180
+فإذا proposition هو false تمام و false true true
+
+168
+00:14:05,180 --> 00:14:11,640
+تمام okay غيرها بدنا نفترض P of X is statement X
+
+169
+00:14:11,640 --> 00:14:17,180
+spends more than five hours every week day in
+
+170
+00:14:17,180 --> 00:14:22,050
+classطب .. بس ناخد بالنا أنه هنا ال university of
+
+171
+00:14:22,050 --> 00:14:26,330
+discourse هي ل students طلاب ف ال domain تبعنا هو
+
+172
+00:14:26,330 --> 00:14:30,430
+x لكل الطلاب و بدنا نفترض أن x هذا اللي هو الطالب
+
+173
+00:14:30,430 --> 00:14:37,530
+x بيستنفذ أو بيعطي دراسته أسبوعيا خمس ساعات .. خمس
+
+174
+00:14:37,530 --> 00:14:44,370
+ساعات أسبوعي في ال .. ال weekday okayتمام بدنا
+
+175
+00:14:44,370 --> 00:14:47,810
+نكتب مجموعة ال expressions ال mathematical
+
+176
+00:14:47,810 --> 00:14:51,210
+expressions اللي موجودة عندنا a,b,c وd لما أقول
+
+177
+00:14:51,210 --> 00:14:56,310
+there exist x P of X بدنا نسميها there exist فإذا
+
+178
+00:14:56,310 --> 00:15:02,310
+there exist student spends more than five hours
+
+179
+00:15:02,310 --> 00:15:06,930
+every day أو every weekday فبسيطة مافيش فيها كتير
+
+180
+00:15:06,930 --> 00:15:13,750
+مشكلة كترجمة تعريف طيب تانية for all x P of Xقول
+
+181
+00:15:13,750 --> 00:15:19,230
+برضه ماعناش أي مشكلة طيب there exist negation P of
+
+182
+00:15:19,230 --> 00:15:27,710
+X معناته
+
+183
+00:15:27,710 --> 00:15:37,260
+يوجد طالب ليدرس او لا .. او اللي هي doesn't spend
+
+184
+00:15:37,260 --> 00:15:42,840
+more than five hours يوجد طالب على الأقل بدرسش خمس
+
+185
+00:15:42,840 --> 00:15:45,860
+ساعات أو بديهش خمس ساعات في الدراسة، بياخدش خمس
+
+186
+00:15:45,860 --> 00:15:51,680
+ساعات في الدراسة الأخيرة للكل
+
+187
+00:15:51,680 --> 00:15:58,220
+.. لكل الطلاب لا يوجد ولا طالب بيعطي خمس ساعات في
+
+188
+00:15:58,220 --> 00:16:03,800
+اليومفإذا no student من الآخر لكل الطلاب معناته no
+
+189
+00:16:03,800 --> 00:16:07,880
+student spends five hours صحيح؟ لكل الطلاب ولا
+
+190
+00:16:07,880 --> 00:16:12,940
+طالب بدرس خمس ساعات فإذا كأنه no student spends
+
+191
+00:16:12,940 --> 00:16:18,860
+more than five hours تمام، كمان غيرها، لو افترضنا
+
+192
+00:16:18,860 --> 00:16:26,020
+في عندى two عندنا هاي two predicates، الأولى x is
+
+193
+00:16:26,020 --> 00:16:33,920
+a comedianكوميدي تمام التانية if of x و x is funny
+
+194
+00:16:33,920 --> 00:16:38,680
+ده إذن كوميدي و funny مضحك و ال domain تبعنا هنا
+
+195
+00:16:38,680 --> 00:16:43,020
+all people لاحظوا ال expression شوية عجدناها
+
+196
+00:16:43,020 --> 00:16:47,080
+عجدناها شوية في هيك حالة كيف بدك تتعامل معاها لما
+
+197
+00:16:47,080 --> 00:16:54,940
+أقولك for all c x then if c of x then if of x إيش
+
+198
+00:16:54,940 --> 00:17:02,060
+معناها؟for all معناته كل كوميدي بالضرورة هيكون
+
+199
+00:17:02,060 --> 00:17:06,940
+funny صح؟
+
+200
+00:17:06,940 --> 00:17:11,740
+ليش؟ خليني معاك انا لأ انت بتقول لأ وين المشكلة
+
+201
+00:17:11,740 --> 00:17:16,600
+عندك؟ بس
+
+202
+00:17:16,600 --> 00:17:17,400
+هل هو funny؟
+
+203
+00:17:20,920 --> 00:17:24,660
+هو يقول اشي تاني انت اشي مصنف و هده مختلفة بس
+
+204
+00:17:24,660 --> 00:17:26,780
+معناه ذلك ان معناته كان ال expression هذا كله
+
+205
+00:17:26,780 --> 00:17:30,720
+بيصلح عليه اذا انت بتحكي عن حالة خاصة و معناته ال
+
+206
+00:17:30,720 --> 00:17:33,680
+expression كله لن يصلح احنا نتكلم الان في اندي
+
+207
+00:17:33,680 --> 00:17:36,740
+expression، بثمانية expression كيف اكتبه language
+
+208
+00:17:36,740 --> 00:17:44,660
+فإذا for all لكل ال x إذا x كوميدي فهو funny فإذا
+
+209
+00:17:44,660 --> 00:17:49,380
+بقولها على طول مباشرة لكل الكوميديان هم funny على
+
+210
+00:17:49,380 --> 00:17:50,100
+طول خلصنا
+
+211
+00:17:52,980 --> 00:18:00,840
+اك طبيعي ايش؟ لأ لأ لأ هيك انتوا .. على فكرة انتوا
+
+212
+00:18:00,840 --> 00:18:03,200
+هيك معناه انتوا مش مذكرين ال implication العكس
+
+213
+00:18:03,200 --> 00:18:05,840
+اللي .. اللي ممكن ان هو ممكن يكون funny بس مش
+
+214
+00:18:05,840 --> 00:18:11,340
+comedian لأ
+
+215
+00:18:11,340 --> 00:18:13,780
+في الطبيعة اشي تاني احنا الآن مش .. مش في الطبيعة
+
+216
+00:18:13,780 --> 00:18:18,660
+لاحظ انا بيعطيك expression ال expression هذا صح او
+
+217
+00:18:18,660 --> 00:18:23,100
+خطأهدا اشي تاني انا بقولك في expression بدنا نكتبه
+
+218
+00:18:23,100 --> 00:18:26,760
+language انت قد ت .. قد تتفق ان هو ال expression
+
+219
+00:18:26,760 --> 00:18:29,900
+من الأساس فيه مشكلة اه ده اشي تاني لكن اه ايوة
+
+220
+00:18:29,900 --> 00:18:33,920
+بالظبط انت لان بتتكلم ما قبل ال expression اما
+
+221
+00:18:33,920 --> 00:18:38,820
+عندك expression هو صح هو غلط بس في واحد قاله
+
+222
+00:18:38,820 --> 00:18:42,840
+الواحد هذا انت ممكن توقف و تقوله false بس هو
+
+223
+00:18:42,840 --> 00:18:46,650
+propositionصح؟ انت من وجه الناس بتقوله fortunately
+
+224
+00:18:46,650 --> 00:18:51,510
+انت حر لكن بدي اعبر عنها ك language و بعدين بنقول
+
+225
+00:18:51,510 --> 00:18:55,010
+ان ال language هذه ك language every comedian is
+
+226
+00:18:55,010 --> 00:19:00,450
+funny هي proposition عندك صح عندك خلط مافي مشكلة
+
+227
+00:19:00,450 --> 00:19:04,230
+.. مافي مشكلة بس في النهاية proposition طيب for
+
+228
+00:19:04,230 --> 00:19:12,470
+all x c of x and f of x comedian and funny
+
+229
+00:19:18,200 --> 00:19:21,240
+أيها funny and comedian فبنسميه funny comedian
+
+230
+00:19:21,240 --> 00:19:26,660
+يعني لغة مش أكتر من هيك فبدك تسميهم و تحطهم واحد
+
+231
+00:19:26,660 --> 00:19:30,180
+صفة للتاني معناته الاتنين مقترنين البعض معناته and
+
+232
+00:19:30,180 --> 00:19:38,260
+طيب there exist cx implies f of x يوجد
+
+233
+00:19:39,610 --> 00:19:44,750
+يوجد على الأقل واحد كوميدي funny، على الأقل يوجد
+
+234
+00:19:44,750 --> 00:19:48,850
+كوميدي funny، هذه ممكن تصبت مع مصطلحك أو انت كيف
+
+235
+00:19:48,850 --> 00:19:53,970
+شايفهاف there exist a person such that ان هو
+
+236
+00:19:53,970 --> 00:19:59,290
+comedian إذا كان هو comedian فهو funny الكلام ده
+
+237
+00:19:59,290 --> 00:20:02,310
+ليس للكل على الأقل في واحد او اتنين او تلاتة حسب
+
+238
+00:20:02,310 --> 00:20:06,750
+أهواك و انت كيف تشوف ال comedians اللي حولنا طيب
+
+239
+00:20:06,750 --> 00:20:14,450
+there exist x, c of x and f of xفإذا تقدر تقول
+
+240
+00:20:14,450 --> 00:20:19,250
+some أو there exist أو some comedians are funny
+
+241
+00:20:19,250 --> 00:20:23,430
+برضه بتمشي مع مصطلحك أو طريقة وجهة نظرك في الموضوع
+
+242
+00:20:23,430 --> 00:20:28,850
+اللي هو some comedians are funny ماشي يعني وجهة
+
+243
+00:20:28,850 --> 00:20:31,530
+نظرك أنت شايفها هدلي true okay في غيرك بيشوفها
+
+244
+00:20:31,530 --> 00:20:36,190
+مختلفة يعني شوية وإلا كان ماتصنفش من الأصل أن هو
+
+245
+00:20:36,190 --> 00:20:40,670
+comedian صحيح بس أكيد في ناس مختلفين معك وإلا كان
+
+246
+00:20:40,670 --> 00:20:41,970
+ماتصنفش من الأساس comedian
+
+247
+00:20:44,720 --> 00:20:49,480
+Okay طب كمان سؤال أنا براحظ بحاول أن أقوللك
+
+248
+00:20:49,480 --> 00:20:52,920
+الأسئلة اللي بتيجي في هيك .. في هيك موضوع جيبناها
+
+249
+00:20:52,920 --> 00:20:56,520
+مرة ب predicate واحد مرة من language ل
+
+250
+00:20:56,520 --> 00:20:59,420
+mathematical form مرة من mathematical form ل
+
+251
+00:20:59,420 --> 00:21:05,160
+language و هكذا هين غيرنا لإيش؟ ل mathematical ..
+
+252
+00:21:05,160 --> 00:21:08,630
+من language ل mathematical formنفس الاشي لو
+
+253
+00:21:08,630 --> 00:21:14,650
+افترضنا ان P of X .. X is perfect F of X .. X is
+
+254
+00:21:14,650 --> 00:21:20,970
+your friend و بدنا مجموعة mathematical language
+
+255
+00:21:20,970 --> 00:21:23,350
+بدنا نحويلها لمثل كده ال expression no one is
+
+256
+00:21:23,350 --> 00:21:30,350
+perfect معناته for all negation بالظبط for all
+
+257
+00:21:30,350 --> 00:21:38,390
+negation طيب not everyone is perfect ليس كل واحدبس
+
+258
+00:21:38,390 --> 00:21:45,570
+let there exist فإذا ليس الكل .. إيش بنسميها؟ ليس
+
+259
+00:21:45,570 --> 00:21:50,150
+الكل perfect ليس الكل perfect طيب all your friends
+
+260
+00:21:50,150 --> 00:21:56,990
+are perfect إذا هو صديقك فهو perfect صحيح؟ فإذا
+
+261
+00:21:56,990 --> 00:22:03,370
+implication إذا هو صديقك فهوperfect طيب at least
+
+262
+00:22:03,370 --> 00:22:06,770
+باينة لحالها at least one of your friends is
+
+263
+00:22:06,770 --> 00:22:13,350
+perfect ف there exist يالا طيب و بتهيألي شرحناها
+
+264
+00:22:13,350 --> 00:22:15,810
+قبل هيك قولنا ان for all بتاخد دايما implication
+
+265
+00:22:15,810 --> 00:22:20,590
+there exist بتاخد and المرة اللي فاتة تتكلمنا عن
+
+266
+00:22:20,590 --> 00:22:24,930
+النقطة هذه و شرحناها بتوسع يعني فممكن ترجع لل
+
+267
+00:22:24,930 --> 00:22:29,240
+video إذا عندك مشكلة فيهاتمام everyone is your
+
+268
+00:22:29,240 --> 00:22:35,360
+friend and is perfect فكل الناس هم أصدقاءك و هم
+
+269
+00:22:35,360 --> 00:22:41,940
+perfect ف for all للكل نعم
+
+270
+00:22:41,940 --> 00:22:46,680
+implication
+
+271
+00:22:46,680 --> 00:22:50,980
+بصفة عامة اذا ما كان .. اه لسه بدأ احكي اذا ماكانش
+
+272
+00:22:50,980 --> 00:22:55,420
+ال .. في قوس و في زي ما بيقول خصوصية تانية
+
+273
+00:22:58,380 --> 00:23:01,880
+by conditional اه اه استنا استنا استنا by
+
+274
+00:23:01,880 --> 00:23:05,380
+conditional تو اخدناها كان لها definition كان لها
+
+275
+00:23:05,380 --> 00:23:11,200
+تعريف التعريف كان if and only if تو لما أخدناها
+
+276
+00:23:11,200 --> 00:23:14,040
+جاب لما نبدأ في الحلول لما جاب لما نبدأ في الحلول
+
+277
+00:23:14,040 --> 00:23:17,180
+كان definition معناه ذلك ان هي ليست implication
+
+278
+00:23:17,180 --> 00:23:22,880
+بصورتها المبسطة اللي انت فاهمها لأ ده كان compound
+
+279
+00:23:22,880 --> 00:23:26,150
+statementكان عبارة عن compound statement ال
+
+280
+00:23:26,150 --> 00:23:29,870
+compound statement بقولك ال a بقولك ان ال number
+
+281
+00:23:29,870 --> 00:23:34,110
+is even if and only if ماتيشيش تقولي مهيها if and
+
+282
+00:23:34,110 --> 00:23:35,270
+only if ماتيشيش تقولي مهيها if and only if ماتيشيش
+
+283
+00:23:35,270 --> 00:23:36,270
+تقولي مهيها if and only if ماتيشيش تقولي مهيها if
+
+284
+00:23:36,270 --> 00:23:36,550
+ماتيشيش تقولي مهيها if and only if ماتيشيش تقولي
+
+285
+00:23:36,550 --> 00:23:37,650
+مهيها if and only if ماتيشيش تقولي مهيها if and
+
+286
+00:23:37,650 --> 00:23:40,670
+only if ماتيشيش تقولي مهيها if and only if ماتيشيش
+
+287
+00:23:40,670 --> 00:23:45,930
+تقولي مهيها if and only if ماتيشيش تقولي مهيها if
+
+288
+00:23:45,930 --> 00:23:47,790
+and only if ماتيشيش تقولي م
+
+289
+00:23:53,340 --> 00:23:57,360
+Okay اعمل implication فش مشكلة بس مدام حطيلك
+
+290
+00:23:57,360 --> 00:24:02,380
+خصوصية بعدها وضح لك لها يعني عمل emphasize عليها
+
+291
+00:24:02,380 --> 00:24:07,000
+أكدلك عليها لأ خلاص احنا يقعد يقولك if and only if
+
+292
+00:24:07,000 --> 00:24:12,880
+ماديش ترجمها بال implication طيب
+
+293
+00:24:12,880 --> 00:24:19,180
+وين احنا كنا okay كان قول الأخيرة not everybody is
+
+294
+00:24:19,180 --> 00:24:25,070
+your friend or someone is notperfect يعني واضح إن
+
+295
+00:24:25,070 --> 00:24:30,930
+هم بعض عن بعض مختلفين or هدى هنا expression هناك
+
+296
+00:24:30,930 --> 00:24:34,530
+expression تاني مختلف تماما فبدك تعمل كل واحدة
+
+297
+00:24:34,530 --> 00:24:38,450
+لحال و تحط بينهم this junction و بس اه لإن هناك
+
+298
+00:24:38,450 --> 00:24:40,550
+بتتكلم عن friend هنا بتتكلم عن perfect و مافيش
+
+299
+00:24:40,550 --> 00:24:46,590
+relation between them بالنسبة ل C يعني لو حطينا X
+
+300
+00:24:46,590 --> 00:24:47,330
+and X
+
+301
+00:24:51,360 --> 00:24:55,020
+أه معنى .. لأ لأ استنى هيختلف المعنى لأنه في
+
+302
+00:24:55,020 --> 00:24:59,680
+الحالة هذه انت بتقول هنا all your friends are
+
+303
+00:24:59,680 --> 00:25:06,580
+perfect مش هيك فكل أصدقاءك perfect بس هل معنى ذلك
+
+304
+00:25:06,580 --> 00:25:13,460
+أنه لو مش صديقك معناته مش perfect؟ صح؟ ماحدش قال
+
+305
+00:25:13,460 --> 00:25:17,180
+أنه لأ مش perfect okay فلان مش صديقك بس هذا مش
+
+306
+00:25:17,180 --> 00:25:20,100
+معناه أنك انت الجملة هذه تشمل أن هو not perfect
+
+307
+00:25:22,870 --> 00:25:27,970
+لحظت؟ أنا هنا بقول كل أصدقاءك perfect تمام؟ فإذا
+
+308
+00:25:27,970 --> 00:25:32,930
+إذا هم أصدقاءك perfect طب إذا مش أصدقاءك ممكن
+
+309
+00:25:32,930 --> 00:25:36,590
+يكونوا perfect فليش تحكولهم ب and و تنفل الصفة
+
+310
+00:25:36,590 --> 00:25:40,470
+عنهم هيك؟ ليش لمجرد إنه هذه كانت true لأن هم
+
+311
+00:25:40,470 --> 00:25:45,270
+perfect لكن هم مش أصدقاءك لما تمانهم and صارت
+
+312
+00:25:45,270 --> 00:25:51,700
+false and true الجملة المجمل false وهذا مش صحيحهيك
+
+313
+00:25:51,700 --> 00:25:55,480
+مش صحيح أما ال implication أكتر وقعية أنه حتى لو
+
+314
+00:25:55,480 --> 00:25:58,360
+مش صاحبك ممكن يكون perfect ليش أنت تحكم على كل
+
+315
+00:25:58,360 --> 00:26:00,940
+البشرية أن هم مش perfect لمجرد أن هم مش أصدقاءك
+
+316
+00:26:00,940 --> 00:26:07,100
+تمامفزي ما قلنا الأخيرة هدى هما جمالتين مختلفات عن
+
+317
+00:26:07,100 --> 00:26:12,860
+بعض هنا بنتكلم عن every one و عن predicate friend
+
+318
+00:26:12,860 --> 00:26:16,460
+و هنا بنتكلم عن predicate تاني مختلف و ب
+
+319
+00:26:16,460 --> 00:26:20,240
+quantifier مختلف تماما فممكن كل واحد لحاله تربطهم
+
+320
+00:26:20,240 --> 00:26:23,220
+حسب إيش الرابط الرابط اللى عناه is or فبتحط ال
+
+321
+00:26:23,220 --> 00:26:28,200
+this junction okay
+
+322
+00:26:28,200 --> 00:26:33,600
+هنا إيش مطلوب السؤال هذا طالبين نعمل negationبدك
+
+323
+00:26:33,600 --> 00:26:37,940
+تعمل negation للجملة اللى موجودة عندك لما نقول for
+
+324
+00:26:37,940 --> 00:26:50,280
+all x, x greater than one بدك تنفيها على
+
+325
+00:26:50,280 --> 00:26:56,280
+خط الأعداد، هاي صفر، هاي one، كل قيم x أكبر
+
+326
+00:26:58,580 --> 00:27:02,840
+من واحد طيب
+
+327
+00:27:02,840 --> 00:27:06,340
+ان فيها احنا بدنا نعمل negation ايش المفروض اقول
+
+328
+00:27:06,340 --> 00:27:10,820
+المفروض اي expression يكون موجود عندى انه لا يوجد
+
+329
+00:27:10,820 --> 00:27:15,620
+حد هنا بالظبط
+
+330
+00:27:15,620 --> 00:27:20,080
+هذه مبدئيا بس انا بدى اعمل negation يعني بدى أن
+
+331
+00:27:20,080 --> 00:27:27,020
+فيها بمعنى ان انا بدأ اتصير هيك what
+
+332
+00:27:27,020 --> 00:27:35,930
+hitبينت معانا negation فهتصبح إعكس there exist x
+
+333
+00:27:35,930 --> 00:27:42,090
+أقل أو أصغر من واحد معانا ذلك أن انت عشان تنفي
+
+334
+00:27:42,090 --> 00:27:51,890
+الجملة هذه معانا جلم؟ عشان تنفي هذه for all إيش
+
+335
+00:27:51,890 --> 00:27:57,030
+معانا for all؟ إن هنا zero
+
+336
+00:27:58,380 --> 00:28:05,080
+صح؟ Zero تماما كله هنا طيب يكفي واحد موجود هنا
+
+337
+00:28:05,080 --> 00:28:13,360
+عشان ال for all هذه تصبح force صح؟
+
+338
+00:28:13,360 --> 00:28:17,890
+واحد بس بيكفيأو أكتر ما هو okay مافيش مشكلة أكتر
+
+339
+00:28:17,890 --> 00:28:22,170
+أكتر بيمشي الحال بس مدام قال لي for all معناته أنا
+
+340
+00:28:22,170 --> 00:28:25,350
+عشان أغيظه زي ما بيقوله بدي بس أطلعله واحد في
+
+341
+00:28:25,350 --> 00:28:28,190
+المكان اللي هو بيقوله ان هو for all جال والله انه
+
+342
+00:28:28,190 --> 00:28:32,070
+نضف القاعة تماما انا مش محتاج أوصخلها كلها بس ورا
+
+343
+00:28:32,070 --> 00:28:36,130
+جايك واحدة ارميها في النص وخلي المشرف يجي يتفرج مش
+
+344
+00:28:36,130 --> 00:28:43,110
+هيك يكفي واحدةما هي هي فهي الفكرة كلها بس واحد فقط
+
+345
+00:28:43,110 --> 00:28:48,590
+فهي هي الواحد there exist x أقل من أو يسوى واحد بس
+
+346
+00:28:48,590 --> 00:28:56,570
+واحد نفها خلصنا طيب اتفضل عكسها
+
+347
+00:28:56,570 --> 00:29:03,010
+لاحظ هنا هذه أكبر من عكس الأكبر من أقل أو يساوي
+
+348
+00:29:03,010 --> 00:29:09,560
+لأن هنا الواحد غير مشمولهنا ال X أكبر من واحد فإذا
+
+349
+00:29:09,560 --> 00:29:17,740
+ال واحد غير مشمول أصغر من بس أكبر
+
+350
+00:29:17,740 --> 00:29:21,180
+أو يساوي بالظبط زي ها يوم جيناك جيناك هي جياك اللي
+
+351
+00:29:21,180 --> 00:29:26,900
+وراها هي اللي وراها أيش عكستلك نفس الكلام كله كنا
+
+352
+00:29:26,900 --> 00:29:30,040
+هنا بدون يساوي هيحطلك اليساوي كنا أكبر منه صارت
+
+353
+00:29:30,040 --> 00:29:36,500
+أصغر منه المفهوم هو هو بس هنرجع نرسمه هيصبح كتالي
+
+354
+00:29:40,480 --> 00:29:48,460
+كله اقل من او يساوي اتنين، ولاحظ اعملتها solid،
+
+355
+00:29:48,460 --> 00:29:53,580
+solid بمعنى ان الاتنين مشمولة، معناته انت بدك على
+
+356
+00:29:53,580 --> 00:29:59,320
+الاقل واحد هنا، بس اكبر من جديش من اتنين، بقولش او
+
+357
+00:29:59,320 --> 00:30:04,420
+يساوي، فش او يساوي، او يساوي معناته صارت مشمولة مع
+
+358
+00:30:04,420 --> 00:30:10,430
+التعريف الاولتمام فتوقع فيش فيها مشكلة طيب حتى
+
+359
+00:30:10,430 --> 00:30:14,010
+التالتة برضه فيش فيها مشكلة بتهيأ ليه؟خلاص هذه
+
+360
+00:30:14,010 --> 00:30:20,710
+برضه مافيها مشكلة للرابعة نفس الاشي برضه مش جثة ال
+
+361
+00:30:20,710 --> 00:30:24,190
+there exist يوجد هي الفكرة الوحيدة كانت ال there
+
+362
+00:30:24,190 --> 00:30:27,810
+exist ان يوجد على الأقل واحد احنا بنقول لأ بدي
+
+363
+00:30:27,810 --> 00:30:31,130
+أنفي الواحد هذا فبقول كله بالعكس فبأضمن ان مافيش
+
+364
+00:30:31,130 --> 00:30:36,990
+ولا واحد في الإيجاب بس ناخد ال E هالوقت ال E بدنا
+
+365
+00:30:36,990 --> 00:30:41,910
+نفهمها لإنه طورت شوية المفهوم صارت الاتنين مع بعض
+
+366
+00:30:45,750 --> 00:30:53,930
+من اتنين سالب واحد سالب one و هنا two و هنا بيقولك
+
+367
+00:30:53,930 --> 00:31:02,550
+or فإذا من هنا لهنا كل ال elements x أقل من سالب
+
+368
+00:31:02,550 --> 00:31:07,130
+واحد أو أكبر من اتنين يعني أنت بدك على الأقل عنصر
+
+369
+00:31:07,130 --> 00:31:12,950
+في المنطقة هذه بس ف there exist between
+
+370
+00:31:15,130 --> 00:31:21,270
+أكبر من أو يساوي سالب واحد وأقل من بس هاي كل
+
+371
+00:31:21,270 --> 00:31:31,970
+الموضوع و ليش negation of or and تمام خلصنا هاي كل
+
+372
+00:31:31,970 --> 00:31:36,050
+الموضوع تمام اللي وراها الفكرة هي هي بتاع اللي
+
+373
+00:31:36,050 --> 00:31:41,230
+خلصت بس هنا يمكن مشموليتها ما بين عنصرين
+
+374
+00:31:44,540 --> 00:31:52,840
+من سالب من أقل من أربعة أقل
+
+375
+00:31:52,840 --> 00:31:57,660
+من أربعة هي أربعة وأكبر من سبعة ورا نفسها بس هنا
+
+376
+00:31:57,660 --> 00:32:05,480
+there exist هنا there exist خد بالك يعني يوجد عنصر
+
+377
+00:32:05,480 --> 00:32:10,460
+أصغر من أربعة أو أكبر من سبعة معناته هنا إيش بده
+
+378
+00:32:10,460 --> 00:32:17,910
+أقول كلهمفي المنطقة المفقودة هنا بحيث أنه أطمن أنه
+
+379
+00:32:17,910 --> 00:32:22,590
+لا يوجد ولا واحد قبل ولا واحد بعد بس I call
+
+380
+00:32:22,590 --> 00:32:28,610
+فبنقولها for all بسيطة الأسئلة مش هيك لاحظ لو ما
+
+381
+00:32:28,610 --> 00:32:31,390
+شرحناهاش على ال link انتوا عارف كانت هتتوهكوا برضه
+
+382
+00:32:31,390 --> 00:32:35,930
+لو فيه هيك فجأة في امتحان فهي أفكار بسيطة وسهلة بس
+
+383
+00:32:35,930 --> 00:32:37,450
+بدأ شويه التركيز أسلة امتحانات
+
+384
+00:32:42,870 --> 00:32:47,210
+الان what are the truth value of these statements
+
+385
+00:32:47,210 --> 00:32:53,630
+لما نقول في عندى there exist exactly one x P of X
+
+386
+00:32:53,630 --> 00:33:02,650
+implies there exist x P of X true ولا false كل
+
+387
+00:33:02,650 --> 00:33:09,470
+المطلوب ان احنا هنا نحط T ولا F بس هل
+
+388
+00:33:09,470 --> 00:33:14,660
+لاحظ كمان مرة نقرأها بهدوء بسهل لما أقول يوجد
+
+389
+00:33:14,660 --> 00:33:24,340
+exactly one P of X is true بتمنلي أن يوجد X P of X
+
+390
+00:33:24,340 --> 00:33:35,100
+is true هنا واحد و هنا there exist تمام فإذا مجرد
+
+391
+00:33:35,100 --> 00:33:39,700
+أن يوجد exactly one فهي there exist فهي هتكون
+
+392
+00:33:39,700 --> 00:33:41,720
+there exist التانية
+
+393
+00:33:46,740 --> 00:33:53,840
+for all x, P of x بيضمن ليه؟ انه there exist
+
+394
+00:33:53,840 --> 00:34:00,100
+exactly one يعني اقول الكل f of x معناته ان there
+
+395
+00:34:00,100 --> 00:34:04,340
+exist exactly one is x true يعني معناه افضل واحد،
+
+396
+00:34:04,340 --> 00:34:08,400
+اذا كل موجود يعني true واحد true واحد true واحد
+
+397
+00:34:08,400 --> 00:34:14,130
+true واحد true واحد ممكن يكون اكتر من واحدممكن
+
+398
+00:34:14,130 --> 00:34:19,750
+يكون اكتر من واحد لان انا قاعد اقول for all لأ
+
+399
+00:34:19,750 --> 00:34:27,730
+لأ انت ال M لاحظ for all for all هنا الحالة
+
+400
+00:34:27,730 --> 00:34:30,490
+الوحيدة اللي قلنا عليها ال implication بكون فيه
+
+401
+00:34:30,490 --> 00:34:38,630
+false هي اللي فحصوها اي حالة true or false true or
+
+402
+00:34:38,630 --> 00:34:43,760
+falseالأصل أنه يكون عنده هنا true وهنا تكون false
+
+403
+00:34:43,760 --> 00:34:51,940
+أنه كلهم مشمولين و لا يوجد exactly one و
+
+404
+00:34:51,940 --> 00:34:56,840
+لا يوجد exactly one فإذا لما أقول for all x خلّيني
+
+405
+00:34:56,840 --> 00:35:00,320
+نرجع نفحصها كمان مرة for all x معناه ذلك أنه ممكن
+
+406
+00:35:00,320 --> 00:35:05,000
+يكون اتنين أو تلاتة أو أربعة موجودين بيضمن ليه أن
+
+407
+00:35:05,000 --> 00:35:06,780
+there exist x
+
+408
+00:35:09,260 --> 00:35:15,160
+is لأ false هدى false هدى false إلا في حالة واحدة
+
+409
+00:35:15,160 --> 00:35:19,780
+كويس هى طلعت إلا خصوصية كمان إلا في حالة واحدة
+
+410
+00:35:19,780 --> 00:35:29,280
+فإذا ممكن تكون X عبارة عن مجموعة ABC مثلا and so
+
+411
+00:35:29,280 --> 00:35:34,740
+on بس ال true في حالة اللى هى أصلا ال university
+
+412
+00:35:34,740 --> 00:35:38,420
+of discourse واحد صح
+
+413
+00:35:43,040 --> 00:35:46,000
+فإذن الحالة الوحيدة اللي بقدر أقول إن هي true صح
+
+414
+00:35:46,000 --> 00:35:50,600
+الإتنين ممكن يعطوا بعض أو خلّينا exactly إن كلهم
+
+415
+00:35:50,600 --> 00:35:54,740
+perfect بضمن لي إن على الأقل يوجد واحد إنه فعليًا
+
+416
+00:35:54,740 --> 00:36:00,100
+exactly واحد perfect exactly واحد perfect أنت
+
+417
+00:36:00,100 --> 00:36:03,380
+فعليًا هنا بيكونوا أكتر من واحد فمعنى ذلك إن هذه
+
+418
+00:36:03,380 --> 00:36:08,820
+بتتطلع false هذه هتطلع هيك false يعني معنى ذلك
+
+419
+00:36:08,820 --> 00:36:16,350
+صارت true falseأكيد منطقيا غلط ال true لإن كلهم
+
+420
+00:36:16,350 --> 00:36:22,150
+هيها a is true, b is true, c is true تمام هذه ال
+
+421
+00:36:22,150 --> 00:36:26,150
+true لكن هل بدمن لي إن there exist exactly one is
+
+422
+00:36:26,150 --> 00:36:32,890
+true لأ لإنه a و b و c التلاتةلو there exist لو
+
+423
+00:36:32,890 --> 00:36:36,770
+there exist كلامك ماشي يعني منطقيا ممكن تظبط بس
+
+424
+00:36:36,770 --> 00:36:40,770
+هنا هذه الحالة الوحيدة عشان تظبط فيها فقط انه
+
+425
+00:36:40,770 --> 00:36:44,270
+أساسا universe of discourse هو just one element
+
+426
+00:36:44,270 --> 00:36:52,750
+ممكن تقول true إذا انتقلت جبلة and all y اما انت
+
+427
+00:36:52,750 --> 00:36:57,670
+دخلت في expression غير هذا صح احنا لأ مش انها تصير
+
+428
+00:36:57,670 --> 00:37:01,740
+صح احنا بنتكلم عن expression هو صح ولا غلط بسصح؟
+
+429
+00:37:01,740 --> 00:37:04,680
+انت بدك تصمحه بيصير اه بتفكر في طريقة انك انت
+
+430
+00:37:04,680 --> 00:37:07,100
+تجلبها لل or اللي بتحكي عليها بتصير كلامك منطقي
+
+431
+00:37:07,100 --> 00:37:12,540
+صحيح أما الآن هذه حسب ما أذكرها مظبوط فإذا هذه
+
+432
+00:37:12,540 --> 00:37:18,300
+false there exist
+
+433
+00:37:18,300 --> 00:37:21,360
+لأ ممكن لأن there exist ممكن بواحد
+
+434
+00:37:23,950 --> 00:37:27,990
+أه بس مجرد الإمكانية اللى بتقول عليها ممكن بتعملك
+
+435
+00:37:27,990 --> 00:37:33,450
+ال truth لأن there exist بواحد بيمشي الحال أما هنا
+
+436
+00:37:33,450 --> 00:37:37,310
+for all بواحد بيمشيش إلا إذا كان هو الواحد الكل
+
+437
+00:37:38,460 --> 00:37:42,220
+يعني ال universe of discourse هو الواحد بس تظبط
+
+438
+00:37:42,220 --> 00:37:45,940
+أكتر من هناك لأ بتظبطش في there exist أه بنفع لأن
+
+439
+00:37:45,940 --> 00:37:50,420
+واحد كافي أنه يحققلك there exist بس هنا for all لأ
+
+440
+00:37:50,420 --> 00:37:55,360
+بنفعش الواحد يكمل يحملها فإذا زي ما قلنا false إلا
+
+441
+00:37:55,360 --> 00:38:00,480
+إذا كان فعلا عندي ال domain تبعي هو consists of
+
+442
+00:38:00,480 --> 00:38:04,040
+just one element okay بتظبط الأخيرة
+
+443
+00:38:07,070 --> 00:38:14,070
+there exist exactly one x لا يحقق P of X بيضمنلنا
+
+444
+00:38:14,070 --> 00:38:20,010
+انه negation او ليس الكل يحقق P of X true مش هيك
+
+445
+00:38:20,010 --> 00:38:26,230
+منطقية واحد فقط لا يحقق معناته انه ليس الكل يحقق
+
+446
+00:38:26,230 --> 00:38:33,130
+خلاص فإذا true منطقيةو انتوا بتحلوا هيكي في ال ..
+
+447
+00:38:33,130 --> 00:38:35,770
+في الرواجان بتكون الأمور أسهل، لو في الامتحان كان
+
+448
+00:38:35,770 --> 00:38:44,270
+شد .. طيب okay اعتقد هننهي يمكن في هذه .. نشوف،
+
+449
+00:38:44,270 --> 00:38:46,730
+الآن بدنا نعمل زي أخر حاجة شرحناها في المصادر ..
+
+450
+00:38:46,730 --> 00:38:49,190
+في ال .. في المحاضرة بتاعت اليوم، اللي هي
+
+451
+00:38:49,190 --> 00:38:54,870
+definition و بدنا نترجمه ل mathematical expression
+
+452
+00:38:55,670 --> 00:38:58,810
+بنعمل translation لل statement the sum of two
+
+453
+00:38:58,810 --> 00:39:04,810
+positive integers is always positive نفس الفكرة
+
+454
+00:39:04,810 --> 00:39:08,650
+فهنا برضه هنجور for all و بنفتح الأقواذ بتاعتنا
+
+455
+00:39:08,650 --> 00:39:16,400
+إذا كانالـ x و y positive أكبر من صفر فبنقول إذا
+
+456
+00:39:16,400 --> 00:39:22,120
+كانت x أكبر من صفر and y أكبر من صفر و بنعمل then
+
+457
+00:39:22,120 --> 00:39:33,380
+z تساوي x and y and z أكبر من صفر أو على طول ممن
+
+458
+00:39:33,380 --> 00:39:37,790
+خير حتى z x زائد y أكبر من صفر و خلاصمباشرة مافيش
+
+459
+00:39:37,790 --> 00:39:41,770
+داعي نحط كمان متغير تالت فمباشرة إذا عرفنا x أكبر
+
+460
+00:39:41,770 --> 00:39:47,070
+من صفر and y أكبر من صفر إذا x زائد y greater than
+
+461
+00:39:47,070 --> 00:39:53,430
+0 وخلاصفإذا على طول مباشرة for all x y إذا كانت x
+
+462
+00:39:53,430 --> 00:39:57,910
+أكبر من صفر و y أكبر من صفر إذا مجموحهم أكبر من
+
+463
+00:39:57,910 --> 00:40:04,870
+صفر بسيطة سهلة وسلسفش كتير فيها مشاكل تمام فالأن
+
+464
+00:40:04,870 --> 00:40:09,450
+كنت خلصنا لهذا الأسبوع الجزء المطلوب منها المرة
+
+465
+00:40:09,450 --> 00:40:12,490
+القادمة ان شاء الله بنبدأ في ال proving strategies
+
+466
+00:40:12,490 --> 00:40:15,810
+و برضه نفس الفكرة الكويسة أن في المحاضرات المصورة
+
+467
+00:40:15,810 --> 00:40:20,270
+جاهزة عندكم فبترجعوها بحيث أنه دائما نحاولفي آخر
+
+468
+00:40:20,270 --> 00:40:24,570
+الأسبوع نوفر هيك نص ساعة زمان نجيبلكوا فيها أسئلة،
+
+469
+00:40:24,570 --> 00:40:27,070
+بتهيألي بيكون أفضل من إنه نضلنا مربوطين مزنوجين في
+
+470
+00:40:27,070 --> 00:40:32,150
+ال .. في المحاضرة ك .. ك theoretical concepts،
+
+471
+00:40:32,150 --> 00:40:34,070
+كتير كويس إن احنا نروح للبرنامج، كلي أعطوكوا
+
+472
+00:40:34,070 --> 00:40:34,350
+العافية
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/tfL57plaSsE_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/tfL57plaSsE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6515b1437089208777895f369ff5775275ff1ad7
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/tfL57plaSsE_raw.srt
@@ -0,0 +1,1892 @@
+1
+00:00:05,150 --> 00:00:07,510
+طيب بسم الله الرحمن الرحيم السلام عليكم يا شباب
+
+2
+00:00:07,510 --> 00:00:11,290
+نكمل اليوم في جزئية ال quantifiers اللي حكينا عنها
+
+3
+00:00:11,290 --> 00:00:15,450
+المرة الماضية نكمل الجزء اللي كان متبقيلنا و زي ما
+
+4
+00:00:15,450 --> 00:00:18,290
+وعدناكوا كل ما هنلاقي معانا وقت فاضي في أخر
+
+5
+00:00:18,290 --> 00:00:22,530
+الأسبوع و فيه واجت هنحل أسئلة هنحل مجموعة أسئلة
+
+6
+00:00:22,530 --> 00:00:25,490
+فاليوم إن شاء الله إذا كان أسعفنا الوقت مجهز
+
+7
+00:00:25,490 --> 00:00:29,050
+مجموعة أسئلة برضه على شوية مواضيع من المواضيع اللي
+
+8
+00:00:29,050 --> 00:00:33,750
+مروا عليناجد ما بنقدر ناخد ناخد و بنشوف بعدين
+
+9
+00:00:33,750 --> 00:00:37,570
+لباقي الأسئلة اللاحقة طيب في ال quantifiers
+
+10
+00:00:37,570 --> 00:00:44,470
+اتكلمنا انه there exist مع for all لنفس المتغير مش
+
+11
+00:00:44,470 --> 00:00:47,890
+هيظبطوا الإتنين مع بعض أخدناها المرة الماضية نفس
+
+12
+00:00:47,890 --> 00:00:54,850
+الكلام لما يكون في عندهfor all x p of x تمام و في
+
+13
+00:00:54,850 --> 00:00:58,370
+اقواس معناه ذلك ان ال quantifier هذا لل p of x فقط
+
+14
+00:00:58,370 --> 00:01:04,370
+و ليس لل q of x مدام غير مشمول الاقواس معها طيب
+
+15
+00:01:04,370 --> 00:01:08,530
+نفس الشغل قولنا لما يكون في عندي for all x p of x
+
+16
+00:01:09,860 --> 00:01:13,800
+مع بعض لحالها and there exist x q of x معناه ذلك
+
+17
+00:01:13,800 --> 00:01:17,380
+أن كل x من تنتين هدول مختلفة عن التانية كل واحدة
+
+18
+00:01:17,380 --> 00:01:21,420
+خاصة بال function أو بال predicate بتاعتها و ال
+
+19
+00:01:21,420 --> 00:01:23,860
+quantifier تبعها of course فهنا هيكون في end
+
+20
+00:01:23,860 --> 00:01:31,020
+different xحكينا عن ال quantifier equivalence laws
+
+21
+00:01:31,020 --> 00:01:35,300
+و شفنا ان for all معناته بتكلم عن مجموعة and و for
+
+22
+00:01:35,300 --> 00:01:40,660
+all there exist بتكلم عن مجموعة or تمام؟ و قلنا ال
+
+23
+00:01:40,660 --> 00:01:43,260
+two properties هدولة و أثبتناهم المرة الماضية
+
+24
+00:01:43,260 --> 00:01:47,560
+أثبتنا كيف ممكن فعلا انحقق التنتين هدولة من خلال
+
+25
+00:01:47,560 --> 00:01:54,060
+دي مورغانطيب لما تكون عندي for all x for all y مين
+
+26
+00:01:54,060 --> 00:01:58,600
+جاب للتاني مش هيفرج for all y for all x برضه مش
+
+27
+00:01:58,600 --> 00:02:02,020
+هتفرجزاه بالظبط لما تكون في ال language بحول من
+
+28
+00:02:02,020 --> 00:02:06,220
+direct ل ish ل n direct ل indirect نفس الكلام لل
+
+29
+00:02:06,220 --> 00:02:10,780
+there exist طيب لما تكون ال for all محكومة بأقواص
+
+30
+00:02:10,780 --> 00:02:15,240
+كاملة لمين لأ ال two predicatestwo predicates مع
+
+31
+00:02:15,240 --> 00:02:19,440
+بعض معناتهم الفرق لل predicate الأول و ال
+
+32
+00:02:19,440 --> 00:02:24,280
+quantifier برضه لل predicate التاني فنقدر نوزحها
+
+33
+00:02:24,280 --> 00:02:26,740
+مدام الأقواص حكمانة ال priority دايما هي اللي
+
+34
+00:02:26,740 --> 00:02:30,560
+بتحكمنا في توزياتنا نفس الكلام لمين الveer exist
+
+35
+00:02:30,560 --> 00:02:38,210
+okay برضهحالات تانية كتير ممكن تتعامل معها انك
+
+36
+00:02:38,210 --> 00:02:41,530
+تلاقي for all x for all y for all z كلهم for all
+
+37
+00:02:41,530 --> 00:02:43,670
+for all for all معناه ذلك ان انا ممكن احط for all
+
+38
+00:02:43,670 --> 00:02:49,530
+واحدة نكتبها for all x y z مع بعض تمام كومز او
+
+39
+00:02:49,530 --> 00:02:53,590
+بدون كومز على طول مباشرة كله بمشي الحال فبتفهم
+
+40
+00:02:53,590 --> 00:02:56,350
+مباشرة ان اذا جالك for all x y z معناته ان انا
+
+41
+00:02:56,350 --> 00:03:00,950
+بتكلم عن for all y for all x for all z صح كلهم
+
+42
+00:03:03,240 --> 00:03:07,560
+تمام نصل لبداية محاضرتنا لليوم اللي هي بدنا نتكلم
+
+43
+00:03:07,560 --> 00:03:10,840
+فيها عن بعد ما عملنا revision سريعة نتكلم فيها عن
+
+44
+00:03:10,840 --> 00:03:15,820
+a new quantifier إضافي غير ال there exist و ال for
+
+45
+00:03:15,820 --> 00:03:18,900
+all اللي أخدناهم المرة الماضية اللي هو there exist
+
+46
+00:03:18,900 --> 00:03:24,170
+exactly onethere exist كلنا عارفين ان هي one or
+
+47
+00:03:24,170 --> 00:03:30,990
+more بديش or هذه for one just one just one فبنعمل
+
+48
+00:03:30,990 --> 00:03:34,670
+there exist exclamation علامة التعجب هذه
+
+49
+00:03:34,670 --> 00:03:38,750
+exclamation x p of x فهذه بفهم منها ان يوجد
+
+50
+00:03:38,750 --> 00:03:44,370
+exactly one value for x such that p of x is true
+
+51
+00:03:44,370 --> 00:03:49,810
+فإذا يوجد قيمة واحدة ل x تحقق p of x وتحديدا واحدة
+
+52
+00:03:50,510 --> 00:03:55,830
+فهنا بتكون تحديدا exactly one تمام طيب هذه إيش
+
+53
+00:03:55,830 --> 00:04:00,150
+معناها؟ معناها لما بدي أجي أحللها ال .. ال new
+
+54
+00:04:00,150 --> 00:04:02,870
+quantifier هذه اللي هي there exist exclamation أو
+
+55
+00:04:02,870 --> 00:04:06,870
+exactly one X P of X هذه تكافئ لإيش؟ ل there exist
+
+56
+00:04:06,870 --> 00:04:14,610
+X تحقق P of X and لا يوجد غيرها يحقق صح؟ مش هيك
+
+57
+00:04:14,610 --> 00:04:20,210
+معناها؟هي لا يوجد Y تحقق P of X بشرط أن Y لا تسوى
+
+58
+00:04:20,210 --> 00:04:24,330
+X بمعنى أن Y هي أي شيء غير X لأن X يحقق
+
+59
+00:04:28,260 --> 00:04:32,620
+there exists exactly one P of X هذي مكافئة لإيش
+
+60
+00:04:32,620 --> 00:04:35,660
+يعني احنا اختزلنا عشان نحط الجملة بهذا الشكل لو
+
+61
+00:04:35,660 --> 00:04:38,920
+كنت فير بهذا الشكل هل كان له فائده ان احطه بهذا
+
+62
+00:04:38,920 --> 00:04:43,180
+الشكل اه كان له فائده لإن هو ده بيختزل ليه form
+
+63
+00:04:43,180 --> 00:04:48,310
+كتير ضخم و كتير كبير اللي هو إيش there exists XP
+
+64
+00:04:48,310 --> 00:04:53,090
+of X فإذا يوجد قيمة ل X تحقق P of X و غيرها لا
+
+65
+00:04:53,090 --> 00:04:56,970
+يحقق مش بدي أترجم كلمة و غيرها لا يحقق لأنها واحد
+
+66
+00:04:56,970 --> 00:05:03,050
+فقط X بس فإذا يحقق P of X and غيرها لا يحقق من
+
+67
+00:05:03,050 --> 00:05:10,750
+غيرها أي حاجة تانية Y معناته لا يوجد Y تحقق P of X
+
+68
+00:05:10,750 --> 00:05:15,550
+بس ناخد بالنا مش يطلعلي بالآخر Y هي نفسها Xأحنا
+
+69
+00:05:15,550 --> 00:05:19,330
+قلنا لو وجد غيرها، غيرها معناته بدي أحدد أن why لا
+
+70
+00:05:19,330 --> 00:05:24,570
+تسوى x لأنه غيرها عشان تكون فعلا غيرها فإذا هنا
+
+71
+00:05:24,570 --> 00:05:29,370
+أنا بكون بدقة كاملة عرفت التعريف بدون ما أنسى أو
+
+72
+00:05:29,370 --> 00:05:35,270
+أخفل أي case ممكن تضرب ليه تعريفي لو ما كتبناش
+
+73
+00:05:35,270 --> 00:05:39,090
+الأخيرة هذه هيجيك واحد يقولك طب ماشي why تسوى x هي
+
+74
+00:05:39,090 --> 00:05:45,810
+بتصبط وصار في عندكconfusion .. confusion واضح انه
+
+75
+00:05:45,810 --> 00:05:50,830
+في اختلاف في المعنيين هذه صارت غير هذه لأ مهمة جدا
+
+76
+00:05:50,830 --> 00:05:56,130
+حتى اخر حاجة انكتبت مهمة جدا فإذا كل كلمة بدنا
+
+77
+00:05:56,130 --> 00:06:00,910
+انعرفها او مهمة في التعريف لازم تكون واضحة في ال
+
+78
+00:06:00,910 --> 00:06:04,830
+expression اللي بتكتبه لابد تكون واضحة ما تختزلش
+
+79
+00:06:04,830 --> 00:06:07,550
+حاجة تقول ما هو معروفة مافيش حاجة ما هو معروفة
+
+80
+00:06:07,550 --> 00:06:11,740
+احنا الآن زي ما قلنا كمان مرةال discrete هذه عشان
+
+81
+00:06:11,740 --> 00:06:15,020
+هتفهم مع الحاسوب الحاسوب بيفهمش ما هي معروفة
+
+82
+00:06:15,020 --> 00:06:19,240
+الحاسوب بيعرفش شي الحاسوب في الآخر silicon رمل
+
+83
+00:06:19,240 --> 00:06:22,440
+يعني تقوله لأ ما هي معروفة انه انا بقول لا يوجد
+
+84
+00:06:22,440 --> 00:06:25,800
+غيرها هقول لك انا ماعرفتش ان انت ايش جصدك بغيرها
+
+85
+00:06:25,800 --> 00:06:30,140
+لازم تحطه ال y لا بساوة x انا عارف ان في حاجات انت
+
+86
+00:06:30,140 --> 00:06:32,920
+by default بتحس تا ماهي منطقة لأ مش فيش حاسوبة
+
+87
+00:06:32,920 --> 00:06:37,080
+منطقية كمان مرة الرمساق تبعنا مش عشاني انا وانت
+
+88
+00:06:37,910 --> 00:06:44,170
+عشان انت بدأت تتعامل مع هال machine هذه فإذا أصبح
+
+89
+00:06:44,170 --> 00:06:49,330
+تعريفنا there is an X such that P of X where is no
+
+90
+00:06:49,330 --> 00:06:56,590
+Y such that P of Y and Y other than X و Y هذي أي
+
+91
+00:06:56,590 --> 00:07:01,190
+شيء تاني غير X عشان مايجيش واحد يضرب للتعريف و
+
+92
+00:07:01,190 --> 00:07:03,770
+يقول طيب ماشي انت حطيت X و Y ما هو ما يمكن نفس
+
+93
+00:07:03,770 --> 00:07:07,730
+القيمة تنتهيX تساوي تلاتة و Y تساوي تلاتة هاي
+
+94
+00:07:07,730 --> 00:07:16,310
+طلعوا بيساوي بعض فمهم جدا Y is other than X تمام
+
+95
+00:07:16,310 --> 00:07:23,110
+ناخد مثلين لتعريفين من ال language أو من English
+
+96
+00:07:23,110 --> 00:07:28,050
+language بدنا نعرفها بشكل mathematical form لما
+
+97
+00:07:28,050 --> 00:07:32,430
+أقول الأعداد الزوجية
+
+98
+00:07:33,970 --> 00:07:37,170
+أعداد زوجية هفترض مبدأي ان انا بتعامل مع ال
+
+99
+00:07:37,170 --> 00:07:39,390
+natural numbers اللي هي من صفر واحد اتنين تلاتة to
+
+100
+00:07:39,390 --> 00:07:44,410
+infinity و بدنا نعرف اي رقم زوجي فبقول a number x
+
+101
+00:07:44,410 --> 00:07:49,290
+is even هي اول تعريف انا بدي اعرف رقم زوجي يعني E
+
+102
+00:07:49,290 --> 00:07:56,910
+of X و E هي اللي بتكلم X is even تمام هذا الكلام
+
+103
+00:07:56,910 --> 00:08:03,060
+صحيح if and only ifit's equal to two times some
+
+104
+00:08:03,060 --> 00:08:12,520
+other number عشان اقول ان X is even فإذا لابد ان X
+
+105
+00:08:12,520 --> 00:08:20,320
+هذي تكون اتنين في some other number Y مثلا وإلا
+
+106
+00:08:20,320 --> 00:08:24,550
+فهي ليست زوجيمعنى ذلك ان هي لسة زوجة التعريف هذا
+
+107
+00:08:24,550 --> 00:08:28,190
+بدنا ان ترجمه بشكل معادلة بس لا أكثر ولا أقل
+
+108
+00:08:28,190 --> 00:08:36,690
+فهنقول for all x لكل قيم x x هذا هيكون even x
+
+109
+00:08:36,690 --> 00:08:43,390
+هيكون even لكن بشرط even if and only if إذا وإذا
+
+110
+00:08:43,390 --> 00:08:49,910
+فقط بمعنى ان هنا ليست implication خد بالك ليست
+
+111
+00:08:49,910 --> 00:08:54,600
+implicationلنوضحها ليست implication ببساطة جدا
+
+112
+00:08:54,600 --> 00:09:00,160
+لأنه إذا كان even فإذا هو اتنين Y بس هل معناه ذلك
+
+113
+00:09:00,160 --> 00:09:03,740
+أنه يمكن يكون اتنين Y بينما هو مش even؟ ولا يمكن
+
+114
+00:09:03,740 --> 00:09:10,500
+صح؟ فإذا implication لن تصلح هنا لابد إنك أنت
+
+115
+00:09:10,500 --> 00:09:15,220
+تستخدم if and only if ال by conditional فإذا لكل
+
+116
+00:09:15,220 --> 00:09:23,400
+قيم X، X evenif and only if there exists y يوجد
+
+117
+00:09:23,400 --> 00:09:30,540
+رقم آخر اتنين تمثل ضعفه اللي هي عفوا x تمثل ضعفه
+
+118
+00:09:30,540 --> 00:09:37,820
+يوجد y اللي هو other than x يوجد y x تسوى اتنين y
+
+119
+00:09:37,820 --> 00:09:42,100
+طبعا هنا مالهاش معنى تقولي اه مسكت الكتابة كثير
+
+120
+00:09:42,100 --> 00:09:48,110
+لأن عادة و بدنا نحط y لا تسوى xمالهاش معنى ال gate
+
+121
+00:09:48,110 --> 00:09:51,810
+ليش لأن أنا جاوب أقولك تسوى 2Y فإذا هي اللي تسويها
+
+122
+00:09:51,810 --> 00:10:00,470
+أصلا صح ال صفر فقط الحالة الصفر الوحيدة تمام فإذا
+
+123
+00:10:00,470 --> 00:10:06,290
+لكل قيم X X is even خلاص if and only if there
+
+124
+00:10:06,290 --> 00:10:13,010
+exist YX تمثل ضعف Y أو تمثل اتنين من Y تمام هذه
+
+125
+00:10:13,010 --> 00:10:17,410
+تعريف لكل المصطلح أو ال definition اللي كنا كتبينه
+
+126
+00:10:17,410 --> 00:10:21,490
+طيب كمان definition و بدنا نحوله لمعادلة ايش ال
+
+127
+00:10:21,490 --> 00:10:26,130
+definition لمين لأرقام ال primes هقول a number is
+
+128
+00:10:26,130 --> 00:10:32,290
+prime الرقم أولي فبسميه P of X انت بيكون الرقم
+
+129
+00:10:32,290 --> 00:10:37,050
+أولي if and only if إذا وإذا فقطit's greater than
+
+130
+00:10:37,050 --> 00:10:42,010
+one ال one مش أولي اتفقنا ال one مش أولي فإذا هو
+
+131
+00:10:42,010 --> 00:10:49,070
+أكبر من واحد and it's not the product of two non
+
+132
+00:10:49,070 --> 00:10:54,690
+unity numbers وهو لا يمكن أن يكون حاصل ضرب رقمين
+
+133
+00:10:54,690 --> 00:11:01,140
+غير الواحدعشان ماتجيش تلغيلي إياها و تقولي ما هي
+
+134
+00:11:01,140 --> 00:11:05,520
+الواحد أو سبعة في واحد أو خلّيني أقول سبعة هي أصلا
+
+135
+00:11:05,520 --> 00:11:10,880
+prime تقولي مثلا أربعة في واحد لأ دير بالك
+
+136
+00:11:10,880 --> 00:11:15,100
+الرقامين اللي لاتصلح إنها ال prime يكون ضربهم
+
+137
+00:11:15,100 --> 00:11:20,400
+الرقامين لازم يكونوش واحد لا الأول واحد ولا التاني
+
+138
+00:11:20,400 --> 00:11:26,200
+واحد فهذه بينات في إيش non unityليس فيهم الواحد
+
+139
+00:11:26,200 --> 00:11:31,760
+تمام هذا الكلام كتعريف لغوي فاهمينه لأن احنا
+
+140
+00:11:31,760 --> 00:11:34,520
+عارفين ال primes من المسبق العداد الأولى عارفينها
+
+141
+00:11:34,520 --> 00:11:38,820
+المسبقات بدنا نترجمها الآن برضه هقول لكل الأرقام
+
+142
+00:11:38,820 --> 00:11:46,760
+او لكل for all X P of X فإذا لكل قيم X X is prime
+
+143
+00:11:46,760 --> 00:11:54,780
+بس if and only if إذا وإذا فقطX أكبر من واحد حسب
+
+144
+00:11:54,780 --> 00:11:58,900
+التعريف هيا بدأنا ب X أكبر من واحد طيب إيش كمان لا
+
+145
+00:11:58,900 --> 00:12:06,500
+يوجد رقمين ضربهم يسوى X لا يوجد خلصنا هذا and لا
+
+146
+00:12:06,500 --> 00:12:15,060
+يوجد مش هي لا يوجد there is no Y Z هاي رقمين لا
+
+147
+00:12:15,060 --> 00:12:22,910
+يوجد Y و Z ضربهم يسوى Xإيش ضال في الآخر؟ بس ناخد
+
+148
+00:12:22,910 --> 00:12:25,870
+بالنا من الواحد عشان الكمبيوتر بيفهمش لحاله
+
+149
+00:12:25,870 --> 00:12:29,870
+الكمبيوتر بيفهمش لحاله فبتجي تقوله and y لا تسوى
+
+150
+00:12:29,870 --> 00:12:34,130
+واحد وزيد لا تسوى واحد لأن زي ما قلنا احنا
+
+151
+00:12:34,130 --> 00:12:37,490
+ماتتعاملش مع بعض احنا متعامل مع الحسوب مع شوية
+
+152
+00:12:37,490 --> 00:12:42,150
+الرمل اللي اتصنعت silicone فصار يفهم وياخد ويعطي
+
+153
+00:12:42,150 --> 00:12:47,390
+معناه عشان هيك لما نكون دقيقين في هذا الكلاممش
+
+154
+00:12:47,390 --> 00:12:50,490
+لأنه بدك تقولي ما احنا فاهمين يا دكتور ماشي بس انت
+
+155
+00:12:50,490 --> 00:12:53,470
+مش بتفهمني شنا ولا بتفهم ازميك لكن انت بدك تفهم
+
+156
+00:12:53,470 --> 00:12:59,250
+الحاسوب تمام فهيها كتعريف تمام هيك احنا بنكون
+
+157
+00:12:59,250 --> 00:13:03,350
+خلينا نقول فيما يخص المادة اللي خاصة بهذا الأسبوع
+
+158
+00:13:03,350 --> 00:13:09,830
+خلصناها فبنقدر ناخد مرتاحين شوية أسئلة على محتوى
+
+159
+00:13:09,830 --> 00:13:13,330
+الأسبوع اللي احنا اشتغلنا فيه طبعا في أسئلة كتير
+
+160
+00:13:13,330 --> 00:13:18,850
+بسيطة انا كنت عاملحسابنا أنه مسبقا أنه فيه عدد
+
+161
+00:13:18,850 --> 00:13:24,990
+كويس فلو قولنا مثلا P of X هي عبارة عن the word X
+
+162
+00:13:24,990 --> 00:13:29,630
+contains the letter A لو افترضنا أنه ال predicate
+
+163
+00:13:29,630 --> 00:13:41,790
+P هي الكلمة X تحتوي على حرف A فلما أجي أقول P of
+
+164
+00:13:41,790 --> 00:13:43,110
+Orange
+
+165
+00:13:46,590 --> 00:13:53,070
+true ولا false؟ true proposition و true طيب P of
+
+166
+00:13:53,070 --> 00:13:56,930
+lemon؟ false فهي proposition و false
+
+167
+00:14:00,660 --> 00:14:05,180
+فإذا proposition هو false تمام و false true true
+
+168
+00:14:05,180 --> 00:14:11,640
+تمام okay غيرها بدنا نفترض P of X is statement X
+
+169
+00:14:11,640 --> 00:14:17,180
+spends more than five hours every week day in
+
+170
+00:14:17,180 --> 00:14:22,050
+classطب .. بس ناخد بالنا أنه هنا ال university of
+
+171
+00:14:22,050 --> 00:14:26,330
+discourse هي ل students طلاب ف ال domain تبعنا هو
+
+172
+00:14:26,330 --> 00:14:30,430
+x لكل الطلاب و بدنا نفترض أن x هذا اللي هو الطالب
+
+173
+00:14:30,430 --> 00:14:37,530
+x بيستنفذ أو بيعطي دراسته أسبوعيا خمس ساعات .. خمس
+
+174
+00:14:37,530 --> 00:14:44,370
+ساعات أسبوعي في ال .. ال weekday okayتمام بدنا
+
+175
+00:14:44,370 --> 00:14:47,810
+نكتب مجموعة ال expressions ال mathematical
+
+176
+00:14:47,810 --> 00:14:51,210
+expressions اللي موجودة عندنا a,b,c وd لما أقول
+
+177
+00:14:51,210 --> 00:14:56,310
+there exist x P of X بدنا نسميها there exist فإذا
+
+178
+00:14:56,310 --> 00:15:02,310
+there exist student spends more than five hours
+
+179
+00:15:02,310 --> 00:15:06,930
+every day أو every weekday فبسيطة مافيش فيها كتير
+
+180
+00:15:06,930 --> 00:15:13,750
+مشكلة كترجمة تعريف طيب تانية for all x P of Xقول
+
+181
+00:15:13,750 --> 00:15:19,230
+برضه ماعناش أي مشكلة طيب there exist negation P of
+
+182
+00:15:19,230 --> 00:15:27,710
+X معناته
+
+183
+00:15:27,710 --> 00:15:37,260
+يوجد طالب ليدرس او لا .. او اللي هي doesn't spend
+
+184
+00:15:37,260 --> 00:15:42,840
+more than five hours يوجد طالب على الأقل بدرسش خمس
+
+185
+00:15:42,840 --> 00:15:45,860
+ساعات أو بديهش خمس ساعات في الدراسة، بياخدش خمس
+
+186
+00:15:45,860 --> 00:15:51,680
+ساعات في الدراسة الأخيرة للكل
+
+187
+00:15:51,680 --> 00:15:58,220
+.. لكل الطلاب لا يوجد ولا طالب بيعطي خمس ساعات في
+
+188
+00:15:58,220 --> 00:16:03,800
+اليومفإذا no student من الآخر لكل الطلاب معناته no
+
+189
+00:16:03,800 --> 00:16:07,880
+student spends five hours صحيح؟ لكل الطلاب ولا
+
+190
+00:16:07,880 --> 00:16:12,940
+طالب بدرس خمس ساعات فإذا كأنه no student spends
+
+191
+00:16:12,940 --> 00:16:18,860
+more than five hours تمام، كمان غيرها، لو افترضنا
+
+192
+00:16:18,860 --> 00:16:26,020
+في عندى two عندنا هاي two predicates، الأولى x is
+
+193
+00:16:26,020 --> 00:16:33,920
+a comedianكوميدي تمام التانية if of x و x is funny
+
+194
+00:16:33,920 --> 00:16:38,680
+ده إذن كوميدي و funny مضحك و ال domain تبعنا هنا
+
+195
+00:16:38,680 --> 00:16:43,020
+all people لاحظوا ال expression شوية عجدناها
+
+196
+00:16:43,020 --> 00:16:47,080
+عجدناها شوية في هيك حالة كيف بدك تتعامل معاها لما
+
+197
+00:16:47,080 --> 00:16:54,940
+أقولك for all c x then if c of x then if of x إيش
+
+198
+00:16:54,940 --> 00:17:02,060
+معناها؟for all معناته كل كوميدي بالضرورة هيكون
+
+199
+00:17:02,060 --> 00:17:06,940
+funny صح؟
+
+200
+00:17:06,940 --> 00:17:11,740
+ليش؟ خليني معاك انا لأ انت بتقول لأ وين المشكلة
+
+201
+00:17:11,740 --> 00:17:16,600
+عندك؟ بس
+
+202
+00:17:16,600 --> 00:17:17,400
+هل هو funny؟
+
+203
+00:17:20,920 --> 00:17:24,660
+هو يقول اشي تاني انت اشي مصنف و هده مختلفة بس
+
+204
+00:17:24,660 --> 00:17:26,780
+معناه ذلك ان معناته كان ال expression هذا كله
+
+205
+00:17:26,780 --> 00:17:30,720
+بيصلح عليه اذا انت بتحكي عن حالة خاصة و معناته ال
+
+206
+00:17:30,720 --> 00:17:33,680
+expression كله لن يصلح احنا نتكلم الان في اندي
+
+207
+00:17:33,680 --> 00:17:36,740
+expression، بثمانية expression كيف اكتبه language
+
+208
+00:17:36,740 --> 00:17:44,660
+فإذا for all لكل ال x إذا x كوميدي فهو funny فإذا
+
+209
+00:17:44,660 --> 00:17:49,380
+بقولها على طول مباشرة لكل الكوميديان هم funny على
+
+210
+00:17:49,380 --> 00:17:50,100
+طول خلصنا
+
+211
+00:17:52,980 --> 00:18:00,840
+اك طبيعي ايش؟ لأ لأ لأ هيك انتوا .. على فكرة انتوا
+
+212
+00:18:00,840 --> 00:18:03,200
+هيك معناه انتوا مش مذكرين ال implication العكس
+
+213
+00:18:03,200 --> 00:18:05,840
+اللي .. اللي ممكن ان هو ممكن يكون funny بس مش
+
+214
+00:18:05,840 --> 00:18:11,340
+comedian لأ
+
+215
+00:18:11,340 --> 00:18:13,780
+في الطبيعة اشي تاني احنا الآن مش .. مش في الطبيعة
+
+216
+00:18:13,780 --> 00:18:18,660
+لاحظ انا بيعطيك expression ال expression هذا صح او
+
+217
+00:18:18,660 --> 00:18:23,100
+خطأهدا اشي تاني انا بقولك في expression بدنا نكتبه
+
+218
+00:18:23,100 --> 00:18:26,760
+language انت قد ت .. قد تتفق ان هو ال expression
+
+219
+00:18:26,760 --> 00:18:29,900
+من الأساس فيه مشكلة اه ده اشي تاني لكن اه ايوة
+
+220
+00:18:29,900 --> 00:18:33,920
+بالظبط انت لان بتتكلم ما قبل ال expression اما
+
+221
+00:18:33,920 --> 00:18:38,820
+عندك expression هو صح هو غلط بس في واحد قاله
+
+222
+00:18:38,820 --> 00:18:42,840
+الواحد هذا انت ممكن توقف و تقوله false بس هو
+
+223
+00:18:42,840 --> 00:18:46,650
+propositionصح؟ انت من وجه الناس بتقوله fortunately
+
+224
+00:18:46,650 --> 00:18:51,510
+انت حر لكن بدي اعبر عنها ك language و بعدين بنقول
+
+225
+00:18:51,510 --> 00:18:55,010
+ان ال language هذه ك language every comedian is
+
+226
+00:18:55,010 --> 00:19:00,450
+funny هي proposition عندك صح عندك خلط مافي مشكلة
+
+227
+00:19:00,450 --> 00:19:04,230
+.. مافي مشكلة بس في النهاية proposition طيب for
+
+228
+00:19:04,230 --> 00:19:12,470
+all x c of x and f of x comedian and funny
+
+229
+00:19:18,200 --> 00:19:21,240
+أيها funny and comedian فبنسميه funny comedian
+
+230
+00:19:21,240 --> 00:19:26,660
+يعني لغة مش أكتر من هيك فبدك تسميهم و تحطهم واحد
+
+231
+00:19:26,660 --> 00:19:30,180
+صفة للتاني معناته الاتنين مقترنين البعض معناته and
+
+232
+00:19:30,180 --> 00:19:38,260
+طيب there exist cx implies f of x يوجد
+
+233
+00:19:39,610 --> 00:19:44,750
+يوجد على الأقل واحد كوميدي funny، على الأقل يوجد
+
+234
+00:19:44,750 --> 00:19:48,850
+كوميدي funny، هذه ممكن تصبت مع مصطلحك أو انت كيف
+
+235
+00:19:48,850 --> 00:19:53,970
+شايفهاف there exist a person such that ان هو
+
+236
+00:19:53,970 --> 00:19:59,290
+comedian إذا كان هو comedian فهو funny الكلام ده
+
+237
+00:19:59,290 --> 00:20:02,310
+ليس للكل على الأقل في واحد او اتنين او تلاتة حسب
+
+238
+00:20:02,310 --> 00:20:06,750
+أهواك و انت كيف تشوف ال comedians اللي حولنا طيب
+
+239
+00:20:06,750 --> 00:20:14,450
+there exist x, c of x and f of xفإذا تقدر تقول
+
+240
+00:20:14,450 --> 00:20:19,250
+some أو there exist أو some comedians are funny
+
+241
+00:20:19,250 --> 00:20:23,430
+برضه بتمشي مع مصطلحك أو طريقة وجهة نظرك في الموضوع
+
+242
+00:20:23,430 --> 00:20:28,850
+اللي هو some comedians are funny ماشي يعني وجهة
+
+243
+00:20:28,850 --> 00:20:31,530
+نظرك أنت شايفها هدلي true okay في غيرك بيشوفها
+
+244
+00:20:31,530 --> 00:20:36,190
+مختلفة يعني شوية وإلا كان ماتصنفش من الأصل أن هو
+
+245
+00:20:36,190 --> 00:20:40,670
+comedian صحيح بس أكيد في ناس مختلفين معك وإلا كان
+
+246
+00:20:40,670 --> 00:20:41,970
+ماتصنفش من الأساس comedian
+
+247
+00:20:44,720 --> 00:20:49,480
+Okay طب كمان سؤال أنا براحظ بحاول أن أقوللك
+
+248
+00:20:49,480 --> 00:20:52,920
+الأسئلة اللي بتيجي في هيك .. في هيك موضوع جيبناها
+
+249
+00:20:52,920 --> 00:20:56,520
+مرة ب predicate واحد مرة من language ل
+
+250
+00:20:56,520 --> 00:20:59,420
+mathematical form مرة من mathematical form ل
+
+251
+00:20:59,420 --> 00:21:05,160
+language و هكذا هين غيرنا لإيش؟ ل mathematical ..
+
+252
+00:21:05,160 --> 00:21:08,630
+من language ل mathematical formنفس الاشي لو
+
+253
+00:21:08,630 --> 00:21:14,650
+افترضنا ان P of X .. X is perfect F of X .. X is
+
+254
+00:21:14,650 --> 00:21:20,970
+your friend و بدنا مجموعة mathematical language
+
+255
+00:21:20,970 --> 00:21:23,350
+بدنا نحويلها لمثل كده ال expression no one is
+
+256
+00:21:23,350 --> 00:21:30,350
+perfect معناته for all negation بالظبط for all
+
+257
+00:21:30,350 --> 00:21:38,390
+negation طيب not everyone is perfect ليس كل واحدبس
+
+258
+00:21:38,390 --> 00:21:45,570
+let there exist فإذا ليس الكل .. إيش بنسميها؟ ليس
+
+259
+00:21:45,570 --> 00:21:50,150
+الكل perfect ليس الكل perfect طيب all your friends
+
+260
+00:21:50,150 --> 00:21:56,990
+are perfect إذا هو صديقك فهو perfect صحيح؟ فإذا
+
+261
+00:21:56,990 --> 00:22:03,370
+implication إذا هو صديقك فهوperfect طيب at least
+
+262
+00:22:03,370 --> 00:22:06,770
+باينة لحالها at least one of your friends is
+
+263
+00:22:06,770 --> 00:22:13,350
+perfect ف there exist يالا طيب و بتهيألي شرحناها
+
+264
+00:22:13,350 --> 00:22:15,810
+قبل هيك قولنا ان for all بتاخد دايما implication
+
+265
+00:22:15,810 --> 00:22:20,590
+there exist بتاخد and المرة اللي فاتة تتكلمنا عن
+
+266
+00:22:20,590 --> 00:22:24,930
+النقطة هذه و شرحناها بتوسع يعني فممكن ترجع لل
+
+267
+00:22:24,930 --> 00:22:29,240
+video إذا عندك مشكلة فيهاتمام everyone is your
+
+268
+00:22:29,240 --> 00:22:35,360
+friend and is perfect فكل الناس هم أصدقاءك و هم
+
+269
+00:22:35,360 --> 00:22:41,940
+perfect ف for all للكل نعم
+
+270
+00:22:41,940 --> 00:22:46,680
+implication
+
+271
+00:22:46,680 --> 00:22:50,980
+بصفة عامة اذا ما كان .. اه لسه بدأ احكي اذا ماكانش
+
+272
+00:22:50,980 --> 00:22:55,420
+ال .. في قوس و في زي ما بيقول خصوصية تانية
+
+273
+00:22:58,380 --> 00:23:01,880
+by conditional اه اه استنا استنا استنا by
+
+274
+00:23:01,880 --> 00:23:05,380
+conditional تو اخدناها كان لها definition كان لها
+
+275
+00:23:05,380 --> 00:23:11,200
+تعريف التعريف كان if and only if تو لما أخدناها
+
+276
+00:23:11,200 --> 00:23:14,040
+جاب لما نبدأ في الحلول لما جاب لما نبدأ في الحلول
+
+277
+00:23:14,040 --> 00:23:17,180
+كان definition معناه ذلك ان هي ليست implication
+
+278
+00:23:17,180 --> 00:23:22,880
+بصورتها المبسطة اللي انت فاهمها لأ ده كان compound
+
+279
+00:23:22,880 --> 00:23:26,150
+statementكان عبارة عن compound statement ال
+
+280
+00:23:26,150 --> 00:23:29,870
+compound statement بقولك ال a بقولك ان ال number
+
+281
+00:23:29,870 --> 00:23:34,110
+is even if and only if ماتيشيش تقولي مهيها if and
+
+282
+00:23:34,110 --> 00:23:35,270
+only if ماتيشيش تقولي مهيها if and only if ماتيشيش
+
+283
+00:23:35,270 --> 00:23:36,270
+تقولي مهيها if and only if ماتيشيش تقولي مهيها if
+
+284
+00:23:36,270 --> 00:23:36,270
+and only if ماتيشيش تقولي مهيها if and only if
+
+285
+00:23:36,270 --> 00:23:36,550
+ماتيشيش تقولي مهيها if and only if ماتيشيش تقولي
+
+286
+00:23:36,550 --> 00:23:37,650
+مهيها if and only if ماتيشيش تقولي مهيها if and
+
+287
+00:23:37,650 --> 00:23:40,670
+only if ماتيشيش تقولي مهيها if and only if ماتيشيش
+
+288
+00:23:40,670 --> 00:23:45,930
+تقولي مهيها if and only if ماتيشيش تقولي مهيها if
+
+289
+00:23:45,930 --> 00:23:47,790
+and only if ماتيشيش تقولي م
+
+290
+00:23:53,340 --> 00:23:57,360
+Okay اعمل implication فش مشكلة بس مدام حطيلك
+
+291
+00:23:57,360 --> 00:24:02,380
+خصوصية بعدها وضح لك لها يعني عمل emphasize عليها
+
+292
+00:24:02,380 --> 00:24:07,000
+أكدلك عليها لأ خلاص احنا يقعد يقولك if and only if
+
+293
+00:24:07,000 --> 00:24:12,880
+ماديش ترجمها بال implication طيب
+
+294
+00:24:12,880 --> 00:24:19,180
+وين احنا كنا okay كان قول الأخيرة not everybody is
+
+295
+00:24:19,180 --> 00:24:25,070
+your friend or someone is notperfect يعني واضح إن
+
+296
+00:24:25,070 --> 00:24:30,930
+هم بعض عن بعض مختلفين or هدى هنا expression هناك
+
+297
+00:24:30,930 --> 00:24:34,530
+expression تاني مختلف تماما فبدك تعمل كل واحدة
+
+298
+00:24:34,530 --> 00:24:38,450
+لحال و تحط بينهم this junction و بس اه لإن هناك
+
+299
+00:24:38,450 --> 00:24:40,550
+بتتكلم عن friend هنا بتتكلم عن perfect و مافيش
+
+300
+00:24:40,550 --> 00:24:46,590
+relation between them بالنسبة ل C يعني لو حطينا X
+
+301
+00:24:46,590 --> 00:24:47,330
+and X
+
+302
+00:24:51,360 --> 00:24:55,020
+أه معنى .. لأ لأ استنى هيختلف المعنى لأنه في
+
+303
+00:24:55,020 --> 00:24:59,680
+الحالة هذه انت بتقول هنا all your friends are
+
+304
+00:24:59,680 --> 00:25:06,580
+perfect مش هيك فكل أصدقاءك perfect بس هل معنى ذلك
+
+305
+00:25:06,580 --> 00:25:13,460
+أنه لو مش صديقك معناته مش perfect؟ صح؟ ماحدش قال
+
+306
+00:25:13,460 --> 00:25:17,180
+أنه لأ مش perfect okay فلان مش صديقك بس هذا مش
+
+307
+00:25:17,180 --> 00:25:20,100
+معناه أنك انت الجملة هذه تشمل أن هو not perfect
+
+308
+00:25:22,870 --> 00:25:27,970
+لحظت؟ أنا هنا بقول كل أصدقاءك perfect تمام؟ فإذا
+
+309
+00:25:27,970 --> 00:25:32,930
+إذا هم أصدقاءك perfect طب إذا مش أصدقاءك ممكن
+
+310
+00:25:32,930 --> 00:25:36,590
+يكونوا perfect فليش تحكولهم ب and و تنفل الصفة
+
+311
+00:25:36,590 --> 00:25:40,470
+عنهم هيك؟ ليش لمجرد إنه هذه كانت true لأن هم
+
+312
+00:25:40,470 --> 00:25:45,270
+perfect لكن هم مش أصدقاءك لما تمانهم and صارت
+
+313
+00:25:45,270 --> 00:25:51,700
+false and true الجملة المجمل false وهذا مش صحيحهيك
+
+314
+00:25:51,700 --> 00:25:55,480
+مش صحيح أما ال implication أكتر وقعية أنه حتى لو
+
+315
+00:25:55,480 --> 00:25:58,360
+مش صاحبك ممكن يكون perfect ليش أنت تحكم على كل
+
+316
+00:25:58,360 --> 00:26:00,940
+البشرية أن هم مش perfect لمجرد أن هم مش أصدقاءك
+
+317
+00:26:00,940 --> 00:26:07,100
+تمامفزي ما قلنا الأخيرة هدى هما جمالتين مختلفات عن
+
+318
+00:26:07,100 --> 00:26:12,860
+بعض هنا بنتكلم عن every one و عن predicate friend
+
+319
+00:26:12,860 --> 00:26:16,460
+و هنا بنتكلم عن predicate تاني مختلف و ب
+
+320
+00:26:16,460 --> 00:26:20,240
+quantifier مختلف تماما فممكن كل واحد لحاله تربطهم
+
+321
+00:26:20,240 --> 00:26:23,220
+حسب إيش الرابط الرابط اللى عناه is or فبتحط ال
+
+322
+00:26:23,220 --> 00:26:28,200
+this junction okay
+
+323
+00:26:28,200 --> 00:26:33,600
+هنا إيش مطلوب السؤال هذا طالبين نعمل negationبدك
+
+324
+00:26:33,600 --> 00:26:37,940
+تعمل negation للجملة اللى موجودة عندك لما نقول for
+
+325
+00:26:37,940 --> 00:26:50,280
+all x, x greater than one بدك تنفيها على
+
+326
+00:26:50,280 --> 00:26:56,280
+خط الأعداد، هاي صفر، هاي one، كل قيم x أكبر
+
+327
+00:26:58,580 --> 00:27:02,840
+من واحد طيب
+
+328
+00:27:02,840 --> 00:27:06,340
+ان فيها احنا بدنا نعمل negation ايش المفروض اقول
+
+329
+00:27:06,340 --> 00:27:10,820
+المفروض اي expression يكون موجود عندى انه لا يوجد
+
+330
+00:27:10,820 --> 00:27:15,620
+حد هنا بالظبط
+
+331
+00:27:15,620 --> 00:27:20,080
+هذه مبدئيا بس انا بدى اعمل negation يعني بدى أن
+
+332
+00:27:20,080 --> 00:27:27,020
+فيها بمعنى ان انا بدأ اتصير هيك what
+
+333
+00:27:27,020 --> 00:27:35,930
+hitبينت معانا negation فهتصبح إعكس there exist x
+
+334
+00:27:35,930 --> 00:27:42,090
+أقل أو أصغر من واحد معانا ذلك أن انت عشان تنفي
+
+335
+00:27:42,090 --> 00:27:51,890
+الجملة هذه معانا جلم؟ عشان تنفي هذه for all إيش
+
+336
+00:27:51,890 --> 00:27:57,030
+معانا for all؟ إن هنا zero
+
+337
+00:27:58,380 --> 00:28:05,080
+صح؟ Zero تماما كله هنا طيب يكفي واحد موجود هنا
+
+338
+00:28:05,080 --> 00:28:13,360
+عشان ال for all هذه تصبح force صح؟
+
+339
+00:28:13,360 --> 00:28:17,890
+واحد بس بيكفيأو أكتر ما هو okay مافيش مشكلة أكتر
+
+340
+00:28:17,890 --> 00:28:22,170
+أكتر بيمشي الحال بس مدام قال لي for all معناته أنا
+
+341
+00:28:22,170 --> 00:28:25,350
+عشان أغيظه زي ما بيقوله بدي بس أطلعله واحد في
+
+342
+00:28:25,350 --> 00:28:28,190
+المكان اللي هو بيقوله ان هو for all جال والله انه
+
+343
+00:28:28,190 --> 00:28:32,070
+نضف القاعة تماما انا مش محتاج أوصخلها كلها بس ورا
+
+344
+00:28:32,070 --> 00:28:36,130
+جايك واحدة ارميها في النص وخلي المشرف يجي يتفرج مش
+
+345
+00:28:36,130 --> 00:28:43,110
+هيك يكفي واحدةما هي هي فهي الفكرة كلها بس واحد فقط
+
+346
+00:28:43,110 --> 00:28:48,590
+فهي هي الواحد there exist x أقل من أو يسوى واحد بس
+
+347
+00:28:48,590 --> 00:28:56,570
+واحد نفها خلصنا طيب اتفضل عكسها
+
+348
+00:28:56,570 --> 00:29:03,010
+لاحظ هنا هذه أكبر من عكس الأكبر من أقل أو يساوي
+
+349
+00:29:03,010 --> 00:29:09,560
+لأن هنا الواحد غير مشمولهنا ال X أكبر من واحد فإذا
+
+350
+00:29:09,560 --> 00:29:17,740
+ال واحد غير مشمول أصغر من بس أكبر
+
+351
+00:29:17,740 --> 00:29:21,180
+أو يساوي بالظبط زي ها يوم جيناك جيناك هي جياك اللي
+
+352
+00:29:21,180 --> 00:29:26,900
+وراها هي اللي وراها أيش عكستلك نفس الكلام كله كنا
+
+353
+00:29:26,900 --> 00:29:30,040
+هنا بدون يساوي هيحطلك اليساوي كنا أكبر منه صارت
+
+354
+00:29:30,040 --> 00:29:36,500
+أصغر منه المفهوم هو هو بس هنرجع نرسمه هيصبح كتالي
+
+355
+00:29:40,480 --> 00:29:48,460
+كله اقل من او يساوي اتنين، ولاحظ اعملتها solid،
+
+356
+00:29:48,460 --> 00:29:53,580
+solid بمعنى ان الاتنين مشمولة، معناته انت بدك على
+
+357
+00:29:53,580 --> 00:29:59,320
+الاقل واحد هنا، بس اكبر من جديش من اتنين، بقولش او
+
+358
+00:29:59,320 --> 00:30:04,420
+يساوي، فش او يساوي، او يساوي معناته صارت مشمولة مع
+
+359
+00:30:04,420 --> 00:30:10,430
+التعريف الاولتمام فتوقع فيش فيها مشكلة طيب حتى
+
+360
+00:30:10,430 --> 00:30:14,010
+التالتة برضه فيش فيها مشكلة بتهيأ ليه؟خلاص هذه
+
+361
+00:30:14,010 --> 00:30:20,710
+برضه مافيها مشكلة للرابعة نفس الاشي برضه مش جثة ال
+
+362
+00:30:20,710 --> 00:30:24,190
+there exist يوجد هي الفكرة الوحيدة كانت ال there
+
+363
+00:30:24,190 --> 00:30:27,810
+exist ان يوجد على الأقل واحد احنا بنقول لأ بدي
+
+364
+00:30:27,810 --> 00:30:31,130
+أنفي الواحد هذا فبقول كله بالعكس فبأضمن ان مافيش
+
+365
+00:30:31,130 --> 00:30:36,990
+ولا واحد في الإيجاب بس ناخد ال E هالوقت ال E بدنا
+
+366
+00:30:36,990 --> 00:30:41,910
+نفهمها لإنه طورت شوية المفهوم صارت الاتنين مع بعض
+
+367
+00:30:45,750 --> 00:30:53,930
+من اتنين سالب واحد سالب one و هنا two و هنا بيقولك
+
+368
+00:30:53,930 --> 00:31:02,550
+or فإذا من هنا لهنا كل ال elements x أقل من سالب
+
+369
+00:31:02,550 --> 00:31:07,130
+واحد أو أكبر من اتنين يعني أنت بدك على الأقل عنصر
+
+370
+00:31:07,130 --> 00:31:12,950
+في المنطقة هذه بس ف there exist between
+
+371
+00:31:15,130 --> 00:31:21,270
+أكبر من أو يساوي سالب واحد وأقل من بس هاي كل
+
+372
+00:31:21,270 --> 00:31:31,970
+الموضوع و ليش negation of or and تمام خلصنا هاي كل
+
+373
+00:31:31,970 --> 00:31:36,050
+الموضوع تمام اللي وراها الفكرة هي هي بتاع اللي
+
+374
+00:31:36,050 --> 00:31:41,230
+خلصت بس هنا يمكن مشموليتها ما بين عنصرين
+
+375
+00:31:44,540 --> 00:31:52,840
+من سالب من أقل من أربعة أقل
+
+376
+00:31:52,840 --> 00:31:57,660
+من أربعة هي أربعة وأكبر من سبعة ورا نفسها بس هنا
+
+377
+00:31:57,660 --> 00:32:05,480
+there exist هنا there exist خد بالك يعني يوجد عنصر
+
+378
+00:32:05,480 --> 00:32:10,460
+أصغر من أربعة أو أكبر من سبعة معناته هنا إيش بده
+
+379
+00:32:10,460 --> 00:32:17,910
+أقول كلهمفي المنطقة المفقودة هنا بحيث أنه أطمن أنه
+
+380
+00:32:17,910 --> 00:32:22,590
+لا يوجد ولا واحد قبل ولا واحد بعد بس I call
+
+381
+00:32:22,590 --> 00:32:28,610
+فبنقولها for all بسيطة الأسئلة مش هيك لاحظ لو ما
+
+382
+00:32:28,610 --> 00:32:31,390
+شرحناهاش على ال link انتوا عارف كانت هتتوهكوا برضه
+
+383
+00:32:31,390 --> 00:32:35,930
+لو فيه هيك فجأة في امتحان فهي أفكار بسيطة وسهلة بس
+
+384
+00:32:35,930 --> 00:32:37,450
+بدأ شويه التركيز أسلة امتحانات
+
+385
+00:32:42,870 --> 00:32:47,210
+الان what are the truth value of these statements
+
+386
+00:32:47,210 --> 00:32:53,630
+لما نقول في عندى there exist exactly one x P of X
+
+387
+00:32:53,630 --> 00:33:02,650
+implies there exist x P of X true ولا false كل
+
+388
+00:33:02,650 --> 00:33:09,470
+المطلوب ان احنا هنا نحط T ولا F بس هل
+
+389
+00:33:09,470 --> 00:33:14,660
+لاحظ كمان مرة نقرأها بهدوء بسهل لما أقول يوجد
+
+390
+00:33:14,660 --> 00:33:24,340
+exactly one P of X is true بتمنلي أن يوجد X P of X
+
+391
+00:33:24,340 --> 00:33:35,100
+is true هنا واحد و هنا there exist تمام فإذا مجرد
+
+392
+00:33:35,100 --> 00:33:39,700
+أن يوجد exactly one فهي there exist فهي هتكون
+
+393
+00:33:39,700 --> 00:33:41,720
+there exist التانية
+
+394
+00:33:46,740 --> 00:33:53,840
+for all x, P of x بيضمن ليه؟ انه there exist
+
+395
+00:33:53,840 --> 00:34:00,100
+exactly one يعني اقول الكل f of x معناته ان there
+
+396
+00:34:00,100 --> 00:34:04,340
+exist exactly one is x true يعني معناه افضل واحد،
+
+397
+00:34:04,340 --> 00:34:08,400
+اذا كل موجود يعني true واحد true واحد true واحد
+
+398
+00:34:08,400 --> 00:34:14,130
+true واحد true واحد ممكن يكون اكتر من واحدممكن
+
+399
+00:34:14,130 --> 00:34:19,750
+يكون اكتر من واحد لان انا قاعد اقول for all لأ
+
+400
+00:34:19,750 --> 00:34:27,730
+لأ انت ال M لاحظ for all for all هنا الحالة
+
+401
+00:34:27,730 --> 00:34:30,490
+الوحيدة اللي قلنا عليها ال implication بكون فيه
+
+402
+00:34:30,490 --> 00:34:38,630
+false هي اللي فحصوها اي حالة true or false true or
+
+403
+00:34:38,630 --> 00:34:43,760
+falseالأصل أنه يكون عنده هنا true وهنا تكون false
+
+404
+00:34:43,760 --> 00:34:51,940
+أنه كلهم مشمولين و لا يوجد exactly one و
+
+405
+00:34:51,940 --> 00:34:56,840
+لا يوجد exactly one فإذا لما أقول for all x خلّيني
+
+406
+00:34:56,840 --> 00:35:00,320
+نرجع نفحصها كمان مرة for all x معناه ذلك أنه ممكن
+
+407
+00:35:00,320 --> 00:35:05,000
+يكون اتنين أو تلاتة أو أربعة موجودين بيضمن ليه أن
+
+408
+00:35:05,000 --> 00:35:06,780
+there exist x
+
+409
+00:35:09,260 --> 00:35:15,160
+is لأ false هدى false هدى false إلا في حالة واحدة
+
+410
+00:35:15,160 --> 00:35:19,780
+كويس هى طلعت إلا خصوصية كمان إلا في حالة واحدة
+
+411
+00:35:19,780 --> 00:35:29,280
+فإذا ممكن تكون X عبارة عن مجموعة ABC مثلا and so
+
+412
+00:35:29,280 --> 00:35:34,740
+on بس ال true في حالة اللى هى أصلا ال university
+
+413
+00:35:34,740 --> 00:35:38,420
+of discourse واحد صح
+
+414
+00:35:43,040 --> 00:35:46,000
+فإذن الحالة الوحيدة اللي بقدر أقول إن هي true صح
+
+415
+00:35:46,000 --> 00:35:50,600
+الإتنين ممكن يعطوا بعض أو خلّينا exactly إن كلهم
+
+416
+00:35:50,600 --> 00:35:54,740
+perfect بضمن لي إن على الأقل يوجد واحد إنه فعليًا
+
+417
+00:35:54,740 --> 00:36:00,100
+exactly واحد perfect exactly واحد perfect أنت
+
+418
+00:36:00,100 --> 00:36:03,380
+فعليًا هنا بيكونوا أكتر من واحد فمعنى ذلك إن هذه
+
+419
+00:36:03,380 --> 00:36:08,820
+بتتطلع false هذه هتطلع هيك false يعني معنى ذلك
+
+420
+00:36:08,820 --> 00:36:16,350
+صارت true falseأكيد منطقيا غلط ال true لإن كلهم
+
+421
+00:36:16,350 --> 00:36:22,150
+هيها a is true, b is true, c is true تمام هذه ال
+
+422
+00:36:22,150 --> 00:36:26,150
+true لكن هل بدمن لي إن there exist exactly one is
+
+423
+00:36:26,150 --> 00:36:32,890
+true لأ لإنه a و b و c التلاتةلو there exist لو
+
+424
+00:36:32,890 --> 00:36:36,770
+there exist كلامك ماشي يعني منطقيا ممكن تظبط بس
+
+425
+00:36:36,770 --> 00:36:40,770
+هنا هذه الحالة الوحيدة عشان تظبط فيها فقط انه
+
+426
+00:36:40,770 --> 00:36:44,270
+أساسا universe of discourse هو just one element
+
+427
+00:36:44,270 --> 00:36:52,750
+ممكن تقول true إذا انتقلت جبلة and all y اما انت
+
+428
+00:36:52,750 --> 00:36:57,670
+دخلت في expression غير هذا صح احنا لأ مش انها تصير
+
+429
+00:36:57,670 --> 00:37:01,740
+صح احنا بنتكلم عن expression هو صح ولا غلط بسصح؟
+
+430
+00:37:01,740 --> 00:37:04,680
+انت بدك تصمحه بيصير اه بتفكر في طريقة انك انت
+
+431
+00:37:04,680 --> 00:37:07,100
+تجلبها لل or اللي بتحكي عليها بتصير كلامك منطقي
+
+432
+00:37:07,100 --> 00:37:12,540
+صحيح أما الآن هذه حسب ما أذكرها مظبوط فإذا هذه
+
+433
+00:37:12,540 --> 00:37:18,300
+false there exist
+
+434
+00:37:18,300 --> 00:37:21,360
+لأ ممكن لأن there exist ممكن بواحد
+
+435
+00:37:23,950 --> 00:37:27,990
+أه بس مجرد الإمكانية اللى بتقول عليها ممكن بتعملك
+
+436
+00:37:27,990 --> 00:37:33,450
+ال truth لأن there exist بواحد بيمشي الحال أما هنا
+
+437
+00:37:33,450 --> 00:37:37,310
+for all بواحد بيمشيش إلا إذا كان هو الواحد الكل
+
+438
+00:37:38,460 --> 00:37:42,220
+يعني ال universe of discourse هو الواحد بس تظبط
+
+439
+00:37:42,220 --> 00:37:45,940
+أكتر من هناك لأ بتظبطش في there exist أه بنفع لأن
+
+440
+00:37:45,940 --> 00:37:50,420
+واحد كافي أنه يحققلك there exist بس هنا for all لأ
+
+441
+00:37:50,420 --> 00:37:55,360
+بنفعش الواحد يكمل يحملها فإذا زي ما قلنا false إلا
+
+442
+00:37:55,360 --> 00:38:00,480
+إذا كان فعلا عندي ال domain تبعي هو consists of
+
+443
+00:38:00,480 --> 00:38:04,040
+just one element okay بتظبط الأخيرة
+
+444
+00:38:07,070 --> 00:38:14,070
+there exist exactly one x لا يحقق P of X بيضمنلنا
+
+445
+00:38:14,070 --> 00:38:20,010
+انه negation او ليس الكل يحقق P of X true مش هيك
+
+446
+00:38:20,010 --> 00:38:26,230
+منطقية واحد فقط لا يحقق معناته انه ليس الكل يحقق
+
+447
+00:38:26,230 --> 00:38:33,130
+خلاص فإذا true منطقيةو انتوا بتحلوا هيكي في ال ..
+
+448
+00:38:33,130 --> 00:38:35,770
+في الرواجان بتكون الأمور أسهل، لو في الامتحان كان
+
+449
+00:38:35,770 --> 00:38:44,270
+شد .. طيب okay اعتقد هننهي يمكن في هذه .. نشوف،
+
+450
+00:38:44,270 --> 00:38:46,730
+الآن بدنا نعمل زي أخر حاجة شرحناها في المصادر ..
+
+451
+00:38:46,730 --> 00:38:49,190
+في ال .. في المحاضرة بتاعت اليوم، اللي هي
+
+452
+00:38:49,190 --> 00:38:54,870
+definition و بدنا نترجمه ل mathematical expression
+
+453
+00:38:55,670 --> 00:38:58,810
+بنعمل translation لل statement the sum of two
+
+454
+00:38:58,810 --> 00:39:04,810
+positive integers is always positive نفس الفكرة
+
+455
+00:39:04,810 --> 00:39:08,650
+فهنا برضه هنجور for all و بنفتح الأقواذ بتاعتنا
+
+456
+00:39:08,650 --> 00:39:16,400
+إذا كانالـ x و y positive أكبر من صفر فبنقول إذا
+
+457
+00:39:16,400 --> 00:39:22,120
+كانت x أكبر من صفر and y أكبر من صفر و بنعمل then
+
+458
+00:39:22,120 --> 00:39:33,380
+z تساوي x and y and z أكبر من صفر أو على طول ممن
+
+459
+00:39:33,380 --> 00:39:37,790
+خير حتى z x زائد y أكبر من صفر و خلاصمباشرة مافيش
+
+460
+00:39:37,790 --> 00:39:41,770
+داعي نحط كمان متغير تالت فمباشرة إذا عرفنا x أكبر
+
+461
+00:39:41,770 --> 00:39:47,070
+من صفر and y أكبر من صفر إذا x زائد y greater than
+
+462
+00:39:47,070 --> 00:39:53,430
+0 وخلاصفإذا على طول مباشرة for all x y إذا كانت x
+
+463
+00:39:53,430 --> 00:39:57,910
+أكبر من صفر و y أكبر من صفر إذا مجموحهم أكبر من
+
+464
+00:39:57,910 --> 00:40:04,870
+صفر بسيطة سهلة وسلسفش كتير فيها مشاكل تمام فالأن
+
+465
+00:40:04,870 --> 00:40:09,450
+كنت خلصنا لهذا الأسبوع الجزء المطلوب منها المرة
+
+466
+00:40:09,450 --> 00:40:12,490
+القادمة ان شاء الله بنبدأ في ال proving strategies
+
+467
+00:40:12,490 --> 00:40:15,810
+و برضه نفس الفكرة الكويسة أن في المحاضرات المصورة
+
+468
+00:40:15,810 --> 00:40:20,270
+جاهزة عندكم فبترجعوها بحيث أنه دائما نحاولفي آخر
+
+469
+00:40:20,270 --> 00:40:24,570
+الأسبوع نوفر هيك نص ساعة زمان نجيبلكوا فيها أسئلة،
+
+470
+00:40:24,570 --> 00:40:27,070
+بتهيألي بيكون أفضل من إنه نضلنا مربوطين مزنوجين في
+
+471
+00:40:27,070 --> 00:40:32,150
+ال .. في المحاضرة ك .. ك theoretical concepts،
+
+472
+00:40:32,150 --> 00:40:34,070
+كتير كويس إن احنا نروح للبرنامج، كلي أعطوكوا
+
+473
+00:40:34,070 --> 00:40:34,350
+العافية
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wEwPxELdkGI_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wEwPxELdkGI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ce9781fe8d44fa658ae27943e2ffb048f9bf8316
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wEwPxELdkGI_raw.json
@@ -0,0 +1 @@
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"end": 212.73, "word": " اتنين", "probability": 0.949951171875}, {"start": 212.73, "end": 213.19, "word": " يا", "probability": 0.78515625}, {"start": 213.19, "end": 213.59, "word": " موجود", "probability": 0.9890950520833334}, {"start": 213.59, "end": 213.73, "word": " يا", "probability": 0.92333984375}, {"start": 213.73, "end": 213.87, "word": " مش", "probability": 0.986328125}, {"start": 213.87, "end": 214.35, "word": " موجود", "probability": 0.9842122395833334}], "temperature": 1.0}, {"id": 10, "seek": 24138, "start": 215.22, "end": 241.38, "text": "الانصر الأول في ال relation الانصر التاني يا موجود يا مش موجود يعني برضه اتنين في اتنين زي ما أخدناه في ال combination التالت يا موجود يا غير موجود فال possibilities تبعته اتنين and so on فإذا انضربوا في بعض كام مرة انتربيا فأثر اتنين هذي in general عدد ال relations اللي ممكن ناخدها من set ال cardinality بتاعتها in", "tokens": [6027, 7649, 9381, 2288, 16247, 12610, 8978, 2423, 9721, 2423, 7649, 9381, 2288, 16712, 7649, 1829, 35186, 3714, 29245, 23328, 35186, 37893, 3714, 29245, 23328, 37495, 22653, 4724, 43042, 3224, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 30767, 1829, 19446, 5551, 9778, 3215, 8315, 3224, 8978, 2423, 6562, 16712, 6027, 2655, 35186, 3714, 29245, 23328, 35186, 32771, 13546, 3714, 29245, 23328, 6156, 6027, 12178, 6055, 3555, 34268, 3224, 1975, 2655, 1863, 9957, 293, 370, 322, 6156, 28814, 15730, 16472, 11242, 25513, 14407, 8978, 45030, 11242, 9122, 10943, 3714, 25720, 16472, 2655, 2288, 21292, 995, 6156, 10721, 49115, 1975, 2655, 1863, 9957, 8032, 8848, 1829, 294, 2674, 6225, 3215, 3215, 2423, 2299, 13672, 1829, 3714, 43020, 8717, 47283, 3215, 11296, 9154, 992, 2423, 2920, 259, 1860, 39894, 995, 34268, 11296, 294], "avg_logprob": -0.14826127729917826, "compression_ratio": 1.9157088122605364, "no_speech_prob": 2.8014183044433594e-06, "words": [{"start": 215.22, "end": 215.72, "word": "الانصر", "probability": 0.76690673828125}, {"start": 215.72, "end": 216.02, "word": " الأول", "probability": 0.900146484375}, {"start": 216.02, "end": 216.16, "word": " في", "probability": 0.92724609375}, {"start": 216.16, "end": 216.3, "word": " ال", "probability": 0.951171875}, {"start": 216.3, "end": 216.62, "word": " relation", "probability": 0.96240234375}, {"start": 216.62, "end": 217.28, "word": " الانصر", "probability": 0.848388671875}, {"start": 217.28, "end": 217.52, "word": " التاني", "probability": 0.8995768229166666}, {"start": 217.52, "end": 217.68, "word": " يا", "probability": 0.38037109375}, {"start": 217.68, "end": 218.0, "word": " موجود", "probability": 0.98828125}, {"start": 218.0, "end": 218.08, "word": " يا", "probability": 0.91357421875}, {"start": 218.08, "end": 218.28, "word": " مش", "probability": 0.71240234375}, {"start": 218.28, "end": 218.74, "word": " موجود", "probability": 0.9832356770833334}, {"start": 218.74, "end": 219.12, "word": " يعني", "probability": 0.8505859375}, {"start": 219.12, "end": 219.36, "word": " برضه", "probability": 0.9724934895833334}, {"start": 219.36, "end": 219.62, "word": " اتنين", "probability": 0.80352783203125}, {"start": 219.62, "end": 219.72, "word": " في", "probability": 0.857421875}, {"start": 219.72, "end": 220.06, "word": " اتنين", "probability": 0.9822998046875}, {"start": 220.06, "end": 220.7, "word": " زي", "probability": 0.93603515625}, {"start": 220.7, "end": 220.78, "word": " ما", "probability": 0.98828125}, {"start": 220.78, "end": 221.1, "word": " أخدناه", "probability": 0.919140625}, {"start": 221.1, "end": 221.14, "word": " في", "probability": 0.94140625}, {"start": 221.14, "end": 221.22, "word": " ال", "probability": 0.96533203125}, {"start": 221.22, "end": 221.58, "word": " combination", "probability": 0.98388671875}, {"start": 221.58, "end": 223.1, "word": " التالت", "probability": 0.9869791666666666}, {"start": 223.1, "end": 223.28, "word": " يا", "probability": 0.57470703125}, {"start": 223.28, "end": 223.62, "word": " موجود", "probability": 0.9952799479166666}, {"start": 223.62, "end": 223.7, "word": " يا", "probability": 0.96728515625}, {"start": 223.7, "end": 223.9, "word": " غير", "probability": 0.994384765625}, {"start": 223.9, "end": 224.18, "word": " موجود", "probability": 0.98681640625}, {"start": 224.18, "end": 224.4, "word": " فال", "probability": 0.80029296875}, {"start": 224.4, "end": 224.78, "word": " possibilities", "probability": 0.92041015625}, {"start": 224.78, "end": 225.16, "word": " تبعته", "probability": 0.74169921875}, {"start": 225.16, "end": 225.44, "word": " اتنين", "probability": 0.9674072265625}, {"start": 225.44, "end": 225.88, "word": " and", "probability": 0.865234375}, {"start": 225.88, "end": 226.08, "word": " so", "probability": 0.939453125}, {"start": 226.08, "end": 226.32, "word": " on", "probability": 0.96044921875}, {"start": 226.32, "end": 227.18, "word": " فإذا", "probability": 0.8971354166666666}, {"start": 227.18, "end": 227.68, "word": " انضربوا", "probability": 0.9110107421875}, {"start": 227.68, "end": 227.74, "word": " في", "probability": 0.8720703125}, {"start": 227.74, "end": 227.9, "word": " بعض", "probability": 0.98583984375}, {"start": 227.9, "end": 228.18, "word": " كام", "probability": 0.649169921875}, {"start": 228.18, "end": 228.52, "word": " مرة", "probability": 0.97607421875}, {"start": 228.52, "end": 230.24, "word": " انتربيا", "probability": 0.5845703125}, {"start": 230.24, "end": 230.64, "word": " فأثر", "probability": 0.8650716145833334}, {"start": 230.64, "end": 231.28, "word": " اتنين", "probability": 0.9041748046875}, {"start": 231.28, "end": 234.52, "word": " هذي", "probability": 0.5559895833333334}, {"start": 234.52, "end": 234.66, "word": " in", "probability": 0.9228515625}, {"start": 234.66, "end": 235.02, "word": " general", "probability": 0.9228515625}, {"start": 235.02, "end": 235.74, "word": " عدد", "probability": 0.9827473958333334}, {"start": 235.74, "end": 236.04, "word": " ال", "probability": 0.97314453125}, {"start": 236.04, "end": 236.62, "word": " relations", "probability": 0.93212890625}, {"start": 236.62, "end": 236.84, "word": " اللي", "probability": 0.9189453125}, {"start": 236.84, "end": 237.14, "word": " ممكن", "probability": 0.989990234375}, {"start": 237.14, "end": 237.74, "word": " ناخدها", "probability": 0.97021484375}, {"start": 237.74, "end": 238.26, "word": " من", "probability": 0.97216796875}, {"start": 238.26, "end": 239.34, "word": " set", "probability": 0.9052734375}, {"start": 239.34, "end": 240.22, "word": " ال", "probability": 0.77783203125}, {"start": 240.22, "end": 240.72, "word": " cardinality", "probability": 0.89404296875}, {"start": 240.72, "end": 241.2, "word": " بتاعتها", "probability": 0.900390625}, {"start": 241.2, "end": 241.38, "word": " in", "probability": 0.919921875}], "temperature": 1.0}, {"id": 11, "seek": 26401, "start": 242.81, "end": 264.01, "text": "اللي هما عادة عناصرها عصرها انت هذه كانت أخر شغلة اتكلمنا فيها المرة الماضية الان نبدأ ناخد مجموعة characteristic او مجموعة ميزات لل relations أول خاصية بدنا نتكلم عنها هي ال reflexivity ال reflexivity او العكسية بمعنى", "tokens": [6027, 20292, 8032, 15042, 6225, 18513, 3660, 18871, 33546, 2288, 11296, 6225, 9381, 2288, 11296, 16472, 2655, 29538, 25961, 2655, 5551, 34740, 13412, 17082, 37977, 1975, 2655, 4117, 19528, 8315, 8978, 11296, 9673, 25720, 9673, 46958, 10632, 2423, 7649, 8717, 44510, 10721, 8717, 47283, 3215, 3714, 7435, 2304, 2407, 27884, 16282, 1975, 2407, 3714, 7435, 2304, 2407, 27884, 3714, 1829, 11622, 9307, 24976, 2299, 5551, 12610, 16490, 33546, 10632, 47525, 8315, 8717, 2655, 4117, 19528, 18871, 11296, 39896, 2423, 23802, 4253, 2423, 23802, 4253, 1975, 2407, 18863, 4117, 3794, 10632, 4724, 2304, 3615, 1863, 7578], "avg_logprob": -0.19628905691206455, "compression_ratio": 1.6985645933014355, "no_speech_prob": 8.64267349243164e-06, "words": [{"start": 242.81, "end": 243.05, "word": "اللي", "probability": 0.6907958984375}, {"start": 243.05, "end": 243.15, "word": " هما", "probability": 0.68212890625}, {"start": 243.15, "end": 243.39, "word": " عادة", "probability": 0.9794921875}, {"start": 243.39, "end": 243.97, "word": " عناصرها", "probability": 0.9373779296875}, {"start": 243.97, "end": 244.63, "word": " عصرها", "probability": 0.83984375}, {"start": 244.63, "end": 244.77, "word": " انت", "probability": 0.3524169921875}, {"start": 244.77, "end": 244.89, "word": " هذه", "probability": 0.2410888671875}, {"start": 244.89, "end": 245.15, "word": " كانت", "probability": 0.961669921875}, {"start": 245.15, "end": 245.35, "word": " أخر", "probability": 0.751220703125}, {"start": 245.35, "end": 245.73, "word": " شغلة", "probability": 0.89599609375}, {"start": 245.73, "end": 246.45, "word": " اتكلمنا", "probability": 0.94580078125}, {"start": 246.45, "end": 246.63, "word": " فيها", "probability": 0.953125}, {"start": 246.63, "end": 246.97, "word": " المرة", "probability": 0.970458984375}, {"start": 246.97, "end": 247.75, "word": " الماضية", "probability": 0.9920247395833334}, {"start": 247.75, "end": 248.13, "word": " الان", "probability": 0.6893310546875}, {"start": 248.13, "end": 248.41, "word": " نبدأ", "probability": 0.8854166666666666}, {"start": 248.41, "end": 248.75, "word": " ناخد", "probability": 0.9881184895833334}, {"start": 248.75, "end": 249.61, "word": " مجموعة", "probability": 0.94169921875}, {"start": 249.61, "end": 251.03, "word": " characteristic", "probability": 0.35791015625}, {"start": 251.03, "end": 251.21, "word": " او", "probability": 0.79296875}, {"start": 251.21, "end": 251.65, "word": " مجموعة", "probability": 0.96337890625}, {"start": 251.65, "end": 252.41, "word": " ميزات", "probability": 0.97119140625}, {"start": 252.41, "end": 253.33, "word": " لل", "probability": 0.6220703125}, {"start": 253.33, "end": 256.39, "word": " relations", "probability": 0.505859375}, {"start": 256.39, "end": 257.17, "word": " أول", "probability": 0.78369140625}, {"start": 257.17, "end": 258.53, "word": " خاصية", "probability": 0.91015625}, {"start": 258.53, "end": 258.73, "word": " بدنا", "probability": 0.670166015625}, {"start": 258.73, "end": 259.05, "word": " نتكلم", "probability": 0.991943359375}, {"start": 259.05, "end": 259.35, "word": " عنها", "probability": 0.97705078125}, {"start": 259.35, "end": 259.69, "word": " هي", "probability": 0.94140625}, {"start": 259.69, "end": 259.97, "word": " ال", "probability": 0.7421875}, {"start": 259.97, "end": 260.59, "word": " reflexivity", "probability": 0.840576171875}, {"start": 260.59, "end": 261.55, "word": " ال", "probability": 0.396240234375}, {"start": 261.55, "end": 262.11, "word": " reflexivity", "probability": 0.948486328125}, {"start": 262.11, "end": 262.23, "word": " او", "probability": 0.67333984375}, {"start": 262.23, "end": 262.95, "word": " العكسية", "probability": 0.77880859375}, {"start": 262.95, "end": 264.01, "word": " بمعنى", "probability": 0.9501953125}], "temperature": 1.0}, {"id": 12, "seek": 28500, "start": 264.68, "end": 285.0, "text": "هذه كانت ال relation R ال relation R هذه مطبقة على ال set A بسميها reflexive if for all A لكل العناصر A اللي موجودة داخل ال set A يوجد علاقة بين العنصر و نفسه", "tokens": [3224, 24192, 25961, 2655, 2423, 9721, 497, 2423, 9721, 497, 29538, 3714, 9566, 3555, 28671, 15844, 2423, 992, 316, 4724, 38251, 1829, 11296, 23802, 488, 498, 337, 439, 316, 5296, 28820, 18863, 1863, 33546, 2288, 316, 13672, 1829, 3714, 29245, 23328, 3660, 11778, 47283, 1211, 2423, 992, 316, 7251, 29245, 3215, 11203, 995, 28671, 49374, 18863, 1863, 9381, 2288, 4032, 8717, 36178, 3224], "avg_logprob": -0.1633300711400807, "compression_ratio": 1.4720496894409938, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 264.68, "end": 264.98, "word": "هذه", "probability": 0.4150390625}, {"start": 264.98, "end": 265.26, "word": " كانت", "probability": 0.97607421875}, {"start": 265.26, "end": 265.52, "word": " ال", "probability": 0.84521484375}, {"start": 265.52, "end": 266.68, "word": " relation", "probability": 0.91796875}, {"start": 266.68, "end": 267.14, "word": " R", "probability": 0.64404296875}, {"start": 267.14, "end": 267.94, "word": " ال", "probability": 0.3017578125}, {"start": 267.94, "end": 268.24, "word": " relation", "probability": 0.9892578125}, {"start": 268.24, "end": 268.5, "word": " R", "probability": 0.87548828125}, {"start": 268.5, "end": 268.84, "word": " هذه", "probability": 0.5302734375}, {"start": 268.84, "end": 269.46, "word": " مطبقة", "probability": 0.8673095703125}, {"start": 269.46, "end": 270.4, "word": " على", "probability": 0.9296875}, {"start": 270.4, "end": 270.68, "word": " ال", "probability": 0.87646484375}, {"start": 270.68, "end": 270.98, "word": " set", "probability": 0.736328125}, {"start": 270.98, "end": 271.58, "word": " A", "probability": 0.8720703125}, {"start": 271.58, "end": 272.72, "word": " بسميها", "probability": 0.9542236328125}, {"start": 272.72, "end": 273.6, "word": " reflexive", "probability": 0.95068359375}, {"start": 273.6, "end": 274.36, "word": " if", "probability": 0.459716796875}, {"start": 274.36, "end": 275.4, "word": " for", "probability": 0.939453125}, {"start": 275.4, "end": 275.82, "word": " all", "probability": 0.951171875}, {"start": 275.82, "end": 276.3, "word": " A", "probability": 0.6279296875}, {"start": 276.3, "end": 277.32, "word": " لكل", "probability": 0.9638671875}, {"start": 277.32, "end": 278.26, "word": " العناصر", "probability": 0.95849609375}, {"start": 278.26, "end": 278.88, "word": " A", "probability": 0.873046875}, {"start": 278.88, "end": 279.2, "word": " اللي", "probability": 0.779052734375}, {"start": 279.2, "end": 279.62, "word": " موجودة", "probability": 0.9853515625}, {"start": 279.62, "end": 280.0, "word": " داخل", "probability": 0.9763997395833334}, {"start": 280.0, "end": 280.22, "word": " ال", "probability": 0.89599609375}, {"start": 280.22, "end": 280.56, "word": " set", "probability": 0.947265625}, {"start": 280.56, "end": 281.94, "word": " A", "probability": 0.50048828125}, {"start": 281.94, "end": 282.9, "word": " يوجد", "probability": 0.95166015625}, {"start": 282.9, "end": 283.94, "word": " علاقة", "probability": 0.9765625}, {"start": 283.94, "end": 284.14, "word": " بين", "probability": 0.96484375}, {"start": 284.14, "end": 284.54, "word": " العنصر", "probability": 0.98974609375}, {"start": 284.54, "end": 284.64, "word": " و", "probability": 0.94287109375}, {"start": 284.64, "end": 285.0, "word": " نفسه", "probability": 0.9091796875}], "temperature": 1.0}, {"id": 13, "seek": 31241, "start": 286.59, "end": 312.41, "text": "فانعكسية هي بينه بنفسه يوجد العلاقة يوجد ضمن ال relation هذه فهذا بنسميه reflexive طيب المكمل له ال reflexive المكمل له ال reflexive معناه ذلك أنه ممكن تجي نحلات لا هي reflexive ولا هي reflexive لا هي انعكسية ولا هي ليست خالية من الانعكسية", "tokens": [5172, 7649, 3615, 4117, 3794, 10632, 39896, 49374, 3224, 44945, 36178, 3224, 7251, 29245, 3215, 18863, 15040, 28671, 7251, 29245, 3215, 48812, 27842, 2423, 9721, 29538, 6156, 3224, 15730, 44945, 38251, 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"probability": 0.9016927083333334}, {"start": 329.98, "end": 330.08, "word": " ال", "probability": 0.646484375}, {"start": 330.08, "end": 330.54, "word": " reflexive،", "probability": 0.8653971354166666}, {"start": 330.54, "end": 330.76, "word": " لأنه", "probability": 0.9319661458333334}, {"start": 330.76, "end": 331.24, "word": " ليست", "probability": 0.900146484375}, {"start": 331.24, "end": 332.56, "word": " مكملة", "probability": 0.9786783854166666}, {"start": 332.56, "end": 333.48, "word": " لل", "probability": 0.884765625}, {"start": 333.48, "end": 334.16, "word": " reflexive،", "probability": 0.8743489583333334}, {"start": 334.16, "end": 334.32, "word": " مش", "probability": 0.9658203125}, {"start": 334.32, "end": 334.78, "word": " مكملة", "probability": 0.9910481770833334}, {"start": 334.78, "end": 335.04, "word": " لل", "probability": 0.642578125}, {"start": 335.04, "end": 336.0, "word": " reflexive", "probability": 0.881103515625}], "temperature": 1.0}, {"id": 15, "seek": 35282, "start": 336.76, "end": 352.82, "text": "طيب فإذا complementary لل relation فإذا المكملة لل R اللي هي reflexive هذه المكملة بتاعتها بنسميها irreflexive، كويس، لاحظ إن ال irreflexive هي مش معناها إن هي not reflexive", "tokens": [9566, 1829, 3555, 6156, 28814, 15730, 40705, 24976, 9721, 6156, 28814, 15730, 9673, 24793, 37977, 24976, 497, 13672, 1829, 39896, 23802, 488, 29538, 9673, 24793, 37977, 39894, 995, 34268, 11296, 44945, 38251, 1829, 11296, 16014, 69, 2021, 488, 12399, 9122, 45865, 3794, 12399, 20193, 5016, 19913, 36145, 2423, 16014, 69, 2021, 488, 39896, 37893, 20449, 8315, 11296, 36145, 39896, 406, 23802, 488], "avg_logprob": -0.19382439955832467, "compression_ratio": 1.5617283950617284, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 336.76, "end": 337.24, "word": "طيب", "probability": 0.9676106770833334}, {"start": 337.24, "end": 337.96, "word": " فإذا", "probability": 0.7814127604166666}, {"start": 337.96, "end": 338.44, "word": " complementary", 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بتصير not reflexive .. not reflexive بس سبحان الله إذا كان كلكوا أصحاب إيثار و كلكوا .. كلكوا هيك فجأة صرتوا أصحاب إيثار ولا واحد ال priority لنفسه كله يعطي priority لغيره جبله هنا بتصير irreflexive بس هنا بتصير for all", "tokens": [3224, 1829, 16490, 1211, 33546, 37495, 22653, 6156, 28543, 9673, 2407, 11242, 45367, 36764, 24401, 7251, 4117, 41185, 14739, 7251, 39648, 5296, 10721, 39896, 5551, 12610, 7578, 9154, 1829, 4386, 16472, 2655, 5551, 12610, 7578, 9154, 1829, 16490, 1211, 33546, 4386, 39896, 4117, 39894, 9381, 13546, 406, 23802, 488, 4386, 406, 23802, 488, 4724, 3794, 8608, 49628, 7649, 21984, 11933, 15730, 25961, 28242, 4117, 14407, 5551, 9381, 5016, 16758, 11933, 1829, 12984, 9640, 4032, 28242, 4117, 14407, 4386, 28242, 4117, 14407, 39896, 4117, 6156, 7435, 10721, 3660, 20328, 43500, 14407, 5551, 9381, 5016, 16758, 11933, 1829, 12984, 9640, 49429, 36764, 24401, 2423, 9365, 5296, 1863, 36178, 3224, 28242, 3224, 37495, 9566, 1829, 9365, 5296, 17082, 13546, 3224, 10874, 36150, 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"probability": 0.9720052083333334}, {"start": 620.82, "end": 621.4, "word": " for", "probability": 0.96826171875}, {"start": 621.4, "end": 621.94, "word": " all", "probability": 0.94775390625}], "temperature": 1.0}, {"id": 26, "seek": 64891, "start": 622.85, "end": 648.91, "text": "not reflexive for all هنا يعني للكل ليست ايه او للكل ايه لكل العناصر لاوجد علاقة بين الأنصر نفسه هنا بتمشي irreflexive تمام", "tokens": [2247, 23802, 488, 337, 439, 34105, 37495, 22653, 5296, 23275, 1211, 32239, 14851, 1975, 1829, 3224, 1975, 2407, 5296, 23275, 1211, 1975, 1829, 3224, 5296, 28820, 18863, 1863, 33546, 2288, 20193, 29245, 3215, 11203, 995, 28671, 49374, 16247, 1863, 9381, 2288, 8717, 36178, 3224, 34105, 39894, 2304, 8592, 1829, 16014, 69, 2021, 488, 46811, 10943], "avg_logprob": -0.20912388206592628, "compression_ratio": 1.4338235294117647, "no_speech_prob": 2.384185791015625e-06, "words": [{"start": 622.85, "end": 623.41, "word": "not", "probability": 0.48876953125}, {"start": 623.41, "end": 624.45, "word": " reflexive", "probability": 0.978515625}, {"start": 624.45, "end": 624.91, "word": " for", "probability": 0.69580078125}, {"start": 624.91, "end": 625.31, "word": " all", "probability": 0.9501953125}, {"start": 625.31, "end": 626.91, "word": " هنا", "probability": 0.1756591796875}, {"start": 626.91, "end": 627.17, "word": " يعني", "probability": 0.808837890625}, {"start": 627.17, "end": 628.11, "word": " للكل", "probability": 0.8056640625}, {"start": 628.11, "end": 629.23, "word": " ليست", "probability": 0.9365234375}, {"start": 629.23, "end": 630.67, "word": " ايه", "probability": 0.87744140625}, {"start": 630.67, "end": 631.77, "word": " او", "probability": 0.7939453125}, {"start": 631.77, "end": 636.59, "word": " للكل", "probability": 0.8782552083333334}, {"start": 636.59, "end": 640.39, "word": " ايه", "probability": 0.9231770833333334}, {"start": 640.39, "end": 642.77, "word": " لكل", "probability": 0.574462890625}, {"start": 642.77, "end": 643.37, "word": " العناصر", "probability": 0.9449462890625}, {"start": 643.37, "end": 643.87, "word": " لاوجد", "probability": 0.90185546875}, {"start": 643.87, "end": 644.35, "word": " علاقة", "probability": 0.9768880208333334}, {"start": 644.35, "end": 644.57, "word": " بين", "probability": 0.93310546875}, {"start": 644.57, "end": 644.87, "word": " الأنصر", "probability": 0.7808837890625}, {"start": 644.87, "end": 645.97, "word": " نفسه", "probability": 0.99072265625}, {"start": 645.97, "end": 646.39, "word": " هنا", "probability": 0.8984375}, {"start": 646.39, "end": 646.97, "word": " بتمشي", "probability": 0.8966064453125}, {"start": 646.97, "end": 648.11, "word": " irreflexive", "probability": 0.7728271484375}, {"start": 648.11, "end": 648.91, "word": " تمام", "probability": 0.967529296875}], "temperature": 1.0}, {"id": 27, "seek": 67577, "start": 650.39, "end": 675.77, "text": "نشوف إيش الأمثلة اللي ميعطينا إياها، ميعطيني ال like طبعا من أعقد أو خلّيني أقول من أكثر ال relations اللي مالهاش rules اللي هي like فلو قولنا likes between people is not reflexive وبرضه not irreflexive فإذا likes، x likes x، ماقدرش أعمل على الكل زي ما احنا طوى قولنا", "tokens": [1863, 8592, 38688, 11933, 1829, 8592, 16247, 2304, 12984, 37977, 13672, 1829, 3714, 1829, 3615, 9566, 1829, 8315, 11933, 25528, 11296, 12399, 3714, 1829, 3615, 9566, 9957, 1829, 2423, 411, 23032, 3555, 3615, 995, 9154, 5551, 3615, 28543, 34051, 16490, 1211, 11703, 9957, 1829, 5551, 39648, 9154, 5551, 4117, 49115, 2423, 2299, 13672, 1829, 3714, 6027, 3224, 33599, 4474, 13672, 1829, 39896, 411, 6156, 1211, 2407, 12174, 12610, 8315, 5902, 1296, 561, 307, 406, 23802, 488, 4032, 26890, 11242, 3224, 406, 16014, 69, 2021, 488, 6156, 28814, 15730, 5902, 12399, 2031, 5902, 2031, 12399, 19446, 28543, 2288, 8592, 5551, 25957, 1211, 15844, 2423, 28820, 30767, 1829, 19446, 1975, 5016, 8315, 23032, 2407, 7578, 12174, 12610, 8315], "avg_logprob": -0.2283653912381229, "compression_ratio": 1.6945606694560669, "no_speech_prob": 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أعقد", "probability": 0.96630859375}, {"start": 655.29, "end": 655.51, "word": " أو", "probability": 0.83349609375}, {"start": 655.51, "end": 655.91, "word": " خلّيني", "probability": 0.775146484375}, {"start": 655.91, "end": 656.15, "word": " أقول", "probability": 0.7271728515625}, {"start": 656.15, "end": 656.69, "word": " من", "probability": 0.9482421875}, {"start": 656.69, "end": 657.09, "word": " أكثر", "probability": 0.935546875}, {"start": 657.09, "end": 657.39, "word": " ال", "probability": 0.9833984375}, {"start": 657.39, "end": 658.05, "word": " relations", "probability": 0.8525390625}, {"start": 658.05, "end": 658.87, "word": " اللي", "probability": 0.974365234375}, {"start": 658.87, "end": 659.21, "word": " مالهاش", "probability": 0.8104248046875}, {"start": 659.21, "end": 659.61, "word": " rules", "probability": 0.85498046875}, {"start": 659.61, "end": 660.79, "word": " اللي", "probability": 0.92724609375}, {"start": 660.79, "end": 661.05, "word": " هي", "probability": 0.9248046875}, {"start": 661.05, "end": 661.59, "word": " like", "probability": 0.8837890625}, {"start": 661.59, "end": 661.89, "word": " فلو", "probability": 0.9075520833333334}, {"start": 661.89, "end": 662.29, "word": " قولنا", "probability": 0.8243815104166666}, {"start": 662.29, "end": 663.11, "word": " likes", "probability": 0.85791015625}, {"start": 663.11, "end": 663.63, "word": " between", "probability": 0.9580078125}, {"start": 663.63, "end": 664.19, "word": " people", "probability": 0.9765625}, {"start": 664.19, "end": 664.91, "word": " is", "probability": 0.96337890625}, {"start": 664.91, "end": 665.53, "word": " not", "probability": 0.9677734375}, {"start": 665.53, "end": 666.29, "word": " reflexive", "probability": 0.975830078125}, {"start": 666.29, "end": 667.17, "word": " وبرضه", "probability": 0.8399658203125}, {"start": 667.17, "end": 667.59, "word": " not", "probability": 0.9638671875}, {"start": 667.59, "end": 668.57, "word": " irreflexive", "probability": 0.8740234375}, {"start": 668.57, "end": 669.39, "word": " فإذا", "probability": 0.7779947916666666}, {"start": 669.39, "end": 671.21, "word": " likes،", "probability": 0.53985595703125}, {"start": 671.21, "end": 671.71, "word": " x", "probability": 0.64599609375}, {"start": 671.71, "end": 672.59, "word": " likes", "probability": 0.69677734375}, {"start": 672.59, "end": 673.67, "word": " x،", "probability": 0.69482421875}, {"start": 673.67, "end": 674.07, "word": " ماقدرش", "probability": 0.8289794921875}, {"start": 674.07, "end": 674.35, "word": " أعمل", "probability": 0.8968098958333334}, {"start": 674.35, "end": 674.47, "word": " على", "probability": 0.4296875}, {"start": 674.47, "end": 674.73, "word": " الكل", "probability": 0.84814453125}, {"start": 674.73, "end": 675.05, "word": " زي", "probability": 0.824951171875}, {"start": 675.05, "end": 675.13, "word": " ما", "probability": 0.9736328125}, {"start": 675.13, "end": 675.25, "word": " احنا", "probability": 0.86865234375}, {"start": 675.25, "end": 675.49, "word": " طوى", "probability": 0.4685465494791667}, {"start": 675.49, "end": 675.77, "word": " قولنا", "probability": 0.9285481770833334}], "temperature": 1.0}, {"id": 28, "seek": 69520, "start": 677.16, "end": 695.2, "text": "بقدرش أعممها على كل ال people مش هيك فإذا بقدرش أقول إن هي reflexive فهي not reflexive بس في نفس الوقت بقدرش أقول إن كل ال people هم لا يفضلوا أنفسهم مش هيك ايه likes ايه بقدرش برضه أقول ايه dislikes ايه", "tokens": [3555, 28543, 2288, 8592, 5551, 25957, 2304, 11296, 15844, 28242, 2423, 561, 37893, 39896, 4117, 6156, 28814, 15730, 4724, 28543, 2288, 8592, 5551, 39648, 36145, 39896, 23802, 488, 6156, 3224, 1829, 406, 23802, 488, 4724, 3794, 8978, 8717, 36178, 2423, 30543, 2655, 4724, 28543, 2288, 8592, 5551, 39648, 36145, 28242, 2423, 561, 8032, 2304, 20193, 7251, 5172, 11242, 1211, 14407, 14739, 36178, 16095, 37893, 39896, 4117, 1975, 1829, 3224, 5902, 1975, 1829, 3224, 4724, 28543, 2288, 8592, 4724, 43042, 3224, 5551, 39648, 1975, 1829, 3224, 43186, 8916, 1975, 1829, 3224], "avg_logprob": -0.1380494515319447, "compression_ratio": 1.8875739644970415, "no_speech_prob": 9.5367431640625e-07, "words": [{"start": 677.16, "end": 677.78, "word": "بقدرش", "probability": 0.885498046875}, {"start": 677.78, "end": 678.14, "word": " أعممها", "probability": 0.6988525390625}, {"start": 678.14, "end": 678.4, "word": " على", "probability": 0.87255859375}, {"start": 678.4, "end": 678.82, "word": " كل", "probability": 0.9619140625}, {"start": 678.82, "end": 678.94, "word": " ال", "probability": 0.98828125}, {"start": 678.94, "end": 679.22, "word": " people", "probability": 0.9775390625}, {"start": 679.22, "end": 679.68, "word": " مش", "probability": 0.494384765625}, {"start": 679.68, "end": 679.98, "word": " هيك", "probability": 0.780517578125}, {"start": 679.98, "end": 680.3, "word": " فإذا", "probability": 0.6588541666666666}, {"start": 680.3, "end": 680.72, "word": " بقدرش", "probability": 0.9644775390625}, {"start": 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691.24, "end": 692.06, "word": " ايه", "probability": 0.8517252604166666}, {"start": 692.06, "end": 692.94, "word": " بقدرش", "probability": 0.925048828125}, {"start": 692.94, "end": 693.16, "word": " برضه", "probability": 0.9549153645833334}, {"start": 693.16, "end": 693.46, "word": " أقول", "probability": 0.872802734375}, {"start": 693.46, "end": 693.9, "word": " ايه", "probability": 0.9358723958333334}, {"start": 693.9, "end": 694.66, "word": " dislikes", "probability": 0.899658203125}, {"start": 694.66, "end": 695.2, "word": " ايه", "probability": 0.8785807291666666}], "temperature": 1.0}, {"id": 29, "seek": 71240, "start": 696.36, "end": 712.4, "text": "لكل ال إيه، فإذا حالة زي هذه مالهاش role، هذه لا هيك ولا هي هيك، على اعتبار أن زي ما قلنا everyone likes themselves مش بالضروري، وفي نفس الوجود not everyone dislikes themselves", "tokens": [1211, 28820, 2423, 11933, 1829, 3224, 12399, 6156, 28814, 15730, 11331, 6027, 3660, 30767, 1829, 29538, 3714, 6027, 3224, 33599, 3090, 12399, 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"text": "طيب مبدئيا symmetric لأ ليش محتاجة كانت أربعة أو واحد مش موجودة فإذا خلصنا منها طيب asymmetric asymmetric تلاتة أو تلاتة أربعة أو أربعة تلاتة أو تلاتة", "tokens": [9566, 1829, 3555, 3714, 44510, 19986, 25528, 32330, 5296, 10721, 32239, 8592, 3714, 33753, 26108, 3660, 25961, 2655, 5551, 25513, 27884, 34051, 36764, 24401, 37893, 3714, 29245, 23328, 3660, 6156, 28814, 15730, 16490, 1211, 9381, 8315, 9154, 11296, 23032, 1829, 3555, 37277, 17475, 37277, 17475, 6055, 1211, 9307, 3660, 34051, 6055, 1211, 9307, 3660, 5551, 25513, 27884, 34051, 5551, 25513, 27884, 6055, 1211, 9307, 3660, 34051, 6055, 1211, 9307, 3660], "avg_logprob": -0.21049735831542754, "compression_ratio": 1.7253521126760563, "no_speech_prob": 1.3113021850585938e-06, "words": [{"start": 1604.57, "end": 1604.89, "word": "طيب", "probability": 0.6973063151041666}, {"start": 1604.89, "end": 1605.47, "word": " مبدئيا", "probability": 0.7781982421875}, {"start": 1605.47, "end": 1606.55, "word": " symmetric", 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2617.53, "word": " اتنين", "probability": 0.97705078125}, {"start": 2617.53, "end": 2617.75, "word": " لاقاش", "probability": 0.3968098958333333}, {"start": 2617.75, "end": 2617.99, "word": " بده", "probability": 0.6112060546875}, {"start": 2617.99, "end": 2618.09, "word": " key", "probability": 0.771484375}, {"start": 2618.09, "end": 2618.39, "word": " اربع", "probability": 0.7948404947916666}, {"start": 2618.39, "end": 2618.51, "word": " او", "probability": 0.96044921875}, {"start": 2618.51, "end": 2618.63, "word": " اتنين", "probability": 0.9820556640625}, {"start": 2618.63, "end": 2621.15, "word": " مظبوط", "probability": 0.91318359375}, {"start": 2621.15, "end": 2628.19, "word": " مظبوطة", "probability": 0.8485107421875}, {"start": 2628.19, "end": 2628.67, "word": " هاي", "probability": 0.5609130859375}, {"start": 2628.67, "end": 2628.91, "word": " اربع", "probability": 0.892578125}, {"start": 2628.91, "end": 2629.01, "word": " او", "probability": 0.8876953125}, {"start": 2629.01, 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{"start": 2652.67, "end": 2653.17, "word": " جربها", "probability": 0.9708658854166666}, {"start": 2653.17, "end": 2653.35, "word": " و", "probability": 0.90380859375}, {"start": 2653.35, "end": 2654.41, "word": " هتشوفها", "probability": 0.7986328125}, {"start": 2654.41, "end": 2654.65, "word": " المرة", "probability": 0.909423828125}, {"start": 2654.65, "end": 2654.87, "word": " الجاية", "probability": 0.8408203125}, {"start": 2654.87, "end": 2655.33, "word": " جربها", "probability": 0.8771158854166666}, {"start": 2655.33, "end": 2655.77, "word": " اعملها", "probability": 0.9339599609375}, {"start": 2655.77, "end": 2656.43, "word": " اعملها", "probability": 0.9144287109375}, {"start": 2656.43, "end": 2656.97, "word": " تصور", "probability": 0.9541015625}, {"start": 2656.97, "end": 2657.49, "word": " بس", "probability": 0.912841796875}, {"start": 2657.49, "end": 2657.87, "word": " اعملها", "probability": 0.964599609375}, {"start": 2657.87, "end": 2658.27, "word": " تصور", "probability": 0.9833984375}, {"start": 2658.27, "end": 2658.47, "word": " على", "probability": 0.8876953125}, {"start": 2658.47, "end": 2659.13, "word": " حالة", "probability": 0.8802083333333334}, {"start": 2659.13, "end": 2659.41, "word": " كبيرة", "probability": 0.9894205729166666}, {"start": 2659.41, "end": 2659.59, "word": " زي", "probability": 0.770751953125}, {"start": 2659.59, "end": 2659.79, "word": " هذه", "probability": 0.68896484375}, {"start": 2659.79, "end": 2660.15, "word": " مثلا", "probability": 0.982177734375}], "temperature": 1.0}, {"id": 102, "seek": 267824, "start": 2661.1, "end": 2678.24, "text": "يعني ممكن تجربها على خمسة تجربها على خمسة طبعا الباقي بالنسبالي هيكون اعتقد كله yes تمام طيب المرة الجاية ان شاء الله بنكمل نبني على ال transitive هنبني على ال transitive في إيش؟ متذكرين ال composition؟", "tokens": [40228, 22653, 3714, 43020, 6055, 7435, 25513, 11296, 15844, 16490, 2304, 3794, 3660, 6055, 7435, 25513, 11296, 15844, 16490, 2304, 3794, 3660, 23032, 3555, 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" المرة", "probability": 0.950439453125}, {"start": 2670.28, "end": 2670.46, "word": " الجاية", "probability": 0.7384440104166666}, {"start": 2670.46, "end": 2670.58, "word": " ان", "probability": 0.86328125}, {"start": 2670.58, "end": 2670.72, "word": " شاء", "probability": 0.978515625}, {"start": 2670.72, "end": 2670.74, "word": " الله", "probability": 0.93603515625}, {"start": 2670.74, "end": 2671.4, "word": " بنكمل", "probability": 0.9352213541666666}, {"start": 2671.4, "end": 2672.7, "word": " نبني", "probability": 0.9397786458333334}, {"start": 2672.7, "end": 2673.26, "word": " على", "probability": 0.84375}, {"start": 2673.26, "end": 2673.54, "word": " ال", "probability": 0.892578125}, {"start": 2673.54, "end": 2674.1, "word": " transitive", "probability": 0.684326171875}, {"start": 2674.1, "end": 2674.98, "word": " هنبني", "probability": 0.8768310546875}, {"start": 2674.98, "end": 2675.08, "word": " على", "probability": 0.82958984375}, {"start": 2675.08, "end": 2675.18, "word": " ال", "probability": 0.93994140625}, {"start": 2675.18, "end": 2675.54, "word": " transitive", "probability": 0.87060546875}, {"start": 2675.54, "end": 2675.74, "word": " في", "probability": 0.8828125}, {"start": 2675.74, "end": 2676.6, "word": " إيش؟", "probability": 0.68304443359375}, {"start": 2676.6, "end": 2677.16, "word": " متذكرين", "probability": 0.87841796875}, {"start": 2677.16, "end": 2677.26, "word": " ال", "probability": 0.970703125}, {"start": 2677.26, "end": 2678.24, "word": " composition؟", "probability": 0.915771484375}], "temperature": 1.0}, {"id": 103, "seek": 270028, "start": 2679.16, "end": 2700.28, "text": "الـ composition فهنعمل برضه composed .. composed ل ال relations فنحاول نشوف نهاية ال relation مع بداية relation تانية إيش ال total بيطلع .. إيش ال total بيطلع فهي برضه نفس عملية ال transit .. ال transitive كأن هو هنا بيقول كش أفحص ال transitive بيقولك جيبلي ال transitive تمام؟ ناخدها المرة الجاية أعطيكوا ألف عافية", "tokens": [6027, 39184, 12686, 6156, 3224, 1863, 25957, 1211, 4724, 43042, 3224, 18204, 4386, 18204, 5296, 2423, 2299, 6156, 1863, 5016, 995, 12610, 8717, 8592, 38688, 8717, 11296, 10632, 2423, 9721, 20449, 4724, 28259, 10632, 9721, 6055, 7649, 10632, 11933, 1829, 8592, 2423, 3217, 4724, 1829, 9566, 1211, 3615, 4386, 11933, 1829, 8592, 2423, 3217, 4724, 1829, 9566, 1211, 3615, 6156, 3224, 1829, 4724, 43042, 3224, 8717, 36178, 6225, 42213, 10632, 2423, 17976, 4386, 2423, 1145, 2187, 9122, 33456, 31439, 34105, 4724, 1829, 39648, 9122, 8592, 5551, 5172, 5016, 9381, 2423, 17976, 488, 4724, 1829, 39648, 4117, 10874, 1829, 3555, 20292, 2423, 1145, 2187, 46811, 10943, 22807, 8717, 47283, 3215, 11296, 9673, 25720, 25724, 995, 10632, 5551, 3615, 9566, 1829, 4117, 14407, 5551, 46538, 6225, 31845, 10632], "avg_logprob": -0.1878690874482703, "compression_ratio": 1.9341563786008231, "no_speech_prob": 3.5762786865234375e-06, "words": [{"start": 2679.16, "end": 2679.42, "word": "الـ", "probability": 0.41162109375}, {"start": 2679.42, "end": 2679.8, "word": " composition", "probability": 0.53369140625}, {"start": 2679.8, "end": 2680.96, "word": " فهنعمل", "probability": 0.82412109375}, {"start": 2680.96, "end": 2681.26, "word": " برضه", "probability": 0.91943359375}, {"start": 2681.26, "end": 2681.94, "word": " composed", "probability": 0.439453125}, {"start": 2681.94, "end": 2682.28, "word": " ..", "probability": 0.666015625}, {"start": 2682.28, "end": 2683.28, "word": " composed", "probability": 0.38623046875}, {"start": 2683.28, "end": 2683.58, "word": " ل", "probability": 0.8095703125}, {"start": 2683.58, "end": 2683.82, "word": " ال", "probability": 0.62451171875}, {"start": 2683.82, "end": 2684.28, "word": " relations", "probability": 0.87890625}, {"start": 2684.28, "end": 2685.9, "word": " فنحاول", "probability": 0.97451171875}, {"start": 2685.9, "end": 2686.16, "word": " نشوف", "probability": 0.9596354166666666}, {"start": 2686.16, "end": 2686.5, "word": " نهاية", "probability": 0.8951822916666666}, {"start": 2686.5, "end": 2686.64, "word": " ال", "probability": 0.99072265625}, {"start": 2686.64, "end": 2687.04, "word": " relation", "probability": 0.98388671875}, {"start": 2687.04, "end": 2687.42, "word": " مع", "probability": 0.990234375}, {"start": 2687.42, "end": 2687.74, "word": " بداية", "probability": 0.9866536458333334}, {"start": 2687.74, "end": 2688.1, "word": " relation", "probability": 0.6162109375}, {"start": 2688.1, "end": 2688.62, "word": " تانية", "probability": 0.9874674479166666}, {"start": 2688.62, "end": 2689.14, "word": " إيش", "probability": 0.7880045572916666}, {"start": 2689.14, "end": 2689.28, "word": " ال", "probability": 0.986328125}, {"start": 2689.28, "end": 2689.54, "word": " total", "probability": 0.89208984375}, {"start": 2689.54, "end": 2690.0, "word": " بيطلع", "probability": 0.772705078125}, {"start": 2690.0, "end": 2690.28, "word": " ..", "probability": 0.5478515625}, {"start": 2690.28, "end": 2690.4, "word": " إيش", "probability": 0.9651692708333334}, {"start": 2690.4, "end": 2690.48, "word": " ال", "probability": 0.99560546875}, {"start": 2690.48, "end": 2690.68, "word": " total", "probability": 0.921875}, {"start": 2690.68, "end": 2691.16, "word": " بيطلع", "probability": 0.98369140625}, {"start": 2691.16, "end": 2691.66, "word": " فهي", "probability": 0.91064453125}, {"start": 2691.66, "end": 2691.9, "word": " برضه", "probability": 0.9658203125}, {"start": 2691.9, "end": 2692.06, "word": " نفس", "probability": 0.99658203125}, {"start": 2692.06, "end": 2692.32, "word": " عملية", "probability": 0.9794921875}, {"start": 2692.32, "end": 2692.44, "word": " ال", "probability": 0.8349609375}, {"start": 2692.44, "end": 2692.68, "word": " transit", "probability": 0.3046875}, {"start": 2692.68, "end": 2692.74, "word": " ..", "probability": 0.83251953125}, {"start": 2692.74, "end": 2692.82, "word": " ال", "probability": 0.89111328125}, {"start": 2692.82, "end": 2693.38, "word": " transitive", "probability": 0.85546875}, {"start": 2693.38, "end": 2694.1, "word": " كأن", "probability": 0.897705078125}, {"start": 2694.1, "end": 2694.38, "word": " هو", "probability": 0.73876953125}, {"start": 2694.38, "end": 2694.62, "word": " هنا", "probability": 0.9384765625}, {"start": 2694.62, "end": 2694.84, "word": " بيقول", "probability": 0.9794921875}, {"start": 2694.84, "end": 2695.04, "word": " كش", "probability": 0.67724609375}, {"start": 2695.04, "end": 2695.36, "word": " أفحص", "probability": 0.78033447265625}, {"start": 2695.36, "end": 2695.44, "word": " ال", "probability": 0.6435546875}, {"start": 2695.44, "end": 2695.9, "word": " transitive", "probability": 0.5400390625}, {"start": 2695.9, "end": 2696.48, "word": " بيقولك", "probability": 0.8983154296875}, {"start": 2696.48, "end": 2696.8, "word": " جيبلي", "probability": 0.852783203125}, {"start": 2696.8, "end": 2696.92, "word": " ال", "probability": 0.9267578125}, {"start": 2696.92, "end": 2697.44, "word": " transitive", "probability": 0.817626953125}, {"start": 2697.44, "end": 2698.7, "word": " تمام؟", "probability": 0.79296875}, {"start": 2698.7, "end": 2699.08, "word": " ناخدها", "probability": 0.83941650390625}, {"start": 2699.08, "end": 2699.34, "word": " المرة", "probability": 0.900146484375}, {"start": 2699.34, "end": 2699.56, "word": " الجاية", "probability": 0.8893229166666666}, {"start": 2699.56, "end": 2699.82, "word": " أعطيكوا", "probability": 0.8667805989583334}, {"start": 2699.82, "end": 2699.98, "word": " ألف", "probability": 0.912353515625}, {"start": 2699.98, "end": 2700.28, "word": " عافية", "probability": 0.9775390625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2700.6896875, "duration_after_vad": 2591.6962499999922}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wu4ONEGCIa0_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wu4ONEGCIa0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..11e60d3476a5484867a397a9557d24565e007343
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wu4ONEGCIa0_postprocess.srt
@@ -0,0 +1,3096 @@
+1
+00:00:05,570 --> 00:00:09,490
+يعطيكوا العفو يا شباب نبدأ ان شاء الله تعالى في
+
+2
+00:00:09,490 --> 00:00:15,230
+جزئية الـ Euclide algorithm اكمالا لموضوع ال GCD
+
+3
+00:00:15,230 --> 00:00:20,130
+اللي أخدناها سابقا في موضوع ال number او ال theory
+
+4
+00:00:20,130 --> 00:00:25,430
+و هنبدأ اللي هي اتكلمنا فيها عننظرية الأعداد، ليش؟
+
+5
+00:00:25,430 --> 00:00:30,510
+لأنه هي الأساس لكل العلوم اللاحقة بعد ذلك، ومنها
+
+6
+00:00:30,510 --> 00:00:34,410
+التشفير و اللي هنصله في آخر محاضرتنا لهذا الموضوع
+
+7
+00:00:34,410 --> 00:00:38,410
+اللي بنتكلم فيها عن عملية ال encryption و كل ما
+
+8
+00:00:38,410 --> 00:00:41,650
+يخص الحقيقة سحر الأرقام و سحر الأعداد، لازم نكون
+
+9
+00:00:41,650 --> 00:00:44,480
+فاهمين أحنا الأعداد .. الأرقام نفسها بالأساسنكون
+
+10
+00:00:44,480 --> 00:00:48,820
+فاهمينها لأنه بشكل أو باخر هي أساس علم الحسوب ..
+
+11
+00:00:48,820 --> 00:00:52,900
+هي أساس علم الحسوب فوصلنا لجزئية أنه والله أخدنا
+
+12
+00:00:52,900 --> 00:00:59,010
+حاجة اسمها ال .. ال moduloالمرة الماضية الموديلو
+
+13
+00:00:59,010 --> 00:01:02,970
+هذه هنيجي نتطلع في إيش ممكن أستخدمها وجدنا أنه
+
+14
+00:01:02,970 --> 00:01:07,010
+هتوفر عليها جهد كتير كبير في جزئية greatest common
+
+15
+00:01:07,010 --> 00:01:11,110
+divisor في greatest common divisor بنقدر نجيب
+
+16
+00:01:11,110 --> 00:01:15,390
+علاقة ما بين greatest common divisor والموديلو
+
+17
+00:01:15,390 --> 00:01:20,950
+operation هنجد أنه احنا سهلنا على حالنا بشكل ضخم
+
+18
+00:01:20,950 --> 00:01:28,810
+كتير جزئية إيجاد ال GCD هذهكيف أني أقول والله أي
+
+19
+00:01:28,810 --> 00:01:36,090
+GCD لأي A وB لأي A وB هي فعليا نفسها ال GCD هي نفس
+
+20
+00:01:36,090 --> 00:01:43,850
+العامل المسترك الأكبر ل A مدلوا B وB هذا على فرض
+
+21
+00:01:43,850 --> 00:01:48,450
+أننا مرتبها أن ال A أكبر من ال B مرتبينها أن ال A
+
+22
+00:01:48,450 --> 00:01:51,570
+أكبر من ال B ففي الحالة هذه لما أقول A مدلوا B
+
+23
+00:01:51,570 --> 00:02:00,500
+هتطلع هنا قيمة أقل من ال Bأكيد ممتاز فصار هنا عندي
+
+24
+00:02:00,500 --> 00:02:05,500
+قيمة أقل من ال B و هنا قيمة ال B يعني معناه ذلك
+
+25
+00:02:05,500 --> 00:02:08,180
+لاحظوا هذا هيك القانون لحاله بس احنا كيف ممكن
+
+26
+00:02:08,180 --> 00:02:11,880
+نستفهم روح أكتر من هيك نرجع نعيد الموضوع كمان مرة
+
+27
+00:02:11,880 --> 00:02:15,600
+بحيث اني اقول لاحظش بده اقول بده اقول هذه صارت ال
+
+28
+00:02:15,600 --> 00:02:21,820
+A لجديدة و القيمة اللي طلعت ك remainder ل modulo
+
+29
+00:02:21,820 --> 00:02:28,430
+هذه صارت ال B لجديدةعشان نرجع .. لاحظ .. نعمل swap
+
+30
+00:02:28,430 --> 00:02:32,990
+و نركبهم بهذا الشكل و نرجع نعيد نفس الكلام كمان
+
+31
+00:02:32,990 --> 00:02:42,030
+مرة لما نصل لصفر بمعنى انه هنا عملية القسمة اللي
+
+32
+00:02:42,030 --> 00:02:48,330
+هيكون فيه متبقي لها مايكونش فيه متبقيأيه بتصل لأنه
+
+33
+00:02:48,330 --> 00:02:51,810
+ما بطل فيه متبقي هنا صفر بناخد القيمة التانية هي
+
+34
+00:02:51,810 --> 00:02:55,410
+ال common .. ال greatest common divisor هتكون هي
+
+35
+00:02:55,410 --> 00:02:59,320
+ال greatest common divisor فهذه ببساطةكيف احنا
+
+36
+00:02:59,320 --> 00:03:06,340
+ممكن نستغل ال modulo operation في إيجاد ال GCD
+
+37
+00:03:06,340 --> 00:03:10,000
+طريقة سهلة وسهلة وسلسة ونقدر نستخدمها في ال
+
+38
+00:03:10,000 --> 00:03:13,260
+algorithms بسهولة كيف هنستخدمها في ال algorithms
+
+39
+00:03:13,260 --> 00:03:16,700
+هناخد طبعا algorithm عليها هناخد algorithms عليها
+
+40
+00:03:16,700 --> 00:03:23,460
+بس خلينا نجرب هذا الموضوع بطريقة numericalبحيث ان
+
+41
+00:03:23,460 --> 00:03:28,560
+نشوف تلاتمية اتنين وسبعين ومية اربعة وستين وبدنا
+
+42
+00:03:28,560 --> 00:03:31,520
+نجيب greatest common divisor between them بكل
+
+43
+00:03:31,520 --> 00:03:34,320
+بساطة هنستخدم نفس القالية هقول greatest common
+
+44
+00:03:34,320 --> 00:03:37,960
+divisor لأ تلاتمية اتنين وسبعين هي نفسها تلاتمية
+
+45
+00:03:37,960 --> 00:03:44,700
+اتنين وسبعين مدله مية اربعة وستين كنتج ومية اربعة
+
+46
+00:03:44,700 --> 00:03:48,740
+وستين هنا النتج تبح مع الإطالة ومع غيره تطلع اربعة
+
+47
+00:03:48,740 --> 00:03:54,570
+واربعين يعني كأنه ال greatestCommon divisor ل 372
+
+48
+00:03:54,570 --> 00:04:01,170
+و 164 هو نفسه ال greatest common divisor بين 164 و
+
+49
+00:04:01,170 --> 00:04:06,450
+44 هو نفسه طيب في الحلقة دي بنرجع نكرر نفس العملية
+
+50
+00:04:06,450 --> 00:04:11,210
+كمان مرة بعد مرتبناهم هنا ال B حطناها مكان ال A و
+
+51
+00:04:11,210 --> 00:04:17,830
+ناتجالـ Modulo حطناها مكان الـ B بنرجع تكرار ال
+
+52
+00:04:17,830 --> 00:04:22,170
+loop بنعيده فلاحظ برمجيا كأنك انت ال loop رجعت
+
+53
+00:04:22,170 --> 00:04:27,790
+عدته كمان مرة بس كويس نفس الفكرة 164 modulo 44 و
+
+54
+00:04:27,790 --> 00:04:33,730
+44 طيب الناتج هنا 32 عكسهم دايما خلي الأول هو
+
+55
+00:04:33,730 --> 00:04:37,250
+الأكبر فصارت هو نفسه greatest common divisor بين
+
+56
+00:04:37,250 --> 00:04:41,950
+ال 44 وال32 و 30 و عيد عيد عيد لما تصل في الآخر ل
+
+57
+00:04:43,460 --> 00:04:46,260
+كلهم يكافئوا ل greatest common divisor ل تمانية
+
+58
+00:04:46,260 --> 00:04:51,360
+مدل و أربعة و أربعة طيب تمانية مدل و أربعة Zero
+
+59
+00:04:51,360 --> 00:04:54,520
+خلاص مدام ظهر عندي Zero معناته الأربعة هي greatest
+
+60
+00:04:54,520 --> 00:04:58,260
+common divisor فإذا الأربعة هي greatest common
+
+61
+00:04:58,260 --> 00:05:03,880
+divisor تمام هذه النظرية الأساسية كيف نكتبها ك كود
+
+62
+00:05:03,880 --> 00:05:07,960
+إذا بدكوا إياها في ال data structure بعدين تكتبوها
+
+63
+00:05:07,960 --> 00:05:14,060
+أبسط شغل إلهاال while و خلصنا ف ال while طول ما ال
+
+64
+00:05:14,060 --> 00:05:19,970
+بي لها قيمةكرر لما تصل لصفر واقف لان احنا لاحظ تو
+
+65
+00:05:19,970 --> 00:05:22,870
+استمرنا لعدم أوصلنا للصفر يعني اذا أوصلنا للصفر
+
+66
+00:05:22,870 --> 00:05:27,830
+وقفنا نفس الجثة هنرجع نكتبها في ال code اللي عندى
+
+67
+00:05:27,830 --> 00:05:31,850
+و لاحظ انه مش مستاهل كله سطرين تلاتة كله سطرين
+
+68
+00:05:31,850 --> 00:05:35,250
+تلاتة ال procedure بس بنحدد ايش ال arguments
+
+69
+00:05:35,250 --> 00:05:37,890
+بتاعتنا او ال input تبعنا فال input هو عبارة عن ال
+
+70
+00:05:37,890 --> 00:05:44,390
+a و ال b اسم البرنامج هو cd ال gcdGCD على أساس أنه
+
+71
+00:05:44,390 --> 00:05:46,590
+معبّر على greatest common divisor إيش ال input
+
+72
+00:05:46,590 --> 00:05:49,430
+تبعته ال A و ال B أكيد يعني أنت بدك ياني أجيب
+
+73
+00:05:49,430 --> 00:05:51,770
+معامل مشترك أكبر طبقين الرقمين اللي بده أجيب بينهم
+
+74
+00:05:51,770 --> 00:05:57,870
+فال A و ال B هي positive integers الآن while B لا
+
+75
+00:05:57,870 --> 00:06:02,930
+تساوي Zero معناته العملية مستمرة عملية البحث طيب
+
+76
+00:06:02,930 --> 00:06:07,090
+عملية البحث دي إيش بدنا من خلالها نعمل هنعمل ال R
+
+77
+00:06:07,090 --> 00:06:10,810
+أو ال remainder تبعنا و اللي هي يساوي ال A modulo
+
+78
+00:06:10,810 --> 00:06:17,310
+Bخلصناها .. خلصناها .. جيبناها هي .. بنحط ..
+
+79
+00:06:17,310 --> 00:06:21,890
+بنستبدل لإن احنا عارفين أن ال B هتكون أكبر من ال R
+
+80
+00:06:21,890 --> 00:06:26,570
+هذي قولة واحدة صحيح؟ و لا يمكن يطلع معاك ال R أكبر
+
+81
+00:06:26,570 --> 00:06:30,650
+من .. من B لما تيجي تعمل ال model operation فإذن
+
+82
+00:06:30,650 --> 00:06:36,990
+بتيجي تعمل تبديل بتخلي ال A هي ال B القديمة و ال B
+
+83
+00:06:36,990 --> 00:06:38,770
+هي ال R
+
+84
+00:06:41,420 --> 00:06:44,520
+بس و بنعمل end لأنه لاحظ احنا عملنا هنا statement
+
+85
+00:06:44,520 --> 00:06:47,680
+أولى، statement تانية و statement تالتة و التلاتة
+
+86
+00:06:47,680 --> 00:06:50,880
+لازم يكونوا جواب لمين لل while عشان كده بنبدأ
+
+87
+00:06:50,880 --> 00:06:54,120
+begin و end هنا بصير ضرورية ضرورية جدا ال begin و
+
+88
+00:06:54,120 --> 00:06:57,860
+ال end او ال care braces اللي انتوا بتكتبوها فهنا
+
+89
+00:06:57,860 --> 00:07:00,620
+بصير ضروري و إجباري لازم تكتبها في الجافة كويس
+
+90
+00:07:00,620 --> 00:07:07,920
+خلاص بتستمر ال loop هيضل ماشي امتى هيجف عند الصفر،
+
+91
+00:07:07,920 --> 00:07:12,820
+ممتازةطيب لما يصل عند صفر لما يصل لقيمة الصفر في
+
+92
+00:07:12,820 --> 00:07:17,460
+الحالة هذه انت هنا كان وصل معاك ان ال R بتساوي صفر
+
+93
+00:07:17,460 --> 00:07:22,900
+صح؟ يعني لاحظ هنا لاقيته .. لاقيته ساوي صفر جيت
+
+94
+00:07:22,900 --> 00:07:27,700
+حسبت ال R بعد ما كنت عملت ال test هذا حسبت ال R
+
+95
+00:07:27,700 --> 00:07:33,780
+طلعت صفر صحيح؟ فإيش عملت انت بعد ما صارت صفر انت
+
+96
+00:07:33,780 --> 00:07:37,060
+حطيت ال A B
+
+97
+00:07:38,190 --> 00:07:44,410
+وحطيت ال B هي ال R اللي هي الصفر فلاحظ جديد فعلياً
+
+98
+00:07:44,410 --> 00:07:48,310
+لجديد اللي صار عندك أن ال A تساوي ال B القديمة
+
+99
+00:07:48,310 --> 00:07:51,670
+وتساوي في الحالة دي ايش؟ ال greatest common
+
+100
+00:07:51,670 --> 00:08:00,130
+divisor لأن ال B تساوي صفر معناه ذلك لما تيجي تعمل
+
+101
+00:08:00,130 --> 00:08:05,470
+return مش هترجع return ال Bانت فعلياً عملت ..
+
+102
+00:08:05,470 --> 00:08:08,290
+غيرتهم .. عملت ال action هذا ال two actions هدول
+
+103
+00:08:08,290 --> 00:08:12,270
+انت عملتهم فعلياً ان ال A أصبحت هي ال B فمعنى ذلك
+
+104
+00:08:12,270 --> 00:08:17,270
+لما أجي أعمل return برجع لل A وضحت .. كتير بسأله
+
+105
+00:08:17,270 --> 00:08:19,270
+كانوا في القصة دي .. اه انت ماشي دكتور و بتقول
+
+106
+00:08:19,270 --> 00:08:23,710
+الصفر و ال B اللي بتضل هي اللي بترجع .. اه بتضل هي
+
+107
+00:08:23,710 --> 00:08:26,790
+اللي بترجع .. بس هذا لو ماعملتش .. لو مش مشمولين
+
+108
+00:08:26,790 --> 00:08:30,340
+ال two statements هدولةفي ال loop لأ هم مشمولين في
+
+109
+00:08:30,340 --> 00:08:34,440
+ال loop فالان بعد ما هذه صارت صفر ابترجع تعمل
+
+110
+00:08:34,440 --> 00:08:39,140
+check على ال B لأ صارت صفر اطلع فانا اللي بديها
+
+111
+00:08:39,140 --> 00:08:44,240
+الان هي ال A مش ال B ال A و ليست ال B اللي هي كانت
+
+112
+00:08:44,240 --> 00:08:48,420
+قيمة A السابقة احنا الان في الحالي احنا الان في
+
+113
+00:08:48,420 --> 00:08:52,080
+الحالي في الحالي لأ بدي قيمة A بس السابقة هي ال B
+
+114
+00:08:52,080 --> 00:08:58,810
+صح كسابقةفإنت جداش فاهم ال code .. قالية كيف ماشي
+
+115
+00:08:58,810 --> 00:09:01,930
+ال code هتسهل عليك إنت إيش اللي بدك إياه مدام أنت
+
+116
+00:09:01,930 --> 00:09:04,390
+مركز في ال code و فاهم إيش اللي بيعملوا خلاص تنتهي
+
+117
+00:09:04,390 --> 00:09:10,850
+القصة طيب فتاخد بالك أن ال two statements هدول
+
+118
+00:09:10,850 --> 00:09:13,010
+مهمين جدا لإن هم اللي عملون ليه عملية ال sorting
+
+119
+00:09:13,010 --> 00:09:17,950
+أنه دائما الأول هو الأكبر الأول كان ترتيبا هو
+
+120
+00:09:17,950 --> 00:09:21,250
+الأكبر فعملنا عملية ال sorting وهذا لازم ومهم جدا
+
+121
+00:09:22,050 --> 00:09:24,150
+في الشغل تبعك إذا بدكش تعملها معناته بدك تعمل
+
+122
+00:09:24,150 --> 00:09:29,810
+reverse في عملية ال ال R بتصير B mod A في الحالة
+
+123
+00:09:29,810 --> 00:09:35,670
+دي ديرو بالكم تمام ال code هذا سريع جدا الحقيقة و
+
+124
+00:09:35,670 --> 00:09:40,150
+مناسب جدا و بسرعة بتحرك أسرع من الطرق اللي أخدناها
+
+125
+00:09:40,150 --> 00:09:46,150
+سابقا طبعا فكرة ان أجوبت أجيب العوامل المشتركة لكل
+
+126
+00:09:46,150 --> 00:09:50,250
+رقم هذا كلام فاضيأفضل من الفاضي لكن الصحيح أنه
+
+127
+00:09:50,250 --> 00:09:53,730
+ممكن نستخدم ال prime factorization لأ هنا أسرع
+
+128
+00:09:53,730 --> 00:09:56,390
+بكتير ال prime factorization انت في الحالة ده
+
+129
+00:09:56,390 --> 00:09:59,270
+هتشتغل بشكل كتير ضخم لإنه بدك تجيب prime
+
+130
+00:09:59,270 --> 00:10:01,550
+factorization للأول و ال prime factorization
+
+131
+00:10:01,550 --> 00:10:06,170
+للتاني و إذا كان الرقم كبير الوضع بصير كارثي لكن
+
+132
+00:10:06,170 --> 00:10:10,130
+هنا انت بتتكلم عن إيش؟ بتتكلم عن طريقة بالظبط
+
+133
+00:10:10,130 --> 00:10:14,170
+عاملة زي ال binary اللي هي بتعملك jump انت بدل ما
+
+134
+00:10:14,170 --> 00:10:19,060
+كنت بتتعامل مع 372 صرت تتعامل مع 44بدل ما كنت
+
+135
+00:10:19,060 --> 00:10:23,880
+تتعامل مع 164 صرت تتعامل مع 32 لحظته ايش اللي
+
+136
+00:10:23,880 --> 00:10:29,240
+بيصير ففعليا logarithmic ففعليا ال code هنا صار
+
+137
+00:10:29,240 --> 00:10:33,580
+logarithmic انت بتعمل jump فبتصير عندك logarithmic
+
+138
+00:10:33,580 --> 00:10:37,360
+بغض النظر ال base تبع ال log بغض النظر ال base
+
+139
+00:10:37,360 --> 00:10:40,180
+احنا قلنا في النهاية كلهم بيظلوا نفس ال order كلهم
+
+140
+00:10:40,180 --> 00:10:44,180
+نفس ال order للأساس العشري للأساس الثنائي ماتفرجش
+
+141
+00:10:44,180 --> 00:10:50,660
+معنا بس في النهاية هنا ال code تبعك هوال big O هو
+
+142
+00:10:50,660 --> 00:10:54,220
+logarithmic، logarithmic لمين منهم؟ للمقسمم، مش
+
+143
+00:10:54,220 --> 00:10:57,660
+هتفرق كتير في النهاية logarithmic، A كبيرة، A
+
+144
+00:10:57,660 --> 00:11:03,500
+صغيرة، ماتفرقش كتير معناه، طيب، اتفضل، انا جيت
+
+145
+00:11:03,500 --> 00:11:07,740
+الطيجة واعتها مية بالمية، بس يعني ليش صح يعني؟ ليش
+
+146
+00:11:07,740 --> 00:11:12,040
+صح يعني؟ كيف احنا من هك و هك و من داخل و داخل؟مش
+
+147
+00:11:12,040 --> 00:11:15,740
+بقولك أن أحيانا في الرياضيات فيها سحر أن فيها
+
+148
+00:11:15,740 --> 00:11:19,560
+علاقات أصلا متجانسة مع بعض العلاقات المتجانسة مع
+
+149
+00:11:19,560 --> 00:11:22,780
+بعض أنت في النهاية greatest common divisor عشان
+
+150
+00:11:22,780 --> 00:11:25,060
+تقول أن فعلا في greatest common divisor أنت في
+
+151
+00:11:25,060 --> 00:11:29,480
+النهاية بدك تقسمهم على بعض صح؟ لأن ال greatest
+
+152
+00:11:29,480 --> 00:11:32,360
+common divisor هو عامل مشترك بمعنى أن الأول يقبل
+
+153
+00:11:32,360 --> 00:11:36,110
+القسم عليه والتاني يقبل القسم عليهفي الآخر كيف بدك
+
+154
+00:11:36,110 --> 00:11:39,970
+تظبط أن الاتنين بيقبلوا القسم على بعض بده يكون رقم
+
+155
+00:11:39,970 --> 00:11:44,530
+لما تعمله model أسماء الأول بيطلع صفر و model
+
+156
+00:11:44,530 --> 00:11:49,150
+أسماء التاني بيطلع صفر، مش هيك؟ فمن هذه الفكرة
+
+157
+00:11:49,150 --> 00:11:53,050
+بتيجي أن معناته طول ما هم مش متفقين وصلوا للصفر
+
+158
+00:11:53,050 --> 00:11:58,410
+معا مع بعضلسه ماوصلتش لل greatest common divisor
+
+159
+00:11:58,410 --> 00:12:01,970
+لما يظلوا مع بعض .. يعني مع بعض الأول مُد الأثلاث
+
+160
+00:12:01,970 --> 00:12:05,750
+تاني و تظلك تاخد اللي هي مشتقاتهم بيصيرش مضعفاتهم
+
+161
+00:12:05,750 --> 00:12:09,050
+مشتقاتهم ال divisors تبعتهم الأصغر الأصغر الأصغر
+
+162
+00:12:09,050 --> 00:12:12,750
+أو المتبقيات بتاعتهم انت بصيره صفر مع أنك متضامن
+
+163
+00:12:12,750 --> 00:12:17,430
+انه وصلت لرقم هو يقبل ال .. الأول يقبل القسم عليه
+
+164
+00:12:17,430 --> 00:12:22,210
+والتاني يقبل القسم عليه لأنه في .. في نهاية سلسلة
+
+165
+00:12:23,070 --> 00:12:27,670
+ال remainders وصلت لصفر مدام وصلت لصفر فاسم يقبل
+
+166
+00:12:27,670 --> 00:12:32,350
+القسم عليه فهي تقبل القسم عليه هي الرياضية فيها
+
+167
+00:12:32,350 --> 00:12:40,570
+حاجات كتير فيها سحر يعني حلوة تمام يعني فرضا مثلا
+
+168
+00:12:40,570 --> 00:12:41,450
+خليني أقولك
+
+169
+00:12:44,780 --> 00:12:49,040
+بعض الأشياء اللي زي ليش مثلا تسعمية و تسعة و تسعين
+
+170
+00:12:49,040 --> 00:12:53,600
+على تسعة زائد تسعة زائد تسعة بساوي تمانية تمانية و
+
+171
+00:12:53,600 --> 00:12:56,300
+تمانين على تمانية زائد تمانية زائد تمانية بساوي
+
+172
+00:12:56,300 --> 00:12:58,860
+سبعمية سبعة و سبعين على سبعة زائد سبعة زائد سبعة
+
+173
+00:12:58,860 --> 00:13:06,630
+هتقوللي ليش الأرقام هيك ال ratio هيكفاهم جصدي؟ هي
+
+174
+00:13:06,630 --> 00:13:10,610
+هيك ال ratio تبعتهم تمام طبعا حاسبوها و دججوا فيها
+
+175
+00:13:10,610 --> 00:13:15,570
+هتلاقوا صحيها دايما طيب نرجع لال .. ال .. ال .. ال
+
+176
+00:13:15,570 --> 00:13:18,850
+.. اللي هي الأرقام و طريقة عد الأرقام احنا كلنا
+
+177
+00:13:18,850 --> 00:13:22,610
+بنعرف ان احنا بنشتغل على ال decimal ال decimal لكن
+
+178
+00:13:22,610 --> 00:13:25,350
+في النهاية في عندي أنظمة أخرى ممكن نتعامل معها
+
+179
+00:13:25,350 --> 00:13:29,050
+بدلاش نخد فيها كتير انتوا طبعا أكيدأدرى في الموضوع
+
+180
+00:13:29,050 --> 00:13:31,350
+هذا واش عارفين الكلام هذا لما بتكلم عن decimal
+
+181
+00:13:31,350 --> 00:13:36,530
+فانا بتكلم عن ten digits from zero to nine هي عندي
+
+182
+00:13:36,530 --> 00:13:40,710
+ال ten digits تبعون ال system هذا بالنسبة لال
+
+183
+00:13:40,710 --> 00:13:44,350
+binary لأ ال binaryواضحة معناته أنا بتكلم عن two
+
+184
+00:13:44,350 --> 00:13:47,810
+digits two digits اللي هو الصفر والواحد لما بتكلم
+
+185
+00:13:47,810 --> 00:13:52,110
+عن ال octal system بتكلم عن التمانية فإذا من الصفر
+
+186
+00:13:52,110 --> 00:13:56,090
+للسبعة هي عدد تمانية عددهم بيطلع تمانية digits لما
+
+187
+00:13:56,090 --> 00:14:00,930
+نتكلم عن ال hexadecimal اللي هو السادس عشر السادس
+
+188
+00:14:00,930 --> 00:14:04,270
+عشر معناته بتكلم عن ستاشر decimal ابتدا من الصفر
+
+189
+00:14:04,270 --> 00:14:08,250
+للخمستعش للخمستعش طب أنا ماعنديش فعليا في طرق العد
+
+190
+00:14:08,250 --> 00:14:12,300
+احنا مااخترعناش حاجة بعد التسعةفحطوا مجموعة ال
+
+191
+00:14:12,300 --> 00:14:15,260
+letters او اول ال letters بداية ال letters بال
+
+192
+00:14:15,260 --> 00:14:19,440
+capital فاطوني اول ستة او الستة المتبقين اللي
+
+193
+00:14:19,440 --> 00:14:22,520
+كانوا ضايقين عننا اللي هم تعاون ال hexa اللي هم
+
+194
+00:14:22,520 --> 00:14:27,540
+تعاون ال hexa a b c d e f فهذا صار ال system اللي
+
+195
+00:14:27,540 --> 00:14:31,200
+موجود كلام انتوا عارفينه اكيد امر عليكوا وازهقتوا
+
+196
+00:14:31,200 --> 00:14:36,500
+منه تمامالان عملية التغيير أو ال conversion من
+
+197
+00:14:36,500 --> 00:14:39,960
+system ل system برضه مش الحاجة الكتير صعبة إذا أنت
+
+198
+00:14:39,960 --> 00:14:44,380
+بتتكلم عن .. بدك تروح ل .. من system كبير ل system
+
+199
+00:14:44,380 --> 00:14:48,160
+أصغر بتبدأ تعمل عملية القسمة و بتجيب ال
+
+200
+00:14:48,160 --> 00:14:52,300
+remainders، إذا من الكبير للصغير، فإذا من العشر
+
+201
+00:14:52,300 --> 00:14:57,020
+بدك تروح لثماني مثلا، فإذا بشتغل كأنه عملت modulus
+
+202
+00:14:58,790 --> 00:15:03,090
+الـ modulus تبعك هذا كأنك تعمل modulo operation
+
+203
+00:15:03,090 --> 00:15:08,670
+فالرقم بالعشري بتجسمه على تمانية بتجسمه على تمانية
+
+204
+00:15:08,670 --> 00:15:14,810
+ايش المتبقي؟ طيب عدد اللفات بترجع تجسمها كمان مرة
+
+205
+00:15:14,810 --> 00:15:19,030
+على تمانية بتشوف ايش المتبقي and so on ففي الآخر
+
+206
+00:15:19,850 --> 00:15:22,150
+الـ remainders اللي موجودين عندك هم اللي بيمثلوا
+
+207
+00:15:22,150 --> 00:15:27,390
+في الآخر الرقم بعد ترتيبه من least significant bit
+
+208
+00:15:27,390 --> 00:15:33,330
+to most significant bit بهذا الشكل فبطلع هذا العدد
+
+209
+00:15:33,330 --> 00:15:39,050
+الموازي لهذا الرقم بس بالمين بال أكتر بيش بال أكتر
+
+210
+00:15:39,050 --> 00:15:45,070
+نفس الكلام اللي بتتكلم من عشري لسادس عشر برضه بدك
+
+211
+00:15:45,070 --> 00:15:49,090
+تجسم عليه الست عشر فالأساس هو اللي ده بتجسم عليهفي
+
+212
+00:15:49,090 --> 00:15:52,630
+الحالة هذه بتكون واضحة عندك الأمور لإنه بتجسم فإيش
+
+213
+00:15:52,630 --> 00:16:00,810
+متبقي بتاخده ك .. بتصير إيش ال a الجديدة ل المدلو
+
+214
+00:16:00,810 --> 00:16:05,790
+متصير ال a الجديدة ل المدلو المتبقي هذا طبعا أول
+
+215
+00:16:05,790 --> 00:16:11,370
+شغل هذا بدك تبدأ تتعامل معاه و ترجعه لقيمته ترجعه
+
+216
+00:16:11,370 --> 00:16:16,570
+لقيمته فعليا جديش عشان تبدأ تتعامل معاه متبقية
+
+217
+00:16:16,570 --> 00:16:20,990
+المتبقي اللي هنابرضه من ال less significant ل ال
+
+218
+00:16:20,990 --> 00:16:26,030
+most significant بترتبهم جان بعض عشان تجيب العنصر
+
+219
+00:16:26,030 --> 00:16:30,150
+النهائي طيب لما بتتكلم من ال binary من ال binary
+
+220
+00:16:30,150 --> 00:16:33,630
+الأمور بتكون شوية أخف أسهل لما بدك تروح لل octal
+
+221
+00:16:33,630 --> 00:16:38,710
+او لل hexadecimal فلو عندك sequence بهذا الشكل او
+
+222
+00:16:38,710 --> 00:16:46,720
+string بهذا الشكل عبارة عن number بال binarysystem
+
+223
+00:16:46,720 --> 00:16:49,880
+automatically إذا بده أروح لثماني عارفين إن
+
+224
+00:16:49,880 --> 00:16:54,400
+الثماني هو كل three digits بشكل تمانية فإذا بجسمهم
+
+225
+00:16:54,400 --> 00:17:04,700
+لتلتات three digits بهذا الشكل وكلنا
+
+226
+00:17:04,700 --> 00:17:10,160
+عارفين إنه صفر في الشمال بيأثرش صفر بالشمال لا
+
+227
+00:17:10,160 --> 00:17:14,870
+يؤثر ف automatically بتشوف جدش الرقم هناأربعة ..
+
+228
+00:17:14,870 --> 00:17:22,350
+سبعة .. واحد .. اتنين .. سبعة .. تلاتة .. فلسنا ..
+
+229
+00:17:22,350 --> 00:17:27,450
+مايه .. وانتهى هذا العليا طيب العكس صحيح برضه لما
+
+230
+00:17:27,450 --> 00:17:31,050
+تكون عندك الرقم من ال octal system ل ال binary
+
+231
+00:17:31,050 --> 00:17:33,610
+system بنفس القلية انت عارف ان كل رقم من الأرقام
+
+232
+00:17:33,610 --> 00:17:38,850
+هدولة بتمثلوا بتلاتة digits فبتروح بتمثل الخمسة ب
+
+233
+00:17:38,850 --> 00:17:43,440
+three digits عونهاالستة بال three digits ساعونها
+
+234
+00:17:43,440 --> 00:17:47,040
+والسبعة بال three digits ساعونها وانتهى طبعا
+
+235
+00:17:47,040 --> 00:17:52,320
+بالhexa كلتا بيكفيش بيصير بدك أربعة مدام هي فعليا
+
+236
+00:17:52,320 --> 00:17:55,980
+انت بتحول لنظام فعلا هو يتوافق تماما مع عدد digits
+
+237
+00:17:56,860 --> 00:18:00,140
+عشان هيك اللي انشهرت اكتر من .. طبعا التساعي فيه
+
+238
+00:18:00,140 --> 00:18:04,420
+تساعي، تسعة مثلا، لكن الانشهر اكتر لأن ال .. ال ..
+
+239
+00:18:04,420 --> 00:18:09,220
+الثماني و ال hexadecimal الست عشر لأنه بالظبط بيجي
+
+240
+00:18:09,220 --> 00:18:12,880
+على عدد ال bits، عندك three bits أو three digits
+
+241
+00:18:12,880 --> 00:18:18,970
+بمثله ال octalfor digits بيمثله ال hexadecimal أما
+
+242
+00:18:18,970 --> 00:18:21,370
+في أنظمة تانية أه في أنظمة تانية يعني أنت بدك تروح
+
+243
+00:18:21,370 --> 00:18:24,690
+للتساعي للسباعي ل .. اعمل اللي بدكيه مافيش مشكلة
+
+244
+00:18:24,690 --> 00:18:28,050
+حول بس بتحول ساعتها بعملية القسمة العادية المطولة
+
+245
+00:18:28,050 --> 00:18:33,210
+لإن مافيش توافق بيصير .. بيصير و مافيش توافقتمام
+
+246
+00:18:33,210 --> 00:18:37,770
+لإيش احنا أخدنا .. خدنا في الموضوع هذا لأن في عند
+
+247
+00:18:37,770 --> 00:18:40,890
+ال binary احنا بنستخدمه كتير .. بنستخدمه كتير في
+
+248
+00:18:40,890 --> 00:18:44,010
+إيش؟ في عملية التشفير واحدة من الأمور انت لما
+
+249
+00:18:44,010 --> 00:18:48,490
+بتبعت ال data عندك في ال transmission linesخطوط
+
+250
+00:18:48,490 --> 00:18:52,470
+الاتصال والتوقع والارسال انت عادة بتبعتها digits
+
+251
+00:18:52,470 --> 00:18:55,870
+بال binary مش هيك مش ال digital كل العلم ال
+
+252
+00:18:55,870 --> 00:18:58,970
+digital اللي الان ماشي ان انت بترسل صفر واحد ممتاز
+
+253
+00:18:58,970 --> 00:19:01,510
+معناه دلك ان صفر واحد اللي انت بعتها دي أحيانا
+
+254
+00:19:01,510 --> 00:19:04,230
+كتير بتكون محتاج تعمل عليها مجموعة عمليات
+
+255
+00:19:04,230 --> 00:19:09,770
+operations ليش؟ منها بعرفش اذا كان أخدتوها مستوى
+
+256
+00:19:09,770 --> 00:19:16,050
+تالت لسه بتهيألي لما يكون عندك مثلاخط إرسال وجايك
+
+257
+00:19:16,050 --> 00:19:19,110
+مجموعة بيانات عبارة عن packets مثلا ال packets هذه
+
+258
+00:19:19,110 --> 00:19:23,490
+بدك تعمل check عليها هل فيها error ولا لأ عشان
+
+259
+00:19:23,490 --> 00:19:26,390
+تعمل عملية correction طيب ممتاز انت عملية ال
+
+260
+00:19:26,390 --> 00:19:28,910
+correction علي إيش بتعملها بتعمل مجموعة عمليات
+
+261
+00:19:28,910 --> 00:19:33,670
+حسابية فعليا على ال digits اللي موجودة صح سواء على
+
+262
+00:19:33,670 --> 00:19:39,160
+ال digits ك bit-wise أو word-wiseمش هتفرق كتير بس
+
+263
+00:19:39,160 --> 00:19:41,660
+في النهاية انت بتعمل مجموعة عمليات عليها وهذا اللي
+
+264
+00:19:41,660 --> 00:19:46,840
+قادنا لفكرة انه بدنا نذكركوا انه في مجموعة systems
+
+265
+00:19:46,840 --> 00:19:49,340
+مختلفة عن ال decimal وعشان هيك الان بدنا ناخد
+
+266
+00:19:49,340 --> 00:19:54,380
+مجموعة acquired على ال binary هتقولي ليش مفيدة؟
+
+267
+00:19:54,380 --> 00:19:56,960
+هقولك بكل بساطة لأن هي بتستخدمها في ال
+
+268
+00:19:56,960 --> 00:20:00,080
+transmission lines انت لما بتيجي بترسل انت بترسل
+
+269
+00:20:00,080 --> 00:20:04,680
+فعليا digit ال digits هذي binary digits يعني يا
+
+270
+00:20:04,680 --> 00:20:07,200
+صفر يا واحد وعشان هيك أصار اسمها العلم digital
+
+271
+00:20:08,440 --> 00:20:10,700
+communication digital communication طب بدك تعمل
+
+272
+00:20:10,700 --> 00:20:14,300
+correction أو بدك تعمل check هل ال check هذا بدك
+
+273
+00:20:14,300 --> 00:20:18,480
+تعملها one إذا كان في one bit error ولا more than
+
+274
+00:20:18,480 --> 00:20:21,160
+one bit error هذه لها techniques و هذه لها
+
+275
+00:20:21,160 --> 00:20:23,960
+techniques بس كلهم في النهاية بيعتمدوا على إنك انت
+
+276
+00:20:23,960 --> 00:20:29,760
+تعمل عمليات الحسابية الأساسية على ال digits هذه
+
+277
+00:20:29,760 --> 00:20:33,720
+طيب عشان نعملها نبدأ بأبسط شغلة أني والله بدي أضيف
+
+278
+00:20:35,810 --> 00:20:39,010
+رقمين binary على بعض نكتب لهم كودة أنا أعرف أن
+
+279
+00:20:39,010 --> 00:20:44,030
+انتوا عارفون تعملوها فأنا مانيين
+
+280
+00:20:44,030 --> 00:20:47,170
+بال code اللي بده يعملها أتوقع ماخدتوش لسه كودة
+
+281
+00:20:47,170 --> 00:20:50,270
+على هيك و لا أخدتوا طيب ممتاز عشان برضه لو
+
+282
+00:20:50,270 --> 00:20:53,890
+انسألتوا فيها في ال data structure تكونوا هي جاهزة
+
+283
+00:20:53,890 --> 00:20:59,620
+عندكم طيب ف procedureعارفين النقاد لأن أنا بعمل
+
+284
+00:20:59,620 --> 00:21:02,700
+إضافة فال code هذا عملية إضافة إضافة ليه إيش؟
+
+285
+00:21:02,700 --> 00:21:05,520
+بنحدد .. بنحدد ال sequence تبعنا هو عبارة عن
+
+286
+00:21:05,520 --> 00:21:11,620
+sequence من A index 0 ل N نقص 1 فأنا عندي فعليا N
+
+287
+00:21:11,620 --> 00:21:18,000
+digits A و B وهذه عبارة عن binary representations
+
+288
+00:21:18,000 --> 00:21:20,660
+with non negative integers يعني احنا مفترض ان هي
+
+289
+00:21:20,660 --> 00:21:22,900
+positive لأن انتوا عارفين جثة ال negative جثة
+
+290
+00:21:22,900 --> 00:21:26,680
+تانية في الها .. هنتكلم عنها قعدنا .. قعدناتمام
+
+291
+00:21:26,680 --> 00:21:30,280
+اول شغل اللي بدنا نحددها هي ال carry ال carry اللي
+
+292
+00:21:30,280 --> 00:21:33,280
+هو بدل ان انت بتجمع فانت عارف ان انت بتجمع مع
+
+293
+00:21:33,280 --> 00:21:36,940
+الحمل مش هيك تجمع مع الحمل فبدنا يكون في خانة
+
+294
+00:21:36,940 --> 00:21:42,640
+space variable يكون لإيش اللي انت بتحمله نتيجة
+
+295
+00:21:42,640 --> 00:21:46,020
+عملية الجمع لل digits هذه okay فحنسميها carry و
+
+296
+00:21:46,020 --> 00:21:52,230
+بداية zero لسه مبدأتش العملية fourال bit index
+
+297
+00:21:52,230 --> 00:21:55,370
+طبعا ال index هو اللي هيكون العامل تبعنا لإن احنا
+
+298
+00:21:55,370 --> 00:21:59,250
+عادة لما بنبنى نجمع بنبنى بنقاش من الأحد الأحد أنا
+
+299
+00:21:59,250 --> 00:22:03,290
+عارف إنه هدى ال index تبعها zero فمعنى ذلك بس
+
+300
+00:22:03,290 --> 00:22:05,930
+تخلصوها بتروحوا للعشرات ال index واحد بعدين
+
+301
+00:22:05,930 --> 00:22:08,450
+بتروحوا للمئات ال index اتنين فمعنى ذلك إنه
+
+302
+00:22:08,450 --> 00:22:11,950
+انتقالي في عملية الجمع هي بناء على ال index أو ال
+
+303
+00:22:11,950 --> 00:22:15,790
+indices تبعتنا هذه فبنحددها بال index يعني حتى
+
+304
+00:22:15,790 --> 00:22:18,390
+المتغيرات اللي بتستعملها لل loop تبعك بدها تكون
+
+305
+00:22:18,390 --> 00:22:23,290
+معبرةفهذه واحدة من أساسيات البرمجة بالمناسبة هي مش
+
+306
+00:22:23,290 --> 00:22:26,430
+حاجة عبثية لأ هي من أساسيات البرمجة و المفروض
+
+307
+00:22:26,430 --> 00:22:29,950
+انتوا عارفين الكلام هذا ال bit index هي ابتداء من
+
+308
+00:22:29,950 --> 00:22:33,610
+الصفر لإيش لإن ناقص واحد بحيث انه مجموحهم in
+
+309
+00:22:33,610 --> 00:22:38,410
+مجموحهم in هي من صفر لإن ناقص واحد begin ابدأ
+
+310
+00:22:38,410 --> 00:22:43,130
+هنبدأ نقول عندي ال bit sum او ال summation لل bits
+
+311
+00:22:43,130 --> 00:22:48,920
+لأنه هاخدها bit by bit هتكون عبارة عن ابال index
+
+312
+00:22:48,920 --> 00:22:52,020
+اللي احنا واقفين عنده اللي هو الأحد هنبدأ .. هنبدأ
+
+313
+00:22:52,020 --> 00:22:55,400
+بالأحد زائد الأحد تعات مين؟ تعات بيه زائد إذا في
+
+314
+00:22:55,400 --> 00:22:58,320
+carry و احنا ال carry مصفرين من الأول لأن يا دو
+
+315
+00:22:58,320 --> 00:23:02,520
+ابن لسه بنبدأ على الأحد مافيش شيء طيب بعد ذلك
+
+316
+00:23:02,520 --> 00:23:08,120
+هنقول ال summation هذه عملية مرحلية و انتوا هيك
+
+317
+00:23:08,120 --> 00:23:10,540
+كنتوا تعملوا فعليا انت كنتوا تعملوا عملية مرحلية
+
+318
+00:23:10,540 --> 00:23:14,720
+قبل ما لسه تحط الرقم انت بتجمع و بتشوف جدش القيمة
+
+319
+00:23:14,720 --> 00:23:16,960
+افرض طلع عندك واحد زائد واحد و كان في ال carry فيه
+
+320
+00:23:16,960 --> 00:23:22,240
+كمان واحديعني فعليا صار عندك تلاتة جمعت تلاتة صحيح
+
+321
+00:23:22,240 --> 00:23:25,900
+طيب التلاتة مش موجودة ضمن ال system ضمن ال system
+
+322
+00:23:25,900 --> 00:23:28,660
+ال binary ولا الإتنين حتى موجودة فعشان هيك إيش
+
+323
+00:23:28,660 --> 00:23:33,720
+بدنا نسوي نقول إن ال S اللي هو ال summation و ال
+
+324
+00:23:33,720 --> 00:23:37,780
+element اللي في العنصر أو موجود في ال index bit
+
+325
+00:23:37,780 --> 00:23:39,840
+index اللي أنا موجود عنده اللي هو الأحد هيكون
+
+326
+00:23:39,840 --> 00:23:48,390
+للناتج يساوي ال bit sum مدله اتنينمدروا اتنين فإذا
+
+327
+00:23:48,390 --> 00:23:52,630
+الناتج هيكون يا صفر يا واحد مافيش اشي تاني يا صفر
+
+328
+00:23:52,630 --> 00:23:56,710
+يا واحد ممتاز خلصناها صفر او واحد ال carry ال
+
+329
+00:23:56,710 --> 00:24:01,150
+carry الآن هو المتبقي مش المفروض هذا المتبقي هيكون
+
+330
+00:24:01,150 --> 00:24:05,390
+اش اللي ضال عندك بعد العملية فهتيجي تقول ال bit
+
+331
+00:24:05,390 --> 00:24:10,770
+sum على اتنين وتاخد ال floor يعني لو كان المجموع
+
+332
+00:24:10,770 --> 00:24:15,340
+تلاتة فعليايعني كان في عندك العنصر الأول one،
+
+333
+00:24:15,340 --> 00:24:20,040
+التاني one، وفي عندك carry هاي صارتلاتة، التلاتة
+
+334
+00:24:20,040 --> 00:24:24,300
+هدول على اتنين واحد و نص، floor واحد، معناته ال
+
+335
+00:24:24,300 --> 00:24:28,900
+carry في واحد، ال carry وجد واحد، end خلصنا هاي
+
+336
+00:24:28,900 --> 00:24:36,360
+إيش حطينا العنصر تعلق حاد عشان نروح لمين؟ للعشرات
+
+337
+00:24:37,120 --> 00:24:40,220
+بس خد بالك إن العشرات الآن قد يكون ال carry إله
+
+338
+00:24:40,220 --> 00:24:45,640
+قيمة صار قد يكون إله قيمة و بستمر لما تخلص لإن
+
+339
+00:24:45,640 --> 00:24:50,100
+ناقص واحد خلصنا إن ناقص واحد انتهى الكلام okay
+
+340
+00:24:50,100 --> 00:24:53,760
+ضايق حاجة لسه ماخدناش بالنا منها إن أنت خلصت لعيني
+
+341
+00:24:53,760 --> 00:24:58,380
+ناقص واحد بس إذا ال carry فيه قيمة فيه إله قيمة
+
+342
+00:24:58,380 --> 00:25:04,880
+القيمة هادة بتروح ليش لإن لأنه أصبح فتحت معاك خانة
+
+343
+00:25:04,880 --> 00:25:09,200
+جديدةزي لما تقول تسعة وتسعين زائد خمسة انت فعلا
+
+344
+00:25:09,200 --> 00:25:13,420
+عندك خنتين بس الناتج صار تلاتة الناتج فعلا بصير
+
+345
+00:25:13,420 --> 00:25:19,120
+تلاتة فمعنى ذلك بده تاخد بالك انه لعند end هنا انت
+
+346
+00:25:19,120 --> 00:25:24,080
+عبيت ال indices تبعونك من صفر ل N نقص واحد طيب ال
+
+347
+00:25:24,080 --> 00:25:28,830
+carry بتحطه في ايش؟ في endصار الآن عندك S هذه ك
+
+348
+00:25:28,830 --> 00:25:34,110
+sequence مخزن لك ناتج عملية الجامعة ابتداء من S
+
+349
+00:25:34,110 --> 00:25:40,310
+012 لندن لندن ف return ب ال sequence هذا return
+
+350
+00:25:40,310 --> 00:25:43,910
+بال sequence هذا اتوقع ان هي بسيطة مش كتير فيها
+
+351
+00:25:43,910 --> 00:25:48,150
+تعقيد ماهياش مشكلة كبيرة فعشان كنا ماشيين ب .. ب
+
+352
+00:25:48,150 --> 00:25:52,710
+.. يعني بطريقة ان انتوا ماخدين عارفين يعني مركزين
+
+353
+00:25:52,710 --> 00:25:57,630
+معنا طيب لما اقول بدي اعمل subtractionعملية الطرح
+
+354
+00:25:57,630 --> 00:26:02,230
+عملية الطرح لأ شوية بدنا نكون حذرين في جزئية من ال
+
+355
+00:26:02,230 --> 00:26:05,190
+binary و احنا بتتعامل مع ال binary عملية الطرح هي
+
+356
+00:26:05,190 --> 00:26:13,370
+معناها ان لما اقول a ناقص b كأني بقول a زائد سالب
+
+357
+00:26:13,370 --> 00:26:21,890
+b سالب b طيب سالب هادي في ال binary فيله قيمة اه
+
+358
+00:26:21,890 --> 00:26:25,900
+ال compliment بس مش ال first complimentال two ..
+
+359
+00:26:25,900 --> 00:26:29,020
+ال two is complement مش ال one complement ال two
+
+360
+00:26:29,020 --> 00:26:33,700
+is complement لأنه لو جيت اشتغلت على ال first او
+
+361
+00:26:33,700 --> 00:26:37,820
+ال .. اه ال one complement و جمعته مع العنصر
+
+362
+00:26:37,820 --> 00:26:41,340
+الأصلي تبعه مش هيطلع معاك صفر بطلعش المجموع صفر
+
+363
+00:26:41,340 --> 00:26:46,740
+بينما وفقليا المفروض يطلع صفر مش هيك منطقي انت
+
+364
+00:26:46,740 --> 00:26:51,770
+اعطي اتخيل لحالك اي قيمة ل Bبال binary و جيب لها
+
+365
+00:26:51,770 --> 00:26:55,790
+ال one complement المفروض انت متخيل ان هو سلب بي
+
+366
+00:26:55,790 --> 00:27:04,990
+طب يجمعهم بطلعش صفر ف plus واحد في ال carry plus
+
+367
+00:27:04,990 --> 00:27:09,230
+واحد ال two's complement ال two's complement بمشي
+
+368
+00:27:09,230 --> 00:27:16,130
+الحال فبتيجي لما تيجي تجمعهم فعليا ال بيتجمعها مع
+
+369
+00:27:16,130 --> 00:27:19,390
+السالب بي بتاعتها انت ضامن انه في الآخر هيروح ليش
+
+370
+00:27:19,390 --> 00:27:26,610
+لزيرو وهو هذا المنطقى كيف انا بقول عليها عكس بي
+
+371
+00:27:26,610 --> 00:27:30,230
+جربوها انتوا اخدتوا طبعا ال one و ال two
+
+372
+00:27:30,230 --> 00:27:32,530
+compliment اتنين ال one compliment اخدتوا و ال two
+
+373
+00:27:32,530 --> 00:27:35,170
+compliment اخدتوا عملتوا check ع الكلام هذا؟
+
+374
+00:27:35,910 --> 00:27:37,730
+المفروض كنت تعمل ال check كمان انت بدك تقل بالظبط
+
+375
+00:27:37,730 --> 00:27:42,470
+خلاص فإذا احنا متفقين ماعناش مشكلة تمام فإذا قيل
+
+376
+00:27:42,470 --> 00:27:48,450
+ال procedures بشكل بسيط بشكل أساسي كانت تالي هنحط
+
+377
+00:27:48,450 --> 00:27:55,610
+ال code تبعنا هيه هي codeنا procedure subtract أي
+
+378
+00:27:55,610 --> 00:28:01,030
+اسم يعبر عن أي عملية اللي بده اعملها ل two binary
+
+379
+00:28:01,030 --> 00:28:05,740
+numbersنمبر أول والتاني عساس انه بدي يكون عبارة عن
+
+380
+00:28:05,740 --> 00:28:12,080
+ال inverse لاحظ inverse يعني مجرد ال once
+
+381
+00:28:12,080 --> 00:28:17,340
+complement اللي هو كل digit بتعكسها فقط هذا ال
+
+382
+00:28:17,340 --> 00:28:21,820
+once complement مش شايف؟ لو حطيت bar فوق فبعرف ان
+
+383
+00:28:21,820 --> 00:28:24,140
+انت بتتكلم عن ال once complement بمعنى اللي هو ال
+
+384
+00:28:24,140 --> 00:28:30,140
+inverseبت وايز بيت وايز ايش يعني يعني بمسكها بت by
+
+385
+00:28:30,140 --> 00:28:33,500
+بت كل بت واحد بجلبها لصفر وكل بت صفر بجلبها لواحد
+
+386
+00:28:33,500 --> 00:28:37,920
+و بس تمام لو جمعتها على الاصلي تبعها مش هتطلع صفر
+
+387
+00:28:37,920 --> 00:28:43,640
+بتطلعش معاك دايما صفر كويس فبنضطر نعمل ال two's
+
+388
+00:28:43,640 --> 00:28:49,250
+complement كيف هنعملها كل الموضوع انه عندكbinary
+
+389
+00:28:49,250 --> 00:28:54,450
+number أول و binary number تاني عكسه انت كل صفر
+
+390
+00:28:54,450 --> 00:28:57,190
+هتجلبها واحد و كل واحد هتجلبه صفر عشان تيجي تعمل
+
+391
+00:28:57,190 --> 00:29:00,210
+.. توصل منه ل two's complement بس ال two's
+
+392
+00:29:00,210 --> 00:29:02,570
+complement عشان تعمل و مش بده تعمل return لاحظ انه
+
+393
+00:29:02,570 --> 00:29:04,990
+دخلنا ع return على طول ليش؟ لأن انا عملت هنا
+
+394
+00:29:04,990 --> 00:29:10,670
+method او function في بعض اللغات التانية عملت
+
+395
+00:29:10,670 --> 00:29:14,390
+calling لمين ل code انت كاتبه سابقا طب احنا كتبناه
+
+396
+00:29:14,390 --> 00:29:18,560
+تول قدمش احنا توي عملنا ال add؟ خلصنا ال add توي
+
+397
+00:29:18,560 --> 00:29:23,300
+عملناها add فانت كله اللي بتعمله add تستدعي ال
+
+398
+00:29:23,300 --> 00:29:26,920
+function اللي اسمها add لمين؟ بتعطيها ال input
+
+399
+00:29:26,920 --> 00:29:36,380
+بتاعتها A و افتح add كمان مرة لمين؟ لل inverse او
+
+400
+00:29:36,380 --> 00:29:41,680
+العكس اللي هو ال once complement ل B و 1 عشان تصير
+
+401
+00:29:41,680 --> 00:29:45,440
+two's complementفناتج الاد هذا هو ال twice
+
+402
+00:29:45,440 --> 00:29:50,740
+complement ل B هو twice complement ل مين؟ ل B انت
+
+403
+00:29:50,740 --> 00:29:56,780
+كان عندك مجموعة digits عكستها و بس فانت بتروح ا
+
+404
+00:29:56,780 --> 00:29:59,400
+روحت على ال once complement once complement فهذه
+
+405
+00:29:59,400 --> 00:30:03,700
+once complement زائد واحد صارت ال twice complement
+
+406
+00:30:03,700 --> 00:30:09,880
+هذه نفسها كناتج بتجمع مع ال A فكأنك جبت A ناقص B
+
+407
+00:30:11,190 --> 00:30:16,390
+خلصت هي خلص الموضوع هي خلص الموضوع بالمناسبة هنا
+
+408
+00:30:16,390 --> 00:30:19,090
+انت بتعملها لمرة واحدة يعني هد مش هيكون في loop
+
+409
+00:30:19,090 --> 00:30:25,250
+هنا مافيش loop لمرة واحدة بتعملها خلاص فكتعقيد لهم
+
+410
+00:30:25,250 --> 00:30:28,790
+ال complexity مش عالية انت لمرة واحدة بتعملها بس
+
+411
+00:30:28,790 --> 00:30:32,770
+لا اكثر ولا اقل تمام ف ..
+
+412
+00:30:35,780 --> 00:30:39,140
+فيش إشكل طيب أحيانا بصير معنى مشكلة فيها في عملية
+
+413
+00:30:39,140 --> 00:30:43,720
+ال .. القذق ال .. اللي هي عملية الطرح هذه عملية
+
+414
+00:30:43,720 --> 00:30:48,760
+الطرح أنه ممكن يكون في عندك carry أكبر من ال N نقص
+
+415
+00:30:48,760 --> 00:30:52,700
+واحد أو في خانة أعلى من ال N نقص واحد ليش؟ لأن انت
+
+416
+00:30:52,700 --> 00:30:57,080
+في النهاية بتتعامل مع add انت حولتها ل add طيب ال
+
+417
+00:30:57,080 --> 00:31:01,940
+carry اللي صار عندك هذا إيش مصيره؟ overflow
+
+418
+00:31:04,600 --> 00:31:08,000
+مش اخدتوا overflow؟ طيب ممتاز هذا overflow ليش؟
+
+419
+00:31:08,000 --> 00:31:11,620
+لأنك انت حولت العملية أصلا لجامعة مدام حمار حولتها
+
+420
+00:31:11,620 --> 00:31:17,460
+لجامعة فتوقع أن ممكن يطلع معاك carry كويس ال carry
+
+421
+00:31:17,460 --> 00:31:25,040
+اللي طلع معاك بكل بساطة اشطبه بكل بساطة احثفه ليش؟
+
+422
+00:31:28,090 --> 00:31:30,830
+لأن أنت بتتعامل مع ال two's complement و أضف إلى
+
+423
+00:31:30,830 --> 00:31:34,030
+ذلك ممكن تظهر في بعض الحالات أنه أساسا الأنصار
+
+424
+00:31:34,030 --> 00:31:41,830
+الأول أصغر من التاني مش هيك قد تظهر ممكن تظهر
+
+425
+00:31:41,830 --> 00:31:45,270
+فمعنى ذلك أنه هتصير انت متلخبط هل هو carry فعليا
+
+426
+00:31:45,270 --> 00:31:50,780
+ولا هو signفكلكوا عارفين أن ال sign كآخر digit
+
+427
+00:31:50,780 --> 00:31:55,380
+عبارة عن واحد فمعناه ذلك أن ال sign تبعتك سالب أو
+
+428
+00:31:55,380 --> 00:31:59,260
+negative فالعنصر negative فانت بتصير انت مش عارف
+
+429
+00:31:59,260 --> 00:32:02,280
+هو المفروض أنه عملية الجامعة اللي أفرزت الواحد هذه
+
+430
+00:32:02,280 --> 00:32:06,540
+ك carry ولا هي لأنه الرقم الأول أصغر من التاني
+
+431
+00:32:06,540 --> 00:32:13,260
+فالمفروض هذه sign فبكل بساطة شيلها فبدك تاخد بالك
+
+432
+00:32:13,260 --> 00:32:17,560
+أن الناتج هيكون لعند إيه ناقص واحد بستمام، الآن
+
+433
+00:32:17,560 --> 00:32:22,280
+نعلى شوية، بدنا نضرب ال binary، بدنا نضرب عملية اه
+
+434
+00:32:22,280 --> 00:32:26,360
+كلهم هتعملوهم، كلهم هتعملهم مع بعض، عملية الضرب
+
+435
+00:32:26,360 --> 00:32:32,840
+الآن عشان نجي نعمل عملية الضرب، شوية هنا بدنا نفصل
+
+436
+00:32:32,840 --> 00:32:39,650
+فيها لأنهحلوة الحقيقة اللي ال code كيف مكتوب هو و
+
+437
+00:32:39,650 --> 00:32:45,450
+ال division فيهم فكرة لو احتجتوها في ال data
+
+438
+00:32:45,450 --> 00:32:50,310
+structure هتنبسطوا عليها عادة لما تكون بدك تعمل
+
+439
+00:32:50,310 --> 00:32:55,190
+مثلا
+
+440
+00:32:55,190 --> 00:33:01,210
+نفترض خلينا نفترض حاجة بهذا الشكل و بدك تضربهم في
+
+441
+00:33:01,210 --> 00:33:08,630
+بعضهاتوا نفكر مع بعض إيش كنا نعمل بنرجع نكرر ..
+
+442
+00:33:08,630 --> 00:33:14,310
+بنكررهم فعليا بس كل مرة ب shift صح؟ تمام فإذا
+
+443
+00:33:14,310 --> 00:33:22,630
+بنيجي بناخد الصفر الأول صفر في واحد صفر واحد كله
+
+444
+00:33:22,630 --> 00:33:34,520
+أصفر طيب التاني بس يبدأ من خيانتهيبدأ من خانته طيب
+
+445
+00:33:34,520 --> 00:33:43,060
+هنا واحد بس هيبدأ من خانته وبتجمع هذه
+
+446
+00:33:43,060 --> 00:33:48,190
+الطريقة اللي بنحكيها كنا ممتازةممتاز معنى ذلك انه
+
+447
+00:33:48,190 --> 00:33:52,770
+انت في كل عملية ضرب هلوقت بنا نطلع بشوية شواهد ايش
+
+448
+00:33:52,770 --> 00:33:55,750
+اللي عملناها بالظبط بدنا نحلل اللي عملناها لأن هذا
+
+449
+00:33:55,750 --> 00:33:59,530
+هو ال code اللي بدنا نشتغله هتنحلل الموضوع فعليا
+
+450
+00:33:59,530 --> 00:34:04,070
+انت لما بتيجي تضرب فيه اي رقم في الخانة في خانة
+
+451
+00:34:04,070 --> 00:34:10,970
+معينة كأنك بتضيف قدامه عدد أصفار بالخانة يعني كأنك
+
+452
+00:34:10,970 --> 00:34:14,390
+انت هنا ضيفت صفر صفركأنك انت هنا ضيفي كمان صفر
+
+453
+00:34:14,390 --> 00:34:18,770
+فلاحظ لما ضربت في الواحد هذا بدأ نطلع واحد بتشوف
+
+454
+00:34:18,770 --> 00:34:26,230
+جداش ال index تبعه و بتضيف عدد أسفار قدامه مش هيك
+
+455
+00:34:26,230 --> 00:34:30,830
+صح يعني هي الفكرة كنا نعملها صح بس ماكنتش كتير
+
+456
+00:34:30,830 --> 00:34:33,630
+معبرة لما كنت بقول shift لأ هي الموضوع أكبر من
+
+457
+00:34:33,630 --> 00:34:37,610
+مجرد shift هي أنا بضيف أسفار الصح أن أنا بضيف
+
+458
+00:34:37,610 --> 00:34:40,810
+أسفار لأنه الآن بدها تبين الأسفار اللي هنضيفها
+
+459
+00:34:41,750 --> 00:34:45,270
+الكمبيوتر مايعرف كلمة shift مايعني shift مش
+
+460
+00:34:45,270 --> 00:34:49,750
+هيفهمها shift هيفهم التالي واضح تهدي اه لإن هو
+
+461
+00:34:49,750 --> 00:34:52,490
+نفسه احنا أكسه على البالكود ال procedure multiply
+
+462
+00:34:52,490 --> 00:34:57,670
+وهي في عند ال two binary numbers بدنا نضربه في بعض
+
+463
+00:34:57,670 --> 00:35:02,830
+بمثله a و b natural number خلاص تمام product zero
+
+464
+00:35:02,830 --> 00:35:06,330
+برضه بدنا نصفر عملية التجميع اللي بدنا نشتغل فيها
+
+465
+00:35:06,330 --> 00:35:09,750
+لأنه لاحظوا أن هي في النهاية عملية تجميع أنا قاعد
+
+466
+00:35:09,750 --> 00:35:15,720
+بجمععملية الضرب ما هي عملية جمع بس حسب الخنات و
+
+467
+00:35:15,720 --> 00:35:20,500
+الأصفار اللي هضيفها لكل خانة طيب نبدأ بال for loop
+
+468
+00:35:20,500 --> 00:35:26,480
+تبعتنا ابتدا من صفر فانا عند الأحد بدأت بالأحد هين
+
+469
+00:35:26,480 --> 00:35:28,800
+بدأ أبدأ أشغل على حد يعني كأنه بدأ أبدأ بالصفر
+
+470
+00:35:28,800 --> 00:35:35,200
+الأول هذا نضربه في الرقم نضربه في الرقم كويسة لعند
+
+471
+00:35:35,200 --> 00:35:39,220
+ما نكمل كل الرقم فإذا كانت بصفر
+
+472
+00:35:41,810 --> 00:35:46,590
+هيها هذه بي صفر تساوي واحد ايش اللي بدنا نعمله؟
+
+473
+00:35:46,590 --> 00:35:51,610
+بدنا ننزل ايه؟ بدنا ننزل ايه؟ فال product هنا
+
+474
+00:35:51,610 --> 00:36:00,410
+بيصير ايه؟ يساوي قيمة a بعدد أصفار حسب ال b بعدد
+
+475
+00:36:00,410 --> 00:36:07,670
+أصفار حسب ال b يعني كأنها بتصير add هيها لأ a وعدد
+
+476
+00:36:07,670 --> 00:36:14,800
+أصفاربال I فانا بديت ب صفر مش محتاج أصفر فبت ..
+
+477
+00:36:14,800 --> 00:36:20,240
+بتنزل ال A زي ما هي لأنه أنا مازلت في الأحد مازلنا
+
+478
+00:36:20,240 --> 00:36:24,940
+في مين؟ في الأحد تنزل كما هي هي ال A ال 101 لو ..
+
+479
+00:36:24,940 --> 00:36:28,040
+لو هنا في عندي واحد فال 101 بتنزل .. اللي هي 101
+
+480
+00:36:28,040 --> 00:36:32,860
+يعني بتنزل زي ما هي هنا مانضفلهاش أي شيء خلاص زي
+
+481
+00:36:32,860 --> 00:36:37,100
+ما هي زائد ال product اللي كان موجود أصلا صفرطيب
+
+482
+00:36:37,100 --> 00:36:44,260
+فعليا اتخزن عندى لان حتى اللحظة الرقم الاول خلاص
+
+483
+00:36:44,260 --> 00:36:54,420
+هذا أصبح said كويس وموجود ضمن product اتنين اي
+
+484
+00:36:54,420 --> 00:36:58,660
+واحد اي واحد معناته بتروح لعنصر اللى ورا and so on
+
+485
+00:36:58,660 --> 00:37:05,710
+بهذا الشكل طيب اذا a و اذا ال b واحديساوي واحد
+
+486
+00:37:05,710 --> 00:37:12,130
+برضه ارجع نزلي A بس على كلامك وماخده shift طب ال
+
+487
+00:37:12,130 --> 00:37:16,990
+shift ده عبارة عن ايش صفر في اليمين معناته زدلي
+
+488
+00:37:16,990 --> 00:37:20,970
+عدد أصفر بقيمة I I قيمتها واحد معناته بزيد صفر
+
+489
+00:37:20,970 --> 00:37:25,670
+واحد فعلا اه هينزدنا صفر واحد فعلا احنا فعلا زدنا
+
+490
+00:37:25,670 --> 00:37:32,360
+صفر واحد تمام و اجمعها على ال product السابقفمعنى
+
+491
+00:37:32,360 --> 00:37:42,380
+ذلك راح جمع الاتنين هدول على بعض مين
+
+492
+00:37:42,380 --> 00:37:46,580
+اللي مش هيتطبّح؟ بالظبط اه اه بالظبط احنا هينا
+
+493
+00:37:46,580 --> 00:37:48,640
+شغالين المفروض ان هو مش هيعمل هذا الكلام اللي لما
+
+494
+00:37:48,640 --> 00:37:51,460
+يتساوي واحد لأنه حتى اللحظة مالهاش معنى اللي احنا
+
+495
+00:37:51,460 --> 00:37:54,220
+عاملينه بالمثال تبعنا المثال تبعنا مالهاش معنى ليش
+
+496
+00:37:54,220 --> 00:37:58,100
+لإن انت بتجمع أصفار فوفر على حالة تجمية الأصفار بس
+
+497
+00:37:58,100 --> 00:38:02,890
+لأكثر ولا قلت انت صارت واحدعند الاتنين مثلا عند
+
+498
+00:38:02,890 --> 00:38:07,150
+الاتنين بدنا نزود واحد سرق قيمتها واحد okay نزلي
+
+499
+00:38:07,150 --> 00:38:14,870
+ال a وعلى يمينها عدد أصفار حسب ال index بتاعت بي
+
+500
+00:38:14,870 --> 00:38:21,410
+طيب جديش index بي؟ اتنين زودلي صفرين على يمينها
+
+501
+00:38:21,410 --> 00:38:24,210
+على ال sequence تبعها لو هذه array انت حاططك الشكل
+
+502
+00:38:24,210 --> 00:38:27,950
+array المعنى انك بتضيفلك صفرين هاي الصفرين
+
+503
+00:38:30,540 --> 00:38:34,040
+فعلا احنا قضفنا صفرين فعملية ال shift هي عملية
+
+504
+00:38:34,040 --> 00:38:38,420
+إضافة أصفر في الضرب هي مش مجرد shift خلاص لأ هي
+
+505
+00:38:38,420 --> 00:38:42,380
+عملية إضافة أصفر ليش؟ لأن انت خلت أصلا الخانة
+
+506
+00:38:42,380 --> 00:38:47,020
+تقعدت تختلف هي بطلت بادية من خانة أحد هي صارت
+
+507
+00:38:47,020 --> 00:38:52,280
+بادية من خانة مئاتطيب معنى ذلك أنه في خانة أحد و
+
+508
+00:38:52,280 --> 00:38:56,180
+عشرات ماحدش بندق لخانة المئات و مالوش في الأحد و
+
+509
+00:38:56,180 --> 00:38:59,160
+العشرات صح؟ مافيش حاجة اسمها هيك أنا والله فجأة
+
+510
+00:38:59,160 --> 00:39:02,700
+بدأت من المئات مافيش اشي هيك اسمه فمدأت .. مدأت من
+
+511
+00:39:02,700 --> 00:39:08,500
+المئات بدي أضيف صفر للعشرات و صفر ليش للأحد خلصنا
+
+512
+00:39:08,500 --> 00:39:12,520
+ال code فضل سؤال ببرمجة أنا ممكن أضيف أصفر جنبها
+
+513
+00:39:12,520 --> 00:39:15,520
+ممكن و لا لازم أعملها method أنا إيش تقولتلك إذا
+
+514
+00:39:15,520 --> 00:39:18,880
+قلتلك إذا أنت متعامل معاها قريه أه بتضيف
+
+515
+00:39:21,470 --> 00:39:23,850
+String ما هي ال array أو ال string او خلاص ما هي
+
+516
+00:39:23,850 --> 00:39:29,030
+string array sequence بتضيفها هالصفرين عليها بمشي
+
+517
+00:39:29,030 --> 00:39:29,270
+الحل
+
+518
+00:39:38,400 --> 00:39:43,180
+لأ لأ عادي عادي بتعملها .. بت .. بدك تعملها هنا
+
+519
+00:39:43,180 --> 00:39:46,600
+method لحالها بتضيف لها four اللي هو في كل مرة
+
+520
+00:39:46,600 --> 00:39:50,540
+بتضيف صفر انت في النهاية على نفس ال array هي هي و
+
+521
+00:39:50,540 --> 00:39:53,160
+ممكن تكون temporary array او temporary string
+
+522
+00:39:54,380 --> 00:39:57,460
+هتستعمله على طول العملية كاملة، ليش؟ لأنه أول مرة
+
+523
+00:39:57,460 --> 00:40:02,560
+أنت هتاخد نسخة من الرقم تبعك، تمام؟ في ال loop ..
+
+524
+00:40:02,560 --> 00:40:05,260
+في ال loop .. ال .. ال .. أول loop في ال loop
+
+525
+00:40:05,260 --> 00:40:09,540
+الأولى، أنت هتضيف one zero، يعني كل اللي هتعمله،
+
+526
+00:40:09,540 --> 00:40:16,960
+method اضيف بس عنصر صفر، بس، في كل لفة هتضيف ..
+
+527
+00:40:16,960 --> 00:40:23,470
+هتضيفلك عنصر، و اتجمعانصر و اتجمع فممكن تعمل ال
+
+528
+00:40:23,470 --> 00:40:26,010
+method و ال method ده تكون عبارة عن كل مرة اضيف
+
+529
+00:40:26,010 --> 00:40:30,150
+واحد لأ
+
+530
+00:40:30,150 --> 00:40:32,750
+اول لفة انا مش هتضيفش ايه هتكون نفس الرقم اللي انت
+
+531
+00:40:32,750 --> 00:40:42,130
+استنسخته من ال a ال a زي ما هي اخدت منها نسخة في
+
+532
+00:40:42,130 --> 00:40:47,060
+temporary space مش هيك او temporary stringOkay
+
+533
+00:40:47,060 --> 00:40:50,100
+وابدأ اشتغل على ال string هذا تمشي احنا هنا زي ما
+
+534
+00:40:50,100 --> 00:40:53,780
+قلتلك كمان مرة في ال pseudocode احنا بنشرح ال
+
+535
+00:40:53,780 --> 00:40:58,760
+concept بعد هيك ممكن طريقة ال Java تختلف ك
+
+536
+00:40:58,760 --> 00:41:02,200
+structure عن ال C++ عن ال Python عن .. okay بس
+
+537
+00:41:02,200 --> 00:41:10,260
+الفكرة واحدة طيب ناخد ال division ال division ايوة
+
+538
+00:41:10,260 --> 00:41:15,660
+خلاص نفهمها كتابة اخدتوها ال division متذكرينها؟
+
+539
+00:41:16,510 --> 00:41:30,930
+طيب ماشي القسمة المطولة اه اظن
+
+540
+00:41:30,930 --> 00:41:33,530
+هذا الرقم اللي هو كان ناتج عندنا صح؟ اعتقد كان
+
+541
+00:41:33,530 --> 00:41:38,070
+ناتج عندنا طيب و هات ناخد هذا فالمتوقع احنا
+
+542
+00:41:38,070 --> 00:41:41,910
+متخيلين ايش اللي لازم يظهر؟ المفروض .. عفوا ايش
+
+543
+00:41:41,910 --> 00:41:44,110
+هذا؟ احنا أخدنا الناتج على طول؟
+
+544
+00:41:48,820 --> 00:41:51,700
+وبدنا النتج هنا واللي احنا متخيله ان الوقش المفروض
+
+545
+00:41:51,700 --> 00:41:59,940
+يطلع 101 اصلا 101 طيب هنا شوية ال code عملها
+
+546
+00:41:59,940 --> 00:42:05,900
+معكوسة عكسها شوية يعني أخد عملية الضرب وافترضها
+
+547
+00:42:05,900 --> 00:42:12,070
+بالعكسأفترضها بشكل عكسي هالوقت هانيش نمشي معها و
+
+548
+00:42:12,070 --> 00:42:15,650
+كل حاجة خطوة نعملها هنا نروح نشتغلها على القسم
+
+549
+00:42:15,650 --> 00:42:19,310
+المطول اللي مكتوب قدامنا بدأ افترض ال procedure و
+
+550
+00:42:19,310 --> 00:42:23,030
+ال division ل ال number تبعنا مافيش أي مشكلة
+
+551
+00:42:23,030 --> 00:42:28,050
+باستخدام الطريقة العادية هالوقت بدأ أقول N هي ال
+
+552
+00:42:28,050 --> 00:42:41,300
+maximum length ما بينو D على اعتبار ان هذا A وهذا
+
+553
+00:42:41,300 --> 00:42:45,060
+D dividend
+
+554
+00:42:45,060 --> 00:42:51,080
+و divisor كويس هنبدأ اللي وابتبعناه من الناقص واحد
+
+555
+00:42:52,290 --> 00:42:57,290
+من N ناقص واحد هنا محدد هو ال length تبع إيش اللي
+
+556
+00:42:57,290 --> 00:43:00,930
+هو ال N محدد ال length على أساس إنه إيش قيمة N
+
+557
+00:43:00,930 --> 00:43:04,370
+يعني بدنا نفرض إنه مين N من الجدشكة هتكون قيمتها
+
+558
+00:43:04,370 --> 00:43:07,650
+هنا N
+
+559
+00:43:07,650 --> 00:43:13,090
+اللي هي ال length of A in bits و ال length of D of
+
+560
+00:43:13,090 --> 00:43:15,470
+lengths و بدنا ناخد ال maximum خمسة
+
+561
+00:43:18,160 --> 00:43:24,520
+صحيح؟ فالأكبر هو ال A ب N تساوي خمسة هنبدأ من
+
+562
+00:43:24,520 --> 00:43:32,140
+أربعة و نكمل و نشوف و نعمل down to فهنا بتصير ال
+
+563
+00:43:32,140 --> 00:43:42,320
+counter عكسي إذا A أكبر من أو يساوي D مع إضافة
+
+564
+00:43:42,320 --> 00:43:44,520
+zeros بعدد الأربعة
+
+565
+00:43:48,260 --> 00:43:53,880
+لأنه هي عكسية لها ديك هتنمسكها شوية شوية يعني كأنه
+
+566
+00:43:53,880 --> 00:43:59,980
+هنا بده يصير ال
+
+567
+00:43:59,980 --> 00:44:04,920
+one صفر صفر وإن ضيف واحد صفر اتنين هاي أربع أصفر
+
+568
+00:44:04,920 --> 00:44:12,740
+هاي أربع أصفر هل ال a أكبر من هذا الرقم أكيد لأ
+
+569
+00:44:12,740 --> 00:44:17,980
+هنا خمسة و هنا صار في عندي سبعةصار عندي سبعة ففي
+
+570
+00:44:17,980 --> 00:44:26,260
+الحالة هذه هنروح ل else ال quotient في الخانة I ب
+
+571
+00:44:26,260 --> 00:44:34,760
+zero فهنا هنبدأ ب zero هنبدأ
+
+572
+00:44:34,760 --> 00:44:38,400
+ب zero تمام بعد هي خلص خلصنا ال loop عشان نرجع
+
+573
+00:44:38,400 --> 00:44:41,980
+لمين لتلاتة
+
+574
+00:44:41,980 --> 00:44:42,640
+100%
+
+575
+00:44:49,320 --> 00:44:56,460
+هل ايه أكبر كمان
+
+576
+00:44:56,460 --> 00:45:03,820
+صفر اتنين
+
+577
+00:45:03,820 --> 00:45:07,960
+اه
+
+578
+00:45:07,960 --> 00:45:12,500
+تمام أكبر بروحش ل else هنروح لمين نبدأ في ال then
+
+579
+00:45:12,500 --> 00:45:17,100
+then أول شغلة ال caution تبعك بواحد okay
+
+580
+00:45:19,420 --> 00:45:25,140
+هي واحد بعدين ال a بدها تتغير حسب القسم المطول
+
+581
+00:45:25,140 --> 00:45:31,560
+المفروض أنه اطرحهم فبنعمل طرح بنفس عدد الأصفر يعني
+
+582
+00:45:31,560 --> 00:45:36,540
+معناه ذلك أن هذا الرقم اللي هو هيطرح مش هذا هذا
+
+583
+00:45:36,540 --> 00:45:40,080
+الرقم اللي هو هيطرح هيها بعدد أصفره بعدد الأصفر
+
+584
+00:45:40,080 --> 00:45:42,940
+تبعته فكأنه أصبح ال
+
+585
+00:45:45,270 --> 00:45:48,230
+العنصر عندي هنا أكمل صفر قدامه أربعة هاي واحد
+
+586
+00:45:48,230 --> 00:46:00,150
+اتنين تلاتة أربعة واحد صفر صفر واحد صفر صفر تمام
+
+587
+00:46:00,150 --> 00:46:05,310
+اللي عندك الآن جيد بهذا الشكل خلصنا أول جزء خلصنا
+
+588
+00:46:05,310 --> 00:46:09,350
+الاتنين هيك الواحد
+
+589
+00:46:18,380 --> 00:46:28,960
+A أكبر منه؟ أكيد لأ فإذا بنضيف صفر خلاص
+
+590
+00:46:28,960 --> 00:46:38,360
+خلصت أصلا طيب أخر شي صفر اللي هو أخر عنصر عندي صفر
+
+591
+00:46:38,360 --> 00:46:43,580
+أخر عنصر خلاص صح؟ هدا الصفر أخر عنصر ففي
+
+592
+00:46:43,580 --> 00:46:47,390
+الحالة دي أكبر أو يساوي؟ أه هو يساوي فعليامعناته
+
+593
+00:46:47,390 --> 00:46:57,070
+أول شغلة حط واحد و اطرح without
+
+594
+00:46:57,070 --> 00:47:03,330
+remainder بدون باقي كمان هل هو المتوقعين و الحل
+
+595
+00:47:03,330 --> 00:47:07,990
+المتوقعين فيه هو الحل المتوقعين فيه فبطريقة عكسية
+
+596
+00:47:07,990 --> 00:47:13,690
+عن عملية الضرب بطريقة عكسية عن عمليةالضرب المتبعة
+
+597
+00:47:13,690 --> 00:47:17,810
+فهي ال code اللي ممكن نستخدمه لعملية ال division
+
+598
+00:47:17,810 --> 00:47:21,150
+لل binary ليش لل binary؟ هاي code مكتوب و مرتب و
+
+599
+00:47:21,150 --> 00:47:27,850
+مظبط و جيد الآن في عندنا شوية تطبيقات مهمة على
+
+600
+00:47:27,850 --> 00:47:29,930
+نظريات الأعداد اللي احنا هيك اتكلمنا عنها اللي
+
+601
+00:47:29,930 --> 00:47:33,070
+أخدناها النظرية التطبيقات دي لها تطبيقات كتير
+
+602
+00:47:33,070 --> 00:47:37,290
+الحقيقة و معظمها حاجات اللي لها علاقة بالتشفيرأو
+
+603
+00:47:37,290 --> 00:47:41,490
+التكويض أو ال encryption في مثلا ال hash functions
+
+604
+00:47:41,490 --> 00:47:44,890
+في عملية ال simulation عملية ال games بناء ال
+
+605
+00:47:44,890 --> 00:47:48,570
+games و ال graphics معتمدة بشكل مش طبيعي على نظرية
+
+606
+00:47:48,570 --> 00:47:52,650
+الأرقام و جدش أنت ماهر في التعامل مع الأرقام جدش
+
+607
+00:47:52,650 --> 00:47:56,230
+أنت بتقدر تتعامل مع الأرقام و تشتغل الشغل اللي
+
+608
+00:47:56,230 --> 00:47:59,050
+أخدناه خلال المحاضرة السابقة و بداية المحاضرة
+
+609
+00:47:59,050 --> 00:48:04,810
+لليوم اللي احنا هنركز عليه فعليا هيالجزئية ال
+
+610
+00:48:04,810 --> 00:48:08,750
+random كيف انا ممكن اعمل generalization او
+
+611
+00:48:08,750 --> 00:48:14,730
+generation ل random numbers مجموعة ارقام عشوائية
+
+612
+00:48:14,730 --> 00:48:21,590
+لانه بدي استخدمها as a mask ك mask تضرب فيها ال
+
+613
+00:48:21,590 --> 00:48:25,050
+data اللي عندك و تبعتها لو انا شفتها مافهمش منها
+
+614
+00:48:25,050 --> 00:48:31,840
+اشي انا مش هفهم منها حاجةبالنسبالي و لا عارف إيش
+
+615
+00:48:31,840 --> 00:48:35,520
+اللي بعدته، لكن في نفس الوجد ال .. ال random هذا
+
+616
+00:48:35,520 --> 00:48:39,100
+لازم تكون انت قادر ترجع ال word له كمان مرة، مش
+
+617
+00:48:39,100 --> 00:48:41,380
+والله random معناته بكل ما تعنيه الكلمة random
+
+618
+00:48:41,380 --> 00:48:47,090
+خلاص هو راح، فبنسميها pseudo randomشبه عشوائي ليش
+
+619
+00:48:47,090 --> 00:48:51,250
+شبه عشوائي؟ لأن انت بتقدر ترجع تجيبه كمان مرة ترجع
+
+620
+00:48:51,250 --> 00:48:54,190
+تقدر تجيبه ليش؟ لأنك انت بعد ما بعدت ال message
+
+621
+00:48:54,190 --> 00:48:56,850
+بعد أسبوع زمان تنسيت أصلاش اللي كنت كاتبه طب أنا
+
+622
+00:48:56,850 --> 00:49:01,290
+بدي أرجع أفك تشفيرها بدنا نرجع نفك تشفيرها عشان
+
+623
+00:49:01,290 --> 00:49:06,550
+تفهمها أو بدك تبعتها لحدة و أنت متفق بينك و بينه
+
+624
+00:49:06,550 --> 00:49:11,790
+كيف ممكن يعيد توليد ال random numbers عشان يرجع
+
+625
+00:49:11,790 --> 00:49:17,370
+يفك و يفهم انت اش كاتبلهيفهم أيش كتبله تمام فهذه
+
+626
+00:49:17,370 --> 00:49:19,870
+هي أكتر أشياء هنشتغل عليها فهنروح لل linear
+
+627
+00:49:19,870 --> 00:49:22,730
+congruential method ال linear congruential method
+
+628
+00:49:22,730 --> 00:49:26,950
+عشان نتعامل معها هي ببساطة جدا تعملنا مجموعة
+
+629
+00:49:26,950 --> 00:49:30,830
+random numbers ال random numbers هذه محتاجين
+
+630
+00:49:30,830 --> 00:49:34,590
+مجموعة parameters عشان نبني ال model تبعنا ال
+
+631
+00:49:34,590 --> 00:49:38,630
+model ببساطة بده ال modulus ال modulus M بدك تحدد
+
+632
+00:49:38,630 --> 00:49:42,550
+قيمة له و بدك تحدد multiplier A قيمة لل A
+
+633
+00:49:49,170 --> 00:49:56,030
+وانصر ابدا فيه هنسميه seed البذرة اللي هتبدأ منها
+
+634
+00:49:56,030 --> 00:50:01,130
+عملية ال generation بحيث ان ال Aاللي هو ال
+
+635
+00:50:01,130 --> 00:50:05,990
+multiplier مايكونش أكبر من ال modulus و يكون اتنين
+
+636
+00:50:05,990 --> 00:50:09,170
+فأكثر مايكونش واحد لإنه ماعرفش معناه واحد في حاجة
+
+637
+00:50:09,170 --> 00:50:11,830
+اسمها multiplier واحد مع أن معناته ماضربتش في إشي
+
+638
+00:50:11,830 --> 00:50:16,210
+صحيح فهو بده يكون على الأقل اتنين فأكثر ال C بتكون
+
+639
+00:50:16,210 --> 00:50:20,530
+أكبر من صفر أو تساوي صفر فإذا كانت تساوي صفر فهي
+
+640
+00:50:20,530 --> 00:50:27,270
+معناته without incrementالـ seed الطبيعي و المنطقي
+
+641
+00:50:27,270 --> 00:50:31,310
+و العجل بيقول أنه لازم تكون أقل من ال modulus ال
+
+642
+00:50:31,310 --> 00:50:35,850
+modulus هذا كأني أقول مثلا ال modulus ألف ألف ألف
+
+643
+00:50:35,850 --> 00:50:38,850
+إيش يعني؟ معناته أنا جاعت بولد أرقام أقل من الألف
+
+644
+00:50:38,850 --> 00:50:43,930
+أنا جاعت بعمل generations لعناصر عشوائية بس أنا
+
+645
+00:50:43,930 --> 00:50:47,050
+عارف أن كلها أقل من الألف طيب ال modulus هذا عملته
+
+646
+00:50:47,050 --> 00:50:51,450
+عشر تلاف فانت جاعت بتولد أرقام أقل من عشر تلاف and
+
+647
+00:50:51,450 --> 00:50:55,360
+so on بهذا الشكلعشان هيك هذه مهمة فما دام linear
+
+648
+00:50:55,360 --> 00:50:59,120
+هنحطها في معادلة linear بتصير مجموعة ال parameters
+
+649
+00:50:59,120 --> 00:51:04,180
+هدولة في المعادلة ال linear بتاعتنا كأنه العنصر
+
+650
+00:51:04,180 --> 00:51:07,880
+اللي هو ال generated number الجديد اللي بده ييجي
+
+651
+00:51:07,880 --> 00:51:12,560
+اللي هو n زائد واحد هو جاي من xn من العنصر اللي
+
+652
+00:51:12,560 --> 00:51:16,120
+جابله بعد ما ضربناه في ال multiplier وجمعناه من ال
+
+653
+00:51:16,120 --> 00:51:23,680
+incrementmodulo للمجرس اللي اختارنا للأمن تمام في
+
+654
+00:51:23,680 --> 00:51:26,680
+الحالة هذه هيكون اعطاني رقم جديد بدي الرقم اللي
+
+655
+00:51:26,680 --> 00:51:32,060
+ورا بستعمل الرقم هذا في المعادلة بجيب n زائد 2
+
+656
+00:51:32,060 --> 00:51:39,120
+بستخدمها في المعادلة اجيب n زائد 3 ممتاز كمعادلة
+
+657
+00:51:39,120 --> 00:51:43,120
+الكل عرفها لكن ماحدش عارف انت ايش ال parameters
+
+658
+00:51:43,120 --> 00:51:46,370
+اللي خدتماحدش عارف إيش ال parameters اللي أخدتها
+
+659
+00:51:46,370 --> 00:51:50,810
+فانت هتبعتلي ال message و تبعتلي معاها العناصر
+
+660
+00:51:50,810 --> 00:51:54,810
+هدول مشفرين مثلا فانا بفكهم بعرفهم برجع برجع بولد
+
+661
+00:51:54,810 --> 00:51:58,850
+ال mask كمان مرة أو برجع بعيد ال random numbers
+
+662
+00:51:58,850 --> 00:52:04,230
+كمان مرة فعرفت انت إيش اللي كنت باعته تمام فببساطة
+
+663
+00:52:04,230 --> 00:52:12,440
+بهذا الشكل الآن معظم العناصر هذه عشان تضمن تضمنإنه
+
+664
+00:52:12,440 --> 00:52:17,740
+التباين عالي للأرقام اللي بتولدها يكون عالية
+
+665
+00:52:17,740 --> 00:52:21,260
+التباين لازم تكون الأرقام هذه و بيميلوا أن هم
+
+666
+00:52:21,260 --> 00:52:27,180
+trends بيروحوا أن تكون الأرقام هذه primes ليش
+
+667
+00:52:27,180 --> 00:52:33,980
+primes؟ الprimes لأنه بضمن أو على الأقل إذا ماكنوش
+
+668
+00:52:33,980 --> 00:52:38,100
+primes pure primes كلهم يعني على الأقل هم ما بينهم
+
+669
+00:52:38,100 --> 00:52:42,450
+وبين بعض relative primesليش؟ لأنه لما نقول
+
+670
+00:52:42,450 --> 00:52:47,930
+relative primes معناه ذلك ببساطة أنه ال greatest
+
+671
+00:52:47,930 --> 00:52:53,030
+common divisor between them واحد يعني مافيش عناصر
+
+672
+00:52:53,030 --> 00:52:59,810
+أقل من M كلهم يقبل القسم عليها هذا بيعطيك تنوع
+
+673
+00:52:59,810 --> 00:53:06,210
+أكبر لأنه لو كان في عناصر بينهم مشتركة هذا بيعني
+
+674
+00:53:06,210 --> 00:53:12,840
+أنه هيكون عندكيعني بطريقة أو باخرى التكرار هيكون
+
+675
+00:53:12,840 --> 00:53:18,860
+مسافاته أقرب أنا بقول random صح؟ ممتاز، بس في
+
+676
+00:53:18,860 --> 00:53:22,740
+الحالة هذه random يعني بولد مجموعة عناصر، لو
+
+677
+00:53:22,740 --> 00:53:27,100
+العنصر الأول اتكرر، ظهر معي، اللي برا كله هيظهر،
+
+678
+00:53:27,100 --> 00:53:31,460
+لأن المعادلة واحدة يعني كأنه رجعت عيدتها بنفس X
+
+679
+00:53:31,460 --> 00:53:35,740
+node أكيد هيرجع X1 زي ما هو يرجع، X2 يرجع، هذه هي
+
+680
+00:53:35,740 --> 00:53:39,170
+الثغرة اللي ال hackers بدوروا عليهاالـ hackers
+
+681
+00:53:39,170 --> 00:53:42,850
+بدورك على إيه انت وين صار التكرار وين بيصير
+
+682
+00:53:42,850 --> 00:53:46,890
+التكرار بمسك التكرار أول شغلة بجيب المسافة دي عارف
+
+683
+00:53:46,890 --> 00:53:52,270
+الموديلوس الموديلوس M عارفها خلصت هي ضربلك أول
+
+684
+00:53:52,270 --> 00:53:56,790
+شغلة و ببدأ بنوعنا عليا شوية شوية في سلسلة من ال
+
+685
+00:53:56,790 --> 00:53:59,730
+procedures اللي بيعملها عشان يكسر كل ال code يفكلك
+
+686
+00:53:59,730 --> 00:54:03,530
+إياه كله انت كيف تتصعب الموضوع عليه؟
+
+687
+00:54:05,010 --> 00:54:08,150
+ممكن مايكونش نفسه هذا إيه له شرط اللي هو المفروض
+
+688
+00:54:08,150 --> 00:54:12,190
+في ال slide اللي ورا هذي هناخده انه العناصر ما
+
+689
+00:54:12,190 --> 00:54:16,750
+بينها و بين بعض اللي هو مايكون .. مايكونلهاش او
+
+690
+00:54:16,750 --> 00:54:22,510
+عفوا يكونلها inverse inverse وحيد داخل ال one
+
+691
+00:54:22,510 --> 00:54:26,570
+period إذا كان عندك أكتر من inverse داخل ال one
+
+692
+00:54:26,570 --> 00:54:31,990
+period بنفعش هذا code بنفعش يكون code لازم يكون
+
+693
+00:54:32,750 --> 00:54:37,070
+Unique Inverse للعناصر اللي بتظهر معاك او لل
+
+694
+00:54:37,070 --> 00:54:41,570
+parameters هذه عشان تضمن ان انت استغلت كل ال
+
+695
+00:54:41,570 --> 00:54:46,750
+modulus كامل على بعضه افرض
+
+696
+00:54:46,750 --> 00:54:51,790
+الف ممكن التكرار يظهر لك بعد خمسمية او بعد متين و
+
+697
+00:54:51,790 --> 00:54:56,290
+خمسين اتلاقي صار فيه تكرارات طبعا هذا بيصير ال
+
+698
+00:54:56,290 --> 00:54:59,910
+code hashال code هذا مدام تكراراته جريبة من بعض
+
+699
+00:54:59,910 --> 00:55:07,470
+هذا هاش جدا ك security لبرايمز لبرايمز لأ بتكون
+
+700
+00:55:07,470 --> 00:55:10,890
+التكرارات كتير أجل من هيك كتير بتكون أجل من هيك
+
+701
+00:55:10,890 --> 00:55:14,870
+إذا كان ال C أفوان
+
+702
+00:55:14,870 --> 00:55:18,290
+C تساوى صفر معناه ذلك إن هي pure multiplicative
+
+703
+00:55:18,290 --> 00:55:23,210
+ليش؟ لأن مافيش ال increment هي معادلة ضربية بس
+
+704
+00:55:24,500 --> 00:55:30,560
+معادلة ضربية وليست linear هي linear أه بلس مش
+
+705
+00:55:30,560 --> 00:55:32,680
+complete linear لأنه في جزء من ال linearity
+
+706
+00:55:32,680 --> 00:55:37,360
+مااتحققتش مثال هاي مثال مثلا لو ال modulus عندك
+
+707
+00:55:37,360 --> 00:55:44,860
+الف زي ما قلنا و ال Cأربعمية و سبعة و ستين ال a
+
+708
+00:55:44,860 --> 00:55:49,380
+بدأنا بتلت مية اشتغلناها تلت مية تلائم متين تلاتة
+
+709
+00:55:49,380 --> 00:55:54,340
+وتسعين و ال seed أربعمية ستة و عشرين معادلة و
+
+710
+00:55:54,340 --> 00:55:58,680
+بتطبقها لا أكثر ولا أقل فبدك تجيب x واحد باستخدام
+
+711
+00:55:58,680 --> 00:56:04,130
+x node اللي هي ال seedعشان تطلع رقم هو نفسه
+
+712
+00:56:04,130 --> 00:56:08,230
+تستخدمه ك X1 عشان تجيب منه X2 and so on بهذا الشكل
+
+713
+00:56:08,230 --> 00:56:13,210
+و تظهر عندك أرقام عشوائية تبدو ان هي عشوائية فهي
+
+714
+00:56:13,210 --> 00:56:16,630
+هيك فعليا تبدو ان هي عشوائية لكن انت جادر ترجع
+
+715
+00:56:16,630 --> 00:56:19,570
+تعيدها كمان مرة جادر ترجع تعملها generation كمان
+
+716
+00:56:19,570 --> 00:56:24,090
+مرة and so on بتضلك مستمر في الحالة هذه لاحظ انه
+
+717
+00:56:24,090 --> 00:56:30,510
+odd even بتشغل الكلام هذا لأن ال M عندكeven فدي
+
+718
+00:56:30,510 --> 00:56:34,010
+واحدة من الشواهد برضه و من سحر الأرقام يعني أنه
+
+719
+00:56:34,010 --> 00:56:38,490
+إذا كانت ال .. ال .. ال modulus even فبصير يعملك
+
+720
+00:56:38,490 --> 00:56:42,650
+تبديل ما بين العناصر اللي بيعطيك إياها مرة فردية
+
+721
+00:56:42,650 --> 00:56:45,610
+مرة زوجية مرة فردية مرة زوجية فهذه شواهد إذا كده
+
+722
+00:56:45,610 --> 00:56:48,470
+مثلا ال hackers برضه بيستفيدوا من الحاجات اللي ..
+
+723
+00:56:48,470 --> 00:56:51,830
+أه بيستفيد من الحاجات اللي زي هذه المعلومات زي هذه
+
+724
+00:56:51,830 --> 00:56:55,930
+بيستفيد منها بيفهم منها بتعطي indication أن والله
+
+725
+00:56:55,930 --> 00:57:01,110
+إيش ممكن يكون ال .. ال modulusتمام هاي كمان مثال
+
+726
+00:57:01,110 --> 00:57:05,930
+اكبر شوية و اوضح شوية كررناها بشكل كامل لما قولنا
+
+727
+00:57:05,930 --> 00:57:09,390
+ال modulus تسعة تسعة معناته انا متوقع انه هيعمل لي
+
+728
+00:57:09,390 --> 00:57:15,410
+تسعة random numbers و يرجع يتكرر تاني لانه مش
+
+729
+00:57:15,410 --> 00:57:18,670
+هيخترع جديد بعد هيك خلص كل ال elements اللي في ال
+
+730
+00:57:18,670 --> 00:57:23,090
+.. ضمن ال modulus طبعه ال multiplier سبعة ال C
+
+731
+00:57:23,090 --> 00:57:28,650
+باربعة و ال seedتلاتة فبدأنا بالتلاتة X node
+
+732
+00:57:28,650 --> 00:57:35,270
+بالتلاتة صار في عندك تلاتة سبعة تمانية ستة واحد
+
+733
+00:57:35,270 --> 00:57:40,870
+اتنين صفر اربعة تلاتة طب لو كملنا ايش هيظهر اكيد
+
+734
+00:57:40,870 --> 00:57:46,570
+اكيد خلاص اتكرر اتكررت فإذا تعالي امسك اه دي ال
+
+735
+00:57:46,570 --> 00:57:53,010
+modulus ايش تسعةوالله بدها تتعجب فيها تصير من
+
+736
+00:57:53,010 --> 00:57:56,290
+مضاعفات التسعة مثلا لو كان في أكتر من inverse لها
+
+737
+00:57:56,290 --> 00:58:00,550
+بدها تصير من مضاعفات التسعة فما اختلفتش مابعتش
+
+738
+00:58:00,550 --> 00:58:06,630
+كتير فانت في الآخر بين معلومة مهمة في ال code بينت
+
+739
+00:58:06,630 --> 00:58:10,390
+معلومة كتير مهمة في ال code طيب عادة إيش اللي كتير
+
+740
+00:58:10,390 --> 00:58:13,490
+الناس بفضله يستخدموها أو يستخدمها كتير هي ال pure
+
+741
+00:58:13,490 --> 00:58:18,140
+multiplicativeبهذا المعادلة بهذا الشكل اتنين to
+
+742
+00:58:18,140 --> 00:58:22,600
+the power واحد تلاتين ناقص واحد هذه قيمة المجلس
+
+743
+00:58:22,600 --> 00:58:28,580
+هذه المجلس اللي هي ال M اللي هي قيمة M هنا فجدش
+
+744
+00:58:28,580 --> 00:58:31,900
+بيستخدموها بفضلوا استخدامها اتنين to the power
+
+745
+00:58:31,900 --> 00:58:35,880
+واحد تلاتين ناقص واحد على أساس ال prime على أساس
+
+746
+00:58:35,880 --> 00:58:40,960
+ال prime طيب و ال multiplier سبعة to the power
+
+747
+00:58:40,960 --> 00:58:52,360
+خمسةفبطلع الرقم حوالي 16807 هذا بيعطيك عدد
+
+748
+00:58:52,360 --> 00:58:55,780
+elements قبل ما ترجع تتكرر حوالي اتنين to the
+
+749
+00:58:55,780 --> 00:59:01,930
+power واحد تلاتين ناقص اتنين يعني حوالي اتنينجداش
+
+750
+00:59:01,930 --> 00:59:10,630
+billion و 147 مليون و 493 647
+
+751
+00:59:10,630 --> 00:59:15,610
+random numbers قبل ما يرجع يتكرر قبل ما يرجع يتكرر
+
+752
+00:59:15,610 --> 00:59:21,090
+فرقم مقبول يعني رقم جيدخلّينا نقول يتشغّل فيه ال
+
+753
+00:59:21,090 --> 00:59:25,910
+hacker قبل ما يشغّل عليه أو يفك تشفيرته .. يفك
+
+754
+00:59:25,910 --> 00:59:29,510
+تشفيرته .. طيب المرة القادمة بدنا نتكلم برضه في
+
+755
+00:59:29,510 --> 00:59:34,090
+نفس القالية أنا صار انديل N بتعامل مع معادلة خطية
+
+756
+00:59:34,090 --> 00:59:38,230
+.. كلكم عارفين أن معادلة الخطية عشان نجيب قيمة X
+
+757
+00:59:38,230 --> 00:59:41,870
+بتاعتها محتاجين نجيب ال inverse لل coefficient
+
+758
+00:59:43,240 --> 00:59:45,340
+الانفرس هي ال coefficient فهذا موضوعنا المرة
+
+759
+00:59:45,340 --> 00:59:50,280
+القادمة اللي هو هيكون عندك ax equivalent او
+
+760
+00:59:50,280 --> 00:59:56,660
+congruent ل b كويس فبد قيم x اللي تحقق هذه
+
+761
+00:59:56,660 --> 01:00:01,720
+المعادلة اكيد طبعا بيصير بدنا نجيب ال inverse كلنا
+
+762
+01:00:01,720 --> 01:00:04,740
+عارفين ال inverse في الرياضيات العادية بس كيف
+
+763
+01:00:04,740 --> 01:00:11,170
+نتعامل معها في ال moduloقصة تانية .. قصة تانية
+
+764
+01:00:11,170 --> 01:00:14,430
+بدنا نتعامل فيها المرة الجاية و نبدأ نشتغل عليها و
+
+765
+01:00:14,430 --> 01:00:18,750
+ناخد عليها أمثلة و بالمناسبة من الأمثلة اللي كتير
+
+766
+01:00:18,750 --> 01:00:22,670
+بتيجي في الامتحاناتلما تدخل كمان على الـ
+
+767
+01:00:22,670 --> 01:00:27,310
+Sodoprimes اللى هى أرقام شبيهة لـ Primes هدى لو
+
+768
+01:00:27,310 --> 01:00:30,670
+انت زى ما بيقوله عجزت انه مش لاجي برايم مناسب لل
+
+769
+01:00:30,670 --> 01:00:34,170
+code تبعك ممكن تتعامل معاها كيف تعملها generation
+
+770
+01:00:34,170 --> 01:00:38,350
+كيف تجيبها برضه هنتكلم عنها لأن هدى بتفيدك بكرا في
+
+771
+01:00:38,350 --> 01:00:40,430
+ال security بكرا بتفيدك في ال security لما بدك
+
+772
+01:00:40,430 --> 01:00:43,110
+تعمل تشفير و بدك تعمل encryption بدك تعمل هدى
+
+773
+01:00:43,110 --> 01:00:45,350
+أرقام كتير مهمة يعطيكوا العافية و نكمل المرة
+
+774
+01:00:45,350 --> 01:00:46,150
+القادمة ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wu4ONEGCIa0_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wu4ONEGCIa0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..13e12727c6487b0663f17a0a5f21fe9cb6f9add1
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wu4ONEGCIa0_raw.json
@@ -0,0 +1 @@
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صفر مع أنك متضامن انه وصلت لرقم هو يقبل ال .. الأول يقبل القسم عليه والتاني يقبل القسم عليه لأنه في .. في نهاية سلسلة", "tokens": [1211, 3794, 3224, 19446, 2407, 36520, 2655, 8592, 24976, 6636, 2689, 25974, 284, 5296, 15042, 7251, 19913, 1211, 14407, 20449, 45030, 11242, 4386, 37495, 22653, 20449, 45030, 11242, 16247, 12610, 3714, 10859, 3215, 16247, 12984, 1211, 5718, 104, 6055, 7649, 1829, 4032, 6055, 19913, 1211, 4117, 6055, 47283, 3215, 13672, 1829, 39896, 37893, 2655, 4587, 9307, 16095, 4724, 1829, 9381, 13546, 8592, 3714, 11242, 3615, 5172, 9307, 16095, 37893, 2655, 4587, 9307, 16095, 2423, 25974, 830, 6055, 3555, 34268, 16095, 16247, 9381, 17082, 2288, 16247, 9381, 17082, 2288, 16247, 9381, 17082, 2288, 34051, 9673, 2655, 3555, 38436, 9307, 39894, 995, 34268, 16095, 16472, 2655, 4724, 9381, 13546, 3224, 20328, 5172, 2288, 20449, 14739, 4117, 44650, 11242, 10943, 1863, 16472, 3224, 4032, 36520, 2655, 5296, 2288, 4587, 2304, 31439, 7251, 4587, 36150, 2423, 4386, 16247, 12610, 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"end": 807.57, "text": "فاهم جصدي؟ هي هيك ال ratio تبعتهم تمام طبعا حاسبوها و دججوا فيها هتلاقوا صحيها دايما طيب نرجع لال .. ال .. ال .. ال .. اللي هي الأرقام و طريقة عد الأرقام احنا كلنا بنعرف ان احنا بنشتغل على ال decimal ال decimal لكن في النهاية في عندي أنظمة أخرى ممكن نتعامل معها بدلاش نخد فيها كتير انتوا طبعا أكيد", "tokens": [5172, 995, 16095, 10874, 9381, 16254, 22807, 39896, 39896, 4117, 2423, 8509, 6055, 3555, 34268, 16095, 46811, 10943, 23032, 3555, 3615, 995, 11331, 32277, 3555, 2407, 11296, 4032, 11778, 7435, 7435, 14407, 8978, 11296, 8032, 2655, 15040, 4587, 14407, 20328, 5016, 1829, 11296, 11778, 47302, 15042, 23032, 1829, 3555, 8717, 47341, 3615, 5296, 6027, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 13672, 1829, 39896, 16247, 2288, 4587, 10943, 4032, 23032, 16572, 28671, 6225, 3215, 16247, 2288, 4587, 10943, 1975, 5016, 8315, 28242, 8315, 44945, 3615, 28480, 16472, 1975, 5016, 8315, 44945, 8592, 2655, 17082, 1211, 15844, 2423, 26601, 2423, 26601, 44381, 8978, 28239, 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بيانات عبارة عن packets مثلا ال packets هذه بدك تعمل check عليها هل فيها error ولا لأ عشان تعمل عملية correction طيب ممتاز انت عملية ال correction علي إيش بتعملها بتعمل مجموعة عمليات حسابية فعليا على ال digits اللي موجودة صح سواء على ال digits ك bit-wise أو word-wise", "tokens": [9778, 9566, 11933, 2288, 3794, 6027, 49610, 47302, 4117, 3714, 7435, 2304, 2407, 27884, 4724, 1829, 7649, 9307, 6225, 3555, 9640, 3660, 18871, 30364, 50113, 15040, 2423, 30364, 29538, 47525, 4117, 6055, 25957, 1211, 1520, 25894, 11296, 8032, 1211, 8978, 11296, 6713, 49429, 5296, 10721, 6225, 8592, 7649, 6055, 25957, 1211, 6225, 42213, 10632, 19984, 23032, 1829, 3555, 3714, 2304, 2655, 31377, 16472, 2655, 6225, 42213, 10632, 2423, 19984, 25894, 11933, 1829, 8592, 39894, 25957, 1211, 11296, 39894, 25957, 1211, 3714, 7435, 2304, 2407, 27884, 6225, 2304, 20292, 9307, 11331, 3794, 16758, 10632, 6156, 3615, 20292, 995, 15844, 2423, 27011, 13672, 1829, 3714, 29245, 23328, 3660, 20328, 5016, 8608, 2407, 16606, 15844, 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"probability": 0.820068359375}, {"start": 1163.49, "end": 1163.75, "word": " تعمل", "probability": 0.98681640625}, {"start": 1163.75, "end": 1163.93, "word": " عملية", "probability": 0.9811197916666666}, {"start": 1163.93, "end": 1164.51, "word": " correction", "probability": 0.95263671875}, {"start": 1164.51, "end": 1165.35, "word": " طيب", "probability": 0.91943359375}, {"start": 1165.35, "end": 1165.87, "word": " ممتاز", "probability": 0.93994140625}, {"start": 1165.87, "end": 1166.05, "word": " انت", "probability": 0.827880859375}, {"start": 1166.05, "end": 1166.27, "word": " عملية", "probability": 0.982421875}, {"start": 1166.27, "end": 1166.39, "word": " ال", "probability": 0.77099609375}, {"start": 1166.39, "end": 1166.63, "word": " correction", "probability": 0.9638671875}, {"start": 1166.63, "end": 1166.85, "word": " علي", "probability": 0.38623046875}, {"start": 1166.85, "end": 1166.97, "word": " إيش", "probability": 0.8181966145833334}, {"start": 1166.97, "end": 1167.47, "word": " بتعملها", "probability": 0.973388671875}, {"start": 1167.47, "end": 1168.25, "word": " بتعمل", "probability": 0.8291829427083334}, {"start": 1168.25, "end": 1168.53, "word": " مجموعة", "probability": 0.9470703125}, {"start": 1168.53, "end": 1168.91, "word": " عمليات", "probability": 0.85357666015625}, {"start": 1168.91, "end": 1169.53, "word": " حسابية", "probability": 0.98681640625}, {"start": 1169.53, "end": 1170.11, "word": " فعليا", "probability": 0.89892578125}, {"start": 1170.11, "end": 1170.57, "word": " على", "probability": 0.60009765625}, {"start": 1170.57, "end": 1170.95, "word": " ال", "probability": 0.66259765625}, {"start": 1170.95, "end": 1171.21, "word": " digits", "probability": 0.93505859375}, {"start": 1171.21, "end": 1171.41, "word": " اللي", "probability": 0.89111328125}, {"start": 1171.41, "end": 1171.97, "word": " موجودة", "probability": 0.9893798828125}, {"start": 1171.97, "end": 1172.53, "word": " صح", "probability": 0.95849609375}, {"start": 1172.53, 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مختلفة عن ال decimal وعشان هيك الان بدنا ناخد مجموعة acquired على ال binary هتقولي ليش مفيدة؟ هقولك بكل بساطة لأن هي بتستخدمها في ال transmission lines انت لما بتيجي بترسل انت بترسل فعليا digit ال digits هذي binary digits يعني يا صفر يا واحد وعشان هيك أصار اسمها العلم digital", "tokens": [2304, 8592, 8032, 2655, 5172, 2288, 4587, 9122, 2655, 13546, 4724, 3794, 8978, 28239, 11296, 10632, 16472, 2655, 39894, 25957, 1211, 3714, 7435, 2304, 2407, 27884, 6225, 2304, 20292, 9307, 25894, 11296, 37037, 15730, 13672, 1829, 12174, 18513, 8315, 5296, 5172, 4117, 25720, 16472, 3224, 47525, 8315, 8717, 8848, 37983, 4117, 14407, 16472, 3224, 8978, 3714, 7435, 2304, 2407, 27884, 3652, 3714, 46456, 46538, 3660, 18871, 2423, 26601, 4032, 3615, 8592, 7649, 39896, 4117, 2423, 7649, 47525, 8315, 8717, 47283, 3215, 3714, 7435, 2304, 2407, 27884, 17554, 15844, 2423, 17434, 8032, 2655, 39648, 1829, 32239, 8592, 3714, 5172, 25708, 3660, 22807, 8032, 39648, 4117, 4724, 28820, 4724, 3794, 41193, 3660, 5296, 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"end": 1205.2, "word": " يا", "probability": 0.931640625}, {"start": 1205.2, "end": 1205.5, "word": " واحد", "probability": 0.995361328125}, {"start": 1205.5, "end": 1205.72, "word": " وعشان", "probability": 0.8751220703125}, {"start": 1205.72, "end": 1205.86, "word": " هيك", "probability": 0.9609375}, {"start": 1205.86, "end": 1206.06, "word": " أصار", "probability": 0.7259114583333334}, {"start": 1206.06, "end": 1206.42, "word": " اسمها", "probability": 0.7568359375}, {"start": 1206.42, "end": 1206.66, "word": " العلم", "probability": 0.985107421875}, {"start": 1206.66, "end": 1207.2, "word": " digital", "probability": 0.876953125}], "temperature": 1.0}, {"id": 51, "seek": 123372, "start": 1208.44, "end": 1233.72, "text": "communication digital communication طب بدك تعمل correction أو بدك تعمل check هل ال check هذا بدك تعملها one إذا كان في one bit error ولا more than one bit error هذه لها techniques و هذه لها techniques بس كلهم في النهاية بيعتمدوا على إنك انت تعمل عمليات الحسابية الأساسية على ال digits هذه طيب عشان نعملها نبدأ بأبسط شغلة أني والله بدي أضيف", "tokens": [25451, 8758, 4562, 6101, 23032, 3555, 47525, 4117, 6055, 25957, 1211, 19984, 34051, 47525, 4117, 6055, 25957, 1211, 1520, 8032, 1211, 2423, 1520, 23758, 47525, 4117, 6055, 25957, 1211, 11296, 472, 11933, 15730, 25961, 8978, 472, 857, 6713, 49429, 544, 813, 472, 857, 6713, 29538, 5296, 11296, 7512, 4032, 29538, 5296, 11296, 7512, 4724, 3794, 28242, 16095, 8978, 28239, 11296, 10632, 4724, 1829, 34268, 2304, 3215, 14407, 15844, 36145, 4117, 16472, 2655, 6055, 25957, 1211, 6225, 2304, 20292, 9307, 21542, 3794, 16758, 10632, 16247, 3794, 32277, 10632, 15844, 2423, 27011, 29538, 23032, 1829, 3555, 6225, 8592, 7649, 8717, 25957, 1211, 11296, 8717, 44510, 10721, 4724, 10721, 3555, 3794, 9566, 13412, 17082, 37977, 14739, 1829, 16070, 43761, 4724, 16254, 5551, 11242, 33911], "avg_logprob": -0.18506660458982968, "compression_ratio": 1.8876404494382022, "no_speech_prob": 2.086162567138672e-06, "words": 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"probability": 0.8463134765625}, {"start": 1226.16, "end": 1226.84, "word": " الأساسية", "probability": 0.9881591796875}, {"start": 1226.84, "end": 1227.56, "word": " على", "probability": 0.8984375}, {"start": 1227.56, "end": 1228.6, "word": " ال", "probability": 0.9892578125}, {"start": 1228.6, "end": 1229.42, "word": " digits", "probability": 0.7880859375}, {"start": 1229.42, "end": 1229.76, "word": " هذه", "probability": 0.74951171875}, {"start": 1229.76, "end": 1230.52, "word": " طيب", "probability": 0.9674479166666666}, {"start": 1230.52, "end": 1230.94, "word": " عشان", "probability": 0.98583984375}, {"start": 1230.94, "end": 1231.48, "word": " نعملها", "probability": 0.994140625}, {"start": 1231.48, "end": 1231.94, "word": " نبدأ", "probability": 0.9541015625}, {"start": 1231.94, "end": 1232.3, "word": " بأبسط", "probability": 0.97939453125}, {"start": 1232.3, "end": 1232.64, "word": " شغلة", "probability": 0.8180338541666666}, {"start": 1232.64, "end": 1232.84, "word": " أني", 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كنا ماشيين ب .. ب .. يعني بطريقة ان انتوا ماخدين عارفين يعني مركزين معنا طيب لما اقول بدي اعمل subtraction", "tokens": [9381, 9640, 6024, 48506, 43242, 4117, 318, 29538, 9122, 8310, 3714, 9778, 11622, 1863, 5296, 4117, 8717, 9307, 7435, 6225, 42213, 10632, 25724, 10943, 27884, 48127, 2655, 3215, 16606, 9154, 318, 23185, 17, 5296, 41260, 1863, 5296, 41260, 1863, 6156, 2736, 4724, 2423, 8310, 23758, 2736, 20666, 8310, 23758, 1975, 2655, 30543, 3615, 16472, 39896, 4724, 3794, 1829, 9566, 3660, 37893, 9122, 2655, 13546, 8978, 11296, 37279, 4587, 25708, 19446, 3224, 1829, 33599, 37893, 28820, 3660, 9122, 3555, 48923, 6156, 3615, 8592, 7649, 9122, 8315, 3714, 33599, 1829, 9957, 4724, 4386, 4724, 4386, 37495, 22653, 4724, 9566, 16572, 28671, 16472, 16472, 2655, 14407, 3714, 47283, 3215, 9957, 6225, 9640, 5172, 9957, 37495, 22653, 3714, 31747, 11622, 9957, 20449, 8315, 23032, 1829, 3555, 5296, 15042, 1975, 39648, 4724, 16254, 1975, 25957, 1211, 16390, 313], "avg_logprob": -0.22353078869741355, 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"word": " و", "probability": 0.6025390625}, {"start": 1650.01, "end": 1650.11, "word": " ال", "probability": 0.9013671875}, {"start": 1650.11, "end": 1650.23, "word": " two", "probability": 0.92431640625}, {"start": 1650.23, "end": 1650.67, "word": " compliment", "probability": 0.2032470703125}, {"start": 1650.67, "end": 1651.13, "word": " اتنين", "probability": 0.698974609375}, {"start": 1651.13, "end": 1651.27, "word": " ال", "probability": 0.66943359375}, {"start": 1651.27, "end": 1651.43, "word": " one", "probability": 0.8291015625}, {"start": 1651.43, "end": 1651.77, "word": " compliment", "probability": 0.79931640625}, {"start": 1651.77, "end": 1652.19, "word": " اخدتوا", "probability": 0.84169921875}, {"start": 1652.19, "end": 1652.33, "word": " و", "probability": 0.701171875}, {"start": 1652.33, "end": 1652.41, "word": " ال", "probability": 0.849609375}, {"start": 1652.41, "end": 1652.53, "word": " two", "probability": 0.95263671875}, {"start": 1652.53, "end": 1652.85, "word": " compliment", "probability": 0.9599609375}, {"start": 1652.85, "end": 1653.33, "word": " اخدتوا", "probability": 0.8736328125}, {"start": 1653.33, "end": 1654.13, "word": " عملتوا", "probability": 0.8629150390625}, {"start": 1654.13, "end": 1654.35, "word": " check", "probability": 0.88623046875}, {"start": 1654.35, "end": 1654.47, "word": " ع", "probability": 0.330810546875}, {"start": 1654.47, "end": 1654.73, "word": " الكلام", "probability": 0.9270833333333334}, {"start": 1654.73, "end": 1655.17, "word": " هذا؟", "probability": 0.625732421875}], "temperature": 1.0}, {"id": 68, "seek": 168177, "start": 1655.91, "end": 1681.77, "text": "المفروض كنت تعمل ال check كمان انت بدك تقل بالظبط خلاص فإذا احنا متفقين ماعناش مشكلة تمام فإذا قيل ال procedures بشكل بسيط بشكل أساسي كانت تالي هنحط ال code تبعنا هيه هي codeنا procedure subtract أي اسم يعبر عن أي عملية اللي بده اعملها ل two binary numbers", "tokens": [45340, 5172, 32887, 11242, 9122, 29399, 6055, 25957, 1211, 2423, 1520, 9122, 2304, 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"probability": 0.8182373046875}, {"start": 1659.61, "end": 1660.11, "word": " مشكلة", "probability": 0.9835611979166666}, {"start": 1660.11, "end": 1660.79, "word": " تمام", "probability": 0.829833984375}, {"start": 1660.79, "end": 1661.51, "word": " فإذا", "probability": 0.8924153645833334}, {"start": 1661.51, "end": 1662.47, "word": " قيل", "probability": 0.908935546875}, {"start": 1662.47, "end": 1662.55, "word": " ال", "probability": 0.3515625}, {"start": 1662.55, "end": 1662.87, "word": " procedures", "probability": 0.78369140625}, {"start": 1662.87, "end": 1663.47, "word": " بشكل", "probability": 0.84716796875}, {"start": 1663.47, "end": 1664.29, "word": " بسيط", "probability": 0.9969482421875}, {"start": 1664.29, "end": 1664.75, "word": " بشكل", "probability": 0.89111328125}, {"start": 1664.75, "end": 1665.59, "word": " أساسي", "probability": 0.9609375}, {"start": 1665.59, "end": 1666.59, "word": " كانت", "probability": 0.790771484375}, {"start": 1666.59, "end": 1666.93, "word": " تالي", "probability": 0.8922526041666666}, {"start": 1666.93, "end": 1668.45, "word": " هنحط", "probability": 0.8887939453125}, {"start": 1668.45, "end": 1668.73, "word": " ال", "probability": 0.67529296875}, {"start": 1668.73, "end": 1668.91, "word": " code", "probability": 0.97119140625}, {"start": 1668.91, "end": 1669.25, "word": " تبعنا", "probability": 0.89453125}, {"start": 1669.25, "end": 1669.63, "word": " هيه", "probability": 0.7724609375}, {"start": 1669.63, "end": 1671.21, "word": " هي", "probability": 0.1787109375}, {"start": 1671.21, "end": 1671.73, "word": " codeنا", "probability": 0.4283447265625}, {"start": 1671.73, "end": 1673.23, "word": " procedure", "probability": 0.771484375}, {"start": 1673.23, "end": 1674.51, "word": " subtract", "probability": 0.56298828125}, {"start": 1674.51, "end": 1675.61, "word": " أي", "probability": 0.7568359375}, {"start": 1675.61, "end": 1675.85, "word": " اسم", "probability": 0.885009765625}, {"start": 1675.85, "end": 1676.19, "word": " يعبر", "probability": 0.840087890625}, {"start": 1676.19, "end": 1676.39, "word": " عن", "probability": 0.89453125}, {"start": 1676.39, "end": 1676.61, "word": " أي", "probability": 0.371337890625}, {"start": 1676.61, "end": 1676.95, "word": " عملية", "probability": 0.87451171875}, {"start": 1676.95, "end": 1677.03, "word": " اللي", "probability": 0.82080078125}, {"start": 1677.03, "end": 1677.21, "word": " بده", "probability": 0.51416015625}, {"start": 1677.21, "end": 1677.85, "word": " اعملها", "probability": 0.8660888671875}, {"start": 1677.85, "end": 1678.35, "word": " ل", "probability": 0.86865234375}, {"start": 1678.35, "end": 1679.05, "word": " two", "probability": 0.7392578125}, {"start": 1679.05, "end": 1681.03, "word": " binary", "probability": 0.81005859375}, {"start": 1681.03, "end": 1681.77, "word": " numbers", "probability": 0.84912109375}], "temperature": 1.0}, {"id": 69, "seek": 170458, "start": 1682.4, "end": 1704.58, "text": "نمبر أول والتاني عساس انه بدي يكون عبارة عن ال inverse لاحظ inverse يعني مجرد ال once complement اللي هو كل digit بتعكسها فقط هذا ال once complement مش شايف؟ لو حطيت bar فوق فبعرف ان انت بتتكلم عن ال once complement بمعنى اللي هو ال inverse", "tokens": [1863, 2304, 26890, 5551, 12610, 16070, 2655, 7649, 1829, 6225, 3794, 32277, 16472, 3224, 4724, 16254, 7251, 30544, 6225, 3555, 9640, 3660, 18871, 2423, 17340, 20193, 5016, 19913, 17340, 37495, 22653, 3714, 7435, 2288, 3215, 2423, 1564, 17103, 13672, 1829, 31439, 28242, 14293, 39894, 3615, 4117, 3794, 11296, 6156, 47432, 23758, 2423, 1564, 17103, 37893, 13412, 995, 33911, 22807, 45164, 11331, 9566, 36081, 2159, 6156, 30543, 6156, 3555, 3615, 28480, 16472, 16472, 2655, 39894, 2655, 4117, 19528, 18871, 2423, 1564, 17103, 4724, 2304, 3615, 1863, 7578, 13672, 1829, 31439, 2423, 17340], "avg_logprob": -0.20380435041759326, "compression_ratio": 1.6883720930232557, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 1682.4, "end": 1682.84, "word": "نمبر", "probability": 0.5913899739583334}, {"start": 1682.84, "end": 1683.16, "word": " أول", "probability": 0.86181640625}, {"start": 1683.16, "end": 1683.9, "word": " والتاني", "probability": 0.81689453125}, {"start": 1683.9, "end": 1684.5, "word": " عساس", "probability": 0.712890625}, {"start": 1684.5, "end": 1684.66, "word": " انه", "probability": 0.746337890625}, {"start": 1684.66, "end": 1684.84, "word": " بدي", "probability": 0.370361328125}, {"start": 1684.84, "end": 1685.06, "word": " يكون", "probability": 0.87890625}, {"start": 1685.06, "end": 1685.44, "word": " عبارة", "probability": 0.992431640625}, {"start": 1685.44, "end": 1685.74, "word": " عن", "probability": 0.99658203125}, {"start": 1685.74, "end": 1687.18, "word": " ال", "probability": 0.8896484375}, {"start": 1687.18, "end": 1688.1, "word": " inverse", "probability": 0.7822265625}, {"start": 1688.1, "end": 1690.04, "word": " لاحظ", "probability": 0.7715657552083334}, {"start": 1690.04, "end": 1690.48, "word": " inverse", "probability": 0.28466796875}, {"start": 1690.48, "end": 1690.68, "word": " يعني", "probability": 0.96142578125}, {"start": 1690.68, "end": 1691.42, "word": " مجرد", "probability": 0.9925537109375}, {"start": 1691.42, "end": 1691.86, "word": " ال", "probability": 0.92333984375}, {"start": 1691.86, "end": 1692.08, "word": " once", "probability": 0.8603515625}, {"start": 1692.08, "end": 1692.48, "word": " complement", "probability": 0.5654296875}, {"start": 1692.48, "end": 1693.02, "word": " اللي", "probability": 0.934326171875}, {"start": 1693.02, "end": 1693.22, "word": " هو", "probability": 0.974609375}, {"start": 1693.22, "end": 1693.66, "word": " كل", "probability": 0.97216796875}, {"start": 1693.66, "end": 1694.7, "word": " digit", "probability": 0.93310546875}, {"start": 1694.7, "end": 1695.46, "word": " بتعكسها", "probability": 0.9814453125}, {"start": 1695.46, "end": 1695.96, "word": " فقط", "probability": 0.986328125}, {"start": 1695.96, "end": 1697.2, "word": " هذا", "probability": 0.77490234375}, {"start": 1697.2, "end": 1697.34, "word": " ال", "probability": 0.98095703125}, {"start": 1697.34, "end": 1697.54, "word": " once", "probability": 0.88720703125}, {"start": 1697.54, "end": 1698.08, "word": " complement", "probability": 0.8125}, {"start": 1698.08, "end": 1698.84, "word": " مش", "probability": 0.73681640625}, {"start": 1698.84, "end": 1699.3, "word": " شايف؟", "probability": 0.57867431640625}, {"start": 1699.3, "end": 1699.98, "word": " لو", "probability": 0.64208984375}, {"start": 1699.98, "end": 1700.36, "word": " حطيت", "probability": 0.9656575520833334}, {"start": 1700.36, "end": 1700.6, "word": " bar", "probability": 0.69091796875}, {"start": 1700.6, "end": 1701.06, "word": " فوق", "probability": 0.897216796875}, {"start": 1701.06, "end": 1701.68, "word": " فبعرف", "probability": 0.9608154296875}, {"start": 1701.68, "end": 1701.82, "word": " ان", "probability": 0.490234375}, {"start": 1701.82, "end": 1702.02, "word": " انت", "probability": 0.75}, {"start": 1702.02, "end": 1702.38, "word": " بتتكلم", "probability": 0.9798583984375}, {"start": 1702.38, "end": 1702.56, "word": " عن", "probability": 0.9931640625}, {"start": 1702.56, "end": 1702.66, "word": " ال", "probability": 0.9580078125}, {"start": 1702.66, "end": 1702.86, "word": " once", "probability": 0.91943359375}, {"start": 1702.86, "end": 1703.2, "word": " complement", "probability": 0.8603515625}, {"start": 1703.2, "end": 1703.64, "word": " بمعنى", "probability": 0.97275390625}, {"start": 1703.64, "end": 1703.82, "word": " اللي", "probability": 0.96435546875}, {"start": 1703.82, "end": 1703.98, "word": " هو", "probability": 0.97802734375}, {"start": 1703.98, "end": 1704.14, "word": " ال", "probability": 0.970703125}, {"start": 1704.14, "end": 1704.58, "word": " inverse", "probability": 0.93310546875}], "temperature": 1.0}, {"id": 70, "seek": 172642, "start": 1706.4, "end": 1726.42, "text": "بت وايز بيت وايز ايش يعني يعني بمسكها بت by بت كل بت واحد بجلبها لصفر وكل بت صفر بجلبها لواحد و بس تمام لو جمعتها على الاصلي تبعها مش هتطلع صفر بتطلعش معاك دايما صفر كويس فبنضطر نعمل ال two's complement كيف هنعملها كل الموضوع انه عندك", "tokens": [3555, 2655, 36764, 1829, 11622, 4724, 36081, 36764, 1829, 11622, 1975, 1829, 8592, 37495, 22653, 37495, 22653, 4724, 2304, 3794, 4117, 11296, 39894, 538, 39894, 28242, 39894, 36764, 24401, 4724, 7435, 46152, 11296, 5296, 9381, 5172, 2288, 4032, 28820, 39894, 20328, 5172, 2288, 4724, 7435, 46152, 11296, 5296, 14407, 24401, 4032, 4724, 3794, 46811, 10943, 45164, 10874, 2304, 34268, 11296, 15844, 2423, 33546, 20292, 6055, 3555, 3615, 11296, 37893, 8032, 2655, 9566, 1211, 3615, 20328, 5172, 2288, 39894, 9566, 1211, 3615, 8592, 20449, 995, 4117, 11778, 47302, 15042, 20328, 5172, 2288, 9122, 45865, 3794, 6156, 3555, 1863, 11242, 9566, 2288, 8717, 25957, 1211, 2423, 732, 311, 17103, 9122, 33911, 8032, 1863, 25957, 1211, 11296, 28242, 9673, 2407, 11242, 45367, 16472, 3224, 43242, 4117], "avg_logprob": 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تعملنا مجموعة random numbers ال random numbers هذه محتاجين مجموعة parameters عشان نبني ال model تبعنا ال model ببساطة بده ال modulus ال modulus M بدك تحدد قيمة له و بدك تحدد multiplier A قيمة لل A", "tokens": [1829, 5172, 16095, 36632, 8592, 9122, 2655, 3555, 43761, 46811, 10943, 6156, 3224, 24192, 39896, 5551, 4117, 2655, 2288, 5551, 8592, 1829, 16606, 8032, 1863, 8592, 2655, 17082, 1211, 25894, 11296, 6156, 3224, 1863, 32887, 5016, 24976, 8213, 8882, 19226, 831, 3170, 2423, 8213, 8882, 19226, 831, 3170, 6225, 8592, 7649, 8717, 2655, 3615, 10943, 1211, 20449, 11296, 39896, 4724, 3555, 3794, 41193, 3660, 10874, 28259, 6055, 25957, 1211, 8315, 3714, 7435, 2304, 2407, 27884, 4974, 3547, 2423, 4974, 3547, 29538, 3714, 33753, 26108, 9957, 3714, 7435, 2304, 2407, 27884, 9834, 6225, 8592, 7649, 8717, 3555, 22653, 2423, 2316, 6055, 3555, 3615, 8315, 2423, 2316, 4724, 3555, 3794, 41193, 3660, 47525, 3224, 2423, 42287, 2423, 42287, 376, 47525, 4117, 6055, 24401, 3215, 12174, 32640, 3660, 46740, 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"probability": 0.9853515625}, {"start": 2963.87, "end": 2964.25, "word": " معها", "probability": 0.918212890625}, {"start": 2964.25, "end": 2964.71, "word": " هي", "probability": 0.671875}, {"start": 2964.71, "end": 2965.67, "word": " ببساطة", "probability": 0.96845703125}, {"start": 2965.67, "end": 2965.97, "word": " جدا", "probability": 0.960205078125}, {"start": 2965.97, "end": 2966.49, "word": " تعملنا", "probability": 0.87548828125}, {"start": 2966.49, "end": 2966.95, "word": " مجموعة", "probability": 0.96728515625}, {"start": 2966.95, "end": 2967.57, "word": " random", "probability": 0.86181640625}, {"start": 2967.57, "end": 2968.07, "word": " numbers", "probability": 0.8505859375}, {"start": 2968.07, "end": 2969.09, "word": " ال", "probability": 0.82568359375}, {"start": 2969.09, "end": 2969.29, "word": " random", "probability": 0.92236328125}, {"start": 2969.29, "end": 2969.65, "word": " numbers", "probability": 0.90478515625}, {"start": 2969.65, "end": 2969.95, "word": " هذه", "probability": 0.322509765625}, {"start": 2969.95, "end": 2970.83, "word": " محتاجين", "probability": 0.986328125}, {"start": 2970.83, "end": 2971.37, "word": " مجموعة", "probability": 0.98017578125}, {"start": 2971.37, "end": 2972.25, "word": " parameters", "probability": 0.890625}, {"start": 2972.25, "end": 2972.83, "word": " عشان", "probability": 0.9923502604166666}, {"start": 2972.83, "end": 2973.23, "word": " نبني", "probability": 0.94580078125}, {"start": 2973.23, "end": 2973.35, "word": " ال", "probability": 0.6328125}, {"start": 2973.35, "end": 2973.55, "word": " model", "probability": 0.8916015625}, {"start": 2973.55, "end": 2973.99, "word": " تبعنا", "probability": 0.932861328125}, {"start": 2973.99, "end": 2974.59, "word": " ال", "probability": 0.66748046875}, {"start": 2974.59, "end": 2974.81, "word": " model", "probability": 0.97802734375}, {"start": 2974.81, "end": 2975.29, "word": " ببساطة", "probability": 0.97802734375}, {"start": 2975.29, "end": 2975.63, "word": " بده", "probability": 0.845947265625}, {"start": 2975.63, "end": 2975.77, "word": " ال", "probability": 0.6396484375}, {"start": 2975.77, "end": 2976.09, "word": " modulus", "probability": 0.9423828125}, {"start": 2976.09, "end": 2976.87, "word": " ال", "probability": 0.64306640625}, {"start": 2976.87, "end": 2977.17, "word": " modulus", "probability": 0.98193359375}, {"start": 2977.17, "end": 2977.55, "word": " M", "probability": 0.587890625}, {"start": 2977.55, "end": 2978.29, "word": " بدك", "probability": 0.65625}, {"start": 2978.29, "end": 2978.63, "word": " تحدد", "probability": 0.98681640625}, {"start": 2978.63, "end": 2978.91, "word": " قيمة", "probability": 0.923828125}, {"start": 2978.91, "end": 2979.13, "word": " له", "probability": 0.91064453125}, {"start": 2979.13, "end": 2979.53, "word": " و", "probability": 0.69287109375}, {"start": 2979.53, "end": 2979.69, "word": " بدك", "probability": 0.7288818359375}, {"start": 2979.69, "end": 2980.15, "word": " تحدد", "probability": 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2989.17, "end": 2990.23, "word": "وانصر", "probability": 0.452880859375}, {"start": 2990.23, "end": 2990.49, "word": " ابدا", "probability": 0.64697265625}, {"start": 2990.49, "end": 2990.83, "word": " فيه", "probability": 0.941162109375}, {"start": 2990.83, "end": 2992.35, "word": " هنسميه", "probability": 0.7631591796875}, {"start": 2992.35, "end": 2993.15, "word": " seed", "probability": 0.83984375}, {"start": 2993.15, "end": 2994.53, "word": " البذرة", "probability": 0.91015625}, {"start": 2994.53, "end": 2995.11, "word": " اللي", "probability": 0.74853515625}, {"start": 2995.11, "end": 2995.59, "word": " هتبدأ", "probability": 0.92724609375}, {"start": 2995.59, "end": 2996.03, "word": " منها", "probability": 0.972412109375}, {"start": 2996.03, "end": 2996.85, "word": " عملية", "probability": 0.982421875}, {"start": 2996.85, "end": 2997.21, "word": " ال", "probability": 0.92041015625}, {"start": 2997.21, "end": 2997.65, "word": " generation", "probability": 0.876953125}, {"start": 2997.65, "end": 2998.83, "word": " بحيث", "probability": 0.9566650390625}, {"start": 2998.83, "end": 2999.01, "word": " ان", "probability": 0.67626953125}, {"start": 2999.01, "end": 2999.65, "word": " ال", "probability": 0.76953125}, {"start": 2999.65, "end": 3000.01, "word": " A", "probability": 0.38037109375}], "temperature": 1.0}, {"id": 120, "seek": 302199, "start": 3000.71, "end": 3021.99, "text": "اللي هو ال multiplier مايكونش أكبر من ال modulus و يكون اتنين فأكثر مايكونش واحد لإنه ماعرفش معناه واحد في حاجة اسمها multiplier واحد مع أن معناته ماضربتش في إشي صحيح فهو بده يكون على الأقل اتنين فأكثر ال C بتكون أكبر من صفر أو تساوي صفر فإذا كانت تساوي صفر فهي معناته without increment", "tokens": [6027, 20292, 31439, 2423, 44106, 19446, 1829, 30544, 8592, 5551, 4117, 26890, 9154, 2423, 42287, 4032, 7251, 30544, 1975, 2655, 1863, 9957, 6156, 10721, 4117, 49115, 19446, 1829, 30544, 8592, 36764, 24401, 5296, 28814, 1863, 3224, 19446, 3615, 28480, 8592, 20449, 8315, 3224, 36764, 24401, 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ماضربتش", "probability": 0.8779296875}, {"start": 3011.25, "end": 3011.39, "word": " في", "probability": 0.81689453125}, {"start": 3011.39, "end": 3011.83, "word": " إشي", "probability": 0.7616373697916666}, {"start": 3011.83, "end": 3012.41, "word": " صحيح", "probability": 0.933837890625}, {"start": 3012.41, "end": 3012.89, "word": " فهو", "probability": 0.91650390625}, {"start": 3012.89, "end": 3013.05, "word": " بده", "probability": 0.5020751953125}, {"start": 3013.05, "end": 3013.27, "word": " يكون", "probability": 0.969482421875}, {"start": 3013.27, "end": 3013.41, "word": " على", "probability": 0.97412109375}, {"start": 3013.41, "end": 3013.69, "word": " الأقل", "probability": 0.94873046875}, {"start": 3013.69, "end": 3014.09, "word": " اتنين", "probability": 0.9600830078125}, {"start": 3014.09, "end": 3014.57, "word": " فأكثر", "probability": 0.9669189453125}, {"start": 3014.57, "end": 3015.67, "word": " ال", "probability": 0.9462890625}, {"start": 3015.67, "end": 3015.83, "word": " C", "probability": 0.5654296875}, {"start": 3015.83, "end": 3016.21, "word": " بتكون", "probability": 0.7236328125}, {"start": 3016.21, "end": 3016.59, "word": " أكبر", "probability": 0.9417317708333334}, {"start": 3016.59, "end": 3016.97, "word": " من", "probability": 0.99658203125}, {"start": 3016.97, "end": 3017.37, "word": " صفر", "probability": 0.9842122395833334}, {"start": 3017.37, "end": 3017.65, "word": " أو", "probability": 0.912109375}, {"start": 3017.65, "end": 3018.03, "word": " تساوي", "probability": 0.77587890625}, {"start": 3018.03, "end": 3018.33, "word": " صفر", "probability": 0.9879557291666666}, {"start": 3018.33, "end": 3018.61, "word": " فإذا", "probability": 0.95703125}, {"start": 3018.61, "end": 3018.95, "word": " كانت", "probability": 0.95458984375}, {"start": 3018.95, "end": 3019.99, "word": " تساوي", "probability": 0.973388671875}, {"start": 3019.99, "end": 3020.29, "word": " صفر", "probability": 0.9860026041666666}, {"start": 3020.29, "end": 3020.53, "word": " فهي", "probability": 0.9435221354166666}, {"start": 3020.53, "end": 3020.91, "word": " معناته", "probability": 0.9905598958333334}, {"start": 3020.91, "end": 3021.35, "word": " without", "probability": 0.939453125}, {"start": 3021.35, "end": 3021.99, "word": " increment", "probability": 0.8916015625}], "temperature": 1.0}, {"id": 121, "seek": 305221, "start": 3024.01, "end": 3052.21, "text": "الـ seed الطبيعي و المنطقي و العجل بيقول أنه لازم تكون أقل من ال modulus ال modulus هذا كأني أقول مثلا ال modulus ألف ألف ألف إيش يعني؟ معناته أنا جاعت بولد أرقام أقل من الألف أنا جاعت بعمل generations لعناصر عشوائية بس أنا عارف أن كلها أقل من الألف طيب ال modulus هذا عملته عشر تلاف فانت جاعت بتولد أرقام أقل من عشر تلاف and so on بهذا الشكل", "tokens": [6027, 39184, 8871, 41950, 21292, 3615, 1829, 4032, 9673, 1863, 9566, 38436, 4032, 18863, 7435, 1211, 4724, 1829, 39648, 14739, 3224, 5296, 31377, 2304, 6055, 30544, 5551, 4587, 1211, 9154, 2423, 42287, 2423, 42287, 23758, 9122, 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numbers", "probability": 0.77001953125}, {"start": 3118.85, "end": 3119.09, "word": " كمان", "probability": 0.9833984375}, {"start": 3119.09, "end": 3119.37, "word": " مرة", "probability": 0.985595703125}, {"start": 3119.37, "end": 3120.71, "word": " فعرفت", "probability": 0.9759521484375}, {"start": 3120.71, "end": 3120.95, "word": " انت", "probability": 0.521240234375}, {"start": 3120.95, "end": 3121.09, "word": " إيش", "probability": 0.8919270833333334}, {"start": 3121.09, "end": 3121.23, "word": " اللي", "probability": 0.99267578125}, {"start": 3121.23, "end": 3121.43, "word": " كنت", "probability": 0.986083984375}, {"start": 3121.43, "end": 3121.89, "word": " باعته", "probability": 0.8818359375}, {"start": 3121.89, "end": 3123.05, "word": " تمام", "probability": 0.696533203125}, {"start": 3123.05, "end": 3124.23, "word": " فببساطة", "probability": 0.91162109375}, {"start": 3124.23, "end": 3124.43, "word": " بهذا", "probability": 0.976318359375}, {"start": 3124.43, "end": 3124.75, 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"end": 3188.33, "text": "ليش؟ لأنه لما نقول relative primes معناه ذلك ببساطة أنه ال greatest common divisor between them واحد يعني مافيش عناصر أقل من M كلهم يقبل القسم عليها هذا بيعطيك تنوع أكبر لأنه لو كان في عناصر بينهم مشتركة هذا بيعني أنه هيكون عندك", "tokens": [20292, 8592, 22807, 5296, 33456, 3224, 5296, 15042, 8717, 39648, 4972, 582, 1532, 20449, 8315, 3224, 29910, 23275, 4724, 3555, 3794, 41193, 3660, 14739, 3224, 2423, 6636, 2689, 25974, 284, 1296, 552, 36764, 24401, 37495, 22653, 19446, 41185, 8592, 18871, 33546, 2288, 5551, 4587, 1211, 9154, 376, 28242, 16095, 7251, 4587, 36150, 25062, 38251, 25894, 11296, 23758, 4724, 40228, 9566, 1829, 4117, 6055, 1863, 45367, 5551, 4117, 26890, 5296, 33456, 3224, 45164, 25961, 8978, 18871, 33546, 2288, 49374, 16095, 37893, 2655, 31747, 3660, 23758, 4724, 40228, 22653, 14739, 3224, 39896, 30544, 43242, 4117], "avg_logprob": -0.14536236844798353, "compression_ratio": 1.5485232067510548, "no_speech_prob": 6.556510925292969e-07, "words": 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لو كملنا ايش هيظهر اكيد اكيد خلاص اتكرر اتكررت فإذا تعالي امسك اه دي ال modulus ايش تسعة", "tokens": [2655, 1211, 9307, 3660, 6156, 44510, 10721, 8315, 20666, 2655, 1211, 9307, 3660, 1783, 9984, 20666, 2655, 1211, 9307, 3660, 20328, 9640, 8978, 43242, 4117, 6055, 1211, 9307, 3660, 8608, 3555, 27884, 46811, 7649, 10632, 8608, 2655, 3660, 36764, 24401, 1975, 2655, 1863, 9957, 20328, 5172, 2288, 1975, 25513, 27884, 6055, 1211, 9307, 3660, 23032, 3555, 45164, 9122, 42213, 8315, 1975, 1829, 8592, 39896, 19913, 3224, 2288, 1975, 4117, 25708, 1975, 4117, 25708, 16490, 1211, 33546, 1975, 2655, 37983, 2288, 1975, 2655, 37983, 43500, 6156, 28814, 15730, 37279, 6027, 1829, 1975, 2304, 3794, 4117, 1975, 3224, 11778, 1829, 2423, 42287, 1975, 1829, 8592, 6055, 3794, 27884], "avg_logprob": -0.136974293494893, "compression_ratio": 1.814207650273224, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 3445.67, "end": 3446.27, "word": "تلاتة", "probability": 0.80487060546875}, {"start": 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7578, 8032, 7578, 5551, 2288, 4587, 10943, 13412, 21292, 3224, 3660, 5296, 39184, 2114, 1532, 8032, 3215, 7578, 45164, 16472, 2655, 30767, 7578, 19446, 4724, 1829, 39648, 3224, 6225, 7435, 11622, 2655, 16472, 3224, 37893, 20193, 7435, 1829, 4724, 23557, 32640, 3714, 8315, 35457, 24976, 3089, 6055, 3555, 3615, 4117, 3714, 43020, 6055, 2655, 3615, 10943, 1211, 20449, 995, 11296, 9122, 33911, 6055, 25957, 1211, 11296, 5125, 9122, 33911, 6055, 7435, 1829, 3555, 11296, 4724, 43042, 3224, 8032, 29399, 4117, 19528, 18871, 11296, 5296, 33456, 8032, 3215, 7578, 39894, 5172, 25708, 4117, 4724, 4117, 23557, 8978, 2423, 3825, 4724, 4117, 23557, 39894, 5172, 25708, 4117, 8978, 2423, 3825, 5296, 15042, 47525, 4117, 6055, 25957, 1211, 6055, 8592, 5172, 13546, 4032, 47525, 4117, 6055, 25957, 1211, 29575, 47525, 4117, 6055, 25957, 1211, 8032, 3215, 7578, 5551, 2288, 4587, 10943, 9122, 2655, 13546, 3714, 16095, 3660, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 4032, 8717, 24793, 1211, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37279, 6027, 7578], "avg_logprob": -0.1569220487789441, "compression_ratio": 1.912912912912913, "no_speech_prob": 1.2099742889404297e-05, "words": [{"start": 3621.31, "end": 3621.61, "word": "لما", "probability": 0.6978759765625}, {"start": 3621.61, "end": 3621.95, "word": " تدخل", "probability": 0.9906005859375}, {"start": 3621.95, "end": 3622.19, "word": " كمان", "probability": 0.9202473958333334}, {"start": 3622.19, "end": 3622.37, "word": " على", "probability": 0.9375}, {"start": 3622.37, "end": 3622.67, "word": " الـ", "probability": 0.626220703125}, {"start": 3622.67, "end": 3623.53, "word": " Sodoprimes", "probability": 0.7073974609375}, {"start": 3623.53, "end": 3624.13, "word": " اللى", "probability": 0.520263671875}, {"start": 3624.13, "end": 3624.33, "word": " هى", "probability": 0.861083984375}, {"start": 3624.33, "end": 3624.77, "word": " أرقام", "probability": 0.9781494140625}, {"start": 3624.77, "end": 3625.39, "word": " شبيهة", "probability": 0.86865234375}, {"start": 3625.39, "end": 3625.55, "word": " لـ", "probability": 0.761962890625}, {"start": 3625.55, "end": 3625.99, "word": " Primes", "probability": 0.73291015625}, {"start": 3625.99, "end": 3626.77, "word": " هدى", "probability": 0.7054036458333334}, {"start": 3626.77, "end": 3627.31, "word": " لو", "probability": 0.8798828125}, {"start": 3627.31, "end": 3627.61, "word": " انت", "probability": 0.820556640625}, {"start": 3627.61, "end": 3627.77, "word": " زى", "probability": 0.878173828125}, {"start": 3627.77, "end": 3627.81, "word": " ما", "probability": 0.97119140625}, {"start": 3627.81, "end": 3628.07, "word": " بيقوله", "probability": 0.7926025390625}, {"start": 3628.07, "end": 3628.63, "word": " عجزت", "probability": 0.9334716796875}, {"start": 3628.63, "end": 3629.23, "word": " انه", "probability": 0.81396484375}, {"start": 3629.23, "end": 3629.35, "word": " مش", "probability": 0.95751953125}, {"start": 3629.35, "end": 3629.61, "word": " لاجي", "probability": 0.6276041666666666}, {"start": 3629.61, "end": 3629.97, "word": " برايم", "probability": 0.646240234375}, {"start": 3629.97, "end": 3630.45, "word": " مناسب", "probability": 0.9493815104166666}, {"start": 3630.45, "end": 3630.67, "word": " لل", "probability": 0.473876953125}, {"start": 3630.67, "end": 3630.91, "word": " code", "probability": 0.89697265625}, {"start": 3630.91, "end": 3631.39, "word": " تبعك", "probability": 0.9674072265625}, {"start": 3631.39, "end": 3631.83, "word": " ممكن", "probability": 0.98095703125}, {"start": 3631.83, "end": 3632.29, "word": " تتعامل", "probability": 0.97216796875}, {"start": 3632.29, "end": 3632.77, "word": " معاها", "probability": 0.8971354166666666}, {"start": 3632.77, "end": 3633.39, "word": " كيف", "probability": 0.935546875}, {"start": 3633.39, "end": 3633.75, "word": " تعملها", "probability": 0.97412109375}, {"start": 3633.75, "end": 3634.17, "word": " generation", "probability": 0.86767578125}, {"start": 3634.17, "end": 3634.45, "word": " كيف", "probability": 0.73974609375}, {"start": 3634.45, "end": 3635.11, "word": " تجيبها", "probability": 0.995703125}, {"start": 3635.11, "end": 3635.89, "word": " برضه", "probability": 0.9694010416666666}, {"start": 3635.89, "end": 3636.39, "word": " هنتكلم", "probability": 0.9429931640625}, {"start": 3636.39, "end": 3637.03, "word": " عنها", "probability": 0.984130859375}, {"start": 3637.03, "end": 3637.45, "word": " لأن", "probability": 0.686767578125}, {"start": 3637.45, "end": 3637.63, "word": " هدى", "probability": 0.8733723958333334}, {"start": 3637.63, "end": 3638.03, "word": " بتفيدك", "probability": 0.97509765625}, {"start": 3638.03, "end": 3638.25, "word": " بكرا", "probability": 0.8597005208333334}, {"start": 3638.25, "end": 3638.35, "word": " في", "probability": 0.56103515625}, {"start": 3638.35, "end": 3638.41, "word": " ال", "probability": 0.92724609375}, {"start": 3638.41, "end": 3638.79, "word": " security", "probability": 0.96240234375}, {"start": 3638.79, "end": 3639.25, "word": " بكرا", "probability": 0.8367513020833334}, {"start": 3639.25, "end": 3639.59, "word": " بتفيدك", "probability": 0.9764404296875}, {"start": 3639.59, "end": 3639.67, "word": " في", "probability": 0.9521484375}, {"start": 3639.67, "end": 3639.75, "word": " ال", "probability": 0.93115234375}, {"start": 3639.75, "end": 3640.09, "word": " security", "probability": 0.9951171875}, {"start": 3640.09, "end": 3640.23, "word": " لما", "probability": 0.970947265625}, {"start": 3640.23, "end": 3640.43, "word": " بدك", "probability": 0.91259765625}, {"start": 3640.43, "end": 3640.79, "word": " تعمل", "probability": 0.9895833333333334}, {"start": 3640.79, "end": 3641.35, "word": " تشفير", "probability": 0.9715576171875}, {"start": 3641.35, "end": 3641.41, "word": " و", "probability": 0.82470703125}, {"start": 3641.41, "end": 3641.57, "word": " بدك", "probability": 0.7271728515625}, {"start": 3641.57, "end": 3641.83, "word": " تعمل", "probability": 0.9908854166666666}, {"start": 3641.83, "end": 3642.17, "word": " encryption", "probability": 0.951171875}, {"start": 3642.17, "end": 3642.47, "word": " بدك", "probability": 0.776611328125}, {"start": 3642.47, "end": 3642.71, "word": " تعمل", "probability": 0.9864908854166666}, {"start": 3642.71, "end": 3643.11, "word": " هدى", "probability": 0.82177734375}, {"start": 3643.11, "end": 3643.41, "word": " أرقام", "probability": 0.993896484375}, {"start": 3643.41, "end": 3643.63, "word": " كتير", "probability": 0.9733072916666666}, {"start": 3643.63, "end": 3644.05, "word": " مهمة", "probability": 0.98876953125}, {"start": 3644.05, "end": 3644.53, "word": " يعطيكوا", "probability": 0.90419921875}, {"start": 3644.53, "end": 3644.77, "word": " العافية", "probability": 0.8125}, {"start": 3644.77, "end": 3644.83, "word": " و", "probability": 0.94140625}, {"start": 3644.83, "end": 3645.09, "word": " نكمل", "probability": 0.8251953125}, {"start": 3645.09, "end": 3645.35, "word": " المرة", "probability": 0.7783203125}, {"start": 3645.35, "end": 3645.65, "word": " القادمة", "probability": 0.9856770833333334}, {"start": 3645.65, "end": 3645.79, "word": " ان", "probability": 0.485595703125}, {"start": 3645.79, "end": 3645.85, "word": " شاء", "probability": 0.802734375}, {"start": 3645.85, "end": 3645.89, "word": " الله", "probability": 0.9423828125}, {"start": 3645.89, "end": 3646.15, "word": " تعالى", "probability": 0.9368489583333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3646.508125, "duration_after_vad": 3528.913124999984}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wu4ONEGCIa0_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wu4ONEGCIa0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..11e60d3476a5484867a397a9557d24565e007343
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/wu4ONEGCIa0_raw.srt
@@ -0,0 +1,3096 @@
+1
+00:00:05,570 --> 00:00:09,490
+يعطيكوا العفو يا شباب نبدأ ان شاء الله تعالى في
+
+2
+00:00:09,490 --> 00:00:15,230
+جزئية الـ Euclide algorithm اكمالا لموضوع ال GCD
+
+3
+00:00:15,230 --> 00:00:20,130
+اللي أخدناها سابقا في موضوع ال number او ال theory
+
+4
+00:00:20,130 --> 00:00:25,430
+و هنبدأ اللي هي اتكلمنا فيها عننظرية الأعداد، ليش؟
+
+5
+00:00:25,430 --> 00:00:30,510
+لأنه هي الأساس لكل العلوم اللاحقة بعد ذلك، ومنها
+
+6
+00:00:30,510 --> 00:00:34,410
+التشفير و اللي هنصله في آخر محاضرتنا لهذا الموضوع
+
+7
+00:00:34,410 --> 00:00:38,410
+اللي بنتكلم فيها عن عملية ال encryption و كل ما
+
+8
+00:00:38,410 --> 00:00:41,650
+يخص الحقيقة سحر الأرقام و سحر الأعداد، لازم نكون
+
+9
+00:00:41,650 --> 00:00:44,480
+فاهمين أحنا الأعداد .. الأرقام نفسها بالأساسنكون
+
+10
+00:00:44,480 --> 00:00:48,820
+فاهمينها لأنه بشكل أو باخر هي أساس علم الحسوب ..
+
+11
+00:00:48,820 --> 00:00:52,900
+هي أساس علم الحسوب فوصلنا لجزئية أنه والله أخدنا
+
+12
+00:00:52,900 --> 00:00:59,010
+حاجة اسمها ال .. ال moduloالمرة الماضية الموديلو
+
+13
+00:00:59,010 --> 00:01:02,970
+هذه هنيجي نتطلع في إيش ممكن أستخدمها وجدنا أنه
+
+14
+00:01:02,970 --> 00:01:07,010
+هتوفر عليها جهد كتير كبير في جزئية greatest common
+
+15
+00:01:07,010 --> 00:01:11,110
+divisor في greatest common divisor بنقدر نجيب
+
+16
+00:01:11,110 --> 00:01:15,390
+علاقة ما بين greatest common divisor والموديلو
+
+17
+00:01:15,390 --> 00:01:20,950
+operation هنجد أنه احنا سهلنا على حالنا بشكل ضخم
+
+18
+00:01:20,950 --> 00:01:28,810
+كتير جزئية إيجاد ال GCD هذهكيف أني أقول والله أي
+
+19
+00:01:28,810 --> 00:01:36,090
+GCD لأي A وB لأي A وB هي فعليا نفسها ال GCD هي نفس
+
+20
+00:01:36,090 --> 00:01:43,850
+العامل المسترك الأكبر ل A مدلوا B وB هذا على فرض
+
+21
+00:01:43,850 --> 00:01:48,450
+أننا مرتبها أن ال A أكبر من ال B مرتبينها أن ال A
+
+22
+00:01:48,450 --> 00:01:51,570
+أكبر من ال B ففي الحالة هذه لما أقول A مدلوا B
+
+23
+00:01:51,570 --> 00:02:00,500
+هتطلع هنا قيمة أقل من ال Bأكيد ممتاز فصار هنا عندي
+
+24
+00:02:00,500 --> 00:02:05,500
+قيمة أقل من ال B و هنا قيمة ال B يعني معناه ذلك
+
+25
+00:02:05,500 --> 00:02:08,180
+لاحظوا هذا هيك القانون لحاله بس احنا كيف ممكن
+
+26
+00:02:08,180 --> 00:02:11,880
+نستفهم روح أكتر من هيك نرجع نعيد الموضوع كمان مرة
+
+27
+00:02:11,880 --> 00:02:15,600
+بحيث اني اقول لاحظش بده اقول بده اقول هذه صارت ال
+
+28
+00:02:15,600 --> 00:02:21,820
+A لجديدة و القيمة اللي طلعت ك remainder ل modulo
+
+29
+00:02:21,820 --> 00:02:28,430
+هذه صارت ال B لجديدةعشان نرجع .. لاحظ .. نعمل swap
+
+30
+00:02:28,430 --> 00:02:32,990
+و نركبهم بهذا الشكل و نرجع نعيد نفس الكلام كمان
+
+31
+00:02:32,990 --> 00:02:42,030
+مرة لما نصل لصفر بمعنى انه هنا عملية القسمة اللي
+
+32
+00:02:42,030 --> 00:02:48,330
+هيكون فيه متبقي لها مايكونش فيه متبقيأيه بتصل لأنه
+
+33
+00:02:48,330 --> 00:02:51,810
+ما بطل فيه متبقي هنا صفر بناخد القيمة التانية هي
+
+34
+00:02:51,810 --> 00:02:55,410
+ال common .. ال greatest common divisor هتكون هي
+
+35
+00:02:55,410 --> 00:02:59,320
+ال greatest common divisor فهذه ببساطةكيف احنا
+
+36
+00:02:59,320 --> 00:03:06,340
+ممكن نستغل ال modulo operation في إيجاد ال GCD
+
+37
+00:03:06,340 --> 00:03:10,000
+طريقة سهلة وسهلة وسلسة ونقدر نستخدمها في ال
+
+38
+00:03:10,000 --> 00:03:13,260
+algorithms بسهولة كيف هنستخدمها في ال algorithms
+
+39
+00:03:13,260 --> 00:03:16,700
+هناخد طبعا algorithm عليها هناخد algorithms عليها
+
+40
+00:03:16,700 --> 00:03:23,460
+بس خلينا نجرب هذا الموضوع بطريقة numericalبحيث ان
+
+41
+00:03:23,460 --> 00:03:28,560
+نشوف تلاتمية اتنين وسبعين ومية اربعة وستين وبدنا
+
+42
+00:03:28,560 --> 00:03:31,520
+نجيب greatest common divisor between them بكل
+
+43
+00:03:31,520 --> 00:03:34,320
+بساطة هنستخدم نفس القالية هقول greatest common
+
+44
+00:03:34,320 --> 00:03:37,960
+divisor لأ تلاتمية اتنين وسبعين هي نفسها تلاتمية
+
+45
+00:03:37,960 --> 00:03:44,700
+اتنين وسبعين مدله مية اربعة وستين كنتج ومية اربعة
+
+46
+00:03:44,700 --> 00:03:48,740
+وستين هنا النتج تبح مع الإطالة ومع غيره تطلع اربعة
+
+47
+00:03:48,740 --> 00:03:54,570
+واربعين يعني كأنه ال greatestCommon divisor ل 372
+
+48
+00:03:54,570 --> 00:04:01,170
+و 164 هو نفسه ال greatest common divisor بين 164 و
+
+49
+00:04:01,170 --> 00:04:06,450
+44 هو نفسه طيب في الحلقة دي بنرجع نكرر نفس العملية
+
+50
+00:04:06,450 --> 00:04:11,210
+كمان مرة بعد مرتبناهم هنا ال B حطناها مكان ال A و
+
+51
+00:04:11,210 --> 00:04:17,830
+ناتجالـ Modulo حطناها مكان الـ B بنرجع تكرار ال
+
+52
+00:04:17,830 --> 00:04:22,170
+loop بنعيده فلاحظ برمجيا كأنك انت ال loop رجعت
+
+53
+00:04:22,170 --> 00:04:27,790
+عدته كمان مرة بس كويس نفس الفكرة 164 modulo 44 و
+
+54
+00:04:27,790 --> 00:04:33,730
+44 طيب الناتج هنا 32 عكسهم دايما خلي الأول هو
+
+55
+00:04:33,730 --> 00:04:37,250
+الأكبر فصارت هو نفسه greatest common divisor بين
+
+56
+00:04:37,250 --> 00:04:41,950
+ال 44 وال32 و 30 و عيد عيد عيد لما تصل في الآخر ل
+
+57
+00:04:43,460 --> 00:04:46,260
+كلهم يكافئوا ل greatest common divisor ل تمانية
+
+58
+00:04:46,260 --> 00:04:51,360
+مدل و أربعة و أربعة طيب تمانية مدل و أربعة Zero
+
+59
+00:04:51,360 --> 00:04:54,520
+خلاص مدام ظهر عندي Zero معناته الأربعة هي greatest
+
+60
+00:04:54,520 --> 00:04:58,260
+common divisor فإذا الأربعة هي greatest common
+
+61
+00:04:58,260 --> 00:05:03,880
+divisor تمام هذه النظرية الأساسية كيف نكتبها ك كود
+
+62
+00:05:03,880 --> 00:05:07,960
+إذا بدكوا إياها في ال data structure بعدين تكتبوها
+
+63
+00:05:07,960 --> 00:05:14,060
+أبسط شغل إلهاال while و خلصنا ف ال while طول ما ال
+
+64
+00:05:14,060 --> 00:05:19,970
+بي لها قيمةكرر لما تصل لصفر واقف لان احنا لاحظ تو
+
+65
+00:05:19,970 --> 00:05:22,870
+استمرنا لعدم أوصلنا للصفر يعني اذا أوصلنا للصفر
+
+66
+00:05:22,870 --> 00:05:27,830
+وقفنا نفس الجثة هنرجع نكتبها في ال code اللي عندى
+
+67
+00:05:27,830 --> 00:05:31,850
+و لاحظ انه مش مستاهل كله سطرين تلاتة كله سطرين
+
+68
+00:05:31,850 --> 00:05:35,250
+تلاتة ال procedure بس بنحدد ايش ال arguments
+
+69
+00:05:35,250 --> 00:05:37,890
+بتاعتنا او ال input تبعنا فال input هو عبارة عن ال
+
+70
+00:05:37,890 --> 00:05:44,390
+a و ال b اسم البرنامج هو cd ال gcdGCD على أساس أنه
+
+71
+00:05:44,390 --> 00:05:46,590
+معبّر على greatest common divisor إيش ال input
+
+72
+00:05:46,590 --> 00:05:49,430
+تبعته ال A و ال B أكيد يعني أنت بدك ياني أجيب
+
+73
+00:05:49,430 --> 00:05:51,770
+معامل مشترك أكبر طبقين الرقمين اللي بده أجيب بينهم
+
+74
+00:05:51,770 --> 00:05:57,870
+فال A و ال B هي positive integers الآن while B لا
+
+75
+00:05:57,870 --> 00:06:02,930
+تساوي Zero معناته العملية مستمرة عملية البحث طيب
+
+76
+00:06:02,930 --> 00:06:07,090
+عملية البحث دي إيش بدنا من خلالها نعمل هنعمل ال R
+
+77
+00:06:07,090 --> 00:06:10,810
+أو ال remainder تبعنا و اللي هي يساوي ال A modulo
+
+78
+00:06:10,810 --> 00:06:17,310
+Bخلصناها .. خلصناها .. جيبناها هي .. بنحط ..
+
+79
+00:06:17,310 --> 00:06:21,890
+بنستبدل لإن احنا عارفين أن ال B هتكون أكبر من ال R
+
+80
+00:06:21,890 --> 00:06:26,570
+هذي قولة واحدة صحيح؟ و لا يمكن يطلع معاك ال R أكبر
+
+81
+00:06:26,570 --> 00:06:30,650
+من .. من B لما تيجي تعمل ال model operation فإذن
+
+82
+00:06:30,650 --> 00:06:36,990
+بتيجي تعمل تبديل بتخلي ال A هي ال B القديمة و ال B
+
+83
+00:06:36,990 --> 00:06:38,770
+هي ال R
+
+84
+00:06:41,420 --> 00:06:44,520
+بس و بنعمل end لأنه لاحظ احنا عملنا هنا statement
+
+85
+00:06:44,520 --> 00:06:47,680
+أولى، statement تانية و statement تالتة و التلاتة
+
+86
+00:06:47,680 --> 00:06:50,880
+لازم يكونوا جواب لمين لل while عشان كده بنبدأ
+
+87
+00:06:50,880 --> 00:06:54,120
+begin و end هنا بصير ضرورية ضرورية جدا ال begin و
+
+88
+00:06:54,120 --> 00:06:57,860
+ال end او ال care braces اللي انتوا بتكتبوها فهنا
+
+89
+00:06:57,860 --> 00:07:00,620
+بصير ضروري و إجباري لازم تكتبها في الجافة كويس
+
+90
+00:07:00,620 --> 00:07:07,920
+خلاص بتستمر ال loop هيضل ماشي امتى هيجف عند الصفر،
+
+91
+00:07:07,920 --> 00:07:12,820
+ممتازةطيب لما يصل عند صفر لما يصل لقيمة الصفر في
+
+92
+00:07:12,820 --> 00:07:17,460
+الحالة هذه انت هنا كان وصل معاك ان ال R بتساوي صفر
+
+93
+00:07:17,460 --> 00:07:22,900
+صح؟ يعني لاحظ هنا لاقيته .. لاقيته ساوي صفر جيت
+
+94
+00:07:22,900 --> 00:07:27,700
+حسبت ال R بعد ما كنت عملت ال test هذا حسبت ال R
+
+95
+00:07:27,700 --> 00:07:33,780
+طلعت صفر صحيح؟ فإيش عملت انت بعد ما صارت صفر انت
+
+96
+00:07:33,780 --> 00:07:37,060
+حطيت ال A B
+
+97
+00:07:38,190 --> 00:07:44,410
+وحطيت ال B هي ال R اللي هي الصفر فلاحظ جديد فعلياً
+
+98
+00:07:44,410 --> 00:07:48,310
+لجديد اللي صار عندك أن ال A تساوي ال B القديمة
+
+99
+00:07:48,310 --> 00:07:51,670
+وتساوي في الحالة دي ايش؟ ال greatest common
+
+100
+00:07:51,670 --> 00:08:00,130
+divisor لأن ال B تساوي صفر معناه ذلك لما تيجي تعمل
+
+101
+00:08:00,130 --> 00:08:05,470
+return مش هترجع return ال Bانت فعلياً عملت ..
+
+102
+00:08:05,470 --> 00:08:08,290
+غيرتهم .. عملت ال action هذا ال two actions هدول
+
+103
+00:08:08,290 --> 00:08:12,270
+انت عملتهم فعلياً ان ال A أصبحت هي ال B فمعنى ذلك
+
+104
+00:08:12,270 --> 00:08:17,270
+لما أجي أعمل return برجع لل A وضحت .. كتير بسأله
+
+105
+00:08:17,270 --> 00:08:19,270
+كانوا في القصة دي .. اه انت ماشي دكتور و بتقول
+
+106
+00:08:19,270 --> 00:08:23,710
+الصفر و ال B اللي بتضل هي اللي بترجع .. اه بتضل هي
+
+107
+00:08:23,710 --> 00:08:26,790
+اللي بترجع .. بس هذا لو ماعملتش .. لو مش مشمولين
+
+108
+00:08:26,790 --> 00:08:30,340
+ال two statements هدولةفي ال loop لأ هم مشمولين في
+
+109
+00:08:30,340 --> 00:08:34,440
+ال loop فالان بعد ما هذه صارت صفر ابترجع تعمل
+
+110
+00:08:34,440 --> 00:08:39,140
+check على ال B لأ صارت صفر اطلع فانا اللي بديها
+
+111
+00:08:39,140 --> 00:08:44,240
+الان هي ال A مش ال B ال A و ليست ال B اللي هي كانت
+
+112
+00:08:44,240 --> 00:08:48,420
+قيمة A السابقة احنا الان في الحالي احنا الان في
+
+113
+00:08:48,420 --> 00:08:52,080
+الحالي في الحالي لأ بدي قيمة A بس السابقة هي ال B
+
+114
+00:08:52,080 --> 00:08:58,810
+صح كسابقةفإنت جداش فاهم ال code .. قالية كيف ماشي
+
+115
+00:08:58,810 --> 00:09:01,930
+ال code هتسهل عليك إنت إيش اللي بدك إياه مدام أنت
+
+116
+00:09:01,930 --> 00:09:04,390
+مركز في ال code و فاهم إيش اللي بيعملوا خلاص تنتهي
+
+117
+00:09:04,390 --> 00:09:10,850
+القصة طيب فتاخد بالك أن ال two statements هدول
+
+118
+00:09:10,850 --> 00:09:13,010
+مهمين جدا لإن هم اللي عملون ليه عملية ال sorting
+
+119
+00:09:13,010 --> 00:09:17,950
+أنه دائما الأول هو الأكبر الأول كان ترتيبا هو
+
+120
+00:09:17,950 --> 00:09:21,250
+الأكبر فعملنا عملية ال sorting وهذا لازم ومهم جدا
+
+121
+00:09:22,050 --> 00:09:24,150
+في الشغل تبعك إذا بدكش تعملها معناته بدك تعمل
+
+122
+00:09:24,150 --> 00:09:29,810
+reverse في عملية ال ال R بتصير B mod A في الحالة
+
+123
+00:09:29,810 --> 00:09:35,670
+دي ديرو بالكم تمام ال code هذا سريع جدا الحقيقة و
+
+124
+00:09:35,670 --> 00:09:40,150
+مناسب جدا و بسرعة بتحرك أسرع من الطرق اللي أخدناها
+
+125
+00:09:40,150 --> 00:09:46,150
+سابقا طبعا فكرة ان أجوبت أجيب العوامل المشتركة لكل
+
+126
+00:09:46,150 --> 00:09:50,250
+رقم هذا كلام فاضيأفضل من الفاضي لكن الصحيح أنه
+
+127
+00:09:50,250 --> 00:09:53,730
+ممكن نستخدم ال prime factorization لأ هنا أسرع
+
+128
+00:09:53,730 --> 00:09:56,390
+بكتير ال prime factorization انت في الحالة ده
+
+129
+00:09:56,390 --> 00:09:59,270
+هتشتغل بشكل كتير ضخم لإنه بدك تجيب prime
+
+130
+00:09:59,270 --> 00:10:01,550
+factorization للأول و ال prime factorization
+
+131
+00:10:01,550 --> 00:10:06,170
+للتاني و إذا كان الرقم كبير الوضع بصير كارثي لكن
+
+132
+00:10:06,170 --> 00:10:10,130
+هنا انت بتتكلم عن إيش؟ بتتكلم عن طريقة بالظبط
+
+133
+00:10:10,130 --> 00:10:14,170
+عاملة زي ال binary اللي هي بتعملك jump انت بدل ما
+
+134
+00:10:14,170 --> 00:10:19,060
+كنت بتتعامل مع 372 صرت تتعامل مع 44بدل ما كنت
+
+135
+00:10:19,060 --> 00:10:23,880
+تتعامل مع 164 صرت تتعامل مع 32 لحظته ايش اللي
+
+136
+00:10:23,880 --> 00:10:29,240
+بيصير ففعليا logarithmic ففعليا ال code هنا صار
+
+137
+00:10:29,240 --> 00:10:33,580
+logarithmic انت بتعمل jump فبتصير عندك logarithmic
+
+138
+00:10:33,580 --> 00:10:37,360
+بغض النظر ال base تبع ال log بغض النظر ال base
+
+139
+00:10:37,360 --> 00:10:40,180
+احنا قلنا في النهاية كلهم بيظلوا نفس ال order كلهم
+
+140
+00:10:40,180 --> 00:10:44,180
+نفس ال order للأساس العشري للأساس الثنائي ماتفرجش
+
+141
+00:10:44,180 --> 00:10:50,660
+معنا بس في النهاية هنا ال code تبعك هوال big O هو
+
+142
+00:10:50,660 --> 00:10:54,220
+logarithmic، logarithmic لمين منهم؟ للمقسمم، مش
+
+143
+00:10:54,220 --> 00:10:57,660
+هتفرق كتير في النهاية logarithmic، A كبيرة، A
+
+144
+00:10:57,660 --> 00:11:03,500
+صغيرة، ماتفرقش كتير معناه، طيب، اتفضل، انا جيت
+
+145
+00:11:03,500 --> 00:11:07,740
+الطيجة واعتها مية بالمية، بس يعني ليش صح يعني؟ ليش
+
+146
+00:11:07,740 --> 00:11:12,040
+صح يعني؟ كيف احنا من هك و هك و من داخل و داخل؟مش
+
+147
+00:11:12,040 --> 00:11:15,740
+بقولك أن أحيانا في الرياضيات فيها سحر أن فيها
+
+148
+00:11:15,740 --> 00:11:19,560
+علاقات أصلا متجانسة مع بعض العلاقات المتجانسة مع
+
+149
+00:11:19,560 --> 00:11:22,780
+بعض أنت في النهاية greatest common divisor عشان
+
+150
+00:11:22,780 --> 00:11:25,060
+تقول أن فعلا في greatest common divisor أنت في
+
+151
+00:11:25,060 --> 00:11:29,480
+النهاية بدك تقسمهم على بعض صح؟ لأن ال greatest
+
+152
+00:11:29,480 --> 00:11:32,360
+common divisor هو عامل مشترك بمعنى أن الأول يقبل
+
+153
+00:11:32,360 --> 00:11:36,110
+القسم عليه والتاني يقبل القسم عليهفي الآخر كيف بدك
+
+154
+00:11:36,110 --> 00:11:39,970
+تظبط أن الاتنين بيقبلوا القسم على بعض بده يكون رقم
+
+155
+00:11:39,970 --> 00:11:44,530
+لما تعمله model أسماء الأول بيطلع صفر و model
+
+156
+00:11:44,530 --> 00:11:49,150
+أسماء التاني بيطلع صفر، مش هيك؟ فمن هذه الفكرة
+
+157
+00:11:49,150 --> 00:11:53,050
+بتيجي أن معناته طول ما هم مش متفقين وصلوا للصفر
+
+158
+00:11:53,050 --> 00:11:58,410
+معا مع بعضلسه ماوصلتش لل greatest common divisor
+
+159
+00:11:58,410 --> 00:12:01,970
+لما يظلوا مع بعض .. يعني مع بعض الأول مُد الأثلاث
+
+160
+00:12:01,970 --> 00:12:05,750
+تاني و تظلك تاخد اللي هي مشتقاتهم بيصيرش مضعفاتهم
+
+161
+00:12:05,750 --> 00:12:09,050
+مشتقاتهم ال divisors تبعتهم الأصغر الأصغر الأصغر
+
+162
+00:12:09,050 --> 00:12:12,750
+أو المتبقيات بتاعتهم انت بصيره صفر مع أنك متضامن
+
+163
+00:12:12,750 --> 00:12:17,430
+انه وصلت لرقم هو يقبل ال .. الأول يقبل القسم عليه
+
+164
+00:12:17,430 --> 00:12:22,210
+والتاني يقبل القسم عليه لأنه في .. في نهاية سلسلة
+
+165
+00:12:23,070 --> 00:12:27,670
+ال remainders وصلت لصفر مدام وصلت لصفر فاسم يقبل
+
+166
+00:12:27,670 --> 00:12:32,350
+القسم عليه فهي تقبل القسم عليه هي الرياضية فيها
+
+167
+00:12:32,350 --> 00:12:40,570
+حاجات كتير فيها سحر يعني حلوة تمام يعني فرضا مثلا
+
+168
+00:12:40,570 --> 00:12:41,450
+خليني أقولك
+
+169
+00:12:44,780 --> 00:12:49,040
+بعض الأشياء اللي زي ليش مثلا تسعمية و تسعة و تسعين
+
+170
+00:12:49,040 --> 00:12:53,600
+على تسعة زائد تسعة زائد تسعة بساوي تمانية تمانية و
+
+171
+00:12:53,600 --> 00:12:56,300
+تمانين على تمانية زائد تمانية زائد تمانية بساوي
+
+172
+00:12:56,300 --> 00:12:58,860
+سبعمية سبعة و سبعين على سبعة زائد سبعة زائد سبعة
+
+173
+00:12:58,860 --> 00:13:06,630
+هتقوللي ليش الأرقام هيك ال ratio هيكفاهم جصدي؟ هي
+
+174
+00:13:06,630 --> 00:13:10,610
+هيك ال ratio تبعتهم تمام طبعا حاسبوها و دججوا فيها
+
+175
+00:13:10,610 --> 00:13:15,570
+هتلاقوا صحيها دايما طيب نرجع لال .. ال .. ال .. ال
+
+176
+00:13:15,570 --> 00:13:18,850
+.. اللي هي الأرقام و طريقة عد الأرقام احنا كلنا
+
+177
+00:13:18,850 --> 00:13:22,610
+بنعرف ان احنا بنشتغل على ال decimal ال decimal لكن
+
+178
+00:13:22,610 --> 00:13:25,350
+في النهاية في عندي أنظمة أخرى ممكن نتعامل معها
+
+179
+00:13:25,350 --> 00:13:29,050
+بدلاش نخد فيها كتير انتوا طبعا أكيدأدرى في الموضوع
+
+180
+00:13:29,050 --> 00:13:31,350
+هذا واش عارفين الكلام هذا لما بتكلم عن decimal
+
+181
+00:13:31,350 --> 00:13:36,530
+فانا بتكلم عن ten digits from zero to nine هي عندي
+
+182
+00:13:36,530 --> 00:13:40,710
+ال ten digits تبعون ال system هذا بالنسبة لال
+
+183
+00:13:40,710 --> 00:13:44,350
+binary لأ ال binaryواضحة معناته أنا بتكلم عن two
+
+184
+00:13:44,350 --> 00:13:47,810
+digits two digits اللي هو الصفر والواحد لما بتكلم
+
+185
+00:13:47,810 --> 00:13:52,110
+عن ال octal system بتكلم عن التمانية فإذا من الصفر
+
+186
+00:13:52,110 --> 00:13:56,090
+للسبعة هي عدد تمانية عددهم بيطلع تمانية digits لما
+
+187
+00:13:56,090 --> 00:14:00,930
+نتكلم عن ال hexadecimal اللي هو السادس عشر السادس
+
+188
+00:14:00,930 --> 00:14:04,270
+عشر معناته بتكلم عن ستاشر decimal ابتدا من الصفر
+
+189
+00:14:04,270 --> 00:14:08,250
+للخمستعش للخمستعش طب أنا ماعنديش فعليا في طرق العد
+
+190
+00:14:08,250 --> 00:14:12,300
+احنا مااخترعناش حاجة بعد التسعةفحطوا مجموعة ال
+
+191
+00:14:12,300 --> 00:14:15,260
+letters او اول ال letters بداية ال letters بال
+
+192
+00:14:15,260 --> 00:14:19,440
+capital فاطوني اول ستة او الستة المتبقين اللي
+
+193
+00:14:19,440 --> 00:14:22,520
+كانوا ضايقين عننا اللي هم تعاون ال hexa اللي هم
+
+194
+00:14:22,520 --> 00:14:27,540
+تعاون ال hexa a b c d e f فهذا صار ال system اللي
+
+195
+00:14:27,540 --> 00:14:31,200
+موجود كلام انتوا عارفينه اكيد امر عليكوا وازهقتوا
+
+196
+00:14:31,200 --> 00:14:36,500
+منه تمامالان عملية التغيير أو ال conversion من
+
+197
+00:14:36,500 --> 00:14:39,960
+system ل system برضه مش الحاجة الكتير صعبة إذا أنت
+
+198
+00:14:39,960 --> 00:14:44,380
+بتتكلم عن .. بدك تروح ل .. من system كبير ل system
+
+199
+00:14:44,380 --> 00:14:48,160
+أصغر بتبدأ تعمل عملية القسمة و بتجيب ال
+
+200
+00:14:48,160 --> 00:14:52,300
+remainders، إذا من الكبير للصغير، فإذا من العشر
+
+201
+00:14:52,300 --> 00:14:57,020
+بدك تروح لثماني مثلا، فإذا بشتغل كأنه عملت modulus
+
+202
+00:14:58,790 --> 00:15:03,090
+الـ modulus تبعك هذا كأنك تعمل modulo operation
+
+203
+00:15:03,090 --> 00:15:08,670
+فالرقم بالعشري بتجسمه على تمانية بتجسمه على تمانية
+
+204
+00:15:08,670 --> 00:15:14,810
+ايش المتبقي؟ طيب عدد اللفات بترجع تجسمها كمان مرة
+
+205
+00:15:14,810 --> 00:15:19,030
+على تمانية بتشوف ايش المتبقي and so on ففي الآخر
+
+206
+00:15:19,850 --> 00:15:22,150
+الـ remainders اللي موجودين عندك هم اللي بيمثلوا
+
+207
+00:15:22,150 --> 00:15:27,390
+في الآخر الرقم بعد ترتيبه من least significant bit
+
+208
+00:15:27,390 --> 00:15:33,330
+to most significant bit بهذا الشكل فبطلع هذا العدد
+
+209
+00:15:33,330 --> 00:15:39,050
+الموازي لهذا الرقم بس بالمين بال أكتر بيش بال أكتر
+
+210
+00:15:39,050 --> 00:15:45,070
+نفس الكلام اللي بتتكلم من عشري لسادس عشر برضه بدك
+
+211
+00:15:45,070 --> 00:15:49,090
+تجسم عليه الست عشر فالأساس هو اللي ده بتجسم عليهفي
+
+212
+00:15:49,090 --> 00:15:52,630
+الحالة هذه بتكون واضحة عندك الأمور لإنه بتجسم فإيش
+
+213
+00:15:52,630 --> 00:16:00,810
+متبقي بتاخده ك .. بتصير إيش ال a الجديدة ل المدلو
+
+214
+00:16:00,810 --> 00:16:05,790
+متصير ال a الجديدة ل المدلو المتبقي هذا طبعا أول
+
+215
+00:16:05,790 --> 00:16:11,370
+شغل هذا بدك تبدأ تتعامل معاه و ترجعه لقيمته ترجعه
+
+216
+00:16:11,370 --> 00:16:16,570
+لقيمته فعليا جديش عشان تبدأ تتعامل معاه متبقية
+
+217
+00:16:16,570 --> 00:16:20,990
+المتبقي اللي هنابرضه من ال less significant ل ال
+
+218
+00:16:20,990 --> 00:16:26,030
+most significant بترتبهم جان بعض عشان تجيب العنصر
+
+219
+00:16:26,030 --> 00:16:30,150
+النهائي طيب لما بتتكلم من ال binary من ال binary
+
+220
+00:16:30,150 --> 00:16:33,630
+الأمور بتكون شوية أخف أسهل لما بدك تروح لل octal
+
+221
+00:16:33,630 --> 00:16:38,710
+او لل hexadecimal فلو عندك sequence بهذا الشكل او
+
+222
+00:16:38,710 --> 00:16:46,720
+string بهذا الشكل عبارة عن number بال binarysystem
+
+223
+00:16:46,720 --> 00:16:49,880
+automatically إذا بده أروح لثماني عارفين إن
+
+224
+00:16:49,880 --> 00:16:54,400
+الثماني هو كل three digits بشكل تمانية فإذا بجسمهم
+
+225
+00:16:54,400 --> 00:17:04,700
+لتلتات three digits بهذا الشكل وكلنا
+
+226
+00:17:04,700 --> 00:17:10,160
+عارفين إنه صفر في الشمال بيأثرش صفر بالشمال لا
+
+227
+00:17:10,160 --> 00:17:14,870
+يؤثر ف automatically بتشوف جدش الرقم هناأربعة ..
+
+228
+00:17:14,870 --> 00:17:22,350
+سبعة .. واحد .. اتنين .. سبعة .. تلاتة .. فلسنا ..
+
+229
+00:17:22,350 --> 00:17:27,450
+مايه .. وانتهى هذا العليا طيب العكس صحيح برضه لما
+
+230
+00:17:27,450 --> 00:17:31,050
+تكون عندك الرقم من ال octal system ل ال binary
+
+231
+00:17:31,050 --> 00:17:33,610
+system بنفس القلية انت عارف ان كل رقم من الأرقام
+
+232
+00:17:33,610 --> 00:17:38,850
+هدولة بتمثلوا بتلاتة digits فبتروح بتمثل الخمسة ب
+
+233
+00:17:38,850 --> 00:17:43,440
+three digits عونهاالستة بال three digits ساعونها
+
+234
+00:17:43,440 --> 00:17:47,040
+والسبعة بال three digits ساعونها وانتهى طبعا
+
+235
+00:17:47,040 --> 00:17:52,320
+بالhexa كلتا بيكفيش بيصير بدك أربعة مدام هي فعليا
+
+236
+00:17:52,320 --> 00:17:55,980
+انت بتحول لنظام فعلا هو يتوافق تماما مع عدد digits
+
+237
+00:17:56,860 --> 00:18:00,140
+عشان هيك اللي انشهرت اكتر من .. طبعا التساعي فيه
+
+238
+00:18:00,140 --> 00:18:04,420
+تساعي، تسعة مثلا، لكن الانشهر اكتر لأن ال .. ال ..
+
+239
+00:18:04,420 --> 00:18:09,220
+الثماني و ال hexadecimal الست عشر لأنه بالظبط بيجي
+
+240
+00:18:09,220 --> 00:18:12,880
+على عدد ال bits، عندك three bits أو three digits
+
+241
+00:18:12,880 --> 00:18:18,970
+بمثله ال octalfor digits بيمثله ال hexadecimal أما
+
+242
+00:18:18,970 --> 00:18:21,370
+في أنظمة تانية أه في أنظمة تانية يعني أنت بدك تروح
+
+243
+00:18:21,370 --> 00:18:24,690
+للتساعي للسباعي ل .. اعمل اللي بدكيه مافيش مشكلة
+
+244
+00:18:24,690 --> 00:18:28,050
+حول بس بتحول ساعتها بعملية القسمة العادية المطولة
+
+245
+00:18:28,050 --> 00:18:33,210
+لإن مافيش توافق بيصير .. بيصير و مافيش توافقتمام
+
+246
+00:18:33,210 --> 00:18:37,770
+لإيش احنا أخدنا .. خدنا في الموضوع هذا لأن في عند
+
+247
+00:18:37,770 --> 00:18:40,890
+ال binary احنا بنستخدمه كتير .. بنستخدمه كتير في
+
+248
+00:18:40,890 --> 00:18:44,010
+إيش؟ في عملية التشفير واحدة من الأمور انت لما
+
+249
+00:18:44,010 --> 00:18:48,490
+بتبعت ال data عندك في ال transmission linesخطوط
+
+250
+00:18:48,490 --> 00:18:52,470
+الاتصال والتوقع والارسال انت عادة بتبعتها digits
+
+251
+00:18:52,470 --> 00:18:55,870
+بال binary مش هيك مش ال digital كل العلم ال
+
+252
+00:18:55,870 --> 00:18:58,970
+digital اللي الان ماشي ان انت بترسل صفر واحد ممتاز
+
+253
+00:18:58,970 --> 00:19:01,510
+معناه دلك ان صفر واحد اللي انت بعتها دي أحيانا
+
+254
+00:19:01,510 --> 00:19:04,230
+كتير بتكون محتاج تعمل عليها مجموعة عمليات
+
+255
+00:19:04,230 --> 00:19:09,770
+operations ليش؟ منها بعرفش اذا كان أخدتوها مستوى
+
+256
+00:19:09,770 --> 00:19:16,050
+تالت لسه بتهيألي لما يكون عندك مثلاخط إرسال وجايك
+
+257
+00:19:16,050 --> 00:19:19,110
+مجموعة بيانات عبارة عن packets مثلا ال packets هذه
+
+258
+00:19:19,110 --> 00:19:23,490
+بدك تعمل check عليها هل فيها error ولا لأ عشان
+
+259
+00:19:23,490 --> 00:19:26,390
+تعمل عملية correction طيب ممتاز انت عملية ال
+
+260
+00:19:26,390 --> 00:19:28,910
+correction علي إيش بتعملها بتعمل مجموعة عمليات
+
+261
+00:19:28,910 --> 00:19:33,670
+حسابية فعليا على ال digits اللي موجودة صح سواء على
+
+262
+00:19:33,670 --> 00:19:39,160
+ال digits ك bit-wise أو word-wiseمش هتفرق كتير بس
+
+263
+00:19:39,160 --> 00:19:41,660
+في النهاية انت بتعمل مجموعة عمليات عليها وهذا اللي
+
+264
+00:19:41,660 --> 00:19:46,840
+قادنا لفكرة انه بدنا نذكركوا انه في مجموعة systems
+
+265
+00:19:46,840 --> 00:19:49,340
+مختلفة عن ال decimal وعشان هيك الان بدنا ناخد
+
+266
+00:19:49,340 --> 00:19:54,380
+مجموعة acquired على ال binary هتقولي ليش مفيدة؟
+
+267
+00:19:54,380 --> 00:19:56,960
+هقولك بكل بساطة لأن هي بتستخدمها في ال
+
+268
+00:19:56,960 --> 00:20:00,080
+transmission lines انت لما بتيجي بترسل انت بترسل
+
+269
+00:20:00,080 --> 00:20:04,680
+فعليا digit ال digits هذي binary digits يعني يا
+
+270
+00:20:04,680 --> 00:20:07,200
+صفر يا واحد وعشان هيك أصار اسمها العلم digital
+
+271
+00:20:08,440 --> 00:20:10,700
+communication digital communication طب بدك تعمل
+
+272
+00:20:10,700 --> 00:20:14,300
+correction أو بدك تعمل check هل ال check هذا بدك
+
+273
+00:20:14,300 --> 00:20:18,480
+تعملها one إذا كان في one bit error ولا more than
+
+274
+00:20:18,480 --> 00:20:21,160
+one bit error هذه لها techniques و هذه لها
+
+275
+00:20:21,160 --> 00:20:23,960
+techniques بس كلهم في النهاية بيعتمدوا على إنك انت
+
+276
+00:20:23,960 --> 00:20:29,760
+تعمل عمليات الحسابية الأساسية على ال digits هذه
+
+277
+00:20:29,760 --> 00:20:33,720
+طيب عشان نعملها نبدأ بأبسط شغلة أني والله بدي أضيف
+
+278
+00:20:35,810 --> 00:20:39,010
+رقمين binary على بعض نكتب لهم كودة أنا أعرف أن
+
+279
+00:20:39,010 --> 00:20:44,030
+انتوا عارفون تعملوها فأنا مانيين
+
+280
+00:20:44,030 --> 00:20:47,170
+بال code اللي بده يعملها أتوقع ماخدتوش لسه كودة
+
+281
+00:20:47,170 --> 00:20:50,270
+على هيك و لا أخدتوا طيب ممتاز عشان برضه لو
+
+282
+00:20:50,270 --> 00:20:53,890
+انسألتوا فيها في ال data structure تكونوا هي جاهزة
+
+283
+00:20:53,890 --> 00:20:59,620
+عندكم طيب ف procedureعارفين النقاد لأن أنا بعمل
+
+284
+00:20:59,620 --> 00:21:02,700
+إضافة فال code هذا عملية إضافة إضافة ليه إيش؟
+
+285
+00:21:02,700 --> 00:21:05,520
+بنحدد .. بنحدد ال sequence تبعنا هو عبارة عن
+
+286
+00:21:05,520 --> 00:21:11,620
+sequence من A index 0 ل N نقص 1 فأنا عندي فعليا N
+
+287
+00:21:11,620 --> 00:21:18,000
+digits A و B وهذه عبارة عن binary representations
+
+288
+00:21:18,000 --> 00:21:20,660
+with non negative integers يعني احنا مفترض ان هي
+
+289
+00:21:20,660 --> 00:21:22,900
+positive لأن انتوا عارفين جثة ال negative جثة
+
+290
+00:21:22,900 --> 00:21:26,680
+تانية في الها .. هنتكلم عنها قعدنا .. قعدناتمام
+
+291
+00:21:26,680 --> 00:21:30,280
+اول شغل اللي بدنا نحددها هي ال carry ال carry اللي
+
+292
+00:21:30,280 --> 00:21:33,280
+هو بدل ان انت بتجمع فانت عارف ان انت بتجمع مع
+
+293
+00:21:33,280 --> 00:21:36,940
+الحمل مش هيك تجمع مع الحمل فبدنا يكون في خانة
+
+294
+00:21:36,940 --> 00:21:42,640
+space variable يكون لإيش اللي انت بتحمله نتيجة
+
+295
+00:21:42,640 --> 00:21:46,020
+عملية الجمع لل digits هذه okay فحنسميها carry و
+
+296
+00:21:46,020 --> 00:21:52,230
+بداية zero لسه مبدأتش العملية fourال bit index
+
+297
+00:21:52,230 --> 00:21:55,370
+طبعا ال index هو اللي هيكون العامل تبعنا لإن احنا
+
+298
+00:21:55,370 --> 00:21:59,250
+عادة لما بنبنى نجمع بنبنى بنقاش من الأحد الأحد أنا
+
+299
+00:21:59,250 --> 00:22:03,290
+عارف إنه هدى ال index تبعها zero فمعنى ذلك بس
+
+300
+00:22:03,290 --> 00:22:05,930
+تخلصوها بتروحوا للعشرات ال index واحد بعدين
+
+301
+00:22:05,930 --> 00:22:08,450
+بتروحوا للمئات ال index اتنين فمعنى ذلك إنه
+
+302
+00:22:08,450 --> 00:22:11,950
+انتقالي في عملية الجمع هي بناء على ال index أو ال
+
+303
+00:22:11,950 --> 00:22:15,790
+indices تبعتنا هذه فبنحددها بال index يعني حتى
+
+304
+00:22:15,790 --> 00:22:18,390
+المتغيرات اللي بتستعملها لل loop تبعك بدها تكون
+
+305
+00:22:18,390 --> 00:22:23,290
+معبرةفهذه واحدة من أساسيات البرمجة بالمناسبة هي مش
+
+306
+00:22:23,290 --> 00:22:26,430
+حاجة عبثية لأ هي من أساسيات البرمجة و المفروض
+
+307
+00:22:26,430 --> 00:22:29,950
+انتوا عارفين الكلام هذا ال bit index هي ابتداء من
+
+308
+00:22:29,950 --> 00:22:33,610
+الصفر لإيش لإن ناقص واحد بحيث انه مجموحهم in
+
+309
+00:22:33,610 --> 00:22:38,410
+مجموحهم in هي من صفر لإن ناقص واحد begin ابدأ
+
+310
+00:22:38,410 --> 00:22:43,130
+هنبدأ نقول عندي ال bit sum او ال summation لل bits
+
+311
+00:22:43,130 --> 00:22:48,920
+لأنه هاخدها bit by bit هتكون عبارة عن ابال index
+
+312
+00:22:48,920 --> 00:22:52,020
+اللي احنا واقفين عنده اللي هو الأحد هنبدأ .. هنبدأ
+
+313
+00:22:52,020 --> 00:22:55,400
+بالأحد زائد الأحد تعات مين؟ تعات بيه زائد إذا في
+
+314
+00:22:55,400 --> 00:22:58,320
+carry و احنا ال carry مصفرين من الأول لأن يا دو
+
+315
+00:22:58,320 --> 00:23:02,520
+ابن لسه بنبدأ على الأحد مافيش شيء طيب بعد ذلك
+
+316
+00:23:02,520 --> 00:23:08,120
+هنقول ال summation هذه عملية مرحلية و انتوا هيك
+
+317
+00:23:08,120 --> 00:23:10,540
+كنتوا تعملوا فعليا انت كنتوا تعملوا عملية مرحلية
+
+318
+00:23:10,540 --> 00:23:14,720
+قبل ما لسه تحط الرقم انت بتجمع و بتشوف جدش القيمة
+
+319
+00:23:14,720 --> 00:23:16,960
+افرض طلع عندك واحد زائد واحد و كان في ال carry فيه
+
+320
+00:23:16,960 --> 00:23:22,240
+كمان واحديعني فعليا صار عندك تلاتة جمعت تلاتة صحيح
+
+321
+00:23:22,240 --> 00:23:25,900
+طيب التلاتة مش موجودة ضمن ال system ضمن ال system
+
+322
+00:23:25,900 --> 00:23:28,660
+ال binary ولا الإتنين حتى موجودة فعشان هيك إيش
+
+323
+00:23:28,660 --> 00:23:33,720
+بدنا نسوي نقول إن ال S اللي هو ال summation و ال
+
+324
+00:23:33,720 --> 00:23:37,780
+element اللي في العنصر أو موجود في ال index bit
+
+325
+00:23:37,780 --> 00:23:39,840
+index اللي أنا موجود عنده اللي هو الأحد هيكون
+
+326
+00:23:39,840 --> 00:23:48,390
+للناتج يساوي ال bit sum مدله اتنينمدروا اتنين فإذا
+
+327
+00:23:48,390 --> 00:23:52,630
+الناتج هيكون يا صفر يا واحد مافيش اشي تاني يا صفر
+
+328
+00:23:52,630 --> 00:23:56,710
+يا واحد ممتاز خلصناها صفر او واحد ال carry ال
+
+329
+00:23:56,710 --> 00:24:01,150
+carry الآن هو المتبقي مش المفروض هذا المتبقي هيكون
+
+330
+00:24:01,150 --> 00:24:05,390
+اش اللي ضال عندك بعد العملية فهتيجي تقول ال bit
+
+331
+00:24:05,390 --> 00:24:10,770
+sum على اتنين وتاخد ال floor يعني لو كان المجموع
+
+332
+00:24:10,770 --> 00:24:15,340
+تلاتة فعليايعني كان في عندك العنصر الأول one،
+
+333
+00:24:15,340 --> 00:24:20,040
+التاني one، وفي عندك carry هاي صارتلاتة، التلاتة
+
+334
+00:24:20,040 --> 00:24:24,300
+هدول على اتنين واحد و نص، floor واحد، معناته ال
+
+335
+00:24:24,300 --> 00:24:28,900
+carry في واحد، ال carry وجد واحد، end خلصنا هاي
+
+336
+00:24:28,900 --> 00:24:36,360
+إيش حطينا العنصر تعلق حاد عشان نروح لمين؟ للعشرات
+
+337
+00:24:37,120 --> 00:24:40,220
+بس خد بالك إن العشرات الآن قد يكون ال carry إله
+
+338
+00:24:40,220 --> 00:24:45,640
+قيمة صار قد يكون إله قيمة و بستمر لما تخلص لإن
+
+339
+00:24:45,640 --> 00:24:50,100
+ناقص واحد خلصنا إن ناقص واحد انتهى الكلام okay
+
+340
+00:24:50,100 --> 00:24:53,760
+ضايق حاجة لسه ماخدناش بالنا منها إن أنت خلصت لعيني
+
+341
+00:24:53,760 --> 00:24:58,380
+ناقص واحد بس إذا ال carry فيه قيمة فيه إله قيمة
+
+342
+00:24:58,380 --> 00:25:04,880
+القيمة هادة بتروح ليش لإن لأنه أصبح فتحت معاك خانة
+
+343
+00:25:04,880 --> 00:25:09,200
+جديدةزي لما تقول تسعة وتسعين زائد خمسة انت فعلا
+
+344
+00:25:09,200 --> 00:25:13,420
+عندك خنتين بس الناتج صار تلاتة الناتج فعلا بصير
+
+345
+00:25:13,420 --> 00:25:19,120
+تلاتة فمعنى ذلك بده تاخد بالك انه لعند end هنا انت
+
+346
+00:25:19,120 --> 00:25:24,080
+عبيت ال indices تبعونك من صفر ل N نقص واحد طيب ال
+
+347
+00:25:24,080 --> 00:25:28,830
+carry بتحطه في ايش؟ في endصار الآن عندك S هذه ك
+
+348
+00:25:28,830 --> 00:25:34,110
+sequence مخزن لك ناتج عملية الجامعة ابتداء من S
+
+349
+00:25:34,110 --> 00:25:40,310
+012 لندن لندن ف return ب ال sequence هذا return
+
+350
+00:25:40,310 --> 00:25:43,910
+بال sequence هذا اتوقع ان هي بسيطة مش كتير فيها
+
+351
+00:25:43,910 --> 00:25:48,150
+تعقيد ماهياش مشكلة كبيرة فعشان كنا ماشيين ب .. ب
+
+352
+00:25:48,150 --> 00:25:52,710
+.. يعني بطريقة ان انتوا ماخدين عارفين يعني مركزين
+
+353
+00:25:52,710 --> 00:25:57,630
+معنا طيب لما اقول بدي اعمل subtractionعملية الطرح
+
+354
+00:25:57,630 --> 00:26:02,230
+عملية الطرح لأ شوية بدنا نكون حذرين في جزئية من ال
+
+355
+00:26:02,230 --> 00:26:05,190
+binary و احنا بتتعامل مع ال binary عملية الطرح هي
+
+356
+00:26:05,190 --> 00:26:13,370
+معناها ان لما اقول a ناقص b كأني بقول a زائد سالب
+
+357
+00:26:13,370 --> 00:26:21,890
+b سالب b طيب سالب هادي في ال binary فيله قيمة اه
+
+358
+00:26:21,890 --> 00:26:25,900
+ال compliment بس مش ال first complimentال two ..
+
+359
+00:26:25,900 --> 00:26:29,020
+ال two is complement مش ال one complement ال two
+
+360
+00:26:29,020 --> 00:26:33,700
+is complement لأنه لو جيت اشتغلت على ال first او
+
+361
+00:26:33,700 --> 00:26:37,820
+ال .. اه ال one complement و جمعته مع العنصر
+
+362
+00:26:37,820 --> 00:26:41,340
+الأصلي تبعه مش هيطلع معاك صفر بطلعش المجموع صفر
+
+363
+00:26:41,340 --> 00:26:46,740
+بينما وفقليا المفروض يطلع صفر مش هيك منطقي انت
+
+364
+00:26:46,740 --> 00:26:51,770
+اعطي اتخيل لحالك اي قيمة ل Bبال binary و جيب لها
+
+365
+00:26:51,770 --> 00:26:55,790
+ال one complement المفروض انت متخيل ان هو سلب بي
+
+366
+00:26:55,790 --> 00:27:04,990
+طب يجمعهم بطلعش صفر ف plus واحد في ال carry plus
+
+367
+00:27:04,990 --> 00:27:09,230
+واحد ال two's complement ال two's complement بمشي
+
+368
+00:27:09,230 --> 00:27:16,130
+الحال فبتيجي لما تيجي تجمعهم فعليا ال بيتجمعها مع
+
+369
+00:27:16,130 --> 00:27:19,390
+السالب بي بتاعتها انت ضامن انه في الآخر هيروح ليش
+
+370
+00:27:19,390 --> 00:27:26,610
+لزيرو وهو هذا المنطقى كيف انا بقول عليها عكس بي
+
+371
+00:27:26,610 --> 00:27:30,230
+جربوها انتوا اخدتوا طبعا ال one و ال two
+
+372
+00:27:30,230 --> 00:27:32,530
+compliment اتنين ال one compliment اخدتوا و ال two
+
+373
+00:27:32,530 --> 00:27:35,170
+compliment اخدتوا عملتوا check ع الكلام هذا؟
+
+374
+00:27:35,910 --> 00:27:37,730
+المفروض كنت تعمل ال check كمان انت بدك تقل بالظبط
+
+375
+00:27:37,730 --> 00:27:42,470
+خلاص فإذا احنا متفقين ماعناش مشكلة تمام فإذا قيل
+
+376
+00:27:42,470 --> 00:27:48,450
+ال procedures بشكل بسيط بشكل أساسي كانت تالي هنحط
+
+377
+00:27:48,450 --> 00:27:55,610
+ال code تبعنا هيه هي codeنا procedure subtract أي
+
+378
+00:27:55,610 --> 00:28:01,030
+اسم يعبر عن أي عملية اللي بده اعملها ل two binary
+
+379
+00:28:01,030 --> 00:28:05,740
+numbersنمبر أول والتاني عساس انه بدي يكون عبارة عن
+
+380
+00:28:05,740 --> 00:28:12,080
+ال inverse لاحظ inverse يعني مجرد ال once
+
+381
+00:28:12,080 --> 00:28:17,340
+complement اللي هو كل digit بتعكسها فقط هذا ال
+
+382
+00:28:17,340 --> 00:28:21,820
+once complement مش شايف؟ لو حطيت bar فوق فبعرف ان
+
+383
+00:28:21,820 --> 00:28:24,140
+انت بتتكلم عن ال once complement بمعنى اللي هو ال
+
+384
+00:28:24,140 --> 00:28:30,140
+inverseبت وايز بيت وايز ايش يعني يعني بمسكها بت by
+
+385
+00:28:30,140 --> 00:28:33,500
+بت كل بت واحد بجلبها لصفر وكل بت صفر بجلبها لواحد
+
+386
+00:28:33,500 --> 00:28:37,920
+و بس تمام لو جمعتها على الاصلي تبعها مش هتطلع صفر
+
+387
+00:28:37,920 --> 00:28:43,640
+بتطلعش معاك دايما صفر كويس فبنضطر نعمل ال two's
+
+388
+00:28:43,640 --> 00:28:49,250
+complement كيف هنعملها كل الموضوع انه عندكbinary
+
+389
+00:28:49,250 --> 00:28:54,450
+number أول و binary number تاني عكسه انت كل صفر
+
+390
+00:28:54,450 --> 00:28:57,190
+هتجلبها واحد و كل واحد هتجلبه صفر عشان تيجي تعمل
+
+391
+00:28:57,190 --> 00:29:00,210
+.. توصل منه ل two's complement بس ال two's
+
+392
+00:29:00,210 --> 00:29:02,570
+complement عشان تعمل و مش بده تعمل return لاحظ انه
+
+393
+00:29:02,570 --> 00:29:04,990
+دخلنا ع return على طول ليش؟ لأن انا عملت هنا
+
+394
+00:29:04,990 --> 00:29:10,670
+method او function في بعض اللغات التانية عملت
+
+395
+00:29:10,670 --> 00:29:14,390
+calling لمين ل code انت كاتبه سابقا طب احنا كتبناه
+
+396
+00:29:14,390 --> 00:29:18,560
+تول قدمش احنا توي عملنا ال add؟ خلصنا ال add توي
+
+397
+00:29:18,560 --> 00:29:23,300
+عملناها add فانت كله اللي بتعمله add تستدعي ال
+
+398
+00:29:23,300 --> 00:29:26,920
+function اللي اسمها add لمين؟ بتعطيها ال input
+
+399
+00:29:26,920 --> 00:29:36,380
+بتاعتها A و افتح add كمان مرة لمين؟ لل inverse او
+
+400
+00:29:36,380 --> 00:29:41,680
+العكس اللي هو ال once complement ل B و 1 عشان تصير
+
+401
+00:29:41,680 --> 00:29:45,440
+two's complementفناتج الاد هذا هو ال twice
+
+402
+00:29:45,440 --> 00:29:50,740
+complement ل B هو twice complement ل مين؟ ل B انت
+
+403
+00:29:50,740 --> 00:29:56,780
+كان عندك مجموعة digits عكستها و بس فانت بتروح ا
+
+404
+00:29:56,780 --> 00:29:59,400
+روحت على ال once complement once complement فهذه
+
+405
+00:29:59,400 --> 00:30:03,700
+once complement زائد واحد صارت ال twice complement
+
+406
+00:30:03,700 --> 00:30:09,880
+هذه نفسها كناتج بتجمع مع ال A فكأنك جبت A ناقص B
+
+407
+00:30:11,190 --> 00:30:16,390
+خلصت هي خلص الموضوع هي خلص الموضوع بالمناسبة هنا
+
+408
+00:30:16,390 --> 00:30:19,090
+انت بتعملها لمرة واحدة يعني هد مش هيكون في loop
+
+409
+00:30:19,090 --> 00:30:25,250
+هنا مافيش loop لمرة واحدة بتعملها خلاص فكتعقيد لهم
+
+410
+00:30:25,250 --> 00:30:28,790
+ال complexity مش عالية انت لمرة واحدة بتعملها بس
+
+411
+00:30:28,790 --> 00:30:32,770
+لا اكثر ولا اقل تمام ف ..
+
+412
+00:30:35,780 --> 00:30:39,140
+فيش إشكل طيب أحيانا بصير معنى مشكلة فيها في عملية
+
+413
+00:30:39,140 --> 00:30:43,720
+ال .. القذق ال .. اللي هي عملية الطرح هذه عملية
+
+414
+00:30:43,720 --> 00:30:48,760
+الطرح أنه ممكن يكون في عندك carry أكبر من ال N نقص
+
+415
+00:30:48,760 --> 00:30:52,700
+واحد أو في خانة أعلى من ال N نقص واحد ليش؟ لأن انت
+
+416
+00:30:52,700 --> 00:30:57,080
+في النهاية بتتعامل مع add انت حولتها ل add طيب ال
+
+417
+00:30:57,080 --> 00:31:01,940
+carry اللي صار عندك هذا إيش مصيره؟ overflow
+
+418
+00:31:04,600 --> 00:31:08,000
+مش اخدتوا overflow؟ طيب ممتاز هذا overflow ليش؟
+
+419
+00:31:08,000 --> 00:31:11,620
+لأنك انت حولت العملية أصلا لجامعة مدام حمار حولتها
+
+420
+00:31:11,620 --> 00:31:17,460
+لجامعة فتوقع أن ممكن يطلع معاك carry كويس ال carry
+
+421
+00:31:17,460 --> 00:31:25,040
+اللي طلع معاك بكل بساطة اشطبه بكل بساطة احثفه ليش؟
+
+422
+00:31:28,090 --> 00:31:30,830
+لأن أنت بتتعامل مع ال two's complement و أضف إلى
+
+423
+00:31:30,830 --> 00:31:34,030
+ذلك ممكن تظهر في بعض الحالات أنه أساسا الأنصار
+
+424
+00:31:34,030 --> 00:31:41,830
+الأول أصغر من التاني مش هيك قد تظهر ممكن تظهر
+
+425
+00:31:41,830 --> 00:31:45,270
+فمعنى ذلك أنه هتصير انت متلخبط هل هو carry فعليا
+
+426
+00:31:45,270 --> 00:31:50,780
+ولا هو signفكلكوا عارفين أن ال sign كآخر digit
+
+427
+00:31:50,780 --> 00:31:55,380
+عبارة عن واحد فمعناه ذلك أن ال sign تبعتك سالب أو
+
+428
+00:31:55,380 --> 00:31:59,260
+negative فالعنصر negative فانت بتصير انت مش عارف
+
+429
+00:31:59,260 --> 00:32:02,280
+هو المفروض أنه عملية الجامعة اللي أفرزت الواحد هذه
+
+430
+00:32:02,280 --> 00:32:06,540
+ك carry ولا هي لأنه الرقم الأول أصغر من التاني
+
+431
+00:32:06,540 --> 00:32:13,260
+فالمفروض هذه sign فبكل بساطة شيلها فبدك تاخد بالك
+
+432
+00:32:13,260 --> 00:32:17,560
+أن الناتج هيكون لعند إيه ناقص واحد بستمام، الآن
+
+433
+00:32:17,560 --> 00:32:22,280
+نعلى شوية، بدنا نضرب ال binary، بدنا نضرب عملية اه
+
+434
+00:32:22,280 --> 00:32:26,360
+كلهم هتعملوهم، كلهم هتعملهم مع بعض، عملية الضرب
+
+435
+00:32:26,360 --> 00:32:32,840
+الآن عشان نجي نعمل عملية الضرب، شوية هنا بدنا نفصل
+
+436
+00:32:32,840 --> 00:32:39,650
+فيها لأنهحلوة الحقيقة اللي ال code كيف مكتوب هو و
+
+437
+00:32:39,650 --> 00:32:45,450
+ال division فيهم فكرة لو احتجتوها في ال data
+
+438
+00:32:45,450 --> 00:32:50,310
+structure هتنبسطوا عليها عادة لما تكون بدك تعمل
+
+439
+00:32:50,310 --> 00:32:55,190
+مثلا
+
+440
+00:32:55,190 --> 00:33:01,210
+نفترض خلينا نفترض حاجة بهذا الشكل و بدك تضربهم في
+
+441
+00:33:01,210 --> 00:33:08,630
+بعضهاتوا نفكر مع بعض إيش كنا نعمل بنرجع نكرر ..
+
+442
+00:33:08,630 --> 00:33:14,310
+بنكررهم فعليا بس كل مرة ب shift صح؟ تمام فإذا
+
+443
+00:33:14,310 --> 00:33:22,630
+بنيجي بناخد الصفر الأول صفر في واحد صفر واحد كله
+
+444
+00:33:22,630 --> 00:33:34,520
+أصفر طيب التاني بس يبدأ من خيانتهيبدأ من خانته طيب
+
+445
+00:33:34,520 --> 00:33:43,060
+هنا واحد بس هيبدأ من خانته وبتجمع هذه
+
+446
+00:33:43,060 --> 00:33:48,190
+الطريقة اللي بنحكيها كنا ممتازةممتاز معنى ذلك انه
+
+447
+00:33:48,190 --> 00:33:52,770
+انت في كل عملية ضرب هلوقت بنا نطلع بشوية شواهد ايش
+
+448
+00:33:52,770 --> 00:33:55,750
+اللي عملناها بالظبط بدنا نحلل اللي عملناها لأن هذا
+
+449
+00:33:55,750 --> 00:33:59,530
+هو ال code اللي بدنا نشتغله هتنحلل الموضوع فعليا
+
+450
+00:33:59,530 --> 00:34:04,070
+انت لما بتيجي تضرب فيه اي رقم في الخانة في خانة
+
+451
+00:34:04,070 --> 00:34:10,970
+معينة كأنك بتضيف قدامه عدد أصفار بالخانة يعني كأنك
+
+452
+00:34:10,970 --> 00:34:14,390
+انت هنا ضيفت صفر صفركأنك انت هنا ضيفي كمان صفر
+
+453
+00:34:14,390 --> 00:34:18,770
+فلاحظ لما ضربت في الواحد هذا بدأ نطلع واحد بتشوف
+
+454
+00:34:18,770 --> 00:34:26,230
+جداش ال index تبعه و بتضيف عدد أسفار قدامه مش هيك
+
+455
+00:34:26,230 --> 00:34:30,830
+صح يعني هي الفكرة كنا نعملها صح بس ماكنتش كتير
+
+456
+00:34:30,830 --> 00:34:33,630
+معبرة لما كنت بقول shift لأ هي الموضوع أكبر من
+
+457
+00:34:33,630 --> 00:34:37,610
+مجرد shift هي أنا بضيف أسفار الصح أن أنا بضيف
+
+458
+00:34:37,610 --> 00:34:40,810
+أسفار لأنه الآن بدها تبين الأسفار اللي هنضيفها
+
+459
+00:34:41,750 --> 00:34:45,270
+الكمبيوتر مايعرف كلمة shift مايعني shift مش
+
+460
+00:34:45,270 --> 00:34:49,750
+هيفهمها shift هيفهم التالي واضح تهدي اه لإن هو
+
+461
+00:34:49,750 --> 00:34:52,490
+نفسه احنا أكسه على البالكود ال procedure multiply
+
+462
+00:34:52,490 --> 00:34:57,670
+وهي في عند ال two binary numbers بدنا نضربه في بعض
+
+463
+00:34:57,670 --> 00:35:02,830
+بمثله a و b natural number خلاص تمام product zero
+
+464
+00:35:02,830 --> 00:35:06,330
+برضه بدنا نصفر عملية التجميع اللي بدنا نشتغل فيها
+
+465
+00:35:06,330 --> 00:35:09,750
+لأنه لاحظوا أن هي في النهاية عملية تجميع أنا قاعد
+
+466
+00:35:09,750 --> 00:35:15,720
+بجمععملية الضرب ما هي عملية جمع بس حسب الخنات و
+
+467
+00:35:15,720 --> 00:35:20,500
+الأصفار اللي هضيفها لكل خانة طيب نبدأ بال for loop
+
+468
+00:35:20,500 --> 00:35:26,480
+تبعتنا ابتدا من صفر فانا عند الأحد بدأت بالأحد هين
+
+469
+00:35:26,480 --> 00:35:28,800
+بدأ أبدأ أشغل على حد يعني كأنه بدأ أبدأ بالصفر
+
+470
+00:35:28,800 --> 00:35:35,200
+الأول هذا نضربه في الرقم نضربه في الرقم كويسة لعند
+
+471
+00:35:35,200 --> 00:35:39,220
+ما نكمل كل الرقم فإذا كانت بصفر
+
+472
+00:35:41,810 --> 00:35:46,590
+هيها هذه بي صفر تساوي واحد ايش اللي بدنا نعمله؟
+
+473
+00:35:46,590 --> 00:35:51,610
+بدنا ننزل ايه؟ بدنا ننزل ايه؟ فال product هنا
+
+474
+00:35:51,610 --> 00:36:00,410
+بيصير ايه؟ يساوي قيمة a بعدد أصفار حسب ال b بعدد
+
+475
+00:36:00,410 --> 00:36:07,670
+أصفار حسب ال b يعني كأنها بتصير add هيها لأ a وعدد
+
+476
+00:36:07,670 --> 00:36:14,800
+أصفاربال I فانا بديت ب صفر مش محتاج أصفر فبت ..
+
+477
+00:36:14,800 --> 00:36:20,240
+بتنزل ال A زي ما هي لأنه أنا مازلت في الأحد مازلنا
+
+478
+00:36:20,240 --> 00:36:24,940
+في مين؟ في الأحد تنزل كما هي هي ال A ال 101 لو ..
+
+479
+00:36:24,940 --> 00:36:28,040
+لو هنا في عندي واحد فال 101 بتنزل .. اللي هي 101
+
+480
+00:36:28,040 --> 00:36:32,860
+يعني بتنزل زي ما هي هنا مانضفلهاش أي شيء خلاص زي
+
+481
+00:36:32,860 --> 00:36:37,100
+ما هي زائد ال product اللي كان موجود أصلا صفرطيب
+
+482
+00:36:37,100 --> 00:36:44,260
+فعليا اتخزن عندى لان حتى اللحظة الرقم الاول خلاص
+
+483
+00:36:44,260 --> 00:36:54,420
+هذا أصبح said كويس وموجود ضمن product اتنين اي
+
+484
+00:36:54,420 --> 00:36:58,660
+واحد اي واحد معناته بتروح لعنصر اللى ورا and so on
+
+485
+00:36:58,660 --> 00:37:05,710
+بهذا الشكل طيب اذا a و اذا ال b واحديساوي واحد
+
+486
+00:37:05,710 --> 00:37:12,130
+برضه ارجع نزلي A بس على كلامك وماخده shift طب ال
+
+487
+00:37:12,130 --> 00:37:16,990
+shift ده عبارة عن ايش صفر في اليمين معناته زدلي
+
+488
+00:37:16,990 --> 00:37:20,970
+عدد أصفر بقيمة I I قيمتها واحد معناته بزيد صفر
+
+489
+00:37:20,970 --> 00:37:25,670
+واحد فعلا اه هينزدنا صفر واحد فعلا احنا فعلا زدنا
+
+490
+00:37:25,670 --> 00:37:32,360
+صفر واحد تمام و اجمعها على ال product السابقفمعنى
+
+491
+00:37:32,360 --> 00:37:42,380
+ذلك راح جمع الاتنين هدول على بعض مين
+
+492
+00:37:42,380 --> 00:37:46,580
+اللي مش هيتطبّح؟ بالظبط اه اه بالظبط احنا هينا
+
+493
+00:37:46,580 --> 00:37:48,640
+شغالين المفروض ان هو مش هيعمل هذا الكلام اللي لما
+
+494
+00:37:48,640 --> 00:37:51,460
+يتساوي واحد لأنه حتى اللحظة مالهاش معنى اللي احنا
+
+495
+00:37:51,460 --> 00:37:54,220
+عاملينه بالمثال تبعنا المثال تبعنا مالهاش معنى ليش
+
+496
+00:37:54,220 --> 00:37:58,100
+لإن انت بتجمع أصفار فوفر على حالة تجمية الأصفار بس
+
+497
+00:37:58,100 --> 00:38:02,890
+لأكثر ولا قلت انت صارت واحدعند الاتنين مثلا عند
+
+498
+00:38:02,890 --> 00:38:07,150
+الاتنين بدنا نزود واحد سرق قيمتها واحد okay نزلي
+
+499
+00:38:07,150 --> 00:38:14,870
+ال a وعلى يمينها عدد أصفار حسب ال index بتاعت بي
+
+500
+00:38:14,870 --> 00:38:21,410
+طيب جديش index بي؟ اتنين زودلي صفرين على يمينها
+
+501
+00:38:21,410 --> 00:38:24,210
+على ال sequence تبعها لو هذه array انت حاططك الشكل
+
+502
+00:38:24,210 --> 00:38:27,950
+array المعنى انك بتضيفلك صفرين هاي الصفرين
+
+503
+00:38:30,540 --> 00:38:34,040
+فعلا احنا قضفنا صفرين فعملية ال shift هي عملية
+
+504
+00:38:34,040 --> 00:38:38,420
+إضافة أصفر في الضرب هي مش مجرد shift خلاص لأ هي
+
+505
+00:38:38,420 --> 00:38:42,380
+عملية إضافة أصفر ليش؟ لأن انت خلت أصلا الخانة
+
+506
+00:38:42,380 --> 00:38:47,020
+تقعدت تختلف هي بطلت بادية من خانة أحد هي صارت
+
+507
+00:38:47,020 --> 00:38:52,280
+بادية من خانة مئاتطيب معنى ذلك أنه في خانة أحد و
+
+508
+00:38:52,280 --> 00:38:56,180
+عشرات ماحدش بندق لخانة المئات و مالوش في الأحد و
+
+509
+00:38:56,180 --> 00:38:59,160
+العشرات صح؟ مافيش حاجة اسمها هيك أنا والله فجأة
+
+510
+00:38:59,160 --> 00:39:02,700
+بدأت من المئات مافيش اشي هيك اسمه فمدأت .. مدأت من
+
+511
+00:39:02,700 --> 00:39:08,500
+المئات بدي أضيف صفر للعشرات و صفر ليش للأحد خلصنا
+
+512
+00:39:08,500 --> 00:39:12,520
+ال code فضل سؤال ببرمجة أنا ممكن أضيف أصفر جنبها
+
+513
+00:39:12,520 --> 00:39:15,520
+ممكن و لا لازم أعملها method أنا إيش تقولتلك إذا
+
+514
+00:39:15,520 --> 00:39:18,880
+قلتلك إذا أنت متعامل معاها قريه أه بتضيف
+
+515
+00:39:21,470 --> 00:39:23,850
+String ما هي ال array أو ال string او خلاص ما هي
+
+516
+00:39:23,850 --> 00:39:29,030
+string array sequence بتضيفها هالصفرين عليها بمشي
+
+517
+00:39:29,030 --> 00:39:29,270
+الحل
+
+518
+00:39:38,400 --> 00:39:43,180
+لأ لأ عادي عادي بتعملها .. بت .. بدك تعملها هنا
+
+519
+00:39:43,180 --> 00:39:46,600
+method لحالها بتضيف لها four اللي هو في كل مرة
+
+520
+00:39:46,600 --> 00:39:50,540
+بتضيف صفر انت في النهاية على نفس ال array هي هي و
+
+521
+00:39:50,540 --> 00:39:53,160
+ممكن تكون temporary array او temporary string
+
+522
+00:39:54,380 --> 00:39:57,460
+هتستعمله على طول العملية كاملة، ليش؟ لأنه أول مرة
+
+523
+00:39:57,460 --> 00:40:02,560
+أنت هتاخد نسخة من الرقم تبعك، تمام؟ في ال loop ..
+
+524
+00:40:02,560 --> 00:40:05,260
+في ال loop .. ال .. ال .. أول loop في ال loop
+
+525
+00:40:05,260 --> 00:40:09,540
+الأولى، أنت هتضيف one zero، يعني كل اللي هتعمله،
+
+526
+00:40:09,540 --> 00:40:16,960
+method اضيف بس عنصر صفر، بس، في كل لفة هتضيف ..
+
+527
+00:40:16,960 --> 00:40:23,470
+هتضيفلك عنصر، و اتجمعانصر و اتجمع فممكن تعمل ال
+
+528
+00:40:23,470 --> 00:40:26,010
+method و ال method ده تكون عبارة عن كل مرة اضيف
+
+529
+00:40:26,010 --> 00:40:30,150
+واحد لأ
+
+530
+00:40:30,150 --> 00:40:32,750
+اول لفة انا مش هتضيفش ايه هتكون نفس الرقم اللي انت
+
+531
+00:40:32,750 --> 00:40:42,130
+استنسخته من ال a ال a زي ما هي اخدت منها نسخة في
+
+532
+00:40:42,130 --> 00:40:47,060
+temporary space مش هيك او temporary stringOkay
+
+533
+00:40:47,060 --> 00:40:50,100
+وابدأ اشتغل على ال string هذا تمشي احنا هنا زي ما
+
+534
+00:40:50,100 --> 00:40:53,780
+قلتلك كمان مرة في ال pseudocode احنا بنشرح ال
+
+535
+00:40:53,780 --> 00:40:58,760
+concept بعد هيك ممكن طريقة ال Java تختلف ك
+
+536
+00:40:58,760 --> 00:41:02,200
+structure عن ال C++ عن ال Python عن .. okay بس
+
+537
+00:41:02,200 --> 00:41:10,260
+الفكرة واحدة طيب ناخد ال division ال division ايوة
+
+538
+00:41:10,260 --> 00:41:15,660
+خلاص نفهمها كتابة اخدتوها ال division متذكرينها؟
+
+539
+00:41:16,510 --> 00:41:30,930
+طيب ماشي القسمة المطولة اه اظن
+
+540
+00:41:30,930 --> 00:41:33,530
+هذا الرقم اللي هو كان ناتج عندنا صح؟ اعتقد كان
+
+541
+00:41:33,530 --> 00:41:38,070
+ناتج عندنا طيب و هات ناخد هذا فالمتوقع احنا
+
+542
+00:41:38,070 --> 00:41:41,910
+متخيلين ايش اللي لازم يظهر؟ المفروض .. عفوا ايش
+
+543
+00:41:41,910 --> 00:41:44,110
+هذا؟ احنا أخدنا الناتج على طول؟
+
+544
+00:41:48,820 --> 00:41:51,700
+وبدنا النتج هنا واللي احنا متخيله ان الوقش المفروض
+
+545
+00:41:51,700 --> 00:41:59,940
+يطلع 101 اصلا 101 طيب هنا شوية ال code عملها
+
+546
+00:41:59,940 --> 00:42:05,900
+معكوسة عكسها شوية يعني أخد عملية الضرب وافترضها
+
+547
+00:42:05,900 --> 00:42:12,070
+بالعكسأفترضها بشكل عكسي هالوقت هانيش نمشي معها و
+
+548
+00:42:12,070 --> 00:42:15,650
+كل حاجة خطوة نعملها هنا نروح نشتغلها على القسم
+
+549
+00:42:15,650 --> 00:42:19,310
+المطول اللي مكتوب قدامنا بدأ افترض ال procedure و
+
+550
+00:42:19,310 --> 00:42:23,030
+ال division ل ال number تبعنا مافيش أي مشكلة
+
+551
+00:42:23,030 --> 00:42:28,050
+باستخدام الطريقة العادية هالوقت بدأ أقول N هي ال
+
+552
+00:42:28,050 --> 00:42:41,300
+maximum length ما بينو D على اعتبار ان هذا A وهذا
+
+553
+00:42:41,300 --> 00:42:45,060
+D dividend
+
+554
+00:42:45,060 --> 00:42:51,080
+و divisor كويس هنبدأ اللي وابتبعناه من الناقص واحد
+
+555
+00:42:52,290 --> 00:42:57,290
+من N ناقص واحد هنا محدد هو ال length تبع إيش اللي
+
+556
+00:42:57,290 --> 00:43:00,930
+هو ال N محدد ال length على أساس إنه إيش قيمة N
+
+557
+00:43:00,930 --> 00:43:04,370
+يعني بدنا نفرض إنه مين N من الجدشكة هتكون قيمتها
+
+558
+00:43:04,370 --> 00:43:07,650
+هنا N
+
+559
+00:43:07,650 --> 00:43:13,090
+اللي هي ال length of A in bits و ال length of D of
+
+560
+00:43:13,090 --> 00:43:15,470
+lengths و بدنا ناخد ال maximum خمسة
+
+561
+00:43:18,160 --> 00:43:24,520
+صحيح؟ فالأكبر هو ال A ب N تساوي خمسة هنبدأ من
+
+562
+00:43:24,520 --> 00:43:32,140
+أربعة و نكمل و نشوف و نعمل down to فهنا بتصير ال
+
+563
+00:43:32,140 --> 00:43:42,320
+counter عكسي إذا A أكبر من أو يساوي D مع إضافة
+
+564
+00:43:42,320 --> 00:43:44,520
+zeros بعدد الأربعة
+
+565
+00:43:48,260 --> 00:43:53,880
+لأنه هي عكسية لها ديك هتنمسكها شوية شوية يعني كأنه
+
+566
+00:43:53,880 --> 00:43:59,980
+هنا بده يصير ال
+
+567
+00:43:59,980 --> 00:44:04,920
+one صفر صفر وإن ضيف واحد صفر اتنين هاي أربع أصفر
+
+568
+00:44:04,920 --> 00:44:12,740
+هاي أربع أصفر هل ال a أكبر من هذا الرقم أكيد لأ
+
+569
+00:44:12,740 --> 00:44:17,980
+هنا خمسة و هنا صار في عندي سبعةصار عندي سبعة ففي
+
+570
+00:44:17,980 --> 00:44:26,260
+الحالة هذه هنروح ل else ال quotient في الخانة I ب
+
+571
+00:44:26,260 --> 00:44:34,760
+zero فهنا هنبدأ ب zero هنبدأ
+
+572
+00:44:34,760 --> 00:44:38,400
+ب zero تمام بعد هي خلص خلصنا ال loop عشان نرجع
+
+573
+00:44:38,400 --> 00:44:41,980
+لمين لتلاتة
+
+574
+00:44:41,980 --> 00:44:42,640
+100%
+
+575
+00:44:49,320 --> 00:44:56,460
+هل ايه أكبر كمان
+
+576
+00:44:56,460 --> 00:45:03,820
+صفر اتنين
+
+577
+00:45:03,820 --> 00:45:07,960
+اه
+
+578
+00:45:07,960 --> 00:45:12,500
+تمام أكبر بروحش ل else هنروح لمين نبدأ في ال then
+
+579
+00:45:12,500 --> 00:45:17,100
+then أول شغلة ال caution تبعك بواحد okay
+
+580
+00:45:19,420 --> 00:45:25,140
+هي واحد بعدين ال a بدها تتغير حسب القسم المطول
+
+581
+00:45:25,140 --> 00:45:31,560
+المفروض أنه اطرحهم فبنعمل طرح بنفس عدد الأصفر يعني
+
+582
+00:45:31,560 --> 00:45:36,540
+معناه ذلك أن هذا الرقم اللي هو هيطرح مش هذا هذا
+
+583
+00:45:36,540 --> 00:45:40,080
+الرقم اللي هو هيطرح هيها بعدد أصفره بعدد الأصفر
+
+584
+00:45:40,080 --> 00:45:42,940
+تبعته فكأنه أصبح ال
+
+585
+00:45:45,270 --> 00:45:48,230
+العنصر عندي هنا أكمل صفر قدامه أربعة هاي واحد
+
+586
+00:45:48,230 --> 00:46:00,150
+اتنين تلاتة أربعة واحد صفر صفر واحد صفر صفر تمام
+
+587
+00:46:00,150 --> 00:46:05,310
+اللي عندك الآن جيد بهذا الشكل خلصنا أول جزء خلصنا
+
+588
+00:46:05,310 --> 00:46:09,350
+الاتنين هيك الواحد
+
+589
+00:46:18,380 --> 00:46:28,960
+A أكبر منه؟ أكيد لأ فإذا بنضيف صفر خلاص
+
+590
+00:46:28,960 --> 00:46:38,360
+خلصت أصلا طيب أخر شي صفر اللي هو أخر عنصر عندي صفر
+
+591
+00:46:38,360 --> 00:46:43,580
+أخر عنصر خلاص صح؟ هدا الصفر أخر عنصر ففي
+
+592
+00:46:43,580 --> 00:46:47,390
+الحالة دي أكبر أو يساوي؟ أه هو يساوي فعليامعناته
+
+593
+00:46:47,390 --> 00:46:57,070
+أول شغلة حط واحد و اطرح without
+
+594
+00:46:57,070 --> 00:47:03,330
+remainder بدون باقي كمان هل هو المتوقعين و الحل
+
+595
+00:47:03,330 --> 00:47:07,990
+المتوقعين فيه هو الحل المتوقعين فيه فبطريقة عكسية
+
+596
+00:47:07,990 --> 00:47:13,690
+عن عملية الضرب بطريقة عكسية عن عمليةالضرب المتبعة
+
+597
+00:47:13,690 --> 00:47:17,810
+فهي ال code اللي ممكن نستخدمه لعملية ال division
+
+598
+00:47:17,810 --> 00:47:21,150
+لل binary ليش لل binary؟ هاي code مكتوب و مرتب و
+
+599
+00:47:21,150 --> 00:47:27,850
+مظبط و جيد الآن في عندنا شوية تطبيقات مهمة على
+
+600
+00:47:27,850 --> 00:47:29,930
+نظريات الأعداد اللي احنا هيك اتكلمنا عنها اللي
+
+601
+00:47:29,930 --> 00:47:33,070
+أخدناها النظرية التطبيقات دي لها تطبيقات كتير
+
+602
+00:47:33,070 --> 00:47:37,290
+الحقيقة و معظمها حاجات اللي لها علاقة بالتشفيرأو
+
+603
+00:47:37,290 --> 00:47:41,490
+التكويض أو ال encryption في مثلا ال hash functions
+
+604
+00:47:41,490 --> 00:47:44,890
+في عملية ال simulation عملية ال games بناء ال
+
+605
+00:47:44,890 --> 00:47:48,570
+games و ال graphics معتمدة بشكل مش طبيعي على نظرية
+
+606
+00:47:48,570 --> 00:47:52,650
+الأرقام و جدش أنت ماهر في التعامل مع الأرقام جدش
+
+607
+00:47:52,650 --> 00:47:56,230
+أنت بتقدر تتعامل مع الأرقام و تشتغل الشغل اللي
+
+608
+00:47:56,230 --> 00:47:59,050
+أخدناه خلال المحاضرة السابقة و بداية المحاضرة
+
+609
+00:47:59,050 --> 00:48:04,810
+لليوم اللي احنا هنركز عليه فعليا هيالجزئية ال
+
+610
+00:48:04,810 --> 00:48:08,750
+random كيف انا ممكن اعمل generalization او
+
+611
+00:48:08,750 --> 00:48:14,730
+generation ل random numbers مجموعة ارقام عشوائية
+
+612
+00:48:14,730 --> 00:48:21,590
+لانه بدي استخدمها as a mask ك mask تضرب فيها ال
+
+613
+00:48:21,590 --> 00:48:25,050
+data اللي عندك و تبعتها لو انا شفتها مافهمش منها
+
+614
+00:48:25,050 --> 00:48:31,840
+اشي انا مش هفهم منها حاجةبالنسبالي و لا عارف إيش
+
+615
+00:48:31,840 --> 00:48:35,520
+اللي بعدته، لكن في نفس الوجد ال .. ال random هذا
+
+616
+00:48:35,520 --> 00:48:39,100
+لازم تكون انت قادر ترجع ال word له كمان مرة، مش
+
+617
+00:48:39,100 --> 00:48:41,380
+والله random معناته بكل ما تعنيه الكلمة random
+
+618
+00:48:41,380 --> 00:48:47,090
+خلاص هو راح، فبنسميها pseudo randomشبه عشوائي ليش
+
+619
+00:48:47,090 --> 00:48:51,250
+شبه عشوائي؟ لأن انت بتقدر ترجع تجيبه كمان مرة ترجع
+
+620
+00:48:51,250 --> 00:48:54,190
+تقدر تجيبه ليش؟ لأنك انت بعد ما بعدت ال message
+
+621
+00:48:54,190 --> 00:48:56,850
+بعد أسبوع زمان تنسيت أصلاش اللي كنت كاتبه طب أنا
+
+622
+00:48:56,850 --> 00:49:01,290
+بدي أرجع أفك تشفيرها بدنا نرجع نفك تشفيرها عشان
+
+623
+00:49:01,290 --> 00:49:06,550
+تفهمها أو بدك تبعتها لحدة و أنت متفق بينك و بينه
+
+624
+00:49:06,550 --> 00:49:11,790
+كيف ممكن يعيد توليد ال random numbers عشان يرجع
+
+625
+00:49:11,790 --> 00:49:17,370
+يفك و يفهم انت اش كاتبلهيفهم أيش كتبله تمام فهذه
+
+626
+00:49:17,370 --> 00:49:19,870
+هي أكتر أشياء هنشتغل عليها فهنروح لل linear
+
+627
+00:49:19,870 --> 00:49:22,730
+congruential method ال linear congruential method
+
+628
+00:49:22,730 --> 00:49:26,950
+عشان نتعامل معها هي ببساطة جدا تعملنا مجموعة
+
+629
+00:49:26,950 --> 00:49:30,830
+random numbers ال random numbers هذه محتاجين
+
+630
+00:49:30,830 --> 00:49:34,590
+مجموعة parameters عشان نبني ال model تبعنا ال
+
+631
+00:49:34,590 --> 00:49:38,630
+model ببساطة بده ال modulus ال modulus M بدك تحدد
+
+632
+00:49:38,630 --> 00:49:42,550
+قيمة له و بدك تحدد multiplier A قيمة لل A
+
+633
+00:49:49,170 --> 00:49:56,030
+وانصر ابدا فيه هنسميه seed البذرة اللي هتبدأ منها
+
+634
+00:49:56,030 --> 00:50:01,130
+عملية ال generation بحيث ان ال Aاللي هو ال
+
+635
+00:50:01,130 --> 00:50:05,990
+multiplier مايكونش أكبر من ال modulus و يكون اتنين
+
+636
+00:50:05,990 --> 00:50:09,170
+فأكثر مايكونش واحد لإنه ماعرفش معناه واحد في حاجة
+
+637
+00:50:09,170 --> 00:50:11,830
+اسمها multiplier واحد مع أن معناته ماضربتش في إشي
+
+638
+00:50:11,830 --> 00:50:16,210
+صحيح فهو بده يكون على الأقل اتنين فأكثر ال C بتكون
+
+639
+00:50:16,210 --> 00:50:20,530
+أكبر من صفر أو تساوي صفر فإذا كانت تساوي صفر فهي
+
+640
+00:50:20,530 --> 00:50:27,270
+معناته without incrementالـ seed الطبيعي و المنطقي
+
+641
+00:50:27,270 --> 00:50:31,310
+و العجل بيقول أنه لازم تكون أقل من ال modulus ال
+
+642
+00:50:31,310 --> 00:50:35,850
+modulus هذا كأني أقول مثلا ال modulus ألف ألف ألف
+
+643
+00:50:35,850 --> 00:50:38,850
+إيش يعني؟ معناته أنا جاعت بولد أرقام أقل من الألف
+
+644
+00:50:38,850 --> 00:50:43,930
+أنا جاعت بعمل generations لعناصر عشوائية بس أنا
+
+645
+00:50:43,930 --> 00:50:47,050
+عارف أن كلها أقل من الألف طيب ال modulus هذا عملته
+
+646
+00:50:47,050 --> 00:50:51,450
+عشر تلاف فانت جاعت بتولد أرقام أقل من عشر تلاف and
+
+647
+00:50:51,450 --> 00:50:55,360
+so on بهذا الشكلعشان هيك هذه مهمة فما دام linear
+
+648
+00:50:55,360 --> 00:50:59,120
+هنحطها في معادلة linear بتصير مجموعة ال parameters
+
+649
+00:50:59,120 --> 00:51:04,180
+هدولة في المعادلة ال linear بتاعتنا كأنه العنصر
+
+650
+00:51:04,180 --> 00:51:07,880
+اللي هو ال generated number الجديد اللي بده ييجي
+
+651
+00:51:07,880 --> 00:51:12,560
+اللي هو n زائد واحد هو جاي من xn من العنصر اللي
+
+652
+00:51:12,560 --> 00:51:16,120
+جابله بعد ما ضربناه في ال multiplier وجمعناه من ال
+
+653
+00:51:16,120 --> 00:51:23,680
+incrementmodulo للمجرس اللي اختارنا للأمن تمام في
+
+654
+00:51:23,680 --> 00:51:26,680
+الحالة هذه هيكون اعطاني رقم جديد بدي الرقم اللي
+
+655
+00:51:26,680 --> 00:51:32,060
+ورا بستعمل الرقم هذا في المعادلة بجيب n زائد 2
+
+656
+00:51:32,060 --> 00:51:39,120
+بستخدمها في المعادلة اجيب n زائد 3 ممتاز كمعادلة
+
+657
+00:51:39,120 --> 00:51:43,120
+الكل عرفها لكن ماحدش عارف انت ايش ال parameters
+
+658
+00:51:43,120 --> 00:51:46,370
+اللي خدتماحدش عارف إيش ال parameters اللي أخدتها
+
+659
+00:51:46,370 --> 00:51:50,810
+فانت هتبعتلي ال message و تبعتلي معاها العناصر
+
+660
+00:51:50,810 --> 00:51:54,810
+هدول مشفرين مثلا فانا بفكهم بعرفهم برجع برجع بولد
+
+661
+00:51:54,810 --> 00:51:58,850
+ال mask كمان مرة أو برجع بعيد ال random numbers
+
+662
+00:51:58,850 --> 00:52:04,230
+كمان مرة فعرفت انت إيش اللي كنت باعته تمام فببساطة
+
+663
+00:52:04,230 --> 00:52:12,440
+بهذا الشكل الآن معظم العناصر هذه عشان تضمن تضمنإنه
+
+664
+00:52:12,440 --> 00:52:17,740
+التباين عالي للأرقام اللي بتولدها يكون عالية
+
+665
+00:52:17,740 --> 00:52:21,260
+التباين لازم تكون الأرقام هذه و بيميلوا أن هم
+
+666
+00:52:21,260 --> 00:52:27,180
+trends بيروحوا أن تكون الأرقام هذه primes ليش
+
+667
+00:52:27,180 --> 00:52:33,980
+primes؟ الprimes لأنه بضمن أو على الأقل إذا ماكنوش
+
+668
+00:52:33,980 --> 00:52:38,100
+primes pure primes كلهم يعني على الأقل هم ما بينهم
+
+669
+00:52:38,100 --> 00:52:42,450
+وبين بعض relative primesليش؟ لأنه لما نقول
+
+670
+00:52:42,450 --> 00:52:47,930
+relative primes معناه ذلك ببساطة أنه ال greatest
+
+671
+00:52:47,930 --> 00:52:53,030
+common divisor between them واحد يعني مافيش عناصر
+
+672
+00:52:53,030 --> 00:52:59,810
+أقل من M كلهم يقبل القسم عليها هذا بيعطيك تنوع
+
+673
+00:52:59,810 --> 00:53:06,210
+أكبر لأنه لو كان في عناصر بينهم مشتركة هذا بيعني
+
+674
+00:53:06,210 --> 00:53:12,840
+أنه هيكون عندكيعني بطريقة أو باخرى التكرار هيكون
+
+675
+00:53:12,840 --> 00:53:18,860
+مسافاته أقرب أنا بقول random صح؟ ممتاز، بس في
+
+676
+00:53:18,860 --> 00:53:22,740
+الحالة هذه random يعني بولد مجموعة عناصر، لو
+
+677
+00:53:22,740 --> 00:53:27,100
+العنصر الأول اتكرر، ظهر معي، اللي برا كله هيظهر،
+
+678
+00:53:27,100 --> 00:53:31,460
+لأن المعادلة واحدة يعني كأنه رجعت عيدتها بنفس X
+
+679
+00:53:31,460 --> 00:53:35,740
+node أكيد هيرجع X1 زي ما هو يرجع، X2 يرجع، هذه هي
+
+680
+00:53:35,740 --> 00:53:39,170
+الثغرة اللي ال hackers بدوروا عليهاالـ hackers
+
+681
+00:53:39,170 --> 00:53:42,850
+بدورك على إيه انت وين صار التكرار وين بيصير
+
+682
+00:53:42,850 --> 00:53:46,890
+التكرار بمسك التكرار أول شغلة بجيب المسافة دي عارف
+
+683
+00:53:46,890 --> 00:53:52,270
+الموديلوس الموديلوس M عارفها خلصت هي ضربلك أول
+
+684
+00:53:52,270 --> 00:53:56,790
+شغلة و ببدأ بنوعنا عليا شوية شوية في سلسلة من ال
+
+685
+00:53:56,790 --> 00:53:59,730
+procedures اللي بيعملها عشان يكسر كل ال code يفكلك
+
+686
+00:53:59,730 --> 00:54:03,530
+إياه كله انت كيف تتصعب الموضوع عليه؟
+
+687
+00:54:05,010 --> 00:54:08,150
+ممكن مايكونش نفسه هذا إيه له شرط اللي هو المفروض
+
+688
+00:54:08,150 --> 00:54:12,190
+في ال slide اللي ورا هذي هناخده انه العناصر ما
+
+689
+00:54:12,190 --> 00:54:16,750
+بينها و بين بعض اللي هو مايكون .. مايكونلهاش او
+
+690
+00:54:16,750 --> 00:54:22,510
+عفوا يكونلها inverse inverse وحيد داخل ال one
+
+691
+00:54:22,510 --> 00:54:26,570
+period إذا كان عندك أكتر من inverse داخل ال one
+
+692
+00:54:26,570 --> 00:54:31,990
+period بنفعش هذا code بنفعش يكون code لازم يكون
+
+693
+00:54:32,750 --> 00:54:37,070
+Unique Inverse للعناصر اللي بتظهر معاك او لل
+
+694
+00:54:37,070 --> 00:54:41,570
+parameters هذه عشان تضمن ان انت استغلت كل ال
+
+695
+00:54:41,570 --> 00:54:46,750
+modulus كامل على بعضه افرض
+
+696
+00:54:46,750 --> 00:54:51,790
+الف ممكن التكرار يظهر لك بعد خمسمية او بعد متين و
+
+697
+00:54:51,790 --> 00:54:56,290
+خمسين اتلاقي صار فيه تكرارات طبعا هذا بيصير ال
+
+698
+00:54:56,290 --> 00:54:59,910
+code hashال code هذا مدام تكراراته جريبة من بعض
+
+699
+00:54:59,910 --> 00:55:07,470
+هذا هاش جدا ك security لبرايمز لبرايمز لأ بتكون
+
+700
+00:55:07,470 --> 00:55:10,890
+التكرارات كتير أجل من هيك كتير بتكون أجل من هيك
+
+701
+00:55:10,890 --> 00:55:14,870
+إذا كان ال C أفوان
+
+702
+00:55:14,870 --> 00:55:18,290
+C تساوى صفر معناه ذلك إن هي pure multiplicative
+
+703
+00:55:18,290 --> 00:55:23,210
+ليش؟ لأن مافيش ال increment هي معادلة ضربية بس
+
+704
+00:55:24,500 --> 00:55:30,560
+معادلة ضربية وليست linear هي linear أه بلس مش
+
+705
+00:55:30,560 --> 00:55:32,680
+complete linear لأنه في جزء من ال linearity
+
+706
+00:55:32,680 --> 00:55:37,360
+مااتحققتش مثال هاي مثال مثلا لو ال modulus عندك
+
+707
+00:55:37,360 --> 00:55:44,860
+الف زي ما قلنا و ال Cأربعمية و سبعة و ستين ال a
+
+708
+00:55:44,860 --> 00:55:49,380
+بدأنا بتلت مية اشتغلناها تلت مية تلائم متين تلاتة
+
+709
+00:55:49,380 --> 00:55:54,340
+وتسعين و ال seed أربعمية ستة و عشرين معادلة و
+
+710
+00:55:54,340 --> 00:55:58,680
+بتطبقها لا أكثر ولا أقل فبدك تجيب x واحد باستخدام
+
+711
+00:55:58,680 --> 00:56:04,130
+x node اللي هي ال seedعشان تطلع رقم هو نفسه
+
+712
+00:56:04,130 --> 00:56:08,230
+تستخدمه ك X1 عشان تجيب منه X2 and so on بهذا الشكل
+
+713
+00:56:08,230 --> 00:56:13,210
+و تظهر عندك أرقام عشوائية تبدو ان هي عشوائية فهي
+
+714
+00:56:13,210 --> 00:56:16,630
+هيك فعليا تبدو ان هي عشوائية لكن انت جادر ترجع
+
+715
+00:56:16,630 --> 00:56:19,570
+تعيدها كمان مرة جادر ترجع تعملها generation كمان
+
+716
+00:56:19,570 --> 00:56:24,090
+مرة and so on بتضلك مستمر في الحالة هذه لاحظ انه
+
+717
+00:56:24,090 --> 00:56:30,510
+odd even بتشغل الكلام هذا لأن ال M عندكeven فدي
+
+718
+00:56:30,510 --> 00:56:34,010
+واحدة من الشواهد برضه و من سحر الأرقام يعني أنه
+
+719
+00:56:34,010 --> 00:56:38,490
+إذا كانت ال .. ال .. ال modulus even فبصير يعملك
+
+720
+00:56:38,490 --> 00:56:42,650
+تبديل ما بين العناصر اللي بيعطيك إياها مرة فردية
+
+721
+00:56:42,650 --> 00:56:45,610
+مرة زوجية مرة فردية مرة زوجية فهذه شواهد إذا كده
+
+722
+00:56:45,610 --> 00:56:48,470
+مثلا ال hackers برضه بيستفيدوا من الحاجات اللي ..
+
+723
+00:56:48,470 --> 00:56:51,830
+أه بيستفيد من الحاجات اللي زي هذه المعلومات زي هذه
+
+724
+00:56:51,830 --> 00:56:55,930
+بيستفيد منها بيفهم منها بتعطي indication أن والله
+
+725
+00:56:55,930 --> 00:57:01,110
+إيش ممكن يكون ال .. ال modulusتمام هاي كمان مثال
+
+726
+00:57:01,110 --> 00:57:05,930
+اكبر شوية و اوضح شوية كررناها بشكل كامل لما قولنا
+
+727
+00:57:05,930 --> 00:57:09,390
+ال modulus تسعة تسعة معناته انا متوقع انه هيعمل لي
+
+728
+00:57:09,390 --> 00:57:15,410
+تسعة random numbers و يرجع يتكرر تاني لانه مش
+
+729
+00:57:15,410 --> 00:57:18,670
+هيخترع جديد بعد هيك خلص كل ال elements اللي في ال
+
+730
+00:57:18,670 --> 00:57:23,090
+.. ضمن ال modulus طبعه ال multiplier سبعة ال C
+
+731
+00:57:23,090 --> 00:57:28,650
+باربعة و ال seedتلاتة فبدأنا بالتلاتة X node
+
+732
+00:57:28,650 --> 00:57:35,270
+بالتلاتة صار في عندك تلاتة سبعة تمانية ستة واحد
+
+733
+00:57:35,270 --> 00:57:40,870
+اتنين صفر اربعة تلاتة طب لو كملنا ايش هيظهر اكيد
+
+734
+00:57:40,870 --> 00:57:46,570
+اكيد خلاص اتكرر اتكررت فإذا تعالي امسك اه دي ال
+
+735
+00:57:46,570 --> 00:57:53,010
+modulus ايش تسعةوالله بدها تتعجب فيها تصير من
+
+736
+00:57:53,010 --> 00:57:56,290
+مضاعفات التسعة مثلا لو كان في أكتر من inverse لها
+
+737
+00:57:56,290 --> 00:58:00,550
+بدها تصير من مضاعفات التسعة فما اختلفتش مابعتش
+
+738
+00:58:00,550 --> 00:58:06,630
+كتير فانت في الآخر بين معلومة مهمة في ال code بينت
+
+739
+00:58:06,630 --> 00:58:10,390
+معلومة كتير مهمة في ال code طيب عادة إيش اللي كتير
+
+740
+00:58:10,390 --> 00:58:13,490
+الناس بفضله يستخدموها أو يستخدمها كتير هي ال pure
+
+741
+00:58:13,490 --> 00:58:18,140
+multiplicativeبهذا المعادلة بهذا الشكل اتنين to
+
+742
+00:58:18,140 --> 00:58:22,600
+the power واحد تلاتين ناقص واحد هذه قيمة المجلس
+
+743
+00:58:22,600 --> 00:58:28,580
+هذه المجلس اللي هي ال M اللي هي قيمة M هنا فجدش
+
+744
+00:58:28,580 --> 00:58:31,900
+بيستخدموها بفضلوا استخدامها اتنين to the power
+
+745
+00:58:31,900 --> 00:58:35,880
+واحد تلاتين ناقص واحد على أساس ال prime على أساس
+
+746
+00:58:35,880 --> 00:58:40,960
+ال prime طيب و ال multiplier سبعة to the power
+
+747
+00:58:40,960 --> 00:58:52,360
+خمسةفبطلع الرقم حوالي 16807 هذا بيعطيك عدد
+
+748
+00:58:52,360 --> 00:58:55,780
+elements قبل ما ترجع تتكرر حوالي اتنين to the
+
+749
+00:58:55,780 --> 00:59:01,930
+power واحد تلاتين ناقص اتنين يعني حوالي اتنينجداش
+
+750
+00:59:01,930 --> 00:59:10,630
+billion و 147 مليون و 493 647
+
+751
+00:59:10,630 --> 00:59:15,610
+random numbers قبل ما يرجع يتكرر قبل ما يرجع يتكرر
+
+752
+00:59:15,610 --> 00:59:21,090
+فرقم مقبول يعني رقم جيدخلّينا نقول يتشغّل فيه ال
+
+753
+00:59:21,090 --> 00:59:25,910
+hacker قبل ما يشغّل عليه أو يفك تشفيرته .. يفك
+
+754
+00:59:25,910 --> 00:59:29,510
+تشفيرته .. طيب المرة القادمة بدنا نتكلم برضه في
+
+755
+00:59:29,510 --> 00:59:34,090
+نفس القالية أنا صار انديل N بتعامل مع معادلة خطية
+
+756
+00:59:34,090 --> 00:59:38,230
+.. كلكم عارفين أن معادلة الخطية عشان نجيب قيمة X
+
+757
+00:59:38,230 --> 00:59:41,870
+بتاعتها محتاجين نجيب ال inverse لل coefficient
+
+758
+00:59:43,240 --> 00:59:45,340
+الانفرس هي ال coefficient فهذا موضوعنا المرة
+
+759
+00:59:45,340 --> 00:59:50,280
+القادمة اللي هو هيكون عندك ax equivalent او
+
+760
+00:59:50,280 --> 00:59:56,660
+congruent ل b كويس فبد قيم x اللي تحقق هذه
+
+761
+00:59:56,660 --> 01:00:01,720
+المعادلة اكيد طبعا بيصير بدنا نجيب ال inverse كلنا
+
+762
+01:00:01,720 --> 01:00:04,740
+عارفين ال inverse في الرياضيات العادية بس كيف
+
+763
+01:00:04,740 --> 01:00:11,170
+نتعامل معها في ال moduloقصة تانية .. قصة تانية
+
+764
+01:00:11,170 --> 01:00:14,430
+بدنا نتعامل فيها المرة الجاية و نبدأ نشتغل عليها و
+
+765
+01:00:14,430 --> 01:00:18,750
+ناخد عليها أمثلة و بالمناسبة من الأمثلة اللي كتير
+
+766
+01:00:18,750 --> 01:00:22,670
+بتيجي في الامتحاناتلما تدخل كمان على الـ
+
+767
+01:00:22,670 --> 01:00:27,310
+Sodoprimes اللى هى أرقام شبيهة لـ Primes هدى لو
+
+768
+01:00:27,310 --> 01:00:30,670
+انت زى ما بيقوله عجزت انه مش لاجي برايم مناسب لل
+
+769
+01:00:30,670 --> 01:00:34,170
+code تبعك ممكن تتعامل معاها كيف تعملها generation
+
+770
+01:00:34,170 --> 01:00:38,350
+كيف تجيبها برضه هنتكلم عنها لأن هدى بتفيدك بكرا في
+
+771
+01:00:38,350 --> 01:00:40,430
+ال security بكرا بتفيدك في ال security لما بدك
+
+772
+01:00:40,430 --> 01:00:43,110
+تعمل تشفير و بدك تعمل encryption بدك تعمل هدى
+
+773
+01:00:43,110 --> 01:00:45,350
+أرقام كتير مهمة يعطيكوا العافية و نكمل المرة
+
+774
+01:00:45,350 --> 01:00:46,150
+القادمة ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/x82rLS0FR9A.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/x82rLS0FR9A.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a23ec619391c4bd94efc68d4628ccc5a21914c70
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/x82rLS0FR9A.srt
@@ -0,0 +1,2027 @@
+
+1
+00:00:04,980 --> 00:00:09,000
+طيب، يعطيكم العفو يا شباب، اليوم إن شاء الله
+
+2
+00:00:09,000 --> 00:00:15,460
+تعالوا بناخذ آخر جزء كان متبقّي في المساق وهو حالة
+
+3
+00:00:15,460 --> 00:00:18,980
+خاصة من الـ graphs زي لما احنا قلنا درسنا الـ
+
+4
+00:00:18,980 --> 00:00:22,320
+relations والـ relations قلنا هذا مظلة كبيرة
+
+5
+00:00:22,710 --> 00:00:27,290
+الـ umbrella الكبيرة، وأخذنا جزء منها الـ graphs
+
+6
+00:00:27,290 --> 00:00:31,610
+بأنواعها الـ directed والـ undirected graph برضه
+
+7
+00:00:31,610 --> 00:00:34,550
+اليوم بدنا نتكلم عن حالة خاصة من الـ graphs اللي هي
+
+8
+00:00:34,550 --> 00:00:38,250
+بيسموها الـ tree، الـ trees أو الـ tree، واللي هي
+
+9
+00:00:38,250 --> 00:00:44,470
+نتكلم عن نوع خاص جداً من أنواع الـ graphs اللي بكل
+
+10
+00:00:44,470 --> 00:00:49,750
+بساطة بنقدر نعرفه تحت مظلة الـ undirected graph، و
+
+11
+00:00:49,750 --> 00:00:55,890
+with no circuits أو self loops أو circuits عموماً،
+
+12
+00:00:55,890 --> 00:00:57,910
+يعني مش مضروبة self loops، self loops احنا بنتكلم
+
+13
+00:00:57,910 --> 00:01:02,150
+عن من الـ node لنفسها، لا هذه أصلاً ما فيش فيها
+
+14
+00:01:02,150 --> 00:01:04,230
+إضافة
+
+15
+00:01:05,360 --> 00:01:09,900
+circuit أو cycle نهائي، مش قصة multigraph، الفكرة أن
+
+16
+00:01:09,900 --> 00:01:16,100
+أنت ممكن يكون عندك connection بهذا الشكل، فلاحظ أنه
+
+17
+00:01:16,100 --> 00:01:20,360
+أنت عملت loop بمعنى أنه صار في عندك cycle، cycle
+
+18
+00:01:20,360 --> 00:01:25,800
+transitivity وصلت أنه من U لـ V بحيث أن U تساوي V
+
+19
+00:01:25,800 --> 00:01:31,320
+تمام، ووصلت لـ U بتساوي V لكن فعلياً هذا غير مسموح في
+
+20
+00:01:31,320 --> 00:01:36,630
+الـ tree، الـ tree بتضل simple graph، simple graph، تمام
+
+21
+00:01:36,630 --> 00:01:41,770
+فإذا أول شرط من شروطها أن هي undirected graph with
+
+22
+00:01:41,770 --> 00:01:47,830
+no circuits أو no cycles، معنى ذلك أنها unique
+
+23
+00:01:47,830 --> 00:01:52,890
+simple graph between any two of its nodes، بين أي
+
+24
+00:01:52,890 --> 00:01:56,770
+نقطتين موجودتين عليها هو simple path موجود بينهم
+
+25
+00:01:56,770 --> 00:02:01,310
+لا يمكن يكون يرجع من نفس الـ path لنفس النقطة أبداً، وهي
+
+26
+00:02:01,310 --> 00:02:05,730
+undirected عشان undirected، طيب مش بالضروري أن
+
+27
+00:02:05,730 --> 00:02:10,270
+الـ undirected graph هذا with ... without simple
+
+28
+00:02:10,270 --> 00:02:14,830
+circuits، أنه يكون كله connected together، لا مش
+
+29
+00:02:14,830 --> 00:02:18,790
+بالضروري، بمعنى أنه ممكن ما تكونش tree واحدة، أكثر من
+
+30
+00:02:18,790 --> 00:02:23,140
+tree لنفس الـ graph هو هو، فبتصير... كيف؟ في
+
+31
+00:02:23,140 --> 00:02:25,960
+isolated، بالضبط، ممكن يكون في isolated، ممكن يكون
+
+32
+00:02:25,960 --> 00:02:29,520
+أكثر من tree في نفس الـ graph الواحد، فبيصير اسمها الـ
+
+33
+00:02:29,520 --> 00:02:31,800
+tree والـ tree والـ tree، إيش بتصير اسمها؟ forest
+
+34
+00:02:31,800 --> 00:02:36,280
+غابة، مش هيك؟ المنطقي بيقول أكثر من tree فبسمّيها
+
+35
+00:02:36,280 --> 00:02:39,700
+على طول غابة forest، فهنا المصطلح جاء أنه مش
+
+36
+00:02:39,700 --> 00:02:43,660
+بالضروري الـ undirected أن هي تكون without symbol
+
+37
+00:02:46,520 --> 00:02:49,560
+لازم تكون one tree، لا، ممكن تكون أكثر من الـ tree
+
+38
+00:02:49,560 --> 00:02:55,040
+فبنسمّيها بهذا الشكل، طيب، فإذا بتكون having disjoint
+
+39
+00:02:55,040 --> 00:02:59,670
+sets of nodes، مجموعة nodes متصلة مع بعض، ومجموعة
+
+40
+00:02:59,670 --> 00:03:02,570
+ثانية متصلة مع بعض، ومجموعة ثالثة متصلة مع بعض، فكل
+
+41
+00:03:02,570 --> 00:03:05,670
+مجموعة من هدول إيش اسمها tree لحالها، لكن كلهم على
+
+42
+00:03:05,670 --> 00:03:11,410
+بعض forest، طيب، مادام forest، معناته بناخد مصطلحنا
+
+43
+00:03:11,410 --> 00:03:15,070
+من كلمة الـ tree نفسها، كل tree بيكون فيها leaves
+
+44
+00:03:15,070 --> 00:03:23,170
+فكل leaf هي terminal node داخل الـ tree، الورقة دائماً
+
+45
+00:03:23,170 --> 00:03:28,310
+هي الطرف للشجرة، هي الطرف النهائي، والمعلّق pendent
+
+46
+00:03:28,310 --> 00:03:32,450
+مش هيك، دائماً بتكون هي المعلّقة هذه، فإذا الـ leaf هي
+
+47
+00:03:32,450 --> 00:03:36,550
+عبارة عن node في الشبكة، في أفواد، في الـ tree أو في
+
+48
+00:03:36,550 --> 00:03:40,310
+الـ forest، سواء tree أو forest، في كلاهما بتكون
+
+49
+00:03:40,310 --> 00:03:43,830
+عبارة عن node، لكن ميزة الـ node هذه أن الـ degree
+
+50
+00:03:43,830 --> 00:03:50,280
+بتاعتها بتساوي بتساوي واحد، فإذا pendent أو isolated
+
+51
+00:03:50,280 --> 00:03:55,160
+ممكن تكون، فإذا كأنها ورقة ساقطة، فـ isolated، درجة الـ
+
+52
+00:03:55,160 --> 00:04:01,740
+degree بتاعتها zero، الـ internal node هي عبارة عن
+
+53
+00:04:01,740 --> 00:04:07,420
+أي non-leaf node، إذا ما كانتش leaf node، فإذا هي
+
+54
+00:04:07,420 --> 00:04:11,280
+internal node، internal node بمعنى إن هي منطقة
+
+55
+00:04:11,280 --> 00:04:17,760
+تشعب أو تفرع، فرع، منطقة تفرع، طيب إيش الميزة زي ما
+
+56
+00:04:17,760 --> 00:04:22,640
+قلنا في الـ leaf إن هي الـ degree بتاعتها صفر؟ فبيصير
+
+57
+00:04:22,640 --> 00:04:27,060
+اسمها isolated أو واحد، فبيصير اسمها abandoned، معلّقة
+
+58
+00:04:27,060 --> 00:04:32,860
+تمام، إذا أكثر من هيك بعرف إنه هذا internal، فإذا الـ
+
+59
+00:04:32,860 --> 00:04:38,300
+internal has degree أكبر من أو يساوي اثنين، اثنين
+
+60
+00:04:38,300 --> 00:04:44,240
+واحد معناته leaf، واحد معناته leaf، فإذا أكبر أو
+
+61
+00:04:44,240 --> 00:04:47,500
+تساوي، فإذا أنا بتكلم عن اثنين، أكبر أو تساوي، فإذا
+
+62
+00:04:47,500 --> 00:04:51,000
+أنا بحكي عن اثنين، تمام، فبتصير automatically على
+
+63
+00:04:51,000 --> 00:04:58,690
+طول internal، طيب، هاي المثال واضح لنا، هاي عندك tree
+
+64
+00:04:58,690 --> 00:05:06,030
+كل الـ green nodes هي عبارة عن leaves، كلها leaves
+
+65
+00:05:06,030 --> 00:05:11,350
+طيب، كل الـ brown nodes أو هنا بالنسبة لكم كأنها red
+
+66
+00:05:11,350 --> 00:05:16,910
+nodes هذه internal، طيب تمام، الـ forest لا، بتكون
+
+67
+00:05:16,910 --> 00:05:22,280
+عندك أكثر من الـ tree، وقد يكون فيه isolated... إيش؟
+
+68
+00:05:22,280 --> 00:05:27,040
+leaf... leaf، تلاحظ؟ فهنا كأنه شجرة أولى، شجرة ثانية،
+
+69
+00:05:27,040 --> 00:05:30,860
+ثالثة، رابعة، خامسة، وهكذا بهذا الشكل اللي أنت شايفه
+
+70
+00:05:30,860 --> 00:05:35,180
+تمام، فبيصير اسمها forest، مادام أكثر من one tree، طيب
+
+71
+00:05:35,180 --> 00:05:39,180
+في الـ tree في حاجة اسم الـ root، فأنت بقدر أقول إن
+
+72
+00:05:39,180 --> 00:05:43,020
+الـ tree هذه هي rooted tree إذا كان لها root واضح
+
+73
+00:05:43,020 --> 00:05:47,100
+إذا لها... لها root واضح، بمعنى لها start point
+
+74
+00:05:47,100 --> 00:05:51,690
+واضحة، root معناته هي الـ start point تبعتك فعلاً، هل
+
+75
+00:05:51,690 --> 00:05:54,830
+إلها start point واضحة ولا لأ، فإذا الـ rooted tree
+
+76
+00:05:54,830 --> 00:06:01,170
+هي الـ tree بحيث إنه يكون في one node مصممة، مجهزة،
+
+77
+00:06:01,170 --> 00:06:07,170
+محددة إن هي root أو start point، هي الـ start point
+
+78
+00:06:07,170 --> 00:06:10,830
+لمين؟ للـ tree أو للـ graph in general، وكل edge
+
+79
+00:06:10,830 --> 00:06:17,130
+موجودة في الرسم المفروض إن هي متصلة فيها، بمعنى بشكل
+
+80
+00:06:17,130 --> 00:06:23,050
+صريح أو بشكل ضمني، هي directed away from the root
+
+81
+00:06:23,050 --> 00:06:28,450
+يعني كلهم طالعين من نفس الـ root، كل الـ leaves... الـ
+
+82
+00:06:28,450 --> 00:06:32,950
+leaves تبعتك، وكل الـ internal nodes هي طالعة من
+
+83
+00:06:32,950 --> 00:06:38,490
+نفس الـ root، فإذا يوجد بكل بساطة edge أو path بينهم
+
+84
+00:06:38,490 --> 00:06:44,070
+وبين الـ root node، تمام، فبنقدر بكل بساطة أن أعرف بعد
+
+85
+00:06:44,070 --> 00:06:47,210
+هيك مجموعة تعريفات، مادام إحنا كل شغلنا صار واضح الآن
+
+86
+00:06:47,210 --> 00:06:51,430
+على أساس أنه هي tree، اتخيّلوا معايا شجرة، لكن نوع
+
+87
+00:06:51,430 --> 00:06:56,330
+خاص من الشجر، الـ trees هذه، اللي هي شجرة العائلة، شجرة
+
+88
+00:06:56,330 --> 00:07:00,240
+العائلة، إيش الـ components بتاعتها؟ parents، مجموعة الـ
+
+89
+00:07:00,240 --> 00:07:05,260
+parents، مش هيك كويس، الـ child أو الـ children، الـ
+
+90
+00:07:05,260 --> 00:07:09,200
+siblings، الأشقاء أو اللي هم الأخوة غير الأشقاء
+
+91
+00:07:09,200 --> 00:07:13,420
+sibling بيسموها، فهنا بتيجي على أساس منه الأشقاء، الـ
+
+92
+00:07:13,420 --> 00:07:18,660
+ancestors، الـ ancestors مين؟ الأجداد أو السلف، والـ
+
+93
+00:07:18,660 --> 00:07:23,760
+descendants، الخلف أو الأحفاد، الـ descendants، طيب
+
+94
+00:07:23,760 --> 00:07:27,440
+leaf عرفنا leaf اللي هي عندك الورقة، والـ internal
+
+95
+00:07:27,440 --> 00:07:29,920
+node عرفناها برضه اللي هي النقاط الداخلية أو
+
+96
+00:07:29,920 --> 00:07:33,160
+التشعّبات الداخلية، والـ sub tree، كل هدول بدنا
+
+97
+00:07:33,160 --> 00:07:37,060
+الآن نتعرف عليهم، كيف بقدر أمثلهم داخل الشبكة، لما
+
+98
+00:07:37,060 --> 00:07:41,700
+نعرف بس أن الـ rooted tree كـ example هي ممكن تكون
+
+99
+00:07:41,700 --> 00:07:49,710
+لاحظ أي internal node، أي internal node ممكن تكون
+
+100
+00:07:49,710 --> 00:07:56,570
+root، ممكن تكون root في الحالة هذه، طيب أقول لك شغل
+
+101
+00:07:56,570 --> 00:08:00,610
+ثاني، ممكن تكون أي node موجودة، أي node موجودة ممكن
+
+102
+00:08:00,610 --> 00:08:04,800
+تكون root، يعني أنت لو أخذنا الـ root هذه، خلاص بتصير
+
+103
+00:08:04,800 --> 00:08:07,920
+هي الرئيسي، كأنك أمسكها وارفعها رأساً عالياً، والـ
+
+104
+00:08:07,920 --> 00:08:12,040
+كل مطالع منها، طيب لو غيرناها وأخذنا root ثانية
+
+105
+00:08:12,040 --> 00:08:16,180
+هنا، وهي نفسها رفعتها عن الرسم رأساً عالياً، والـ
+
+106
+00:08:16,180 --> 00:08:22,240
+الباقي كله متفرع منها، فإذا أي نقطة ممكن تكون هي الـ
+
+107
+00:08:22,240 --> 00:08:26,260
+root حسب الـ design تبعك، حسب الـ design تبعك، فإذا في
+
+108
+00:08:26,260 --> 00:08:31,340
+الحالة هذه الـ un rooted tree within nodes ممكن
+
+109
+00:08:31,340 --> 00:08:35,420
+يكون في إلها indifferent rooted trees، ليش؟ لأن أي
+
+110
+00:08:35,420 --> 00:08:39,020
+نقطة ممكن تكون root، أقول لك ممكن تكون هذه الـ root،
+
+111
+00:08:39,020 --> 00:08:46,100
+هذه هي الـ root، أمسكها وارفعها لحالها، وتصير هي
+
+112
+00:08:46,100 --> 00:08:50,880
+الرأس، رأس الهرم، يعني هي الجد الأكبر، نفترض الجد
+
+113
+00:08:50,880 --> 00:08:56,140
+الأكبر للـ tree هذه، فبتصير بهذا الشكل هيها، وعندك
+
+114
+00:08:56,140 --> 00:09:00,520
+نازل منها نقطة node ثانية، فإذا بتيجي node ثانية
+
+115
+00:09:00,520 --> 00:09:05,620
+هيها، عشان بعدين تتجسّم لواحد، اثنين، ثلاثة، يطلع منها
+
+116
+00:09:05,620 --> 00:09:10,300
+ثلاثة، فبتقدر تعيد تشكيل الـ tree بناءً على الـ route
+
+117
+00:09:10,300 --> 00:09:13,190
+اللي أنت اخترته، لكن في النهاية اللي يهمنا من الـ
+
+118
+00:09:13,190 --> 00:09:18,990
+slide أنه جدّ عدد الـ... الـ... الـ rooted tree اللي
+
+119
+00:09:18,990 --> 00:09:25,110
+بقدر آخذها من رسمة موجودة فيها n nodes، حقيقة n
+
+120
+00:09:25,110 --> 00:09:33,300
+rooted tree، لأن كل واحدة ممكن تكون نفسها root، جيد
+
+121
+00:09:33,300 --> 00:09:38,620
+طيب، هيأخذ مثل high rooted tree examples، ميعطيني
+
+122
+00:09:38,620 --> 00:09:45,780
+مباشرة، هذه A، أعطاني E، أو هذه الـ tree T، آه هنا مش
+
+123
+00:09:45,780 --> 00:09:53,420
+كثير، بيبين عندكم، هي B، F، G، أعتقد C، D، E، عشان تكون
+
+124
+00:09:53,420 --> 00:10:02,700
+سهلة تتفاعلوا معانا، هي H، K، I، J، L، وM، تمام، الآن لما
+
+125
+00:10:02,700 --> 00:10:07,080
+نقول بالنسبة للحالات اللي عندنا بدنا نحلها، the
+
+126
+00:10:07,080 --> 00:10:16,580
+parent of C، هاي C، الـ parent، الـ parents اللي هو
+
+127
+00:10:16,580 --> 00:10:21,560
+الأم والأب، شايف؟ يعني بمعنى إنه في الشجرة هم
+
+128
+00:10:21,560 --> 00:10:26,580
+الأعلى، مش شايف؟ هاي الأعلى، مين الأعلى منها؟ B فقط
+
+129
+00:10:26,580 --> 00:10:38,280
+فقط، B فقط، B، تمام، الـ children لـ G، وين G؟ هاي G، صحيح؟
+
+130
+00:10:38,280 --> 00:10:46,460
+H، I، وJ، تمام، إيش كمان؟ siblings of H، وين H؟ هاي H
+
+131
+00:10:46,460 --> 00:10:53,220
+I، وJ، مش هيك؟ ليش؟ لأن هدول الأشقاء، مين الأشقاء؟
+
+132
+00:10:53,220 --> 00:10:57,260
+بمعنى إنه مشتركين في الـ parent، مشتركين إن كلهم لهم
+
+133
+00:10:57,260 --> 00:11:02,740
+نفس الـ parent، okay، معناته I وJ، طيب الـ ancestors...
+
+134
+00:11:02,740 --> 00:11:10,200
+الـ ancestors هدول لمين؟ لـ E، وين E؟ هي E، هي E،
+
+135
+00:11:10,200 --> 00:11:14,900
+معناته بتتكلم عن الخط الـ simple path بينهم وبين الـ
+
+136
+00:11:14,900 --> 00:11:22,370
+root، كل node بيمر فيها هو ancestor، لما يصل للجد
+
+137
+00:11:22,370 --> 00:11:30,330
+الأول، فإذن C، B، وA، C، B، وA حسب ترتيبهم، طيب الـ
+
+138
+00:11:30,330 --> 00:11:35,070
+descendants أو الـ... بالعكس، اللي هي الأحفاد، لمين؟
+
+139
+00:11:35,070 --> 00:11:40,490
+... لـ B، وين B؟ هاي B، فإذن
+
+140
+00:11:40,490 --> 00:11:48,180
+نزول، لما تصل لكل الـ leaves اللي طالعين منها، فعندك
+
+141
+00:11:48,180 --> 00:11:58,780
+C، وD، وE، C، وD، وE، تمام، الـ internal vertices، خلصنا من
+
+142
+00:11:58,780 --> 00:12:04,680
+العلاقات كلهم عموماً، الـ internal vertices، لاحظ أنه
+
+143
+00:12:04,680 --> 00:12:07,660
+بدنا نحط باللون الأحمر هدول الـ leaves،
+
+144
+00:12:18,640 --> 00:12:25,300
+والمتبقي بما فيهم الـ route، تمام، فإذا الأخضر هذا
+
+145
+00:12:25,300 --> 00:12:28,660
+عندك الـ internal، عندك هاي الستة internal nodes،
+
+146
+00:12:28,660 --> 00:12:35,040
+وعندك سبعة leaves، سبعة leaves، okay، هاي الستة الـ
+
+147
+00:12:35,040 --> 00:12:38,080
+internal مظبوطين هيك، معناته؟ مظبوطين، تمام،
+
+148
+00:12:38,080 --> 00:12:43,250
+والمتبقيين مين؟ الـ leaves، فإذا الـ relations بسيطة،
+
+149
+00:12:43,250 --> 00:12:46,410
+سهلة جداً، ما فيش فيها كثير مشكلة، عشان نفهم إيش هي الـ
+
+150
+00:12:46,410 --> 00:12:55,590
+tree، هاي الـ sub tree at g، معناته من g جسّمها كأنه
+
+151
+00:12:55,590 --> 00:13:01,080
+هذا فرع الشجرة، هذا جزءها، شوف إيش اللي بينزل معاه
+
+152
+00:13:01,080 --> 00:13:06,840
+فإذا من G بنزل كلها، فهذه أحسن ما صار إيش؟ sub tree
+
+153
+00:13:06,840 --> 00:13:11,880
+rooted at G، فصار كأن الـ root تبعها هي الـ G، ليش؟
+
+154
+00:13:11,880 --> 00:13:15,740
+لأنك بدك تأخذ الـ... زي ما أقوله الـ branch هذا تجسّمه
+
+155
+00:13:15,740 --> 00:13:21,220
+وتقلّمه بشكل معين، وتزرعه يبدأ من جديد لحاله كشجرة
+
+156
+00:13:21,220 --> 00:13:26,160
+لحاله، تمام، okay، طيب، هي أننا برضه نفس الكلام، بدك
+
+157
+00:13:26,160 --> 00:13:30,240
+تجيب الـ parent للـ children، الـ siblings، الـ
+
+158
+00:13:30,240 --> 00:13:36,860
+ancestors، والـ descendants، لمين؟ لـ F؟ وين F؟ وينك
+
+159
+00:13:36,860 --> 00:13:37,960
+يا F؟ هاي F
+
+160
+00:13:41,650 --> 00:13:45,970
+أقربّط لك إياها، بس أعطاك مين؟ الـ root، مهم جداً الـ root
+
+161
+00:13:45,970 --> 00:13:49,330
+لإن الـ root هو اللي بدك تنسب إليه في النهاية الـ
+
+162
+00:13:49,330 --> 00:13:53,130
+tree تبعتك، نبدأ بواحدة واحدة، الـ parent كيف بدي
+
+163
+00:13:53,130 --> 00:13:56,610
+أعرف إن الـ parent هذا ولا هذا ولا هذا؟ الـ root
+
+164
+00:13:56,610 --> 00:14:00,790
+بالضبط هو مش المتصل أوي، هو أول خط وأنا رايح ناحية
+
+165
+00:14:00,790 --> 00:14:04,330
+الـ root، هو أول node وأنا رايح في الـ path طبعاً
+
+166
+00:14:04,330 --> 00:14:09,610
+فإذا هي الـ C، فعلياً هنا الـ children
+
+167
+00:14:13,120 --> 00:14:20,900
+وكوال siblings G
+
+168
+00:14:20,900 --> 00:14:27,080
+أحسنت، صح
+
+169
+00:14:27,080 --> 00:14:34,080
+كلاهما بيشترك في نفس الـ parent، تمام، إيش ضال عندنا؟
+
+170
+00:14:34,080 --> 00:14:41,600
+الـ ancestors،
+
+223
+00:19:14,930 --> 00:19:17,690
+من الـ yes/no decisions
+
+224
+00:19:21,640 --> 00:19:25,780
+بهذا الشكل حسب الحالة حسب الحالات اللي بتشتغل
+
+225
+00:19:25,780 --> 00:19:30,480
+عليها تمام، هذه ممكن تكون بداية فكرة الـ expert
+
+226
+00:19:30,480 --> 00:19:35,300
+systems، الأنظمة الخبيرة اللي هو الـ AI، لأن الـ AI هو
+
+227
+00:19:35,300 --> 00:19:37,620
+معتمد على مجموعة conditions  إحصلنا عليها عشان
+
+228
+00:19:37,620 --> 00:19:40,300
+نقدر نقول لك إيش المرض اللي عندك، الشيء، الحالات اللي
+
+229
+00:19:40,300 --> 00:19:44,460
+بدك تبقى هي الأعراض، بكل بساطة هيقول لك في درجة.. في
+
+230
+00:19:44,460 --> 00:19:51,860
+حرارة yes/no؟ طيب، مافيش حرارة مثلاً، طيب بتكح
+
+231
+00:19:51,860 --> 00:19:57,780
+yes or no؟ كويس؟ طيب، حاسس بوجع لما بتتنفس yes or no؟
+
+232
+00:19:57,780 --> 00:20:01,460
+عشان يوصلك بإيش في الـ decision في النهاية، هاي أبسط
+
+233
+00:20:01,460 --> 00:20:04,240
+أسلوب من أساليب الـ AI، واللي مبنية على الـ tree
+
+234
+00:20:04,240 --> 00:20:07,940
+فواضح أنه لأ، عرفنا إحنا ليش رايحين للـ tree، إيش
+
+235
+00:20:07,940 --> 00:20:10,780
+فايدة الـ tree؟ مش مجرد أنه والله هيها الـ tree
+
+236
+00:20:10,780 --> 00:20:13,820
+اسمها حلو، الشجرة وخلصناها، لأ، دي كانت بداية علم
+
+237
+00:20:13,820 --> 00:20:18,080
+طويل عريض، بداية علم طويل عريض، بكل بساطة هنقدر
+
+238
+00:20:18,080 --> 00:20:22,410
+نستثمره من البرمجة بتاعتكم، من شغل البرمجة واللي
+
+239
+00:20:22,410 --> 00:20:26,830
+لما بعملها modeling، الـ model تبعه بيطلع الـ tree، الـ
+
+240
+00:20:26,830 --> 00:20:30,530
+model شكله بيطلع الـ tree، فكان مهم جداً أن نفهم إشي
+
+241
+00:20:30,530 --> 00:20:32,930
+عن الـ tree في البداية، بتهيأ لي واضحة ليش إحنا راح
+
+242
+00:20:32,930 --> 00:20:36,590
+روحنا للـ tree، هذي هي، مش مجرد إن والله إشي حلو و
+
+243
+00:20:36,590 --> 00:20:41,430
+graph، خلاص تمام، يمكن أهم حالة من الحالات اللي
+
+244
+00:20:41,430 --> 00:20:44,410
+بتنحل بهذا الشكل هي الـ comparison اللي أخذناها
+
+245
+00:20:44,410 --> 00:20:47,890
+بتاعة الـ binary search، الـ binary search، أنت كل اللي
+
+246
+00:20:47,890 --> 00:20:51,310
+بتعمله كنت بتقول في عندي الـ array بتاعتي وبعيجي
+
+247
+00:20:51,310 --> 00:20:58,410
+عنده النص وبعيجي بحط condition، X أكبر من A أم لأ؟
+
+248
+00:20:58,410 --> 00:21:05,550
+لأ؟ طب معناته هنا yes or no، أيوة yes or no، كنا بناءً
+
+249
+00:21:05,550 --> 00:21:09,030
+عليها أن نعمل شوية معطيات، نعمل شوية action، نعمل
+
+250
+00:21:09,030 --> 00:21:12,730
+تدخل، أن نقول والله معناته غير لي الـ limits، البداية
+
+251
+00:21:12,730 --> 00:21:15,970
+والنهاية للـ array بتاعتنا، فصار في interval
+
+252
+00:21:15,970 --> 00:21:21,870
+جديدة، صح؟ كنا بنعمل interval جديدة هنا أكيد لأن
+
+253
+00:21:21,870 --> 00:21:25,710
+ساعتها بدي أختصر واحد من الـ two parts هدول، واحد من
+
+254
+00:21:25,710 --> 00:21:29,370
+الاتنين هدول، بدي أعمله elimination، طيب بناءً على
+
+255
+00:21:29,370 --> 00:21:34,090
+الشرط هذا yes or no، بحدد أي part اللي بتعمله
+
+256
+00:21:34,090 --> 00:21:38,390
+elimination، فهذا كان مثال كتير واضح لاستخدام الـ
+
+257
+00:21:38,390 --> 00:21:42,710
+tree، فبنعرف بذلك أن أنا بقدر أمثل الـ problem كلها
+
+258
+00:21:42,710 --> 00:21:46,390
+على بعض بشكل tree، بشكل الـ tree هذه، هنعرف منها
+
+259
+00:21:46,390 --> 00:21:51,090
+حاجات كتيرة لقدام، أنت كنت مضطر تحسبها حساباً سابقاً،
+
+260
+00:21:51,090 --> 00:21:54,950
+إحنا هنا هتبين معاك بشكل أسرع كتير، بشكل كتير أسرع
+
+261
+00:21:54,950 --> 00:22:01,260
+منها الـ complexity، الـ complexity لما يكون عندك n
+
+262
+00:22:01,260 --> 00:22:04,440
+element في الـ array بتاعتك، هادي الـ array بتاعتك، هادي
+
+263
+00:22:04,440 --> 00:22:07,460
+فيها n elements، قد إيش محتاج عدد خطوات، بمعنى قد إيش الـ
+
+264
+00:22:07,460 --> 00:22:11,160
+complexity أو الـ time complexity، إحنا حلّيناها سابقاً،
+
+265
+00:22:11,160 --> 00:22:14,200
+جِبناها، ما كانش عندنا مشكلة، بس جِبناها، شوية قعدنا
+
+266
+00:22:14,200 --> 00:22:17,340
+نفهمكوا بيعمل كذا عشان يصل للواحد، ومن الواحد رجع
+
+267
+00:22:17,340 --> 00:22:21,120
+ورجع، قصة طويلة عريضة، مش هيك، عشان نجيبها، هنشوف
+
+268
+00:22:21,120 --> 00:22:24,480
+الآن مع مفهوم أن هي Tree يا جماعة الخير، في النهاية
+
+269
+00:22:24,480 --> 00:22:27,420
+طلعت إيش اللي بده يتغير علينا في الـ process،
+
+270
+00:22:27,420 --> 00:22:33,300
+هنشوفها عندنا لما ناخدها فعلياً، طيب الآن مين من
+
+271
+00:22:33,300 --> 00:22:38,020
+هدول الحالتين اللي قدامنا بقدر أسميها binary tree،
+
+272
+00:22:42,690 --> 00:22:47,410
+إيش المشكلة في اللي على الشمال؟ هي بـ.. سبحان الله
+
+273
+00:22:47,410 --> 00:22:50,090
+بادية على طول، واحد، اتنين، تلاتة، هي الـ tree باينة
+
+274
+00:22:50,090 --> 00:22:53,930
+على طول، فأنت بتحط الـ tree هذه مباشرة فوق عشان
+
+275
+00:22:53,930 --> 00:22:58,510
+تطلع منها في الآخر تلاتة، فإذا مش binary وإحنا قلنا
+
+276
+00:22:58,510 --> 00:23:02,210
+عشان أقول إن هي two array أو binary، معناته إن هي
+
+277
+00:23:02,210 --> 00:23:07,810
+أقل، المفروض من أو اتنين، فـ أقل من اتنين، فـ واضح
+
+278
+00:23:07,810 --> 00:23:13,030
+أنه هنا لأ، هذه أكبر، طيب إيش الـ definitions اللي بدي إياها،
+
+279
+00:23:13,030 --> 00:23:17,310
+منها: "a given rooted tree is a binary tree if and
+
+280
+00:23:17,310 --> 00:23:22,010
+only if every node other than the root has degree
+
+281
+00:23:23,120 --> 00:23:27,340
+أقل من أو يساوي اتنين، طيب، "and the root has
+
+282
+00:23:27,340 --> 00:23:34,800
+degree، برضه اتنين، برضه اتنين، نفس الكلام، ما هو
+
+283
+00:23:34,800 --> 00:23:38,540
+أصلًا إيش اللي خلانا نقول هذا مش binary؟ إن الـ root
+
+284
+00:23:38,540 --> 00:23:45,120
+نفسه تلاتة، إن الـ root نفسه كان تلاتة،
+
+285
+00:23:45,120 --> 00:23:45,520
+تمام
+
+286
+00:23:48,640 --> 00:23:53,560
+طيب، الـ ordered rooted tree، الـ order إحنا واضح إنه
+
+287
+00:23:53,560 --> 00:23:56,500
+مهم، بدي أستخدمه كـ model، الـ tree هذه بستخدمها كـ
+
+288
+00:23:56,500 --> 00:23:59,620
+model، معناته بيهمني الـ order، لأن في applications
+
+289
+00:23:59,620 --> 00:24:03,060
+كتيرة مهمة فيها الـ order، okay، أنا مش بدي أمثل الـ
+
+290
+00:24:03,060 --> 00:24:05,940
+بيانات وخلاص، لما جينا حطينا هنا الرسمة وقلنا yes
+
+291
+00:24:05,940 --> 00:24:09,920
+no، yes، no، yes، no، أحياناً الـ expert system هذه في
+
+292
+00:24:09,920 --> 00:24:14,810
+أسئلة أولى من أسئلة، في إشي أو conditions أولى من
+
+293
+00:24:14,810 --> 00:24:18,650
+condition، لأنه ممكن تسهل عليّ في الآخر الشغل، ما..
+
+294
+00:24:18,650 --> 00:24:22,390
+ما يجينيش واحد بكح، وآخر سؤال أقول له أنت بتكح ولا
+
+295
+00:24:22,390 --> 00:24:27,110
+بتكحش؟ ما هذا المفروض أول سؤال، أول سؤال يجيني ويكون
+
+296
+00:24:27,110 --> 00:24:30,610
+والله كأنه في كورونا، أول حاجة بسأله الأسئلة اللي خاصة بالكورونا، مش بسأله أسئلة
+
+297
+00:24:30,610 --> 00:24:33,370
+جانبية، معناته اللي بدي أوصله أنه في priority
+
+298
+00:24:34,130 --> 00:24:38,150
+لمين؟ للـ leaves، في priority للـ leaves، مين اللي
+
+299
+00:24:38,150 --> 00:24:42,810
+المفروض تكون قبل التانية؟ معناه ذلك أنه هل الـ
+
+300
+00:24:42,810 --> 00:24:45,730
+tree ممكن تكون ordered؟
+
+301
+00:24:45,730 --> 00:24:50,370
+ممكن تكون ordered بحيث أنه أشتغل، أرسم الـ tree
+
+302
+00:24:50,370 --> 00:24:55,090
+كاملة وتكون عندها الـ priority، left to right، left to
+
+303
+00:24:55,090 --> 00:25:01,880
+right، طيب بس الـ left to right هنا شوية بدها دقة، هي
+
+304
+00:25:01,880 --> 00:25:05,960
+مش للـ leaves فقط، هي كمان للـ left subtree to right
+
+305
+00:25:05,960 --> 00:25:10,760
+subtree، هذا لما تكون binary، لأن أنت فعلياً binary
+
+306
+00:25:10,760 --> 00:25:14,480
+عندك left و right بس، طيب لكن لما تكون أكتر من
+
+307
+00:25:14,480 --> 00:25:18,940
+binary، بمعنى الـ array بتاعتها، in array، الـ in array
+
+308
+00:25:18,940 --> 00:25:23,760
+لأ، معناته أنا بتكلم هنا عن most left، left، right،
+
+309
+00:25:23,760 --> 00:25:28,820
+most right، بحيث إن الاتجاه يكون واضح من الـ left to
+
+310
+00:25:28,820 --> 00:25:34,270
+right، من left to right، هذا إذا كانت الـ degree
+
+311
+00:25:34,270 --> 00:25:38,950
+بتاعتهم أكتر من اتنين أو الـ array بتاعتها أكتر من
+
+312
+00:25:38,950 --> 00:25:44,670
+اتنين، فهي نقول left must to right must، جيد، هنشوف
+
+313
+00:25:44,670 --> 00:25:50,650
+هنا مش كاتبها، معناته إحنا مضطرين نكتبها، فكرة حلوة،
+
+314
+00:25:50,650 --> 00:25:55,010
+نرسمها هنا، حالة بهذا الشكل، عشان نوضح بس قصة الـ sub
+
+315
+00:25:55,010 --> 00:26:02,020
+tree، هل وجدت لما بدنا نعمل order لهذا الكلام، كيف
+
+316
+00:26:02,020 --> 00:26:08,540
+بقدر.. بدي أرقمهم.. أحط لهم أرقام حسب الـ order
+
+317
+00:26:08,540 --> 00:26:12,000
+تبعهم.. حسب الـ order تبعهم.. هقول.. هبدأ من هنا
+
+318
+00:26:12,000 --> 00:26:16,020
+.. هننزل.. لاحظوا.. هننزل.. هاي واحد
+
+319
+00:26:16,020 --> 00:26:22,520
+.. هي واحد، هذا اللي هو إيش الـ most أو الـ.. الـ left
+
+320
+00:26:25,540 --> 00:26:30,140
+هي واحد، هذا اللي هو إيش الـ most أو الـ.. الـ left
+
+321
+00:26:30,140 --> 00:26:37,340
+most left most، طيب مين بيجي بعده؟ تلاتة،
+
+322
+00:26:37,340 --> 00:26:41,020
+طيب،
+
+323
+00:26:41,020 --> 00:26:43,900
+إيش اللي عملنا إحنا هنا؟ عملنا كأنه هاد هيك sub tree
+
+324
+00:26:43,900 --> 00:26:48,820
+وهاد sub tree تانية، فخلصت الـ sub tree الأولى وبعدين
+
+325
+00:26:48,820 --> 00:26:52,980
+بعدين انتقلت للـ sub tree التانية، طيب خلصنا بنطلع للـ
+
+326
+00:26:52,980 --> 00:26:59,040
+level اللي أعلى، أربعة هنا وين هتيجي الخمسة؟ خمسة
+
+327
+00:26:59,040 --> 00:27:04,840
+عفواً، أربعة إحنا كتبناها هنا، خمسة، ستة، سبعة،
+
+328
+00:27:04,840 --> 00:27:15,220
+ثمانية، تسعة، وعشرة طبعاً،
+
+329
+00:27:15,220 --> 00:27:22,040
+فلاحظ أنه خلصنا الـ subtree هذه في
+
+330
+00:27:22,040 --> 00:27:27,580
+الأول، قبل ما نبدأ في أي sub-tree تانية جاية على
+
+331
+00:27:27,580 --> 00:27:32,780
+يمينها، فبنخلصها sub-tree by sub-tree، داخل كل sub
+
+332
+00:27:32,780 --> 00:27:38,840
+-tree بتعامل معاها node by node أو leaf by leaf، بس
+
+333
+00:27:38,840 --> 00:27:44,620
+بالأساس ببدأ بـ sub-tree، الـ sub-tree دي بخلصها
+
+334
+00:27:44,620 --> 00:27:48,580
+كاملة لأنها جاية في الـ left، ثم ببدأ أشوف اللي
+
+335
+00:27:48,580 --> 00:27:54,220
+وراها، ثم بنشوف مين اللي وراها، واضحة؟ تمام، فهيك
+
+336
+00:27:54,220 --> 00:27:56,840
+بنقدر نقول الـ order بهذا الشكل اللي إحنا شايفينه،
+
+337
+00:27:56,840 --> 00:28:02,040
+إيش طيب في models واضحة، بنقدر نمثل.. نمثلها بالـ
+
+338
+00:28:02,040 --> 00:28:07,240
+Tree، يمكن أوضحهم هي الـ structured hydrocarbons أو
+
+339
+00:28:07,240 --> 00:28:10,380
+hydrocarbons اللي موجودة في الـ chemistry اللي
+
+340
+00:28:10,380 --> 00:28:12,280
+إنتوا كنتوا بتاخدوها زمان في الـ chemistry، التركيبات
+
+341
+00:28:12,280 --> 00:28:16,880
+الكيميائية اللي هي حلقة، مجموعة من ذرات الـ carbon و
+
+342
+00:28:16,880 --> 00:28:22,560
+متصلة بالـ hydrogen عشان يعطيك الـ hydrocarbon، الـ
+
+343
+00:28:22,560 --> 00:28:25,640
+hydrocarbons component هذه هي عبارة عن زي ما إنتوا
+
+344
+00:28:25,640 --> 00:28:30,020
+شايفين هنا، لما بتكون رباعية اللي هي زي البوتان،
+
+345
+00:28:30,020 --> 00:28:35,680
+البوتين أو البوتان، غاز البوتان، بوتين هذا من
+
+346
+00:28:35,680 --> 00:28:38,340
+الغازات اللي إنتوا عارفينها، مشتعلة، ملتهبة بشكل
+
+347
+00:28:38,340 --> 00:28:43,780
+سريع، هي عبارة عن أربع ذرات من الـ carbons وكل واحدة
+
+348
+00:28:43,780 --> 00:28:49,320
+مشبعة، مشبعة عشان هي اسمها saturated، بمعنى إن
+
+349
+00:28:49,320 --> 00:28:53,200
+الغلاف الخارجي ليها الـ carbon رباعي، مش هيك عشان
+
+350
+00:28:53,200 --> 00:28:56,960
+يصير متشبع محتاج أكم رابطة تساهمية مع ذرات أخرى؟
+
+351
+00:28:56,960 --> 00:29:01,140
+أربعة، عشان يسكر، هاي واحدة hydrogen، تانية
+
+352
+00:29:01,140 --> 00:29:04,660
+hydrogen، تالتة hydrogen، والرابعة carbon، فهي
+
+353
+00:29:04,660 --> 00:29:08,460
+الأربعة التساهمية، التعاون أو الرابطة التساهمية
+
+354
+00:29:08,460 --> 00:29:13,320
+تبعته، عشان هيك أصبح متشبع، وهنا نفس الكلام، هي واحدة،
+
+355
+00:29:13,320 --> 00:29:18,220
+اتنين، تلاتة، وهي الرابعة، فهتلاقي كله أصبح متشبع،
+
+356
+00:29:21,780 --> 00:29:28,080
+كذرات متكاملة، فهنا أصبح البوتين أو غاز البوتان أو
+
+357
+00:29:28,080 --> 00:29:32,740
+غاز البوتان، طيب في عندكوا البنتين أو غاز البنتان،
+
+358
+00:29:32,740 --> 00:29:39,080
+هذا خماسي، والهكسين اللي هو الهكسة، من هكسة، الهكسان
+
+359
+00:29:39,080 --> 00:29:43,540
+بيسموه بالعربي الهكسان، الهكسين هذا برضه سداسي، بس
+
+360
+00:29:43,540 --> 00:29:46,760
+كله طبعاً متصل بشكل كامل، الآن لما نيجي نتطلع على
+
+361
+00:29:46,760 --> 00:29:50,120
+أما هذه عبارة عن الـ tree، في النهاية أنت راح تلاحظ
+
+362
+00:29:50,120 --> 00:29:55,940
+إيش رسمت؟ رسمت tree، هاي الـ connection اللي هي الـ
+
+363
+00:29:55,940 --> 00:30:01,440
+edges بتاعتها، وهي الـ nodes هذه، الـ nodes، كل ما في
+
+364
+00:30:01,440 --> 00:30:07,470
+الموضوع إنه هنا بيقول إن هي unrooted Tree، شيك، أنا
+
+365
+00:30:07,470 --> 00:30:11,670
+ماعنديش root واحدة، والـ co طالعة منها هي تساهمية
+
+366
+00:30:11,670 --> 00:30:16,850
+بالنسبة لذرات الـ carbon، كويس، لعند ما تصل الـ.. الـ
+
+367
+00:30:16,850 --> 00:30:23,630
+.. الـ heptane، ثم الـ octane أو الـ octa الثماني، طيب،
+
+368
+00:30:23,630 --> 00:30:28,050
+طبعاً في الـ nine وفي الـ deca اللي هو ضايل التسعة و
+
+369
+00:30:28,050 --> 00:30:29,590
+العشرة، تسعة وعشرة،
+
+370
+00:30:32,640 --> 00:30:39,280
+متذكرينهم الأرقام هذه؟ الأرقام اللاتينية كيف؟ طب،
+
+371
+00:30:39,280 --> 00:30:45,300
+هو ممتاز، طيب الـ organizational structure هذا كمان
+
+372
+00:30:45,300 --> 00:30:49,240
+نوع ثاني من الأنواع اللي بنقدر نمثل الـ model فيها
+
+373
+00:30:49,240 --> 00:30:54,640
+بشكل tree، هو ببساطة جداً التركيب البنائي للمؤسسات،
+
+374
+00:30:54,640 --> 00:30:59,740
+التركيب البنائي للمؤسسات، بقدر أقول إن والله في عند
+
+375
+00:30:59,740 --> 00:31:01,680
+المدير،
+
+376
+00:31:05,450 --> 00:31:12,780
+وفي عنده، المدير هذا عنده مجموعة نواب، في نائب أول،
+
+377
+00:31:12,780 --> 00:31:17,180
+نفترض، خلينا ناخد الجامعة مثلاً، رئيس الجامعة وفي عندك
+
+378
+00:31:17,180 --> 00:31:21,660
+نائب أكاديمي، في عندك نائب إداري، في عندك بعض
+
+379
+00:31:21,660 --> 00:31:25,380
+العمادات اللي تتبع مباشرة، زي عمادة القبول والتسجيل،
+
+380
+00:31:25,380 --> 00:31:31,480
+زي عمادة العلاقات الخارجية، عمادة الجودة، عمادة المشـ..
+
+381
+00:31:31,480 --> 00:31:35,720
+عارف إيه، بهذا الشكل، طيب، داخلها هتيجي عند الشؤون
+
+382
+00:31:35,720 --> 00:31:40,160
+الأكاديمية مثلاً، هتلاقي إنه في مجموعات، كلية
+
+383
+00:31:42,890 --> 00:31:46,690
+كلية هندسة، كلية طب، كلية علوم، كلية.. كلية
+
+384
+00:31:46,690 --> 00:31:54,690
+الهندسة، أقسام وهكذا، طيب، داخل الأقسام هتيجي تقول
+
+385
+00:31:54,690 --> 00:31:58,050
+الدكاترة.. الدكاترة.. الدكاترة.. الدكاترة..
+
+386
+00:31:58,050 --> 00:31:58,290
+الدكاترة.. الدكاترة.. الدكاترة.. الدكاترة..
+
+387
+00:31:58,290 --> 00:31:59,670
+الدكاترة.. الدكاترة.. الدكاترة.. الدكاترة..
+
+388
+00:31:59,670 --> 00:32:02,810
+الدكاترة.. الدكاترة.. الدكاترة.. الدكاترة..
+
+389
+
+445
+00:36:25,860 --> 00:36:35,890
+إلا ال root  هي جاية لحالها عشان هيك ناجس واحد كل
+
+446
+00:36:35,890 --> 00:36:39,950
+node بيجي مع ال edge تبعتها كل node مع ال edge
+
+447
+00:36:39,950 --> 00:36:42,830
+المقابل إليها كل node مع edgeها كل node مع edgeها
+
+448
+00:36:42,830 --> 00:36:47,810
+فإذن هم السوين باستثناء أن الأولى without an edge
+
+449
+00:36:47,810 --> 00:36:52,930
+فإذن جديش عددهم ال nodes عددهم n فإذن ال edges  are n
+
+450
+00:36:52,930 --> 00:36:58,090
+ناقص واحد  و أظن مش فيها كتير غلط إن شاء الله طيب
+
+451
+00:36:58,090 --> 00:37:03,450
+بالنسبة لل full M-ary tree، ال full M-ary tree بمعنى أن أنت عندك
+
+452
+00:37:03,450 --> 00:37:09,700
+زيها دي هيك مجسمة لـ M Nodes و نفس الكلام هنا M
+
+453
+00:37:09,700 --> 00:37:14,340
+Nodes بهذا الشكل لو افترضنا أنه تلتات لو افترضنا
+
+454
+00:37:14,340 --> 00:37:19,440
+أن هي مقصود فيها تلتات فهنا عدد الـ Internal Nodes
+
+455
+00:37:19,440 --> 00:37:26,260
+في الحالة هذه هيكون بيساوي اللي هو ال N أو ال M
+
+456
+00:37:26,260 --> 00:37:35,250
+هنا ال I بتاعتها هنسميها I و في عندي N أساسًا
+
+457
+00:37:35,250 --> 00:37:42,130
+nodes كلها كاملة تمام ال I ال internal nodes فبيظل
+
+458
+00:37:42,130 --> 00:37:46,610
+عندنا المتبقي ال leaves هنسميها L عشان المصطلحات
+
+459
+00:37:46,610 --> 00:37:49,950
+اللي موجودة  لا نريد الخلط بينها هنا
+
+460
+00:37:49,950 --> 00:37:54,350
+مثلا نتكلم عن I رغم أن احنا هنا كتبنا N لكن أنا
+
+461
+00:37:54,350 --> 00:37:59,760
+أتكلم عن I في الآخر الـ I internal nodes ال N total
+
+462
+00:37:59,760 --> 00:38:03,960
+nodes كلهم على بعض ال L هي ال leaves أو ال leaf
+
+463
+00:38:03,960 --> 00:38:07,920
+node تمام فإذا المبدأ إذا كانت تعرفت أن ال I هي
+
+464
+00:38:07,920 --> 00:38:12,220
+internal nodes معناه ذلك أنه بقدر أقول إن ال total
+
+465
+00:38:12,220 --> 00:38:20,650
+كله على بعضه بيساوي M. في I زائد واحد  M في I
+
+466
+00:38:20,650 --> 00:38:26,070
+زائد واحد جديش عدد ال tree ال branching تبعتنا ال
+
+467
+00:38:26,070 --> 00:38:29,330
+branching اللي هو كل node بنعملها branching لأكم
+
+468
+00:38:29,330 --> 00:38:35,870
+node ثانية أم كل واحدة بنجسمها لـ M nodes
+
+469
+00:38:39,180 --> 00:38:42,260
+ما دام أنا من الأساس بقول إن أنا بتكلم عن full M-
+
+470
+00:38:42,260 --> 00:38:51,020
+ary tree فإذن بنتعامل مع I في M زائد واحد طيب ال
+
+471
+00:38:51,020 --> 00:38:54,640
+leaves في الحالة هذه المفروض أن الفارق بينهم
+
+472
+00:38:54,640 --> 00:38:59,340
+المفروض أن الفارق ما بين الاتنين فعلى اعتبار أن ال
+
+473
+00:38:59,340 --> 00:39:04,600
+leaves المفروض أنه في الحالة هذه بقدر أجيبها على
+
+474
+00:39:04,600 --> 00:39:07,000
+أساس أنها N ناقص I
+
+475
+00:39:11,700 --> 00:39:18,540
+منطقي ال leaves كل ال nodes وسميناها N ناقص ال
+
+476
+00:39:18,540 --> 00:39:22,020
+internal nodes فبيظل ال leaves اللي هو ال terminal
+
+477
+00:39:22,020 --> 00:39:27,600
+nodes فبيصير بهذا الشكل ال N هيها بنجيبها و
+
+478
+00:39:27,600 --> 00:39:32,700
+بنحطها هنا و بناخد ال I مشترك  ناخد ال I مشترك خلاص
+
+479
+00:39:32,700 --> 00:39:38,340
+مجرد تثبيت المعادلة مع بعضها عشان ناخد I مشتركة و
+
+480
+00:39:38,340 --> 00:39:43,580
+الواحدة بتظل زي ما هي الواحد كما هي فما فيش مشكلة
+
+481
+00:39:43,580 --> 00:39:49,280
+بيظل عندك M ناقص واحد تاعة ال I هذه فبيظهر عندك M
+
+482
+00:39:49,280 --> 00:39:55,880
+ناقص واحد في I زائد واحد هي اللي موجودة عندك طيب
+
+483
+00:39:55,880 --> 00:40:00,040
+من خلال مجموعة ال .. أكمن رول اللي أخدناهم هدولة
+
+484
+00:40:00,040 --> 00:40:03,920
+واضح جدًا أنه لو أنا عارف ال M-ary tree تبعتي ال array
+
+485
+00:40:03,920 --> 00:40:08,160
+تبعتي أو ال branching تبعنا جديش عدده أي قيمة من
+
+486
+00:40:08,160 --> 00:40:12,690
+القيم هدول كافية لإني أقدر أجيب باقي القيم كافية أنه
+
+487
+00:40:12,690 --> 00:40:17,270
+أقدر منها أجيب باقي القيم كاملة لو كانت full
+
+488
+00:40:17,270 --> 00:40:21,950
+طبعًا، معناه ذلك أن ال M أنت عارفها ولها قيمة في
+
+489
+00:40:21,950 --> 00:40:26,430
+الحالة هذه أي واحدة من التلت أو حتى الرابع معهم هي
+
+490
+00:40:26,430 --> 00:40:32,410
+ال E كمان E و N و I و L أعرف أي واحدة منهم الباقي
+
+491
+00:40:32,410 --> 00:40:38,900
+كله بنعرفه ما دام أنت عارف أن هي full M-ary tree كويس
+
+492
+00:40:38,900 --> 00:40:42,280
+واحدة اتنين تلاتة أربعة تمام يكفي واحدة منها أنت
+
+493
+00:40:42,280 --> 00:40:47,340
+عارفها طيب الآن نيجي على مفهوم ثاني المفهوم الثاني
+
+494
+00:40:47,340 --> 00:40:52,260
+هو ال height أو الارتفاع بتاع الشجرة أنت عندك شجرة
+
+495
+00:40:52,260 --> 00:40:55,160
+بتطلع و قاعدة بتفرع طب جديش ارتفاعها على ارتفاع
+
+496
+00:40:55,160 --> 00:40:59,700
+لها جديش على ارتفاع على ارتفاع هنا يقاس جديش عدد
+
+497
+00:40:59,700 --> 00:41:07,060
+مرات ال branching لأبعد leaf جديش وصلت بمعنى ال order
+
+498
+00:41:07,060 --> 00:41:10,900
+تبعها لل length ال length احنا قلنا من relation
+
+499
+00:41:10,900 --> 00:41:13,540
+لل relation فمن node ل node هي relation من node ل
+
+500
+00:41:13,540 --> 00:41:17,120
+node هي relation طب لما نصل ل ال leaf ال leaf
+
+501
+00:41:17,120 --> 00:41:20,620
+بتاعتنا أكم relation عملت فإذا ال length تبع ال
+
+502
+00:41:20,620 --> 00:41:24,300
+path تبعها جديش طوله هي ال height اللي حنحكي عنها
+
+503
+00:41:25,620 --> 00:41:31,420
+الـ level لـ ال node هو ال length فعليًا لـ simple
+
+504
+00:41:31,420 --> 00:41:35,160
+path from the root to a certain node لـ ال node
+
+505
+00:41:35,160 --> 00:41:38,800
+المحددة هو المعني كويس فبنسميها ال height وهذه هي
+
+506
+00:41:38,800 --> 00:41:42,560
+ال maximum node level طيب بالنسبة لي ال rooted M-
+
+507
+00:41:42,560 --> 00:41:48,660
+ary Tree with height H بنسميها balanced إذا كانت
+
+508
+00:41:48,660 --> 00:41:57,530
+كل ال leaves at level H و H ناقص واحد بمعنى لما
+
+509
+00:41:57,530 --> 00:42:00,790
+تروح تيجي تطلع على الشجرة اللي بيقلموها بيعملوها ال
+
+510
+00:42:00,790 --> 00:42:04,310
+pruning ال pruning هذا لما بتقلم و بتلاقي مرسوم
+
+511
+00:42:04,310 --> 00:42:09,730
+مصطرة هذا balanced لأنه عارف أن كلهم لنفس
+
+512
+00:42:09,730 --> 00:42:13,150
+ال level  مش هيك لو واحدة نازلة شوية بس هي
+
+513
+00:42:13,150 --> 00:42:15,810
+بتكون في ال level اللي أقل لكن شجرة مش مقلمة
+
+514
+00:42:15,810 --> 00:42:19,090
+هتلاقي فيه فرع هنا و فرع في آخر الدنيا جدًا فكل
+
+515
+00:42:19,090 --> 00:42:23,470
+واحد في level غير الثاني فهدي unbalanced هتكون إيش
+
+516
+00:42:23,470 --> 00:42:26,110
+اسمها unbalanced أنت بقدر تسميها balanced مش
+
+517
+00:42:26,110 --> 00:42:29,230
+بضروري كلهم في نفس ال level لكن في ال maximum
+
+518
+00:42:29,230 --> 00:42:34,140
+level أو أقل بواحد ماشي بيظل اسمها balanced بيظل
+
+519
+00:42:34,140 --> 00:42:38,020
+اسمها balanced فإذا H و H هذه حددناها هي ال
+
+520
+00:42:38,020 --> 00:42:45,100
+maximum node level أو أقل بواحد مش الحالة تمام في
+
+521
+00:42:45,100 --> 00:42:55,250
+الحالة هذه  M to the power h leaves in an M-ary tree of
+
+522
+00:42:55,250 --> 00:42:59,270
+height h بتاع ليه كتير منطقية برضه هذه هالوقت
+
+523
+00:42:59,270 --> 00:43:02,970
+تعالى تطلع هنا في الحالة اللي احنا رسمينها عاملين
+
+524
+00:43:02,970 --> 00:43:05,090
+جديش level
+
+525
+00:43:08,130 --> 00:43:11,490
+ال level اتنين تلاتة مظبوط فحتيجي تتطلع بدنا نعوض
+
+526
+00:43:11,490 --> 00:43:14,150
+في الكلام هذا هاي الصفر ال level zero لسه لما
+
+527
+00:43:14,150 --> 00:43:17,010
+عملتش branching بعد أول branch ال level الأول و ال
+
+528
+00:43:17,010 --> 00:43:23,830
+level الثاني جيد فإذا ال H اتنين H هنا بـ اتنين طيب
+
+529
+00:43:23,830 --> 00:43:29,650
+ال branching اللي هي ال M هنا جديش ال M تلاتة طيب
+
+530
+00:43:29,650 --> 00:43:34,010
+لو قلنا تلاتة to the power اتنين تسعة واحد اتنين
+
+531
+00:43:34,010 --> 00:43:36,290
+تلاتة أربعة خمسة ستة سبعة ثمانية تسعة
+
+532
+00:43:39,230 --> 00:43:43,470
+صحيح؟ at most بمعنى ممكن تكون أقل ممكن تكون أقل؟
+
+533
+00:43:43,470 --> 00:43:46,890
+أه ممكن تكون أقل ليش؟ لأن احنا قلنا ال height
+
+534
+00:43:46,890 --> 00:43:49,890
+ممكن تكون كلها في نفس ال height أو اللي أقل منه
+
+535
+00:43:49,890 --> 00:43:54,850
+يعني ممكن تصدف إن واحدة منهم ما عملتش branching ف
+
+536
+00:43:54,850 --> 00:44:00,250
+at most maximum هتكون تسعة لو كملناها ال level
+
+537
+00:44:00,250 --> 00:44:06,510
+الثاني طب لو عملنا level ثالث 27 27 ÷ 3 تصير 9 ÷
+
+538
+00:44:06,510 --> 00:44:13,110
+3 مظبوط تمام طيب هذا الكلام الآن هيسهل علينا ال
+
+539
+00:44:13,110 --> 00:44:17,810
+binary search ال binary search مش هيك مستوحاة كلها
+
+540
+00:44:17,810 --> 00:44:23,930
+من بعض كلها مستوحاة من بعض عشان تصل لنفس القرار أن
+
+541
+00:44:23,930 --> 00:44:27,270
+والله أنت عم شبه عملت ال search ال search هذا كان
+
+542
+00:44:27,270 --> 00:44:29,570
+لجديش العدد ال leaves
+
+543
+00:44:32,260 --> 00:44:35,920
+لاحظ اللي أنت بعتك اللي هو جديش عدد ال elements داخل
+
+544
+00:44:35,920 --> 00:44:38,920
+ال array اللي أنت بدك تبحث فيها باستخدام ال binary
+
+545
+00:44:38,920 --> 00:44:42,660
+باستخدام binary خلينا بس عشان كمان تكون واضحة ال
+
+546
+00:44:42,660 --> 00:44:45,640
+binary معناته المفروض اتنين ما نخلطش مع
+
+547
+00:44:45,640 --> 00:44:52,080
+الثلاثة خلينا مع الاثنين عشان تكون ماشية مع هاي ال
+
+548
+00:44:52,080 --> 00:44:59,600
+level صفر وهي واحد وهي اثنين وخلينا
+
+549
+00:44:59,600 --> 00:45:05,480
+نعمل كمان واحدة تمام؟ جيد احنا كنا نشتغل بهذا
+
+550
+00:45:05,480 --> 00:45:11,060
+الشكل انجسم اثنينات طيب في الآخر أنا عارف أن عدد
+
+551
+00:45:11,060 --> 00:45:16,160
+ال elements في ال array اللي بتبحث داخله المفروض
+
+552
+00:45:16,160 --> 00:45:21,900
+هيعطيني عدد ال leaves أساسًا طيب ال leaves هذه
+
+553
+00:45:21,900 --> 00:45:26,260
+بطريقة عكسية أنا أستنتجها من كم level
+
+554
+00:45:28,920 --> 00:45:34,120
+من كم level بمعنى أنه جديش أنا محتاج yes no yes
+
+555
+00:45:34,120 --> 00:45:38,520
+no yes no عشان أصل فعلًا لتمثيل العدد ال leaves
+
+556
+00:45:38,520 --> 00:45:43,540
+الكامل صارت بطريقة عكسية معناه ذلك كأنه العدد هذا
+
+557
+00:45:43,540 --> 00:45:51,540
+كله بأكم step بقدر أطلع منه عنصر واحد فقط اللي هي
+
+558
+00:45:51,540 --> 00:45:54,860
+بتعطيك ال complexity في الآخر طيب ما دام أنا عارف
+
+559
+00:45:54,860 --> 00:46:01,360
+أنه في الآخر ال leaves M to the power of H هذه
+
+560
+00:46:01,360 --> 00:46:04,680
+معطاة لأن هتكون جاية لك من الأول ال array تبعتك
+
+561
+00:46:04,680 --> 00:46:10,720
+فيها 100 عنصر 100 عنصر كم step محتاج بال binary
+
+562
+00:46:10,720 --> 00:46:16,620
+search عشان تصل للحل معناه أن أنت ال N اللي بتحكي
+
+563
+00:46:16,620 --> 00:46:20,740
+عنها جديش العدد هي معطاة هتكون هنا و اللي هي هتكون
+
+564
+00:46:20,740 --> 00:46:31,060
+جديش نسميه N مثلا أو لا هي ال L هنا تمثل L تمثل ال
+
+565
+00:46:31,060 --> 00:46:34,860
+leaves تمثل ال leaves طيب هذه معطى عندي لأن أنا
+
+566
+00:46:34,860 --> 00:46:37,580
+عارفها مسبقًا أنا قلت لك هي ال array ال array دي
+
+567
+00:46:37,580 --> 00:46:43,460
+فيها مائة عنصر المائة عنصر هدول كم مرة بدك تعمل
+
+568
+00:46:43,460 --> 00:46:48,000
+ال binary search عشان تصل للحل مش هيك السؤال كان
+
+569
+00:46:48,000 --> 00:46:51,220
+عندكم كم مرة بدك تعمله عشان تصل للحل معنى ذلك أن
+
+570
+00:46:51,220 --> 00:46:57,460
+أنا أعطيك المائة و ال branching أكيد أنت عارفه لأن
+
+571
+00:46:57,460 --> 00:47:01,800
+في كل level أنت بتجسيم بتعمل اثنين yes or no
+
+572
+00:47:01,800 --> 00:47:05,180
+condition واحد و بتقول يا yes يا no فإذا أنت محتاج
+
+573
+00:47:05,180 --> 00:47:10,120
+ال H أنت محتاج H فإذا بتصير كأنها اثنين to the
+
+574
+00:47:10,120 --> 00:47:13,000
+power of the height تساوي ال L و ال L given معطى
+
+575
+00:47:13,000 --> 00:47:18,320
+بدك H فخذ log للطرفين طلعت نفس اللي أخذنا المرة
+
+576
+00:47:18,320 --> 00:47:22,380
+السابقة برضه logarithmic فبتطلع في الآخر
+
+577
+00:47:22,380 --> 00:47:25,680
+logarithmic لأن أنا بدي آخذ log للطرفين بحيث أنها
+
+578
+00:47:25,680 --> 00:47:33,580
+تصبح H في log 2 تساوي log L تساوي log ال L و اقسم
+
+579
+00:47:33,580 --> 00:47:38,540
+على log 2 عشان تصبح in general in general ال H
+
+580
+00:47:38,540 --> 00:47:47,860
+تساوي log L على log اثنين اللي هي mean M in
+
+581
+00:47:47,860 --> 00:47:52,700
+general جديش أنا عملت branching في حالة ال binary
+
+582
+00:47:52,700 --> 00:47:57,340
+كنت بتعمل اثنين branching فكنت بتكسب على log اثنين
+
+583
+00:47:57,340 --> 00:48:01,700
+طيب in general هذه الصورة كنا بنقولها في الحالة
+
+584
+00:48:01,700 --> 00:48:09,590
+هذه log للأساس M لـ L و بس كنا بنعملها للأساس فهي ك
+
+585
+00:48:09,590 --> 00:48:12,670
+logarithmic هتضل ال order تبعك logarithmic
+
+586
+00:48:12,670 --> 00:48:16,310
+logarithmic okay المرة القادمة إن شاء الله تعالى
+
+587
+00:48:16,310 --> 00:48:19,430
+بناخذ الجزء المتبقي و هي ال applications هنبدأ
+
+588
+00:48:19,430 --> 00:48:23,450
+نشوف مجموعة applications تحل باستخدام  كان ضايق
+
+589
+00:48:23,450 --> 00:48:26,350
+الشيء هنا لا خلصناه ال applications اللي ممكن
+
+590
+00:48:26,350 --> 00:48:29,670
+نستخدم فيها ال tree لحلها هناخد ال binary search
+
+591
+00:48:29,670 --> 00:48:33,350
+هنرجع لها ال binary search و كيف بقدر أمثله أحطه
+
+592
+00:48:33,350 --> 00:48:39,460
+هنا كيف نقدر نمثله داخل ال tree ممكن نتكلم برضه في
+
+593
+00:48:39,460 --> 00:48:43,020
+جزئية ال insertion  متذكرين ال insertion ال
+
+594
+00:48:43,020 --> 00:48:46,360
+insertion sort برضه نفس الكلام ممكن نتكلم أو
+
+595
+00:48:46,360 --> 00:48:49,380
+sorting حتى في عملية ال sorting ممكن نشتغل على ال
+
+596
+00:48:49,380 --> 00:48:52,160
+sorting نجيب مثال على ال sorting باستخدام tree
+
+597
+00:48:52,160 --> 00:48:57,940
+نعمل model tree و أبدأ أزرع ال tree اللي هو بتعمل
+
+598
+00:48:57,940 --> 00:49:01,920
+insertion فأنت فعليًا كأنك بتحط branch إضافي بس هذا
+
+599
+00:49:01,920 --> 00:49:04,500
+مكانه المفروض يكون هنا .. هذا مكانه المفروض يكون
+
+600
+00:49:04,500 --> 00:49:07,740
+هنا .. هذا مكانه المفروض يكون هنا .. عشان تكون
+
+601
+00:49:07,740 --> 00:49:11,340
+ordered بتوعي أخذنا احنا ال order بناء على ال rule
+
+602
+00:49:11,340 --> 00:49:15,340
+بتاعة ال order طب بعد ما أنشئ ال tree كويس اعمل
+
+603
+00:49:15,340 --> 00:49:19,860
+scan عليها حسب ال order تبعها طلعت الحل طلعنا ال
+
+604
+00:49:19,860 --> 00:49:22,440
+order اللي هو عملت sorting في الآخر اللي هي
+
+605
+00:49:22,440 --> 00:49:25,780
+باستخدام tree model بعدين هنتكلم عن ال maximum
+
+606
+00:49:25,780 --> 00:49:29,240
+comparison in a sorting algorithm عشان تصنف
+
+607
+00:49:29,240 --> 00:49:34,560
+algorithm معين أو تمالق sorting كم level محتاج،
+
+608
+00:49:34,560 --> 00:49:37,560
+برضه لها علاقة بال complexity، لأن أنا بتكلم عن
+
+609
+00:49:37,560 --> 00:49:41,020
+minimum comparisons، comparisons معناته خطوات، كم
+
+610
+00:49:41,020 --> 00:49:44,540
+خطوة محتاج أعمل، time complexity، فإذا هذا الكلام
+
+611
+00:49:44,540 --> 00:49:47,020
+هناخده المرة القادمة، اللي هو هناخده تطبيقات على
+
+612
+00:49:47,020 --> 00:49:49,680
+ال trees، تطبيقات حيوية من الحاجة اللي مرت عليكم
+
+613
+00:49:49,680 --> 00:49:51,900
+سابقا، يعطيكم العافية و بنشوفكم المرة القادمة إن
+
+614
+00:49:51,900 --> 00:49:52,380
+شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/x82rLS0FR9A_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/x82rLS0FR9A_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0dba421ebac8538b42413bf53b25cc8f0f73f356
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/x82rLS0FR9A_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2232, "start": 4.98, "end": 22.32, "text": "طيب، يعطيكوا العفو يا شباب، اليوم ان شاء الله تعالى بناخد آخر جزء كان متبقى في المساق و هو حالة خاصة من ال graphs زي لما احنا قولنا درسنا ال relations و ال relations قولنا هاد مظلة كبيرة", "tokens": [9566, 1829, 3555, 12399, 37495, 9566, 1829, 4117, 14407, 18863, 5172, 2407, 35186, 13412, 3555, 16758, 12399, 45595, 20498, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 44945, 47283, 3215, 19753, 34740, 10874, 11622, 38207, 25961, 44650, 3555, 4587, 7578, 8978, 9673, 3794, 995, 4587, 4032, 31439, 11331, 6027, 3660, 16490, 33546, 3660, 9154, 2423, 24877, 30767, 1829, 5296, 15042, 1975, 5016, 8315, 12174, 12610, 8315, 11778, 2288, 3794, 8315, 2423, 2299, 4032, 2423, 2299, 12174, 12610, 8315, 8032, 18513, 3714, 19913, 37977, 9122, 3555, 48923], "avg_logprob": -0.17441860898289568, "compression_ratio": 1.6368421052631579, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 4.98, "end": 5.5, "word": "طيب،", 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{"id": 3, "seek": 6423, "start": 39.57, "end": 64.23, "text": "نوع خاص جدا من أنواع ال graphs اللي بكل بساطة بنقدر نعرفه تحت مظلة ال undirected graph و with no circuits او self loops او circuits عموما، يعني مش مضروح self loops، self loops احنا بنتكلم عن من ال node لنفسها، لأ هذه اصلا مافيش فيها انلاجة", "tokens": [1863, 45367, 16490, 33546, 10874, 28259, 9154, 14739, 14407, 3615, 2423, 24877, 13672, 1829, 4724, 28820, 4724, 3794, 41193, 3660, 44945, 28543, 2288, 8717, 3615, 28480, 3224, 6055, 33753, 3714, 19913, 37977, 2423, 674, 11890, 292, 4295, 4032, 365, 572, 26354, 1975, 2407, 2698, 16121, 1975, 2407, 26354, 6225, 2304, 2407, 15042, 12399, 37495, 22653, 37893, 3714, 11242, 32887, 5016, 2698, 16121, 12399, 2698, 16121, 1975, 5016, 8315, 4724, 29399, 4117, 19528, 18871, 9154, 2423, 9984, 5296, 1863, 36178, 11296, 12399, 5296, 10721, 29538, 1975, 9381, 15040, 19446, 41185, 8592, 8978, 11296, 16472, 15040, 7435, 3660], "avg_logprob": -0.15020941213234185, "compression_ratio": 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leaves .. ال leaves تبعتك و كل ال internal nodes هي طالعة من نفس ال root فإذا يوجد بكل بساطة edge أو path بينهم وبين ال root node تمام", "tokens": [3555, 2304, 3615, 1863, 7578, 4724, 8592, 28820, 20328, 16572, 5016, 34051, 4724, 8592, 28820, 48812, 27842, 1829, 39896, 12898, 1314, 490, 264, 5593, 37495, 22653, 28242, 16095, 23032, 6027, 3615, 9957, 9154, 8717, 36178, 2423, 5593, 28242, 2423, 5510, 4386, 2423, 5510, 6055, 3555, 34268, 4117, 4032, 28242, 2423, 6920, 13891, 39896, 23032, 6027, 27884, 9154, 8717, 36178, 2423, 5593, 6156, 28814, 15730, 7251, 29245, 3215, 4724, 28820, 4724, 3794, 41193, 3660, 4691, 34051, 3100, 49374, 16095, 46599, 9957, 2423, 5593, 9984, 46811, 10943], "avg_logprob": -0.07826126332199851, "compression_ratio": 1.6161137440758293, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 375.87, "end": 376.49, "word": "بمعنى", "probability": 0.975}, {"start": 376.49, "end": 377.13, "word": " بشكل", "probability": 0.9794921875}, {"start": 377.13, "end": 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من", "probability": 0.994140625}, {"start": 1285.71, "end": 1286.03, "word": " الاتنين", "probability": 0.828857421875}, {"start": 1286.03, "end": 1286.25, "word": " هدول", "probability": 0.9832356770833334}, {"start": 1286.25, "end": 1286.47, "word": " بدي", "probability": 0.61627197265625}, {"start": 1286.47, "end": 1286.75, "word": " أعمله", "probability": 0.78662109375}, {"start": 1286.75, "end": 1287.11, "word": " elimination", "probability": 0.9443359375}], "temperature": 1.0}, {"id": 55, "seek": 131611, "start": 1288.19, "end": 1316.11, "text": "طيب بناء على الشرط هذا yes or no بحدد any part اللي بتعمله elimination فهذا كان مثال كتير واضح لاستخدام ال tree فبعنا ذلك ان انا بقدر امثل ال problem كلها على بعض بشكل tree بشكل ال tree هذه هنعرف منها حاجات كتيرة لقدام انت كنت مضطر تحسبها حساب سابقا احنا هنا هتبين معاك بشكل أسرع كتير بشكل كتير أسرع منها ال complexity", "tokens": [9566, 1829, 3555, 44945, 16606, 15844, 25124, 2288, 9566, 23758, 2086, 420, 572, 4724, 24401, 3215, 604, 644, 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هنشوفها عندنا لما ناخدها فعليا طيب الآن مين من هدولة الحالتين اللي قدامنا بقدر أسميها binary tree", "tokens": [10721, 5016, 8315, 11331, 1211, 8315, 11296, 8608, 16758, 4587, 995, 10874, 1829, 3555, 8315, 11296, 19446, 41361, 8592, 43242, 8315, 37893, 28820, 3660, 4724, 3794, 10874, 1829, 3555, 8315, 11296, 13412, 2407, 10632, 12174, 22488, 8315, 8717, 5172, 16095, 4117, 14407, 4724, 1829, 25957, 1211, 9122, 15730, 6225, 8592, 7649, 7251, 36520, 24976, 14407, 24401, 4032, 9154, 2423, 14407, 24401, 12602, 7435, 3615, 4032, 47341, 45367, 12174, 9381, 3660, 23032, 2407, 26895, 3660, 6225, 16572, 11242, 3660, 37893, 39896, 4117, 6225, 8592, 7649, 8717, 7435, 1829, 3555, 11296, 8032, 1863, 8592, 38688, 6024, 48506, 20449, 3714, 5172, 3224, 20498, 14739, 39896, 22291, 35186, 10874, 15042, 27884, 33962, 13546, 8978, 28239, 11296, 10632, 23032, 1211, 34268, 11933, 1829, 8592, 13672, 1829, 47525, 3224, 7251, 2655, 17082, 13546, 25894, 8315, 8978, 2423, 1399, 8032, 1863, 8592, 38688, 11296, 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طيب بس ال left to right هنا شوية بدها دقة هي مش لل leaves فقط هي كمان لل left subtree to right subtree هذا لما تكون binary لإن انت فعليا binary عندك left و right بس طيب لكن لما تكون أكتر من binary بمعنى ال array تبعتها in array ال in array لأ معناته أنا بتكلم هنا عن most left left right most right", "tokens": [41761, 281, 558, 23032, 1829, 3555, 4724, 3794, 2423, 1411, 281, 558, 34105, 13412, 2407, 10632, 47525, 11296, 11778, 28671, 39896, 37893, 24976, 5510, 6156, 47432, 39896, 9122, 2304, 7649, 24976, 1411, 7257, 701, 281, 558, 7257, 701, 23758, 5296, 15042, 6055, 30544, 17434, 5296, 28814, 1863, 16472, 2655, 6156, 3615, 20292, 995, 17434, 43242, 4117, 1411, 4032, 558, 4724, 3794, 23032, 1829, 3555, 44381, 5296, 15042, 6055, 30544, 5551, 4117, 2655, 2288, 9154, 17434, 4724, 2304, 3615, 1863, 7578, 2423, 10225, 6055, 3555, 34268, 11296, 294, 10225, 2423, 294, 10225, 5296, 10721, 20449, 8315, 47395, 41850, 39894, 4117, 19528, 34105, 18871, 881, 1411, 1411, 558, 881, 558], 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0.831298828125}, {"start": 1514.78, "end": 1515.04, "word": " left", "probability": 0.90673828125}, {"start": 1515.04, "end": 1515.96, "word": " و", "probability": 0.97314453125}, {"start": 1515.96, "end": 1516.24, "word": " right", "probability": 0.92236328125}, {"start": 1516.24, "end": 1516.66, "word": " بس", "probability": 0.87744140625}, {"start": 1516.66, "end": 1517.34, "word": " طيب", "probability": 0.9415690104166666}, {"start": 1517.34, "end": 1517.8, "word": " لكن", "probability": 0.86669921875}, {"start": 1517.8, "end": 1517.96, "word": " لما", "probability": 0.966064453125}, {"start": 1517.96, "end": 1518.24, "word": " تكون", "probability": 0.995361328125}, {"start": 1518.24, "end": 1518.7, "word": " أكتر", "probability": 0.9066162109375}, {"start": 1518.7, "end": 1518.94, "word": " من", "probability": 0.99462890625}, {"start": 1518.94, "end": 1519.64, "word": " binary", "probability": 0.92822265625}, {"start": 1519.64, "end": 1520.16, "word": " بمعنى", "probability": 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رسمينها هنا حالة بهذا الشكل", "tokens": [49628, 1829, 12984, 16472, 2423, 9307, 7435, 40294, 7251, 30544, 4032, 46958, 5016, 9154, 2423, 1411, 281, 558, 9154, 1411, 281, 558, 23758, 11933, 15730, 25961, 2655, 2423, 4314, 39894, 995, 34268, 16095, 1975, 4117, 2655, 2288, 9154, 1975, 2655, 1863, 9957, 1975, 2407, 2423, 10225, 39894, 995, 34268, 11296, 1975, 4117, 2655, 2288, 9154, 1975, 2655, 1863, 9957, 6156, 3224, 1829, 8717, 39648, 1411, 1633, 5296, 558, 1633, 10874, 25708, 8032, 2655, 1863, 8592, 38688, 34105, 37893, 9122, 9307, 3555, 11296, 20449, 8315, 47395, 1975, 5016, 8315, 3714, 11242, 9566, 2288, 9957, 8717, 4117, 2655, 3555, 11296, 6156, 37983, 2655, 11331, 1211, 2407, 12602, 38251, 9957, 11296, 34105, 11331, 6027, 3660, 39627, 15730, 25124, 28820], "avg_logprob": -0.16092414275193825, "compression_ratio": 1.8181818181818181, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 1531.03, "end": 1531.41, "word": "بحيث", "probability": 0.9153645833333334}, {"start": 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"probability": 0.9937744140625}, {"start": 2945.78, "end": 2946.0, "word": " يكون", "probability": 0.99169921875}, {"start": 2946.0, "end": 2946.24, "word": " هنا", "probability": 0.99560546875}, {"start": 2946.24, "end": 2946.76, "word": " ..", "probability": 0.82666015625}, {"start": 2946.76, "end": 2947.54, "word": " عشان", "probability": 0.7534993489583334}, {"start": 2947.54, "end": 2947.74, "word": " تكون", "probability": 0.98681640625}, {"start": 2947.74, "end": 2948.22, "word": " ordered", "probability": 0.60888671875}, {"start": 2948.22, "end": 2948.94, "word": " بتوعي", "probability": 0.3306477864583333}, {"start": 2948.94, "end": 2949.2, "word": " أخدنا", "probability": 0.8966064453125}, {"start": 2949.2, "end": 2949.38, "word": " احنا", "probability": 0.84619140625}, {"start": 2949.38, "end": 2949.46, "word": " ال", "probability": 0.86376953125}, {"start": 2949.46, "end": 2949.72, "word": " order", "probability": 0.74755859375}, {"start": 2949.72, "end": 2950.42, "word": " بناء", "probability": 0.724853515625}, {"start": 2950.42, "end": 2950.62, "word": " على", "probability": 0.744140625}, {"start": 2950.62, "end": 2951.18, "word": " ال", "probability": 0.91455078125}, {"start": 2951.18, "end": 2951.34, "word": " rule", "probability": 0.458740234375}, {"start": 2951.34, "end": 2951.56, "word": " بتاعة", "probability": 0.4739583333333333}, {"start": 2951.56, "end": 2951.68, "word": " ال", "probability": 0.98046875}, {"start": 2951.68, "end": 2951.94, "word": " order", "probability": 0.96142578125}, {"start": 2951.94, "end": 2952.18, "word": " طب", "probability": 0.71337890625}, {"start": 2952.18, "end": 2952.4, "word": " بعد", "probability": 0.9560546875}, {"start": 2952.4, "end": 2952.54, "word": " ما", "probability": 0.875}, {"start": 2952.54, "end": 2952.96, "word": " أنشئ", "probability": 0.7046712239583334}, {"start": 2952.96, "end": 2953.12, "word": " ال", "probability": 0.95361328125}, {"start": 2953.12, "end": 2953.46, "word": " tree", "probability": 0.8681640625}, {"start": 2953.46, "end": 2954.96, "word": " كويس", "probability": 0.9161783854166666}, {"start": 2954.96, "end": 2955.34, "word": " اعمل", "probability": 0.9005533854166666}, {"start": 2955.34, "end": 2955.68, "word": " scan", "probability": 0.896484375}, {"start": 2955.68, "end": 2956.1, "word": " عليها", "probability": 0.98583984375}, {"start": 2956.1, "end": 2956.36, "word": " حسب", "probability": 0.983154296875}, {"start": 2956.36, "end": 2956.48, "word": " ال", "probability": 0.986328125}, {"start": 2956.48, "end": 2956.7, "word": " order", "probability": 0.97119140625}, {"start": 2956.7, "end": 2957.12, "word": " تبعها", "probability": 0.8602294921875}, {"start": 2957.12, "end": 2957.6, "word": " طلعت", "probability": 0.9205729166666666}, {"start": 2957.6, "end": 2957.9, "word": " الحل", "probability": 0.985107421875}], "temperature": 1.0}, {"id": 122, "seek": 297012, "start": 2958.78, "end": 2970.12, "text": "طلعنا ال order اللي هو عملت sorting في الآخر اللي هي باستخدام tree model بعدين هنتكلم عن ال maximum comparison in sorting algorithm عشان تصنف algorithm معين", "tokens": [9566, 1211, 3615, 8315, 2423, 1668, 13672, 1829, 31439, 6225, 42213, 2655, 32411, 8978, 6024, 95, 34740, 13672, 1829, 39896, 4724, 995, 14851, 9778, 3215, 10943, 4230, 2316, 39182, 9957, 8032, 29399, 4117, 19528, 18871, 2423, 6674, 9660, 294, 32411, 9284, 6225, 8592, 7649, 6055, 9381, 1863, 5172, 9284, 20449, 9957], "avg_logprob": -0.19621394431361786, "compression_ratio": 1.389937106918239, "no_speech_prob": 1.4901161193847656e-06, "words": [{"start": 2958.78, "end": 2959.32, "word": "طلعنا", "probability": 0.78826904296875}, {"start": 2959.32, "end": 2959.86, "word": " ال", "probability": 0.7568359375}, {"start": 2959.86, "end": 2960.24, "word": " order", "probability": 0.8046875}, {"start": 2960.24, "end": 2960.48, "word": " اللي", "probability": 0.739501953125}, {"start": 2960.48, "end": 2960.6, "word": " هو", "probability": 0.927734375}, {"start": 2960.6, "end": 2960.9, "word": " عملت", "probability": 0.9383138020833334}, {"start": 2960.9, "end": 2961.26, "word": " sorting", "probability": 0.95556640625}, {"start": 2961.26, "end": 2961.42, "word": " في", "probability": 0.88916015625}, {"start": 2961.42, "end": 2961.8, "word": " الآخر", "probability": 0.9256184895833334}, {"start": 2961.8, "end": 2962.36, "word": " اللي", "probability": 0.56475830078125}, {"start": 2962.36, "end": 2962.44, "word": " هي", "probability": 0.2330322265625}, {"start": 2962.44, "end": 2963.0, "word": " باستخدام", "probability": 0.9603678385416666}, {"start": 2963.0, "end": 2963.48, "word": " tree", "probability": 0.27880859375}, {"start": 2963.48, "end": 2964.04, "word": " model", "probability": 0.94287109375}, {"start": 2964.04, "end": 2964.68, "word": " بعدين", "probability": 0.80615234375}, {"start": 2964.68, "end": 2965.2, "word": " هنتكلم", "probability": 0.9600830078125}, {"start": 2965.2, "end": 2965.38, "word": " عن", "probability": 0.96923828125}, {"start": 2965.38, "end": 2965.5, "word": " ال", "probability": 0.66455078125}, {"start": 2965.5, "end": 2965.78, "word": " maximum", "probability": 0.95361328125}, {"start": 2965.78, "end": 2966.42, "word": " comparison", "probability": 0.91748046875}, {"start": 2966.42, "end": 2967.22, "word": " in", "probability": 0.87548828125}, {"start": 2967.22, "end": 2967.62, "word": " sorting", "probability": 0.89501953125}, {"start": 2967.62, "end": 2968.16, "word": " algorithm", "probability": 0.880859375}, {"start": 2968.16, "end": 2968.7, "word": " عشان", "probability": 0.9620768229166666}, {"start": 2968.7, "end": 2969.24, "word": " تصنف", "probability": 0.9112548828125}, {"start": 2969.24, "end": 2969.62, "word": " algorithm", "probability": 0.82177734375}, {"start": 2969.62, "end": 2970.12, "word": " معين", "probability": 0.987548828125}], "temperature": 1.0}, {"id": 123, "seek": 299238, "start": 2970.86, "end": 2992.38, "text": "أو تمالق sorting أكم level محتاج، برضه لها علاقة بال complexity، لأنه أنا بتكلم عن minimum comparisons، comparisons معناته خطوات، أكم خطوة محتاج أعمل، time complexity، فإذا هذا الكلام هناخده المرة القادمة، اللي هو هناخده تطبيقات على ال trees، تطبيقات حيوية من الحجة اللي مرت عليكم سابقا، يعطيكم العافية و بنشوفكم المرة القادمة ان شاء الله تعالى", "tokens": [10721, 2407, 46811, 6027, 4587, 32411, 5551, 24793, 1496, 3714, 33753, 26108, 12399, 4724, 43042, 3224, 5296, 11296, 11203, 995, 28671, 20666, 14024, 12399, 5296, 33456, 3224, 41850, 39894, 4117, 19528, 18871, 7285, 33157, 12399, 33157, 20449, 8315, 47395, 16490, 9566, 2407, 9307, 12399, 5551, 24793, 16490, 9566, 2407, 3660, 3714, 33753, 26108, 5551, 25957, 1211, 12399, 565, 14024, 12399, 6156, 28814, 15730, 23758, 2423, 28820, 10943, 8032, 1863, 47283, 3215, 3224, 9673, 25720, 25062, 18513, 46007, 12399, 13672, 1829, 31439, 8032, 1863, 47283, 3215, 3224, 6055, 9566, 21292, 4587, 9307, 15844, 2423, 5852, 12399, 6055, 9566, 21292, 4587, 9307, 11331, 1829, 2407, 10632, 9154, 21542, 7435, 3660, 13672, 1829, 3714, 43500, 25894, 24793, 8608, 16758, 4587, 995, 12399, 37495, 9566, 1829, 24793, 18863, 31845, 10632, 4032, 44945, 8592, 38688, 24793, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37279, 6027, 7578], "avg_logprob": -0.1482204824893011, "compression_ratio": 1.8922558922558923, "no_speech_prob": 1.1861324310302734e-05, "words": [{"start": 2970.86, "end": 2971.12, "word": "أو", "probability": 0.73486328125}, {"start": 2971.12, "end": 2971.6, "word": " تمالق", "probability": 0.591796875}, {"start": 2971.6, "end": 2972.04, "word": " sorting", "probability": 0.470947265625}, {"start": 2972.04, "end": 2972.68, "word": " أكم", "probability": 0.877197265625}, {"start": 2972.68, "end": 2973.44, "word": " level", "probability": 0.96728515625}, {"start": 2973.44, "end": 2974.56, "word": " محتاج،", "probability": 0.81201171875}, {"start": 2974.56, "end": 2974.92, "word": " برضه", "probability": 0.9430338541666666}, {"start": 2974.92, "end": 2975.12, "word": " لها", "probability": 0.540496826171875}, {"start": 2975.12, "end": 2975.4, "word": " علاقة", "probability": 0.9768880208333334}, {"start": 2975.4, "end": 2975.5, "word": " بال", "probability": 0.9833984375}, {"start": 2975.5, "end": 2976.58, "word": " complexity،", "probability": 0.5718994140625}, {"start": 2976.58, "end": 2976.84, "word": " لأنه", "probability": 0.7127278645833334}, {"start": 2976.84, "end": 2976.92, "word": " أنا", "probability": 0.80859375}, {"start": 2976.92, "end": 2977.3, "word": " بتكلم", "probability": 0.9025065104166666}, {"start": 2977.3, "end": 2977.56, "word": " عن", "probability": 0.99169921875}, {"start": 2977.56, "end": 2978.06, "word": " minimum", "probability": 0.91796875}, {"start": 2978.06, "end": 2979.36, "word": " comparisons،", "probability": 0.6505126953125}, {"start": 2979.36, "end": 2979.8, "word": " comparisons", "probability": 0.95556640625}, {"start": 2979.8, "end": 2980.2, "word": " معناته", "probability": 0.9347330729166666}, {"start": 2980.2, "end": 2980.8, "word": " خطوات،", "probability": 0.92060546875}, {"start": 2980.8, "end": 2981.02, "word": " أكم", "probability": 0.95849609375}, {"start": 2981.02, "end": 2981.42, "word": " خطوة", "probability": 0.9842529296875}, {"start": 2981.42, "end": 2981.76, "word": " محتاج", "probability": 0.9921875}, {"start": 2981.76, "end": 2982.62, "word": " أعمل،", "probability": 0.9364013671875}, {"start": 2982.62, "end": 2982.82, "word": " time", "probability": 0.7998046875}, {"start": 2982.82, "end": 2983.8, "word": " complexity،", "probability": 0.874267578125}, {"start": 2983.8, "end": 2984.02, "word": " فإذا", "probability": 0.88134765625}, {"start": 2984.02, "end": 2984.22, "word": " هذا", "probability": 0.79931640625}, {"start": 2984.22, "end": 2984.54, "word": " الكلام", "probability": 0.9523111979166666}, {"start": 2984.54, "end": 2984.92, "word": " هناخده", "probability": 0.949609375}, {"start": 2984.92, "end": 2985.14, "word": " المرة", "probability": 0.98388671875}, {"start": 2985.14, "end": 2985.74, "word": " القادمة،", "probability": 0.9261474609375}, {"start": 2985.74, "end": 2985.84, "word": " اللي", "probability": 0.981201171875}, {"start": 2985.84, "end": 2985.98, "word": " هو", "probability": 0.98046875}, {"start": 2985.98, "end": 2986.38, "word": " هناخده", "probability": 0.90830078125}, {"start": 2986.38, "end": 2986.84, "word": " تطبيقات", "probability": 0.977734375}, {"start": 2986.84, "end": 2987.02, "word": " على", "probability": 0.9111328125}, {"start": 2987.02, "end": 2987.14, "word": " ال", "probability": 0.68212890625}, {"start": 2987.14, "end": 2987.82, "word": " trees،", "probability": 0.93603515625}, {"start": 2987.82, "end": 2988.24, "word": " تطبيقات", "probability": 0.9767578125}, {"start": 2988.24, "end": 2988.62, "word": " حيوية", "probability": 0.970458984375}, {"start": 2988.62, "end": 2988.74, "word": " من", "probability": 0.96337890625}, {"start": 2988.74, "end": 2988.96, "word": " الحجة", "probability": 0.7754720052083334}, {"start": 2988.96, "end": 2989.12, "word": " اللي", "probability": 0.931396484375}, {"start": 2989.12, "end": 2989.4, "word": " مرت", "probability": 0.831298828125}, {"start": 2989.4, "end": 2989.68, "word": " عليكم", "probability": 0.9658203125}, {"start": 2989.68, "end": 2990.32, "word": " سابقا،", "probability": 0.95576171875}, {"start": 2990.32, "end": 2990.64, "word": " يعطيكم", "probability": 0.8372802734375}, {"start": 2990.64, "end": 2990.9, "word": " العافية", "probability": 0.88232421875}, {"start": 2990.9, "end": 2990.98, "word": " و", "probability": 0.7373046875}, {"start": 2990.98, "end": 2991.28, "word": " بنشوفكم", "probability": 0.8646240234375}, {"start": 2991.28, "end": 2991.5, "word": " المرة", "probability": 0.985595703125}, {"start": 2991.5, "end": 2991.78, "word": " القادمة", "probability": 0.9918619791666666}, {"start": 2991.78, "end": 2991.9, "word": " ان", "probability": 0.62109375}, {"start": 2991.9, "end": 2992.02, "word": " شاء", "probability": 0.906982421875}, {"start": 2992.02, "end": 2992.06, "word": " الله", "probability": 0.9453125}, {"start": 2992.06, "end": 2992.38, "word": " تعالى", "probability": 0.9759114583333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2992.4484375, "duration_after_vad": 2869.038124999988}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0c904e789c4d3aba4b04519afc6255a33193af0f
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0.srt
@@ -0,0 +1,1406 @@
+
+1
+00:00:05,400 --> 00:00:07,780
+بسم الله الرحمن الرحيم، يا أعطيكم العفو يا شباب،
+
+2
+00:00:07,780 --> 00:00:13,300
+اليوم نكمل في مصطلحاتنا، في عندنا موضوع شوية جديد و
+
+3
+00:00:13,300 --> 00:00:18,520
+مكمل لجزء أخذناه سابقا و .. و اللي هو ال
+
+4
+00:00:18,520 --> 00:00:21,720
+mathematical induction أو الـ inductive، الـ
+
+5
+00:00:21,720 --> 00:00:25,310
+induction أو الـ inductive اللي هو الحث، هنشوف
+
+6
+00:00:25,310 --> 00:00:29,550
+إيش نظرية الحث هذه، وبعدين هنستخدمها كطريقة إثبات
+
+7
+00:00:29,550 --> 00:00:33,050
+هذه، بيستخدموها كواحدة من طرق الإثباتات اللي ممكن
+
+8
+00:00:33,050 --> 00:00:39,550
+استخدامها، تابعا يعني يتبع لموضوع الـ proof
+
+9
+00:00:39,550 --> 00:00:41,750
+strategies اللي أخذناها سابقا، اللي أخذنا فيها
+
+10
+00:00:41,750 --> 00:00:46,090
+مجموعة أنواع منها الـ direct و الـ indirect و الـ
+
+11
+00:00:46,090 --> 00:00:49,610
+contrapositive، إذا متذكرين الكلام هذا، اليوم
+
+12
+00:00:49,610 --> 00:00:53,680
+هنتعرف عليها بكمان طريقة جديدة ممكن استخدامها، واللي هي
+
+13
+00:00:53,680 --> 00:00:59,660
+الـ inductive method، نفهم فكرتها الأول، جزئية الحث
+
+14
+00:00:59,660 --> 00:01:02,940
+معنى كلمة الحث بتكون واضحة تماما في الـ domino
+
+15
+00:01:02,940 --> 00:01:07,380
+لعبة الـ domino هذه بتكون واضحة جدا، كيف واضحة جدا؟
+
+16
+00:01:07,380 --> 00:01:12,360
+بتكون كل قطعة من القطع تحث الثانية على action
+
+17
+00:01:12,360 --> 00:01:17,240
+معين، إذا هيصار لها الـ action، أنتم كلكم عارفين
+
+18
+00:01:17,240 --> 00:01:20,840
+أنه ممكن نصطفهم ورا بعض، كل اللي أنتم محتاجينه إنكم
+
+19
+00:01:20,840 --> 00:01:26,440
+تنزلوا أول حجر عشان تضمنوا بصورة أكيدة  أنه كلهم
+
+20
+00:01:26,440 --> 00:01:30,800
+هيقعوا، مش هيك؟ طيب، عشان نقول إن كلهم هيقعوا، لازم
+
+21
+00:01:30,800 --> 00:01:36,480
+نتحقق أول شغلة، إن الحجر الأول يقع، مش هيك؟ هل
+
+22
+00:01:36,480 --> 00:01:40,460
+هيقعوا كلهم إذا الأول ما وقعش؟ لأ، والشغلة
+
+23
+00:01:40,460 --> 00:01:47,710
+الثانية، إن كل حجر، بقدر أسميه إن، إذا وقع، فإن  N زائد
+
+24
+00:01:47,710 --> 00:01:51,410
+واحد لازم يقع، واضحة.
+
+25
+00:01:52,170 --> 00:01:56,070
+إذا كان فعلًا ضمنّا، لأنه مش ممكن تعملي خمس حجار
+
+26
+00:01:56,070 --> 00:02:00,030
+ورا بعض، وبعدين تعملي فضاء، والرقم ستة بعيد عنهم،
+
+27
+00:02:00,030 --> 00:02:03,730
+فمعنى ذلك أن الخامس والسادس بيحققوش هذه المعادلة،
+
+28
+00:02:03,730 --> 00:02:07,910
+فكرة أنه إذا وقع الخامس، لازم يقع السادس، مش هيك؟
+
+29
+00:02:07,910 --> 00:02:14,270
+إذا كان ضمنّا أن كل حجر ترتيبه N سيقع بالضرورة،
+
+30
+00:02:14,270 --> 00:02:18,570
+سيقع N زائد واحد، معنى ذلك أنه بنقدر نقول هذه
+
+31
+00:02:18,570 --> 00:02:23,870
+المتسلسلة، وكل واحد هيقع تبعا للي جابه، واضحة هذه
+
+32
+00:02:23,870 --> 00:02:27,670
+اللعبة بتاعتنا اللي كنا عارفينها، طيب، نترجمها رياضيا،
+
+33
+00:02:27,670 --> 00:02:32,810
+نترجمها كـ mathematical form، هقول إذا كان P of 0
+
+34
+00:02:32,810 --> 00:02:37,140
+is true، الشيء P of Zero اللي هو الحجر الأول اللي
+
+35
+00:02:37,140 --> 00:02:40,760
+وقعناه احنا بإيدينا، يعني أنتم مضمونين إن احنا وقعناه،
+
+36
+00:02:40,760 --> 00:02:45,480
+أو إن هو فعلا وقع، تمام، هذا is true، طيب وإذا كان
+
+37
+00:02:45,480 --> 00:02:50,480
+أنا ضامن أنه لكل N أكبر من صفر، أكبر من الـ initial
+
+38
+00:02:50,480 --> 00:02:55,760
+اللي احنا عملناه، من الـ initial فأكثر، إذا وقع الحجر
+
+39
+00:02:55,760 --> 00:02:59,820
+N، فمعنى ذلك يتبع وقوع الحجر N زائد واحد، فإذا كانت
+
+40
+00:02:59,820 --> 00:03:06,930
+حدثت N، يضمن حدوث N زائد واحد، إذا تحقق الشرطان هذول،
+
+41
+00:03:06,930 --> 00:03:10,690
+معناته بقدر أقول، إذا الـ conclusion تبعنا لكل قيم N
+
+42
+00:03:10,690 --> 00:03:18,470
+أكبر من صفر هتقع، فإذا P of N is true، إذا كان الـ
+
+43
+00:03:18,470 --> 00:03:23,850
+action، هذا اللي هي الـ P، هذا كـ predicate، هي إنه يقع
+
+44
+00:03:23,850 --> 00:03:28,870
+الحجر، هي كـ predicate logic، بدي أقول إن الـ P هذا هي
+
+45
+00:03:28,870 --> 00:03:33,850
+الـ function تبع وقوع الحجر، فإذا X وقع، X هذا بيـ
+
+46
+00:03:33,850 --> 00:03:38,510
+تشير ترتيبه N ولا N زائد واحد ولا N زائد اثنين ولا N
+
+47
+00:03:38,510 --> 00:03:43,330
+equal to zero، فهو الحالة الأولى، فهدا تنطبق تماما
+
+48
+00:03:43,330 --> 00:03:48,030
+على فكرة الـ domino، لكن كيف ممكن نستخدمها بالحقيقة؟
+
+49
+00:03:48,180 --> 00:03:52,780
+في إثباتاتنا، مبدئيا حاجة بسيطة جدا من لعبة
+
+50
+00:03:52,780 --> 00:03:59,340
+ابتكرو لها معادلة، المعادلة هذه واضحة جدا، يقع الحجر
+
+51
+00:03:59,340 --> 00:04:03,080
+الأول، هذا شرط ضروري، فإذا فعلا تحقق، إذا هو true،
+
+52
+00:04:03,080 --> 00:04:08,020
+وإذا أنا ضامن إنه كل حجر بيوقع اللي وراه، فإذا لكل
+
+53
+00:04:08,020 --> 00:04:12,940
+قيم N اللي أكبر من أو تساوي صفر، إذا كان P of N وقع،
+
+54
+00:04:12,940 --> 00:04:17,540
+فمعنى ذلك بضمن إن P of N زائد واحد برضه هيقع، هذه
+
+55
+00:04:17,540 --> 00:04:22,040
+الشرطان، معنى ذلك أنه بضمن إنه كلهم، حاجة بقدر أستنتج
+
+56
+00:04:22,040 --> 00:04:27,100
+أنه، معنى ذلك خلاص منتهية كلهم، حاجة متأكدين تماما
+
+57
+00:04:27,100 --> 00:04:30,620
+أنه كلهم هيقعوا، تمام، هذه بيسموها الـ first principle
+
+58
+00:04:30,620 --> 00:04:36,300
+of mathematical induction، هذا المبدأ الأول لـ الـ
+
+59
+00:04:36,300 --> 00:04:40,460
+inductive أو الـ induction فعليا، طيب كيف ممكن منها
+
+60
+00:04:40,460 --> 00:04:44,620
+أعمل عملية الـ inductive proof؟ بكل بساطة، إذا احنا
+
+61
+00:04:44,620 --> 00:04:50,300
+بدنا نثبت أنه لكل قيم N، P of N is true، مثل حاجة
+
+62
+00:04:50,300 --> 00:04:54,480
+جاية، الله يثبت لنا إنه لكل قيم N، P of N is true، زي
+
+63
+00:04:54,480 --> 00:04:58,190
+الأمثلة اللي هناخدها لاحقا، إن والله في قاعدة معينة،
+
+64
+00:04:58,190 --> 00:05:01,730
+وبدي أقول لك إن القاعدة هذه أثبت إنها فعلا صحيحة لكل
+
+65
+00:05:01,730 --> 00:05:06,690
+قيم N، مثلا أكبر من واحد أو N أكبر من صفر أو N
+
+66
+00:05:06,690 --> 00:05:11,070
+أكبر من خمسة، أثبت إنها دائما ستكون صحيحة لكل
+
+67
+00:05:11,070 --> 00:05:15,370
+الأرقام، طبعا مش منطقي إن أنت تروح تجرب كل الأرقام،
+
+68
+00:05:16,190 --> 00:05:21,610
+صحيح؟ مش منطق، فبدنا نعملها بـ inductive proof،
+
+69
+00:05:21,610 --> 00:05:24,830
+طيب، الـ inductive proof، الـ rules تبعونه أو الـ two
+
+70
+00:05:24,830 --> 00:05:28,570
+steps الأساسيات بتاعته زي تبعون الـ domino، بدي أضمن
+
+71
+00:05:28,570 --> 00:05:33,900
+إن P of 0 هو true، هو فعلا بيتحقق، عشان أضمن إنه الـ
+
+72
+00:05:33,900 --> 00:05:36,580
+trigger الأولى، الحجر الأول هو وقع فعلا، فإذا الـ
+
+73
+00:05:36,580 --> 00:05:41,440
+initial element هو فعلا صحيح، وبناء عليه الشغلة،
+
+74
+00:05:41,440 --> 00:05:45,940
+الثانية، بنثبتها، إنه لكل N، يقع N زائد واحد هيقع،
+
+75
+00:05:45,940 --> 00:05:52,830
+طبعا هنا بنقول At n, P of n is true، مش بالضرورة يقع
+
+76
+00:05:52,830 --> 00:05:56,870
+كـ domino، ولكن يحقق الـ function اللي بدنا نثبتها،
+
+77
+00:05:56,870 --> 00:06:02,170
+إذا كان فعلا P of n تحققت، هل فعلا يتبع ذلك
+
+78
+00:06:02,170 --> 00:06:06,470
+بالضرورة أن N زائد واحد هتتحقق، إذا أثبتت الجزء هذا،
+
+79
+00:06:06,470 --> 00:06:10,130
+وأنا مثبت أساسا أن P of zero is true، معناته خلاص
+
+80
+00:06:10,130 --> 00:06:14,450
+لكل قيم N أكيد هتتحقق، أكيد هتتحقق، وهنشوف الإثبات،
+
+81
+00:06:14,450 --> 00:06:19,020
+فإذا الـ step الأولى اللي هي بنسميها الـ base، base
+
+82
+00:06:19,020 --> 00:06:25,180
+step، الخطوة الأساسية، الخطوة الأولى، إنه نحقق P of
+
+83
+00:06:25,180 --> 00:06:29,940
+Zero، نشوف فيها الفرضية بتبدأ من وين، ممكن بكل بساطة
+
+84
+00:06:29,940 --> 00:06:35,530
+تجربها مباشرة، تجربها مباشرة at N equal to zero، طب
+
+85
+00:06:35,530 --> 00:06:40,110
+جرب N equal to zero لـ P of N مباشرة، هل هي صحيحة
+
+86
+00:06:40,110 --> 00:06:42,850
+ولا لأ، خلاص، وبعد ذلك بدنا نشوف كيف بدنا نعمل
+
+87
+00:06:42,850 --> 00:06:45,810
+الخطوة الثانية اللي هي inductive step، واللي من
+
+88
+00:06:45,810 --> 00:06:50,830
+خلالها بنثبت إنه لكل قيم N، إذا تحقق P of N يتبعها
+
+89
+00:06:50,830 --> 00:06:56,070
+P of N زائد واحد هتتحقق، تمام، فهذه هيك ببساطة
+
+90
+00:06:56,070 --> 00:06:59,650
+الإثباتين اللي بنقدر نعملهم، عشان نشتغلهم، نشتغلهم
+
+91
+00:06:59,650 --> 00:07:04,650
+بالـ direct proof عادي جدا، مش هنقعد نخبط الدنيا
+
+92
+00:07:04,650 --> 00:07:08,290
+فيهم، هنشتغل على direct proof، بمعنى إنه هنفرض إن P
+
+93
+00:07:08,290 --> 00:07:13,760
+of N is true، فعليا هنا إن P of N is true، فهقول اه،
+
+94
+00:07:13,760 --> 00:07:17,940
+أنا بدي أفترض إن هي صحيحة، طيب إذا كانت صحيحة، هل
+
+95
+00:07:17,940 --> 00:07:22,520
+يتبع ذلك إن P of N زائد واحد هتكون صحيحة ولا لأ، بس
+
+96
+00:07:22,520 --> 00:07:28,500
+هاي كل الفكرة، ففرضية الـ assumption لـ P of N،
+
+97
+00:07:28,500 --> 00:07:33,600
+نفترضها احنا إن هي is true، ثم بحاول أثبت من هذه الـ
+
+98
+00:07:33,600 --> 00:07:37,060
+assumption إن والله P of N زائد واحد برضه هتكون
+
+99
+00:07:37,060 --> 00:07:40,620
+true، إذا أثبتنا هذه الجزئية فاحنا بنكون أثبتنا الـ
+
+100
+00:07:40,620 --> 00:07:45,120
+inductive step، والـ base أو الـ basis step،
+
+101
+00:07:45,120 --> 00:07:48,940
+فاش فيها مشكلة؟ بتشوف الـ sequence تبعك من وين بده
+
+102
+00:07:48,940 --> 00:07:53,200
+يبدأ، في أول عنصر مباشرة، نطبق في المعادلة، وخلاص، و
+
+103
+00:07:53,200 --> 00:07:56,040
+ريح راسك فيه، ففي الحالة هذه إذا اتحققوا الشرطان،
+
+104
+00:07:56,040 --> 00:07:59,100
+فبنضمن إنه بالـ inductive inference أو بالاستدلال،
+
+105
+00:07:59,100 --> 00:08:05,690
+الحثي، الاستدلال الحثي، لأن أنا حققت الـ two steps، فبستدل
+
+106
+00:08:05,690 --> 00:08:11,250
+من تحقيقهم، إنه معنى ذلك لكل قيم N، P of N is true،
+
+107
+00:08:11,250 --> 00:08:19,790
+فإذا P of N تتحقق لكل قيم N الممكنة، طيب عشان نعمل
+
+108
+00:08:19,790 --> 00:08:23,630
+generalization للكلام هذا، مش بالضروري أن P of 0 هي
+
+109
+00:08:23,630 --> 00:08:29,090
+اللي أبدأ منها، ممكن أبدأ من P of C، ممكن أبدأ من صفر،
+
+110
+00:08:29,090 --> 00:08:31,570
+أبدأ من واحد، أبدأ من خمسة، أبدأ من عشرة، تكون هي الـ
+
+111
+00:08:31,570 --> 00:08:33,990
+initial بتاعتي، وخلاص، هي اللي بتبدأ فيها كـ basis
+
+112
+00:08:33,990 --> 00:08:37,790
+step، فمعنى ذلك in general بقدر أقول إن، أقول قيم N
+
+113
+00:08:37,790 --> 00:08:42,730
+اللي أكبر من C، مش بالضروري الـ zero، لسة بالضروري الـ
+
+114
+00:08:42,730 --> 00:08:47,130
+zero، من C، P of N is true، ففي الحالة هذه الطبيعي
+
+115
+00:08:47,130 --> 00:08:49,170
+اللي بيختلف، الشغل الوحيد اللي بيتغير إن الـ
+
+116
+00:08:49,170 --> 00:08:52,350
+inductive stuff مش هتتغير، أنت بتفرض P of N is true،
+
+117
+00:08:52,350 --> 00:08:55,970
+وبناء عليها بتحاول تثبت إن P of N زائد واحد برضه
+
+118
+00:08:55,970 --> 00:09:00,270
+هتتحقق كـ true، طيب، إيش اللي بيختلف؟ بيختلف فقط الـ
+
+119
+00:09:00,270 --> 00:09:04,990
+P of Zero، بتعود مكانها بـ P of C، مش أكتر من هيك، هي
+
+120
+00:09:04,990 --> 00:09:10,470
+الخطوة الوحيدة اللي بتعملها، نبدأ نشوف أمثلة على
+
+121
+00:09:10,470 --> 00:09:15,750
+هذا الموضوع، لما نقول بدنا نثبت إنه مجموع الـ first
+
+122
+00:09:15,750 --> 00:09:25,570
+N odd positive integers is N square، بمعنى واحد،
+
+123
+00:09:25,570 --> 00:09:34,030
+اثنين، عفوا، ثلاثة، الـ odd first N odd integers، فأنا
+
+124
+00:09:34,030 --> 00:09:41,050
+بمعنى الـ odd integers، خمسة، سبعة، تسعة، أحد عشر،
+
+125
+00:09:42,890 --> 00:09:48,110
+and so on، تكمل، الآن إيش بده مني؟ بده يقول لي إنه
+
+126
+00:09:48,110 --> 00:09:55,870
+مجموع الـ N first odd، هاي أول N عددهم، جداش الـ N؟
+
+127
+00:09:55,870 --> 00:09:59,770
+اثنين، فإذا المفروض إنه اثنين تربيع بيساوي مجموعهم،
+
+128
+00:09:59,770 --> 00:10:04,190
+طيب، ثلاثة، المفروض إن ثلاثة تربيع بتساوي مجموعهم،
+
+129
+00:10:05,510 --> 00:10:08,630
+عددهم أربعة، أربعة تربيع المفروض أنه مجموعهم،
+
+130
+00:10:08,630 --> 00:10:12,350
+عددهم خمسة، خمسة تربيع المفروض أنه مجموعهم، ستة،
+
+131
+00:10:12,350 --> 00:10:15,490
+ستة تربيع، مجموعهم، وصلت الـ الـ rule اللي بدنا
+
+132
+00:10:15,490 --> 00:10:19,150
+نثبتها، rule بسيطة وحلوة وكويسة، طيب تمام، هات
+
+133
+00:10:19,150 --> 00:10:23,310
+نحاول نثبتها، يعني كأنني بدي أقول إن لكل قيم N اللي
+
+134
+00:10:23,310 --> 00:10:26,310
+أكبر من واحد، لأن احنا بدنا نبدأ من أول location،
+
+135
+00:10:26,310 --> 00:10:30,990
+فأنا ببدأ أفرض أن هذا، لو N كـ location واحد، اثنين،
+
+136
+00:10:30,990 --> 00:10:38,720
+ثلاثة، أربعة، خمسة، ستة، سبعة، and so on، and so on، جيد،
+
+137
+00:10:38,720 --> 00:10:41,720
+فإذا لو أكبر من واحد، على اعتبار إن الـ odds ببدأ من
+
+138
+00:10:41,720 --> 00:10:46,000
+الواحد، لـ summation، هذا بنعمل هنا summation لمين؟
+
+139
+00:10:46,000 --> 00:10:49,740
+لما جمعنا الـ odds، والـ odds عرفناها سابقا لما
+
+140
+00:10:49,740 --> 00:10:52,940
+اتكلمنا عن الـ proof، اللي هي 2I ناقص واحد،
+
+141
+00:10:52,940 --> 00:10:58,020
+بدأناها 2I ناقص واحد، لو حطيت I هنا بواحد،
+
+142
+00:10:58,020 --> 00:11:02,280
+حيساوي واحد، معناته إن أنا بتكلم عن أول odds، لو
+
+143
+00:11:02,280 --> 00:11:07,920
+حطيت I باثنين، فمعنى ذلك بتكلم عن ثلاثة وهكذا،
+
+144
+00:11:07,920 --> 00:11:12,000
+فعليا هيها واحد تقابل الواحد، الاثنين المفروض
+
+145
+00:11:12,000 --> 00:11:16,380
+تقابل الثلاثة، الثلاثة تقابل الخمسة، وهذا فعليا
+
+146
+00:11:16,380 --> 00:11:20,820
+اللي بتحقق من الـ index اللي احنا حاطينه فعليا،
+
+147
+00:11:20,820 --> 00:11:26,240
+فإذا نفترض الستة، الستة المفروض إنه هنا لو I=6 يعني
+
+148
+00:11:26,240 --> 00:11:29,760
+أنا بتكلم عن العنصر رقم ستة، هل العنصر رقم ستة بيساوي
+
+149
+00:11:29,760 --> 00:11:33,530
+2×6 ناقص واحد، أحد عشر، فعلا هو أحد عشر، فعلا هو 11،
+
+150
+00:11:33,530 --> 00:11:37,970
+فإذا بنعمل الـ summation هدول ابتدا من الواحد لـ N،
+
+151
+00:11:37,970 --> 00:11:43,930
+حسب ما هو بيقول لي، first N odd integers، اللي
+
+152
+00:11:43,930 --> 00:11:49,450
+المفروض إنه يساوي الـ N تربيع، مش شايف، فإذا هذه الـ
+
+153
+00:11:49,450 --> 00:11:51,810
+relation اللي بدنا نحققها، حتى الآن، لعندي لعين بس،
+
+154
+00:11:51,810 --> 00:11:56,070
+إحنا قاعدين نشرح السؤال، لعندي لعين بس بدنا نتكلم
+
+155
+00:11:56,070 --> 00:12:00,090
+عن السؤال، فسرنا السؤال، أول شغلة الـ initial تبعنا
+
+156
+00:12:00,090 --> 00:12:04,750
+بده من وين؟ من الواحد، بده من الواحد فعليا، بده
+
+157
+00:12:04,750 --> 00:12:08,890
+هنا، فإذا مباشرة نطبق على الواحد، فبيكون هو الـ
+
+158
+00:12:08,890 --> 00:12:12,190
+basis step، خلصنا، هاي أول خطوة خلصت، هاي أول
+
+159
+00:12:12,190 --> 00:12:16,910
+خطوة خلصت على السريع، تمام، فعند الـ N بتساوي واحد هنا،
+
+160
+00:12:16,910 --> 00:12:21,790
+هتساوي 2 ناقص واحد، فهذه واحد، وهي من واحد لواحد،
+
+161
+00:12:21,790 --> 00:12:26,070
+هتكون، لأن N بس واحد، فهتساوي واحد، طيب واحد تربيع،
+
+162
+00:12:26,070 --> 00:12:30,210
+يساوي الواحد اللي هو المجموع، الواحد، فإذا الـ P at
+
+163
+00:12:30,210 --> 00:12:36,790
+one is true، خلاص خلصنا، هاي أول حاجة أثبتناها إن هي
+
+164
+00:12:36,790 --> 00:12:41,660
+صحيحة، طيب، الشغل الثاني، بعد هيك بدنا نثبت، بدنا
+
+165
+00:12:41,660 --> 00:12:46,660
+نقول إثبات عادي جدا، إنه بدي أفرض إنه لو هذه فعلا
+
+166
+00:12:46,660 --> 00:1
+
+223
+00:17:42,680 --> 00:17:46,940
+من لأ و أقل من هذه بتزيد عمقا كمان كل ما بتزيد
+
+224
+00:17:46,940 --> 00:17:50,520
+قيمة n هنا كان الفرق بينهم واحد هنا واحد هنا صار
+
+225
+00:17:50,520 --> 00:17:55,920
+اتنين هنا صار خمسة and so on بزيد كل ما بزيد طيب
+
+226
+00:17:55,920 --> 00:17:58,900
+احنا بدنا نثبت الآن أن العلاقة هذه صحيحة باستخدام
+
+227
+00:17:58,900 --> 00:18:03,580
+الـ inductive step inductive step كمان مرة محتاج
+
+228
+00:18:03,580 --> 00:18:09,250
+أول حاجة الـ basis و الـ basis مدام أكبر من صفر معناه
+
+229
+00:18:09,250 --> 00:18:12,370
+ذلك حتى الصفر بدوش إياها مش هنستخدم أبدا أكبر من
+
+230
+00:18:12,370 --> 00:18:15,570
+صفر معناه تبقى أبدا من من؟ من الواحد فهذه هتصبح
+
+231
+00:18:15,570 --> 00:18:22,070
+عندي الـ basis الـ basis step
+
+232
+00:18:25,610 --> 00:18:29,350
+مهتمة خلصنا الـ basis step مش محتاج كل الباقي مش
+
+233
+00:18:29,350 --> 00:18:32,770
+محتاج إلا واحدة بس هي أول answer الباقي عادي الآن
+
+234
+00:18:32,770 --> 00:18:37,710
+المفروض أنه بدنا نفترضه أن بدي أثبت إذا P of N is
+
+235
+00:18:37,710 --> 00:18:42,630
+true إذا P of N زائد واحد is true is true بكل
+
+236
+00:18:42,630 --> 00:18:47,030
+بساطة بدك تفرض أن هذه صحيحة اللي هي N أقل من 2 to
+
+237
+00:18:47,030 --> 00:18:51,090
+the power N فدي true فعليا على اعتبار أن هي الفرضية
+
+238
+00:18:51,090 --> 00:18:53,430
+و أنا ما أقولش direct على طول خلاص direct إيش
+
+239
+00:18:53,430 --> 00:18:57,890
+يعني direct يعني الـ premise is true و منه بتحاول
+
+240
+00:18:57,890 --> 00:19:00,790
+تجيبي الـ conclusion خلاص يعني هذه بتفرضها دائما
+
+241
+00:19:00,790 --> 00:19:05,390
+بتاعة الـ implication البادئ للـ implication is true
+
+242
+00:19:05,390 --> 00:19:09,330
+و بتجيب منه اللاحق أو الـ conclusion أنت بدك تستنتج
+
+243
+00:19:09,330 --> 00:19:13,630
+اللاحق خلاص تمام في الحالة هذه بتقدر ببساطة تقول
+
+244
+00:19:13,630 --> 00:19:19,980
+أن زائد بدنا نثبت منها أن in زائد واحد هتكون دائما
+
+245
+00:19:19,980 --> 00:19:24,260
+أقل من اتنين to the power in زائد واحد ببساطة جدا
+
+246
+00:19:24,260 --> 00:19:29,400
+هذه كل اللي هي محتاجها زائد واحد عشان تصبح نثبت
+
+247
+00:19:29,400 --> 00:19:34,520
+منها هذا الـ term هذا الـ term اللي هو in زائد واحد
+
+248
+00:19:34,520 --> 00:19:38,540
+أقل من اتنين to the power in زائد واحد طيب إيش
+
+249
+00:19:38,540 --> 00:19:42,860
+الفرق بين هذا و هذا أني أزيد واحد على الطرفين بنزيد
+
+250
+00:19:42,860 --> 00:19:47,240
+واحد على الطرفين عشان نوحد الطرف الشمال فالطرف
+
+251
+00:19:47,240 --> 00:19:52,340
+الشمال أنا بدي أثبت أن زائد واحد و أشوف جداش بتطلع
+
+252
+00:19:52,340 --> 00:19:56,020
+خلينا نشوف ف أنا عندي in لحالها فبتصير in زائد واحد
+
+253
+00:19:56,020 --> 00:20:00,040
+أقل من اتنين in برضه زائد واحد واحد على الطرفين و
+
+254
+00:20:00,040 --> 00:20:07,020
+مش أكثر واحد على الطرفين لا أكثر ولا أقل طيب تمام و
+
+255
+00:20:07,020 --> 00:20:10,400
+هنا هنا في الآخر و نقول أقل من اتنين to the power
+
+256
+00:20:10,400 --> 00:20:18,080
+n طيب واحد هذه واحد هذه دائما هتكون أقل من اتنين
+
+257
+00:20:18,080 --> 00:20:24,600
+to the power جداش to the power n لأنه
+
+258
+00:20:24,600 --> 00:20:29,680
+أنت بادئ أكبر من صفر صح و كل ما زادت in الـ حد
+
+259
+00:20:29,680 --> 00:20:34,420
+بيزيد أكثر كمان بيزيد أكثر و أكثر كمان بس أنت ضامن
+
+260
+00:20:34,420 --> 00:20:38,700
+أنه دائما الواحد هيكون أقل من اتنين to the power
+
+261
+00:20:38,700 --> 00:20:46,680
+واحد هذا على اعتبار أول قيمة ممكن لـ in أول قيمة
+
+262
+00:20:46,680 --> 00:20:51,760
+ممكن لـ in واحد صحيح فأنت ضامن اتنين to the power
+
+263
+00:20:51,760 --> 00:20:54,600
+واحد هيكون أكبر من الواحد والله إذا كان أنت عند in
+
+264
+00:20:54,600 --> 00:20:57,380
+بالساوية عشرة فأنت ضامن أنه أكبر و مرتاح كمان في
+
+265
+00:20:57,380 --> 00:21:01,400
+الأكبر مرتاح جدا كمان في الأكبر، معناه ذلك أن الـ
+
+266
+00:21:01,400 --> 00:21:05,780
+term هذا الواحد لأ أنت هتضيف له قيمة أكبر، معناه ذلك
+
+267
+00:21:05,780 --> 00:21:13,120
+بتقدر تقول زائد اتنين to the power n أكبر من زادت،
+
+268
+00:21:13,120 --> 00:21:17,910
+بس ضالة صحيحة، correlation صحيحة correlation صحيحة
+
+269
+00:21:17,910 --> 00:21:22,370
+جدا طيب n زائد واحد ضالة زي ما هي و كل ما بقى n
+
+270
+00:21:22,370 --> 00:21:26,990
+زائد واحد بتزيد قيمته كل ما زادت n عن الـ term اللي
+
+271
+00:21:26,990 --> 00:21:31,350
+على الشمال وهذا بكل بساطة الآن جمعه لما تجمعه إيش
+
+272
+00:21:31,350 --> 00:21:37,610
+بيصير اتنين to the power n زائد واحد على اعتبار
+
+273
+00:21:37,610 --> 00:21:42,330
+كأنها هدف فعليا اتنين في اتنين to the power n
+
+274
+00:21:45,520 --> 00:21:49,280
+مجموعة مرتين يعني كأنه اتنين في العدد .. اتنين في
+
+275
+00:21:49,280 --> 00:21:53,220
+العدد .. و اتنين في العدد هي power واحد فصارت زي
+
+276
+00:21:53,220 --> 00:22:01,560
+.. هاي المطلوب .. هاي المطلوب .. هذا المطلوب ..
+
+277
+00:22:01,560 --> 00:22:06,170
+تمام الآن الـ second principle هذه الـ first
+
+278
+00:22:06,170 --> 00:22:10,070
+principle كل المطلوب أن عشان تثبت أن P of N زائد
+
+279
+00:22:10,070 --> 00:22:16,770
+واحد is true بدك تفترض أن P of N is true طيب الـ
+
+280
+00:22:16,770 --> 00:22:20,870
+second principle لأ شوية أعمق إيش يعني أعمق يعني
+
+281
+00:22:20,870 --> 00:22:29,150
+عشان نثبت أنه فعلا لكل قيم n اللي أكبر من أو تساوي
+
+282
+00:22:29,150 --> 00:22:34,490
+صفر كويس هي true بدنا نقول الـ basis مش مشكلة فيه
+
+283
+00:22:34,490 --> 00:22:38,970
+زي الـ first principle بس في الـ inductive لأ هيقول
+
+284
+00:22:38,970 --> 00:22:48,910
+لأن كل قيم n أكبر أو تساوي صفر كل القيم اللي من n
+
+285
+00:22:48,910 --> 00:22:55,390
+فأقل إذا كانت true إذن P of N زائد واحد is true
+
+286
+00:22:55,390 --> 00:23:00,350
+فإذا P of N زائد واحد is true هي مش مبنية فقط على
+
+287
+00:23:00,350 --> 00:23:05,890
+P of N لحالها يعني لا يكفي .. لا يكفي إنها تكون P
+
+288
+00:23:05,890 --> 00:23:10,650
+of N لحالها is true عشان أثبت منها أنه n زائد واحد
+
+289
+00:23:10,650 --> 00:23:17,730
+is true لأ محتاج أنه n و كل ما قبلها أكون مفترض أن
+
+290
+00:23:17,730 --> 00:23:22,330
+هم كلهم true عشان نثبت من خلالها أن P of N زائد
+
+291
+00:23:22,330 --> 00:23:24,950
+واحد is true طبعا هذه بأحيان بيسموها الـ strong
+
+292
+00:23:24,950 --> 00:23:29,930
+principle أو الـ strong proof الـ proof الأقوى لأنه
+
+293
+00:23:29,930 --> 00:23:33,750
+إذا تحقق أصلا إذا تحقق فهنشوف الأمثلة اللي ممكن
+
+294
+00:23:33,750 --> 00:23:37,230
+تحقيقها شيء هتقولي صعبة و كيف تعملها لأ هي سهلة
+
+295
+00:23:37,230 --> 00:23:40,470
+جدا و هنشوفها في الأمثلة يمكن أكثر بس هنا بنقول k
+
+296
+00:23:40,470 --> 00:23:46,980
+فإذا لكل القيم من صفر to N of k لازم يكونوا is
+
+297
+00:23:46,980 --> 00:23:52,520
+true عشان أستنتج منه أنه بقى P of N زائد واحد is
+
+298
+00:23:52,520 --> 00:24:00,500
+true تمام هذا بده مثال عشان يوضحها بشكل أكبر
+
+299
+00:24:08,400 --> 00:24:13,480
+هياجي المثال طيب بدنا نفرض أو بدنا نثبت أن لكل
+
+300
+00:24:13,480 --> 00:24:18,720
+قيم n اللي أكبر من واحد اللي أكبر من واحد يمكن
+
+301
+00:24:18,720 --> 00:24:23,660
+كتابتها بشكل primes مضروبة في بعض أو product of
+
+302
+00:24:23,660 --> 00:24:26,920
+primes الحاجة اللي إحنا خدناها جاب الحستين جاب
+
+303
+00:24:26,920 --> 00:24:30,960
+المحاضرتين كويس وقلنا أن كل عنصر إذا كان سواء
+
+304
+00:24:30,960 --> 00:24:36,030
+prime أو composite number هو عبارة عن مجموعة of
+
+305
+00:24:36,030 --> 00:24:40,050
+primes في بعض إذا هو prime فهو هو نفسه بحد ذاته
+
+306
+00:24:40,050 --> 00:24:44,690
+prime أو إذا كان composite فهو عبارة عن two primes
+
+307
+00:24:44,690 --> 00:24:47,990
+أو أكثر مضروبين في بعض مجموعة of primes مضروبة في
+
+308
+00:24:47,990 --> 00:24:53,150
+بعض أثبت ذلك، هاي المطلوب طيب عشان نثبت ذلك إيش
+
+309
+00:24:53,150 --> 00:25:00,070
+محتاج؟ محتاج أقول أنه بدي أبدأ من n أكبر من واحد
+
+310
+00:25:00,070 --> 00:25:04,090
+فإذا بدي أبدأ من مين؟ من الاثنين الـ basis step
+
+311
+00:25:04,090 --> 00:25:08,190
+بتاعتي هنا هتكون هي الاثنين اللي هي أكبر من الـ ..
+
+312
+00:25:08,190 --> 00:25:12,190
+البداية الـ initial تبعنا فعند الاثنين هيكون عندي
+
+313
+00:25:12,190 --> 00:25:16,490
+مجموعة الـ primes واحد هو prime واحد فقط اللي هو
+
+314
+00:25:16,490 --> 00:25:19,730
+مين؟ الاثنين بس ليش؟ لأنه الاثنين هي بحد ذاتها
+
+315
+00:25:19,730 --> 00:25:24,750
+prime هي بحد ذاتها prime و الـ prime الوحيد الـ
+
+316
+00:25:24,750 --> 00:25:30,270
+even صحيح؟ الـ prime الوحيد الـ even في الدنيا كويس
+
+317
+00:25:31,860 --> 00:25:36,100
+طب تخيل أنه في أي prime ثاني even غيره، مستحيل
+
+318
+00:25:36,100 --> 00:25:39,480
+لأنه بيقبل القسمة على اثنين، هيكون بيقبل القسمة على
+
+319
+00:25:39,480 --> 00:25:42,900
+اثنين، صحيح؟ فإذا هو الـ answer الوحيد اللي بقدر
+
+320
+00:25:42,900 --> 00:25:48,690
+أسميه even prime تمام فهي الـ basis صحيحة مش فيها
+
+321
+00:25:48,690 --> 00:25:53,390
+مشكلة الـ basis اللي هي أول عنصر فعليا حقق المعادلة
+
+322
+00:25:53,390 --> 00:25:57,870
+صح تمام في الـ inductive step بدي أقول أن لو بدي
+
+323
+00:25:57,870 --> 00:26:02,050
+أفرض الفرضية بتاعتي اللي هي is true أن لكل قيم n
+
+324
+00:26:02,050 --> 00:26:07,450
+أكبر من أو تساوي اثنين هيها اللي هي هنبدأ فيها
+
+325
+00:26:07,450 --> 00:26:15,450
+فرضيتنا كل القيم من اثنين to N هي تحقق P of k يعني
+
+326
+00:26:15,450 --> 00:26:21,330
+بمعنى أن هي كلها مجموعة primes كل الأعداد ابتداء
+
+327
+00:26:21,330 --> 00:26:27,510
+من الاثنين لعند N هي كلها عبارة عن مجموعة product
+
+328
+00:26:27,510 --> 00:26:33,350
+لـ primes كل عنصر أي .. أي رقم أختاره هيك عشوائيا من
+
+329
+00:26:33,350 --> 00:26:38,130
+اثنين لـ N أي رقم لازم هيكون عبارة عن ضرب مجموعة
+
+330
+00:26:38,130 --> 00:26:41,830
+primes في بعض هذه هي الفرضية اللي بنقول assume
+
+331
+00:26:41,830 --> 00:26:44,210
+that فإذا is it true؟
+
+332
+00:26:47,650 --> 00:26:51,250
+تمام طبعا هتقولي كيف أثبت أنه is true الإثبات الآن
+
+333
+00:26:51,250 --> 00:26:54,270
+في الـ inductive هيثبت لك أن الكلام صحيح هذا الوقت
+
+334
+00:26:54,270 --> 00:26:58,950
+هنفرض n زائد واحد n زائد واحد لأن عشان أثبت أن هي
+
+335
+00:26:58,950 --> 00:27:03,570
+فعلا برضه هتحقق نفس الكلام عندها احتمالين إما أن
+
+336
+00:27:03,570 --> 00:27:08,150
+هي نفسها prime هي نفسها prime مش هيك مش في احتمال
+
+337
+00:27:08,150 --> 00:27:13,490
+أن تكون هي n زائد واحد أصلا prime فإذا أريحنا هي
+
+338
+00:27:13,490 --> 00:27:16,730
+prime لحالها معناه ذلك في الحالة هذه بقدر أقول أن
+
+339
+00:27:16,730 --> 00:27:20,150
+مجموع الـ primes هي واحد prime واحد هي قيمة n زائد
+
+340
+00:27:20,150 --> 00:27:24,070
+واحد هذا is a prime طيب إذا مش prime و هذه الفرضية
+
+341
+00:27:24,070 --> 00:27:26,810
+الثانية معناه ذلك أن الـ n زائد واحد هو عبارة عن
+
+342
+00:27:26,810 --> 00:27:31,230
+عدد مش prime معناته بينفع يكون ضرب رقمين معروفين
+
+343
+00:27:31,230 --> 00:27:35,430
+صحيح هي a و b بغض النظر a و b هم primes ولا لأ
+
+344
+00:27:36,480 --> 00:27:41,960
+تمام؟ لكن a و b هدول أكيد هيكونوا أقل من n زائد
+
+345
+00:27:41,960 --> 00:27:50,060
+واحد صح؟ أكيد و حتماً و أقل من n كمان أكيد هيكونوا
+
+346
+00:27:50,060 --> 00:27:54,700
+أقل من n طيب مدام أقل من n معناته ينطبق عليهم
+
+347
+00:27:54,700 --> 00:28:01,000
+الفرضية لأن هم معناته بين الاثنين و الـ n معناه ذلك
+
+348
+00:28:01,000 --> 00:28:06,410
+أن هم نفسهم ممكن يكونوا n زائد واحد افترضهم
+
+349
+00:28:06,410 --> 00:28:11,830
+نفسهم ممكن يكونوا n زائد واحد فإذا a أكيد هتكون من
+
+350
+00:28:11,830 --> 00:28:17,190
+الواحد للـ n و الـ b نفس الكلام عشان فعلا ضربهم
+
+351
+00:28:17,190 --> 00:28:21,350
+يعطيك n زائد واحد فلازم يكونوا عددهم أقل ففي
+
+352
+00:28:21,350 --> 00:28:24,850
+الحالة دي a أنت ضامن أن هي عبارة عن مجموعة primes
+
+353
+00:28:24,850 --> 00:28:30,850
+جد ما يطلع يطلع عددهم t مثلا و p هي عبارة عن مجموعة
+
+354
+00:28:30,850 --> 00:28:34,730
+primes u ففي الحالة هذه بيقول أن n زائد واحد هي
+
+355
+00:28:34,730 --> 00:28:42,050
+عبارة عن مضروب مجموعة primes عددهم t زائد u اللي
+
+356
+00:28:42,050 --> 00:28:45,790
+هي الـ primes تبعت a مضروبة في الـ primes تبعت p
+
+357
+00:28:45,790 --> 00:28:51,350
+لأنه a في p فـ n زائد واحد هي مجموعة الـ primes كلها
+
+358
+00:28:51,350 --> 00:28:57,160
+مضروبة في بعض جداش عدد الـ primes t زائد u هتكون t
+
+359
+00:28:57,160 --> 00:29:00,660
+زائد u طب أنت هتقول ليه طب ليه أثبت أنه هذا فعلا
+
+360
+00:29:00,660 --> 00:29:05,220
+كلهم true هقول لك بكل بساطة أتعامل مع الموضوع أن n
+
+361
+00:29:05,220 --> 00:29:09,820
+زائد واحد اللي أنت بدك تثبت recursion متذكرين أو
+
+362
+00:29:09,820 --> 00:29:13,060
+أخذتوا فكرة الـ recursion تمام فإذا بدي أتعامل مع a
+
+363
+00:29:13,060 --> 00:29:19,920
+كأنه هي n زائد واحد لـ problem جديدة و b هي n زائد واحد لـ
+
+364
+00:29:19,920 --> 00:29:23,940
+problem جديدة أثبت بدا أثبته نفس الكلام معناته إذا
+
+365
+00:29:23,940 --> 00:29:30,720
+الـ a ممكن أقول عليها c في d صح؟
+
+366
+00:29:30,720 --> 00:29:37,560
+لما نصِل لمين؟ للـ basis أو الـ prime هي نفسها الـ
+
+367
+00:29:37,560 --> 00:29:45,820
+prime هي نفسها الـ prime أو نصِل للـ اثنين صحيح؟
+
+368
+00:29:45,820 --> 00:29:52,780
+فمنطقيا هي بتفتح لنا الموضوع اللي بعد ذلك و اللي هو
+
+369
+00:29:52,780 --> 00:29:58,540
+الـ recursion فالفكرة جاية متسلسلة عادي و مش صعبة و لا
+
+370
+00:29:58,540 --> 00:30:02,080
+هي غلط، ليش؟ لأنه بكل بساطة أنت هتقولي طب أنت
+
+371
+00:30:02,080 --> 00:30:06,280
+أثبتت أو خليني أفترض .. فرضت أن هم كلهم true، ليش؟
+
+372
+00:30:06,280 --> 00:30:09,900
+ليش؟ لأنه بكل بساطة بدأت أتعامل معاها أنه إيه؟ هي
+
+373
+00:30:09,900 --> 00:30:13,380
+كأنها n زائد واحد problem جديدة و آخذها لحالها أحلها
+
+374
+00:30:13,990 --> 00:30:17,650
+و بـ نفس الكلام آخذها لحالها أحلها طيب a هذه يمكن
+
+375
+00:30:17,650 --> 00:30:21,290
+تطلع لـ c و d c لحالها بدي أحلها كأنها n زائد واحد
+
+376
+00:30:21,290 --> 00:30:24,430
+و d بدي أحلها لحالها كأنها n زائد واحد هتبقى
+
+377
+00:30:24,430 --> 00:30:28,430
+تتحل معاها تتفكك معاها recursion صحيح؟
+
+378
+00:30:28,430 --> 00:30:34,270
+recursive steps لما تصل للـ prime أو للـ basis
+
+379
+00:30:36,020 --> 00:30:39,980
+هتضلك تتفكك تتحل معاك لما تصل لواحد من هذين
+
+380
+00:30:39,980 --> 00:30:46,460
+يا هو prime بحد ذاته أو تصل للـ basis صحيح هتأخذ
+
+381
+00:30:46,460 --> 00:30:50,080
+معاك وقت هتأخذ معاك وقت صحيح لكن مش الوقت اللي
+
+382
+00:30:50,080 --> 00:30:58,680
+أنت متخيله ليش؟ لأنه الـ code هنا هو مش linear صح الـ
+
+383
+00:30:58,680 --> 00:31:01,870
+code هنا مش linear هنا logarithmic فالـ complexity
+
+384
+00:31:01,870 --> 00:31:05,190
+هنا مش زي ما أنت متخيلها هتكون كبيرة مش هتكون
+
+385
+00:31:05,190 --> 00:31:12,190
+كبيرة واضح تهيأ لي المثال أه؟ بدكم ترجعوا له برضه و
+
+386
+00:31:12,190 --> 00:31:14,770
+تركزوا فيه لأن recursion هذا فكرة الـ recursion if
+
+387
+00:31:14,770 --> 00:31:17,510
+أنتم أخذتم recursion if أنتم أخذتم recursion
+
+388
+00:31:17,510 --> 00:31:21,790
+بسيط جدا فكرة حتى أنك تعمله إثبات أو تعمله code
+
+389
+00:31:21,790 --> 00:31:27,530
+طيب نفس الكلام و ننهي في كمان مثال
+
+390
+00:31:30,660 --> 00:31:36,500
+المثال هذا مطلوب إثبات أن لكل amount of postage
+
+391
+00:31:36,500 --> 00:31:44,220
+لكل قيمة جواب أو اللي هو بنسميه جواب بوستا اللي هو
+
+392
+00:31:44,220 --> 00:31:49,680
+جواب بريدي كويس أو كتاب بريدي لكل كتاب بريدي of
+
+393
+00:31:49,
+
+445
+00:36:25,170 --> 00:36:31,910
+هتكون اتنين فرق تلاتة، الأربعة عشر.. الأربعة.. تلاتة
+
+446
+00:36:31,910 --> 00:36:35,570
+خمسة.. لأ هو مظبوط، الفرق أربعة، تلاتة، خمسة، خمسة عشر
+
+447
+00:36:35,570 --> 00:36:41,150
+من الخمسة عشر، جدعش، الخمسة عشر كانت تلاتة في خمسة زائد
+
+448
+00:36:41,150 --> 00:36:45,170
+أربعة زائد
+
+449
+00:36:45,170 --> 00:36:49,870
+أربعة، فمعنى ذلك، طول ما عندك الأربعات فيهم وافرة
+
+450
+00:36:49,870 --> 00:36:55,710
+أنت مش جالجان حسب الـ.. الـ inductive step اللي
+
+451
+00:36:55,710 --> 00:36:58,390
+احنا اشتغلنا عليها حسب الـ inductive step اللي
+
+452
+00:36:58,390 --> 00:36:59,730
+اشتغلنا عليها
+
+453
+00:37:03,340 --> 00:37:09,420
+طبعا هي هيك تقريبا، الموضوع الخفيف السريع بيجي في
+
+454
+00:37:09,420 --> 00:37:14,480
+الامتحانات، في جزئية الإثبات، لكن الأهم من ذلك أن هو
+
+455
+00:37:14,480 --> 00:37:17,940
+المقدمة عشان نروح للـ recursion عشان نروح للـ
+
+456
+00:37:17,940 --> 00:37:21,400
+recursion و recursive algorithm لأنه هناخد مجموعة
+
+457
+00:37:21,400 --> 00:37:26,770
+algorithms المرة القادمة، كيف نعيد حلها بالـ.. بالـ
+
+458
+00:37:26,770 --> 00:37:30,650
+recursive code .. recursive code، فيعطيكم العافية
+
+459
+00:37:30,650 --> 00:37:31,710
+نهينا هي محاضرتنا
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0_postprocess.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..602e0c2372da63647b46c0347bc24b8bcd746596
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0_postprocess.srt
@@ -0,0 +1,1836 @@
+1
+00:00:05,400 --> 00:00:07,780
+بسم الله الرحمن الرحيم، يا عطيكوا العفو يا شباب،
+
+2
+00:00:07,780 --> 00:00:13,300
+اليوم نكمل في مصاقنا، في عندنا موضوع شوية جديد و
+
+3
+00:00:13,300 --> 00:00:18,520
+مكمل لجزء أخدناه سابقا و .. و اللي هو ال
+
+4
+00:00:18,520 --> 00:00:21,720
+mathematical induction أو ال inductive، ال
+
+5
+00:00:21,720 --> 00:00:25,310
+induction أو ال inductive اللي هو الحثالحث هنشوف
+
+6
+00:00:25,310 --> 00:00:29,550
+إيش نظرية الحث هذه و بعدين هنستخدمها كطريقة إثبات
+
+7
+00:00:29,550 --> 00:00:33,050
+هذه بيستخدموها كواحدة من طرق الإثباتات اللي ممكن
+
+8
+00:00:33,050 --> 00:00:39,550
+استخدامها تابعا يعني يتبع لموضوع ال proof
+
+9
+00:00:39,550 --> 00:00:41,750
+strategies اللي أخدناها سابقا اللي أخدنا فيها
+
+10
+00:00:41,750 --> 00:00:46,090
+مجموعة أنواع منها ال direct و ال indirect و ال
+
+11
+00:00:46,090 --> 00:00:49,610
+contrapositive إذا متذكرين الكلام هذا اليوم
+
+12
+00:00:49,610 --> 00:00:53,680
+هنتبحها بكمان طريقة جديدةممكن استخدامها و اللي هي
+
+13
+00:00:53,680 --> 00:00:59,660
+ال inductive method فنفهم فكرتها الأول جزئية الحث
+
+14
+00:00:59,660 --> 00:01:02,940
+معناه كلمة الحث بتكون واضحة تماما في ال domino
+
+15
+00:01:02,940 --> 00:01:07,380
+لعبة ال domino هذه بتكون واضحة جدا كيف واضحة جدا
+
+16
+00:01:07,380 --> 00:01:12,360
+بتكون كل جطعة من الجطعة تحث التانية على action
+
+17
+00:01:12,360 --> 00:01:17,240
+معين إذا هيصار لها ال action فانتوا كلكوا عارفين
+
+18
+00:01:17,240 --> 00:01:20,840
+انه ممكن نصفطهم مرا بعض كل انتوا محتاجينه انكوا
+
+19
+00:01:20,840 --> 00:01:26,440
+تنزله اول حجر عشان تضمن بصورة و باخرة انه كلهم
+
+20
+00:01:26,440 --> 00:01:30,800
+هيجعوا مش هيك؟ طيب عشان نقول انه كلهم هيجعوا لازم
+
+21
+00:01:30,800 --> 00:01:36,480
+احققوا اول شغلة انه الحجر الاول وجع مش هيك؟ هل
+
+22
+00:01:36,480 --> 00:01:40,460
+هيجعوا كلهم اذا الاول لسه موجعش؟ لأ والشغلة
+
+23
+00:01:40,460 --> 00:01:47,710
+التانية انه كل حجر بقدر اسميهإن إذا وقع فان زائد
+
+24
+00:01:47,710 --> 00:01:51,410
+واحد لازم هيقع واضحة
+
+25
+00:01:52,170 --> 00:01:56,070
+إذا كان فعلًا ضمنّا لأنه مش ممكن تعملي خمس حجار
+
+26
+00:01:56,070 --> 00:02:00,030
+ورا بعض و بعدين تعملي فضة و الرقم ست بعيد عنهم
+
+27
+00:02:00,030 --> 00:02:03,730
+فمعنى ذلك أن الخامس والسادس بيحققوش هذه المعادلة
+
+28
+00:02:03,730 --> 00:02:07,910
+فكرة أنه إذا وقع الخامس لازم يقع السادس مش هيك؟
+
+29
+00:02:07,910 --> 00:02:14,270
+إذا كان ضمنّا أنه كل حجر ترتيبه N سيقع بالضرورة
+
+30
+00:02:14,270 --> 00:02:18,570
+سيقع N زائد واحد معنى ذلك أنه بنقدر نقولهذه
+
+31
+00:02:18,570 --> 00:02:23,870
+متسلسلة و كل واحد هيقع تبعا للي جابله واضحة هذه
+
+32
+00:02:23,870 --> 00:02:27,670
+اللعبة بتاعي اللي كنا عارفينها طيب انترجمها رياضية
+
+33
+00:02:27,670 --> 00:02:32,810
+انترجمها ك mathematical form هقول إذا كان P of 0
+
+34
+00:02:32,810 --> 00:02:37,140
+is trueالشي P of Zero اللي هو الحجر الأول اللي
+
+35
+00:02:37,140 --> 00:02:40,760
+وجعناه احنا بيدنا يعني انت مضمنين ان احنا وجعناه
+
+36
+00:02:40,760 --> 00:02:45,480
+او ان هو فعلا وقع تمام هذا is true طيب وإذا كان
+
+37
+00:02:45,480 --> 00:02:50,480
+انا ضامن انه لكل N أكبر من صفر أكبر من ال initial
+
+38
+00:02:50,480 --> 00:02:55,760
+اللي احنا عملناه من ال initial فأكثر إذا وقع الحجر
+
+39
+00:02:55,760 --> 00:02:59,820
+N فمعنى ذلك يتبع وقوع الحجر N زايد واحد فإذا كانت
+
+40
+00:02:59,820 --> 00:03:06,930
+حدثتن يضمن حدوث n زائد واحد إذا تحقق الشرطين هذول
+
+41
+00:03:06,930 --> 00:03:10,690
+معناته بقدر أقول إذا ال conclusion تبعنا لكل قيم n
+
+42
+00:03:10,690 --> 00:03:18,470
+أكبر من صفر هتقع فإذا P of N is true إذا كانالـ
+
+43
+00:03:18,470 --> 00:03:23,850
+action هدى اللى هى ال P هدى ك predicate هي انه يقع
+
+44
+00:03:23,850 --> 00:03:28,870
+الحجر هي ك predicate logic بدي اقول ان ال P هدى هى
+
+45
+00:03:28,870 --> 00:03:33,850
+ال function تبع وقوع الحجر فإذا X وقع X هدى بتش
+
+46
+00:03:33,850 --> 00:03:38,510
+ترتيبه N ولا N زائد واحد ولا N زائد اتنين ولا N
+
+47
+00:03:38,510 --> 00:03:43,330
+equal to zero فهو الحالة الأولى فهدى تنطبق تماما
+
+48
+00:03:43,330 --> 00:03:48,030
+على فكرة ال domino لكن كيف ممكن نستخدمها الحقيقة؟
+
+49
+00:03:48,180 --> 00:03:52,780
+في إثباتاتنا مبدأيا حاجة بسيطة جدا من لعبة
+
+50
+00:03:52,780 --> 00:03:59,340
+ابتكرولها معادلة المعادلة هذه واضحة جدا يقع الحجر
+
+51
+00:03:59,340 --> 00:04:03,080
+الأول هذا شرط ضروري فإذا فعلا تحقق إذا هو true
+
+52
+00:04:03,080 --> 00:04:08,020
+وإذا أنا ضامن إنه كل حجر بيوقق اللي ورا فإذا لكل
+
+53
+00:04:08,020 --> 00:04:12,940
+قيم N اللي أكبر من أو تساوي صفر إذا كان P of N وقع
+
+54
+00:04:12,940 --> 00:04:17,540
+فمعنى ذلك بضمن لإن P of N زائد واحد برضه هيقعهذه
+
+55
+00:04:17,540 --> 00:04:22,040
+شرطين معناه ذلك أنه بضمن أنه كلهم حاجة بقدر أستنتج
+
+56
+00:04:22,040 --> 00:04:27,100
+أنه معناه ذلك خلاص منتهية كلهم حاجة متأكدين تماما
+
+57
+00:04:27,100 --> 00:04:30,620
+أنه كلهم حاجة تمام هذه بيسموها ال first principle
+
+58
+00:04:30,620 --> 00:04:36,300
+of mathematical induction هذا المبدأ الأول ل ال
+
+59
+00:04:36,300 --> 00:04:40,460
+inductive أو ال induction فعليا طيب كيف ممكن منها
+
+60
+00:04:40,460 --> 00:04:44,620
+أعمل عملية ال inductive proofبكل بساطة إذا أحنا
+
+61
+00:04:44,620 --> 00:04:50,300
+بدنا نثبت أنه لكل قيم N P of N is true مثل حاجة
+
+62
+00:04:50,300 --> 00:04:54,480
+جالك الله يثبت لنا أنه لكل قيم N P of N is true زي
+
+63
+00:04:54,480 --> 00:04:58,190
+الأمثل اللي هناخدها لاحقاإن والله في قاعدة معينة
+
+64
+00:04:58,190 --> 00:05:01,730
+وبدي أقولك إن القاعدة هذه أثبت إنها فعلا صحيحة لكل
+
+65
+00:05:01,730 --> 00:05:06,690
+قيم إن مثلا أكبر من واحد أو إن أكبر من صفر أو إن
+
+66
+00:05:06,690 --> 00:05:11,070
+أكبر من خمسة أثبت إنها دائما ستكون صحيحة لكل
+
+67
+00:05:11,070 --> 00:05:15,370
+الأرقام طبعا مش منطقي إن أنت تروح تجرب كل الأرقام
+
+68
+00:05:16,190 --> 00:05:21,610
+صحيح؟ مش منطق فبدنا نعملها بيصير inductive proof
+
+69
+00:05:21,610 --> 00:05:24,830
+طيب ال inductive proof ال rules تبعونه أو ال two
+
+70
+00:05:24,830 --> 00:05:28,570
+steps الأساسيات بتاعه زي تبعون ال domino بدي أضمن
+
+71
+00:05:28,570 --> 00:05:33,900
+أن P of 0 هو trueهو فعلا بتحقق عشان أضمن أنه ال
+
+72
+00:05:33,900 --> 00:05:36,580
+trigger الأولى الحجر الأول هو وجع فعلا فإذا ال
+
+73
+00:05:36,580 --> 00:05:41,440
+initial element هو فعلا صحيح وبناء عليه الشغلة
+
+74
+00:05:41,440 --> 00:05:45,940
+التانية بتثبتها أنه لكل N يقع N زائد واحد هيقع
+
+75
+00:05:45,940 --> 00:05:52,830
+طبعا هنا بنقولAt n, P of n is true مش بالضرورة يقع
+
+76
+00:05:52,830 --> 00:05:56,870
+ك domino ولكن يحقق ال function اللي بدنا نثبتها
+
+77
+00:05:56,870 --> 00:06:02,170
+إذا كان فعلا P of n تحققت هل فعلا يتبع ذلك
+
+78
+00:06:02,170 --> 00:06:06,470
+بالضرورة أن n زائد واحد هتتحقق إذا أثبتت الجزء هذا
+
+79
+00:06:06,470 --> 00:06:10,130
+وأنا مثبت أساسا أن P of zero is true معناته خلاص
+
+80
+00:06:10,130 --> 00:06:14,450
+لكل قيم n أكيد هتتحقق أكيد هتتحقق و هنشوف الأثبات
+
+81
+00:06:14,450 --> 00:06:19,020
+فإذا ال step الأولى اللي هي بنسميها ال baseBases
+
+82
+00:06:19,020 --> 00:06:25,180
+step الخطوة الأساسية الخطوة الأولى انه نحقق P of
+
+83
+00:06:25,180 --> 00:06:29,940
+Zero نشوف فيها الفرضية بتبدأ من وين ممكن بكل بساطة
+
+84
+00:06:29,940 --> 00:06:35,530
+تجربها مباشرةتجربها مباشرة at n equal to zero طب
+
+85
+00:06:35,530 --> 00:06:40,110
+جرب n equal to zero ل P of n مباشرة هل هي صحيحة
+
+86
+00:06:40,110 --> 00:06:42,850
+ولا لأ خلاص و بعد ذلك بدنا نشوف كيف بدنا نعمل
+
+87
+00:06:42,850 --> 00:06:45,810
+الخطوة التانية اللي هي inductive step و اللي من
+
+88
+00:06:45,810 --> 00:06:50,830
+خلالها بنثبت أنه لكل قيم n إذا تحقق P of n يتبعها
+
+89
+00:06:50,830 --> 00:06:56,070
+P of n زائد واحد هتتحققتمام فهذه هيك ببساطة
+
+90
+00:06:56,070 --> 00:06:59,650
+الإثباتين اللي بنقدر نعملهم عشان نشتغلهم نشتغلهم
+
+91
+00:06:59,650 --> 00:07:04,650
+بال direct proof عادي جدا مش هنقعد نخبط الدنيا
+
+92
+00:07:04,650 --> 00:07:08,290
+فيهم هنشتغل على direct proof بمعنى انه هنفرض ان P
+
+93
+00:07:08,290 --> 00:07:13,760
+of N is true فعليا هناإن P of N is true فهقول اه
+
+94
+00:07:13,760 --> 00:07:17,940
+انا بده افترض ان هي صحيحة طيب إذا كانت صحيحة هل
+
+95
+00:07:17,940 --> 00:07:22,520
+يتبع ذلك ان P of N زائد واحد هتكون صحيحة ولا لأ بس
+
+96
+00:07:22,520 --> 00:07:28,500
+هاي كل الفكرة ففرضية ال assumption ل P of N
+
+97
+00:07:28,500 --> 00:07:33,600
+نفترضها احنا ان هي is true ثم بحاول اثبت من هذه ال
+
+98
+00:07:33,600 --> 00:07:37,060
+assumption ان والله P of N زائد واحد برضه هتكون
+
+99
+00:07:37,060 --> 00:07:40,620
+trueإذا أثبتنا هذه الجزئية فاحنا بنكون أثبتنا ال
+
+100
+00:07:40,620 --> 00:07:45,120
+inductive step و ال base أو ال بقى ال basis step
+
+101
+00:07:45,120 --> 00:07:48,940
+فاش فيها مشكلة بتشوف ال sequence تبعك من وين بده
+
+102
+00:07:48,940 --> 00:07:53,200
+طبق في أول عنصر مباشرة نطبق في المعادلة و خلاص و
+
+103
+00:07:53,200 --> 00:07:56,040
+ريح راسك فيه ففي الحالة هذه إذا اتحققوا الشرطين
+
+104
+00:07:56,040 --> 00:07:59,100
+فبنضمن أنه بال inductive inference أو بالاستدلال
+
+105
+00:07:59,100 --> 00:08:05,690
+الحثي الاستدلال الحثي لإن أنا حققت2 steps فبستدل
+
+106
+00:08:05,690 --> 00:08:11,250
+من تحقيقهم أنه معنى ذلك لكل قيم N P of N is true
+
+107
+00:08:11,250 --> 00:08:19,790
+فإذا P of N تتحقق لكل قيم N الممكنة طيب عشان نعمل
+
+108
+00:08:19,790 --> 00:08:23,630
+generalization للكلام هذا مش بالضروري أن P of 0 هي
+
+109
+00:08:23,630 --> 00:08:29,090
+اللي أبدأ منها ممكن أبدأ من P of Cممكن أبدأ من صفر
+
+110
+00:08:29,090 --> 00:08:31,570
+أبدأ من واحد أبدأ من خمس أبدأ من عشرة تكون هي ال
+
+111
+00:08:31,570 --> 00:08:33,990
+initial تبعتي و خلاص هي اللي بتبدأ فيها ك basis
+
+112
+00:08:33,990 --> 00:08:37,790
+step فمعنى ذلك in general بقدر أقول أن أقول قيم N
+
+113
+00:08:37,790 --> 00:08:42,730
+اللي أكبر من C مش بالضروري ال zeroلسة بالضروري الـ
+
+114
+00:08:42,730 --> 00:08:47,130
+zero من C P of N is true ففي الحالة هذه الطبيعي
+
+115
+00:08:47,130 --> 00:08:49,170
+اللي بيختلف الشغل الوحيد اللي بتختلف ان ال
+
+116
+00:08:49,170 --> 00:08:52,350
+inductive stuff مش هتتغير انت بتفرض P of N is true
+
+117
+00:08:52,350 --> 00:08:55,970
+وبناء عليها بتحاول تثبت ان P of N زائد واحد برضه
+
+118
+00:08:55,970 --> 00:09:00,270
+هتتبحى ك true طيب، ايش اللي بيختلف؟ بيختلف فقط ال
+
+119
+00:09:00,270 --> 00:09:04,990
+P of Zero بتعود مكانه ب P of C مش اكتر من هيك هي
+
+120
+00:09:04,990 --> 00:09:10,470
+الخطوة الوحيدة اللي بتعملها نبدأ نشوف أمثلة على
+
+121
+00:09:10,470 --> 00:09:15,750
+هذا الموضوعلما نقول بدنا نثبت انه مجموع ال first
+
+122
+00:09:15,750 --> 00:09:25,570
+in odd positive integers is in square بمعنى واحد
+
+123
+00:09:25,570 --> 00:09:34,030
+اتنين عفوا تلاتة ال odd first in odd integers فانا
+
+124
+00:09:34,030 --> 00:09:41,050
+معنى بال odd integers خمسة سبعة تسعة احداشر
+
+125
+00:09:42,890 --> 00:09:48,110
+and so on تكمل الان ايش بده منيه بده يقولي انه
+
+126
+00:09:48,110 --> 00:09:55,870
+مجموع ال n first odd هاي أول n عددهم جديش ال n
+
+127
+00:09:55,870 --> 00:09:59,770
+اتنين فإذا المفروض انه اتنين تربية بيسووا مجموحهم
+
+128
+00:09:59,770 --> 00:10:04,190
+طيب تلاتة المفروض ان تلاتة تربية بتسووا مجموحهم
+
+129
+00:10:05,510 --> 00:10:08,630
+عددهم أربعة .. أربعة تربيع المفروض أنه مجموحهم
+
+130
+00:10:08,630 --> 00:10:12,350
+عددهم خمسة .. خمسة تربيع المفروض أنه مجموحهم ستة
+
+131
+00:10:12,350 --> 00:10:15,490
+.. ستة تربيع مجموحهم وصلت ال .. ال role اللي بدنا
+
+132
+00:10:15,490 --> 00:10:19,150
+نثبتها role بسيطة و حلوة و كويسة طيب تمام هات
+
+133
+00:10:19,150 --> 00:10:23,310
+نحاول نثبتها يعني كأنني بدي أقول أن لكل قيم N اللي
+
+134
+00:10:23,310 --> 00:10:26,310
+أكبر من واحد لأن احنا بدنا نبدأ من أول location
+
+135
+00:10:26,310 --> 00:10:30,990
+فانا بدأ أفترض أن هذا لو N ك location واحد اتنين
+
+136
+00:10:30,990 --> 00:10:38,720
+تلاتة أربعة خمسة ستة سبعة and so onand so on جيد
+
+137
+00:10:38,720 --> 00:10:41,720
+فإذا لو أكبر من واحد على اعتبار ان ال odds ببدأ من
+
+138
+00:10:41,720 --> 00:10:46,000
+الواحد ل summation هيدا بنعمل هنا summation لمين
+
+139
+00:10:46,000 --> 00:10:49,740
+لما جمعتوا ال odds وال odds عرفناها سابقا لما
+
+140
+00:10:49,740 --> 00:10:52,940
+اتكلمنا عن ال proof اللي هي اتنين I ناقص واحد
+
+141
+00:10:52,940 --> 00:10:58,020
+بدأناها اتنين I ناقص واحد لو حطيت I هنا بواحد
+
+142
+00:10:58,020 --> 00:11:02,280
+حيسروا واحد معناته ان انا بتكلم عن اول odds لو
+
+143
+00:11:02,280 --> 00:11:07,920
+حطيت I باتنينفمعنى ذلك بتتكلم عن تلاتة و هكذا
+
+144
+00:11:07,920 --> 00:11:12,000
+فعلياً هيها واحد تقابل الواحد الاتنين المفروض
+
+145
+00:11:12,000 --> 00:11:16,380
+تقابل التلاتة التلاتة تقابل الخمسة وهذا فعلياً
+
+146
+00:11:16,380 --> 00:11:20,820
+اللي بتحقق من ال index اللي احنا حاطينه فعلياً
+
+147
+00:11:20,820 --> 00:11:26,240
+فإذا نفترض الستة الستة المفروض انه هنا لو I6 يعني
+
+148
+00:11:26,240 --> 00:11:29,760
+أنا بتكلم عن العنصر رقم ستة هل العنصر رقم ستة بسوء
+
+149
+00:11:29,760 --> 00:11:33,530
+اتناش ناقص واحد احداش فعلاً هو واحداشفعلا هو 11
+
+150
+00:11:33,530 --> 00:11:37,970
+فإذا بنعمله ال summation هدولة ابتدا من الواحد ل N
+
+151
+00:11:37,970 --> 00:11:43,930
+حسب ما هو بيقوللي first N odd integers اللي
+
+152
+00:11:43,930 --> 00:11:49,450
+المفروض أنه يسوى ال Inter بي ..مش شاك، فإذا هذه ال
+
+153
+00:11:49,450 --> 00:11:51,810
+relation اللي بدنا نحققها حتى الآن، لعندي لعين بس
+
+154
+00:11:51,810 --> 00:11:56,070
+إحنا قاعدين نشرح السؤال، لعندي لعين بس بدنا نتكلم
+
+155
+00:11:56,070 --> 00:12:00,090
+عن السؤال، فسرنا السؤال أول شغلة ال initial تبعنا
+
+156
+00:12:00,090 --> 00:12:04,750
+بده من وين؟ من الواحد، بده من الواحد فعليا، بده
+
+157
+00:12:04,750 --> 00:12:08,890
+هنا، فإذا مباشرة نطبق على الواحد فبيكون هو ال
+
+158
+00:12:08,890 --> 00:12:12,190
+business step، خلصنا، هاي أول خطوة خلصت، هاي أول
+
+159
+00:12:12,190 --> 00:12:16,910
+خطوة خلصت على السريعتمام فعند ال N بتساوي واحد هنا
+
+160
+00:12:16,910 --> 00:12:21,790
+هتساوي اتنين ناقص واحد فهذه واحد وهي من واحد لواحد
+
+161
+00:12:21,790 --> 00:12:26,070
+هتكون لأن N بس واحد فهتساوي واحد طيب واحد تربيع
+
+162
+00:12:26,070 --> 00:12:30,210
+يساوي الواحد اللي هو المجموع الواحد فإذا ال B at
+
+163
+00:12:30,210 --> 00:12:36,790
+one is true خلاص خلصنا هاي أول حاجة أثبتناها أن هي
+
+164
+00:12:36,790 --> 00:12:41,660
+صحيحة طيبالشغل التاني لبعد هيك بدنا نثبت .. بدنا
+
+165
+00:12:41,660 --> 00:12:46,660
+نقول إثبات عادي جدا أنه بدي أفرض أنه لو هذه فعلا
+
+166
+00:12:46,660 --> 00:12:54,310
+ال trueهتلي عند n زائد واحد هل بتكون true ولا لأ
+
+167
+00:12:54,310 --> 00:12:59,770
+اعمل الشيء الضروري عشان تصبح اتحولها من n ل n زائد
+
+168
+00:12:59,770 --> 00:13:03,130
+واحد كل اللي بدك تعمله تضيف العنصر n زائد واحد بس
+
+169
+00:13:03,130 --> 00:13:08,710
+و تشوف هل المجموعة فعلا هيظهر هنا ك n زائد واحد
+
+170
+00:13:08,710 --> 00:13:14,850
+تربيعه ولا لأ هاي كل الفكرة انك انت هنا هتضطر تضيف
+
+171
+00:13:14,850 --> 00:13:20,640
+P of n زائد واحد على ال total هنالأن هو العنصر
+
+172
+00:13:20,640 --> 00:13:24,580
+الإضاءة اللي قضيفش دي ازيادة وانت مفترض تماما
+
+173
+00:13:24,580 --> 00:13:29,480
+ومقتنع وعمل assumption واضحة تماما ان هذا true طيب
+
+174
+00:13:29,480 --> 00:13:34,800
+لو ضفنا لها العنصر في location B N زائد واحد
+
+175
+00:13:34,800 --> 00:13:39,320
+ضفناها إضافة لإلها هل فعلا المجموع هيطلع N زائد
+
+176
+00:13:39,320 --> 00:13:43,600
+واحد تربيع ولا لأ؟ هذه الفكرةو قلنا بال direct
+
+177
+00:13:43,600 --> 00:13:47,880
+يعني مش محتاجين لأ تقعد تفكر في القصص اللي أخدناها
+
+178
+00:13:47,880 --> 00:13:51,200
+في chapter اتنين في chapter اتنين كانت ولا لأ ولا
+
+179
+00:13:51,200 --> 00:13:54,900
+تلاتة المهم في ال proof strategies مش محتاج تقعد
+
+180
+00:13:54,900 --> 00:13:57,920
+تفكر فيها هي direct على طول و خلاص تفرض الأولى
+
+181
+00:13:57,920 --> 00:14:03,140
+صحيحة و بتجيب منها التانية فكأولى صحيحة هنا
+
+182
+00:14:12,730 --> 00:14:16,830
+بداك تعمل ال summation من اش من واحد to in زائد
+
+183
+00:14:16,830 --> 00:14:20,510
+واحد to in زائد واحد بس انت عارف انه اللي صح اللي
+
+184
+00:14:20,510 --> 00:14:24,290
+انت متأكد منه ان هو صحيح هي هذا ال term من واحد to
+
+185
+00:14:24,290 --> 00:14:29,230
+in بس لانك انت فرضه اصلا ان هو true فمعنى ذلك ان
+
+186
+00:14:29,230 --> 00:14:36,710
+in زائد واحد هي فعليا ل in و باضافة من ال
+
+187
+00:14:36,710 --> 00:14:38,410
+summation من اش من وين ل وين
+
+188
+00:14:42,830 --> 00:14:47,010
+من حاجات الامتحان اللي إجتنا في الامتحان و معدودين
+
+189
+00:14:47,010 --> 00:14:52,150
+اللي حلوها هيك الكل راح اشتغل على الحسبة و كله
+
+190
+00:14:52,150 --> 00:14:56,290
+عملته غلط يعني احنا ماطلبناش على حسبة احنا كنا
+
+191
+00:14:56,290 --> 00:15:02,570
+بدنا manipulation كنا بدنا نعمل هيك تمام فإذا كل
+
+192
+00:15:02,570 --> 00:15:07,520
+اللي بقى اللي بده يضاف عند مين termSummation
+
+193
+00:15:07,520 --> 00:15:11,300
+للعنصر الأخير طب هي العنصر الأخير اللي هو عند مين
+
+194
+00:15:11,300 --> 00:15:17,040
+I بتساوي N زائد واحد خلاص عوض تنين في N زائد واحد
+
+195
+00:15:17,040 --> 00:15:22,180
+ناقص واحد هاي ال term اللي ضايل هذا تمام تمام طب
+
+196
+00:15:22,180 --> 00:15:26,940
+ممتاز جدا احنا من الأساس قلنا ان هذا is true مدام
+
+197
+00:15:26,940 --> 00:15:31,300
+is true يعني جداش قيمتها انتر بيع خلاص هي انتر بيع
+
+198
+00:15:31,300 --> 00:15:37,310
+وهنااتنين و هنا اتنين ناقص واحد بتصير زائد واحد
+
+199
+00:15:37,310 --> 00:15:43,830
+حللها تطلع ان زائد واحد كله تربيع فإذا فعليا
+
+200
+00:15:43,830 --> 00:15:48,590
+summation من واحد لان زائد واحد هتساوي ان زائد
+
+201
+00:15:48,590 --> 00:15:53,930
+واحد كله تربيعخلصنا هي أثبتنا ال basis اللي هي عند
+
+202
+00:15:53,930 --> 00:15:59,430
+n بتساوي واحد و أثبتنا إنه إذا كانت P of n is true
+
+203
+00:15:59,430 --> 00:16:04,270
+فعليا لإنها أثبتت فرضناها فعليا إنه is true فمدام
+
+204
+00:16:04,270 --> 00:16:08,230
+is true عوضنا مكانها ب N تربيع معناه ذلك إنه يلحق
+
+205
+00:16:08,230 --> 00:16:15,190
+ذلك إن P of n زائد واحد برضه is true هذا بيدل ليه
+
+206
+00:16:15,190 --> 00:16:20,890
+معناته لكل قيم N بغض النظر كده قيمةستة سبعة عشر
+
+207
+00:16:20,890 --> 00:16:24,810
+أحداش عشرين مية متين خمسمية هتكون دائما ال rule is
+
+208
+00:16:24,810 --> 00:16:30,230
+true دائما is true في الحالة هذه ليش لأن احنا
+
+209
+00:16:30,230 --> 00:16:33,910
+محددناش ان هنا جدش معنى ذلك انه ممكن تكون خمسمية
+
+210
+00:16:33,910 --> 00:16:36,730
+معنى ذلك ان خمسمية زي واحد صحيحة برضه ممكن تكون
+
+211
+00:16:36,730 --> 00:16:40,350
+عشرة معنى ذلك ان أحداش هتكون صحيحة و هكذا ما هي
+
+212
+00:16:40,350 --> 00:16:44,730
+سلسلة من بعض سلسلة من بعض محددناش قيمة ان بدون
+
+213
+00:16:44,730 --> 00:16:51,560
+تحديد لقيمة لقيمة انOkay طيب كمان مثال المثال
+
+214
+00:16:51,560 --> 00:16:58,080
+التاني لكل قيم n بدنا نقول إنه إذا كانت n أكبر من
+
+215
+00:16:58,080 --> 00:17:02,840
+صفر معنى ذلك إن n دائما أقل من 2 to the power n
+
+216
+00:17:02,840 --> 00:17:06,280
+طبعا هذه حاجة بدهية احنا عارفينها شئ بدهية أكيد
+
+217
+00:17:06,280 --> 00:17:10,260
+كلنا عارفينه خلصنا
+
+218
+00:17:10,260 --> 00:17:16,890
+المثال هذا المثال التانيانه لكل قيم N أكبر من صفر
+
+219
+00:17:16,890 --> 00:17:22,730
+دائما N هتكون اقل من اتنين to the power N طيب
+
+220
+00:17:22,730 --> 00:17:30,050
+فابتداء من الصفر اقل من واحد عند الواحد واحد اقل
+
+221
+00:17:30,050 --> 00:17:35,090
+من اتنين عند الاتنين اتنين اقل من اربعة عند
+
+222
+00:17:35,090 --> 00:17:42,680
+التلاتة and so on وكمل طبعا انت هتلاقي انه فعلاأقل
+
+223
+00:17:42,680 --> 00:17:46,940
+من لأ و أقل من هذه بتزيد عمقا كمان كل ما بتزود
+
+224
+00:17:46,940 --> 00:17:50,520
+قيمة n هنا كان الفرق بينهم واحد هنا واحد هنا صار
+
+225
+00:17:50,520 --> 00:17:55,920
+اتنين هنا صار خمسة and so on بزيد كل ما بزيد طيب
+
+226
+00:17:55,920 --> 00:17:58,900
+احنا بدنا نثبت الان ان العلاقة هذه صحيحة باستخدام
+
+227
+00:17:58,900 --> 00:18:03,580
+ال inductive step inductive step كمان مرة محتاج
+
+228
+00:18:03,580 --> 00:18:09,250
+اول حاجة ال basesو ال basis مدام أكبر من صفر معناه
+
+229
+00:18:09,250 --> 00:18:12,370
+ذلك حتى الصفر بدوش إياها مش هنستخدم أبدا أكبر من
+
+230
+00:18:12,370 --> 00:18:15,570
+صفر معناه تبقى أبدا من من؟ من الواحد فهذه هتصبح
+
+231
+00:18:15,570 --> 00:18:22,070
+عندى ال ال basis ال basis step
+
+232
+00:18:25,610 --> 00:18:29,350
+مهتمة خلصنا ال business step مش محتاج كل الباقي مش
+
+233
+00:18:29,350 --> 00:18:32,770
+محتاج الا واحدة بس هي اول answer الباقي عادى الان
+
+234
+00:18:32,770 --> 00:18:37,710
+المفروض انه بدنا نفترضه ان بدي اثبت اذا P of N is
+
+235
+00:18:37,710 --> 00:18:42,630
+true اذا P of N زائد واحد is true is true بكل
+
+236
+00:18:42,630 --> 00:18:47,030
+بساطة بدك تفرض انه هذه صحيحة اللي هي N اقل من 2 to
+
+237
+00:18:47,030 --> 00:18:51,090
+the power N فدي true فعلياعلى اعتبار ان هي الفرضية
+
+238
+00:18:51,090 --> 00:18:53,430
+وانا مانتش اقول direct على طول خلاص direct ايش
+
+239
+00:18:53,430 --> 00:18:57,890
+يعني direct يعني ال premise is true ومنه بتحاول
+
+240
+00:18:57,890 --> 00:19:00,790
+تجيبي ال conclusion خلاص يعني هذه بتفرضها دائما
+
+241
+00:19:00,790 --> 00:19:05,390
+بتاعة ال implication البادئ لل implication is true
+
+242
+00:19:05,390 --> 00:19:09,330
+و بتجيب منه اللاحق او ال conclusion انت بدك تستنتج
+
+243
+00:19:09,330 --> 00:19:13,630
+اللاحق خلاص تمام في الحالة هذه بتقدر ببساطة تقول
+
+244
+00:19:13,630 --> 00:19:19,980
+ان زائدبدا نثبت منها ان in زائد واحد هتكون دايما
+
+245
+00:19:19,980 --> 00:19:24,260
+اقل من اتنين to the power in زائد واحد ببساطة جدا
+
+246
+00:19:24,260 --> 00:19:29,400
+هذه كل اللي هي محتاجها زائد واحد عشان تصبح نثبت
+
+247
+00:19:29,400 --> 00:19:34,520
+منها هذا ال term هذا ال term اللي هو in زائد واحد
+
+248
+00:19:34,520 --> 00:19:38,540
+اقل من اتنين to the power in زائد واحد طيب ايش
+
+249
+00:19:38,540 --> 00:19:42,860
+الفرق بين هذا و هذا اني ازيد واحد على الطرفينبنزيد
+
+250
+00:19:42,860 --> 00:19:47,240
+واحد على الطرفين عشان نوحد الطرف الشمال فالطرف
+
+251
+00:19:47,240 --> 00:19:52,340
+الشمال انا بدي اثبت ان زائد واحد و اشوف جدش بتطلع
+
+252
+00:19:52,340 --> 00:19:56,020
+خلينا نشوف فانا عندي ان لحالها فبتصير ان زائد واحد
+
+253
+00:19:56,020 --> 00:20:00,040
+اقل من اتنين ان برضه زائد واحد واحد على الطرفين و
+
+254
+00:20:00,040 --> 00:20:07,020
+مش اكتر واحد على الطرفينلا أكثر ولا أقل طيب تمام و
+
+255
+00:20:07,020 --> 00:20:10,400
+هنا هنا في الآخر و نقول أقل من اتنين to the power
+
+256
+00:20:10,400 --> 00:20:18,080
+n طيب واحد هذه واحد هذه دائما هتكون أقل من اتنين
+
+257
+00:20:18,080 --> 00:20:24,600
+to the power جداش to the power n لأنه
+
+258
+00:20:24,600 --> 00:20:29,680
+انت بادب أكبر من صفر صح و كل ما زادت in الوسع حد
+
+259
+00:20:29,680 --> 00:20:34,420
+بزيد أكتر كمانهيزيد اكتر و اكتر كمان بس انت ضامن
+
+260
+00:20:34,420 --> 00:20:38,700
+انه دائما الواحد هيكون اقل من اتنين to the power
+
+261
+00:20:38,700 --> 00:20:46,680
+واحد هذا على اعتبار اول قيمة ممكن ل in اول قيمة
+
+262
+00:20:46,680 --> 00:20:51,760
+ممكن ل in واحد صحيح فانت ضامن اتنين to the power
+
+263
+00:20:51,760 --> 00:20:54,600
+واحد هيكون اكبر من الواحد والله اذا كان انت عند in
+
+264
+00:20:54,600 --> 00:20:57,380
+بالساوية عشرة فانت ضامن انه اكبر و مرتاح كمان في
+
+265
+00:20:57,380 --> 00:21:01,400
+الاكبرمرتاح جدا كمان في الأكبر، معناه ذلك أن ال
+
+266
+00:21:01,400 --> 00:21:05,780
+term هذا الواحد لأ انت هضفله قيمة أكبر، معناه ذلك
+
+267
+00:21:05,780 --> 00:21:13,120
+بتقدر تقول زائد اتنين to the power n أكبر من زادت،
+
+268
+00:21:13,120 --> 00:21:17,910
+بس ضالت صحيحة، correlation صحيحةCorrelation صحيحة
+
+269
+00:21:17,910 --> 00:21:22,370
+جداً طيب N زائد واحد ضالت زي ما هي و كل ما بقى N
+
+270
+00:21:22,370 --> 00:21:26,990
+زائد واحد بتجل قيمة كل ما زادت N عن ال term اللي
+
+271
+00:21:26,990 --> 00:21:31,350
+على الشمال وهذا بكل بساطة الان جمعه لما تجمعه ايش
+
+272
+00:21:31,350 --> 00:21:37,610
+بيصير اتنين to the power N زائد واحد على اعتبار
+
+273
+00:21:37,610 --> 00:21:42,330
+كأنها هدف فعليا اتنين في اتنين to the power N
+
+274
+00:21:45,520 --> 00:21:49,280
+مجموعة مرتين يعني كأنه اتنين في العدد .. اتنين في
+
+275
+00:21:49,280 --> 00:21:53,220
+العدد .. و اتنين في العدد هي power واحد فصارت زي
+
+276
+00:21:53,220 --> 00:22:01,560
+.. هاي المطلوب .. هاي المطلوب .. هذا المطلوب ..
+
+277
+00:22:01,560 --> 00:22:06,170
+تمامالان ال second principle هذه ال first
+
+278
+00:22:06,170 --> 00:22:10,070
+principle كل المطلوب انه عشان تثبت ان P of N زائد
+
+279
+00:22:10,070 --> 00:22:16,770
+واحد is true بدك تفترض ان P of N is true طيب ال
+
+280
+00:22:16,770 --> 00:22:20,870
+second principle لأ شوية اعمق ايش يعني اعمق يعني
+
+281
+00:22:20,870 --> 00:22:29,150
+عشان نثبتإنه فعلا لكل قيم N اللي أكبر من أو تساوي
+
+282
+00:22:29,150 --> 00:22:34,490
+صفر كويس هي true بدنا نقول ال basis مش مشكلة فيه
+
+283
+00:22:34,490 --> 00:22:38,970
+زي ال first principle بس في ال inductive لأ هيقول
+
+284
+00:22:38,970 --> 00:22:48,910
+لإن كل قيم N أكبر أو تساوي صفر كل القيم اللي من N
+
+285
+00:22:48,910 --> 00:22:55,390
+فأقلإذا كانت true إذن P of N زائد واحد is true
+
+286
+00:22:55,390 --> 00:23:00,350
+فإذا P of N زائد واحد is true هي مش مبنية فقط على
+
+287
+00:23:00,350 --> 00:23:05,890
+P of N لحالها يعني لا يكفي .. لا يكفي إنها تكون P
+
+288
+00:23:05,890 --> 00:23:10,650
+of N لحالها is true عشان أثبت منها إنه N زائد واحد
+
+289
+00:23:10,650 --> 00:23:17,730
+is true لأ محتاج إنه N وكل ما قبلها أكون مفترض إن
+
+290
+00:23:17,730 --> 00:23:22,330
+هم كلهم trueعشان نثبت من خلالها ان P of N زائد
+
+291
+00:23:22,330 --> 00:23:24,950
+واحد is true طبعا هذه بأحيان بيسموها ال strong
+
+292
+00:23:24,950 --> 00:23:29,930
+principle أو ال strong proof ال proof الأقوى لأنه
+
+293
+00:23:29,930 --> 00:23:33,750
+إذا تحقق اصلا إذا تحقق فهنشوف الأمثلة اللي ممكن
+
+294
+00:23:33,750 --> 00:23:37,230
+تحقيقها إشي هتقولي صعبة و كيف تعملها لأ هي سهلة
+
+295
+00:23:37,230 --> 00:23:40,470
+جدا و هنشوفها في الأمثلة يمكن أكتر بس هنا بنقول K
+
+296
+00:23:40,470 --> 00:23:46,980
+فإذا لكل القيم من صفر to NB of K لازم يكونوا is
+
+297
+00:23:46,980 --> 00:23:52,520
+true عشان أستنتج منه إنه بقى بيه of N زائد واحد is
+
+298
+00:23:52,520 --> 00:24:00,500
+true تمام هذا بده مثال عشان يوضحها بشكل أكبر
+
+299
+00:24:08,400 --> 00:24:13,480
+هي ايجي المثال طيب بدنا نفرض او بدنا نثبت انه لكل
+
+300
+00:24:13,480 --> 00:24:18,720
+قيم n اللي اكبر من واحد اللي اكبر من واحد يمكن
+
+301
+00:24:18,720 --> 00:24:23,660
+كتابتها بشكل primes مضروبة في بعض او product of
+
+302
+00:24:23,660 --> 00:24:26,920
+primes الحاجة اللي احنا خدناها جاب الحستين جاب
+
+303
+00:24:26,920 --> 00:24:30,960
+المحاضرتين كويس وقولنا ان كل عنصر اذا كان سواء
+
+304
+00:24:30,960 --> 00:24:36,030
+prime اوcomposite number هو عبارة عن مجموعة of
+
+305
+00:24:36,030 --> 00:24:40,050
+primes في بعض إذا هو prime فهو هو نفسه بحد ذاته
+
+306
+00:24:40,050 --> 00:24:44,690
+prime أو إذا كان composite فهو عبارة عن two primes
+
+307
+00:24:44,690 --> 00:24:47,990
+أو أكتر مضروبين في بعض مجموعة of primes مضروبة في
+
+308
+00:24:47,990 --> 00:24:53,150
+بعض أثبت ذلك، هاي المطلوب طيب عشان نثبت ذلك إيش
+
+309
+00:24:53,150 --> 00:25:00,070
+محتاج؟ محتاج أقول إنه بدي أبدأ من in أكبر من واحد
+
+310
+00:25:00,070 --> 00:25:04,090
+فإذا بدي أبدأ من مين؟ من الإتنينال business tip
+
+311
+00:25:04,090 --> 00:25:08,190
+بتاعتي هنا هتكون هي الأتنين اللي هي أكبر من ال ..
+
+312
+00:25:08,190 --> 00:25:12,190
+البداية ال initial تبعنا فعند الأتنين هيكون عندي
+
+313
+00:25:12,190 --> 00:25:16,490
+مجموعة ال primes واحد هو prime واحد فقط اللي هو
+
+314
+00:25:16,490 --> 00:25:19,730
+مين؟ الأتنين بس ليش؟ لأنه الأتنين هي بن حد ذاتها
+
+315
+00:25:19,730 --> 00:25:24,750
+prime هي بن حد ذاتها prime و ال prime الوحيد ال
+
+316
+00:25:24,750 --> 00:25:30,270
+even صحيح؟ ال prime الوحيد ال even في الدنيا كويس
+
+317
+00:25:31,860 --> 00:25:36,100
+طب تخيل إنه في أي prime تاني even غيره، مستحيل
+
+318
+00:25:36,100 --> 00:25:39,480
+لأنه بيقبل الجسم على اتنين، هيكون بيقبل الجسم على
+
+319
+00:25:39,480 --> 00:25:42,900
+اتنين، صحيح؟ فإذا هو ال answer الوحيد اللي بقدر
+
+320
+00:25:42,900 --> 00:25:48,690
+أسميه even primeتمام فهي ال basis صحيحة مش فيها
+
+321
+00:25:48,690 --> 00:25:53,390
+مشكلة ال basis اللي هي أول عنصر فعليا حقق المعادلة
+
+322
+00:25:53,390 --> 00:25:57,870
+صح تمام في ال inductive step بدي أقول أنه لو بدي
+
+323
+00:25:57,870 --> 00:26:02,050
+أفرض الفرضية تبعتي اللي هي is true أنه لكل قيم n
+
+324
+00:26:02,050 --> 00:26:07,450
+أكبر من أو تساوي اتنين هيها اللي هي هنبدأ فيها
+
+325
+00:26:07,450 --> 00:26:15,450
+فرضيتنا كل القيم من اتنين to N هي تحقق P of Kيعني
+
+326
+00:26:15,450 --> 00:26:21,330
+بمعنى إن هي كلها مجموعة primes كل الأعداد ابتداء
+
+327
+00:26:21,330 --> 00:26:27,510
+من الاتنين لعند N هي كلها عبارة عن مجموعة product
+
+328
+00:26:27,510 --> 00:26:33,350
+لprimes كل عنصر أي .. أي رقم اختاره هيك عشوائيا من
+
+329
+00:26:33,350 --> 00:26:38,130
+اتنين ل N أي رقم لازم هيكون عبارة عن ضرب مجموعة
+
+330
+00:26:38,130 --> 00:26:41,830
+primes في بعض هذه هي الفرضية اللي بنقول assume
+
+331
+00:26:41,830 --> 00:26:44,210
+that فإذا is it true؟
+
+332
+00:26:47,650 --> 00:26:51,250
+تمام طبعا هتقولي كيف أثبت أنه is true الإثبات الآن
+
+333
+00:26:51,250 --> 00:26:54,270
+في ال inductive هيثبت لك أنه الكلام صحيح هذا الوقت
+
+334
+00:26:54,270 --> 00:26:58,950
+هنفرض N زائد واحد N زائد واحد لان عشان أثبت أن هي
+
+335
+00:26:58,950 --> 00:27:03,570
+فعلا برضه هتحقق نفس الكلام عندها احتمالين إما أن
+
+336
+00:27:03,570 --> 00:27:08,150
+هي نفسها prime هي نفسها prime مش هيك مش في احتمال
+
+337
+00:27:08,150 --> 00:27:13,490
+أن تكون هي N زائد واحد أصلا prime فإذاأريحنا هي
+
+338
+00:27:13,490 --> 00:27:16,730
+prime لحالها معناه ذلك في الحالة هذه بقدر أقول أن
+
+339
+00:27:16,730 --> 00:27:20,150
+مجموع ال primes هي واحد prime واحد هي قيمة n زائد
+
+340
+00:27:20,150 --> 00:27:24,070
+واحد هذا is a prime طيب إذا مش prime وهذه الفرضية
+
+341
+00:27:24,070 --> 00:27:26,810
+التانية معناه ذلك أن ال n زائد واحد هو عبارة عن
+
+342
+00:27:26,810 --> 00:27:31,230
+مدى مش prime معناته بنفع يكون ضرب رقمين معروفة
+
+343
+00:27:31,230 --> 00:27:35,430
+صحيح هي a و b بغض النظر a و b هم primes ولا لأ
+
+344
+00:27:36,480 --> 00:27:41,960
+تمام؟ لكن a و b هدول أكيد هيكونوا أقل من n زائد
+
+345
+00:27:41,960 --> 00:27:50,060
+واحد صح؟ أكيد وحتما و أجل من n كمان أكيد هيكونوا
+
+346
+00:27:50,060 --> 00:27:54,700
+أقل من n طيب مدام أقل من n معناته ينطبق عليهم
+
+347
+00:27:54,700 --> 00:28:01,000
+الفرضية لأن هم معناته بين الاتنين و ال n معناه ذلك
+
+348
+00:28:01,000 --> 00:28:06,410
+أن هم نفسهم ممكن يكونوا n زائد واحد افترضهمهم
+
+349
+00:28:06,410 --> 00:28:11,830
+نفسهم ممكن يكونوا N زائد واحد فإذا A أكيد هتكون من
+
+350
+00:28:11,830 --> 00:28:17,190
+الواحد لل N و ال B نفس الكلام عشان فعلا ضربهم
+
+351
+00:28:17,190 --> 00:28:21,350
+يعطيك N زائد واحد فلازم يكونوا عددهم أقل ففي
+
+352
+00:28:21,350 --> 00:28:24,850
+الحالة دي A انت ضامن ان هي عبارة عن مجموعة Primes
+
+353
+00:28:24,850 --> 00:28:30,850
+جد ما يطلع يطلع عددهم Tمثلا و P هي عبارة عن مجموعة
+
+354
+00:28:30,850 --> 00:28:34,730
+Primes U ففي الحالة هذه بيقول ان N زائد واحد هي
+
+355
+00:28:34,730 --> 00:28:42,050
+عبارة عن مضروب مجموعة Primes عددهم T زائد U اللي
+
+356
+00:28:42,050 --> 00:28:45,790
+هي ال Primes تبعت A مضروبة في ال Primes تبعت P
+
+357
+00:28:45,790 --> 00:28:51,350
+لأنه A في P فN زائد واحد هي مجموعة ال Primes كلها
+
+358
+00:28:51,350 --> 00:28:57,160
+مضروبة في بعض جديش عدد ال Primes T زائد Uهتكون T
+
+359
+00:28:57,160 --> 00:29:00,660
+زائد U طب انت هتقول ليه طب ليه أثبت أنه هذا فعلا
+
+360
+00:29:00,660 --> 00:29:05,220
+كلهم true هقولك بكل بساطة اتعامل مع الموضوع انه N
+
+361
+00:29:05,220 --> 00:29:09,820
+زائد 1 اللي انت بدك تثبت recursion متذكرين او
+
+362
+00:29:09,820 --> 00:29:13,060
+أخدتوا فكرة ال recursion تمام فإذا بدي أتعامل مع A
+
+363
+00:29:13,060 --> 00:29:19,920
+كأنه هي N زائد 1 ل problem جديدة و B هي N زائد 1 ل
+
+364
+00:29:19,920 --> 00:29:23,940
+problem جديدة أثبت بدا ثبته نفس الكلام معناته إذا
+
+365
+00:29:23,940 --> 00:29:30,720
+ال Aممكن أقول عليها C في D صح؟
+
+366
+00:29:30,720 --> 00:29:37,560
+لما نصلى مين؟ لل basis أو ال prime هي نفسها ال
+
+367
+00:29:37,560 --> 00:29:45,820
+prime هي نفسها ال prime أو نصلى الأتنين صحيح؟
+
+368
+00:29:45,820 --> 00:29:52,780
+فمنطقيا هي بتفتحلنا الموضوع اللي بعد ذلك و اللي هو
+
+369
+00:29:52,780 --> 00:29:58,540
+ال recursionفالفكرة جاينة متسلسل عادي ومش صعبة ولا
+
+370
+00:29:58,540 --> 00:30:02,080
+هي غلط، ليش؟ لأنه بكل بساطة أنت هتقولي طب أنت
+
+371
+00:30:02,080 --> 00:30:06,280
+أثبتت أو خليني أفترض .. فردت أن هم كلهم true، ليش؟
+
+372
+00:30:06,280 --> 00:30:09,900
+ليش؟ لأنه بكل بساطة بدت أتعامل معاها أنه إيه؟ هي
+
+373
+00:30:09,900 --> 00:30:13,380
+كأنها n زائد واحد problem جديدة واخدها لحالة أحلها
+
+374
+00:30:13,990 --> 00:30:17,650
+و بيه نفس الكلام أخدها لحالها أحلها طيب A هذي يمكن
+
+375
+00:30:17,650 --> 00:30:21,290
+تطلع ل C و D C لحالها بدي أحلها كأنها N زائد واحد
+
+376
+00:30:21,290 --> 00:30:24,430
+و D بدي أحلها لحالها كأنها N زائد واحد هتبقى
+
+377
+00:30:24,430 --> 00:30:28,430
+تتحلحل معاها تتفتفت معاها recursion صحيح؟
+
+378
+00:30:28,430 --> 00:30:34,270
+recursive steps لما تصل ل ال prime أو ال basis
+
+379
+00:30:36,020 --> 00:30:39,980
+هتضلك تتفك فتتحلحل معاك لما تصل لواحد من هالاتنين
+
+380
+00:30:39,980 --> 00:30:46,460
+يا هو prime بحجذ ذاته او تصل لل bases صحيح هتاخد
+
+381
+00:30:46,460 --> 00:30:50,080
+معاك وجد هتاخد معاك وجد صحيح لكن مش هالوجد اللي
+
+382
+00:30:50,080 --> 00:30:58,680
+انت متخيله ليش لأنه ال code هنا هو مش linear صح ال
+
+383
+00:30:58,680 --> 00:31:01,870
+code هنا مش linear هنا logarithmicفال complexity
+
+384
+00:31:01,870 --> 00:31:05,190
+هنا مش زي ما انت متخيلها هتكون كبيرة مش هتكون
+
+385
+00:31:05,190 --> 00:31:12,190
+كبيرة واضح تهيألي المثال اه؟ بدكم ترجعوله برضه و
+
+386
+00:31:12,190 --> 00:31:14,770
+تركزوا فيه لأنه recursion هذا فكرة ال recursion if
+
+387
+00:31:14,770 --> 00:31:17,510
+أنتوا ماخدين recursion if أنتوا ماخدين recursion
+
+388
+00:31:17,510 --> 00:31:21,790
+بسيط جدا فكرة حتى أنك تعمله إثبات أو تعمله code
+
+389
+00:31:21,790 --> 00:31:27,530
+طيب نفس الكلام و ننهي في كمان مثال
+
+390
+00:31:30,660 --> 00:31:36,500
+المثال هذا مطلوب اثبات انه لكل amount of postage
+
+391
+00:31:36,500 --> 00:31:44,220
+لكل قيمة جواب او اللي هو بنسميه جواب بوستا اللي هو
+
+392
+00:31:44,220 --> 00:31:49,680
+جواب بريدي كويس او كتاب بريدي لكل كتاب بريدي of
+
+393
+00:31:49,680 --> 00:31:53,440
+اتناشر cent اللي هو بنحط عليه طابع باتناشر cent
+
+394
+00:31:53,440 --> 00:32:01,120
+تكلفته اتناشر cent كويس او اكتركل جواب بريدي ب 12
+
+395
+00:32:01,120 --> 00:32:09,380
+cents أو أكتر يمكن تمثيله باستخدام 4 و 5 cents من
+
+396
+00:32:09,380 --> 00:32:15,380
+ال stamps أو من الطوابق فإذا تبع البريد ماعندهش
+
+397
+00:32:15,380 --> 00:32:18,620
+إلا طوابق اللي دلت من فئة الأربعة cents و الخمسة
+
+398
+00:32:18,620 --> 00:32:22,140
+cents بس ماعندهش لا تلاتة ولا خمسة ولا سبعة ولا
+
+399
+00:32:22,140 --> 00:32:26,450
+ستة ماعندهش إلا الأربعة والخمسةبدنا نثبت ان هي
+
+400
+00:32:26,450 --> 00:32:31,070
+كافية جدا لأي رسالة بتجيك جداش تكلفتها تكون مش
+
+401
+00:32:31,070 --> 00:32:37,770
+مشكلة المهم ان هي اكتر من اتناشعشرين، خمسة وعشرين،
+
+402
+00:32:37,770 --> 00:32:42,250
+سبعين، مية، خمس مية بتقدر تشكلها من مجموعة ال ..
+
+403
+00:32:42,250 --> 00:32:46,490
+ال .. ال two stems اللي هي الأربعة والخمسة بدنا
+
+404
+00:32:46,490 --> 00:32:49,590
+نثبت هذا الكلام عشان تثبت هذا الكلام هنا هيكون
+
+405
+00:32:49,590 --> 00:32:54,070
+عندك ال basis case أو ال basis step ال .. ال basis
+
+406
+00:32:54,070 --> 00:32:58,270
+step هتكون عبارة عن أن الإطماعش نفسها هي تلطوة من
+
+407
+00:32:58,270 --> 00:33:05,250
+M الأربعة صحيح؟ طيب التلطعشهي عبارة عن طابعين
+
+408
+00:33:05,250 --> 00:33:10,850
+أربعة و طابع خمسة هذا اللي هي تلت طعش طيب الأربع
+
+409
+00:33:10,850 --> 00:33:15,790
+طعش بالعكس بتصير هذه واحد وهذه اتنين فبتصير طابع
+
+410
+00:33:15,790 --> 00:33:20,950
+أبو الأربعة و طابعين أبو الخمسة عشان نصلّها خمس
+
+411
+00:33:20,950 --> 00:33:24,570
+طعش عبارة عن تلت طوابع خمسة فاحنا بدينا بتلاتة
+
+412
+00:33:24,570 --> 00:33:33,600
+تلاتة صفر اتنين واحد واحد اتنينصفر تلاتة والان
+
+413
+00:33:33,600 --> 00:33:39,400
+المفروض يرجعاش يتكرر هترجع تتكرر برضهrecursion
+
+414
+00:33:39,400 --> 00:33:43,020
+هنرجع تاني لل recursion فإذا assume that أنه فعلا
+
+415
+00:33:43,020 --> 00:33:48,400
+لكل القيم من 12 ل N هي is true عشان نثبت منها N
+
+416
+00:33:48,400 --> 00:33:52,740
+زائد واحد طب N زائد واحد هذه بدنا نكون عارفين أنه
+
+417
+00:33:52,740 --> 00:33:56,180
+الفارق بين كل واحدة و التانية هي N ناقص تلاتة
+
+418
+00:33:56,180 --> 00:34:03,060
+بمعنى من 12 ل N ما بينهم N ناقص تلاتة كلهم true
+
+419
+00:34:03,060 --> 00:34:08,430
+هيكونواكلهم true طيب ليش ان ناقص تلاتة لأنه بكون
+
+420
+00:34:08,430 --> 00:34:13,390
+ضامن هنا في الحالة هذه ان ان زائد واحد هتكون زائد
+
+421
+00:34:13,390 --> 00:34:19,870
+أربعة لاحظ معايا ليش حط المعادلة بتبعته بهذا الشكل
+
+422
+00:34:19,870 --> 00:34:26,770
+ان هي is true على أساس ان ان زائد واحد هتكون فارقة
+
+423
+00:34:26,770 --> 00:34:29,070
+عن الاطمعش بجداش باربعة
+
+424
+00:34:32,050 --> 00:34:35,990
+لعند ال N الفارق تلاتة طب أنا ماتكلمش عن ال N اللي
+
+425
+00:34:35,990 --> 00:34:41,410
+عند ال N هي true بتكلم عن N زائد واحد فبتصير بدل
+
+426
+00:34:41,410 --> 00:34:44,310
+ما الفارق تلاتة الفارق بيصير أربعة الأربعة مناسب
+
+427
+00:34:44,310 --> 00:34:49,910
+جدا لأنه بيصير إمكانية إضافة مين فقط stamp واحدة
+
+428
+00:34:49,910 --> 00:34:54,730
+باربعة cent stamp واحدة باربعة cent كأنه ال N زائد
+
+429
+00:34:54,730 --> 00:35:01,900
+واحد هتكون بتماثل N ناقص تلاتةبزيادة كمان طابع
+
+430
+00:35:01,900 --> 00:35:07,660
+باربعة الفرق بينهم كم؟ اربعة فارق بينهم اربعة فعلا
+
+431
+00:35:07,660 --> 00:35:13,120
+فصار هو ال index
+
+432
+00:35:13,120 --> 00:35:17,040
+اللي بتقدر تشتغل عليه ليش؟ لأن ال index هذا هو جاب
+
+433
+00:35:17,040 --> 00:35:23,280
+ال index ال n زائد واحد باربعة خلاص مناسب معناته
+
+434
+00:35:23,280 --> 00:35:29,120
+بيكفي اربعة طابع اربعة فإذا مدام احنا مثبتينإنه
+
+435
+00:35:29,120 --> 00:35:34,800
+أنا جادر أشكل أي جواب بقيمة n زائد أربعة بمجموعة
+
+436
+00:35:34,800 --> 00:35:38,160
+ال stamps اللي عندى معنى ذلك n زائد واحد مش هتكون
+
+437
+00:35:38,160 --> 00:35:44,400
+صعبة لإن هو نفسها n ناقص تلاتة و بضيف كمان stamp
+
+438
+00:35:44,400 --> 00:35:50,040
+زيادة من أبو الأربعة فقط بيصير stamp زيادة من أبو
+
+439
+00:35:50,040 --> 00:36:00,430
+الأربعة بمعنى إنه ال 12 هي مكافئة لل 16الـ12 كيف
+
+440
+00:36:00,430 --> 00:36:05,950
+شكلناها؟ تلاتة في أربعة هنا زيد عليها كمان واحدة
+
+441
+00:36:05,950 --> 00:36:12,310
+باربعة بالظبط أربعة أربعة، هاي ستة عشر، هاي ستة
+
+442
+00:36:12,310 --> 00:36:16,770
+عشر فالفارق دائما هيكون فكرة الأربعة الفارق لما
+
+443
+00:36:16,770 --> 00:36:21,430
+نقول التسعة عشر التسعة
+
+444
+00:36:21,430 --> 00:36:25,170
+عشر المفروض أنه مين اللي عندي يظل اللي عندي هنا؟
+
+445
+00:36:25,170 --> 00:36:31,910
+هتكون اتنين فارق تلاتة الأربعة عشرالاربعة .. تلات
+
+446
+00:36:31,910 --> 00:36:35,570
+خمس .. لأ هو مظبوط الفرق أربعة تلات خمسات خمستعش
+
+447
+00:36:35,570 --> 00:36:41,150
+من الخمستعش جديش الخمستعش كانت تلاتة في خمسة زائد
+
+448
+00:36:41,150 --> 00:36:45,170
+أربعة زائد
+
+449
+00:36:45,170 --> 00:36:49,870
+أربعة فمعنى ذلك طول ما عندك الأربعات فيهم وافرة
+
+450
+00:36:49,870 --> 00:36:55,710
+انت مش جالجان حسب ال .. ال inductive step اللي
+
+451
+00:36:55,710 --> 00:36:58,390
+احنا اشتغلنا عليها حسب ال inductive step اللي
+
+452
+00:36:58,390 --> 00:36:59,730
+اشتغلنا عليها
+
+453
+00:37:03,340 --> 00:37:09,420
+طبعا هي هيك تقريبا الموضوع الخفيف السريع بيجي في
+
+454
+00:37:09,420 --> 00:37:14,480
+الامتحانات في جزئية الإثبات لكن الأهم من ذلك أن هو
+
+455
+00:37:14,480 --> 00:37:17,940
+المقدمة عشان نروح لل recursion عشان نروح لل
+
+456
+00:37:17,940 --> 00:37:21,400
+recursion و recursive algorithm لأنه هناخد مجموعة
+
+457
+00:37:21,400 --> 00:37:26,770
+algorithms المرة القادمة كيف نعيد حلهابال .. بال
+
+458
+00:37:26,770 --> 00:37:30,650
+recursive code .. recursive code فيعطيكوا العافية
+
+459
+00:37:30,650 --> 00:37:31,710
+نهينا هي محاضرتنا
+
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0_raw.json b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..9f7b1fab869986636a0797a4aba6758e6db56174
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2326, "start": 5.4, "end": 23.26, "text": "بسم الله الرحمن الرحيم، يا عطيكوا العفو يا شباب، اليوم نكمل في مصاقنا، في عندنا موضوع شوية جديد و مكمل لجزء أخدناه سابقا و .. و اللي هو ال mathematical induction أو ال inductive، ال induction أو ال inductive اللي هو الحث", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 12399, 35186, 6225, 9566, 1829, 4117, 14407, 18863, 5172, 2407, 35186, 13412, 3555, 16758, 12399, 45595, 20498, 8717, 24793, 1211, 8978, 3714, 9381, 995, 4587, 8315, 12399, 8978, 43242, 8315, 3714, 2407, 11242, 45367, 13412, 2407, 10632, 10874, 16254, 3215, 4032, 3714, 24793, 1211, 5296, 7435, 11622, 38207, 5551, 9778, 3215, 8315, 3224, 8608, 16758, 4587, 995, 4032, 4386, 4032, 13672, 1829, 31439, 2423, 18894, 33371, 34051, 2423, 31612, 488, 12399, 2423, 33371, 34051, 2423, 31612, 488, 13672, 1829, 31439, 21542, 12984], "avg_logprob": -0.12287704039203085, "compression_ratio": 1.780612244897959, "no_speech_prob": 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answer الوحيد اللي بقدر أسميه even prime", "tokens": [9566, 3555, 6055, 9778, 26895, 36145, 3224, 8978, 36632, 5835, 6055, 7649, 1829, 754, 32771, 13546, 3224, 12399, 3714, 14851, 5016, 26895, 5296, 33456, 3224, 4724, 1829, 4587, 36150, 25724, 38251, 15844, 1975, 2655, 1863, 9957, 12399, 39896, 30544, 4724, 1829, 4587, 36150, 25724, 38251, 15844, 1975, 2655, 1863, 9957, 12399, 20328, 5016, 1829, 5016, 22807, 6156, 28814, 15730, 31439, 2423, 1867, 2423, 2407, 5016, 25708, 13672, 1829, 4724, 28543, 2288, 5551, 38251, 1829, 3224, 754, 5835], "avg_logprob": -0.16846955452974027, "compression_ratio": 1.6047904191616766, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1531.86, "end": 1532.1, "word": "طب", "probability": 0.74560546875}, {"start": 1532.1, "end": 1532.44, "word": " تخيل", "probability": 0.9876302083333334}, {"start": 1532.44, "end": 1532.62, "word": " إنه", "probability": 0.5421142578125}, {"start": 1532.62, "end": 1532.74, "word": " في", "probability": 0.9169921875}, {"start": 1532.74, "end": 1532.92, "word": " أي", "probability": 0.78759765625}, {"start": 1532.92, "end": 1533.2, "word": " prime", "probability": 0.48193359375}, {"start": 1533.2, "end": 1533.68, "word": " تاني", "probability": 0.9638671875}, {"start": 1533.68, "end": 1534.02, "word": " even", "probability": 0.62451171875}, {"start": 1534.02, "end": 1535.58, "word": " غيره،", "probability": 0.80816650390625}, {"start": 1535.58, "end": 1536.1, "word": " مستحيل", "probability": 0.988525390625}, {"start": 1536.1, "end": 1536.42, "word": " لأنه", "probability": 0.8590494791666666}, {"start": 1536.42, "end": 1536.66, "word": " بيقبل", "probability": 0.914794921875}, {"start": 1536.66, "end": 1536.94, "word": " الجسم", "probability": 0.99267578125}, {"start": 1536.94, "end": 1537.06, "word": " على", "probability": 0.329833984375}, {"start": 1537.06, "end": 1538.38, "word": " اتنين،", "probability": 0.92099609375}, {"start": 1538.38, "end": 1538.66, "word": " هيكون", "probability": 0.6527099609375}, {"start": 1538.66, "end": 1539.12, "word": " بيقبل", "probability": 0.84039306640625}, {"start": 1539.12, "end": 1539.36, "word": " الجسم", "probability": 0.993408203125}, {"start": 1539.36, "end": 1539.48, "word": " على", "probability": 0.88623046875}, {"start": 1539.48, "end": 1539.82, "word": " اتنين،", "probability": 0.95048828125}, {"start": 1539.82, "end": 1540.58, "word": " صحيح؟", "probability": 0.96279296875}, {"start": 1540.58, "end": 1540.88, "word": " فإذا", "probability": 0.8409830729166666}, {"start": 1540.88, "end": 1541.34, "word": " هو", "probability": 0.98193359375}, {"start": 1541.34, "end": 1541.54, "word": " ال", "probability": 0.8759765625}, {"start": 1541.54, "end": 1541.98, "word": " answer", "probability": 0.859375}, {"start": 1541.98, "end": 1542.5, "word": " الوحيد", "probability": 0.961669921875}, {"start": 1542.5, "end": 1542.62, "word": " اللي", "probability": 0.975341796875}, {"start": 1542.62, "end": 1542.9, "word": " بقدر", "probability": 0.9103190104166666}, {"start": 1542.9, "end": 1544.0, "word": " أسميه", "probability": 0.8509521484375}, {"start": 1544.0, "end": 1544.42, "word": " even", "probability": 0.84326171875}, {"start": 1544.42, "end": 1544.84, "word": " prime", "probability": 0.8818359375}], "temperature": 1.0}, {"id": 66, "seek": 157407, "start": 1546.59, "end": 1574.07, "text": "تمام فهي ال basis صحيحة مش فيها مشكلة ال basis اللي هي أول عنصر فعليا حقق المعادلة صح تمام في ال inductive step بدي أقول أنه لو بدي أفرض الفرضية تبعتي اللي هي is true أنه لكل قيم n أكبر من أو تساوي اتنين هيها اللي هي هنبدأ فيها فرضيتنا كل القيم من اتنين to N هي تحقق P of K", "tokens": [39237, 10943, 6156, 3224, 1829, 2423, 5143, 20328, 5016, 1829, 5016, 3660, 37893, 8978, 11296, 37893, 28820, 3660, 2423, 5143, 13672, 1829, 39896, 5551, 12610, 18871, 9381, 2288, 6156, 3615, 20292, 995, 11331, 4587, 4587, 9673, 3615, 18513, 37977, 20328, 5016, 46811, 10943, 8978, 2423, 31612, 488, 1823, 4724, 16254, 5551, 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0.97822265625}, {"start": 1548.37, "end": 1548.49, "word": " مش", "probability": 0.42236328125}, {"start": 1548.49, "end": 1548.69, "word": " فيها", "probability": 0.9580078125}, {"start": 1548.69, "end": 1549.17, "word": " مشكلة", "probability": 0.98486328125}, {"start": 1549.17, "end": 1549.75, "word": " ال", "probability": 0.9541015625}, {"start": 1549.75, "end": 1550.13, "word": " basis", "probability": 0.89697265625}, {"start": 1550.13, "end": 1550.33, "word": " اللي", "probability": 0.904052734375}, {"start": 1550.33, "end": 1550.45, "word": " هي", "probability": 0.85009765625}, {"start": 1550.45, "end": 1550.73, "word": " أول", "probability": 0.85888671875}, {"start": 1550.73, "end": 1551.19, "word": " عنصر", "probability": 0.9892578125}, {"start": 1551.19, "end": 1551.77, "word": " فعليا", "probability": 0.86328125}, {"start": 1551.77, "end": 1552.59, "word": " حقق", "probability": 0.9703776041666666}, {"start": 1552.59, "end": 1553.39, "word": " المعادلة", "probability": 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0.9072265625}, {"start": 1558.33, "end": 1559.01, "word": " الفرضية", "probability": 0.9462890625}, {"start": 1559.01, "end": 1559.35, "word": " تبعتي", "probability": 0.708984375}, {"start": 1559.35, "end": 1559.45, "word": " اللي", "probability": 0.962890625}, {"start": 1559.45, "end": 1559.61, "word": " هي", "probability": 0.88623046875}, {"start": 1559.61, "end": 1559.77, "word": " is", "probability": 0.90087890625}, {"start": 1559.77, "end": 1560.11, "word": " true", "probability": 0.65087890625}, {"start": 1560.11, "end": 1560.93, "word": " أنه", "probability": 0.734619140625}, {"start": 1560.93, "end": 1561.37, "word": " لكل", "probability": 0.986572265625}, {"start": 1561.37, "end": 1561.71, "word": " قيم", "probability": 0.971923828125}, {"start": 1561.71, "end": 1562.05, "word": " n", "probability": 0.5234375}, {"start": 1562.05, "end": 1562.89, "word": " أكبر", "probability": 0.9690755208333334}, {"start": 1562.89, "end": 1563.05, "word": " من", "probability": 0.98779296875}, {"start": 1563.05, "end": 1563.21, "word": " أو", "probability": 0.92333984375}, {"start": 1563.21, "end": 1563.71, "word": " تساوي", "probability": 0.9805908203125}, {"start": 1563.71, "end": 1564.45, "word": " اتنين", "probability": 0.8519287109375}, {"start": 1564.45, "end": 1565.53, "word": " هيها", "probability": 0.5361328125}, {"start": 1565.53, "end": 1566.15, "word": " اللي", "probability": 0.96240234375}, {"start": 1566.15, "end": 1566.41, "word": " هي", "probability": 0.908203125}, {"start": 1566.41, "end": 1567.09, "word": " هنبدأ", "probability": 0.9300537109375}, {"start": 1567.09, "end": 1567.45, "word": " فيها", "probability": 0.99072265625}, {"start": 1567.45, "end": 1568.41, "word": " فرضيتنا", "probability": 0.9715576171875}, {"start": 1568.41, "end": 1569.79, "word": " كل", "probability": 0.9765625}, {"start": 1569.79, "end": 1570.41, "word": " القيم", "probability": 0.958984375}, {"start": 1570.41, "end": 1570.95, "word": " من", "probability": 0.9931640625}, {"start": 1570.95, "end": 1571.47, "word": " اتنين", "probability": 0.9423828125}, {"start": 1571.47, "end": 1571.75, "word": " to", "probability": 0.9287109375}, {"start": 1571.75, "end": 1572.07, "word": " N", "probability": 0.421142578125}, {"start": 1572.07, "end": 1572.53, "word": " هي", "probability": 0.9345703125}, {"start": 1572.53, "end": 1573.15, "word": " تحقق", "probability": 0.975341796875}, {"start": 1573.15, "end": 1573.37, "word": " P", "probability": 0.53759765625}, {"start": 1573.37, "end": 1573.87, "word": " of", "probability": 0.77978515625}, {"start": 1573.87, "end": 1574.07, "word": " K", "probability": 0.92822265625}], "temperature": 1.0}, {"id": 67, "seek": 160421, "start": 1575.13, "end": 1604.21, "text": "يعني بمعنى إن هي كلها مجموعة primes كل الأعداد ابتداء من الاتنين لعند N هي كلها عبارة عن مجموعة product لprimes كل عنصر أي .. أي رقم اختاره هيك عشوائيا من اتنين ل N أي رقم لازم هيكون عبارة عن ضرب مجموعة primes في بعض هذه هي الفرضية اللي بنقول assume that فإذا is it true؟", "tokens": [40228, 22653, 4724, 2304, 3615, 1863, 7578, 36145, 39896, 28242, 11296, 3714, 7435, 2304, 2407, 27884, 1790, 5814, 28242, 16247, 22488, 18513, 48127, 2655, 3215, 16606, 9154, 2423, 9307, 1863, 9957, 5296, 3615, 41260, 426, 39896, 28242, 11296, 6225, 3555, 9640, 3660, 18871, 3714, 7435, 2304, 2407, 27884, 1674, 5296, 1424, 1532, 28242, 18871, 9381, 2288, 36632, 4386, 36632, 12602, 4587, 2304, 1975, 46456, 9640, 3224, 39896, 4117, 6225, 8592, 2407, 16373, 25528, 9154, 1975, 2655, 1863, 9957, 5296, 426, 36632, 12602, 4587, 2304, 5296, 31377, 2304, 39896, 30544, 6225, 3555, 9640, 3660, 18871, 48812, 25513, 3714, 7435, 2304, 2407, 27884, 2886, 279, 8978, 45030, 11242, 29538, 39896, 27188, 43042, 10632, 13672, 1829, 44945, 39648, 6552, 300, 6156, 28814, 15730, 307, 309, 2074, 22807], "avg_logprob": -0.1683750057220459, "compression_ratio": 1.7959183673469388, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1575.13, "end": 1575.45, "word": "يعني", "probability": 0.88330078125}, {"start": 1575.45, "end": 1575.87, "word": " بمعنى", "probability": 0.9796875}, {"start": 1575.87, "end": 1576.05, "word": " إن", "probability": 0.419677734375}, {"start": 1576.05, "end": 1576.23, "word": " هي", "probability": 0.51708984375}, {"start": 1576.23, "end": 1577.15, "word": " كلها", "probability": 0.967041015625}, {"start": 1577.15, "end": 1578.83, "word": " مجموعة", "probability": 0.9517578125}, {"start": 1578.83, "end": 1579.47, "word": " primes", "probability": 0.4764556884765625}, {"start": 1579.47, "end": 1579.77, "word": " كل", "probability": 0.71142578125}, {"start": 1579.77, "end": 1580.43, "word": " الأعداد", "probability": 0.94677734375}, {"start": 1580.43, "end": 1581.33, "word": " ابتداء", "probability": 0.7808837890625}, {"start": 1581.33, "end": 1581.49, "word": " من", "probability": 0.89404296875}, {"start": 1581.49, "end": 1581.93, "word": " الاتنين", "probability": 0.7830810546875}, {"start": 1581.93, "end": 1582.31, "word": " لعند", "probability": 0.7892252604166666}, {"start": 1582.31, "end": 1582.53, "word": " N", "probability": 0.365234375}, {"start": 1582.53, "end": 1583.63, "word": " هي", "probability": 0.859375}, {"start": 1583.63, "end": 1584.27, "word": " كلها", "probability": 0.9501953125}, {"start": 1584.27, "end": 1584.73, "word": " عبارة", "probability": 0.9970703125}, {"start": 1584.73, "end": 1585.03, "word": " عن", "probability": 0.99072265625}, {"start": 1585.03, "end": 1586.83, "word": " مجموعة", "probability": 0.984375}, {"start": 1586.83, "end": 1587.51, "word": " product", "probability": 0.89501953125}, {"start": 1587.51, "end": 1588.87, "word": " لprimes", "probability": 0.7135416666666666}, {"start": 1588.87, "end": 1589.79, "word": " كل", "probability": 0.8974609375}, {"start": 1589.79, "end": 1590.21, "word": " عنصر", "probability": 0.9446614583333334}, {"start": 1590.21, "end": 1590.45, "word": " أي", "probability": 0.49853515625}, {"start": 1590.45, "end": 1590.57, "word": " ..", "probability": 0.391845703125}, {"start": 1590.57, "end": 1590.75, "word": " أي", "probability": 0.78369140625}, {"start": 1590.75, "end": 1591.13, "word": " رقم", "probability": 0.99609375}, {"start": 1591.13, "end": 1592.01, "word": " اختاره", "probability": 0.96044921875}, {"start": 1592.01, "end": 1592.29, "word": " هيك", "probability": 0.773681640625}, {"start": 1592.29, "end": 1593.17, "word": " عشوائيا", "probability": 0.90185546875}, {"start": 1593.17, "end": 1593.35, "word": " من", "probability": 0.98193359375}, {"start": 1593.35, "end": 1593.73, "word": " اتنين", "probability": 0.9342041015625}, {"start": 1593.73, "end": 1593.91, "word": " ل", "probability": 0.99365234375}, {"start": 1593.91, "end": 1594.15, "word": " N", "probability": 0.74072265625}, {"start": 1594.15, "end": 1595.03, "word": " أي", "probability": 0.6669921875}, {"start": 1595.03, "end": 1595.45, "word": " رقم", "probability": 0.9972330729166666}, {"start": 1595.45, "end": 1596.03, 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جديدة", "probability": 0.9851888020833334}, {"start": 1811.9, "end": 1812.56, "word": " واخدها", "probability": 0.8009033203125}, {"start": 1812.56, "end": 1812.94, "word": " لحالة", "probability": 0.86322021484375}, {"start": 1812.94, "end": 1813.38, "word": " أحلها", "probability": 0.989501953125}], "temperature": 1.0}, {"id": 76, "seek": 183427, "start": 1813.99, "end": 1834.27, "text": "و بيه نفس الكلام أخدها لحالها أحلها طيب A هذي يمكن تطلع ل C و D C لحالها بدي أحلها كأنها N زائد واحد و D بدي أحلها لحالها كأنها N زائد واحد هتبقى تتحلحل معاها تتفتفت معاها recursion صحيح؟ recursive steps لما تصل ل ال prime أو ال basis", "tokens": [2407, 4724, 1829, 3224, 8717, 36178, 2423, 28820, 10943, 5551, 9778, 3215, 11296, 5296, 5016, 6027, 11296, 5551, 5016, 1211, 11296, 23032, 1829, 3555, 316, 8032, 8848, 1829, 7251, 43020, 6055, 9566, 1211, 3615, 5296, 383, 4032, 413, 383, 5296, 5016, 6027, 11296, 47525, 1829, 5551, 5016, 1211, 11296, 9122, 33456, 11296, 426, 30767, 16373, 3215, 36764, 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4724, 1829, 7435, 1829, 8978, 2423, 10943, 2655, 5016, 7649, 9307, 8978, 10874, 11622, 19986, 10632, 33688, 12984, 3555, 9307, 44381, 16247, 16095, 9154, 29910, 23275, 14739, 31439, 9673, 28543, 46007, 6225, 8592, 7649, 8717, 32887, 5016, 24976, 20560, 313, 6225, 8592, 7649, 8717, 32887, 5016, 24976, 20560, 313, 4032, 20560, 488, 9284, 5296, 33456, 3224, 8032, 1863, 47283, 3215, 3714, 7435, 2304, 2407, 27884, 14642, 9673, 25720, 25062, 18513, 46007, 9122, 33911, 8717, 3615, 25708, 11331, 1211, 11296], "avg_logprob": -0.14629288821243772, "compression_ratio": 1.7710280373831775, "no_speech_prob": 3.7550926208496094e-06, "words": [{"start": 2223.34, "end": 2224.3, "word": "طبعا", "probability": 0.764404296875}, {"start": 2224.3, "end": 2225.26, "word": " هي", "probability": 0.419677734375}, {"start": 2225.26, "end": 2225.66, "word": " هيك", "probability": 0.927490234375}, {"start": 2225.66, "end": 2226.12, "word": " تقريبا", "probability": 0.9515625}, {"start": 2226.12, "end": 2226.5, "word": " الموضوع", "probability": 0.992431640625}, {"start": 2226.5, "end": 2226.96, "word": " الخفيف", "probability": 0.9547526041666666}, {"start": 2226.96, "end": 2228.04, "word": " السريع", "probability": 0.89501953125}, {"start": 2228.04, "end": 2229.3, "word": " بيجي", "probability": 0.90576171875}, {"start": 2229.3, "end": 2229.42, "word": " في", "probability": 0.8681640625}, {"start": 2229.42, "end": 2229.92, "word": " الامتحانات", "probability": 0.9209798177083334}, {"start": 2229.92, "end": 2230.14, "word": " في", "probability": 0.78369140625}, {"start": 2230.14, "end": 2230.64, "word": " جزئية", "probability": 0.9583740234375}, {"start": 2230.64, "end": 2232.8, "word": " الإثبات", "probability": 0.804779052734375}, {"start": 2232.8, "end": 2233.28, "word": " لكن", "probability": 0.81884765625}, {"start": 2233.28, "end": 2233.7, "word": " الأهم", "probability": 0.892333984375}, {"start": 2233.7, "end": 2233.88, "word": " من", "probability": 0.9853515625}, {"start": 2233.88, "end": 2234.08, "word": " ذلك", "probability": 0.99609375}, {"start": 2234.08, "end": 2234.22, "word": " أن", "probability": 0.458251953125}, {"start": 2234.22, "end": 2234.48, "word": " هو", "probability": 0.64208984375}, {"start": 2234.48, "end": 2235.38, "word": " المقدمة", "probability": 0.9851888020833334}, {"start": 2235.38, "end": 2236.08, "word": " عشان", "probability": 0.9609375}, {"start": 2236.08, "end": 2236.28, "word": " نروح", "probability": 0.98974609375}, {"start": 2236.28, "end": 2236.42, "word": " لل", "probability": 0.7060546875}, {"start": 2236.42, "end": 2236.98, "word": " recursion", "probability": 0.94384765625}, {"start": 2236.98, "end": 2237.5, "word": " عشان", "probability": 0.776611328125}, {"start": 2237.5, "end": 2237.72, "word": " نروح", "probability": 0.99365234375}, {"start": 2237.72, "end": 2237.94, "word": " لل", "probability": 0.50439453125}, {"start": 2237.94, "end": 2238.56, "word": " recursion", "probability": 0.9599609375}, {"start": 2238.56, "end": 2238.9, "word": " و", "probability": 0.80517578125}, {"start": 2238.9, "end": 2239.52, "word": " recursive", "probability": 0.762451171875}, {"start": 2239.52, "end": 2240.0, "word": " algorithm", "probability": 0.90283203125}, {"start": 2240.0, "end": 2240.76, "word": " لأنه", "probability": 0.7464192708333334}, {"start": 2240.76, "end": 2241.12, "word": " هناخد", "probability": 0.9437255859375}, {"start": 2241.12, "end": 2241.4, "word": " مجموعة", "probability": 0.94990234375}, {"start": 2241.4, "end": 2241.98, "word": " algorithms", "probability": 0.8046875}, {"start": 2241.98, "end": 2242.42, "word": " المرة", "probability": 0.982177734375}, {"start": 2242.42, "end": 2242.98, "word": " القادمة", "probability": 0.9925130208333334}, {"start": 2242.98, "end": 2243.68, "word": " كيف", "probability": 0.95751953125}, {"start": 2243.68, "end": 2244.48, "word": " نعيد", "probability": 0.8159993489583334}, {"start": 2244.48, "end": 2245.22, "word": " حلها", "probability": 0.8916015625}], "temperature": 1.0}, {"id": 93, "seek": 225171, "start": 2245.91, "end": 2251.71, "text": "بال .. بال recursive code .. recursive code فيعطيكوا العافية نهينا هي محاضرتنا", "tokens": [3555, 6027, 4386, 20666, 20560, 488, 3089, 4386, 20560, 488, 3089, 6156, 40228, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 8717, 3224, 1829, 8315, 39896, 3714, 5016, 46958, 43500, 8315], "avg_logprob": -0.22341229261890536, "compression_ratio": 1.2258064516129032, "no_speech_prob": 0.0, "words": [{"start": 2245.91, "end": 2246.37, "word": "بال", "probability": 0.90380859375}, {"start": 2246.37, "end": 2246.51, "word": " ..", "probability": 0.6708984375}, {"start": 2246.51, "end": 2246.77, "word": " بال", "probability": 0.81396484375}, {"start": 2246.77, "end": 2247.41, "word": " recursive", "probability": 0.9365234375}, {"start": 2247.41, "end": 2248.11, "word": " code", "probability": 0.95458984375}, {"start": 2248.11, "end": 2248.33, "word": " ..", "probability": 0.41162109375}, {"start": 2248.33, "end": 2248.85, "word": " recursive", "probability": 0.949951171875}, {"start": 2248.85, "end": 2249.13, "word": " code", "probability": 0.97021484375}, {"start": 2249.13, "end": 2250.19, "word": " فيعطيكوا", "probability": 0.768798828125}, {"start": 2250.19, "end": 2250.65, "word": " العافية", "probability": 0.784912109375}, {"start": 2250.65, "end": 2251.03, "word": " نهينا", "probability": 0.8634033203125}, {"start": 2251.03, "end": 2251.13, "word": " هي", "probability": 0.73095703125}, {"start": 2251.13, "end": 2251.71, "word": " محاضرتنا", "probability": 0.88203125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2251.8711875, "duration_after_vad": 2170.9131249999923}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0_raw.srt b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..602e0c2372da63647b46c0347bc24b8bcd746596
--- /dev/null
+++ b/PL9fwy3NUQKwZhC2eomQhHTffLApa8bETi/ydqnWnt2c-0_raw.srt
@@ -0,0 +1,1836 @@
+1
+00:00:05,400 --> 00:00:07,780
+بسم الله الرحمن الرحيم، يا عطيكوا العفو يا شباب،
+
+2
+00:00:07,780 --> 00:00:13,300
+اليوم نكمل في مصاقنا، في عندنا موضوع شوية جديد و
+
+3
+00:00:13,300 --> 00:00:18,520
+مكمل لجزء أخدناه سابقا و .. و اللي هو ال
+
+4
+00:00:18,520 --> 00:00:21,720
+mathematical induction أو ال inductive، ال
+
+5
+00:00:21,720 --> 00:00:25,310
+induction أو ال inductive اللي هو الحثالحث هنشوف
+
+6
+00:00:25,310 --> 00:00:29,550
+إيش نظرية الحث هذه و بعدين هنستخدمها كطريقة إثبات
+
+7
+00:00:29,550 --> 00:00:33,050
+هذه بيستخدموها كواحدة من طرق الإثباتات اللي ممكن
+
+8
+00:00:33,050 --> 00:00:39,550
+استخدامها تابعا يعني يتبع لموضوع ال proof
+
+9
+00:00:39,550 --> 00:00:41,750
+strategies اللي أخدناها سابقا اللي أخدنا فيها
+
+10
+00:00:41,750 --> 00:00:46,090
+مجموعة أنواع منها ال direct و ال indirect و ال
+
+11
+00:00:46,090 --> 00:00:49,610
+contrapositive إذا متذكرين الكلام هذا اليوم
+
+12
+00:00:49,610 --> 00:00:53,680
+هنتبحها بكمان طريقة جديدةممكن استخدامها و اللي هي
+
+13
+00:00:53,680 --> 00:00:59,660
+ال inductive method فنفهم فكرتها الأول جزئية الحث
+
+14
+00:00:59,660 --> 00:01:02,940
+معناه كلمة الحث بتكون واضحة تماما في ال domino
+
+15
+00:01:02,940 --> 00:01:07,380
+لعبة ال domino هذه بتكون واضحة جدا كيف واضحة جدا
+
+16
+00:01:07,380 --> 00:01:12,360
+بتكون كل جطعة من الجطعة تحث التانية على action
+
+17
+00:01:12,360 --> 00:01:17,240
+معين إذا هيصار لها ال action فانتوا كلكوا عارفين
+
+18
+00:01:17,240 --> 00:01:20,840
+انه ممكن نصفطهم مرا بعض كل انتوا محتاجينه انكوا
+
+19
+00:01:20,840 --> 00:01:26,440
+تنزله اول حجر عشان تضمن بصورة و باخرة انه كلهم
+
+20
+00:01:26,440 --> 00:01:30,800
+هيجعوا مش هيك؟ طيب عشان نقول انه كلهم هيجعوا لازم
+
+21
+00:01:30,800 --> 00:01:36,480
+احققوا اول شغلة انه الحجر الاول وجع مش هيك؟ هل
+
+22
+00:01:36,480 --> 00:01:40,460
+هيجعوا كلهم اذا الاول لسه موجعش؟ لأ والشغلة
+
+23
+00:01:40,460 --> 00:01:47,710
+التانية انه كل حجر بقدر اسميهإن إذا وقع فان زائد
+
+24
+00:01:47,710 --> 00:01:51,410
+واحد لازم هيقع واضحة
+
+25
+00:01:52,170 --> 00:01:56,070
+إذا كان فعلًا ضمنّا لأنه مش ممكن تعملي خمس حجار
+
+26
+00:01:56,070 --> 00:02:00,030
+ورا بعض و بعدين تعملي فضة و الرقم ست بعيد عنهم
+
+27
+00:02:00,030 --> 00:02:03,730
+فمعنى ذلك أن الخامس والسادس بيحققوش هذه المعادلة
+
+28
+00:02:03,730 --> 00:02:07,910
+فكرة أنه إذا وقع الخامس لازم يقع السادس مش هيك؟
+
+29
+00:02:07,910 --> 00:02:14,270
+إذا كان ضمنّا أنه كل حجر ترتيبه N سيقع بالضرورة
+
+30
+00:02:14,270 --> 00:02:18,570
+سيقع N زائد واحد معنى ذلك أنه بنقدر نقولهذه
+
+31
+00:02:18,570 --> 00:02:23,870
+متسلسلة و كل واحد هيقع تبعا للي جابله واضحة هذه
+
+32
+00:02:23,870 --> 00:02:27,670
+اللعبة بتاعي اللي كنا عارفينها طيب انترجمها رياضية
+
+33
+00:02:27,670 --> 00:02:32,810
+انترجمها ك mathematical form هقول إذا كان P of 0
+
+34
+00:02:32,810 --> 00:02:37,140
+is trueالشي P of Zero اللي هو الحجر الأول اللي
+
+35
+00:02:37,140 --> 00:02:40,760
+وجعناه احنا بيدنا يعني انت مضمنين ان احنا وجعناه
+
+36
+00:02:40,760 --> 00:02:45,480
+او ان هو فعلا وقع تمام هذا is true طيب وإذا كان
+
+37
+00:02:45,480 --> 00:02:50,480
+انا ضامن انه لكل N أكبر من صفر أكبر من ال initial
+
+38
+00:02:50,480 --> 00:02:55,760
+اللي احنا عملناه من ال initial فأكثر إذا وقع الحجر
+
+39
+00:02:55,760 --> 00:02:59,820
+N فمعنى ذلك يتبع وقوع الحجر N زايد واحد فإذا كانت
+
+40
+00:02:59,820 --> 00:03:06,930
+حدثتن يضمن حدوث n زائد واحد إذا تحقق الشرطين هذول
+
+41
+00:03:06,930 --> 00:03:10,690
+معناته بقدر أقول إذا ال conclusion تبعنا لكل قيم n
+
+42
+00:03:10,690 --> 00:03:18,470
+أكبر من صفر هتقع فإذا P of N is true إذا كانالـ
+
+43
+00:03:18,470 --> 00:03:23,850
+action هدى اللى هى ال P هدى ك predicate هي انه يقع
+
+44
+00:03:23,850 --> 00:03:28,870
+الحجر هي ك predicate logic بدي اقول ان ال P هدى هى
+
+45
+00:03:28,870 --> 00:03:33,850
+ال function تبع وقوع الحجر فإذا X وقع X هدى بتش
+
+46
+00:03:33,850 --> 00:03:38,510
+ترتيبه N ولا N زائد واحد ولا N زائد اتنين ولا N
+
+47
+00:03:38,510 --> 00:03:43,330
+equal to zero فهو الحالة الأولى فهدى تنطبق تماما
+
+48
+00:03:43,330 --> 00:03:48,030
+على فكرة ال domino لكن كيف ممكن نستخدمها الحقيقة؟
+
+49
+00:03:48,180 --> 00:03:52,780
+في إثباتاتنا مبدأيا حاجة بسيطة جدا من لعبة
+
+50
+00:03:52,780 --> 00:03:59,340
+ابتكرولها معادلة المعادلة هذه واضحة جدا يقع الحجر
+
+51
+00:03:59,340 --> 00:04:03,080
+الأول هذا شرط ضروري فإذا فعلا تحقق إذا هو true
+
+52
+00:04:03,080 --> 00:04:08,020
+وإذا أنا ضامن إنه كل حجر بيوقق اللي ورا فإذا لكل
+
+53
+00:04:08,020 --> 00:04:12,940
+قيم N اللي أكبر من أو تساوي صفر إذا كان P of N وقع
+
+54
+00:04:12,940 --> 00:04:17,540
+فمعنى ذلك بضمن لإن P of N زائد واحد برضه هيقعهذه
+
+55
+00:04:17,540 --> 00:04:22,040
+شرطين معناه ذلك أنه بضمن أنه كلهم حاجة بقدر أستنتج
+
+56
+00:04:22,040 --> 00:04:27,100
+أنه معناه ذلك خلاص منتهية كلهم حاجة متأكدين تماما
+
+57
+00:04:27,100 --> 00:04:30,620
+أنه كلهم حاجة تمام هذه بيسموها ال first principle
+
+58
+00:04:30,620 --> 00:04:36,300
+of mathematical induction هذا المبدأ الأول ل ال
+
+59
+00:04:36,300 --> 00:04:40,460
+inductive أو ال induction فعليا طيب كيف ممكن منها
+
+60
+00:04:40,460 --> 00:04:44,620
+أعمل عملية ال inductive proofبكل بساطة إذا أحنا
+
+61
+00:04:44,620 --> 00:04:50,300
+بدنا نثبت أنه لكل قيم N P of N is true مثل حاجة
+
+62
+00:04:50,300 --> 00:04:54,480
+جالك الله يثبت لنا أنه لكل قيم N P of N is true زي
+
+63
+00:04:54,480 --> 00:04:58,190
+الأمثل اللي هناخدها لاحقاإن والله في قاعدة معينة
+
+64
+00:04:58,190 --> 00:05:01,730
+وبدي أقولك إن القاعدة هذه أثبت إنها فعلا صحيحة لكل
+
+65
+00:05:01,730 --> 00:05:06,690
+قيم إن مثلا أكبر من واحد أو إن أكبر من صفر أو إن
+
+66
+00:05:06,690 --> 00:05:11,070
+أكبر من خمسة أثبت إنها دائما ستكون صحيحة لكل
+
+67
+00:05:11,070 --> 00:05:15,370
+الأرقام طبعا مش منطقي إن أنت تروح تجرب كل الأرقام
+
+68
+00:05:16,190 --> 00:05:21,610
+صحيح؟ مش منطق فبدنا نعملها بيصير inductive proof
+
+69
+00:05:21,610 --> 00:05:24,830
+طيب ال inductive proof ال rules تبعونه أو ال two
+
+70
+00:05:24,830 --> 00:05:28,570
+steps الأساسيات بتاعه زي تبعون ال domino بدي أضمن
+
+71
+00:05:28,570 --> 00:05:33,900
+أن P of 0 هو trueهو فعلا بتحقق عشان أضمن أنه ال
+
+72
+00:05:33,900 --> 00:05:36,580
+trigger الأولى الحجر الأول هو وجع فعلا فإذا ال
+
+73
+00:05:36,580 --> 00:05:41,440
+initial element هو فعلا صحيح وبناء عليه الشغلة
+
+74
+00:05:41,440 --> 00:05:45,940
+التانية بتثبتها أنه لكل N يقع N زائد واحد هيقع
+
+75
+00:05:45,940 --> 00:05:52,830
+طبعا هنا بنقولAt n, P of n is true مش بالضرورة يقع
+
+76
+00:05:52,830 --> 00:05:56,870
+ك domino ولكن يحقق ال function اللي بدنا نثبتها
+
+77
+00:05:56,870 --> 00:06:02,170
+إذا كان فعلا P of n تحققت هل فعلا يتبع ذلك
+
+78
+00:06:02,170 --> 00:06:06,470
+بالضرورة أن n زائد واحد هتتحقق إذا أثبتت الجزء هذا
+
+79
+00:06:06,470 --> 00:06:10,130
+وأنا مثبت أساسا أن P of zero is true معناته خلاص
+
+80
+00:06:10,130 --> 00:06:14,450
+لكل قيم n أكيد هتتحقق أكيد هتتحقق و هنشوف الأثبات
+
+81
+00:06:14,450 --> 00:06:19,020
+فإذا ال step الأولى اللي هي بنسميها ال baseBases
+
+82
+00:06:19,020 --> 00:06:25,180
+step الخطوة الأساسية الخطوة الأولى انه نحقق P of
+
+83
+00:06:25,180 --> 00:06:29,940
+Zero نشوف فيها الفرضية بتبدأ من وين ممكن بكل بساطة
+
+84
+00:06:29,940 --> 00:06:35,530
+تجربها مباشرةتجربها مباشرة at n equal to zero طب
+
+85
+00:06:35,530 --> 00:06:40,110
+جرب n equal to zero ل P of n مباشرة هل هي صحيحة
+
+86
+00:06:40,110 --> 00:06:42,850
+ولا لأ خلاص و بعد ذلك بدنا نشوف كيف بدنا نعمل
+
+87
+00:06:42,850 --> 00:06:45,810
+الخطوة التانية اللي هي inductive step و اللي من
+
+88
+00:06:45,810 --> 00:06:50,830
+خلالها بنثبت أنه لكل قيم n إذا تحقق P of n يتبعها
+
+89
+00:06:50,830 --> 00:06:56,070
+P of n زائد واحد هتتحققتمام فهذه هيك ببساطة
+
+90
+00:06:56,070 --> 00:06:59,650
+الإثباتين اللي بنقدر نعملهم عشان نشتغلهم نشتغلهم
+
+91
+00:06:59,650 --> 00:07:04,650
+بال direct proof عادي جدا مش هنقعد نخبط الدنيا
+
+92
+00:07:04,650 --> 00:07:08,290
+فيهم هنشتغل على direct proof بمعنى انه هنفرض ان P
+
+93
+00:07:08,290 --> 00:07:13,760
+of N is true فعليا هناإن P of N is true فهقول اه
+
+94
+00:07:13,760 --> 00:07:17,940
+انا بده افترض ان هي صحيحة طيب إذا كانت صحيحة هل
+
+95
+00:07:17,940 --> 00:07:22,520
+يتبع ذلك ان P of N زائد واحد هتكون صحيحة ولا لأ بس
+
+96
+00:07:22,520 --> 00:07:28,500
+هاي كل الفكرة ففرضية ال assumption ل P of N
+
+97
+00:07:28,500 --> 00:07:33,600
+نفترضها احنا ان هي is true ثم بحاول اثبت من هذه ال
+
+98
+00:07:33,600 --> 00:07:37,060
+assumption ان والله P of N زائد واحد برضه هتكون
+
+99
+00:07:37,060 --> 00:07:40,620
+trueإذا أثبتنا هذه الجزئية فاحنا بنكون أثبتنا ال
+
+100
+00:07:40,620 --> 00:07:45,120
+inductive step و ال base أو ال بقى ال basis step
+
+101
+00:07:45,120 --> 00:07:48,940
+فاش فيها مشكلة بتشوف ال sequence تبعك من وين بده
+
+102
+00:07:48,940 --> 00:07:53,200
+طبق في أول عنصر مباشرة نطبق في المعادلة و خلاص و
+
+103
+00:07:53,200 --> 00:07:56,040
+ريح راسك فيه ففي الحالة هذه إذا اتحققوا الشرطين
+
+104
+00:07:56,040 --> 00:07:59,100
+فبنضمن أنه بال inductive inference أو بالاستدلال
+
+105
+00:07:59,100 --> 00:08:05,690
+الحثي الاستدلال الحثي لإن أنا حققت2 steps فبستدل
+
+106
+00:08:05,690 --> 00:08:11,250
+من تحقيقهم أنه معنى ذلك لكل قيم N P of N is true
+
+107
+00:08:11,250 --> 00:08:19,790
+فإذا P of N تتحقق لكل قيم N الممكنة طيب عشان نعمل
+
+108
+00:08:19,790 --> 00:08:23,630
+generalization للكلام هذا مش بالضروري أن P of 0 هي
+
+109
+00:08:23,630 --> 00:08:29,090
+اللي أبدأ منها ممكن أبدأ من P of Cممكن أبدأ من صفر
+
+110
+00:08:29,090 --> 00:08:31,570
+أبدأ من واحد أبدأ من خمس أبدأ من عشرة تكون هي ال
+
+111
+00:08:31,570 --> 00:08:33,990
+initial تبعتي و خلاص هي اللي بتبدأ فيها ك basis
+
+112
+00:08:33,990 --> 00:08:37,790
+step فمعنى ذلك in general بقدر أقول أن أقول قيم N
+
+113
+00:08:37,790 --> 00:08:42,730
+اللي أكبر من C مش بالضروري ال zeroلسة بالضروري الـ
+
+114
+00:08:42,730 --> 00:08:47,130
+zero من C P of N is true ففي الحالة هذه الطبيعي
+
+115
+00:08:47,130 --> 00:08:49,170
+اللي بيختلف الشغل الوحيد اللي بتختلف ان ال
+
+116
+00:08:49,170 --> 00:08:52,350
+inductive stuff مش هتتغير انت بتفرض P of N is true
+
+117
+00:08:52,350 --> 00:08:55,970
+وبناء عليها بتحاول تثبت ان P of N زائد واحد برضه
+
+118
+00:08:55,970 --> 00:09:00,270
+هتتبحى ك true طيب، ايش اللي بيختلف؟ بيختلف فقط ال
+
+119
+00:09:00,270 --> 00:09:04,990
+P of Zero بتعود مكانه ب P of C مش اكتر من هيك هي
+
+120
+00:09:04,990 --> 00:09:10,470
+الخطوة الوحيدة اللي بتعملها نبدأ نشوف أمثلة على
+
+121
+00:09:10,470 --> 00:09:15,750
+هذا الموضوعلما نقول بدنا نثبت انه مجموع ال first
+
+122
+00:09:15,750 --> 00:09:25,570
+in odd positive integers is in square بمعنى واحد
+
+123
+00:09:25,570 --> 00:09:34,030
+اتنين عفوا تلاتة ال odd first in odd integers فانا
+
+124
+00:09:34,030 --> 00:09:41,050
+معنى بال odd integers خمسة سبعة تسعة احداشر
+
+125
+00:09:42,890 --> 00:09:48,110
+and so on تكمل الان ايش بده منيه بده يقولي انه
+
+126
+00:09:48,110 --> 00:09:55,870
+مجموع ال n first odd هاي أول n عددهم جديش ال n
+
+127
+00:09:55,870 --> 00:09:59,770
+اتنين فإذا المفروض انه اتنين تربية بيسووا مجموحهم
+
+128
+00:09:59,770 --> 00:10:04,190
+طيب تلاتة المفروض ان تلاتة تربية بتسووا مجموحهم
+
+129
+00:10:05,510 --> 00:10:08,630
+عددهم أربعة .. أربعة تربيع المفروض أنه مجموحهم
+
+130
+00:10:08,630 --> 00:10:12,350
+عددهم خمسة .. خمسة تربيع المفروض أنه مجموحهم ستة
+
+131
+00:10:12,350 --> 00:10:15,490
+.. ستة تربيع مجموحهم وصلت ال .. ال role اللي بدنا
+
+132
+00:10:15,490 --> 00:10:19,150
+نثبتها role بسيطة و حلوة و كويسة طيب تمام هات
+
+133
+00:10:19,150 --> 00:10:23,310
+نحاول نثبتها يعني كأنني بدي أقول أن لكل قيم N اللي
+
+134
+00:10:23,310 --> 00:10:26,310
+أكبر من واحد لأن احنا بدنا نبدأ من أول location
+
+135
+00:10:26,310 --> 00:10:30,990
+فانا بدأ أفترض أن هذا لو N ك location واحد اتنين
+
+136
+00:10:30,990 --> 00:10:38,720
+تلاتة أربعة خمسة ستة سبعة and so onand so on جيد
+
+137
+00:10:38,720 --> 00:10:41,720
+فإذا لو أكبر من واحد على اعتبار ان ال odds ببدأ من
+
+138
+00:10:41,720 --> 00:10:46,000
+الواحد ل summation هيدا بنعمل هنا summation لمين
+
+139
+00:10:46,000 --> 00:10:49,740
+لما جمعتوا ال odds وال odds عرفناها سابقا لما
+
+140
+00:10:49,740 --> 00:10:52,940
+اتكلمنا عن ال proof اللي هي اتنين I ناقص واحد
+
+141
+00:10:52,940 --> 00:10:58,020
+بدأناها اتنين I ناقص واحد لو حطيت I هنا بواحد
+
+142
+00:10:58,020 --> 00:11:02,280
+حيسروا واحد معناته ان انا بتكلم عن اول odds لو
+
+143
+00:11:02,280 --> 00:11:07,920
+حطيت I باتنينفمعنى ذلك بتتكلم عن تلاتة و هكذا
+
+144
+00:11:07,920 --> 00:11:12,000
+فعلياً هيها واحد تقابل الواحد الاتنين المفروض
+
+145
+00:11:12,000 --> 00:11:16,380
+تقابل التلاتة التلاتة تقابل الخمسة وهذا فعلياً
+
+146
+00:11:16,380 --> 00:11:20,820
+اللي بتحقق من ال index اللي احنا حاطينه فعلياً
+
+147
+00:11:20,820 --> 00:11:26,240
+فإذا نفترض الستة الستة المفروض انه هنا لو I6 يعني
+
+148
+00:11:26,240 --> 00:11:29,760
+أنا بتكلم عن العنصر رقم ستة هل العنصر رقم ستة بسوء
+
+149
+00:11:29,760 --> 00:11:33,530
+اتناش ناقص واحد احداش فعلاً هو واحداشفعلا هو 11
+
+150
+00:11:33,530 --> 00:11:37,970
+فإذا بنعمله ال summation هدولة ابتدا من الواحد ل N
+
+151
+00:11:37,970 --> 00:11:43,930
+حسب ما هو بيقوللي first N odd integers اللي
+
+152
+00:11:43,930 --> 00:11:49,450
+المفروض أنه يسوى ال Inter بي ..مش شاك، فإذا هذه ال
+
+153
+00:11:49,450 --> 00:11:51,810
+relation اللي بدنا نحققها حتى الآن، لعندي لعين بس
+
+154
+00:11:51,810 --> 00:11:56,070
+إحنا قاعدين نشرح السؤال، لعندي لعين بس بدنا نتكلم
+
+155
+00:11:56,070 --> 00:12:00,090
+عن السؤال، فسرنا السؤال أول شغلة ال initial تبعنا
+
+156
+00:12:00,090 --> 00:12:04,750
+بده من وين؟ من الواحد، بده من الواحد فعليا، بده
+
+157
+00:12:04,750 --> 00:12:08,890
+هنا، فإذا مباشرة نطبق على الواحد فبيكون هو ال
+
+158
+00:12:08,890 --> 00:12:12,190
+business step، خلصنا، هاي أول خطوة خلصت، هاي أول
+
+159
+00:12:12,190 --> 00:12:16,910
+خطوة خلصت على السريعتمام فعند ال N بتساوي واحد هنا
+
+160
+00:12:16,910 --> 00:12:21,790
+هتساوي اتنين ناقص واحد فهذه واحد وهي من واحد لواحد
+
+161
+00:12:21,790 --> 00:12:26,070
+هتكون لأن N بس واحد فهتساوي واحد طيب واحد تربيع
+
+162
+00:12:26,070 --> 00:12:30,210
+يساوي الواحد اللي هو المجموع الواحد فإذا ال B at
+
+163
+00:12:30,210 --> 00:12:36,790
+one is true خلاص خلصنا هاي أول حاجة أثبتناها أن هي
+
+164
+00:12:36,790 --> 00:12:41,660
+صحيحة طيبالشغل التاني لبعد هيك بدنا نثبت .. بدنا
+
+165
+00:12:41,660 --> 00:12:46,660
+نقول إثبات عادي جدا أنه بدي أفرض أنه لو هذه فعلا
+
+166
+00:12:46,660 --> 00:12:54,310
+ال trueهتلي عند n زائد واحد هل بتكون true ولا لأ
+
+167
+00:12:54,310 --> 00:12:59,770
+اعمل الشيء الضروري عشان تصبح اتحولها من n ل n زائد
+
+168
+00:12:59,770 --> 00:13:03,130
+واحد كل اللي بدك تعمله تضيف العنصر n زائد واحد بس
+
+169
+00:13:03,130 --> 00:13:08,710
+و تشوف هل المجموعة فعلا هيظهر هنا ك n زائد واحد
+
+170
+00:13:08,710 --> 00:13:14,850
+تربيعه ولا لأ هاي كل الفكرة انك انت هنا هتضطر تضيف
+
+171
+00:13:14,850 --> 00:13:20,640
+P of n زائد واحد على ال total هنالأن هو العنصر
+
+172
+00:13:20,640 --> 00:13:24,580
+الإضاءة اللي قضيفش دي ازيادة وانت مفترض تماما
+
+173
+00:13:24,580 --> 00:13:29,480
+ومقتنع وعمل assumption واضحة تماما ان هذا true طيب
+
+174
+00:13:29,480 --> 00:13:34,800
+لو ضفنا لها العنصر في location B N زائد واحد
+
+175
+00:13:34,800 --> 00:13:39,320
+ضفناها إضافة لإلها هل فعلا المجموع هيطلع N زائد
+
+176
+00:13:39,320 --> 00:13:43,600
+واحد تربيع ولا لأ؟ هذه الفكرةو قلنا بال direct
+
+177
+00:13:43,600 --> 00:13:47,880
+يعني مش محتاجين لأ تقعد تفكر في القصص اللي أخدناها
+
+178
+00:13:47,880 --> 00:13:51,200
+في chapter اتنين في chapter اتنين كانت ولا لأ ولا
+
+179
+00:13:51,200 --> 00:13:54,900
+تلاتة المهم في ال proof strategies مش محتاج تقعد
+
+180
+00:13:54,900 --> 00:13:57,920
+تفكر فيها هي direct على طول و خلاص تفرض الأولى
+
+181
+00:13:57,920 --> 00:14:03,140
+صحيحة و بتجيب منها التانية فكأولى صحيحة هنا
+
+182
+00:14:12,730 --> 00:14:16,830
+بداك تعمل ال summation من اش من واحد to in زائد
+
+183
+00:14:16,830 --> 00:14:20,510
+واحد to in زائد واحد بس انت عارف انه اللي صح اللي
+
+184
+00:14:20,510 --> 00:14:24,290
+انت متأكد منه ان هو صحيح هي هذا ال term من واحد to
+
+185
+00:14:24,290 --> 00:14:29,230
+in بس لانك انت فرضه اصلا ان هو true فمعنى ذلك ان
+
+186
+00:14:29,230 --> 00:14:36,710
+in زائد واحد هي فعليا ل in و باضافة من ال
+
+187
+00:14:36,710 --> 00:14:38,410
+summation من اش من وين ل وين
+
+188
+00:14:42,830 --> 00:14:47,010
+من حاجات الامتحان اللي إجتنا في الامتحان و معدودين
+
+189
+00:14:47,010 --> 00:14:52,150
+اللي حلوها هيك الكل راح اشتغل على الحسبة و كله
+
+190
+00:14:52,150 --> 00:14:56,290
+عملته غلط يعني احنا ماطلبناش على حسبة احنا كنا
+
+191
+00:14:56,290 --> 00:15:02,570
+بدنا manipulation كنا بدنا نعمل هيك تمام فإذا كل
+
+192
+00:15:02,570 --> 00:15:07,520
+اللي بقى اللي بده يضاف عند مين termSummation
+
+193
+00:15:07,520 --> 00:15:11,300
+للعنصر الأخير طب هي العنصر الأخير اللي هو عند مين
+
+194
+00:15:11,300 --> 00:15:17,040
+I بتساوي N زائد واحد خلاص عوض تنين في N زائد واحد
+
+195
+00:15:17,040 --> 00:15:22,180
+ناقص واحد هاي ال term اللي ضايل هذا تمام تمام طب
+
+196
+00:15:22,180 --> 00:15:26,940
+ممتاز جدا احنا من الأساس قلنا ان هذا is true مدام
+
+197
+00:15:26,940 --> 00:15:31,300
+is true يعني جداش قيمتها انتر بيع خلاص هي انتر بيع
+
+198
+00:15:31,300 --> 00:15:37,310
+وهنااتنين و هنا اتنين ناقص واحد بتصير زائد واحد
+
+199
+00:15:37,310 --> 00:15:43,830
+حللها تطلع ان زائد واحد كله تربيع فإذا فعليا
+
+200
+00:15:43,830 --> 00:15:48,590
+summation من واحد لان زائد واحد هتساوي ان زائد
+
+201
+00:15:48,590 --> 00:15:53,930
+واحد كله تربيعخلصنا هي أثبتنا ال basis اللي هي عند
+
+202
+00:15:53,930 --> 00:15:59,430
+n بتساوي واحد و أثبتنا إنه إذا كانت P of n is true
+
+203
+00:15:59,430 --> 00:16:04,270
+فعليا لإنها أثبتت فرضناها فعليا إنه is true فمدام
+
+204
+00:16:04,270 --> 00:16:08,230
+is true عوضنا مكانها ب N تربيع معناه ذلك إنه يلحق
+
+205
+00:16:08,230 --> 00:16:15,190
+ذلك إن P of n زائد واحد برضه is true هذا بيدل ليه
+
+206
+00:16:15,190 --> 00:16:20,890
+معناته لكل قيم N بغض النظر كده قيمةستة سبعة عشر
+
+207
+00:16:20,890 --> 00:16:24,810
+أحداش عشرين مية متين خمسمية هتكون دائما ال rule is
+
+208
+00:16:24,810 --> 00:16:30,230
+true دائما is true في الحالة هذه ليش لأن احنا
+
+209
+00:16:30,230 --> 00:16:33,910
+محددناش ان هنا جدش معنى ذلك انه ممكن تكون خمسمية
+
+210
+00:16:33,910 --> 00:16:36,730
+معنى ذلك ان خمسمية زي واحد صحيحة برضه ممكن تكون
+
+211
+00:16:36,730 --> 00:16:40,350
+عشرة معنى ذلك ان أحداش هتكون صحيحة و هكذا ما هي
+
+212
+00:16:40,350 --> 00:16:44,730
+سلسلة من بعض سلسلة من بعض محددناش قيمة ان بدون
+
+213
+00:16:44,730 --> 00:16:51,560
+تحديد لقيمة لقيمة انOkay طيب كمان مثال المثال
+
+214
+00:16:51,560 --> 00:16:58,080
+التاني لكل قيم n بدنا نقول إنه إذا كانت n أكبر من
+
+215
+00:16:58,080 --> 00:17:02,840
+صفر معنى ذلك إن n دائما أقل من 2 to the power n
+
+216
+00:17:02,840 --> 00:17:06,280
+طبعا هذه حاجة بدهية احنا عارفينها شئ بدهية أكيد
+
+217
+00:17:06,280 --> 00:17:10,260
+كلنا عارفينه خلصنا
+
+218
+00:17:10,260 --> 00:17:16,890
+المثال هذا المثال التانيانه لكل قيم N أكبر من صفر
+
+219
+00:17:16,890 --> 00:17:22,730
+دائما N هتكون اقل من اتنين to the power N طيب
+
+220
+00:17:22,730 --> 00:17:30,050
+فابتداء من الصفر اقل من واحد عند الواحد واحد اقل
+
+221
+00:17:30,050 --> 00:17:35,090
+من اتنين عند الاتنين اتنين اقل من اربعة عند
+
+222
+00:17:35,090 --> 00:17:42,680
+التلاتة and so on وكمل طبعا انت هتلاقي انه فعلاأقل
+
+223
+00:17:42,680 --> 00:17:46,940
+من لأ و أقل من هذه بتزيد عمقا كمان كل ما بتزود
+
+224
+00:17:46,940 --> 00:17:50,520
+قيمة n هنا كان الفرق بينهم واحد هنا واحد هنا صار
+
+225
+00:17:50,520 --> 00:17:55,920
+اتنين هنا صار خمسة and so on بزيد كل ما بزيد طيب
+
+226
+00:17:55,920 --> 00:17:58,900
+احنا بدنا نثبت الان ان العلاقة هذه صحيحة باستخدام
+
+227
+00:17:58,900 --> 00:18:03,580
+ال inductive step inductive step كمان مرة محتاج
+
+228
+00:18:03,580 --> 00:18:09,250
+اول حاجة ال basesو ال basis مدام أكبر من صفر معناه
+
+229
+00:18:09,250 --> 00:18:12,370
+ذلك حتى الصفر بدوش إياها مش هنستخدم أبدا أكبر من
+
+230
+00:18:12,370 --> 00:18:15,570
+صفر معناه تبقى أبدا من من؟ من الواحد فهذه هتصبح
+
+231
+00:18:15,570 --> 00:18:22,070
+عندى ال ال basis ال basis step
+
+232
+00:18:25,610 --> 00:18:29,350
+مهتمة خلصنا ال business step مش محتاج كل الباقي مش
+
+233
+00:18:29,350 --> 00:18:32,770
+محتاج الا واحدة بس هي اول answer الباقي عادى الان
+
+234
+00:18:32,770 --> 00:18:37,710
+المفروض انه بدنا نفترضه ان بدي اثبت اذا P of N is
+
+235
+00:18:37,710 --> 00:18:42,630
+true اذا P of N زائد واحد is true is true بكل
+
+236
+00:18:42,630 --> 00:18:47,030
+بساطة بدك تفرض انه هذه صحيحة اللي هي N اقل من 2 to
+
+237
+00:18:47,030 --> 00:18:51,090
+the power N فدي true فعلياعلى اعتبار ان هي الفرضية
+
+238
+00:18:51,090 --> 00:18:53,430
+وانا مانتش اقول direct على طول خلاص direct ايش
+
+239
+00:18:53,430 --> 00:18:57,890
+يعني direct يعني ال premise is true ومنه بتحاول
+
+240
+00:18:57,890 --> 00:19:00,790
+تجيبي ال conclusion خلاص يعني هذه بتفرضها دائما
+
+241
+00:19:00,790 --> 00:19:05,390
+بتاعة ال implication البادئ لل implication is true
+
+242
+00:19:05,390 --> 00:19:09,330
+و بتجيب منه اللاحق او ال conclusion انت بدك تستنتج
+
+243
+00:19:09,330 --> 00:19:13,630
+اللاحق خلاص تمام في الحالة هذه بتقدر ببساطة تقول
+
+244
+00:19:13,630 --> 00:19:19,980
+ان زائدبدا نثبت منها ان in زائد واحد هتكون دايما
+
+245
+00:19:19,980 --> 00:19:24,260
+اقل من اتنين to the power in زائد واحد ببساطة جدا
+
+246
+00:19:24,260 --> 00:19:29,400
+هذه كل اللي هي محتاجها زائد واحد عشان تصبح نثبت
+
+247
+00:19:29,400 --> 00:19:34,520
+منها هذا ال term هذا ال term اللي هو in زائد واحد
+
+248
+00:19:34,520 --> 00:19:38,540
+اقل من اتنين to the power in زائد واحد طيب ايش
+
+249
+00:19:38,540 --> 00:19:42,860
+الفرق بين هذا و هذا اني ازيد واحد على الطرفينبنزيد
+
+250
+00:19:42,860 --> 00:19:47,240
+واحد على الطرفين عشان نوحد الطرف الشمال فالطرف
+
+251
+00:19:47,240 --> 00:19:52,340
+الشمال انا بدي اثبت ان زائد واحد و اشوف جدش بتطلع
+
+252
+00:19:52,340 --> 00:19:56,020
+خلينا نشوف فانا عندي ان لحالها فبتصير ان زائد واحد
+
+253
+00:19:56,020 --> 00:20:00,040
+اقل من اتنين ان برضه زائد واحد واحد على الطرفين و
+
+254
+00:20:00,040 --> 00:20:07,020
+مش اكتر واحد على الطرفينلا أكثر ولا أقل طيب تمام و
+
+255
+00:20:07,020 --> 00:20:10,400
+هنا هنا في الآخر و نقول أقل من اتنين to the power
+
+256
+00:20:10,400 --> 00:20:18,080
+n طيب واحد هذه واحد هذه دائما هتكون أقل من اتنين
+
+257
+00:20:18,080 --> 00:20:24,600
+to the power جداش to the power n لأنه
+
+258
+00:20:24,600 --> 00:20:29,680
+انت بادب أكبر من صفر صح و كل ما زادت in الوسع حد
+
+259
+00:20:29,680 --> 00:20:34,420
+بزيد أكتر كمانهيزيد اكتر و اكتر كمان بس انت ضامن
+
+260
+00:20:34,420 --> 00:20:38,700
+انه دائما الواحد هيكون اقل من اتنين to the power
+
+261
+00:20:38,700 --> 00:20:46,680
+واحد هذا على اعتبار اول قيمة ممكن ل in اول قيمة
+
+262
+00:20:46,680 --> 00:20:51,760
+ممكن ل in واحد صحيح فانت ضامن اتنين to the power
+
+263
+00:20:51,760 --> 00:20:54,600
+واحد هيكون اكبر من الواحد والله اذا كان انت عند in
+
+264
+00:20:54,600 --> 00:20:57,380
+بالساوية عشرة فانت ضامن انه اكبر و مرتاح كمان في
+
+265
+00:20:57,380 --> 00:21:01,400
+الاكبرمرتاح جدا كمان في الأكبر، معناه ذلك أن ال
+
+266
+00:21:01,400 --> 00:21:05,780
+term هذا الواحد لأ انت هضفله قيمة أكبر، معناه ذلك
+
+267
+00:21:05,780 --> 00:21:13,120
+بتقدر تقول زائد اتنين to the power n أكبر من زادت،
+
+268
+00:21:13,120 --> 00:21:17,910
+بس ضالت صحيحة، correlation صحيحةCorrelation صحيحة
+
+269
+00:21:17,910 --> 00:21:22,370
+جداً طيب N زائد واحد ضالت زي ما هي و كل ما بقى N
+
+270
+00:21:22,370 --> 00:21:26,990
+زائد واحد بتجل قيمة كل ما زادت N عن ال term اللي
+
+271
+00:21:26,990 --> 00:21:31,350
+على الشمال وهذا بكل بساطة الان جمعه لما تجمعه ايش
+
+272
+00:21:31,350 --> 00:21:37,610
+بيصير اتنين to the power N زائد واحد على اعتبار
+
+273
+00:21:37,610 --> 00:21:42,330
+كأنها هدف فعليا اتنين في اتنين to the power N
+
+274
+00:21:45,520 --> 00:21:49,280
+مجموعة مرتين يعني كأنه اتنين في العدد .. اتنين في
+
+275
+00:21:49,280 --> 00:21:53,220
+العدد .. و اتنين في العدد هي power واحد فصارت زي
+
+276
+00:21:53,220 --> 00:22:01,560
+.. هاي المطلوب .. هاي المطلوب .. هذا المطلوب ..
+
+277
+00:22:01,560 --> 00:22:06,170
+تمامالان ال second principle هذه ال first
+
+278
+00:22:06,170 --> 00:22:10,070
+principle كل المطلوب انه عشان تثبت ان P of N زائد
+
+279
+00:22:10,070 --> 00:22:16,770
+واحد is true بدك تفترض ان P of N is true طيب ال
+
+280
+00:22:16,770 --> 00:22:20,870
+second principle لأ شوية اعمق ايش يعني اعمق يعني
+
+281
+00:22:20,870 --> 00:22:29,150
+عشان نثبتإنه فعلا لكل قيم N اللي أكبر من أو تساوي
+
+282
+00:22:29,150 --> 00:22:34,490
+صفر كويس هي true بدنا نقول ال basis مش مشكلة فيه
+
+283
+00:22:34,490 --> 00:22:38,970
+زي ال first principle بس في ال inductive لأ هيقول
+
+284
+00:22:38,970 --> 00:22:48,910
+لإن كل قيم N أكبر أو تساوي صفر كل القيم اللي من N
+
+285
+00:22:48,910 --> 00:22:55,390
+فأقلإذا كانت true إذن P of N زائد واحد is true
+
+286
+00:22:55,390 --> 00:23:00,350
+فإذا P of N زائد واحد is true هي مش مبنية فقط على
+
+287
+00:23:00,350 --> 00:23:05,890
+P of N لحالها يعني لا يكفي .. لا يكفي إنها تكون P
+
+288
+00:23:05,890 --> 00:23:10,650
+of N لحالها is true عشان أثبت منها إنه N زائد واحد
+
+289
+00:23:10,650 --> 00:23:17,730
+is true لأ محتاج إنه N وكل ما قبلها أكون مفترض إن
+
+290
+00:23:17,730 --> 00:23:22,330
+هم كلهم trueعشان نثبت من خلالها ان P of N زائد
+
+291
+00:23:22,330 --> 00:23:24,950
+واحد is true طبعا هذه بأحيان بيسموها ال strong
+
+292
+00:23:24,950 --> 00:23:29,930
+principle أو ال strong proof ال proof الأقوى لأنه
+
+293
+00:23:29,930 --> 00:23:33,750
+إذا تحقق اصلا إذا تحقق فهنشوف الأمثلة اللي ممكن
+
+294
+00:23:33,750 --> 00:23:37,230
+تحقيقها إشي هتقولي صعبة و كيف تعملها لأ هي سهلة
+
+295
+00:23:37,230 --> 00:23:40,470
+جدا و هنشوفها في الأمثلة يمكن أكتر بس هنا بنقول K
+
+296
+00:23:40,470 --> 00:23:46,980
+فإذا لكل القيم من صفر to NB of K لازم يكونوا is
+
+297
+00:23:46,980 --> 00:23:52,520
+true عشان أستنتج منه إنه بقى بيه of N زائد واحد is
+
+298
+00:23:52,520 --> 00:24:00,500
+true تمام هذا بده مثال عشان يوضحها بشكل أكبر
+
+299
+00:24:08,400 --> 00:24:13,480
+هي ايجي المثال طيب بدنا نفرض او بدنا نثبت انه لكل
+
+300
+00:24:13,480 --> 00:24:18,720
+قيم n اللي اكبر من واحد اللي اكبر من واحد يمكن
+
+301
+00:24:18,720 --> 00:24:23,660
+كتابتها بشكل primes مضروبة في بعض او product of
+
+302
+00:24:23,660 --> 00:24:26,920
+primes الحاجة اللي احنا خدناها جاب الحستين جاب
+
+303
+00:24:26,920 --> 00:24:30,960
+المحاضرتين كويس وقولنا ان كل عنصر اذا كان سواء
+
+304
+00:24:30,960 --> 00:24:36,030
+prime اوcomposite number هو عبارة عن مجموعة of
+
+305
+00:24:36,030 --> 00:24:40,050
+primes في بعض إذا هو prime فهو هو نفسه بحد ذاته
+
+306
+00:24:40,050 --> 00:24:44,690
+prime أو إذا كان composite فهو عبارة عن two primes
+
+307
+00:24:44,690 --> 00:24:47,990
+أو أكتر مضروبين في بعض مجموعة of primes مضروبة في
+
+308
+00:24:47,990 --> 00:24:53,150
+بعض أثبت ذلك، هاي المطلوب طيب عشان نثبت ذلك إيش
+
+309
+00:24:53,150 --> 00:25:00,070
+محتاج؟ محتاج أقول إنه بدي أبدأ من in أكبر من واحد
+
+310
+00:25:00,070 --> 00:25:04,090
+فإذا بدي أبدأ من مين؟ من الإتنينال business tip
+
+311
+00:25:04,090 --> 00:25:08,190
+بتاعتي هنا هتكون هي الأتنين اللي هي أكبر من ال ..
+
+312
+00:25:08,190 --> 00:25:12,190
+البداية ال initial تبعنا فعند الأتنين هيكون عندي
+
+313
+00:25:12,190 --> 00:25:16,490
+مجموعة ال primes واحد هو prime واحد فقط اللي هو
+
+314
+00:25:16,490 --> 00:25:19,730
+مين؟ الأتنين بس ليش؟ لأنه الأتنين هي بن حد ذاتها
+
+315
+00:25:19,730 --> 00:25:24,750
+prime هي بن حد ذاتها prime و ال prime الوحيد ال
+
+316
+00:25:24,750 --> 00:25:30,270
+even صحيح؟ ال prime الوحيد ال even في الدنيا كويس
+
+317
+00:25:31,860 --> 00:25:36,100
+طب تخيل إنه في أي prime تاني even غيره، مستحيل
+
+318
+00:25:36,100 --> 00:25:39,480
+لأنه بيقبل الجسم على اتنين، هيكون بيقبل الجسم على
+
+319
+00:25:39,480 --> 00:25:42,900
+اتنين، صحيح؟ فإذا هو ال answer الوحيد اللي بقدر
+
+320
+00:25:42,900 --> 00:25:48,690
+أسميه even primeتمام فهي ال basis صحيحة مش فيها
+
+321
+00:25:48,690 --> 00:25:53,390
+مشكلة ال basis اللي هي أول عنصر فعليا حقق المعادلة
+
+322
+00:25:53,390 --> 00:25:57,870
+صح تمام في ال inductive step بدي أقول أنه لو بدي
+
+323
+00:25:57,870 --> 00:26:02,050
+أفرض الفرضية تبعتي اللي هي is true أنه لكل قيم n
+
+324
+00:26:02,050 --> 00:26:07,450
+أكبر من أو تساوي اتنين هيها اللي هي هنبدأ فيها
+
+325
+00:26:07,450 --> 00:26:15,450
+فرضيتنا كل القيم من اتنين to N هي تحقق P of Kيعني
+
+326
+00:26:15,450 --> 00:26:21,330
+بمعنى إن هي كلها مجموعة primes كل الأعداد ابتداء
+
+327
+00:26:21,330 --> 00:26:27,510
+من الاتنين لعند N هي كلها عبارة عن مجموعة product
+
+328
+00:26:27,510 --> 00:26:33,350
+لprimes كل عنصر أي .. أي رقم اختاره هيك عشوائيا من
+
+329
+00:26:33,350 --> 00:26:38,130
+اتنين ل N أي رقم لازم هيكون عبارة عن ضرب مجموعة
+
+330
+00:26:38,130 --> 00:26:41,830
+primes في بعض هذه هي الفرضية اللي بنقول assume
+
+331
+00:26:41,830 --> 00:26:44,210
+that فإذا is it true؟
+
+332
+00:26:47,650 --> 00:26:51,250
+تمام طبعا هتقولي كيف أثبت أنه is true الإثبات الآن
+
+333
+00:26:51,250 --> 00:26:54,270
+في ال inductive هيثبت لك أنه الكلام صحيح هذا الوقت
+
+334
+00:26:54,270 --> 00:26:58,950
+هنفرض N زائد واحد N زائد واحد لان عشان أثبت أن هي
+
+335
+00:26:58,950 --> 00:27:03,570
+فعلا برضه هتحقق نفس الكلام عندها احتمالين إما أن
+
+336
+00:27:03,570 --> 00:27:08,150
+هي نفسها prime هي نفسها prime مش هيك مش في احتمال
+
+337
+00:27:08,150 --> 00:27:13,490
+أن تكون هي N زائد واحد أصلا prime فإذاأريحنا هي
+
+338
+00:27:13,490 --> 00:27:16,730
+prime لحالها معناه ذلك في الحالة هذه بقدر أقول أن
+
+339
+00:27:16,730 --> 00:27:20,150
+مجموع ال primes هي واحد prime واحد هي قيمة n زائد
+
+340
+00:27:20,150 --> 00:27:24,070
+واحد هذا is a prime طيب إذا مش prime وهذه الفرضية
+
+341
+00:27:24,070 --> 00:27:26,810
+التانية معناه ذلك أن ال n زائد واحد هو عبارة عن
+
+342
+00:27:26,810 --> 00:27:31,230
+مدى مش prime معناته بنفع يكون ضرب رقمين معروفة
+
+343
+00:27:31,230 --> 00:27:35,430
+صحيح هي a و b بغض النظر a و b هم primes ولا لأ
+
+344
+00:27:36,480 --> 00:27:41,960
+تمام؟ لكن a و b هدول أكيد هيكونوا أقل من n زائد
+
+345
+00:27:41,960 --> 00:27:50,060
+واحد صح؟ أكيد وحتما و أجل من n كمان أكيد هيكونوا
+
+346
+00:27:50,060 --> 00:27:54,700
+أقل من n طيب مدام أقل من n معناته ينطبق عليهم
+
+347
+00:27:54,700 --> 00:28:01,000
+الفرضية لأن هم معناته بين الاتنين و ال n معناه ذلك
+
+348
+00:28:01,000 --> 00:28:06,410
+أن هم نفسهم ممكن يكونوا n زائد واحد افترضهمهم
+
+349
+00:28:06,410 --> 00:28:11,830
+نفسهم ممكن يكونوا N زائد واحد فإذا A أكيد هتكون من
+
+350
+00:28:11,830 --> 00:28:17,190
+الواحد لل N و ال B نفس الكلام عشان فعلا ضربهم
+
+351
+00:28:17,190 --> 00:28:21,350
+يعطيك N زائد واحد فلازم يكونوا عددهم أقل ففي
+
+352
+00:28:21,350 --> 00:28:24,850
+الحالة دي A انت ضامن ان هي عبارة عن مجموعة Primes
+
+353
+00:28:24,850 --> 00:28:30,850
+جد ما يطلع يطلع عددهم Tمثلا و P هي عبارة عن مجموعة
+
+354
+00:28:30,850 --> 00:28:34,730
+Primes U ففي الحالة هذه بيقول ان N زائد واحد هي
+
+355
+00:28:34,730 --> 00:28:42,050
+عبارة عن مضروب مجموعة Primes عددهم T زائد U اللي
+
+356
+00:28:42,050 --> 00:28:45,790
+هي ال Primes تبعت A مضروبة في ال Primes تبعت P
+
+357
+00:28:45,790 --> 00:28:51,350
+لأنه A في P فN زائد واحد هي مجموعة ال Primes كلها
+
+358
+00:28:51,350 --> 00:28:57,160
+مضروبة في بعض جديش عدد ال Primes T زائد Uهتكون T
+
+359
+00:28:57,160 --> 00:29:00,660
+زائد U طب انت هتقول ليه طب ليه أثبت أنه هذا فعلا
+
+360
+00:29:00,660 --> 00:29:05,220
+كلهم true هقولك بكل بساطة اتعامل مع الموضوع انه N
+
+361
+00:29:05,220 --> 00:29:09,820
+زائد 1 اللي انت بدك تثبت recursion متذكرين او
+
+362
+00:29:09,820 --> 00:29:13,060
+أخدتوا فكرة ال recursion تمام فإذا بدي أتعامل مع A
+
+363
+00:29:13,060 --> 00:29:19,920
+كأنه هي N زائد 1 ل problem جديدة و B هي N زائد 1 ل
+
+364
+00:29:19,920 --> 00:29:23,940
+problem جديدة أثبت بدا ثبته نفس الكلام معناته إذا
+
+365
+00:29:23,940 --> 00:29:30,720
+ال Aممكن أقول عليها C في D صح؟
+
+366
+00:29:30,720 --> 00:29:37,560
+لما نصلى مين؟ لل basis أو ال prime هي نفسها ال
+
+367
+00:29:37,560 --> 00:29:45,820
+prime هي نفسها ال prime أو نصلى الأتنين صحيح؟
+
+368
+00:29:45,820 --> 00:29:52,780
+فمنطقيا هي بتفتحلنا الموضوع اللي بعد ذلك و اللي هو
+
+369
+00:29:52,780 --> 00:29:58,540
+ال recursionفالفكرة جاينة متسلسل عادي ومش صعبة ولا
+
+370
+00:29:58,540 --> 00:30:02,080
+هي غلط، ليش؟ لأنه بكل بساطة أنت هتقولي طب أنت
+
+371
+00:30:02,080 --> 00:30:06,280
+أثبتت أو خليني أفترض .. فردت أن هم كلهم true، ليش؟
+
+372
+00:30:06,280 --> 00:30:09,900
+ليش؟ لأنه بكل بساطة بدت أتعامل معاها أنه إيه؟ هي
+
+373
+00:30:09,900 --> 00:30:13,380
+كأنها n زائد واحد problem جديدة واخدها لحالة أحلها
+
+374
+00:30:13,990 --> 00:30:17,650
+و بيه نفس الكلام أخدها لحالها أحلها طيب A هذي يمكن
+
+375
+00:30:17,650 --> 00:30:21,290
+تطلع ل C و D C لحالها بدي أحلها كأنها N زائد واحد
+
+376
+00:30:21,290 --> 00:30:24,430
+و D بدي أحلها لحالها كأنها N زائد واحد هتبقى
+
+377
+00:30:24,430 --> 00:30:28,430
+تتحلحل معاها تتفتفت معاها recursion صحيح؟
+
+378
+00:30:28,430 --> 00:30:34,270
+recursive steps لما تصل ل ال prime أو ال basis
+
+379
+00:30:36,020 --> 00:30:39,980
+هتضلك تتفك فتتحلحل معاك لما تصل لواحد من هالاتنين
+
+380
+00:30:39,980 --> 00:30:46,460
+يا هو prime بحجذ ذاته او تصل لل bases صحيح هتاخد
+
+381
+00:30:46,460 --> 00:30:50,080
+معاك وجد هتاخد معاك وجد صحيح لكن مش هالوجد اللي
+
+382
+00:30:50,080 --> 00:30:58,680
+انت متخيله ليش لأنه ال code هنا هو مش linear صح ال
+
+383
+00:30:58,680 --> 00:31:01,870
+code هنا مش linear هنا logarithmicفال complexity
+
+384
+00:31:01,870 --> 00:31:05,190
+هنا مش زي ما انت متخيلها هتكون كبيرة مش هتكون
+
+385
+00:31:05,190 --> 00:31:12,190
+كبيرة واضح تهيألي المثال اه؟ بدكم ترجعوله برضه و
+
+386
+00:31:12,190 --> 00:31:14,770
+تركزوا فيه لأنه recursion هذا فكرة ال recursion if
+
+387
+00:31:14,770 --> 00:31:17,510
+أنتوا ماخدين recursion if أنتوا ماخدين recursion
+
+388
+00:31:17,510 --> 00:31:21,790
+بسيط جدا فكرة حتى أنك تعمله إثبات أو تعمله code
+
+389
+00:31:21,790 --> 00:31:27,530
+طيب نفس الكلام و ننهي في كمان مثال
+
+390
+00:31:30,660 --> 00:31:36,500
+المثال هذا مطلوب اثبات انه لكل amount of postage
+
+391
+00:31:36,500 --> 00:31:44,220
+لكل قيمة جواب او اللي هو بنسميه جواب بوستا اللي هو
+
+392
+00:31:44,220 --> 00:31:49,680
+جواب بريدي كويس او كتاب بريدي لكل كتاب بريدي of
+
+393
+00:31:49,680 --> 00:31:53,440
+اتناشر cent اللي هو بنحط عليه طابع باتناشر cent
+
+394
+00:31:53,440 --> 00:32:01,120
+تكلفته اتناشر cent كويس او اكتركل جواب بريدي ب 12
+
+395
+00:32:01,120 --> 00:32:09,380
+cents أو أكتر يمكن تمثيله باستخدام 4 و 5 cents من
+
+396
+00:32:09,380 --> 00:32:15,380
+ال stamps أو من الطوابق فإذا تبع البريد ماعندهش
+
+397
+00:32:15,380 --> 00:32:18,620
+إلا طوابق اللي دلت من فئة الأربعة cents و الخمسة
+
+398
+00:32:18,620 --> 00:32:22,140
+cents بس ماعندهش لا تلاتة ولا خمسة ولا سبعة ولا
+
+399
+00:32:22,140 --> 00:32:26,450
+ستة ماعندهش إلا الأربعة والخمسةبدنا نثبت ان هي
+
+400
+00:32:26,450 --> 00:32:31,070
+كافية جدا لأي رسالة بتجيك جداش تكلفتها تكون مش
+
+401
+00:32:31,070 --> 00:32:37,770
+مشكلة المهم ان هي اكتر من اتناشعشرين، خمسة وعشرين،
+
+402
+00:32:37,770 --> 00:32:42,250
+سبعين، مية، خمس مية بتقدر تشكلها من مجموعة ال ..
+
+403
+00:32:42,250 --> 00:32:46,490
+ال .. ال two stems اللي هي الأربعة والخمسة بدنا
+
+404
+00:32:46,490 --> 00:32:49,590
+نثبت هذا الكلام عشان تثبت هذا الكلام هنا هيكون
+
+405
+00:32:49,590 --> 00:32:54,070
+عندك ال basis case أو ال basis step ال .. ال basis
+
+406
+00:32:54,070 --> 00:32:58,270
+step هتكون عبارة عن أن الإطماعش نفسها هي تلطوة من
+
+407
+00:32:58,270 --> 00:33:05,250
+M الأربعة صحيح؟ طيب التلطعشهي عبارة عن طابعين
+
+408
+00:33:05,250 --> 00:33:10,850
+أربعة و طابع خمسة هذا اللي هي تلت طعش طيب الأربع
+
+409
+00:33:10,850 --> 00:33:15,790
+طعش بالعكس بتصير هذه واحد وهذه اتنين فبتصير طابع
+
+410
+00:33:15,790 --> 00:33:20,950
+أبو الأربعة و طابعين أبو الخمسة عشان نصلّها خمس
+
+411
+00:33:20,950 --> 00:33:24,570
+طعش عبارة عن تلت طوابع خمسة فاحنا بدينا بتلاتة
+
+412
+00:33:24,570 --> 00:33:33,600
+تلاتة صفر اتنين واحد واحد اتنينصفر تلاتة والان
+
+413
+00:33:33,600 --> 00:33:39,400
+المفروض يرجعاش يتكرر هترجع تتكرر برضهrecursion
+
+414
+00:33:39,400 --> 00:33:43,020
+هنرجع تاني لل recursion فإذا assume that أنه فعلا
+
+415
+00:33:43,020 --> 00:33:48,400
+لكل القيم من 12 ل N هي is true عشان نثبت منها N
+
+416
+00:33:48,400 --> 00:33:52,740
+زائد واحد طب N زائد واحد هذه بدنا نكون عارفين أنه
+
+417
+00:33:52,740 --> 00:33:56,180
+الفارق بين كل واحدة و التانية هي N ناقص تلاتة
+
+418
+00:33:56,180 --> 00:34:03,060
+بمعنى من 12 ل N ما بينهم N ناقص تلاتة كلهم true
+
+419
+00:34:03,060 --> 00:34:08,430
+هيكونواكلهم true طيب ليش ان ناقص تلاتة لأنه بكون
+
+420
+00:34:08,430 --> 00:34:13,390
+ضامن هنا في الحالة هذه ان ان زائد واحد هتكون زائد
+
+421
+00:34:13,390 --> 00:34:19,870
+أربعة لاحظ معايا ليش حط المعادلة بتبعته بهذا الشكل
+
+422
+00:34:19,870 --> 00:34:26,770
+ان هي is true على أساس ان ان زائد واحد هتكون فارقة
+
+423
+00:34:26,770 --> 00:34:29,070
+عن الاطمعش بجداش باربعة
+
+424
+00:34:32,050 --> 00:34:35,990
+لعند ال N الفارق تلاتة طب أنا ماتكلمش عن ال N اللي
+
+425
+00:34:35,990 --> 00:34:41,410
+عند ال N هي true بتكلم عن N زائد واحد فبتصير بدل
+
+426
+00:34:41,410 --> 00:34:44,310
+ما الفارق تلاتة الفارق بيصير أربعة الأربعة مناسب
+
+427
+00:34:44,310 --> 00:34:49,910
+جدا لأنه بيصير إمكانية إضافة مين فقط stamp واحدة
+
+428
+00:34:49,910 --> 00:34:54,730
+باربعة cent stamp واحدة باربعة cent كأنه ال N زائد
+
+429
+00:34:54,730 --> 00:35:01,900
+واحد هتكون بتماثل N ناقص تلاتةبزيادة كمان طابع
+
+430
+00:35:01,900 --> 00:35:07,660
+باربعة الفرق بينهم كم؟ اربعة فارق بينهم اربعة فعلا
+
+431
+00:35:07,660 --> 00:35:13,120
+فصار هو ال index
+
+432
+00:35:13,120 --> 00:35:17,040
+اللي بتقدر تشتغل عليه ليش؟ لأن ال index هذا هو جاب
+
+433
+00:35:17,040 --> 00:35:23,280
+ال index ال n زائد واحد باربعة خلاص مناسب معناته
+
+434
+00:35:23,280 --> 00:35:29,120
+بيكفي اربعة طابع اربعة فإذا مدام احنا مثبتينإنه
+
+435
+00:35:29,120 --> 00:35:34,800
+أنا جادر أشكل أي جواب بقيمة n زائد أربعة بمجموعة
+
+436
+00:35:34,800 --> 00:35:38,160
+ال stamps اللي عندى معنى ذلك n زائد واحد مش هتكون
+
+437
+00:35:38,160 --> 00:35:44,400
+صعبة لإن هو نفسها n ناقص تلاتة و بضيف كمان stamp
+
+438
+00:35:44,400 --> 00:35:50,040
+زيادة من أبو الأربعة فقط بيصير stamp زيادة من أبو
+
+439
+00:35:50,040 --> 00:36:00,430
+الأربعة بمعنى إنه ال 12 هي مكافئة لل 16الـ12 كيف
+
+440
+00:36:00,430 --> 00:36:05,950
+شكلناها؟ تلاتة في أربعة هنا زيد عليها كمان واحدة
+
+441
+00:36:05,950 --> 00:36:12,310
+باربعة بالظبط أربعة أربعة، هاي ستة عشر، هاي ستة
+
+442
+00:36:12,310 --> 00:36:16,770
+عشر فالفارق دائما هيكون فكرة الأربعة الفارق لما
+
+443
+00:36:16,770 --> 00:36:21,430
+نقول التسعة عشر التسعة
+
+444
+00:36:21,430 --> 00:36:25,170
+عشر المفروض أنه مين اللي عندي يظل اللي عندي هنا؟
+
+445
+00:36:25,170 --> 00:36:31,910
+هتكون اتنين فارق تلاتة الأربعة عشرالاربعة .. تلات
+
+446
+00:36:31,910 --> 00:36:35,570
+خمس .. لأ هو مظبوط الفرق أربعة تلات خمسات خمستعش
+
+447
+00:36:35,570 --> 00:36:41,150
+من الخمستعش جديش الخمستعش كانت تلاتة في خمسة زائد
+
+448
+00:36:41,150 --> 00:36:45,170
+أربعة زائد
+
+449
+00:36:45,170 --> 00:36:49,870
+أربعة فمعنى ذلك طول ما عندك الأربعات فيهم وافرة
+
+450
+00:36:49,870 --> 00:36:55,710
+انت مش جالجان حسب ال .. ال inductive step اللي
+
+451
+00:36:55,710 --> 00:36:58,390
+احنا اشتغلنا عليها حسب ال inductive step اللي
+
+452
+00:36:58,390 --> 00:36:59,730
+اشتغلنا عليها
+
+453
+00:37:03,340 --> 00:37:09,420
+طبعا هي هيك تقريبا الموضوع الخفيف السريع بيجي في
+
+454
+00:37:09,420 --> 00:37:14,480
+الامتحانات في جزئية الإثبات لكن الأهم من ذلك أن هو
+
+455
+00:37:14,480 --> 00:37:17,940
+المقدمة عشان نروح لل recursion عشان نروح لل
+
+456
+00:37:17,940 --> 00:37:21,400
+recursion و recursive algorithm لأنه هناخد مجموعة
+
+457
+00:37:21,400 --> 00:37:26,770
+algorithms المرة القادمة كيف نعيد حلهابال .. بال
+
+458
+00:37:26,770 --> 00:37:30,650
+recursive code .. recursive code فيعطيكوا العافية
+
+459
+00:37:30,650 --> 00:37:31,710
+نهينا هي محاضرتنا
+